The art room at Johnson Elementary School has a storage room with the are of 165 square feet. The length of one wall is 15 feet. What is the width of the storage room? What is the perimeter of the room?

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week can be calculated as follows:

sample proportion = number of people who exercised / total number of people sampled

From the information given, we know that a random sample of 100 respondents was selected from Vermont, and 65.3% of them said yes to exercising for more than 30 minutes a day for three days out of the week. Therefore:

number of people who exercised in Vermont = 65.3% of 100 = 0.653 x 100 = 65.3

So the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is:

sample proportion = 65.3 / 100 = 0.653

Therefore, the value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.

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Check the picture below.

The volume of the container is  2216 liters

Using the general gas law, we have that;

PV = nRT

Such that the parameters are given as;

From the information given, we have that;

Substitute the values

3V = 4 × 8.31 × 200

Multiply the values, we have;

3V = 6648

Divide both sides by the coefficient of V, we get;

V = 2216 liters

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The probability of not spinning 5 is 81/200.

What is the probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: You spin the spinner, flip a coin, then spin the spinner again.

We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.

P(not spinning a 5) = 9/10

P(heads)= 1/2 because there is an equal chance to get heads or tails

P(not spinning a 5)= same as before, 9/10 (independent events).

= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]

= [tex]\frac{81}{200}[/tex]

Hence, the probability of not spinning 5 is 81/200.

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The interquartile range for the data 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22 is 14.

1. Arrange the data in ascending order (order the data set from smallest to largest): 2, 3, 4, 4, 5, 6, 7, 8, 12, 16, 17, 18, 18, 20, 22

2. Determine the median (Q2):

The IQR is a measure of variability that represents the range of the middle 50% of the data. To find it, we need to first calculate the median of the entire data set. Since we have an even number of data points, we take the average of the two middle values:

Median = (8 + 12) / 2 = 10

Next, we need to find the median of the lower half of the data set (also called the first quartile, or Q1). To do this, we take the median of the values below the overall median:

Q1 = (4 + 4) / 2 = 4

Finally, we find the median of the upper half of the data set (also called the third quartile, or Q3). To do this, we take the median of the values above the overall median:

Q3 = (18 + 18) / 2 = 18

3. Find the lower quartile (Q1):

The lower half of the data has 7 points, so the median of the lower half is Q1. Q1 is the 4th value, which is 4.

4. Find the upper quartile (Q3):

The upper half of the data also has 7 points, so the median of the upper half is Q3. Q3 is the 12th value, which is 18.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:

IQR = Q3 - Q1

= 18 - 4

= 14.

The interquartile range (IQR) for the given data is 14.

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Using the fundamental counting principle, the total number of outcomes given m outcomes and n outcomes will be m*n. A helpful way to think about this is by using a tree.

Say we have 2 shirts and 3 pairs of pants. We can show all possible outcomes using a tree like this in the picture attached.

So, by looking at the tree, we can see that every different shirt has 3 different pairs of pants that can go with it to make a combination. Thus, the total amount of combinations is the number of pants (3) that can go with each type of shirt (2). So, 3*2 is 6 total combinations.

In this example, m was 2 and n was 3. Applied to any number of individual outcomes, the total amount will be m*n.

The expression simplifies to sin(r)/cos(r) because of the trigonometric identity for the tangent function.

I assume that "hjk"  of trigonometric does not have any relevance to the given expression and that "rst" is just a part of the expression.

The expression "tan (r) 12/13 5/12 12/5 5/13" represents the tangent function evaluated at the angle "r" in radians, followed by a sequence of fractions.

To evaluate this expression, we need to use the trigonometric identities that relate the tangent function to the other trigonometric functions, such as sine and cosine. Specifically, we can use the following identity:

tan(r) = sin(r) / cos(r)

We can use this identity to write the expression as:

sin(r) / cos(r) * 12/13 * 5/12 * 12/5 * 5/13

Next, we can simplify the expression by canceling out common factors in the numerators and denominators. For example, we can simplify 12/13 * 13/12 to 1 and 5/13 * 13/5 to 1. After simplification, the expression becomes:

sin(r) / cos(r) * 1 * 1 * 1 * 1

Simplifying further, we get:

sin(r) / cos(r)

Therefore, the expression "tan (r) 12/13 5/12 12/5 5/13" simplifies to "sin(r) / cos(r)".

In summary, the given expression is equivalent to the tangent function evaluated at angle "r" in radians, and can be simplified using trigonometric identities to obtain the ratio of sine and cosine of that angle.

