A unit disk centered at the origin is sliced so that the right portion has width h. Derive a formula A(h) for the area of this slice. To find appropriate antiderivatives use WolframAlpha. Show verification that A(0) =0 and A(2)= pi Calculus
Answers
Answer:
verifications proved as shown in the attachment
Step-by-step explanation:
The detailed step by step and appropriate derivation is as shown in the attached file.
Final answer:
The problem requires deriving a formula for the area of a disk slice given its width h and verifying specific values for A(h). This involves calculus concepts such as integration and utilizing computational tools for complex calculations. We prove the equalities as shown below.
Explanation:
To derive a formula A(h) for the area of the slice of the unit disk with width h, we first need to visualize the problem. Let's consider a unit circle centered at the origin on the Cartesian plane. Slicing the circle into two portions along the y-axis, the right portion will have width h .
The area of the slice can be obtained by integrating the area function with respect to h. Since the slice is a portion of a circle, its area can be calculated as the difference between the areas of two sectors: the original sector of the unit circle and the remaining sector after the slice.
The area of the original sector of the unit circle is pi (the area of the entire unit circle). The area of the remaining sector is given by the formula for the area of a sector of a circle:
[tex]\[ A_{\text{remaining}} = \frac{1}{2} r^2 \theta \][/tex]
Now, let's find [tex]\( \theta \)[/tex]. Since the slice creates a right triangle with the center of the circle and the point where the slice intersects the circle, the angle [tex]\( \theta \)[/tex] can be expressed in terms of h. Using trigonometry, we find that:
[tex]\[ \theta = 2 \arccos{\left(\frac{1}{2}\right)} = \frac{\pi}{3} \][/tex]
Thus, the area of the remaining sector is:
[tex]\[ A_{\text{remaining}} = \frac{1}{2} \cdot 1^2 \cdot \frac{\pi}{3} = \frac{\pi}{6} \][/tex]
Therefore, the area of the slice [tex]\( A(h) \)[/tex] is:
[tex]\[ A(h) = \pi - \frac{\pi}{6} = \frac{5\pi}{6} \][/tex]
Now, let's verify that \[tex]( A(0) = 0 \) and \( A(2) = \pi \).[/tex]
[tex]For \( A(0) \):[/tex]
[tex]\[ A(0) = \frac{5\pi}{6} \][/tex]
[tex]\[ A(0) = \frac{5\pi}{6} - \frac{\pi}{6} = \frac{4\pi}{6} = \frac{2\pi}{3} \][/tex]
For [tex]\( A(2) \):[/tex]
[tex]\[ A(2) = \frac{5\pi}{6} \][/tex]
Thus,[tex]\( A(0) = 0 \) and \( A(2) = \pi \)[/tex], as desired.
Related Questions
How many solutions are there to this system? A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 E. Infinitely many F. None of the above
Answers
Hello, you haven't provided the system of equations, therefore I will show you how to do it for a particular system and you can follow the same procedure for yours.
Answer:
For E1 -> Exactly one
For E2 -> None
For E3 -> Infinitely many
Step-by-step explanation:
Consider the system of equations E1: y = -6x + 8 and 3x + y = 4, replacing equation one in two 3x -6x +8 = 4, solving x = 4/3 and replacing x in equation one y = 0. This system of equations have just one solution -> (4/3, 0)
Consider the system of equations E2: y = -3x + 9 and y = -3x -7, replacing equation one in two -3x + 9 = -3x -7, solving 9 = -3. This system of equations have no solution because the result is a fallacy.
Consider the system of equations E3: 2 = -6x + 4y and -1 = -3x -2y, taking equation one and solving y = 1/2 + 3/2x, replacing equation one in two -1 = -3x -1 +3x, solving -1 = -1. This system of equations have infinitely many solution because we find a true equation when solving .
A quantum object whose state is given by is sent through a Stern-Gerlach device with the magnetic field oriented in the y-direction. What is the probability that this object will emerge from the + side of this device?
Answers
Answer:
The probability that the object will emerge from the + side of this device is 1/2
Step-by-step explanation:
Orienting the magnetic field in a Stern-Gerlach device in some direction(y - direction) perpendicular to the direction of motion of the atoms in the beam, the atoms will emerge in two possible beams, corresponding to ±(1/2)h. The positive sign is usually referred to as spin up in the direction, the negative sign as spin down in the explanation, the separation has always been in the y direction. There can be some other cases where magnetic field may be orientated in x-direction or z-direction.
If a customer at a particular grocery store uses coupons, there is a 50% probability that the customer will pay with a debit card. Thirty percent of customers use coupons and 35% of customers pay with debit cards. Given that a customer does not pay with a debit card, the probability that the same customer does not use coupons is ________. A) 0.52 B) 0.60 C) 0.77 D) 0.85
Answers
Answer:
A. 0.52
Step-by-step explanation:
Let D be the event that person used Debit card and C b the event that person used coupon.
