Answer:
Step-by-step explanation:
Given that you choose at random a real number X from the interval [2, 10].
a) Since this is a contnuous interval with all number in between equally likely
E = probability for choosing a real number is U(2,10)
pdf of E is [tex]\frac{1}{8}[/tex]
b) P(X>5) = [tex]\int\limits^10_5 {1/8} \, dx = \frac{5}{8}[/tex]
[tex]P(5<x<7) = \frac{2}{8} =\frac{1}{4}[/tex]
For
[tex]x^2-12x+35 >0\\(x-5)(x-7)>0\\x<5 or x >7[/tex]
P(X<5 or x>7) = 1-P(5<x<7)
= [tex]\frac{3}{4}[/tex]
The density function of a real number selected randomly within the range [2,10] is 1/8, with the probability of an event being the difference between the two values divided by 8. The probabilities that X is greater than 5, lies between 5 and 7 and that the inequality X^2 - 12X + 35 > 0 always holds are 5/8, 1/4 and 1 respectively.
Explanation:The subject of this question is probability, particularly continuous uniform distribution. (a) A real number X selected from a certain interval [2, 10] has a continuous uniform distribution. Hence, the density function f(x) = 1/(b-a) = 1/8 for 2 ≤ x ≤ 10 and0otherwise. The probability of an event E, where E is [a,b], is the integral of f(x) from a to b, which is (b-a)/(10-2).
(b) Probability that X > 5 is the integral of f(x) from 5 to 10, which is (10-5)/8 = 5/8. Probability that 5 < X < 7 is the integral from 5 to 7, which is (7-5)/8 = 1/4. Lastly, the inequality X^2 - 12X + 35 > 0 factors out to (X-5)^2 + 10 > 0 which is always true as square number is always non-negative, thus the probability is 1.
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The Commerce Department reported receiving the following applications for the Malcolm Baldrige National Quality Award: 23 from large manufacturing firms, 18 from large service firms, and 30 from small businesses.
1. Is type of business a qualitative or quantitative variable?
2. What percentage of the applications came from small businesses (to 1 decimal)?
Answer:
Categorical42.25%Step-by-step explanation:
CATEGORICAL, because the type of business will not be numerical.30 of the 71 (23+18+30) businesses are small businesses.30/71 = 0.4225 = 42.25%
The area of a triangle is given by the formula A = 1 2bh, where A is the area, b is the length of the base, and h is the triangle's height. Of a triangle has a base 5 meters long and a height twice the length of the base, find its area.
Answer: The area of triangle is 25 sq. meters.
Step-by-step explanation:
Given : Area of a triangle = [tex]\dfrac{1}{2}bh[/tex] m, where b= base of triangle
h= height of triangle.
If a triangle has 5 meters long base and a height twice the length of the base,
that means b = 5 meters and h= 2(5) = 19=0 meters
Then the area of triangle becomes [tex]A=\dfrac{1}{2}(5)(10)=25 m^2[/tex] [Put alll values in the given formula]
Hence, the area of triangle is 25 sq. meters.
The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 304 people entered the park, and the admission fees collected totaled $856. Let x be the number of children that were admitted and let y be the number of adults that were admitted.?
Answer:
x = 144 children
y = 160 adults
Step-by-step explanation:
We have parameters already defined. Number of children that entered is x while number of admitted adults is y.
Since the total number of people admitted was 304, this means:
x + y = 304
Total fees for that day was 856
Mathematically:
1.5x + 4y = 856
From the first equation, we can say y = 304 - x
We then substitute this into the second equation:
1.5x + 4(304 - x) = 856
1.5x + 1216 - 4x = 856
1216-856 = 4x-1.5x
2.5x = 360
x = 360/2.5 = 144
Since y = 304 - 144
y = 160
The number of children admitted was 144 and the number of adult is 160
Please explain if you can
Answer:
Therefore,
[tex]x=9\\\\y=7[/tex]
Step-by-step explanation:
Given:
D,E,F are the midpoints of side AB, BC,and AC such that
AB = 4x - 18
BC = 2x - 4
DF = x
FE = y
To Find:
x = ?
y = ?