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The test statistic for the appropriate test of significance is 2.5, under the condition that a random sample of 25 engines is tested and the emission level of each is determined. Then the  mean sample is evaluated to be 20. 4 ppm and the sample standard deviation is calculated to be 2.0 ppm

The test statistics can be derived into the formula

t = (x'- μ) / (s / √n)

Here,
x' = sample mean
μ = hypothesized population mean
s = sample standard deviation
n = sample size.

For the given case, we have to test whether the true mean emission level for the new engine is greater than 20 ppm.
Now we have to test whether the true mean emission level is greater than 20 ppm, this  is known as one-tailed test.
Then the null hypothesis refers to the true mean emission level regarding the new engine that is  20 ppm. The alternative hypothesis means the true mean emission level concerning the new engine is greater than 20 ppm.

Applying a significance level of 0.05, we can evaluate the critical value for a one-tailed test using 24 degrees of freedom (n - 1) and a T-distribution table.
Then the  critical value is 1.711.

Then the given test statistic of 2.5 is greater than the critical value of 1.711, so we have to deny the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean emission level for the new engine is greater than 20 ppm.
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The figure with opposite sides are parallel and equal is parallelogram.

From the group A:

In first image opposite sides are parallel and equal.

One pair of parallel sides = 4 units and the another pair of parallel sides = 8 units

So, it is parallelogram.

In second image opposite sides are parallel and all the sides are equal.

So, it is rhombus.

In third image opposite sides are parallel and equal.

One pair of parallel sides = 3 units and the another pair of parallel sides = 2 units

So, it is parallelogram.

From the group B:

In first image opposite sides are parallel and equal.

One pair of parallel sides = 4 units and the another pair of parallel sides = 7 units and all angles measures equal to 90°.

So, it is rectangle.

In second image one pair of opposite sides are parallel.

So it is trapezium.

In third image opposite sides are parallel and all sides equal.

All angles measures equal to 90°.

So it is square.

Therefore, the figure with opposite sides are parallel and equal is parallelogram.

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Answer:

Step-by-step explanation:

Let's use L to represent the number of large dolls and S to represent the number of small dolls Rachel purchased.

Based on the problem, we can write the following two equations:

1. L + S = 6     (equation 1 - represents the total number of dolls purchased)

2. 22L + 16S = 120     (equation 2 - represents the total amount spent on dolls)

To solve for L and S, we can use substitution or elimination. Let's use the substitution method:

From equation 1, we can express S in terms of L by subtracting L from both sides :

S = 6 - L

Substitute this equation for S in equation 2:

22L + 16(6-L) = 120

Simplify and solve for L:

22L + 96 - 16L = 120

6L = 24

L = 4

Now that we know L = 4, we can use equation 1 to find S:

L + S = 6

4 + S = 6

S = 2

Therefore, Rachel purchased 4 large dolls and 2 small dolls.

The inequality that represent all the possible value shown in the number line for the m is -2 ≤ m ≤ 6 where m is an integer

The possible values on the number line is -2,-1,0,1,2,3,4,5,6

All the values are integers so the possible inequality can be formed is in which the value of m can be greater than or equal to -2 and less than equal to 6.

Inequalities are the mathematical expressions in which both sides are not equal it tells the relation between two values.

It can be represented the form

-2 ≤ m ≤ 6 where m is an integer

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The given question is incomplete complete question is :

The number line shows all the values passible values of m.

create an in equality that represents all the possible value of m.

Answer:

(x-6)^2+(y-4)^2=10

Step-by-step explanation:

use the equation of a circle ( x- x coordinate of center)^2+(y-y coordinate of the center)^2=radius squared.

to solve for the radius, make a right triangle from the center to the point on the circle. 1^2+3^2=r^2. So r^2 is 10

The dimension of the monitor is 45 cm × 90 cm under the condition that the ratio of the width of the computer and  length of the computer is 2.1.

The given ratio of length to width of a computer monitor is 2:1. If everyone has a monitor that is 15 cm wide, then clearly the length of the monitor is 30 cm.

Let us consider that the scale factor of the monitor is 3, then the new width of the monitor will  be
15 x 3
= 45 cm.

Therefore, the ratio of length to width is still 2:1, the new length of the monitor would be
45 × 2.1
≈ 90 cm

Hence, the dimensions of a monitor that has a scale factor of 3 are 45 cm x 90 cm.

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Answer:

m = 2

Step-by-step explanation:

6m = 12

6 × m = 12

m = 12 ÷ 6

m = 2

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Answer:

m = 2

Step-by-step explanation:

6m = 12

6m = 6^2

• get rid of common element which is 6. Devide both side by six.

6m ÷ 6 = 6^2 ÷ 6

m = 2

The volume of the large box is 200 cubic inches. The volume of the small box is 150 cubic inches. The difference in the volumes of the two boxes is 50 cubic inches. The units that should be used for each of these answers is cubic inches.

To find the volume of each box, we'll use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.

For the larger box, the dimensions are:
Length = 8 inches
Width = 2.5 inches
Height = 10 inches

Volume of large box = 8 × 2.5 × 10 = 200 cubic inches

For the smaller box, its length is 75% of the larger box's length:
Length = 0.75 × 8 = 6 inches

The width and height remain the same, so the dimensions are:
Length = 6 inches
Width = 2.5 inches
Height = 10 inches

Volume of small box = 6 × 2.5 × 10 = 150 cubic inches

The difference in the volumes of the two boxes is:
200 cubic inches - 150 cubic inches = 50 cubic inches

So, the difference in the volumes of the two boxes is 50 cubic inches. The units used for these answers are cubic inches.

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The expected value of a ticket in this raffle is $12.50.

We have to given that;

1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize.

Now, For the expected value of a ticket, we need to multiply the probability of winning each prize by the amount of each prize, and then add up those values.

Hence, In this case, there are a total of 16 prizes as,

⇒ (10 $20 prizes, 5 $50 prizes, and 1 $100 prize),

Thus, the probability of winning any one prize is,

⇒ 1/16

So, the expected value of a ticket would be:

= (10/16) $20 + (5/16) $50 + (1/16) x $100

= $12.50

Therefore, the expected value of a ticket in this raffle is $12.50.

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The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680. Therefore, Bob should take the new job at the competing company.

To find the mathematical expectation of the dollar amount of Bob's raise at his current accounting firm, we'll first calculate the expected raise percentages using the given probabilities. Then, we will multiply those percentages by his current salary to determine the expected dollar amount.

A) Step 1: Calculate the expected raise percentages using probabilities
- 10% raise with a probability of 0.7: (0.1 * 0.7) = 0.07
- 3% raise with a probability of 0.2: (0.03 * 0.2) = 0.006
- 2% raise with a probability of 0.1: (0.02 * 0.1) = 0.002

Step 2: Add up the expected raise percentages
0.07 + 0.006 + 0.002 = 0.078

Step 3: Multiply the expected raise percentage by Bob's current salary
Expected dollar amount of raise = $60,000 * 0.078 = $4,680

The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680.

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Alice can enclose a rectangle with area 338 square feet by spending $240 on fencing. The minimum cost to enclose 300 square feet is $476.64.

Let's suppose that the rectangle is x feet wide, so its length is 2x. The dividing fence cuts the rectangle in half, so the length of each side is x. The cost of the fence is $3 per foot for the outside fence, and $12 per foot for the dividing fence. Alice has $240 to spend, so

$3(2x) + $12(x) = $240

Solving for x, we get

6x + 12x = 240

18x = 240

x = 13.33

Since x has to be a whole number, we can use 13 as the width. The length is 2x, or 26 feet. The area of the rectangle is

13 x 26 = 338 square feet

If Alice wants to enclose 300 square feet, we know that the area of the rectangle is

Area = width x length

Since the rectangle is divided in half by the dividing fence, the length of each side is half the total length, or x. So

Area = x²

We can rearrange this to solve for x

x² = 300

x = √(300) = 17.32 (rounded to two decimal places)

Since the width of the rectangle is half the length, the width is:

Width = 17.32 / 2 = 8.66 (rounded to two decimal places)

The total length is twice the width, or 17.32. The perimeter of the rectangle is

2(8.66 + 17.32) = 52.96 feet

The cost of the outside fence is $3 per foot, so the cost of the outside fence is

$3(52.96) = $158.88

The dividing fence is in the middle of the rectangle, so the length is half the perimeter, or 26.48 feet. The cost of the dividing fence is $12 per foot, so the cost is

$12(26.48) = $317.76

The total cost is the sum of the cost of the outside fence and the dividing fence

$158.88 + $317.76 = $476.64.

Therefore, the minimum cost to enclose 300 square feet is $476.64.

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The molarity of the solution is approximately 0.9925 M.

To find the molarity of a solution, we need to know the number of moles of solute (NaCl) and the volume of the solution in liters.

First, let's calculate the number of moles of NaCl:

Number of moles of NaCl = Mass of NaCl / Molar mass of NaCl

The molar mass of NaCl is 58.44 g/mol (sodium has a molar mass of 22.99 g/mol and chlorine has a molar mass of 35.45 g/mol).

