suppose that there are two types of tickets to a show: advance and same-day. advance tickets cost and same-day tickets cost . for one performance, there were tickets sold in all, and the total amount paid for them was . how many tickets of each type were sold?

A standard normal distribution table or a calculator that can perform the calculations based on the given z-scores.

To solve these problems, we'll use the properties of the normal distribution. Let's go through each question step by step:

b. What is the distribution of ¯xx¯? ¯xx¯~ N( ? ), (?)

The average of a sample follows a normal distribution with the same mean as the population and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the population mean is 65, and the population standard deviation is 17. Since we have 50 randomly selected tires, the sample size is 50.

Therefore, the distribution of the sample mean ¯xx¯ is ¯xx¯~N(65, 17/√50).

c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 67.4 and 69.6?

To find this probability, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value we're interested in, μ is the population mean, and σ is the population standard deviation.

For 67.4:

z1 = (67.4 - 65) / 17

For 69.6:

z2 = (69.6 - 65) / 17

We can now use these z-scores to find the probabilities associated with the values using a standard normal distribution table or a calculator. The probability will be the difference between the two probabilities:

P(67.4 ≤ x ≤ 69.6) = P(z1 ≤ Z ≤ z2)

d. For the 50 tires tested, find the probability that the average miles (in thousands) before the need for replacement is between 67.4 and 69.6?

Since we're dealing with the average of the sample, we use the distribution ¯xx¯~N(65, 17/√50) as calculated in part b.

Again, we'll use the z-score formula to standardize the values:

z1 = (67.4 - 65) / (17 / √50)

z2 = (69.6 - 65) / (17 / √50)

Using these z-scores, we can find the probability:

P(67.4 ≤ ¯xx¯ ≤ 69.6) = P(z1 ≤ Z ≤ z2)

Please note that to obtain the precise probabilities, we would need to use a standard normal distribution table or a calculator that can perform the calculations based on the given z-scores.

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For consumption smoothers, the marginal propensity to consume out of anticipated changes in income is one. Option 4 is answer.

Consumption smoothers are individuals who smooth out their consumption patterns in the face of anticipated changes in income. In other words, they tend to spend a smaller portion of any additional income than those who do not smooth their consumption. Therefore, the marginal propensity to consume out of anticipated changes in income is one, meaning that for every additional unit of anticipated income, consumption increases by one unit. Option 4 is the correct answer.

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Answer:

Step-by-step explanation:

Side A has a length of 80 ft, side b has a length of 150 ft, and side c (the hypotenuse) has a length of 170 ft. Side A will represent a in the pythagorean theorem, side B will represent b, and side C (hypotenuse) will represent c in the equation. If the equation holds true, then the triangle is a right triangle.

So, we plug it in. a^2 + b^2 = c^2 becomes (80)^2 + (150)^2 = (170)^2

(80)^2 + (150)^2= 28,900

(170)^2= 28,900

since the answers are the same, we know the equation holds true, and thus the triangle is a right triangle. Hope this helps!!

The value of x is 9. Thus, the correct answer choice is (b) 9.

We know that the sum of the angles in a right angle is 90 degrees.

One part of the angle measures 30 degrees, and the other part measures 5x + 15 degrees.

So, we can write the equation:

30 + 5x + 15 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 9

Thus, the correct answer choice is (b) 9.

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Utilization=  0.90909 or 90.909%

Average number of jobs in the system=10

Average number of jobs in queue = 9.091

End to end response time = 500

Queuing time = 454.545

Probability of 5 or more jobs in the system=0.59049

What is probability?

Probability means possibility of any incident. It is a branch of mathematics which deals with the occurrence of any random event. The value can be  expressed from zero to one. Probability has been introduced in Mathematics to give a  prediction of how likely events are to happen. The meaning of probability is nothing but the extent to which something is likely to happen.

In a M/M/1 model the expected  inter-arrival time is 50 msec and the expected service time is 45 msec.