Solution:
Midpoint Theorem:
The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
E and F are Midpoint of Sides BC and AC, then
[tex]FE=\dfrac{1}{2}AB[/tex] ......By Midpoint Theorem
Substituting the values we get
[tex]x=\dfrac{1}{2}(4x-18)=2x-9\\\\2x-x=9\\\\x=9[/tex]
Similarly,
D and Fare Midpoint of Sides AB and AC, then
[tex]DF=\dfrac{1}{2}BC[/tex] ......By Midpoint Theorem
Substituting the values we get
[tex]y=\dfrac{1}{2}(2x-4)=x-2\\\\Substitute\ x=9\\\\y=9-2=7[/tex]
Therefore,
[tex]x=9\\\\y=7[/tex]
Jun has 120 meters of fencing to make a rectangular enclosure. She also wants to use some fencing to split the enclosure into two parts with a fence parallel to two of the sides. What dimensions should the enclosure have to have the maximum possible area?
Answer:
Lenght = 20m
Width = 30m
Step-by-step explanation:
Perimeter of a rectangular enclosure = 2(L+W)
Adding a length of the fence parallel to one side of the sudden to split the closure, the total is 2(L+W) + L = 120
Area of a rectangular closure = L*W
To find the dimension that would maximize the area solve for L and W.
2(L+W) + L = 120
2L + 2W + L = 120
3L + 2W = 120
2W = 120 - 3L
W = (120 - 3L)/2
Put the value of W into Area formula
A = L*W
A = L *(120 - 3L) /2
= L(60 - 1.5L)
= 60L - 1.5L^2
= -1.5L^2 + 60L
This is a quadratic equation. Compare to ax^2 + bx + c
L = -b/2a
a = -1.5, b= 60, c= 0
L = -60/2(-1.5)
= -60/-3
= 20m
Put L = 20 into the value of W
W = (120 - 3L) /2
W= (120 - 3*20) / 2
= (120 - 60)/2
= 60 / 2
= 30m
The dimensions are 20m by 30m
PLZ HELP, GIVING BRAINLIEST, LOOK AT THE PIC FOR GRAPH!!
Which of the following is the equation of the circle seen in the graph below?
A. (x + 2)^2 + (y - 1)^2 = 16
B. (x + 2)^2 + (y + 1)^2 = 4
C. (x - 2)^2 + (y + 1)^2 = 16
D. (x + 2)^2 + (y - 1)^2 = 4
Answer:
The answer to your question is letter C
Step-by-step explanation:
From the graph, we get the center and the radius
- The center is the point shown in the graph and its coordinates are (2, -1).
- The length of the radius is 4 units, from the center we count horizontally the number of squares (4)
Substitution
(x - 2)² + (y + 1)² = 4²
or (x - 2)² + (y + 1)² = 16
Answer:
A or B
Step-by-step explanation:
Because of the negtive 1
After production, an electrical circuit is given a quality score of A, B. C, or D. Over a certain period of time, 77% of the circuits were given a quality score A. 11% were given a quality score B, 7% were given a quality score C, and 5% were given a quality score D. Furthermore, it was found that 2% of the circuits given a quality score A eventually failed, and the failure rate was 10% for circuits given a quality score B. 14% for circuits given a quality given a quality score C, and 25% for circuits given a quality score D. Show all your work and circle your final answers. Use four decimal places for your calculations. a) Find the probability of a circuit failing. b) If a circuit failed, what is the probability that it had received a quality score either C or D?
Answer:
a) 0.0125
b) 0.4579
Step-by-step explanation:
For this question use tree diagram method to solve the question or by simply listing down the probabilities as I have done in the attached picture. Firstly, we need to convert all percentages in to decimal and those decimals will represent probability of each event. For example if we consider probability of quality score A it can be found by diving 77 with 100:
77/100 = 0.77
Similarly all probabilities can be found by simply dividing percentages with 100.
Part (b) is a conditional probability question. Given that a circuit failed is the condition. So we need to use conditional probability method to solve it.
Final answer:
The probability of a circuit failing is 4.87%. If a circuit failed, there is a 45.77% chance that it received a quality score of C or D.
Explanation:
Calculating the Probability of Circuit Failure
To find the probability of a circuit failing, we multiply the probability of receiving each quality score by the probability of failure for that score, then add these together:
A score: 0.77 * 0.02 = 0.0154 (1.54%)
B score: 0.11 * 0.10 = 0.0110 (1.10%)
C score: 0.07 * 0.14 = 0.0098 (0.98%)
D score: 0.05 * 0.25 = 0.0125 (1.25%)
The total probability of failure is the sum of these values: 0.0154 + 0.0110 + 0.0098 + 0.0125 = 0.0487 or 4.87%.
Probability of a Failed Circuit Having a C or D Score
If a circuit failed, to find the probability that it had a quality score of C or D, we divide the sum of the probabilities of failure for C and D by the total probability of failure:
(Probability of C failure + Probability of D failure) / Total probability of failure
= (0.0098 + 0.0125) / 0.0487
= 0.0223 / 0.0487
= 0.4577 or 45.77%.
