During the period 2000-2016, the average costs B (in dollars) for a new boat and the average costs H (in dollars) for a hovercraft can be modeled


by the following functions:


B = 30 +140 and H=-1012 +350 + 400


where t is the number of years since 2000


(a) How can the difference of the costs of a hovercraft and the costs of a boat be expressed? (4 points)


(b) About how much was the difference in the year 2010? (2 points)

Answer:

Length: 22 inches × 3.5 = 77 inches

Width: 10 inches × 3.5 = 35 inches

Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.

Given coordinates of points A, B and C

A(6, 10), B(2, -8), C(-4 , -7)

After reflection  (x, y) ---> (-x, y).

Thus,  Coordinates of image of points A', B' and C' are-

A'(-6, 10), B'(-2, -8), C'(4 , -7)

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Connor will have $ 1975.4 if he invests $1,400 with a 9% interest rate that compounds annually for 4 years.

Compound interest is given by the formula:

A = P [tex](1 + \frac{r}{n})^{nt[/tex]

where A is the amount

P is the principal

r is the rate of interest

n is the frequency with the interest is compounded in a year

t is the time

P = $ 1,400

r = 9% or 0.09

t = 4 years

Since the interest is compounded annually the frequency of the compounding is 1.

n = 1

A = 1400 [tex](1 +\frac{0.09}{1})^{1*4[/tex]

= 1400 [tex](1.09)^4[/tex]

= 1400 * 1.411

= $ 1975.4

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Answer:

c = 12

Step-by-step explanation:

[tex] {5}^{2} + {c}^{2} = {13}^{2} [/tex]

[tex]25 + {c}^{2} = 169[/tex]

[tex] {c}^{2} = 144[/tex]

[tex]c = 12[/tex]

The best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.

The sampling distribution of the mean of a sample is approximately normal if the sample size is sufficiently large, regardless of the distribution of the population from which the sample is drawn.

According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean, which is $3.2$ million. The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size, which is [tex]$2/\sqrt{40} \approx 0.3162$[/tex] million.

Therefore, the best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.

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One if the functions of a protein macromolecule is: c. moving material in and out of cells

Proteins can be described as a complex macromolecules that are responsible for several key functions such as the regulation of cells, tissue, and organs of living organisms including their structure.

Proteins also help in performing the following:

Regulation of gene expression

Structural support, and

Many other cellular processes.

Therefore, a function of a protein macromolecule is: c. moving material in and out of cells.

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The annual rate as a percent is approximately 4.86% per year.

To find the annual rate as a percent, we first need to understand the function that Robert is using. The function [tex]f(x) = 1000(1.0375)^x[/tex] represents the amount of money Robert earns each year based on his initial investment of $1000 and the interest rate of 3.75% (as represented by the value 1.0375, which is 1 + 0.0375).

To calculate the annual rate as a percent, we need to isolate the interest rate from the function. We can do this by using logarithms. Taking the logarithm of both sides of the equation, we get:

log(f(x)) = log(1000) + x*log(1.0375)

Now, we can solve for the interest rate (represented by the value of 1.0375) by dividing both sides of the equation by x and then taking the antilog of the result:

1.0375 = antilog[(log(f(x)) - log(1000))/x]

Using this formula, we can plug in any value for x (representing the number of years Robert has held his investment) and find the corresponding interest rate. For example, if Robert has held his investment for 5 years, we can calculate the interest rate as:

1.0375 = antilog[(log(f(5)) - log(1000))/5]

This gives us an interest rate of approximately 4.86% per year. So, to answer the original question, the annual rate as a percent is approximately 4.86%.

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An equation that models the situation, where p represents the number of pineapples Chad can purchase and w represents the number of watermelons he can purchase will be; 2.15p + 3.75w = 25.20.

Let's use the given information to create an equation to model this situation. We know that Chad spends a total of $29.68 on the fruit salad, so we can start with;

2.15p + 3.75w + 4.48 = 29.68

This equation represents the total cost of the fruit salad, which includes the cost of the pineapples (2.15p), the cost of the watermelons (3.75w), and the cost of the bag of grapes (4.48).

To make this equation more specific to the problem of finding the number of pineapples and watermelons Chad can purchase, we need to use the variables p and w to represent those quantities. We can set up a second equation based on the information given about the total number of fruits;

p + w + 1 = T

Here, T represents the total number of fruits in the salad, and we add 1 to account for the bag of grapes.

