On January 2, 2021, Twilight Hospital purchased a $100,000 special radiology scanner from Bella Inc. The scanner had a useful life of 4 years and was estimated to have no disposal value at the end of its useful life. The straight-line method of depreciation is used on this scanner. Annual operating costs with this scanner are $105,000. Use incremental analysis for retaining or replacing equipment decision. Approximately one year later, the hospital is approached by Dyno Technology salesperson, Jacob Cullen, who indicated that purchasing the scanner in 2021 from Bella Inc. Was a mistake. He points out that Dyno has a scanner that will save Twilight Hospital $25,000 a year in operating expenses over its 3-year useful life. Jacob notes that the new scanner will cost $110,000 and has the same capabilities as the scanner purchased last year. The hospital agrees that both scanners are of equal quality. The new scanner will have no disposal value. Jacob agrees to buy the old scanner from Twilight Hospital for $50,000. Instructions a. If Twilight Hospital sells its old scanner on January 2, 2022, compute the gain or loss on the sale. B. Using incremental analysis, determine if Twilight Hospital should purchase the new scanner on January 2, 2022. C. Explain why Twilight Hospital might be reluctant to purchase the new scanner, regardless of the results indicated by the incremental analysis in (b)

Answers

Answer 1

a. The hospital will incur a loss of $25,000 on the sale of the old scanner.

b. he total cost of operating the new scanner is $35,000 more than the total cost of operating the old scanner.

c. Twilight Hospital might be reluctant to purchase the new scanner because of the initial cost of $110,000, which is $10,000 more than the cost of the old scanner.

a. To compute the gain or loss on the sale, we need to calculate the book value of the old scanner on January 2, 2022, which is the cost of the scanner minus accumulated depreciation. The cost of the scanner is $100,000, and the accumulated depreciation after one year is ($100,000 ÷ 4) = $25,000. Therefore, the book value is $75,000. Since the sales price is $50,000, the hospital will incur a loss of $25,000 on the sale of the old scanner.

b. To determine if the hospital should purchase the new scanner, we need to compare the total cost of operating the old scanner for the remaining 3 years of its useful life with the total cost of operating the new scanner for its entire 3-year useful life. The total cost of operating the old scanner for 3 years is:

$105,000 × 3 = $315,000

The total cost of operating the new scanner for 3 years is:

($110,000 − $50,000) + ($80,000 × 3) = $350,000

Therefore, the total cost of operating the new scanner is $35,000 more than the total cost of operating the old scanner. Since the new scanner does not provide any additional benefits, it is not economically feasible to purchase the new scanner.

c. Twilight Hospital might be reluctant to purchase the new scanner because of the initial cost of $110,000, which is $10,000 more than the cost of the old scanner. Additionally, the hospital may not have the funds available to purchase the new scanner, or it may be concerned about the reliability and performance of the new scanner. Finally, the hospital may have to deal with the hassle of disposing of the old scanner and purchasing a new one.

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Related Questions

Auto Loans ~ George works for a credit union that serves a large, urban area. For his annual report, he wants to estimate the mean interest rate for 60-month fixed-rate auto loans at lending institutions (banks, credit unions, auto dealers, etc. ) in his area. George selects a random sample of 12 lending institutions and obtains the following rates:

Answers

The estimated mean interest rate for 60-month fixed-rate auto loans at lending institutions in the urban area is 3.59% (the calculated mean from the given data).

To calculate the estimated mean interest rate, we need to find the average of the interest rates provided by the 12 lending institutions. The given data is as follows:

3.25%, 3.50%, 3.75%, 3.25%, 3.80%, 3.90%, 3.95%, 3.75%, 3.40%, 3.50%, 3.60%, 3.65%

The mean is calculated by adding up all the interest rates and then dividing by the total number of rates. Therefore,

Mean = (3.25 + 3.50 + 3.75 + 3.25 + 3.80 + 3.90 + 3.95 + 3.75 + 3.40 + 3.50 + 3.60 + 3.65)/12

Mean = 3.59%

Hence, the estimated mean interest rate for 60-month fixed-rate auto loans at lending institutions in the urban area is 3.59%.

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In two or more complete sentences, describe the transformation(s) that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2

Answers

The transformations that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2 are horizontal compression and vertical shift.

What transformations took place in the function?

The transformations are a horizontal compression and a vertical shift.