ALG TWO HELP ASAP?
What is the period to the graph in problem 1?
the amplitude of the function is 2.
Answer:
Therefore the period of the sinusoidal wave = 3.14.
The amplitude of the function = 2.
Step-by-step explanation:
The period of a sinusiodal wave is given by the length of x axis which covers one full cycle of the wave, which one positive half-cycle and one negative half cycle.
From the graph we can see that one of the cycles starts at -3.14 / 4 and ends at 3.14 [tex]\times[/tex] 3/4.
Therefore we can sutract the start point value from the end point value to get the period
Therefore period = (3.14 [tex]\times[/tex] 3/4) - (-3.14 / 4) = (3.14 [tex]\times[/tex] 3/4) + (3.14 / 4) = 3.14
Therefore the period of the sinusoidal wave = 3.14.
The amplitude of the function = 2.
Lea sold 2 cherry pies and 4 pumpkin pies for a total of $116. Kali sold 7 cherry pies and 8 pumpkins pies for a total of $286. What is the cost of one cherry pie and of one pumpkin pie
Answer: the cost of one cherry pie is $18 and the cost of one pumpkin pie is $20
Step-by-step explanation:
Let x represent the cost of one cherry pie.
Let y represent the cost of one pumpkin pie.
Lea sold 2 cherry pies and 4 pumpkin pies for a total of $116. This means that
2x + 4y = 116 - - - - - - - - - - - - - -1
Kali sold 7 cherry pies and 8 pumpkins pies for a total of $286. This means that
7x + 8y = 286 - - - - - - - - - - - - 2
Multiplying equation 1 by 7 and equation 2 by 2, it becomes
14x + 28y = 812
14x + 16y = 572
Subtracting, it becomes
12y = 240
y = 240/12 = 20
Substituting y = 20 into equation 1, it becomes
2x + 4 × 20 = 116
2x + 80 = 116
2x = 116 - 80 = 36
x = 36/2 = 18
This problem has been solved!
See the answer
Suppose a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students for a total of 1000 students. (a) Suppose one of the 20 classes is chosen at random, let Y be the number of students in that class. Write out the p.m.f. for Y and use it to calculate the average class size at this school. (b) Suppose that one of the 1000 students is chosen at random. Let X be the size of the class to which the student belongs. Write out the p.m.f. of X and find E[X]. (c) Fill in the following: On average, a student at this school is in a class with students. On average, a class at this school has students. Comment
Answer:
Step-by-step explanation:
Given that a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students for a total of 1000 students.
a) Y = no of students in the class out of 20 selected at random
Y can take values as
Y 25 100 300 Total
freq 16 3 1 20
P(Y) 16/20 3/20 1/20 1
y*p 20 15 15 50
E(Y) = 50
b) X = size of student from which one student is taken at random
X 25 100 300 Total
No of classes 16 3 1 20
Total students
(X*no of classes) 400 300 300 1000
P(x) 0.4 0.3 0.3 1
X*P 160 90 90 240
E(x) =240
c) On an average, a student at this school is in a class with 240 students. On average, a class at this school has 50 students.
i.e. expectation of number of students in a class is 50 while expectation of a student having students in the class is 240
Suppose the wait through immigration at JFK Airport in New York is thought to be bell-shaped and symmetrical with a mean of 22 minutes. It is known that 68 percent of travelers will spend between 16 and 28 minutes waiting to pass through immigration. The standard deviation for the wait time through immigration is_________.
Answer: 6 minutes
Step-by-step explanation:
According to the Empirical rule ,
About 68% of the population lies within one standard deviation from the mean.
Given : Suppose the wait through immigration at JFK Airport in New York is thought to be bell-shaped and symmetrical with a mean of 22 minutes.
It is known that 68 percent of travelers will spend between 16 and 28 minutes waiting to pass through immigration.
i.e. Mean - standard deviation= 16
and Mean + standard deviation =28
Since , Mean=22 , so we have
22+ standard deviation =28
⇒ standard deviation =28 -22 =6
Hence, the standard deviation for the wait time through immigration is 6 minutes .
The standard deviation for the wait time through immigration is 6 minutes.
To find the standard deviation, we can use the properties of the normal distribution, specifically the 68-95-99.7 rule, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Given that 68% of travellers wait between 16 and 28 minutes, we can determine that these times represent one standard deviation from the mean. The mean wait time is 22 minutes. The range from 16 to 28 minutes is 12 minutes wide (28 - 16 = 12). Since this range represents one standard deviation on either side of the mean, we can divide this range by 2 to find the value of one standard deviation:
Standard deviation = (28 - 16) / 2 = 12 / 2 = 6 minutes.
