Answer:
a) P(X = 0) for raisins = 0.33287
b) P(X = 2) for chocolate chips = 0.14379
c) P(X ≥ 2) for both bits = 0.59399
Step-by-step explanation:
The average amount of raisin per cookie is 600/500 = 1.2
The average amount of chocolate chips per cookie = 400/500 = 0.8
a) Using Poisson's distribution function
P(X = x) = (e^-λ)(λˣ)/x!
For raisin, Mean = λ = 1.1
x = 0
P(X = 0) = (e⁻¹•¹)(1.1⁰)/(0!) = 0.33287
b) Using Poisson's distribution function
P(X = x) = (e^-λ)(λˣ)/x!
For chocolate chips, Mean = λ = 0.8
x = 2
P(X = 2) = (e⁻⁰•⁸)(0.8²)/(2!) = 0.14379
c) the probability that a randomly chosen cookie will have at least two bits (raisins or chips) in it.
For this, the average number of bit in a raisin = (600+400)/500 = 2 bits per raisin.
P(X ≥ 2) = 1 - [P(X = 0) + P(X = 1)]
For P(X = 0)
P(X = x) = (e^-λ)(λˣ)/x!
Mean = λ = 2
x = 0
P(X = 0) = (e⁻²)(2⁰)/(0!) = 0.13534
For P(X = 1)
P(X = x) = (e^-λ)(λˣ)/x!
Mean = λ = 2
x = 1
P(X = 1) = (e⁻²)(2¹)/(1!) = 0.27067
P(X ≥ 2) = 1 - [P(X = 0) + P(X = 1)]
P(X ≥ 2) = 1 - (0.13534 + 0.27067) = 1 - 0.40601 = 0.59399
Using the Poisson distribution, it is found that there is a:
a) 0.3012 = 30.12% probability that a randomly picked cookie will have exactly two chocolate chips.
b) 0.1438 = 14.38% probability that a randomly picked cookie will have exactly two chocolate chips.
c) 0.594 = 59.4% probability that a randomly chosen cookie will have at least two bits (raisins or chips) in it.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes e = 2.71828 is the Euler number [tex]\mu[/tex] is the mean in the given interval.Item a:
600 raisins in 500 cookies, hence, the mean is:
[tex]\mu = \frac{600}{500} = 1.2[/tex]
The probability is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.2}1.2^{0}}{(0)!} = 0.3012[/tex]
0.3012 = 30.12% probability that a randomly picked cookie will have exactly two chocolate chips.
Item b:
400 chips in 500 cookies, hence, the mean is:
[tex]\mu = \frac{400}{500} = 0.8[/tex]
The probability is P(X = 2), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 2) = \frac{e^{-0.8}0.8^{2}}{(2)!} = 0.1438[/tex]
0.1438 = 14.38% probability that a randomly picked cookie will have exactly two chocolate chips.
Item c:
1000 bits, as 600 + 400 = 1000, in 500 cookies, hence, the mean is:
[tex]\mu = \frac{1000}{500} = 2[/tex]
The probability is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X = 1) = \frac{e^{-2}2^{1}}{(1)!} = 0.2707[/tex]
Hence:
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.1353 + 0.2707 = 0.4060[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.406 = 0.594[/tex]
0.594 = 59.4% probability that a randomly chosen cookie will have at least two bits (raisins or chips) in it.
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The probability is 0.271 that the gestation period of a woman will exceed 9 months. In 3000 human gestation periods, roughly how many will exceed 9 months?
Answer:
813 will exceed 9 months.
Step-by-step explanation:
For each women, there are only two possible outcomes. Either they will exceed the gestation period, or they will not. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this problem, we have that:
[tex]n = 3000, p = 0.271[/tex]
In 3000 human gestation periods, roughly how many will exceed 9 months?
[tex]E(X) = np = 3000*0.271 = 813[/tex]
813 will exceed 9 months.
The gestation period should be exceed 9 month is 813.
Given that,
The probability is 0.271 that the gestation period of a woman will exceed 9 months. And, there is 3000 human gestation periodsBased on the above information, the calculation is as follows:
[tex]= 0.271 \times 3,000[/tex]
= 813
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The last digit of the heights of 66 statistics students were obtained as part of an experiment conducted for a class. Use the frequency distribution to construct a histogram.
Digit Frequency
0 16
1 3
2 5
3 4
4 5
5 14
6 5
7 5
8 4
9 5
What can be concluded from the distribution of the digits?
The histogram is shown below.
You'll have 10 bars. Under each bar is a label from 0 to 9. The height of each bar represents the frequency of each units digit.
The histogram shows two bars that are relatively large compared to the rest. These bars have frequency of 16 and 14 (for units digits of 0 and 5 respectively). The distribution is nearly bimodal. If the two frequencies mentioned were the same, say both 16, then it would be exactly bimodal. As you can probably guess, bimodal means "two modes".
The rest of the bar heights are nearly the same, so the remaining portion of the distribution is nearly uniform. A uniform distribution has every bar the same height. Collectively, all the bars of a uniform distribution forms a larger rectangle.
We roll two fair 6-sided dice, A and B. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Find the probability that dice A is larger than dice B. 2) Given that the roll resulted in a sum of 5 or less, find the conditional probability that the two dice were equal. 3) Given that the two dice land on different numbers, find the conditional probability that the two dice differed by 2.
Answer:
1) 41.67% probability that dice A is larger than dice B.
2) Given hat the roll resulted in a sum of 5 or less, there is a 20% conditional probability that the two dice were equal.
3) Given that the two dice land on different numbers there is a 26.67% conditional probability that the two dice differed by 2.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, we have these possible outcomes:
Format(Dice A, Dice B)
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes.
1) Find the probability that dice A is larger than dice B.
Desired outcomes:
(2,1)
(3,1), (3,2)
(4,1), (4,2), (4,3)
(5,1), (5,2), (5,3), (5,4)
(6,1), (6,2), (6,3), (6,4), (6,5)
There are 15 outcomes in which dice A is larger than dice B.
There are 36 total outcomes.
So there is a 15/36 = 0.4167 = 41.67% probability that dice A is larger than dice B.
2) Given that the roll resulted in a sum of 5 or less, find the conditional probability that the two dice were equal.