Horizontal compression: The factor of 3 in the argument of the logarithm function causes a horizontal compression by a factor of 1/3. This means that the graph of g(x) is narrower than the graph of f(x) and it is shifted to the left.Vertical shift: The constant term of -2 is subtracted from the logarithm function, causing a vertical shift downwards by 2 units.

Therefore, the transformations can be expressed mathematically as follows:

g(x) = log(-3x - 6) - 2

= log(-3(x + 2)) - 2

= log(1/3)log(-3(x + 2)) - 2

Therefore, the transformations are a horizontal compression by a factor of 1/3 and a vertical shift downwards by 2 units.

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Determine an equation for an exponential that model this data set in form p=a(b)^t justify both your values of a and b round b to the nearest hundredth​

Answers

The equation for an exponential that models this data set is: p = 10(2)^t

To determine an equation for an exponential that models the given data set in the form p = a(b)^t, we first need to identify the values of a and b. To do this, we can use two points from the data set and solve for a and b. Let's choose the points (0, 10) and (2, 40):

When t = 0, p = 10: 10 = a(b)^0 = a
When t = 2, p = 40: 40 = a(b)²

Dividing the second equation by the first, we get:

4 = (b)²

Taking the square root of both sides, we get:

b = 2

Now that we have the value of b, we can use one of the original equations to solve for a:

10 = a(2)^0 = a

So, a = 10.

Therefore, the equation for an exponential that models this data set is:

p = 10(2)^t

We can check this equation by plugging in the other data points and verifying that they satisfy the equation. And rounding b to the nearest hundredth gives us b = 2.00.

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If there are 30 people in a classroom, what is the probability that at least two have the same birthday

Answers

The probability that at least two people in a group of 30 have the same birthday is about 0.7063 or 70.63%.

To calculate the probability that at least two people in a group of 30 have the same birthday, we can use the complement rule:

P(at least 2 people have the same birthday) = 1 - P(all people have different birthdays)

The probability that the first person has a unique birthday is 1 (since there are no other people to share with yet).

The probability that the second person also has a unique birthday is 364/365 (since there are now 364 days left out of 365 that they could have a different birthday from the first person).

Similarly, the probability that the third person has a unique birthday is 363/365, and so on. So, we can write:

P(all people have different birthdays) = 1 x 364/365 x 363/365 x ... x 336/365

Using a calculator or computer program, we can evaluate this expression to be approximately 0.2937.

Therefore,

P(at least 2 people have the same birthday) = 1 - 0.2937 = 0.7063

So the probability that at least two people in a group of 30 have the same birthday is about 0.7063 or 70.63%.

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please help i’ll give brainlist :)










1. A forest fire has been burning for several days. The burned area in acres, is given by


the equation y = (4. 800) 2 where d is the number of days since the area of the


fire was first measured



a. Complete the table



b. Look at the value of y = 4,800 2d when d = -1 what does it tell you about the area burned in the fire? what about when d = -3?




c. How much area had the fire burned a week before it measured 4,800 acres, explain your reasoning

Answers

The fire had burned half the area (2,400 acres) one week before it measured 4,800 acres.

How to evaluate Days (d) and Burned area (y), the area burned in the fire, and the area the fire has burned a week before it measured 4,800 acres?

a. To complete the table, we substitute the values of d and evaluate the expression for y.

Days (d)      Burned area (y)

0                      0

1                      23,040

2                      92,160

3                      207,360

4                         368,640

b. When d = -1, the value of y = (4,800)^(2*(-1)) = (4,800)^(-2) = 3.255e-8. This value is very small, indicating that the burned area was negligible or not measurable at this point in time.

When d = -3, the value of y = (4,800)^(2*(-3)) = (4,800)^(-6) = 1.130e-34. This value is extremely small, indicating that there was essentially no burned area at this point in time.

c. To determine the number of days before the fire measured 4,800 acres, we need to solve the equation y = (4,800)^2 for d.

4,800^2 = (4,800)^2d

1 = 2dlog(4,800)

d = log(4,800) / (2log(4,800)) = 0.5

Therefore, the fire had burned half the area (2,400 acres) one week before it measured 4,800 acres. This is because the area burned increases quadratically with time, so the area burned one week before is the square root of the area measured at the time.

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Cassie wants to buy a shirt for $15. 75 and some shoes for $10. 25. If the sales tax is 8. 25%, what is the TOTAL amount Cassie will pay?