Now we can use substitution to eliminate the variable T. Solving for T in terms of p and w;

T = p + w + 1

Substitute this expression for T into first equation;

2.15p + 3.75w + 4.48 = 29.68

Simplify;

2.15p + 3.75w = 25.20

Therefore, the model of this situation is; 2.15p + 3.75w = 25.20

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The absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.

To find the absolute maximum and minimum values of the function f(x) = 1 - 5x² on the interval [-3, 2], we first find the critical points of f(x) and then evaluate f(x) at the critical points and endpoints of the interval.

The derivative of f(x) is:

f'(x) = -10x

Setting f'(x) = 0, we get:

-10x = 0

which has only one critical point at x = 0.

Now, we evaluate f(x) at the critical point and endpoints of the interval:

f(-3) = 1 - 5(-3)² = -44

f(0) = 1 - 5(0)² = 1

f(2) = 1 - 5(2)² = -49

Therefore, the absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.

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Number of balls ≈ [tex]1.03 * 10^9[/tex]

To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.

Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.

The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:

V = (4/3)πr³

where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:

V = (4/3) x 3.14 x 0.04³

[tex]V =2.14 * 10^{-5} m^3[/tex]

Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.

Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:

V = l x w x h

where l is the length, w is the width, and h is the height. Plugging in the given values, we get:

V = 20 x 10 x 110

V = 22000 m³

Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:

Number of balls ≈ [tex]V_building / V_ball[/tex]

Number of balls ≈ 22000 / 2.14 x [tex]10^-5[/tex]

Number of balls ≈ [tex]1.03 * 10^9[/tex]

So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.

As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.

For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.

Additionally, we rounded some of our values and used approximations for pi.

Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.

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The equipment's value after 8 years, given its original value was $75,000 and it depreciates by 12% each year, is approximately $27,506.62.

To find the value of the equipment after 8 years, we need to calculate its value at the end of each year, taking into account the 12% depreciation per year.

At the end of year 1, the equipment will be worth 88% of its original value

Value at end of year 1 = 0.88 x $75,000 = $66,000

At the end of year 2, the equipment will be worth 88% of its value at the end of year 1

Value at end of year 2 = 0.88 x $66,000 = $58,080

We can continue this process for each year

Value at end of year 3 = 0.88 x $58,080 = $51,206.40

Value at end of year 4 = 0.88 x $51,206.40 = $45,065.91

Value at end of year 5 = 0.88 x $45,065.91 = $39,654.02

Value at end of year 6 = 0.88 x $39,654.02 = $34,991.23

Value at end of year 7 = 0.88 x $34,991.23 = $31,191.80

Value at end of year 8 = 0.88 x $31,191.80 = $27,506.62

Therefore, the value of the equipment after 8 years is $27,506.62.

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The cost for one donut is $0.32, so the cost for one dozen donuts is:

12 donuts x $0.32/donut = $3.84

The cost for the cardboard box is $0.18 per square foot of cardboard, and there are 144 square inches in 1 square foot, so the cost per square inch of cardboard is:

$0.18 / 144 sq in = $0.00125/sq in

If t represents the total surface area of the box in square inches, then the cost of the box is:

t x $0.00125/sq in

To convert square inches to square feet, we divide by 144:

t/144 square feet x $0.18/square foot = t x $0.00125/sq in

Thus, the expression to model the total cost for one dozen donuts where t represents the total surface area of the box in square feet is:

$3.84 + (t/144) x $0.18

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Check the picture below.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=5\\ r=3 \end{cases}\implies A=\pi (5^2-3^2)\implies A\approx 50.27~cm^2[/tex]

The function f(x) = -4*sin(x/2) - 1 is the solution that meets the specified conditions.

To find the function, f, that satisfies the given conditions f"(x) = -sin(x/2), f'(π) = 0, and f(π/3) = -3, we need to integrate the given second derivative twice and apply the boundary conditions. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x).
1. Integrate f"(x) = -sin(x/2) with respect to x to find f'(x):
  f'(x) = ∫(-sin(x/2)) dx = -2*cos(x/2) + C1, where C1 is the integration constant
2. Apply the boundary condition f'(π) = 0:
  0 = -2*cos(π/2) + C1
  C1 = 0, since cos(π/2) = 0.
3. Now, f'(x) = -2*cos(x/2).
4. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x):
  f(x) = ∫(-2*cos(x/2)) dx = -4*sin(x/2) + C2, where C2 is the integration constant.
5. Apply the boundary condition f(π/3) = -3:
  -3 = -4*sin(π/6) + C2
  -3 = -4*(1/2) + C2
  C2 = -1.
So, the function f(x) that satisfies the given conditions is f(x) = -4*sin(x/2) - 1.