Desired outcomes:
Sum of 5 or less and equal
(1,1), (2,2)
There are 2 desired outcomes
Total outcomes:
Sum of 5 or less
(1,1), (1,2), (1,3), (1,4)
(2,1), (2,2), (2,3)
(3,1), (3,2)
(4,1)
There are 10 total outcomes.
So given hat the roll resulted in a sum of 5 or less, there is a 2/10 = 20% conditional probability that the two dice were equal.
3) Given that the two dice land on different numbers, find the conditional probability that the two dice differed by 2.
Desired outcomes
Differed by 2
(1,3), (2,4), (3,1), (3,5),(4,2),(4,6), (5,3), (6,4).
There are 8 total outcomes in which the dices differ by 2.
Total outcomes:
There are 30 outcomes in which the two dice land of different numbers.
So given that the two dice land on different numbers there is a 8/30 = 0.2667 = 26.67% conditional probability that the two dice differed by 2.
A large consumer goods company ran a television advertisement for one of its soap products.
On the basis of a survey that was conducted, probabilities were assigned to the following
events.
B = individual purchased the product S = individual recalls seeing the advertisement B∩S = individual purchased the product and recalls seeing the advertisement
The probabilities assigned were P(B)=.20,P(S)=.40, and P(B∩S)=.12
a. What is the probability of an individual’s purchasing the product given that the individual
recalls seeing the advertisement? Does seeing the advertisement increase
the probability that the individual will purchase the product? As a decision maker,
would you recommend continuing the advertisement (assuming that the cost is
reasonable)?
b. Assume that individuals who do not purchase the company’s soap product buy from
its competitors. What would be your estimate of the company’s market share? Would
you expect that continuing the advertisement will increase the company’s market
share? Why or why not?
"c. The company also tested another advertisement and assigned it values of P(S)=.30
and P(B∩S)=.10. What is P(B|S) for this other advertisement? Which advertise-
ment seems to have had the bigger effect on customer purchases?"
a. The probability is 0.30. The advertisement seems to have a positive effect on customer purchases.
b. The market share is 0.20. The advertisement could potentially increase the company's market share
c. The conditional purchase probability of 0.333. The second advertisement seems to have had a slightly bigger effect on customer purchases.
a. We are asked to find the probability of an individual purchasing the product given that the individual recalls seeing the advertisement, i.e., P(B|S).
Using the formula for conditional probability:
P(B|S) = P(B∩S) / P(S)
Given:
P(B∩S) = 0.12
P(S) = 0.40
So, P(B|S)
= 0.12 / 0.40
= 0.30
Seeing the advertisement increases the probability that an individual will purchase the product from 0.20 (P(B)) to 0.30 (P(B|S)). Therefore, the advertisement seems to have a positive effect on customer purchases.
As a decision maker, if the cost of the advertisement is reasonable, it would be recommended to continue the advertisement since it increases the likelihood of product purchases.
b. The company's market share can be estimated by considering the probability of individuals purchasing the company's soap product and the probability of individuals purchasing from competitors.
The probability of an individual purchasing from competitors
= 1 - P(B)
= 1 - 0.20
= 0.80
Therefore, the company's market share is:
Market Share = P(B)
= 0.20
Continuing the advertisement could potentially increase the company's market share since the advertisement has a positive effect on customer purchases, as shown in part (a).
c. For the other advertisement:
Given:
P(S) = 0.30
P(B∩S) = 0.10
Using the formula for conditional probability:
P(B|S) = P(B∩S) / P(S)
So, P(B|S)
= 0.10 / 0.30
= 0.333
Comparing the two advertisements, the first advertisement had a conditional purchase probability of 0.30, while the second advertisement had a conditional purchase probability of 0.333. Therefore, the second advertisement seems to have had a slightly bigger effect on customer purchases.
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The advertisements increase the chance for an individual to purchase the product. The second advertisement yields a higher likelihood of purchase, implying it's more effective.
Explanation:The problem is related to conditional probability. To solve the question:
The probability of an individual purchasing the product given that the individual recalls seeing the advertisement is calculated by P(B|S) = P(B∩S) / P(S) = .12 / .40 = .30 or 30%. This is greater than the overall probability of purchasing the product, P(B) = .20 or 20%. Meaning the advertisement does increase the probability for an individual to purchase the product.The estimated market share of the company is simply P(B) = .20 or 20%. As advertisement increases the probability of purchase, it would likely increase the market share as long as the cost of advertising does not outweigh the added revenue.For the other advertisement, P(B|S) = P(B∩S) / P(S) = .10 / .30 = .33 or 33%, which is higher than the first advertisement. Therefore, the other advertisement has a larger effect on customer purchases.Learn more about Conditional Probability here:https://brainly.com/question/32171649
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The formula d = 6 t − 11 d=6t-11 expresses a car's distance (in feet) from a stop sign, d d, in terms of the number of seconds t t since it started moving. Determine the car's average speed over each of the following intervals of time.a. From t=3 to t=6 seconds...
b. From t=6 to t=6.5 seconds...
c. From t=6.5 to t=7 seconds...
Answer:
a) 6feet/secs
b) 6feet/secs
c) 6feet/secs
Step-by-step explanation:
The detailed steps are as shown in the attachment
The average speed of the car in each time interval is calculated by first evaluating the distance formula at the endpoints of the interval, subtracting to find the distance travelled, and then dividing by the time taken to travel that distance.
Explanation:The given formula is
d = 6t - 11
, where 'd' is the distance in feet, and 't' is the time in seconds since the car started moving. Firstly, to find the average speed, which is the distance travelled divided by time taken, we need to calculate the distance travelled in each interval. For instance, for the interval from 't=3' to 't=6', we first calculate the distances 'd' at t=3 and t=6 by substituting them into the equation, then subtracting the two to get the distance travelled over this time interval. Similarly, the distances travelled in the intervals from t=6 to t=6.5 seconds and t=6.5 to t=7 seconds were calculated. Finally, the
average speed
in each time interval is obtained by dividing that interval's travelled distance by the time taken.