How many toothpicks do I need to make a acutangle scalene triangle
Answer:
The (minimum) number of toothpicks required to make an acute angle scalene triangle is 3.
Step-by-step explanation:
The (minimum) number of toothpicks required to make an acute angle scalene triangle is 3.
All the angles in a an acute angled scalene triangle are less than 90°.
The above condition can be satisfied with a minimum of three toothpicks.
To create an acute-angled scalene triangle, three toothpicks are required.
To create an acute-angled scalene triangle, you would need 3 toothpicks. You can stick the toothpicks into a marshmallow or a gumdrop and position them in a way that forms a triangle with angles less than 90 degrees and with all sides of different lengths.
Need help with this
Answer:
2nd option
Step-by-step explanation:
given
BD = 4x
CE = 2x + 2
test each answer option by substituting the given values of x into each of the above equations and see if it is consistent with the given values for BD and CD in the answer options.
1st option, when x = 5,
BD = 4x = 4(5) = 20 (Consistent)
CE = 2x + 2 = 2(5) + 2 = 10 + 2 = 12 ( not consistent with CE=8)
2nd option, when x = 3/7,
BD = 4x = 4(3/7) = 12/7 (Consistent)
CE = 2x + 2 = 2(3/7) + 2 = 6/7 + 2 = 20/7 ( consistent with CE=20/7) (ANSWER)
3rd option, when x = 3,
BD = 4x = 4(3) = 12 (Consistent)
CE = 2x + 2 = 2(3) + 2 = 6 + 2 = 8 ( not consistent with CE=20)
Christy purchased 6.75 pounds of red licorice and 2.37 pounds of black licorice. How much licorice does she need to put in a bag if she divides the total amount into 10 equal-sized bags?
Answer: The amount she puts in a bag = 0.912 pound.
Step-by-step explanation:
Given : Amount of red licorice purchased by Christy = 6.75 pounds
Amount of black licorice purchased by Christy = 2.37 pounds
Total amount of licorice purchased by Christy = 6.75 + 2.37 pounds
= 9.12 pounds
Then, if she divides the total amount into 10 equal-sized bags , the amount she put in a bag = (Total amount of licorice purchased) ÷ 10
= 9.12 ÷ 10 = 0.912 pound
Hence, the amount she puts in a bag = 0.912 pound.
Final answer:
To find how much licorice Christy needs to put into each of 10 bags, add the weights of red and black licorice and then divide by 10. She will need to put 0.912 pounds of licorice into each bag.
Explanation:
Christy purchased 6.75 pounds of red licorice and 2.37 pounds of black licorice. To find the total amount of licorice, we add the weight of the red and black licorice together:
Total weight of licorice = [tex]6.75 pounds + 2.37 pounds = 9.12 pounds.[/tex]
If she divides the total amount into 10 equal-sized bags, we divide the total weight by 10:
Weight per bag = [tex]9.12 pounds / 10 bags = 0.912 pounds per bag.[/tex]
In a survey of 545 human resource professionals, each was asked about the importance of the age of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.
Answer:
The sampling method described in this question appears to be sound
Step-by-step explanation:
It appears to be sound because the data are not biased in any way, since every member and set of members has an equal chance of being included in the sample selection. Also, random samples are usually fairly representative since they don't favor certain members.
How do you solve this problem? Emma and Anna went to the market to buy 25 fruits. Emma got a few apples that cost $2 each, and Anna bought some oranges which cost $3 each. If their combined total is $60, how many oranges did Anna get?
Anna bought 10 oranges
Explanation:
Let x denote the number of apples.
Let y denote the number of oranges.
The system of equations can be written as
[tex]x+y=25[/tex] and [tex]2x+3y=60[/tex]
Let us solve the equation by substitution method.
Thus, from [tex]x+y=25[/tex], the value of y can be determined such that [tex]y=25-x[/tex]
Using the y value [tex]y=25-x[/tex] in the equation [tex]2x+3y=60[/tex], we get,
[tex]2x+3(25-x)=60[/tex]
Multiplying 3 within the bracket,
[tex]2x+75-3x=60[/tex]
Adding the terms,
[tex]75-x=60[/tex]
Subtracting both sides by 75, we have,
[tex]x=15[/tex]
Thus, substituting [tex]x=15[/tex] in [tex]y=25-x[/tex], we get,
[tex]y=25-15\\y=10[/tex]
Thus, Anna get 10 Oranges.