So the mean rate of arrival (λ) = 1/ 50 = 0.02

The mean service rate(μ) = 1/ 45= 0.022

a) Utilization = λ/μ = 0.02/ 0.022= 0.90909 or 90.909%

b) Average number of jobs in the system= λ/ (μ-λ)

                                                                     = 0.02/(0.022-0.02)

                                                                       = 10

c) Average number of jobs in queue = λ² / (μ(μ-λ))

                                                           = 0.0004/ 0.000044

                                                            = 9.091

d) End to end response time = Average number of time in the system/ arrival rate

                                               = 10/ 0.02

                                              = 500

e) Queuing time = λ/( μ(μ-λ))

                           = 0.02/ 0.000044

                           = 454.545

f) Probability of 5 or more jobs in the system= P(n≥5)= (λ/μ)⁵

                                                                                          = (0.9)⁵

                                                                                         = 0.59049

Hence,

Utilization=  0.90909 or 90.909%

Average number of jobs in the system=10

Average number of jobs in queue = 9.091

End to end response time = 500

Queuing time = 454.545

Probability of 5 or more jobs in the system=0.59049

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Correct question is "a computer system is modeled as a m/m/1 queue. the expected inter-arrival time is 50 msec and the expected service time is 45 msec. calculate the following measures of system performance:

The probability that both people own a dog is approximately 0.4096, or 40.96%.

To solve this problem, we can use the formula for calculating the probability of the intersection of two independent events: P(A and B) = P(A) x P(B).

Let's define A as the event that the first person owns a dog, and B as the event that the second person owns a dog. Since the two people are chosen at random, we can assume that these events are independent.

According to the problem, P(A) = P(B) = 0.64, since 64% of people own dogs. Therefore, the probability of both events occurring is:

P(A and B) = P(A) x P(B) = 0.64 x 0.64 = 0.4096

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Each text book cost 5cedis for the amount.

The word "amount" refers to a thing's quantity or sum. It is a blanket phrase that can be used to many different dimensions or amounts. The precise meaning of "amount" depends on the context in which it is used. It can be used to describe a numerical value, such as the volume of liquid in a container, the balance in a bank account, or the duration of an activity. It can also be used to indicate an elusive number, such the degree of someone's enjoyment or worry. In general, the word "amount" communicates the sense of measuring or quantifying a specific thing or quality.

If the boy earned 75cedis and saved 20cedis, then he used 75-20=<<75-20=55>>55cedis to buy text books.

To find the price of each text book, we need to divide the total amount spent on text books by the number of text books bought.

Total amount spent on text books = 55cedis
Number of text books bought = 11
Price of each text book = Total amount spent on text books / Number of text books bought

Price of each text book = 55cedis / 11

Price of each text book = 5cedis

Therefore, each text book cost 5cedis.

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An equation for the plane consisting of all points equidistant from the points (5, 0, −2) and (7, 8, 0) is -2y + 8z = -8x + 32.

To find an equation for the plane consisting of all points equidistant from the points (5, 0, -2) and (7, 8, 0), we can use the fact that the set of points equidistant from two non-coincident points forms the perpendicular bisector of the line segment joining those two points.

First, we can find the midpoint of the line segment joining the two points:

midpoint = ((5 + 7) / 2, (0 + 8) / 2, (-2 + 0) / 2) = (6, 4, -1)

Next, we can find the direction vector of the line segment joining the two points:

direction vector = (7, 8, 0) - (5, 0, -2) = (2, 8, 2)

Now, we can find a vector normal to the plane by taking the cross product of the direction vector and any vector in the plane. Let's use the vector (1, 0, 0):

normal vector = (2, 8, 2) x (1, 0, 0) = (0, -2, 8)

Finally, we can use the point-normal form of the equation for a plane to write the equation of the plane:

0(x - 6) - 2(y - 4) + 8(z + 1) = 0

Simplifying:

-2y + 8z = -8x + 32

Therefore, an equation for the plane consisting of all points equidistant from the points (5, 0, −2) and (7, 8, 0) is -2y + 8z = -8x + 32.