Answers

The sales tax is 8.25% of the total cost of the shirt and shoes, so we need to add this to the cost of the items:

Cost of shirt = $15.75

Cost of shoes = $10.25

Total cost before tax = $15.75 + $10.25 = $26.00

Sales tax = 8.25% of $26.00 = 0.0825 x $26.00 = $2.15

Therefore, the TOTAL amount Cassie will pay is:

Total cost after tax = $26.00 + $2.15 = $28.15

So, Cassie will pay $28.15 in total.

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I need help. Assume the base is 2

Answers

a = 5

b = 4

c= 0

Therefore, the equation for graph C is Y = a ^b + c

Y = 5 ^4 + 0

What is a graph?

A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Graphs are a popular tool for graphically illuminating data relationships.

A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.

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Gabriella needs 120 meters of fence to surround a rectangular garden.
the length of the garden is three times its width, w.
how wide is the fence?
(please solve how the answer is formatted, i already looked at the other posts people made on this question and they did not help)

Answers

Answer is 15 meters


To solve this problem, we can use the formula for the perimeter of a rectangle, which is

P = 2l + 2w,

where P is the perimeter, l is the length, and w is the width.

We are given that Gabriella needs 120 meters of fence, which means that

P = 120.

We are also given that the length of the garden is three times its width, or

l = 3w.

Substituting these values into the formula, we get:

120 = 2(3w) + 2w

Simplifying this equation, we get:

120 = 8w

Dividing both sides by 8, we get:

w = 15

Therefore, the width of the garden is 15 meters.

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A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?

Answers

The correct interpretation of the 95% confidence level is that if we were to repeat this sampling process multiple times and construct confidence intervals in the same way, about 95% of the intervals would contain the true mean number of suitable apples produced per tree.

In other words, we are 95% confident that the true mean number of suitable apples produced per tree is between 375 and 520 based on this particular sample of 40 trees. However, we cannot say with certainty that the true mean falls within this interval, nor can we say that it falls outside of this interval with 95% confidence.

It's important to note that the confidence level refers to the long-run behavior of the method of constructing confidence intervals, rather than the probability that the true mean falls within the specific interval calculated from this one sample.

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The second part of the new coaster is a parabola.

Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.

Answers

The unique equation of the given parabola in the form of f(x) = (x - a)(x - b) is given by, f(x) = x(x + 6).

The y intercept of the parabola is at (0,0).

Zeros of the parabola are at x = 0, -6.

Given the model equation for the parabola is f(x) = (x - a)(x - b)

It is the standard equation of a parabola with zeros x = a, b.

Here from the graph we can see that at x = -6, 0 the value of y reaches 0 that is the parabola has zeros at x = 0, -6.

So, a = 0 and b = -6

So, f(x) = (x - 0)(x - (-6))

f(x) = x(x + 6)

From the graph we can also see that the parabola is downward negative Y axis.

At y intercepts x = 0

So, the equation becomes in that case,

f(x) = 0.

So (0, 0) is the only y intercept of the parabola.

Hence, the equation of the unique parabola is, f(x) = x(x + 6) and Y intercept is at (0, 0) and zeros are at x = 0, -6.

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The question is incomplete. The complete question will be -

"The second part of the new coaster is a parabola.

Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros."

Harvey won some money on a

scratch-and-win ticket. Then, he won a

$2 bonus. When he arrived at the counter,

he noticed that he had also won a "triple

your winnings" ticket. As Harvey was

cashing in his prize, the cashier told him

he was the 100th customer, so his total

winnings were automatically doubled. Write two algebraic expressions to

describe Harvey’s winnings

Answers

First algebraic expression: x + 2. Second algebraic expression: 6x + 12.

We can represent Harvey's winnings using algebraic expressions.

Let's use the variable 'x' to represent the amount Harvey won on the scratch-and-win ticket. Harvey then won a $2 bonus, so we add 2 to 'x':

1) x + 2

Next, Harvey won a "triple your winnings" ticket, so we need to multiply the current winnings by 3:

2) 3(x + 2)

Finally, as the 100th customer, Harvey's total winnings were doubled:

3) 2 * 3(x + 2)

So, the two algebraic expressions to describe Harvey's winnings are:

1) x + 2 (initial winnings with the $2 bonus)
2) 2 * 3(x + 2) (total winnings after tripling and doubling)

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In a discussion between Modise and Benjamin about functions, Benjamin said that the diagram below represents a function, but Modise argued that it does not. Who is right? Motivate your answer. x - Input value C 5 8 y-Output value 2 5 1 9​

Answers

Answer:

Modise is right.

This diagram does not represent a function because each input value does not correspond to exactly one output value. The input value 5 corresponds to two outputs, 2 and 9.