Mr. Clements painted his barn for 3 3/5 hours in the morning. He painted the barn for 5 3/4 hours in the afternoon. For 15a-15cn select True of False for each statement.
Answer:
True
Step-by-step explanation:
A common denominator of the mixed numbers is 20. select True or false
Mr. Clements painted his barn for 3 3/5 hours in the morning.
[tex]3\frac{3}{5}=\frac{18}{5}[/tex]
He painted the barn for 5 3/4 hours in the afternoon.
[tex]5\frac{3}{4}=\frac{23}{4}[/tex]
Now we consider the denominator of both fractions 18/5 and 23/4
Least common denominator is 5 times 4 = 20
So its true that the common denominator of mixed numbers is 20
The questions on a multiple choice test each have 4 answer choices. Describe a model that you could use to simulate the outcome of guessing tje correct answers to a 50 question test
Answer:
The outcome of guessing the correct answers to a 50 question test is 12.5.
Step-by-step explanation:
Let us first consider one question.
Since it has 4 options so we can say that;
Total number of possible outcomes = 4
Since 1 answer is correct so we can say that;
Favorable outcome = 1
Now we can say that;
Probability for choosing correct answer can be calculated by Favorable outcome divided by Total number of possible outcomes.
framing in equation form we get;
[tex]P(Correct\ Answer) = \frac{1}{4}[/tex]
Now Given:
Total number of question = 50
So we can say that;
Total number of correct answer out of 50 is equal to Probability for choosing correct answer multiplied by Total number of question.
framing in equation form we get;
Guessing number of correct answer out of 50 = [tex]\frac14 \times 50 = 12.5[/tex]
Hence The outcome of guessing the correct answers to a 50 question test is 12.5.
You can use a binomial distribution model to simulate guessing the correct answers on a 50-question test with 4 answer choices per question. The probability of getting at least 30 correct answers.
Explanation:To simulate the outcome of guessing the correct answers to a 50 question test, you can use a binomial distribution model. A binomial distribution represents the probability of a certain number of successful outcomes in a fixed number of independent trials. In this case, the success would be guessing the correct answer.
Each question has 4 answer choices, so the probability of guessing the correct answer for each question is 1/4. The number of successful guesses in a 50-question test can follow a binomial distribution with parameters n = 50 (number of trials) and p = 1/4 (probability of success).
Using this model, you can calculate probabilities of various outcomes, such as the probability of getting exactly 20 correct answers by guessing
Hence, the probability of getting at least 30 correct answers.
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A car with an initial cost of $23,000 is decreasing in value at a rate of 8% each year. Write the exponential decay function described in this situation. Then use your function to determine when the value of the car will be $15,000, to the nearest year.
Answer:
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r/n)^ nt
Where
A represents the value after t years.
n represents the period for which the decrease in value is calculated
t represents the number of years.
P represents the value population.
r represents rate of decrease.
From the information given,
P = 23000
r = 8% = 8/100 = 0.08
n = 1
Therefore, the exponential decay function described in this situation is
A = 23000(1 - 0.08/n)1)^ 1 × t
A = 23000(0.92)^t
If A = 15000, then
15000 = 23000(0.92)^t
0.92^t = 15000/23000 = 0.6522
Taking log of both sides to base 10
Log 0.92^t = log 0.6522
tlog 0.92 = log 0.6522
- 0.036t = - 0.1856
t = - 0.1856/- 0.036
t = 5 years to the nearest year
The value of the car will be $15,000 after approximately 4 years.
To model the situation with an exponential decay function, we use the formula:
[tex]\[ V(t) = P \times (1 - r)^t \][/tex]
Given that the initial cost [tex]P[/tex] is $23,000 and the annual depreciation rate r is 8%, or 0.08 in decimal form, we can write the exponential decay function as:
[tex]\[ V(t) = 23000 \times (1 - 0.08)^t \][/tex]
[tex]\[ V(t) = 23000 \times (0.92)^t \][/tex]
To find out when the value of the car will be $15,000, we set [tex]V(t)[/tex] equal to $15,000 and solve for t.
[tex]\[ \frac{15000}{23000} = (0.92)^t \][/tex]
[tex]\[ 0.652173913043478 = (0.92)^t \][/tex]
Using a calculator, we find:
[tex]\[ t \approx \frac{\ln(0.652173913043478)}{\ln(0.92)} \approx 4.037 \][/tex]
Since we are looking for the time in whole years, we round to the nearest year:
[tex]\[ t \approx 4 \][/tex]
Therefore, the value of the car will be $15,000 after approximately 4 years.