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The following two functions have a common input, year t: R gives the average price, in dollars, of a gallon of regular unleaded gasoline, and P gives the purchasing power of the dollar as measured by consumer prices based on 2010 dollars (a) Using function notation, show how to combine the two functions to create a new function giving the price of gasoline in constant 2010 dollars. 2010 dollars (RP)(t) dollars (at pump) dollars Rit dollars gallon + P(t) gallon gallon gallon O R(t) dollars - P(t) 2010 dolars(R P)(t) 2010 dollars gallon dollars (at pump) dollars (at pump) R(t) gallon · dollars (at pump) R(t)--+ P() dollars (at pump) A(t) dollars . Pit), 2010 dollars 2010 dollars 2010 dollars _- (R- P)(t) dollars gallon 2010 dollars dollars 2010 dollars _- (R + P)(t) gallon (b) What are the output units of the new function? 2010 dollars per gallon gallons per 2010 dollar dollars per gallon 2010 dollars per dollar (at pump) gallons per dollar
Answer:
a) F(t) = R[P(t)]
b) the output units of the new function = F(t) in dollars per gallon
Step-by-step explanation:
a) There are two function R(t) which shows the average price in dollars of a gallon of regular unleaded gasoline and P(t) which shows the purchasing power of the dollar as measured by consumer prices based on 2010 dollars.
To write the function which gives the rice of gasoline in constant 2010 dollars ;
From the analysis , this is an example of a composition of function as such the relationship =
F(t) = R[P(t)]
b) the output units of the new function = F(t) in dollars per gallon
This shows that the value of F(t) is the dependent variable
Final answer:
To determine the real price of gasoline in constant 2010 dollars, combine the functions R(t) and P(t) using the formula R(t) ÷ P(t). This calculation adjusts the nominal price of gasoline for inflation, resulting in the price of gasoline in terms of 2010 dollars, with the output units being 2010 dollars per gallon.
Explanation:
To combine the two functions representing the average price of a gallon of regular unleaded gasoline, R(t), and the purchasing power of the dollar as measured by consumer prices based on 2010 dollars, P(t), into a new function giving the price of gasoline in constant 2010 dollars, we use the formula:
R(t) ÷ P(t)
This formula represents the price of gasoline adjusted for inflation, giving us the real price of gasoline in terms of 2010 dollars. Here, R(t) gives the average price of gasoline in year t, and P(t) gives the purchasing power of the dollar in year t, compared to 2010 dollars. By dividing R(t) by P(t), we adjust the nominal price of gasoline to reflect its real value, accounting for changes in the purchasing power of the dollar over time.
The output units of this new function would be 2010 dollars per gallon. This metric allows economists and analysts to compare the price of gasoline across different years on a level playing field, eliminating the effects of inflation.
NEED HELP ASAP!!!!!! What is another way to say "to the third power"?
Answer:
A number to the third power would be a number cubed, so the answer is "Cubed".
The curves r1(t) = 3t, t2, t4 and r2(t) = sin(t), sin(2t), 5t intersect at the origin. Find their angle of intersection, θ, correct to the nearest degree.
To find the angle of intersection (θ) between the curves r1(t) and r2(t) at the origin, we calculate the dot product of their tangent vectors and use the arccosine formula. θ ≈ 79 degrees.
To find the angle of intersection (θ) between the curves r1(t) = (3t, [tex]t^2[/tex], [tex]t^4[/tex]) and r2(t) = (sin(t), sin(2t), 5t) at the origin, we can use the dot product formula for angles between vectors.
First, we need to calculate the tangent vectors at the origin for both curves. The tangent vector for r1(t) is (3, 2t, [tex]4t^3[/tex]), and for r2(t), it is (cos(t), 2cos(2t), 5).
Next, evaluate these vectors at t = 0 (the origin) to get the tangent vectors at the point of intersection: r1'(0) = (3, 0, 0) and r2'(0) = (1, 2, 5).
Now, calculate the dot product of these vectors:
r1'(0) · r2'(0) = (3 × 1) + (0 × 2) + (0 × 5) = 3.
The magnitude of r1'(0) is [tex]\sqrt{ (3^2 + 0^2 + 0^2)[/tex] = 3, and the magnitude of r2'(0) is [tex]\sqrt{(1^2 + 2^2 + 5^2[/tex]) = [tex]\sqrt{(1 + 4 + 25)[/tex] = √30.
Now, use the dot product formula for angles:
cos(θ) = (r1'(0) · r2'(0)) / (|r1'(0)| ×|r2'(0)|)
cos(θ) = 3 / (3 × [tex]\sqrt{30}[/tex]) = 1 / [tex]\sqrt30}[/tex]
Now, find θ:
θ = arc cos(1 / [tex]\sqrt{30[/tex])
Using a calculator, θ ≈ 79 degrees (rounded to the nearest degree).
So, the angle of intersection θ is approximately 79 degrees.
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PLEASE HELP 50 COINS!!!!
Answer:
Therefore the measurement of EF,
[tex]EF=1.98\ units[/tex]
Step-by-step explanation:
Given:
In Right Angle Triangle DEF,
m∠E=90°
m∠D=26°
∴sin 26 ≈ 0.44
DF = Hypotenuse = 4.5
To Find:
EF = ? (Opposite Side to angle D)
Solution:
In Right Angle Triangle DEF, Sine Identity,
[tex]\sin D= \dfrac{\textrm{side opposite to angle D}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\sin 26= \dfrac{EF}{DF}=\dfrac{EF}{4.5}[/tex]
Also, sin 26 ≈ 0.44 .....Given
[tex]EF = 4.5\times 0.44=1.98\ units[/tex]
Therefore the measurement of EF,
[tex]EF=1.98\ units[/tex]
There are 39 members on the Central High School student government council. When a vote took place on a certain proposal, all of the seniors and none of the freshmen voted for it. Some of the juniors and some of the sophomores voted for the proposal and some voted against it.
If a simple majority of the votes cast is required for the proposal to be adopted, which of the following statements, if true, would enable you to determine whether the proposal was adopted?
a. There are more seniors than freshmen on the council.
b. A majority of the freshmen and a majority of the sophomores voted for the proposal.
c. There are 18 seniors on the council.
d. There are the same number of seniors and freshmen combined as there are sophomores and juniors combined.
e. There are more juniors than sophomores and freshmen combined, and more than 90% of the juniors voted against the proposal.