The area of a rectangle is represented by the expression x^2-9x+14 units^2. Find the expressions that could represent the length and width of the rectangle

Answers

The expressions that could represent the length and width are (x - 2) units and (x - 7) units respectively.

To find the expressions that represent the length and width of the rectangle, we need to factor the given expression.

x² - 9x + 14 = (x - 2)(x - 7)

The length and width of the rectangle are represented by two factors of the expression.


To find the length and width of the rectangle, we need to understand the formula for the area of a rectangle, which is length multiplied by width. The given expression x²-9x+14 represents the area of the rectangle. To find the expressions that represent the length and width, we need to factor the given expression.

We can do this by finding two numbers that multiply to 14 and add up to -9. These numbers are -2 and -7. Therefore, we can factor the given expression as (x - 2)(x - 7). From this, we can see that the length of the rectangle is represented by the factor (x - 2) units and the width is represented by the factor (x - 7) units.

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A rectangular square prism cage with a side that measures 10 inches will hold 5 basketballs. The height of the basketballs, when stacked on top of each other, measures 48 3/4 inches. (a) What is the volume of the cage?

Answers

The volume of the rectangular square prism cage is 12,000 cubic inches.

Let the dimensions of the rectangular square prism cage be l x w x h, where l = w = 10 inches (since it's a square prism), and h is the height of the basketballs when stacked on top of each other. We can find the value of h using the given information as follows:

h = 5 basketballs x 48 3/4 inches/basketball = 243 3/4 inches

Therefore, the volume of the cage can be calculated as:

Volume = l x w x h = 10 in x 10 in x 243 3/4 in = 12,000 cubic inches.

Hence, the volume of the cage is 12,000 cubic inches.

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Whats the difference between correlation coefficient and determination coefficient?

Answers

Answer: The correlation coefficient (r) and determination coefficient (r²) are both measures of the strength and direction of the linear relationship between two variables in a dataset.

The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation. The correlation coefficient only tells us the strength and direction of the relationship; it does not tell us anything about the proportion of variation in one variable that is explained by the variation in the other variable.

The determination coefficient (r²), also known as the coefficient of determination, is a measure of the proportion of variation in one variable that is explained by the variation in the other variable. It ranges from 0 to 1, with 0 indicating that none of the variation in one variable is explained by the variation in the other variable, and 1 indicating that all of the variation in one variable is explained by the variation in the other variable. The determination coefficient is calculated as the square of the correlation coefficient, so r² always has the same sign as r. A value of r² close to 1 indicates that the relationship between the variables is strong and that a large proportion of the variation in one variable can be explained by the variation in the other variable.

In summary, the correlation coefficient tells us about the strength and direction of the linear relationship between two variables, while the determination coefficient tells us about the proportion of variation in one variable that is explained by the variation in the other variable.

While correlation coefficient measures the strength and direction of the relationship between two variables, determination coefficient measures how much of the variability in one variable can be explained by the other variable.

The correlation coefficient and determination coefficient are two related statistical measures that help us understand the strength and direction of a relationship between two variables. The correlation coefficient (denoted as r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a strong negative relationship, 1 indicating a strong positive relationship, and 0 suggesting no relationship.

On the other hand, the determination coefficient (represented as R²) quantifies the proportion of variance in the dependent variable that is predictable from the independent variable. It ranges from 0 to 1, with 0 indicating no explanatory power and 1 indicating perfect prediction. R² is simply the square of the correlation coefficient (r²).

In summary, while the correlation coefficient shows the strength and direction of a linear relationship, the determination coefficient indicates the extent to which one variable can predict the other. Both are important in determining the nature of relationships between variables in a data set.

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Mario had 40 shares of stock that each lost $75 during the half of the year. He also had 24 shares of a different stock that gained $50 each. What was his net change during this time period on these stocks?

Answers

The net change in the stock is $1800

How to calculate the net change ?

Mario has 40 shares of stick that each lost $75 during half of the year

He also had 24 shares of a different stock that gained $50

The net change can be calculated as follows

-40 × 75

= -3000

= 24 × 50

= 1200

Net change

-3000 + 1200

= -1800

Hence the net change in the stocks is $1800

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3 + v = 2 (2v -1) -----------

Answers

3 +v =4v-2
4v-v =-2-3
3v=-5
V=-5 over 3

whats the answer!???????

Answers

7c^2-23cd+6d^2 you just distribute a bunch

Find dy/dx implicitly. X^2e^{-x } + 3y^2 – xy = 0 dy/dx = ?