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a) The (9,009, 10,585) range represents the 99% confidence interval for the mean number of steps taken on an average workday for all New York City employees who wear activity trackers. No, we are unable to determine the likelihood of specific values using the confidence interval. Only inferences about the population mean can be drawn from it.

A 99% confidence interval for the mean needs to be calculated.

Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.

Sample Mean(M) = 9,797

Sample Standard Deviation(s) = 2,313.

Sample Size(N) = 61

When σ is unknown, an estimation of σM is made by dividing s by the square root of N:

S = s/√n

S = 2313/√61

S = 2313/7.8102

S = 296.1512

These sample size's degrees of freedom are:

df = n - 1

df = 61 - 1

df = 60

With 61 degrees of freedom and a 99% confidence interval, the t-value is 2.66.

The Margin of Error calculated as:

MOE = t × S

MOE = 2.66 × 296.1512

MOE = 787.7622

The confidence interval's lower and upper bounds are as follows:

Lower Bound = M - MOE

Lower Bound = 9797 - 787.7622

Lower Bound = 9,009.2378

Lower Bound = 9,009(approx)

Upper Bound = M + MOE

Upper Bound = 9797 + 787.7622

Upper Bound = 10,584.7622

Upper Bound = 10,585(approx)

We have a 95% confidence interval between 9,009 and 10,585 steps as the mean number of steps taken on a normal workday for all New York City employees using activity trackers.

b) The value of 8,500 steps is outside the confidence interval, which indicates that it is a high figure for the average number of steps taken by all New Yorkers using activity trackers.

The confidence interval cannot be used to calculate the likelihood of specific values.

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The complete question is:

Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.

a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.

b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.

To find the values of k for which the matrix a is singular, we need to determine when the determinant of a is equal to 0.

The determinant of a 2x2 matrix is simply the product of the diagonal elements minus the product of the off-diagonal elements. For a 3x3 matrix like a, we need to use a more complex formula:

det(a) = 1*(2*2 - k*1) - 2*(1*2 - k*1) + k*(1*2 - 2*k)

Simplifying this expression, we get:

det(a) = 4 - 2k - 4 + 2k + 2k²
det(a) = 2k²

So, det(a) is equal to 0 when k is equal to 0 or when k is equal to 0. Therefore, the matrix a is singular when k is equal to 0.

Explanation: To determine when a matrix is singular, we need to find when its determinant is equal to 0. We used the formula for the determinant of a 3x3 matrix to calculate the determinant of a and then solved for the values of k that make det(a) equal to 0.

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The area of the yellow tile is 0.28 cm² greater than the area of the blue tile.

To compare the areas covered by the blue and yellow tiles, we need to convert the measurements to the same units. Let's convert the measurements for the yellow tile from millimeters to centimeters, since the measurements for the blue tile are in centimeters.

To convert millimeters to centimeters, we divide by 10:

Length of yellow tile: y/10 cm (where y is the length in millimeters)

Width of yellow tile: 6.8 cm (since 68 mm = 6.8 cm)

Now we can calculate the areas of each tile:

Area of blue tile: 8 cm x 6 cm = 48 cm²

Area of yellow tile: (y/10 cm) x 6.8 cm = (0.68y) cm²

To compare the areas, we can set up an inequality:

0.68y > 48

Solving for y:

y > 48/0.68 = 70.59

So the yellow tile must be longer than 70.59 millimeters to cover a greater area than the blue tile.

To find how much greater the area is, we can substitute y = 71 (rounding up from 70.59) into the equation for the area of the yellow tile:

Area of yellow tile = (71/10 cm) x 6.8 cm = 48.28 cm²

The area of the yellow tile is 48.28 cm² - 48 cm² = 0.28 cm² greater than the area of the blue tile.

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Therefore, The double integral in polar coordinates involves integrating the function that defines the height of the solid over the region of the polar plane that defines the base of the solid.