Answer:
Option a
Step-by-step explanation:
Given that all of the seniors and none of the freshmen voted for it.
Some of the juniors and some of the sophomores voted for the proposal and some voted against it.
If the proposal was to be adopted then a simple of majority of votes should have been cast.
Since all seniors voted for it, and no freshmen number of freshmen has to be less than seniors then only majority would have voted.
Regarding juniors and sophomores we assume some voted and some against thus approximately nullifying their votes.
So the correct option would be
a. There are more seniors than freshmen on the council.
Option b wrong since only some voted for it.
C is wrong because actual seniors were not given.
D is wrong because while seniors voted for sophomores voted against.
e is wrong since sophomores and freshmen nullified each other
A multiple choice test has 10 questions with 3 choices each. a. How many ways are there to answer the test? b. What is the probability that two papers have the same answers?
Answer:
a. 59049 ways
b. [tex]1.69\times10^{-5}[/tex]
Step-by-step explanation:
If the multiple choice test has 10 questions with 3 choices each, for the each question there are 3 ways to answer the test. Then for n question there are [tex]3^n[/tex] ways to answer the test
The total number of ways to answer 10 questions at 3 choices each is
[tex]3^{10} = 59049[/tex]ways
b. There are 59049 ways to answer the test but if one test must match one other test then the probability for that to happen is
[tex]\frac{1}{59049} = 1.69\times10^{-5}[/tex]
There are 59,049 ways to answer a 10-question test with 3 choices per question. The probability of two tests having the same answers, with all answer patterns being equally likely, is 1/59,049.
Explanation:This problem belongs to the domain of combinatorics. (a) As there are 3 choices for each question and 10 questions, there are 3^10 or 59,049 ways to answer the test. This assumes you are answering every question. (b) This is essentially the question of the probability that two randomly selected tests are identically answered. Assuming all ways to answer a test are equally likely, there are 59,049 different ways to answer, so the probability that two randomly answered tests are the same is 1/59,049 or approximately 0.000017.
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What is the difference between the population and sample regression functions? Is this a distinction without difference?
Answer:
See explanation below.
Step-by-step explanation:
When we want to fit a linear model given by:
[tex] y = \beta_0 + \beta_1 x[/tex]
Where y is a vector with the observations of the dependent variable, [tex]\beta_0 , \beta_1 [/tex] the parameters of the model and x the vector with the observations of the independent variable.
For this case this population regression function represent the conditional mean of the variable Y with values of X constant. And since is a population regression the parameters are not known, for this reason we use the sample data to obtain the sample regression in order to estimate the parameters of interest [tex] \beta_0, \beta_1[/tex]
We can use any method in order to estimate the parameters for example least squares minimizing the difference between the fitted and the real observations for the dependenet variable. After we find the estimators for the regression model then we have a model with the estimated parameters like this one:
[tex] \hat y = \hat b_0 +\hat b_1 x[/tex]
With [tex] \hat \beta_0 = b_o , \hat \beta_1 = b_1[/tex]
And this model represent the sample regression function, and this equation shows to use the estimated relation between the dependent and the independent variable.
Whats an explicit rule for this? 14, 20, 26, 32, etc. Write an explicit formula for the nth term an.
Answer:
a(n)=14+6(n-1)
Step-by-step explanation:
The first term is 14. This would be an arithmetic sequence, so you will add 6 to every term: the common difference is 6.
14+6= 20
20+6=26
You have the formula a(n)= a(1)+d(n-1)
a(n)= 14+6(n-1)
14 for the first term, 6 for the common difference.
An author collected the times (in minutes) it took him to run 4 miles on various courses during a 10-year period. The accompanying histogram shows the times. Describe the distribution and summarize the important features. What is it about running that might account for the shape of the histogram?
Answer:
By looking at the histogram, we can conclude that the distribution is unimodal and skewed to the right. The modal value lies around 30 to 31 minutes and most of the running times range between 29 and 32 minutes.
The histogram is skewed to the right with most of the outliers present at the higher running times because practically, it is most likely possible for a person to run slow and take more time to run 4 miles rather than run fast and take less time.
Step-by-step explanation:
We say that the distribution is unimodal because there is only one peak which is the highest.
The distribution is skewed to the right because most of the outliers are present at the left side of the peak.
Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult aged 20 20 years and over at random. Define two events: A = A= the person chosen is obese B = B= the person chosen is overweight, but not obese
Answer:
Part a: The two events are termed as disjoint because the event B clearly rules out the obese person
Part b: In the plain language, the event "A or B" means that the person is overweight or obese. Its probability is 0.74.
Part c: If C is the event that the person chosen has normal weight or less, its probability is 0.26.
Step-by-step explanation:
As per the question obtained from the google search, the question has 3 parts as follows:
Part a
Explain why events A and B are disjoint.
Solution
The two events are termed as disjoint because the event B clearly rules out the obese person so the events are disjoint. so the correct option as given in the complete question is A.
Part b
Say in plain language what the event "A or B" is.
What is P(A or B)? (Enter your answer to two decimal places.)
Solution
In the plain language, the event "A or B" means that the person is overweight or obese. The correction option as given in the complete question is a.
P(A or B) is given as
P(A or B)=P(AUB)=P(A)+P(B)-P(A∩B)
Here from the data of
P(A)=0.41
P(B)=0.33
P(A∩B)=0 (As the events are disjoint)
P(A or B)=P(AUB)=0.41+0.33-0
P(AUB)=0.74
So the probability of A or B is 0.74.
Part c
If C is the event that the person chosen has normal weight or less, what is
P(C)? (Enter your answer to two decimal places.)
Solution
P(C) is given as
P(C)=1-P(AUB)
P(C)=1-0.74
P(C)=0.26
So the probability of event C is 0.26.
The vector w=ai+bj is perpendicular to the line ax+by=c and parallel to the line bx−ay=c. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below. yx+9y=0, −4x+5y=3
Answer with Step-by-step explanation:
We are given that
[tex]yx+9y=0[/tex]
[tex]-4x+5y=3[/tex]
We have to find the angle between the lines.