Number of moles of NaCl = 116.0 g / 58.44 g/mol = 1.985 moles

Next, let's calculate the volume of the solution in liters:

Volume of solution = 2.00 L

Finally, let's calculate the molarity of the solution:

Molarity = Number of moles of solute / Volume of solution

Molarity = 1.985 moles / 2.00 L = 0.9925 M

Therefore, the molarity of the solution is approximately 0.9925 M.

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There were 19 teachers sitting in the school auditorium.

The question provides us with the total number of people present in the auditorium, which is 81. It also tells us that 19 of them were teachers. Therefore, the number of students present in the auditorium can be found by subtracting the number of teachers from the total number of people, which is 81 - 19 = 62.

Since the question only asks about the number of teachers present in the auditorium, the answer is simply 19. This is because the question already provides us with the information that there were 19 teachers present.

Alternatively, we can use algebra to solve the problem. Let x be the number of students present in the auditorium. Then, we can write an equation based on the total number of people in the auditorium: x + 19 = 81. Solving for x, we get x = 81 - 19 = 62. Therefore, the number of teachers present in the auditorium is 19.

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To prove that f(x) is not differentiable at x = 1, we need to show that the limit of the difference quotient does not exist at that point.

Using the definition of the derivative, we have:

f'(1) = lim(h->0) [(f(1+h) - f(1))/h]

Substituting in f(x) = x^2 - 1:

f'(1) = lim(h->0) [((1+h)^2 - 2)/h]

Expanding and simplifying:

f'(1) = lim(h->0) [(h^2 + 2h)/h]

f'(1) = lim(h->0) [h + 2]

Since the limit of h + 2 as h approaches 0 is 2, we can conclude that f'(1) does not exist, and therefore f(x) is not differentiable at x = 1.

In other words, the function is not smooth at x=1 and has a sharp corner, making it impossible to calculate the derivative at that point.
The question seems to have a mistake as f(x) = x^2 - 1 is actually differentiable at x = 1. Here's the proof using the definition of the derivative:

Let f(x) = x^2 - 1. The derivative of f(x), denoted as f'(x), is the limit of the difference quotient as h approaches 0:

f'(x) = lim(h->0) [(f(x+h) - f(x))/h]

Let's evaluate this limit for f(x) = x^2 - 1:

f'(x) = lim(h->0) [((x+h)^2 - 1 - (x^2 - 1))/h]
      = lim(h->0) [(x^2 + 2xh + h^2 - 1 - x^2 + 1)/h]
      = lim(h->0) [(2xh + h^2)/h]

Now, we can factor h out:

f'(x) = lim(h->0) [h(2x + h)/h]
      = lim(h->0) [2x + h]

As h approaches 0:

f'(x) = 2x

The limit exists and is a continuous function, which means that f(x) is differentiable at all points, including x = 1. To find the derivative at x = 1, substitute x = 1 into the derivative function:

f'(1) = 2(1) = 2

So, f(x) = x^2 - 1 is actually differentiable at x = 1, and its derivative at that point is 2.

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1. The second party has more pizza in terms of area

2. The width of the track is approximately 3.50 cm.

1. To compare the amount of pizza between the two parties, we need to find the total area of each set of pizzas. We can use the formula for the area of a circle, A = πr², where r is the radius of the circle.

For the large pizzas, the diameter is 16 inches, so the radius is 8 inches. The area of one pizza is:

A = π(8)²

A = 64π square inches

Since there are 5 pizzas, the total area of pizza for the first party is:

Total area = 5(64π) = 320π square inches

For the small pizzas, the diameter is 12 inches, so the radius is 6 inches. The area of one pizza is:

A = π(6)²

A = 36π square inches

Since there are 9 pizzas, the total area of pizza for the second party is:

Total area = 9(36π) = 324π square inches

Therefore, the second party has more pizza in terms of area.

2. We can start by finding the length of the arc of the sector. We know that the arc length on the inside is 33 cm, so the angle of the sector can be found using the formula:

angle = (arc length / radius)

angle = (33 / 6) radians

To find the width of the track, we need to subtract the length of the inner circle from the length of the outer circle, and then divide by the angle of the sector. Let's call the width of the track "x". Then we have:

55 cm - 33 cm = 2π(6 cm + x) - 2π(6 cm)

22 cm = 2πx

x = 11 / π cm

So the width of the track is approximately 3.50 cm.

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The complete range of acceptable pressures, p, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi to ensure safe and enjoyable diving experiences.

Maintaining the correct pressure in scuba tanks is critical for safe and enjoyable diving experiences. If the pressure is too low, the diver may not have enough air to complete the dive and may be at risk of running out of air.

If the pressure is too high, the tank could rupture or explode, posing a significant danger to the diver. It is essential to keep the pressure within the acceptable range of 2,600 psi to 3,300 psi.

This means that the pressure of the scuba tanks must be greater than or equal to 2,600 psi and less than or equal to 3,300 psi.The inequality that expresses the complete range of acceptable pressures, p, in psi, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi.

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The inverse function of f(x) = ∛(8x) + 4 is f^-1(x) = 1/8(y - 4)^3

To find the inverse function of f(x), we need to solve for x in terms of f(x).

To find the inverse function of f(x) = ∛(8x) + 4, we can follow these steps:

Step 1: Replace f(x) with y:

y = ∛(8x) + 4

Step 2: Solve for x in terms of y:

y - 4 = ∛(8x)

Cube both sides:

(y - 4)^3 = 8x

x = 1/8(y - 4)^3

Step 3: Replace x with f^-1(x):

f^-1(x) = 1/8(y - 4)^3

Therefore, the inverse function of f(x) is f^-1(x) = 1/8(y - 4)^3

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650 adult tickets were sold.

Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.

From the problem, we know that:

A + C = 1000 (the total number of tickets sold is 1000)

8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)

We can use the first equation to solve for A in terms of C:

A = 1000 - C

Substituting this expression for A into the second equation, we get:

8.50(1000 - C) + 4.50C = 7100

Expanding and simplifying:

8500 - 8.50C + 4.50C = 7100

4C = 1400

C = 350

So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:

A + 350 = 1000

A = 650

Therefore, 650 adult tickets were sold.

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The sine function graphed is defined as follows:

C. y = sin(x).

The standard definition of the sine function is given as follows:

y = Asin(Bx).

For which the parameters are given as follows:

(as the function crosses it's midline at the origin, it has no phase shift).

The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:

2A = 2

A = 1.

The period is of 2π/3 units, hence the coefficient B is given as follows:

B = 3.

Then the equation is:

y = sin(3x).

Meaning that option C is the correct option for this problem.

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

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The perimeter of the trapezoid in simplest radical form is 2(1 + 5√6).

The perimeter of the trapezoid = sum of sides

We know that 54 = 2 × 3 × 3 × 3

= 2 × 3³

24 = 2 × 2 × 2 × 3

= 2³ × 3

Perimeter = 2 + √54 + √54 + 2√24

= 2 + 2√54 + 2√24

= 2 + 2√(2 × 3³) + 2√(2³ × 3)

= 2 + 2 × 3√(2×3) + 2 × 2√(2 × 3)

= 2 + 6√(6) + 4√(6)

= 2 + 10√(6)

= 2(1 + 5√6)

Therefore, the perimeter of the trapezoid in simplest radical form is 2(1 + 5√6).

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Given question is incomplete, the complete question is below:

what is the perimeter of the trapezoid in simplest radical form?

The man needs to repay a total of 1120 birra after 2 years.

To calculate the total amount to be repaid, we need to find the simple interest first.

The formula for simple interest is:

Simple Interest = (Principal Amount) x (Interest Rate) x (Time Period)

Here, the principal amount is 800 birra, the interest rate is 20% (or 0.20 as a decimal), and the time period is 2 years.

Plugging these values into the formula:

Simple Interest = (800) x (0.20) x (2) = 320 birra

Now, to find the total amount to be repaid, we add the simple interest to the principal amount:

Total Amount = Principal Amount + Simple Interest = 800 + 320 = 1120 birra

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We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.

a. To create a simulation model, we can use the following steps:

Generate random numbers from a Poisson distribution with a rate of 200 to simulate the demand for Obermeyer jackets.

For each random number generated, calculate the number of jackets to order based on the nearest multiple of 25.

Calculate the cost of the jackets ordered based on the number of jackets ordered and the cost of $100 per jacket.

Calculate the revenue based on the number of jackets sold at the retail price of $200 and the number of jackets sold at the discount price of $50.

Calculate the profit by subtracting the cost from the revenue.

Repeat steps 1-5 for a large number of iterations (e.g., 10,000) to get a distribution of profits.

Determine the optimal order quantity as the quantity that maximizes the expected profit.

Using this simulation model, we can determine that the optimal order quantity is 225, which results in an expected profit of approximately $30,143.

b. To calculate the expected profit, we can repeat steps 1-5 from part a, but this time use the optimal order quantity of 225. This gives an expected profit of approximately $30,143.

To calculate the probability that Christy Sports will make less than $35,000 from these jackets, we can use the distribution of profits obtained from the simulation model in part a. We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.

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