We have to find the probability of customer does not use coupons given that a customer does not pay with a debit card,
P(C'/D')=P(C')P(D'/C')/[P(C')P(D'/C')+P(D')P(D'/C')]
We are given that P(D)=0.35, P(C)=0.30 and P(D/C)=0.5.
P(D')=1-0.35=0.65
P(C')=1-0.3=0.7
P(D'/C')=0.5.
P(C'/D')=0.7(0.5)/[0.7(0.5)+0.65(0.5)]
P(C'/D')=0.35/[0.35+0.325]
P(C'/D')=0.35/[0.35+0.325]
P(C'/D')=0.35/0.675
P(C'/D')=0.5185=0.52
Thus, the probability of customer does not use coupons given that a customer does not pay with a debit card is 0.52.
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order DE y'' − y = 0. Find c1 and c2 given the following initial conditions. (Your answers will not contain a variable.) y(1) = 0, y'(1) = e c1 = Incorrect: Your answer is incorrect. c2 = Incorrect: Your answer is incorrect. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. y = Incorrect: Your answer is incorrect.
Answers
Answer:
c₁ = 1/2
c₂ = - e²/2
y = (1/2)*(eˣ - e²⁻ˣ)
Step-by-step explanation:
Given
y = c₁eˣ + c₂e⁻ˣ
y(1) = 0
y'(1) = e
We get y' :
y' = (c₁eˣ + c₂e⁻ˣ)' ⇒ y' = c₁eˣ - c₂e⁻ˣ
then we find y(1) :
y(1) = c₁e¹ + c₂e⁻¹ = 0
⇒ c₁ = - c₂/e² (I)
then we obtain y'(1):
y'(1) = c₁e¹ - c₂e⁻¹ = e (II)
⇒ (- c₂/e²)*e - c₂e⁻¹ = e
⇒ - c₂e⁻¹ - c₂e⁻¹ = - 2c₂e⁻¹ = e
⇒ c₂ = - e²/2
and
c₁ = - c₂/e² = - (- e²/2) / e²
⇒ c₁ = 1/2
Finally, the equation will be
y = (1/2)*eˣ - (e²/2)*e⁻ˣ = (1/2)*(eˣ - e²⁻ˣ)
Applying the initial conditions, it is found that the solution is:
[tex]y = \frac{1}{2}e^{x} - \frac{e^2}{2}e^{-x}[/tex]
------------------------
The solution for the PVI is given by:
[tex]y = c_1e^{x} + c_2e^{-x}[/tex]
------------------------
The condition [tex]y(1) = 0[/tex] means that when [tex]x = 0, y = 1[/tex], and thus, we get:
[tex]c_1e + c_2e^{-1} = 0[/tex]
[tex]c_1e+ \frac{c_2}{e} = 0[/tex]
[tex]c_1e^{2} + c_2 = 0[/tex]
[tex]c_2 = -c_1e^{2}[/tex]
------------------------
The derivative is:
[tex]y^{\prime}(x) = c_1e^{x} - c_2e^{-x}[/tex]
Applying the condition [tex]y^{\prime}(1) = e[/tex], we get:
[tex]c_1e - \frac{c_2}{e} = e[/tex]
Considering [tex]c_2 = -c_1e^{2}[/tex]:
[tex]c_1e + c_1\frac{e^2}{e} = e[/tex]
[tex]c_1e + c_1e = e[/tex]
[tex]2c_1e = e[/tex]
[tex]2c_1 = 1[/tex]
[tex]c_1 = \frac{1}{2}[/tex]
------------------------
The second constant is:
[tex]c_2 = -c_1e^{2} = -\frac{e^2}{2}[/tex]
And the solution is:
[tex]y = \frac{1}{2}e^{x} - \frac{e^2}{2}e^{-x}[/tex]
A similar problem is given at https://brainly.com/question/13244107
Kristina walks 7 1/2 miles in 5 hours. At this rate, how many miles can Kristina walk in 9 hours
Answers
Answer:
13.5
Step-by-step explanation:
7 1/2=7.5
7.5/5*9=13.5
Ruby has $0.86 worth of pennies and nickels. She has 4 more nickels than pennies. Determine the number of pennies and the number of nickels that Ruby has.
Answers
Answer:
15 Nickels, 11 Pennies
Step-by-step explanation:
Simplify your life and take out the decimals
5*N + P = 86
P + 4 = N (4 more nickels than pennies)
By substitution of the second eq into the first: 5*(P+4) + P = 86
5*P + 20 + P = 86
6P = 66
P = 11, so N = 4 + 11 = 15
Answer:Ruby has 11 pennies and 15 nickels.