[tex]y(x+9)=0[/tex]
[tex]y=0,x+9=0\implies x=-9[/tex]
[tex]y=0[/tex]..(1)
[tex]x=-9[/tex]..(2)
[tex]-4x+5y=3[/tex]..(3)
The angle between two lines
[tex]a_1x+b_1y+c_1=0[/tex]
[tex]a_2x+b_2y+c_2=0[/tex]
[tex]tan\theta=\mid \frac{a_1b_2-b_1a_2}{a_1a_2+b_1b_2}\mid[/tex]
By using the formula the angle between equation (1) and equation (2) is given by
[tex]tan\theta_1=\mid\frac{0\times 0-1\times 1}{0+0}\mid=\infty=90^{\circ}[/tex]degree
[tex]tan90^{\circ}=\infty[/tex]
It is not possible because we are given that the acute angle between intersecting lines that do not cross at right angles is same as the angle determined by vectors that either normal to the lines or parallel to lines.
By using the formula the angle between equation (2) and equation(3)
[tex]tan\theta_2=\mid\frac{1(5)-0(4)}{-4(1)+5(0)}\mid=\frac{5}{4}[/tex]
[tex]\theta_2=tan^{-1}(1.25)[/tex] degree
By using the formula the angle between equation (3) and equation(1)
[tex]tan\theta_3=\mid\frac{-4(1)-5(0)}{-4(0)+5(1)}\mid=\frac{4}{5}[/tex]
[tex]\theta_3=tan^{-1}(\frac{4}{5})[/tex]degree
A wallet contains five $10 bills, three $5 bills, six $1 bills, and no larger denominations. If bills are randomly selected one-by-one from the wallet, what is the probability that at least two bills must be selected to obtain the first $10 bill?
Final answer:
The probability that at least two bills must be selected to obtain the first $10 bill is approximately 24.7%.
Explanation:
To find the probability that at least two bills must be selected to obtain the first $10 bill, we need to calculate the probability of not drawing a $10 bill on the first draw and then drawing a $10 bill on the second draw. In total, there are 5 + 3 + 6 = 14 bills in the wallet.
On the first draw, the probability of not getting a $10 bill is the number of non-$10 bills over the total number of bills, which is (3 $5 bills + 6 $1 bills) / 14 total bills = 9/14.
Assuming a non-$10 bill was drawn first, there are now 13 bills left in the wallet. The probability of drawing a $10 bill on the second draw is now the number of $10 bills remaining over the total number of bills left, which is 5/13.
The combined probability of these two events happening in sequence (not drawing a $10 bill first and then drawing a $10 bill) is the product of their probabilities: (9/14) * (5/13).
Thus, the total probability is (9/14) * (5/13) = 45/182, which simplifies to approximately 0.247 or 24.7%.
Strain-displacement relationship) Consider a unit cube of a solid occupying the region 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1 After loads are applied, the displacements are
Answer:
please see answers are as in the explanation.
Step-by-step explanation:
As from the data of complete question,
[tex]0\leq x\leq 1\\0\leq y\leq 1\\0\leq z\leq 1\\u= \alpha x\\v=\beta y\\w=0[/tex]
The question also has 3 parts given as
Part a: Sketch the deformed shape for α=0.03, β=-0.01 .
Solution
As w is 0 so the deflection is only in the x and y plane and thus can be sketched in xy plane.
the new points are calculated as follows
Point A(x=0,y=0)
Point A'(x+αx,y+βy)
Point A'(0+(0.03)(0),0+(-0.01)(0))
Point A'(0,0)
Point B(x=1,y=0)
Point B'(x+αx,y+βy)
Point B'(1+(0.03)(1),0+(-0.01)(0))
Point B'(1.03,0)
Point C(x=1,y=1)
Point C'(x+αx,y+βy)
Point C'(1+(0.03)(1),1+(-0.01)(1))
Point C'(1.03,0.99)
Point D(x=0,y=1)
Point D'(x+αx,y+βy)
Point D'(0+(0.03)(0),1+(-0.01)(1))
Point D'(0,0.99)
So the new points are A'(0,0), B'(1.03,0), C'(1.03,0.99) and D'(0,0.99)
The plot is attached with the solution.
Part b: Calculate the six strain components.
Solution
Normal Strain Components
[tex]\epsilon_{xx}=\frac{\partial u}{\partial x}=\frac{\partial (\alpha x)}{\partial x}=\alpha =0.03\\\epsilon_{yy}=\frac{\partial v}{\partial y}=\frac{\partial ( \beta y)}{\partial y}=\beta =-0.01\\\epsilon_{zz}=\frac{\partial w}{\partial z}=\frac{\partial (0)}{\partial z}=0\\[/tex]
Shear Strain Components
[tex]\gamma_{xy}=\gamma_{yx}=\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}=0\\\gamma_{xz}=\gamma_{zx}=\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x}=0\\\gamma_{yz}=\gamma_{zy}=\frac{\partial w}{\partial y}+\frac{\partial v}{\partial z}=0[/tex]
Part c: Find the volume change
[tex]\Delta V=(1.03 \times 0.99 \times 1)-(1 \times 1 \times 1)\\\Delta V=(1.0197)-(1)\\\Delta V=0.0197\\[/tex]
Also the change in volume is 0.0197
For the unit cube, the change in terms of strains is given as
[tex]\Delta V={V_0}[(1+\epsilon_{xx})]\times[(1+\epsilon_{yy})]\times [(1+\epsilon_{zz})]-[1 \times 1 \times 1]\\\Delta V={V_0}[1+\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}+\epsilon_{xx}\epsilon_{yy}+\epsilon_{xx}\epsilon_{zz}+\epsilon_{yy}\epsilon_{zz}+\epsilon_{xx}\epsilon_{yy}\epsilon_{zz}-1]\\\Delta V={V_0}[\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}]\\[/tex]
As the strain values are small second and higher order values are ignored so
[tex]\Delta V\approx {V_0}[\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}]\\ \Delta V\approx [\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}]\\[/tex]
As the initial volume of cube is unitary so this result can be proved.