Answers

To find dy/dx implicitly, we need to differentiate both sides of the equation with respect to x, treating y as a function of x and using the chain rule.

In this problem, we are given the equation X^2e^{-x} + 3y^2 - xy = 0, and we need to find dy/dx. To do this, we first differentiate each term with respect to x, using the product rule for the xy term and the chain rule for the y^2 term. Then we can solve for dy/dx by isolating the derivative term on one side of the equation. Implicit differentiation is a powerful technique used in calculus to find derivatives of functions that are not easily expressed in terms of a single variable. This technique is used extensively in many areas of mathematics, science, and engineering, including optimization, physics, and economics.

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The diagram shows a pyramid with a square base.
The triangular faces are congruent isosceles triangles.
(a) Write down the number of planes of symmetry of this pyramid.

Answers

Answer:

4

Step-by-step explanation:

You can cut it 4 ways to obtain equal parts on both sides. It's along the same as the symmetry of a square.

Your friends, Fernando and Amelia, each own a video game designer company. They both want you to join their company. You currently have a part-time job making $8. 00 per hour. Fernando offers to pay you $15 per hour for the first month and then increase your hourly rate by $1. 00 each month. Amelia says she will start your pay at $8. 00 per hour but she will increase your hourly rate by 10% each month. In order to make the best decision, you decide to use the mathematics to choose the best offer based on the best hourly wage per month.



Write the equations to represent Fernando’s job offer and Amelia’s job offer. Let x = number of months, y = hourly wage.



Under what time period would you accept Fernando’s offer? Use mathematics to support your reasoning.



Under what time period would you prefer Amelia’s offer? Use mathematics to support your reasoning.



Now that we have looked at the different figures for Fernando and Amelia, which job would you take for the long run? Use mathematics to justify your answer

Answers

Answer:

The equation to represent Fernando's job offer is:

y = 15 + x

Where y is the hourly wage and x is the number of months worked.

The equation to represent Amelia's job offer is:

y = 8(1 + 0.1)^x

Where y is the hourly wage and x is the number of months worked.

To determine the time period for which Fernando's offer is better, we need to find the point where his hourly wage is greater than Amelia's. We can set the two equations equal to each other and solve for x:

15 + x = 8(1 + 0.1)^x

15 + x = 8(1.1)^x

x ≈ 20.44

Therefore, Fernando's offer is better for any time period greater than 20.44 months.

To determine the time period for which Amelia's offer is better, we need to find the point where her hourly wage is greater than Fernando's. We can set the two equations equal to each other and solve for x:

8(1 + 0.1)^x = 15 + x

8(1.1)^x = 15 + x

x ≈ 14.45

Therefore, Amelia's offer is better for any time period less than 14.45 months.

For the long run, we need to determine which offer has a higher hourly wage after a certain number of months. We can compare the two equations by finding their limits as x approaches infinity:

lim (y = 15 + x) as x → ∞ = ∞

lim (y = 8(1 + 0.1)^x) as x → ∞ = ∞

Therefore, both offers have the same long-term hourly wage of infinity. However, Fernando's offer has a faster rate of increase, so it may be more beneficial in the long run.

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at the end of practice, there are 240 ounces of sports drink left in the cooler. every player had some sports drink from the cooler. based on the equation y = 648 - 24x, how many players were at practice?

10
15
17
21

Answers

Answer: 17 or C

Step-by-step explanation:

24 times 17 is 408 and 648 - 408 is 240 ounces

pleasee helppp!!!!!!

Answers

The volume of the cone with a radius of 8cm and height of 15 cm is V = 1005.3 cm³, so the correct option is C.

How to get the volume of the cone?

Remember that for a cone of radius R, and height H, the volume is given by the formula below:

V = (1/3)*pi*R²*H

Where pi = 3.1416

In this case, we know that the radius of the cone is 8cm and the height is 15cm, replacing that in the volume formula we will get:

V = (1/3)*3.1416*(8cm)²*15cm = 1,005.3 cm³

Then the correct option is c.

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Michael and Susan are a combined height of 132 inches. If Michael is 71
inches tall, how tall is Susan?

Answers

Answer: 61 in.

Step-by-step explanation:

What you do first is you must find the total number if inches of both humans combined

132 in.

Then, you want to take the 71 in. from Michael's height, and subtract it from the total number.

132

-71

61

----------

61 in. is your answer.

HELP PLEASE I’m struggling

Answers

A) we can forecast that 15,007 will attend this year's county fair.

B) we can expect approximately 1,001 people to receive a prize.

How did we get the above conclusions?

Using the attendance data given, we can find the %increase in attendance from year to year as follows

From year 1 to year 2 -  (10,365 - 9,278)/9,278

≈ 0.117 or 11.7%

From year 2 to year 3   -  (12,128 - 10,365)/10,365

≈ 0.170 or 17.0%

From year 3 to year 4   -  (13,304 - 12,128)/12,128

≈ 0.097 or 9.7%

finding the average of the tree percentages, we have

(11.7% + 17.0% + 9.7%)/3 ≈ 12.8 %


So applying this to the last years attenance we have:

1.129 x 13,304 = 15020.216

Or 15,020 since people cannot be in decimal format.

2)

Since the first 20% of people attending the fair will receive a raffle ticket, we can estimate the number of raffle tickets as follows ....

15,007 ×0.20 =  3, 001.4

Now we can estimate the number of people who will receive a prize by taking one-third of the number of raffle tickets...

3,002 ÷ 3 ≈1 ,000.7

which is approximatly 1001 people.

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Ayo can people who read team katsudon sus mangas rate my favorite ones. Number 1 : life with my cat kacchan. Number 2: whatever my pets say. Rn rate them only if you read then

Answers

The quality of a manga is subjective and it varies from person to person.

Quality of a manga is depending on their interests, preferences, and tastes.

Therefore,If anything favourite of one person that not mean another person also like the thing.

Manga ratings can be found on various online platforms such as MyAnimeList, MangaUpdates and Goodreads.

These all websites have a community of users who rate and review manga based on their own opinions and experiences.

If we want to get a rating for our favorite manga,

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Alan buys a bag of cookies that contains 5 chocolate chip cookies, 5 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies. What is the probability that Alan randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a peanut butter cookie? Express you answer as a reduced fraction

Answers

The probability of selecting a chocolate chip cookie on the first draw is 5/24, since there are 5 chocolate chip cookies in the bag out of a total of 24 cookies. After eating the chocolate chip cookie, there are 23 cookies left in the bag, including 5 peanut butter cookies. So the probability of selecting a peanut butter cookie on the second draw is 5/23.

To find the probability of both events happening, we multiply the probabilities:

P(select chocolate chip then peanut butter) = P(select chocolate chip) × P(select peanut butter after selecting chocolate chip)
= (5/24) × (5/23)

We can reduce this fraction by finding the greatest common factor of the numerator and denominator, which is 1 in this case:

P(select chocolate chip then peanut butter) = (5/24) × (5/23) = 25/1104

Therefore, the probability that Alan randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a peanut butter cookie is 25/1104.

Is the following data an example of a linear function?

Answers

Yes, The given table is an example of a linear function.

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

To check the following data an example of a linear function.

Now, We can check the slope of given tables as;

⇒ Slope = (3 - (- 2)) / (0 - (- 7))

             = (5 / 7)

⇒ Slope = (8 - 3) / (7 - 0)

             = (5 / 7)

Thus, This table represent the an example of a linear function.

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Room and board charges for on-campus students at the local college have increased 3.1% each year since 2000. In 2000, students paid $4,291for room and board.
Write a function to model the cost C after t years since 2000.

If the trend continues, how much would a student expect to pay for room and board in 2017? Express your answer as a decimal rounded to the nearest hundredth.

Answers

A student would expect to pay approximately $7,096.47 for room and board in 2017. Rounded to the nearest hundredth, this is $7,096.47 rounded to $7,096.50.

What is Function ?

In mathematics, a function is a rule that assigns each element in a set (the domain) to a unique element in another set (the range). The domain and range can be any sets, but they are typically sets of real numbers.

The cost of room and board after t years since 2000 can be modeled by the equation:

C(t) = 4291[tex](1 + 0.031)^{t}[/tex]

where C(t) is the cost after t years.

To find out how much a student would expect to pay in 2017, we need to plug in t = 17 (since 2017 is 17 years after 2000) into the equation:

C(17) = 4291[tex](1 + 0.031)^{17}[/tex]

≈ 7,096.47

Therefore, a student would expect to pay approximately $7,096.47 for room and board in 2017. Rounded to the nearest hundredth, this is $7,096.47 rounded to $7,096.50.

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please help asap!!, the image is attached, 30 points !!

Answers

21.75 or 21 & 3/4, because 3 time 7.25 is 21.75
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