To find the volume V of the solid bounded by the graphs of the equations using a double integral in polar coordinates, we first need to determine the limits of integration. This can be done by finding the intersection points of the curves. Once we have the limits, we can set up the integral as follows:
V = ∬R f(r,θ) rdrdθ
where R is the region in the polar plane bounded by the curves, and f(r,θ) is the height of the solid at each point (r,θ). We then evaluate the integral using the appropriate limits to obtain the volume of the solid.
The double integral in polar coordinates allows us to calculate the volume of a three-dimensional solid bounded by two or more surfaces defined in polar coordinates. It involves integrating the function that defines the height of the solid over the region of the polar plane that defines the base of the solid. The limits of integration are determined by finding the intersection points of the curves that bound the region. Once the limits are established, the integral is evaluated to find the volume of the solid.

Therefore, The double integral in polar coordinates involves integrating the function that defines the height of the solid over the region of the polar plane that defines the base of the solid.

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In each case, we evaluated the function by substituting the given values of x and y into the formula for f(x,y).

At (-1,-3):

f(x,y) = x + yx^5

f(-1,-3) = (-1) + (-3)(-1)^5 = -2

At (-2,4):

f(x,y) = x + yx^5

f(-2,4) = (-2) + (4)(-2)^5 = -126

At (2,-2):

f(x,y) = x + yx^5

f(2,-2) = (2) + (-2)(2)^5 = -30

For example, when evaluating f(-1,-3), we substituted x = -1 and y = -3 into the formula to get f(-1,-3) = (-1) + (-3)(-1)^5 = -2. Similarly, for f(-2,4), we substituted x = -2 and y = 4 into the formula to get f(-2,4) = (-2) + (4)(-2)^5 = -126. Finally, for f(2,-2), we substituted x = 2 and y = -2 into the formula to get f(2,-2) = (2) + (-2)(2)^5 = -30.

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The probability that the car is behind door C given that the host opened door B and revealed that there is no car behind it is 2/3.

In this classic scenario known as the Monty Hall problem, you initially had a 1 in 3 chance of choosing the door with the car behind it. Let's call this event A. The probability of event A is P(A) = 1/3.

After you chose door C, the host opened door B and revealed that it did not have the car behind it. Let's call this event B. The probability of event B, given that the car is not behind door C, is P(B|not C) = 1.

We are interested in the probability of the car being behind door C, given that door B was opened and revealed to not have the car behind it. Let's call this event C. We want to calculate P(C|B).

To solve the problem, we can use Bayes' theorem, which states that:

P(C|B) = P(B|C) * P(C) / P(B)

where P(B|C) is the probability of observing event B given that the car is behind door C, P(C) is the prior probability of the car being behind door C before any information is revealed, and P(B) is the probability of observing event B (i.e., the host opening door B) regardless of which door the car is behind.

Using the Law of Total Probability, we can calculate P(B) as:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|A) is the probability of observing event B given that the car is behind door A, P(not A) is the probability that the car is not behind door A, and P(B|not A) is the probability of observing event B given that the car is not behind door A.

Since we know that the host opened door B and revealed that there is no car behind it, we can simplify the expression for P(B) to:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A|B)

where P(not A|B) is the probability that the car is not behind door A given that the host opened door B and revealed that there is no car behind it. We can calculate P(not A|B) using Bayes' theorem:

P(not A|B) = P(B|not A) * P(not A) / P(B)

Now we can substitute these values into the expression for P(C|B):

P(C|B) = P(B|C) * P(C) / P(B)

where P(B|C) is the probability of observing event B given that the car is behind door C. In this case, the host cannot open door C to reveal the car, so P(B|C) = 1.

P(C) is the prior probability of the car being behind door C before any information is revealed. Initially, this probability was 1/3, since there were three doors and only one car. So P(C) = 1/3.

We have already calculated P(B), which is the probability of observing event B regardless of which door the car is behind. We found that:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A|B)

where P(A) is the probability that the car is behind door A, which is also 1/3, and P(not A|B) is the probability that the car is not behind door A given that the host opened door B and revealed that there is no car behind it.

Using Bayes' theorem, we found that:

P(not A|B) = P(B|not A) * P(not A) / P(B)

We can calculate P(B|not A) as follows:

P(B|not A) = P(B and not A) / P(not A)

Since the host will always open a door with no car behind it, we know that P(B and not A) = 1/2, since there are two remaining doors after you choose door C. Therefore:

P(B|not A) = (1/2) / (2/3) = 1/3

Substituting these values into the expression for P(not A|B), we get:

P(not A|B) = (1/3) * (2/3) / P(B)

Substituting P(B|C) = 1, P(C) = 1/3, and the above expression for P(not A|B) into the expression for P(C|B), we get:

P(C|B) = (1 * 1/3) / ((1/3)(1) + (1/3)(1/3)*(2/3)) = 2/3

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The 74th apple will be placed in second basket of apples.

Apples are distributed, one at a time, into six baskets. the first apple goes into basket one, the second into basket two, the third into basket three, and so on, until each basket has one apple.  

This pattern is repeated, beginning each time with basket one

Since there are 6 baskets, the pattern of distribution repeats every 6 apples.

Hence, to determine which basket the 74th apple will be placed in, we need to find the remainder when 74 is divided by 6:

=> 74 ÷ 6 = 12 remainder 2

This means that the 74th apple will be placed in the second basket, since it follows the pattern of distributing apples starting with the first basket.

Therefore,

The 74th apple will be placed in second basket of apples.

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Answer:

An area is calculated by multiplying the length of a shape by its width

is this the answer your looking for?

Step-by-step explanation:

To determine the number of passes required to sort the elements using insertion sort, we need to first understand how insertion sort works. It involves comparing each element with the previous elements in the list and inserting it into the correct position.

So for this particular list of elements: 14, 12, 16, 6, 3, 10, we can see that the first pass would involve comparing the second element (12) with the first element (14) and swapping them to get: 12, 14, 16, 6, 3, 10.

The second pass would involve comparing the third element (16) with the second element (14) and leaving it in place, then comparing it with the first element (12) and swapping them to get: 12, 14, 16, 6, 3, 10.

Similarly, the third pass would involve comparing the fourth element (6) with the previous elements and inserting it into the correct position, resulting in: 6, 12, 14, 16, 3, 10.

The fourth pass would involve comparing the fifth element (3) with the previous elements and inserting it into the correct position, resulting in: 3, 6, 12, 14, 16, 10.

Finally, the fifth pass would involve comparing the sixth element (10) with the previous elements and inserting it into the correct position, resulting in the fully sorted list: 3, 6, 10, 12, 14, 16.

Therefore, the answer to this question would be 5, which is one of the answer choices given.

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The length of the curve is approximately 0.873 units.

To find the length of the curve, we use the formula:

L = ∫a^b ||r'(t)|| dt

where r'(t) is the derivative of r(t), and ||r'(t)|| is the magnitude of r'(t).

First, let's find the derivative of r(t):

r'(t) = -5sin(5t) i + 5cos(5t) j - (5sin(t)/cos(t)) k

= -5sin(5t) i + 5cos(5t) j - 5tan(t) k

Next, let's find the magnitude of r'(t):

||r'(t)|| = sqrt[(-5sin(5t))^2 + (5cos(5t))^2 + (-5tan(t))^2]

= sqrt[25 + 25tan^2(t)]

Now, we can find the length of the curve:

L = ∫0^(π/4) sqrt[25 + 25tan^2(t)] dt

To solve this integral, we make the substitution u = tan(t), du/dt = sec^2(t), dt = du/sec^2(t), and rewrite the integral as:

L = ∫0^1 sqrt[25 + 25u^2] du/[(1 + u^2)^(1/2)]

Next, we make the substitution v = u/5, dv = du/5, and rewrite the integral as:

L = 5 ∫0^0.2 sqrt[1 + v^2] dv

Using the formula for the integral of the square root of a quadratic, we get:

L = 5/2 [(1/2)(1 + (0.2)^2)^(3/2) - (1/2)(1 + 0^(2))^(3/2)]

= 5/2 [(1.04)^(3/2) - 1]

≈ 0.873

Therefore, the length of the curve is approximately 0.873 units.

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Taryn saved $13.50 by shopping on tax-free weekend, since she did not have to pay any sales tax on her $180 purchase.

to calculate how much taryn saved by shopping on tax-free weekend, we first need to calculate how much she would have paid in sales tax if she had bought her school supplies on a regular day.

if the sales tax is normally 7.5%, then the amount of sales tax taryn would have paid is:

0.075 x $180 = $13.50 the answer is (b) $13.50.

Taryn bought all her school supplies on tax-free weekend and spent $180. If sales tax is normally 7. 5%,

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The value of the car in the year 2017 will be $4973.

Given that a car's value is decreasing, it had a value of $38,000 in the year 2007.

By 2013, the value had depreciated to $11,000.

The car’s value continues to drop by the same percentage, we need to find the price of the car in year 2017.

So, 2013-2007 = 6 years

Using the exponential decay formula,

P = P₀(1-r)ⁿ

11000 = 38000(1-r)⁶

0.29 = (1-r)⁶

Taking log to both sides,

㏒(0.29) = 6 ㏒(1-r)

-0.53 / 6 = ㏒(1-r)

-0.089 = ㏒(1-r)

r = 18%

Now, 2017 - 2013 = 4

So,

P = 11000(1-0.18)⁴

P = 4973.33

Hence the value of the car in the year 2017 will be $4973.

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Answer: To compare the final amounts, we need to calculate the compound interest for Brianna and the simple interest for Audra.

For compound interest, the formula to calculate the future value is:

A = P(1 + r/n)^(nt)

Where:

A = the future value/amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times that interest is compounded per year

t = the number of years

For Brianna:

P = $16,500

r = 8% = 0.08

n = 1 (compounded annually)

t = 13 years

A = 16500(1 + 0.08/1)^(1*13)

A = 16500(1.08)^13

A ≈ $42,159.84

After 13 years, Brianna will have approximately $42,159.84.

For simple interest, the formula to calculate the future value is:

A = P(1 + rt)

Where:

A = the future value/amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the number of years

For Audra:

P = $16,500

r = 8% = 0.08

t = 13 years

A = 16500(1 + 0.08*13)

A = 16500(1 + 1.04)

A ≈ $39,720

After 13 years, Audra will have approximately $39,720.

To determine who will have more and by how much, we subtract Audra's amount from Brianna's amount:

Difference = Brianna's amount - Audra's amount

Difference = $42,159.84 - $39,720

Difference ≈ $2,439.84

Therefore, at the end of 13 years, Brianna will have approximately $2,439.84 more than Audra.

Step-by-step explanation: :)

Answer:

Brianna will have approximately $2,439.84 more than Audra.

hope it helps u

Step-by-step explanation:

The curve is given by f(x) = 2x^(3/2) - 14, which passes through (9, 4) and has a slope of 3√(x) at each point.

To find the curve y=f(x) in the xy-plane that passes through a given point and has a given slope at each point, we need to integrate the slope function to get the formula for f(x) and use the initial point to determine the value of the constant of integration.

The slope of the curve at each point is given by 3√(x). This means that df/dx = 3√(x), where f(x) is the desired function. Integrating both sides with respect to x gives:

f(x) = 2x^3/2 + C

where C is the constant of integration.

To determine the value of C, we use the fact that the curve passes through the point (9, 4). Substituting x=9 and y=4 into the equation for f(x), we get:

4 = 2(9)^3/2 + C

Simplifying this equation gives C = -14.

Therefore, the curve y=f(x) that passes through the point (9, 4) and has a slope of 3√(x) at each point is given by:

f(x) = 2x^3/2 - 14

This curve passes through points (9,4) and has a slope of 3√(x) at each point, as desired.