A normal deck of cards has 52 cards, consisting of 13 each of four suits: spades, hearts, diamonds, and clubs. Hearts and diamonds are red, while spades and clubs are black. Each suit has an ace, nine cards numbered 2 through 10, and three "face cards." The face cards are a jack, a queen, and a king. Answer the following questions for a single card drawn at random from a well-shuffled deck of cards. a. What is the probability of drawing a king of any suit? b. What is the probability of drawing a face card that is also a spade? c. What is the probability of drawing a card without a number on it? d. What is the probability of drawing a red card? What is the probability of drawing an ace? What is the probability of drawing a red ace? Arc these events ("ace" and "red") mutually exclusive? Are they independent? List two events that are mutually exclusive
Final answer:
a. The probability of drawing a king of any suit is 1/13. b. The probability of drawing a face card that is also a spade is 3/26. c. The probability of drawing a card without a number is 4/13. d. The probability of drawing a red card is 1/2. The probability of drawing an ace is 1/13. The probability of drawing a red ace is 1/26.
Explanation:
a. There are 4 kings in a deck of cards, one for each suit. So, the probability of drawing a king of any suit is the number of king cards divided by the total number of cards in the deck: 4/52 = 1/13 = 0.077 or 7.7%.
b. There are 3 face cards in each suit, and there are 2 black suits (spades and clubs). So, the probability of drawing a face card that is also a spade is the number of face cards (3) multiplied by the number of black suits (2), divided by the total number of cards in the deck: (3 * 2)/52 = 6/52 = 3/26 = 0.115 or 11.5%.
c. A card without a number refers to a face card (jack, queen, or king) or an ace. There are 12 face cards and 4 aces in a deck. So, the probability of drawing a card without a number is the number of face cards plus the number of aces divided by the total number of cards in the deck: (12 + 4)/52 = 16/52 = 4/13 = 0.308 or 30.8%.
d. There are 26 red cards in a deck (hearts and diamonds) and 52 total cards. So, the probability of drawing a red card is the number of red cards divided by the total number of cards: 26/52 = 1/2 = 0.5 or 50%. The probability of drawing an ace is 4/52 = 1/13 = 0.077 or 7.7%. The probability of drawing a red ace is the number of red aces divided by the total number of cards: 2/52 = 1/26 = 0.038 or 3.8%.
These events are mutually exclusive because a card cannot be an ace and also be a non-ace card at the same time. However, they are not independent because the probability of drawing a red ace would change if an ace had already been drawn.
Two events that are mutually exclusive are drawing a spade and drawing a heart. You cannot draw a card that is both a spade and a heart at the same time.
A circle has the center of (1,-5) and a radius of 5 determine the location of the point (4,-1)
"determine the location" or namely, is it inside the circle, outside the circle, or right ON the circle?
well, we know the center is at (1,-5) and it has a radius of 5, so the distance from the center to any point on the circle will just be 5, now if (4,-1) is less than that away, is inside, if more than that is outiside and if it's exactly 5 is right ON the circle.
well, we can check by simply getting the distance from the center to the point (4,-1).
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{center}{(\stackrel{x_1}{1}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[4-1]^2+[-1-(-5)]^2}\implies d=\sqrt{(4-1)^2+(-1+5)^2} \\\\\\ d = \sqrt{3^2+4^2}\implies d =\sqrt{9+16}\implies d=\sqrt{25}\implies \stackrel{\textit{right on the circle}}{d = 5}[/tex]
A sales representative must visit nine cities. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.
Answer:
362880
Step-by-step explanation:
Given that a sales representative must visit nine cities. There are direct air connections between each of the cities
Since there are direct connections between any two pairs the sales rep can visit in any order as he wishes.
He has 9 ways to select first city, now remaining cities are 8. He can visit any one in 8 ways.
i.e. No of ways of visiting 9 cities in any order = 9P9
= 9!
= 362880
So no of ways he visits the cities since there are direct connections between any two cities is
362880
This is a permutation problem. The sales representative has 9 factorial (9*8*7*6*5*4*3*2*1 = 362,880) different choices for the order to visit the cities.
Explanation:The subject of this question is a part of combinatorics, specifically Permutations. In this scenario, the sales representative has 9 different cities to visit and the order in which the cities are visited is important.
Using the multiplication rule of counting, the number of ways he can visit these cities is 9 factorial (9!). In general, the abbreviation 'n!' denotes the product of all positive integers less than or equal to n.
So for 9 cities this would be: 9*8*7*6*5*4*3*2*1 = 362,880 different choices for order to visit the cities.
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The Consumer Reports National Research Center conducted a telephone survey of 2000 adults to learn about the major economic concerns for the future (Consumer Reports, January 2009). The survey results showed that 1760 of the respondents think the future health of Social Security is a major economic concern.
a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern (to 2 decimals)?
b. At 90% confidence, what is the margin of error (to 4 decimals)?
c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern (to 3 decimals).(, )
d. Develop a 95% confidence interval for this population proportion (to 4 decimals).
Answer:
a) [tex] \hat p =\frac{X}{n}=\frac{1760}{2000}=0.88[/tex]
b) [tex]ME=1.64* \sqrt{\frac{0.88*(1-0.88)}{2000}}=0.0119[/tex]
c) [tex]0.88 - 1.64 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.868[/tex]
[tex]0.88 + 1.64 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.892[/tex]
And the 90% confidence interval would be given (0.868;0.892).
d) [tex]0.88 - 1.96 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.8658[/tex]
[tex]0.88 + 1.96 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.8942[/tex]
And the 90% confidence interval would be given (0.8658;0.8942).
Step-by-step explanation:
Part a
For this case the point of estimate for the population proportion is given by:
[tex] \hat p =\frac{X}{n}=\frac{1760}{2000}=0.88[/tex]
Part b
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 90% confidence interval the value of [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.64[/tex]
The margin of error is given by:
[tex] ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
And if we replace we got:
[tex]ME=1.64* \sqrt{\frac{0.88*(1-0.88)}{2000}}=0.0119[/tex]
Part c
And replacing into the confidence interval formula we got:
[tex]0.88 - 1.64 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.868[/tex]
[tex]0.88 + 1.64 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.892[/tex]
And the 90% confidence interval would be given (0.868;0.892).
Part d
For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.96[/tex]
[tex]0.88 - 1.96 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.8658[/tex]
[tex]0.88 + 1.96 \sqrt{\frac{0.88(1-0.88)}{2000}}=0.8942[/tex]
And the 90% confidence interval would be given (0.8658;0.8942).