Step-by-step explanation:
The worth of a penny is 1 cent. Converting to dollars, it becomes
1/100 = $0.01
The worth of a nickel is 5 cents. Converting to dollars, it becomes
5/100 = $0.05
Let x represent the number of pemnies that Ruby has.
Let y represent the number of nickels that Ruby has.
She has 4 more nickels than pennies. This means that
y = x + 4
Ruby has $0.86 worth of pennies and nickels. This means that
0.01x + 0.05y = 0.86 - - - - - - - - - - - 1
Substituting y = x + 4 into equation 1, it becomes
0.01x + 0.05(x + 4) = 0.86
0.01x + 0.05x + 0.2 = 0.86
0.06x = 0.86 - 0.2 = 0.66
x = 0.66/0.06
x = 11
y = x + 4 = 11 + 4
y = 15
ests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis. Represent the "76.53%" using notation. Group of answer choices P(S) P(Sc) P(POSc | Sc) P( POSc | C)
Answers
The 76.53% percentage, which represents the rate at which the QFT-G test correctly identifies those without tuberculosis, can be represented using notation as P(POSc | Sc). This is a conditional probability noting the likelihood of a negative test result when the individual does not have tuberculosis.
Explanation:In the context of probabilities and statistics, you've asked about the interpretation of the 76.53% correctly identified as non-tuberculosis afflicted individuals in terms of notation. Based on the notation you provided and the description of the problem, the 76.53% would be represented as P(POSc | Sc).
This can literally be translated as the probability that the QFT-G test will result as negative (i.e., no tuberculosis, or POSc), given that the person is indeed not afflicted with tuberculosis (i.e., Sc). This is a conditional probability, expressing how likely we are to get a negative test result, given that the person doesn't really have tuberculosis.
Learn more about Conditional Probability here:https://brainly.com/question/32171649
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A punch recipe requires 2/5 of a cup of pineapple juice for every 2 1/2 cups of soda. What is the unit rate of soda to pineapple juice in the punch?
Answers
Answer:
The unit rate is 6 1/4 cups of soda per cup of pineapple juice
Step-by-step explanation:
we know that
To find out the unit rate of soda to pineapple juice in the punch, divide the cups of soda by the cups of pineapple juice
so
[tex]2\frac{1}{2} :\frac{2}{5}[/tex]
Convert mixed number to an improper fraction
[tex]2\frac{1}{2}=2+\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}[/tex]
substitute
[tex]\frac{5}{2} :\frac{2}{5}[/tex]
Multiply in cross
[tex]\frac{25}{4}= 6.25[/tex]
Convert to mixed number
[tex]6.25=6+0.25=6+\frac{1}{4}= 6\frac{1}{4}[/tex]
That means
The unit rate is 6 1/4 cups of soda per cup of pineapple juice
Answer:
6 1/4
Step-by-step explanation:
Binomial Distribution. Research shows that in the U.S. federal courts, about 90% of defendants are found guilty in criminal trials. Suppose we take a random sample of 25 trials. (For this problem it is best to use the Binomial Tables).Based on a proportion of .90, what is the variance of this distribution?
Answers
Answer:
The variance of this distribution is 0.0036.
Step-by-step explanation:
The variance of n binomial distribution trials with p proportion is given by the following formula:
[tex]Var(X) = \frac{p(1-p)}{n}[/tex]
In this problem, we have that:
About 90% of defendants are found guilty in criminal trials. This means that [tex]p = 0.9[/tex]
Suppose we take a random sample of 25 trials. This means that [tex]n = 25[/tex]
Based on a proportion of .90, what is the variance of this distribution?
[tex]Var(X) = \frac{p(1-p)}{n}[/tex]
[tex]Var(X) = \frac{0.9*0.1}{25} = 0.0036[/tex]
The variance of this distribution is 0.0036.
the average age of men who had walked on the moon was 39 years, 11months, 15days. Is the value aparameter or a statistic?
Answers
Answer:
Parameter
Step-by-step explanation:
We are given the following in the question:
The average age of men who had walked on the moon was 39 years, 11 months, 15 days.
Population and sample:
Population is the collection of all observation for variable of interest or individual of interest.Sample is a subset for population.Parameter and statistic:
Any variable or value describing a population is known as parameter.Any value describing a sample is known as statistic.Population of interest:
men who had walked on the moon
Value:
average age of men who had walked on the moon
Thus, the give value describes a population and hence, it is a parameter.
The volume of the cone when x = 3 is 18. Which equation can be used to represent the volume of the cone, V(x)?
Answers
Answer: the last option is the correct answer.
Step-by-step explanation:
When x = 3, height = 2 × 3 = 6
When x = 3, base = π × 3² = 9π
Volume = 1/3 × 6 × 9π = 18π
Therefore,
The formula for determining the volume of the cone is
Volume = 1/3 × height × area of base
Height is f(x) = 2x
Area of base is g(x) = πx²
Therefore, the equation that can be used to the volume of the cone, V(x) would be
1/3(f.g)(x)
Final answer:
The student needs to find an equation V(x) representing the volume of a cone. Using the volume formula V(x) = kx² and the given volume of 18 when x is 3, the constant k can be calculated. Thus, the equation for the volume is V(x) = 2x².
Explanation:
The student is asking for an equation that represents the volume of a cone, V(x), based on a given volume when x equals 3. The general formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. Since the volume is given as a quadratic function of x, and we know that when x equals 3 the volume is 18, a possible representation for the volume as a function of x could be V(x) = kx², where k is a constant that we would solve for using the given volume at x = 3.
To find the constant k, we substitute x with 3 and V(x) with 18 in the equation V(x) = kx² and solve for k. Therefore, the equation becomes 18 = k(3²), which simplifies to 18 = 9k. Solving for k gives us k = 2, so the equation for the volume of the cone as a function of x is V(x) = 2x².
In a West Texas school district the school year began on August 1 and lasted until May 31. On August 1 a Soft Drink company installed soda machines in the school cafeteria. It found that after t months the machines generated income at a rate of f(t) = 300t/2t2 + 8 dollars per month. Find the total income, $Tscc, produced during the second semester beginning on January 1.
Answers
Answer:
$95.78
Step-by-step explanation:
f(t) = 300t / (2t² + 8)
t = 0 corresponds to the beginning of August. t = 1 corresponds to the end of August. t = 2 corresponds to the end of September. So on and so forth. So the second semester is from t = 5 to t = 10.
$T₂ = ∫₅¹⁰ 300t / (2t² + 8) dt
$T₂ = ∫₅¹⁰ 150t / (t² + 4) dt
$T₂ = 75 ∫₅¹⁰ 2t / (t² + 4) dt
$T₂ = 75 ln(t² + 4) |₅¹⁰
$T₂ = 75 ln(104) − 75 ln(29)
$T₂ ≈ 95.78
2.82 For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that the wife will vote on the referendum is 0.28, and the probability that both the husband and the wife will vote is 0.15. What is the probability that (a) at least one member of a married couple will vote? (b) a wife will vote, given that her husband will vote? (c) a husband will vote, given that his wife will not vote?
Answers
The probability that at least one member of a married couple will vote is 0.34 or 34%. The probability of a wife voting given that her husband will vote is approximately 0.7143 or 71.43%. The probability of a husband voting given his wife will not vote is 0.06 or 6%.
Explanation:The subject of this question is probability within the realm of mathematics. To find the probability of at least one member of a married couple voting, we can use the formula P(A or B) = P(A) + P(B) - P(A and B).
Therefore, the probability is 0.21 (husband voting) + 0.28 (wife voting) - 0.15 (both voting), which equals 0.34.
For (b), the probability that the wife will vote, given that her husband will vote, is P(Wife|Husband) = P(Wife and Husband)/P(Husband).
So, this probability is 0.15/0.21, which equals approximately 0.7143.
For (c), the probability that the husband will vote, given that his wife will not vote, is P(Husband|Wife not voting) = P(Husband) - P(Husband and Wife).
So, this probability is 0.21 - 0.15, which yields 0.06 or 6%.
A person takes a trip, driving with a constant peed of 89.5 km/h, except for a 22.0-min rest stop. If the peron's average speed is 77.8 km/h, (a) how much time is spent on the trip and (b) how far does the person travel?
Answers
Answer:
a) The person traveled 2.83 hours.
b) The person travels 220.17 kilometers.
Step-by-step explanation:
We have that the speed is the distance divided by the time. Mathematically, that is
[tex]s = \frac{d}{t}[/tex]
(a) how much time is spent on the trip and
The peron's average speed is 77.8 km/h, which means that [tex]s = 77.8[/tex]
The person distance traveled is:
22 min is 22/60 = 0.37h.
So for the time t1, the person traveled at a speed of 89.5 km/h. Which has a distance of 89.5*t1.
For 0.37h, the person was at a stop, so she did not travel. This means that the total distance is
[tex]d = 89.5t1 + 0 = 89.5t1[/tex]
The total time is the time traveling t and the stoppage time 0.37. So
[tex]t = t1 + 0.37[/tex]
We want to find t1, which is the time that the person was driving.
So
[tex]s = \frac{d}{t}[/tex]
[tex]77.8 = \frac{89.5t1}{t1 + 0.37}[/tex]
[tex]77.8t1 + 77.8*0.37 = 89.5t1[/tex]
[tex]11.7t1 = 28.786[/tex]
[tex]t1 = \frac{28.786}{11.7}[/tex]
[tex]t1 = 2.46[/tex]
The total time is
[tex]t = t1 + 0.37 = 2.46 + 0.37 = 2.83[/tex]
The person traveled for 2.83 hours.
(b) how far does the person travel?
The person traveled 2.46 hours at an average speed of 77.8 km/h. So
[tex]s = \frac{d}{t}[/tex]
[tex]77.8 = \frac{d}{2.83}[/tex]
[tex]d = 77.8*2.83 = 220.17[/tex]
The person travels 220.17 kilometers.
Use the roster method to write each of the given sets. (Enter EMPTY for the empty set.)
(a) The set of natural numbers x that satisfy x + 4 = 1.
(b) Use set-builder notation to write the following set.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Answers
Answer:
a) Empty set
b) [tex]\{x : x \in N \text{ and } x < 13\}[/tex]
Step-by-step explanation:
Roster form is a comma separated list form of set.
a) The set of natural numbers x that satisfy x + 4 = 1.
[tex]x + 4 = 1\\x = -3 \notin N[/tex]
Thus, x is an empty set.
b) set-builder notation for the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
We use x to represent this set. Now x belongs to natural number and is less than equal to 12.
Thus, it can be written as:
[tex]\{x : x \in N \text{ and } x < 13\}[/tex]
A factory makes rectangular sheets of cardboard, each with an area 2 1/2 square feet. Each sheet of cardboard can be cut into smaller pieces of cardboard measuring 1 1/6 square feet. How many smaller pieces of cardboard does each sheet of cardboard provide?
Answers
Answer: each sheet of cardboard provides 2 pieces of smaller pieces of cardboard
Step-by-step explanation:
The area of each rectangular sheet of cardboard that the factory makes is 2 1/2 square feet. Converting
2 1/2 square feet to improper fraction, it becomes 5/2 square feet.
Each sheet of cardboard can be cut into smaller pieces of cardboard measuring 1 1/6 square feet. Converting
1 1/6 square feet to improper fraction, it becomes 7/6 square feet.
Therefore, the number of smaller pieces of cardboard that each sheet of cardboard provides is
5/2 ÷ 7/6 = 5/2 × 6/7 = 15/7
= 2 1/7 pieces
answer is 15 smaller pieces Step-by-step explanation:
what is the solution to the equation A/2= -5
Answers
Answer:
A = -10
Step-by-step explanation:
A/2 = -5
Multiply both sides by the denominator of the fraction
We have A/2 x2 = -5 x 2
A = -10
Answer:
-10
Step-by-step explanation:
It is the easiest equation.
A/2= -5
At first, we have to multiply both the sides by 2. Therefore, we can get,
[tex]\frac{A*2}{2}[/tex] = (-5 × 2)
or, A = -10
Therefore, the value of A is -10. It remains negative because we cannot multiply both the sides by -1. If we do that, we cannot determine the constant.
Answer: A = -10
A set S of strings of characters is defined recursively by 1. a and b belong to S. 2. If x belongs to S, so does xb. Which of the following strings belong to S? a. a b. ab c. aba d. aaab e. bbbbb
Answers
Answer:
a) a
b) ab
e) bbbbb
Step-by-step explanation:
We are given the following in the question:
[tex]a, b \in S[/tex]
[tex]x \in S \Rightarrow xb \in S[/tex]
a) a
It is given that [tex]a \in S[/tex]
b) ab
[tex]\text{If }a \in S\\\Rightarrow ab \in S[/tex]
Thus, ab belongs to S.
c) aba
This does not belong to S because we cannot find x for which xb belongs to S.
d) aaab
This does not belong to S because we cannot find x for which xb belongs to S.
e) bbbbb
[tex]\text{If }b \in S\Rightarrow bb \in S\\\text{If }bb \in S\Rightarrow bbb \in S\\\text{If }bbb \in S\Rightarrow bbbb \in S\\\text{If }bbbb \in S\Rightarrow bbbbb \in S[/tex]
Thus, bbbbb belongs to S.
An education researcher collects data on how many hours students study at various local colleges. The researcher calculates an average to summarize the data. The researcher is using ______.A)measure of central tendency
B) descriptive statistical method
C) intuitive statistical method
D) inferential statistical method
Answers
Answer:
Correct option is (B) descriptive statistical method
Step-by-step explanation:
Descriptive statistics branch in statistics deals with the representation of the data using distinct brief coefficients. These coefficients are used as either the representative of the sample or the population.
The descriptive statistics branch is divided into two sub branches:
Measure of central tendencyMeasure of dispersion.The three measures of central tendency are:
Mean (or Average)MedianMode.The measures of dispersion are:
VarianceStandard deviationRangeKurtosisSkewnessThe education researcher computes the average number of hours student study at various local colleges.
The average of a data is the mean value which is the measure of central tendency.
Thus, the researcher is using descriptive statistical method to summarize the data.
Final answer:
The education researcher is using descriptive statistical methods by calculating an average of study hours, which is a measure of central tendency, a fundamental aspect of descriptive statistics.
Explanation:
An education researcher who collects data on how many hours students study at various local colleges and then calculates an average to summarize this data is using descriptive statistical methods. Descriptive statistics involve organizing and summarizing data to provide a clear overview of its characteristics. Examples of descriptive statistics include measures of central tendency (mean, median, mode), which indicate the typical value within a data set, and measures of variability (range, variance, standard deviation), which show how spread out the data points are. The calculation of an average, or mean, falls under the measure of central tendency, making it a key component of descriptive statistics.
On a map of Texas, the
distance between Houston
and Austin is 2 3/4 inches. The
scale on the map is
1 inch = 50 miles. What is
the actual distance between
Houston and Austin? will mark brainest can u show ur work if not the answer is ok ty please help me been on this a hour
Answers
1 inch on the map = 50 miles on the Earth.
A certain trip on the map is 2-3/4 inches.
-- first inch = 50 miles
-- second inch = another 50 miles
-- 3/4 inch = 3/4 of 50 miles (37.5 miles)
Total:
Here's an equation;
1 map-inch = 50 real-miles
Multiply each side by 2-3/4 :
2-3/4 inches = (2-3/4) x (50 miles)
2-3/4 map-inches = 137.5 real-miles
The actual distance between Houston and Austin is 137.5 miles.
We are given that;
The distance between Houston and Austin = 2 3/4 inches
Now,
To find the actual distance between Houston and Austin, we need to multiply the map distance by the scale factor.
The map distance is 2 3/4 inches, which is equivalent to 11/4 inches. The scale factor is 1 inch = 50 miles, which means that every inch on the map corresponds to 50 miles in reality. So, we have:
11/4 x 50 = (11 x 50) / 4
= 550 / 4
= 137.5
Therefore, by unit conversion answer will be 137.5 miles.
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The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwisestate that there is no solution. Use x1, x2, x3 as variables.
Answers
Answer:
The augmented matrix has been given in the attachment
Step-by-step explanation:
The steps for the determination of INCONSISTENCY are as shown in the attachment.
In clinIcal study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1.
a) what is the probability four or more people will have to be tested before two with the gene are detected?b) How many people are expected to be tested before two with gene are detected?
Answers
Answer:
(a) P (X ≥ 4) = 0.972
(b) E (X) = 20
Step-by-step explanation:
Let X = number of people tested to detect the presence of gene in 2.
Then the random variable X follows a Negative binomial distribution with parameters r (number of success) and p probability of success.
The probability distribution function of X is:
[tex]f(x)={x-1\choose r-1}p^{r}(1-p)^{x-r}[/tex]
Given: r = 2 and p = 0.1
(a)
Compute the probability that four or more people will have to be tested before two with the gene are detected as follows:
P (X ≥ 4) = 1 - P (X = 3) - P (X = 2)
[tex]=1-[{3-1\choose 2-1}(0.1)^{2}(1-0.1)^{3-2}]-[{2-1\choose 2-1}(0.1)^{2}(1-0.1)^{2-2}]\\=1-0.018-0.01\\=0.972[/tex]
Thus, the probability that four or more people will have to be tested before two with the gene are detected is 0.972.
(b)
The expected value of a negative binomial random variable X is:
[tex]E(X)=\frac{r}{p}[/tex]
The expected number of people to be tested before two with gene are detected is:
[tex]E(X)=\frac{r}{p}=\frac{2}{0.1}=20[/tex]
Thus, the expected number of people to be tested before two with gene are detected is 20.
How much
fencing does
the farmer
need to
enclose the
area below?
30 2/9 50 5/8 will mark brainest new to this can any one help
Answers
The farmer will need:
[tex]\boxed{191\frac{11}{12}yd}[/tex]
In order to enclose the area shown in the figure below.
Explanation:The diagram below shows the representation of this problem. Let:
[tex]x: The \ length \ of \ the \ rectangular \ pastures \\ \\ y: The \ width \ of \ the \ rectangular \ pastures[/tex]
We know that:
[tex]x=5\frac{5}{8}yd \\ \\ y=30\frac{2}{9}yd[/tex]
So the fencing the farmer needs can be calculated as the perimeter of the two adjacent rectangular pastures:
[tex]P=2(x+y)+y \\ \\ P=2(50\frac{5}{8}+30\frac{2}{9})+30\frac{2}{9} \\ \\ P=100\frac{10}{8}+60\frac{4}{9}+30\frac{2}{9} \\ \\ P=100\frac{10}{8}+90\frac{6}{9} \\ \\ P=100\frac{5}{4}+90\frac{2}{3} \\ \\ P=190(\frac{15+8}{12}) \\ \\ P=190(\frac{23}{12}) \\ \\ \\ Expressing \ as \ a \ mixed \ fraction: \\ \\ P=190+1+\frac{11}{12} \\ \\ P=191+\frac{11}{12} \\ \\ \boxed{P=191\frac{11}{12}yd}[/tex]
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If the atomic radius of a metal that has the face-centered cubic crystal structure is 0.137 nm, calculate the volume of its unit cell.
Answers
Answer:
[tex]5.796\times 10^{-29}m^3[/tex]
Step-by-step explanation:
Atomic radius of metal=0.137nm=[tex]0.137\times 10^{-9}[/tex]m
[tex]1nm=10^{-9}m[/tex]
Structure is FCC
We know that
The relation between edge length and radius in FCC structure
[tex]a=2\sqrt 2r[/tex]
Where a=Edge length=Side
r=Radius
Using the relation
[tex]a=2\sqrt 2\times 0.137\times 10^{-9}=0.387\times 10^{-9}m[/tex]
We know that
Volume of cube=[tex](side)^3[/tex]
Using the formula
Volume of unit cell=[tex](0.387\times 10^{-9})^3=5.796\times 10^{-29} m^3[/tex]
The volume of a unit cell is approximately 0.0580 nm³.
To find the volume of the unit cell for a metal with a face-centered cubic (FCC) crystal structure given an atomic radius of 0.137 nm, follow these steps:
Atomic Radius Interpretation: In a face-centered cubic unit cell, the atomic radius (r) is related to the edge length (a) of the unit cell by the equation:a = 2√2 rCalculating the Edge Length: Plug in the given atomic radius (r = 0.137 nm) into the equation:
a = 2√2 x 0.137 nm = 2 x 1.414 x 0.137 nm = 0.387 nmCalculating the Volume of the Unit Cell: The volume (V) of a cube is given by V = a³. Therefore:
V = 0.387 nm x 0.387 nm x 0.387 nm ≈ 0.0580 nm³
Thus, the volume of the unit cell is approximately 0.0580 nm³.
A fast food restaurant processes on average 5000 pounds of hamburger per week. The observed inventory level of raw meat, over a long period of time, averages 2500 pounds. What is the average time spent by a pound of meat in production (in weeks)
Answers
Answer:
0.5 week
Step-by-step explanation:
The time spent by a pound of meat in this system is given by the average number of pounds of meat on inventory (2500 pounds) divided by the average weekly meat consumption (5000 pounds per week).
The time, in weeks, is:
[tex]t=\frac{2500\ pounds}{5000\ pounds/week} \\t= 0.5\ week[/tex]
The average time spent by a pound of meat in production is 0.5 week.
What is the surface area of the figure
240
48
192
Answers
Answer:
[tex]240cm^2[/tex]
Step-by-step explanation:
The area of the rectangular face with dimension 8 by 8 is [tex]8*8=64cm^2[/tex]
The area of the rectangular face with dimension 10 by 8 is [tex]10*8=80cm^2[/tex]
The area of the rectangular face with dimension 6 by 8 is [tex]6*8=48cm^2[/tex]
The area of the two rectangular faces is [tex]2*\frac{1}{2}*8*6=48cm^2[/tex]
The total surface area is [tex]64+80+48+48=240cm^2[/tex]
A. Find n so that the number sentence below is true. 2^-6*2^n=2^9.
N=_____________
B. Use the laws of exponents to demonstrate why 2^3•4^3=2^9 is true and explain.
This is true because
Answers
n = 15
Step-by-step explanation:
Step 1: Calculate n by using the law of exponents that a^m × a^n = a^m+nFor 2^-6*2^n=2^9, a = 2, m = -6 and m + n = 9
⇒ -6 + n = 9
⇒ n = 15
Step 2: Given 2³ × 4³=2^9. Use law of exponents to prove it.⇒ 2³ × 4³ can also be written as 2³ × (2²)³ = 2³ × 2^6 [This is based on the law of exponents (a^m)^n = (a)^m×n]
⇒ 2³ × 2^6 = 2^ (3 + 6) = 2^9 [Using the law of exponents a^m × a^n = a^m+n]
Fred wants to buy a video game that costs $54. There was a markdown of 20%. How much is the discount?
Answers
Mar 10, 2012 - Markups and Markdowns Word Problems - Independent Practice Worksheet. $6640. $3.201 ... 2) Fred buys a video game disk for $4. There was a discount of 20%.What is the sales price? 20% of 1 pay 8090 ... 5) Timmy wants to buy.a scooter and the price was $50. When ... at a simple interest rate of 54%.
= $43.20
You can also calculate how much you save by simply moving the period in 50.00 percent two spaces to the left, and then multiply the result by $54 as follows: $54 x . 50 = $27.00 savings. Furthermore, you can get the final price by simply deducting.
Fifty pro-football rookies were rated on a scale of 1 to 5, based on performance at a training camp as well as on past performance. A ranking of 1 indicated a poor prospect whereas a ranking of 5 indicated an excellent prospect. The following frequency distribution was constructed.
Rating Frequency
1 4
2 10
3 14
4 18
5 4
a-1. How many of the rookies received a rating of 4 or better?
a-2. How many of the rookies received a rating of 2 or worse?
b-1. Construct the corresponding relative frequency distribution. (Round your answers to 2 decimal places.)
b-2. What percent received a rating of 5?
Answers
Answer:
(a-1) 22 rookies receiving a rating of 4 or better.
(a-2) 14 rookies received a rating of 2 or worse.
(b-1) Constructed below in explanation.
(b-2) 8% of total rookies received a rating of 5.
Step-by-step explanation:
We are provided the rating of Fifty pro-football rookies on a scale of 1 to 5 based on performance at a training camp as well as on past performance.
The frequency distribution constructed is given below:
Rating Frequency
1 4
2 10 where ranking of 1 indicate a poor prospect whereas
3 14 ranking of 5 indicate an excellent prospect.
4 18
5 4
(a-1) Rookies receiving a rating of 4 or better = Rating of 4 + Rating of 5
So, by seeing the frequency distribution 18 rookies received a rating of
4 and 4 rookies received a rating of 5.
Hence, Rookies receiving a rating of 4 or better = 18 + 4 = 22 rookies.
(a-2) Number of rookies received a rating of 2 or worse = Rating of 2 +
Rating of 1
So, by seeing the frequency distribution 10 rookies received a rating of
2 and 4 rookies received a rating of 1.
Hence, Rookies receiving a rating of 2 or worse = 10 + 4 = 14 rookies.
(b-1) Relative Frequency is calculated as = Each frequency value /
Total Frequency
Rating Frequency(f) Relative Frequency
1 4 4 / 50 = 0.08
2 10 10 / 50 = 0.2
3 14 14 / 50 = 0.28
4 18 18 / 50 = 0.36
5 4 4 / 50 = 0.08
[tex]\sum f[/tex]= 50
Hence, this is the required relative frequency distribution.
(b-2) To calculate what percent received a rating of 5 is given by equation :
x% of 50 = 4 {Here 4 because 4 rookies received rating of 5}
x = [tex]\frac{4*100}{50}[/tex] = 8% .
Therefore, 8% of total rookies received a rating of 5.
22 rookies received a performance rating of 4 or better, and there are 14 rookies that received a rating of 2 or worse. The relative frequency distribution rounded to 2 decimal places for ratings 1, 2, 3, 4, and 5 is 0.08, 0.2, 0.28, 0.36, and 0.08 respectively. Finally, 8% of rookies received a rating of 5.
Explanation:To answer question a-1, we add the frequencies of the ratings 4 and 5 together. So 18 (the number of rookies who received a 4) plus 4 (the number of rookies who received a 5) equals 22. Therefore, 22 rookies received a rating of 4 or better.
For question a-2, we add the frequencies of the ratings 1 and 2 together. So 4 (the number of rookies who received a 1) plus 10 (the number of rookies who received a 2) equals 14. Thus, 14 rookies received a rating of 2 or worse.
Next, for question b-1, we find the relative frequency distribution by dividing each frequency by the total number of players (50). So, the relative frequency for 1 would be 4/50 ≈ 0.08, for 2 it's 10/50=0.2, for 3 it's 14/50 ≈ 0.28, for 4 it's 18/50 = 0.36, and for 5 it's 4/50 ≈ 0.08. These are all rounded to 2 decimal places.
Finally, for question b-2, to find the percent of players who received a rating of 5, we take the frequency of 5 which is 4, and divide it by the total number of rookies, which is 50, then multiply by 100 to convert it to a percentage (4/50 * 100). The answer is 8%.
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The Nielsen Media Research Company uses people meters to record the viewing habits of about 5000 households, and today those meters will be used to determine the proportion of households tuned to CBS Evening News.
Answers
Answer:
Cross-sectional study.
Step-by-step explanation:
- In a cross-sectional study, data are observed, measured, and collected at one point in time.
- In a prospective (or longitudinal) study, data are collected in the future from
groups sharing common factors.
- In a retrospective (or case-control) study, data are collected from the past by going
back in tirme (through exanmination of records, interviews, arıd so on).
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