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Answer:

2

Step-by-step explanation:

In an arithmetic sequence, the common difference refers to the constant amount added or subtracted between consecutive terms. To find the common difference, we can subtract any term from the following term.

Let's subtract the second term (-13) from the first term (-15):

-13 - (-15) = -13 + 15 = 2

So, the common difference in the arithmetic sequence -15, -13, -11, ... is 2.

The required half-life of the substance is 1 hour and 2 hours.

To determine the half-life of a substance undergoing exponential decay, we can use the formula:

[tex]N = N₀ * (1/2)^{(t / h)}[/tex]

where:

N is the remaining amount of the substance,

N₀ is the initial amount of the substance,

t is the time that has elapsed, and

h is the half-life of the substance.

In this case, we know that N₀ = 128 ounces and N = 28 ounces after a certain number of hours. Plugging in these values, we get:

[tex]28 = 128 * (1/2)^{(t / h)}[/tex]

We can rearrange this equation to solve for t / h:

[tex](1/2)^{(t / h) }= 28 / 128.[/tex]

Taking the logarithm of both sides with base 1/2, we have:

[tex]log₂((1/2)^{(t / h))} = log₂(28 / 128).[/tex]

Applying the logarithmic identity, we can bring the exponent down:

(t / h) * log₂(1/2) = log₂(28 / 128).

Simplifying further, we know that log₂(1/2) is -1:

-(t / h) = log₂(28 / 128).

Multiplying both sides by -1, we have:

t / h = -log₂(28 / 128).

Using a calculator, we find that -log₂(28 / 128) is approximately 1.609.

Therefore, t / h ≈ 1.609.

Since t is the time elapsed and h is the half-life, t / h represents the number of half-lives that have occurred. If t / h is approximately 1.609, it means that around 1.609 half-lives have passed.

Now we can determine the possible options for the half-life based on the given choices:

(A) Less than 1 hour: This would mean the half-life is less than 1 hour. However, 1.609 is greater than 1, so this option can be eliminated.

(B) Between 1 hour and 2 hours: This option is a possibility, as 1.609 is between 1 and 2.

(C) Between 2 hours and 3 hours: This option is not possible since 1.609 is less than 2.

(D) Between 3 hours and 4 hours: This option is not possible either since 1.609 is less than 3.

(E) Greater than 4 hours: This option is also not possible as 1.609 is less than 4.

Based on the analysis, the correct answer is (B) Between 1 hour and 2 hours.

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The probability that 4 or more students score 85 percent or higher on the exam is 0.1209 or approximately 12.09 percent.

To solve this problem, we need to use the binomial distribution formula. We know that the probability of each student scoring 85 percent or higher on the exam is p = 0.2 (since 20 percent is equivalent to 85 percent or higher). We also know that n = 10 students took the exam.

Now we need to find the probability that 4 or more students score 85 percent or higher. We can use the binomial probability formula to calculate this:

P(X ≥ 4) = 1 - P(X < 4)

= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

= [tex]1 - [(10 choose 0) * 0.2^0 * (0.8)^10 + (10 choose 1) * 0.2^1 * (0.8)^9 + (10 choose 2) * 0.2^2 * (0.8)^8 + (10 choose 3) * 0.2^3 * (0.8)^7][/tex]
= 1 - (0.1074 + 0.2684 + 0.3020 + 0.2013)

= 0.1209

Therefore, the probability that 4 or more students score 85 percent or higher on the exam is 0.1209 or approximately 12.09 percent.

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Answer:

0.375 gallons

Step-by-step explanation:

The solution is :

There are 240 students in the school.

Here, we have,

Givens

55% of the total number of students in a school are girls.

Equation

55/100 * x = 132

Solution

Multiply both sides of the equation  by 100

55/100x * 100  = 132 * 100

55x = 13200                        [  Divide by 55  ]

55x/55  = 13200/55

x = 240

Hence, The solution is :

There are 240 students in the school.

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complete question:

Of the students at milton middle school, 132 are girls. if 55% of the students are girls, how many total students are there at milton middle school?