The Main Answer for:
a. The point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern is approximately [tex]0.88[/tex].
b. The margin of error at [tex]90[/tex]% confidence is approximately [tex]0.0120[/tex].
c. The [tex]90[/tex]% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is approximately ([tex]0.868, 0.892[/tex]).
d. The [tex]95[/tex]% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is approximately ([tex]0.8657, 0.8943[/tex]).
a. Point Estimate: The point estimate of the population proportion can be calculated by dividing the number of respondents who think the future health of Social Security is a major economic concern by the total number of respondents surveyed.
Point Estimate = Number of respondents concerned about Social Security / Total number of respondents
Given: Number of respondents concerned about Social Security = [tex]1760[/tex]
Total number of respondents surveyed = [tex]2000[/tex]
Point Estimate = [tex]1760 / 2000 =0.88[/tex]
So, the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern is approximately [tex]0.88[/tex].
b. Margin of Error: The margin of error (E) can be calculated using the formula:
[tex]E=z*\sqrt{p(1-p)/n}[/tex]
where:
• z is the z-score corresponding to the desired confidence level
• p is the point estimate of the population proportion
• n is the sample size
Since we are aiming for a 90% confidence interval, we find the z-score corresponding to a 90% confidence level, which is approximately 1.645 (you can find this value in a standard normal distribution table).
[tex]E=1.645*\sqrt{0.88(1-0.88)/ 2000} \\E=1.645*\sqrt{0.88*0.12/2000} \\E=1.645*\sqrt{0.1056/2000} \\E=1.645*\sqrt{0.0000528} \\E=1.645*0.00727\\E=0.01196[/tex]
So, the margin of error at [tex]90[/tex]% confidence is approximately [tex]0.0120[/tex].
c. Confidence Interval (90%): The confidence interval can be calculated using the point estimate and the margin of error.
[tex]CI=(p-E,p+E)\\CI=(0.88-0.0120,0.88+0.0120)\\CI=(0.868,0.892)[/tex]
So, the [tex]90[/tex]% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is approximately ([tex]0.868, 0.892[/tex]).
d. Confidence Interval (95%): To calculate the 95% confidence interval, we use the same formula but with a different z-score. For a 95% confidence level, the z-score is approximately 1.96.
[tex]E=1.96*\sqrt{0.88(1-0.88)/ 2000} \\E=1.96*\sqrt{0.0000528} \\E=1.96*0.00727\\E=0.01427\\CI=(0.88-0.0143,0.88+0.0143)\\CI=(0.8657,0.8943)\\[/tex]
So, the [tex]95[/tex]% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is approximately ([tex]0.8657, 0.8943[/tex]).
COMPLETE QUESTION:
The Consumer Reports National Research Center conducted a telephone survey of [tex]2000[/tex] adults to learn about the major economic concerns for the future (Consumer Reports, January [tex]2009[/tex]). The survey results showed that [tex]1760[/tex] of the respondents think the future health of Social Security is a major economic concern.
a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern (to 2 decimals)?
b. At [tex]90[/tex]% confidence, what is the margin of error (to 4 decimals)?
c. Develop a [tex]90[/tex]% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern (to 3 decimals).(, )
d. Develop a [tex]95[/tex]% confidence interval for this population proportion (to 4 decimals).
A painter is placing a ladder to reach the third story window, which is 19 feet above the ground and makes an angle with the ground of 80. How far out from the building does the base of the latter need to be positioned? Round your answer to the nearest 10th. The base of the latter needs to be positioned__ feet out from the building
Answer:
The answer to your question is 3.35 ft
Step-by-step explanation:
Data
height = 19 ft
angle = 80°
Process
1.- It is formed a right triangle so use a trigonometric function that relates the opposite side and the adjacent side. This trigonometric function is tangent.
tan Ф = Opposite side/adjacent side
adjacent side = Opposite side / tan Ф
adjacent side = 19 / tan 80
adjacent side = 19 / 5.67
adjacent side = 3.35 ft
Answer: The base of the latter needs to be positioned 3.6 feet out from the building.
Step-by-step explanation:
The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the where the top of the ladder touches the window to the base of the building represents the opposite side of the right angle triangle.
The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.
To determine distance,h from the bottom of the ladder to the base of the building, we would apply
the tangent trigonometric ratio.
Tan θ = opposite side/adjacent.
Tan 80 = 19/h
h = 19/Tan 80 = 19/5.6713
h = 3.6 feet
Which measurement is most accurate to describe the amount that a teacup can hold? 6 fl. oz. 2 cups 1 pint 1.5 quarts
Answer:
6 fl. oz
Step-by-step explanation:
The most accurate measurement for the volume a teacup can hold is 6 fluid ounces.
To determine the most accurate measurement for the amount that a teacup can hold, we need to consider the typical volume of a teacup and understand the relationship between different units of capacity. A standard teacup holds about 6 fluid ounces. Given the unit conversion factors, we know that:
1 cup = 8 fluid ounces
1 pint = 2 cups = 16 fluid ounces
1 quart = 2 pints = 32 fluid ounces
1.5 quarts = 48 fluid ounces
Considering these units:
6 fluid ounces is less than 1 cup (8 fl oz).
2 cups equal 16 fluid ounces, which is more than a typical teacup can hold.
1 pint (16 fluid ounces) is also more than what a teacup can hold.
1.5 quarts (48 fluid ounces) is significantly more than a teacup's capacity.
Therefore, the most accurate measurement to describe the amount a teacup can hold is 6 fluid ounces.
You toss a fair coin 5 times. What is the probability of at least one head? Round to the nearest ten- thousandth.
Answer:
0.9688
Step-by-step explanation:
For each time the coin is tossed, there are only two possible outcomes. Either it is heads, or it is tails. The probabilities for each coin toss are independent from each other. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this problem we have that:
For each time the coin is tossed, heads or tails are equally as likely, since the coin is fair. So [tex]p = \frac{1}{2} = 0.5[/tex]
You toss a fair coin 5 times. What is the probability of at least one head?
Either there are no heads, or there is at least one head. The sum of the probabilities of these events is decimal 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want to find [tex]P(X \geq 1)[/tex], when [tex]n = 5[/tex].