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The statement that  describes how the graph of h is different from the graph of g is: B. The graph of h is the graph of g vertically shifted up 1 unit.

The function h(x) = g(x) + 1 is obtained by adding a constant (1) to the output of the function g(x) = x^2. This means that the graph of h(x) will be the same as the graph of g(x), except that every point on the graph of h(x) will be shifted vertically upward by 1 unit.

Therefore, the correct statement is: B. The graph of h is the graph of g vertically shifted up 1 unit.

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The experimental probability of weather causing school to be canceled in at least three of the next four school years is (3+1)/24, which simplifies to 1/6 or approximately 0.1667.

To find the experimental probability of weather causing school to be canceled in at least three of the next four school years, we need to count the number of times there were three or more cancellations in each set of four years and divide that by the total number of sets of four years.

According to the table of simulated values, there are 24 sets of four years. Out of these, there were three or more cancellations in three sets of four years, and there were four cancellations in one set of four years.  Therefore, the experimental probability of weather causing school to be canceled in at least three of the next four school years is 20%.

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Answer:

x = 30 , y = 54

Step-by-step explanation:

the figure is a trapezium

each lower base angle is supplementary to the upper base angle on the same side, then

4x + y + 6 = 180 ( subtract 6 from both sides )

4x + y = 174 ( subtract 4x from both sides )

y = 174 - 4x → (1)

and

2x + 12 + 2y = 180 → (2)

substitute y = 174 - 4x into (2)

2x + 12 + 2(174 - 4x) = 180

2x + 12 + 348 - 8x = 180

- 6x + 360 = 180 ( subtract 360 from both sides )

- 6x = - 180 ( divide both sides by - 6 )

x = 30

substitute x = 30 into (1)

y = 174 - 4(30) = 174 - 120 = 54

thus x = 30 and y = 54

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.

The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.

However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.

Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.

Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.

The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

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a) The table is completed as follows:

b) The graph is given by the image presented at the end of the answer.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

y=  x + 2.

Hence the numeric values of the function are given as follows:

Then the graph is constructed connecting two of these points and tracing a line through them.

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The true statements about the rectangular prism are Prism B has a greater volume than Prism C, Prism B has the greatest volume, and Prism A has the least volume.

To understand, the differences between the prisms and therefore to verify the statements about them, let's calculate the volume of each by using the formula length x width x height.

Prism A: 2 x 2 x  3= 12 cubic units

Prism B: 2 x 3 x 4 = 24 cubic units

Prism C: 3 x 2 x 3 = 18cubic units

Based on this, the statements A, D, and E are correct.

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Sin theta = -5/sqrt(26) Is the correct option , To find the six trigonometric functions of theta, we need to first find the values of x and y on the terminal side of theta. From the given equation, 5x + y = 0 and x ≥ 0, we can solve for y in terms of x:

y = -5x

Since x ≥ 0, we know that (x, y) lies in the fourth quadrant. We can now use the Pythagorean theorem to find the length of the hypotenuse:

r =[tex]sqrt(x^2 + y^2) = sqrt(x^2 + (-5x)^2) = sqrt(26x^2)[/tex]

Now we can find the six trigonometric functions:

sin(theta) = y/r = [tex]-5x/sqrt(26x^2) = -5/sqrt(26)[/tex]

cos(theta) = x/r =[tex]x/sqrt(26x^2) = 1/sqrt(26)[/tex]

tan(theta) = y/x = -5x/x = -5

csc(theta) = r/y = [tex]sqrt(26x^2)/(-5x) = -sqrt(26)/5[/tex]

sec(theta) = r/x = sqrt(26x^2)/x = sqrt(26)/1 = sqrt(26)

cot(theta) = 1/tan(theta) = -1/5

Therefore, the exact values of the six trigonometric functions of theta are:

sin(theta) = -5/sqrt(26)

cos(theta) = 1/sqrt(26)

tan(theta) = -5

csc(theta) = -sqrt(26)/5

sec(theta) = sqrt(26)

cot(theta) = -1/5

Answer: A. sin theta = -5/sqrt(26)

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The area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

From the question, we have the following parameters that can be used in our computation:

Radii = 21 cm, 81 ft, 45/2 cm

The area of a circle is calculated as

Area = πr²

substitute the known values in the above equation, so, we have the following representation

Area = 3.14 * 21² = 1384.74

Area = 3.14 * 81² = 20601.54

Area = 3.14 * (45/2)² = 1589.625

Hence, the area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

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The meaning of the intercept of the regression line is option B- When 38. 7 pounds of nitrogen is added to the field, 0. 43 bushels of com are produced

We are given the equation of the experiment that tells a relationship.

y = 0.43x + 28.5

The linear regression line is an algebraic model to show the relationship between the two models by putting the value of one variable to get the value of the other.

A linear regression line can be represented as,

y = Ax + B

Here y is the dependent variable and x is the explanatory variable. A is the slope of the line and

B is the intercept here. In the given equation there are two variables given.

Variable x representsthe amount of nitrogen added, and the variable y represents the number of bushels of corn produced.

As putting the value of x, y increases with the value of number 0.43. Therefore, as we are increasing the value of the nitrogen by one unit, the number of bushels of corn produced is increasing by 0.43 units. Hence, for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.

Therefore option B is the correct option.

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The complete question is "An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a cornfield and the number of

bushels of corn produced. This is the regression line of the data, where y is measured in bushels of corn and x is measured in pounds of

nitrogen.

y = 0.43x + 28.5

What is the meaning of the slope of the regression line?

O A. For every 0.43 pounds of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.

OB. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.

OC. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.

OD. For every 28.5 pounds of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels."

To determine the number of liters needed for an order of Kefzol 1.125 g IV q6h, we first need to convert the grams to milligrams.
1.125 g = 1,125 mg

Next, we need to calculate the total volume of Kefzol needed for each dose.

225 mg is equal to 4 mL, so:

1,125 mg ÷ 225 mg/mL = 5 mL

Therefore, each dose of Kefzol requires 5 mL.

To determine the number of liters needed for the entire order, we need to know how many doses will be given per day.

Assuming a standard dosing schedule of q6h, this means the patient will receive 4 doses per day.

So, the total volume of Kefzol needed per day is:

4 doses/day x 5 mL/dose = 20 mL/day

To convert this to liters, we divide by 1000:

20 mL/day ÷ 1000 = 0.02 L/day

Therefore, for an order of Kefzol 1.125 g IV q6h, we will need approximately 0.02 liters per day.

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the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3. Thus, option B is correct.

To write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans, we need to find the common factor between the number of pairs of blue jeans each person donated.

Hallie donated 4 pairs of blue jeans, and Mattie donated 6 pairs of blue jeans.

The common factor between 4 and 6 is 2. We can divide both 4 and 6 by 2 to get:

Hallie donated 2 pairs of blue jeans.

Mattie donated 3 pairs of blue jeans.

Now we can write the ratio of Hallie's donation to Mattie's donation as:

2:3

Therefore, the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3.

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The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.

A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.

Volume of cube = length × breadth × height

length = 5 unit

breadth = 5 unit

height = 5 unit

Volume = 5 × 5 × 5

= 125 unit³

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Answer:

The present ages of A and B will be 48 and 18 years.

Step-by-step explanation:

Let the coefficient be x.

A's age = 8x

B's age = 3x

Six years hence,

Ages will be 8x+6 and 3x+6.

Now, As per the question,

(8x+6) /(3x+6) = 9/4

32x+24 = 27x+54

5x = 30

x = 6.

The null and alternative hypotheses are H₀: μ₁ - μ₂ = 0 and H₁: μ₁- μ₂ ≠ 0 and the test statistic value is equal to 0.45.

The null hypothesis (H₀) states,

That there is no significant difference between the population means of the experimental group and the control group.

The alternative hypothesis (H₁) states that there is a significant difference between the two means.

State the hypotheses as,

H₀: μ₁ - μ₂ = 0 (there is no difference in means)

H₁: μ₁- μ₂ ≠ 0 (there is a difference in means)

where μ₁ is the population mean of the experimental group

And μ₂ is the population mean of the control group.

The test statistic,

Use the t-test formula,

t = (x - μ) / (s / sqrt(n))

where x is the sample mean = 102

μ is the hypothesized population mean = 100

s is the sample standard deviation =88

n is the sample size= 10

Plugging in the values, we get,

t = (102 - 100) / (88 / sqrt(10))

 = 0.45

Therefore, the null and the alternative hypotheses states that H₀: μ₁ - μ₂ = 0 there is no difference in means and H₁: μ₁- μ₂ ≠ 0 there is a difference in means and the test statistic for a sample mean of 102 is 0.45.

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The given question is incomplete, I answer the question in general according to my knowledge:

If a researcher finds a small difference in average test scores between a large sample of 700 experimental participants with a standard deviation of  88, a mean of 100, and with a sample size of 10.  

a. State the null and the alternative hypotheses.

b. Compute the test statistic for sample mean 102.