Alan is loading a pallet with boxes that each weighs 55 pounds. The pallet can safely support no more than 1595 pounds. How many boxes can he safely load onto the pallet?
Answer:
At most 29 boxes can be safely loaded onto the pallet.
Step-by-step explanation:
Given:
Weight of each box = 55 pound
Weight pallet can support [tex]\leq[/tex] 1595 pounds.
We need to find the number of boxes .
Solution:
Let the number of boxes loaded safely onto the pallet be 'x'.
So we can say that;
Weight of each box Multiplied by number of boxes should be less than or equal to Weight pallet can support.
framing in equation form we get;
[tex]55x\leq 1595[/tex]
Dividing both side by 55 we get;
[tex]\frac{55x}{55}\leq \frac{1595}{55}\\\\x\leq 29[/tex]
Hence At most 29 boxes can be safely loaded onto the pallet.
Alan can safely load 29 boxes onto the pallet.
Explanation:To determine how many boxes Alan can safely load onto the pallet, we need to divide the maximum weight the pallet can support by the weight of each box. The maximum weight the pallet can support is 1595 pounds, and each box weighs 55 pounds.
To find the number of boxes, we can divide the maximum weight by the weight of each box: 1595 ÷ 55 = 29.
Therefore, Alan can safely load 29 boxes onto the pallet.
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Steve invests 1,800 in an account that earns 3.7% annual interest, compounded continuously. What is the value of the account after 10 years? Round your answer to the nearest dollar.
Answer: the value of the account after 10 years is $2606
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 1800
r = 3.7% = 3.7/100 = 0.037
t = 10 years
Therefore,
A = 1800 x 2.7183^(0.037 x 10)
A = 1800 x 2.7183^(0.37)
A = $2606 to the nearest dollar
To solve such problems we must know about Continuous Compound Interest.
Continuous Compound Interest[tex]A = Pe^{rt}[/tex]
where,
A is the principal amount after t number of years,
r is the rate at which the principal is been compounded, and P is the principal amount.
The value of Steve's account after 10 years will be $2,606.
Given to usSteve invests 1,800 in an account that earns 3.7% annual interest, compounded continuously.Time period money invested for 10 years, SolutionAs it is given in the problem, the account of Steve is compounding continuously.
Statement 1Steve invests 1,800 in an account that earns 3.7% annual interest, compounded continuously.
Principal amount = $1,800 Rate of interest = 3.7% = 0.037Statement 2Time period money invested for 10 years,
time period, t = 10 yearsValue of the accountSubstituting the values in the formula of Continuous Compound Interest,
[tex]A = Pe^{rt}[/tex]
[tex]\begin{aligned}A&=\$1800\times e^{0.037\times10}\\ &=\$2605.9\approx\$2606\\ \end{aligned}[/tex]
Hence, the value of Steve's account after 10 years will be $2,606.
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what is the y-intercept of the line y=7?
Answer:
Step-by-step explanation:
The value of the y-intercept is (0,7)
So the y intercept is 0,7
Officials project that between 201020102010 and 205020502050, the population of a certain city will drastically change. The model below gives the projection of the city's population , PPP, in thousands, with respect to time, ttt, in years, where 201020102010 corresponds to t=0t=0t, equals, 0. \quad P = 175 + \dfrac{11}{2}tP=175+ 2 11 tP, equals, 175, plus, start fraction, 11, divided by, 2, end fraction, t What does the 175175175 mean in the equation?
Answer:
175 means the city's population is 175 thousands in 2010.
Step-by-step explanation:
The model below gives the projection of the city's population , P, in thousands, with respect to time, t, in years, where 2010 corresponds to t=0.
The given equation is
[tex]P=175+\dfrac{11}{2}t[/tex]
We need to interpret 175 for the given model.
Substitute t=0 in the above equation.
[tex]P=175+\dfrac{11}{2}(0)[/tex]
[tex]P=175[/tex]
At t=0 the value of P is 175 it means the city's population is 175 thousands in 2010.
Mike has $6000 to invest. He invested part of his total into an account earning 6% interest and the rest in an account earning 11% interest. If at the end of the year, he earned $460.00 in interest, how much money was invested in each account?
Answer:$4000 was invested into the account earning 6% interest.
$2000 was invested into the account earning 11% interest.
Step-by-step explanation:
Let x represent the amount invested into the account earning 6% interest.
Let y represent the amount invested into the account earning 11% interest.
Mike has $6000 to invest. He invested part of his total into an account earning 6% interest and the rest in an account earning 11% interest. This means that
x + y = 6000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
Considering the account earning 6% interest, the interest would be
I = (x × 6 × 1)/100 = 0.06x
Considering the account earning 11% interest, the interest would be
I = (x × 11 × 1)/100 = 0.11y
If at the end of the year, he earned $460.00 in interest, it means that
0.06x + 0.11y = 460 - - - - - - - - - - -1
Substituting x = 6000 - y into equation 1, it becomes
0.06(6000 - y) + 0.11y = 460
360 - 0.06y + 0.11y = 460
- 0.06y + 0.11y = 460 - 360
0.05y = 100
y = 100/0.05 = $2000
x = 6000 - y = 6000 - 2000
x = $4000
The point A (8, 2) is reflected over the line x = 5, and then is reflected over the line x = -1. What are the coordinates of A'?
Answer:
A'(8, -10)
Step-by-step explanation:
Firstly we have to know the distance from the point A to the line, the point is (8, 2) and the line is x = 5 .
the point has two components, at x and y
the component in y will give us the distance we have on the axis of the X thas is 2.
T he line is 5 units from the axis.
Now to know the distance we have to subtract
2 - 5 = -3
Here is the point with respect to the line x = 5
For the reflected over the line we just need to change the sign, now we got +3 . To this we add the value of the line that is 5
3 + 5 = 8.
So the reflected point over the line x = 5 is (8, 8)
We do the same with the line x = -1.
(8, 8) and x = -1
..
8 - (-1) = 9
..
(-9) + (-1) = -10
(8, -10)
Mary purchased an annuity that pays her $500 per month for the rest of her life. She paid $70,000 for the annuity. Based on IRS annuity tables, Mary's life expectancy is 16 years. How much of the first $500 payment will Mary include in her gross income (round to two decimals)?
Answer: $135.42
Step-by-step explanation:
Based on IRS tables, Mary is expected to receive 192 (16 years x 12 months) annuity payments. Her investment in the annuity is $70,000 and her return of capital for each annuity payment is $70,000/192 = $364.58. The return of capital portion of each annuity payment is not taxable (not included in gross income). Mary must include the excess received ($500.00 – 364.58) of $135.42 in her gross income.
To calculate how much of the first $500 payment Mary will include in her gross income, we need to determine the exclusion ratio. The exclusion ratio is the ratio of the investment in the annuity to the expected return. In this case, Mary will include $36.45 of the first $500 payment in her gross income.
Explanation:To determine how much of the first $500 payment Mary will include in her gross income, we need to calculate the exclusion ratio. The exclusion ratio is the ratio of the investment in the annuity to the expected return. In this case, Mary paid $70,000 for the annuity and her life expectancy is 16 years, so the exclusion ratio is $70,000 / ($500/month * 12 months/year * 16 years) = 0.0729. To determine the amount she will include in her gross income, we multiply the monthly payment by the exclusion ratio: $500 * 0.0729 = $36.45. Therefore, Mary will include $36.45 of the first $500 payment in her gross income.
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From a random sample of 50 people, sitting pulse rates and standing pulse rates were measured for each person. A coin was flipped to determine whether the sitting or the standing pulse rate would be measured first. Let μsitting represent the mean sitting pulse rate in the population, μstanding represent the mean standing pulse rate of the population, and μd represent the mean difference between the sitting and standing (sitting – standing) pulse rates of the population. Which of the following represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population?1. A two-sample t-test withH0 : μsitting = μstandingHA : μsitting ≠ μstanding2. A two-sample t-test withH0 : μsitting = μstandingHA : μsitting < μstanding3. A matched-pairs t-test withH0 : μd = 0HA : μd ≠ 04. A matched-pairs t-test withH0 : μd = 0HA : μd < 0
Answer:
3. A matched-pairs t-test with H0 : μd = 0, HA : μd ≠ 0
Step-by-step explanation:
An investigator wants to asses the difference in mean pulses rates between sitting and standing persons in population.
The matched paired t-test is appropriate choice because the observations in the data are paired. The observations in the data are the calculated pulse rates of 50 persons while sitting and standing. For each person. sitting and standing pulse rates are measured and this indicates the before and after effect is measured. The before and after effect is measured through matched paired t test.
Also, an investigator wants to determine whether there is difference in mean pulse rates between sitting and standing in population. This indicates two tailed test. so, the hypotheses would be
Null hypotheses : μd = 0
Alternative hypotheses: μd ≠ 0.
Thus, situation indicates a matched-pairs t-test with H0 : μd = 0, HA : μd ≠ 0.
The option that represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population is: Option C: A matched-pairs t-test with [tex]H_0 : \mu_d = 0\\H_A : \mu_d \neq 0[/tex]
When do we use two-sample t-test?The two-sample t-test is used to determine if two population means are equal.
When there has to be done comparison between means of two sets of paired data, then we use matched pair t test.
How to form the hypotheses?There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
For this case, we want to determine if there is a difference in mean pulse rates between sitting and standing in the population.
That is the reason why we will use matched pair t-test.
Where paired data is the pair of data obtained from each of those 50 people, the pair of data being sitting pulse rate and standing pulse rate.
Now, since we want to determine if there's any difference, so the null hypothesis will nullify the presence of any difference.
Thus, we get:
Null hypothesis = [tex]H_0: \mu_d = 0[/tex] (the difference between mean of sitting pulse rate and that of standing pulse rate is 0, therefore no difference).
This can be rewritten as: [tex]H_0: \mu_{\text{sitting}} = \mu_{\text{standing}}[/tex]
Alternate hypothesis = [tex]H_A: \mu_d \neq 0[/tex] or [tex]H_A: \mu_{\text{sitting}} \neq \mu_{\text{standing}}[/tex]
Thus, the option that represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population is: Option C: A matched-pairs t-test with [tex]H_0 : \mu_d = 0\\H_A : \mu_d \neq 0[/tex]
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Bill says the equation 600 equals 12×50 means 600 is four times as many as 50 Sarah says the equation means 650 more than 12 who do you agree with explain
Answer:
neither
Step-by-step explanation:
The equation means that 600 is twelve times as many as 50 (not four times). Bill needs to rethink the meaning of "four" relative to the meaning of "12".
__
"650 more than 12" is an expression (12+650), not an equation. Sarah seems to be clueless.
__
Neither Bill nor Sarah have described the meaning of the equation.
A 2016 Pew Research poll estimated the proportion of people supporting each presidential candidate in the fall election. They based their estimates on telephone interviews of 2, 010 adults living in all 50 U.S. states They asked each participant which presidential and vice presidential candidate they support, and used that data to calculate the proportions. What is the statistic in this experiment? Select the correct answer below: a.The candidate each participant supports. b.The number of people Pew Research interviews. c.The number of people in the United States. d.The proportions of participants who support each presidential candidate. e.The proportions of U.S. adults who support each presidential candidate.
Answer:
option A- The candidate each participant supports.
Step-by-step explanation: the question asks about the 'statistics in the experiment', meaning the major factor or say the most important data to be considered to achieve the desired aim/result of the experiment.
From the question, the aim/result of the Research poll was to get 'the PROPORTION of people supporting each presidential candidate in the fall election'. Note that to find 'PROPORTION', you must first find the individual values and then compare them. That's what 'PROPORTION' is all about - comparing number of things or people.
So to achieve this, the most important data-'statistics' in this experiment is knowing the candidate each participant supports.
For example, if there are 5 presidential candidates: Mr A, B, C, D & E and after interviewing 2,010 adults, you find out that:
134 people supports Mr A;
268 people supports Mr B;
402 people supports Mr C;
536 people supports Mr D and
670 people supports Mr E.
Now because you know the candidate each participant supports, you can now derive the 'PROPORTION' of people supporting each candidate which is 134:268:402:536:670. NB: you have to always leave your answer in its lowest term, so the proprtion here is 1:2:3:4:5.
Answer:
The proportions of participants who support each presidential candidate.
Step-by-step explanation
Six less than the product of 11 and a number
Use the variable n to represent the unknown number.
11n - 6 is the algebraic expression for six less than the product of 11 and a number
Solution:
Given that,
Six less than the product of 11 and a number
Let "n" be the unknown number
Let us understand and break the given sentence
Six less than the product of 11 and a number
Which means,
six less than product of 11 and "n"
Which can be written as,
[tex]11n-6[/tex]
Thus the given sentence is translated into algebraic expression
The algebraic expression which represents 'six less than the product of 11 and a number' is 11n - 6, where n is the unknown number.
Explanation:The question is asking for an algebraic expression representing 'six less than the product of 11 and a number'. To translate this to mathematical terms, first, the 'product of 11 and a number' indicates multiplication between 11 and the unknown number, which we represent with the variable n. The 'six less than' part indicates that we subtract 6 from this product.
So, the algebraic expression that represents 'six less than the product of 11 and a number' is 11n - 6.
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