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.03125 = 0.96875[/tex]
Rounding to the nearest ten-thousandth(four decimal places), this probability is 0.9688.
The probability of getting at least one head when tossing a fair coin 5 times is 31/32 or 0.96875 when rounded to the nearest ten-thousandth.
Explanation:The subject of this question is probability, a field within Mathematics. To answer your question: the probability of getting at least one head when tossing a fair coin 5 times can be found by calculating the probability of not getting a head (which is tossing tails 5 times in a row) and then subtracting that from 1 (representing certainty). Each toss of the fair coin has two outcomes, heads or tails, with equal probability of 1/2. If you toss the coin 5 times, the total number outs comes is 2^5, or 32. The chance of getting all tails is (1/2)^5, which is 1/32.
So, the probability of not getting a head (only tails) in 5 tosses is 1/32. Subtract this from 1 to find the probability of getting at least one head: This equals 1 - 1/32 = 31/32 = 0.96875, when rounded to the nearest ten-thousandth.
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Given the following sequence, what is the 10th term of the sequence? Assume that the sequences start with an index of 1. Sequence: The nth term is 3.
Answer:
the 10th term of the sequence is 3
Step-by-step explanation:
A sequence is a list of numbers or objects in a specific order
The nth term given in the question is not a function of n
i.e aₙ= 3
Since the sequence starts with an index of 1
a₁=3
All other terms in the sequence will also be 3. Meaning that it is an arithmetic progression with a common difference of 0.
The 10th term is given by
a₁₀= 3
Mary's 25th birthday is today, and she hopes to retire on her 65th birthday. She has determined that she will need to have $1,000,000 in her retirement savings account in order to live comfortably. Mary currently has no retirement savings, and her investments will earn 6% annually. How much must she deposit into her account at the end of each of the next 40 years to meet her retirement savings goal
Answer:
I think 25000
Step-by-step explanation:
Please help!
This is about CIRCLES AND POLYGONS!
Answer:
Step-by-step explanation:
The formula for finding the sum of the measure of the interior angles in a regular polygon is expressed as (n - 2) × 180. Therefore,
(n - 2) × 180 = 9000
180n - 360 = 9000
180n = 9000 + 360 = 9360
n = 9360/180
n = 52
The regular polygon has 52 sides
7) The sum of the angles in the quadrilateral is 360°. Let x represent the missing angle. Therefore,
64 + 116 + 120 + x = 360
300 + x = 360
x = 360 - 300
x = 60°
8a) let x represent the missing side. Therefore,
24/15 = x/10
Cross multiplying,
15x = 240
x = 240/15 = 16
8b) let x represent the missing side. Therefore,
6/12 = 5/x
6x = 60
x = 60/6 = 10
A bacteria culture is initially 10 grams at t=0 hours and grows at a rate proportional to its size. After an hour the bacteria culture weighs 11 grams. At what time will the bacteria have tripled in size?
Answer: It will take 11.56 hours .
Step-by-step explanation:
Exponential growth in population or size formula :
[tex]P(t)=P_0e^{rt}[/tex]
, where [tex]P_0[/tex] = initial size
r= rate of growth
t= time period
As per given , we have
[tex]P_0=10[/tex] grams
At t= 1 , P(t)= 11 grams
Then,
[tex]11=10e^{r(1)}\\\\ 1.1= e^r\\\\\text{Taking natural log on both sides , we get} \\\\\ln (1.1)=r\ln (e)\\\\ r=\ln (1.1)\\\\ r=0.0953101798043\approx0.095[/tex]
When, the bacteria have tripled in size , P(t) = 3 x10 = 30
Then,
[tex]30=10e^{0.095t}\\\\ 3=e^{0.095t}[/tex]
[tex]\text{Taking natural log on both sides , we get}\\\\ \ln 3=0.095t\\\\ t=\dfrac{\ln3}{0.095}\\\\ t=\dfrac{1.09861228867}{0.095}\approx11.56[/tex]
Hence, it will take 11.56 hours .
A bacteria culture is initially 10 grams at t=0 hours & grows at a rate proportional to its size , After an hour the bacteria culture weighs 11 grams , The bacteria takes 11.56 hours to have tripled in size.
To find the time of bacteria when increasing the growth to tripled.
Given : when time=0 hours , weight=10 grams.
when time=1 hours , weight=11 grams.
To find: when time= ? hours , weight=30grams.
Here according to question, initial size = 10 grams we have asked for tripled in size i.e. 30 grams.
Now we knows that,
The formula for exponential growth in population or size is
[tex]\rm (P)=P_0e^{rt}[/tex] where,
[tex]\rm P_0=initial\;size\\\\r= rate\;of\;growth\\\\t= time \;period[/tex]
Now, we put the value in formula we get,
[tex]\rm P_0=10\;grams \\\\when ,\\\;\;t=1\;hour P(t)=11 grams\\Then,\\11=10e^{r(1)\\1.1 =e^r\\\\\rm Taking \;log(natural)\;both\;the\; side \;on \;solving\;we\;get,\\ln(1.1)=r\;ln(e)\\r=ln(1.1)\\r=0.953101798043\approx0.095[/tex]
Now when the bacteria increase its size to triple
[tex]\rm P(t) = 3 \times 10 = 30[/tex]
Then, according to the formula we substitute values in the formula,
[tex]\rm 30=10e^{0.095t}\\\\3=e^{0.095t}\\\\Again \;we \;take\;natural\;log\;on \;both\;the\;sides, we\;get\\ln\;3=0.095t\\\\t=\dfrac{\rm ln\;3}{0.095}\\\\\\\\\rm t= \dfrac{1.09861228867}{0.095} \\\\\ t=approx \; 11.56[/tex]
Therefore, The bacteria takes 11.56 hours to have tripled in size.
Learn more about logical questions here : https://brainly.com/question/15046576
A marijuana survey included 1610 responses from a list of approximately 241,500,000 adults 10) in the U.S. from which every 150.000 name was surveyed. Identify which of these types of sampling is used: A) Stratified B) Cluster C) ConvenienceD) Systematic E) Simple random
Answer:
the Fact that 1610 responses where gotten from the original population of
241 500 000 makes this a convenience sampling.
Step-by-step explanation:
convenience Sampling : this is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand.