Alicia's class is making care packages for a local shelter. They can make eight care packages with 240 food items. How many care packages can they make with 500 food items? a) 20 b) 16 c) 10 d) 25

Answers

Answer 1

Answer: To find out how many care packages Alicia's class can make with 500 food items, we can set up a proportion.

Let's say x represents the number of care packages.

We can set up the proportion:

8/240 = x/500

To solve for x, we can cross-multiply and then divide:
240x = 8 * 500
240x = 4000
x = 4000/240
x ≈ 16.67

Since we cannot have a fraction of a care package, we round down to the nearest whole number.

Therefore, Alicia's class can make approximately 16 care packages with 500 food items.

The answer is option b) 16.

(hopefully everything is correct! let me know if anything is off!)

Answer 2

Answer:

Final answer:

Alicia's class can make 16 care packages with 500 food items.

Explanation:

To find out how many care packages Alicia's class can make with 500 food items, we can set up a proportion using the given information. The proportion is:

8 care packages / 240 food items = x care packages / 500 food items

Cross multiplying, we get:

240x = 8 * 500
x = (8 * 500) / 240
x = 16.67

Since we can't make a fraction of a care package, we round down to the nearest whole number. Therefore, Alicia's class can make 16 care packages with 500 food items.

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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]

Answers

Final answer:

The absolute maximum and minimum of a function on a given interval can be found by calculating the function's critical points and evaluating the function at these points and the interval endpoints, then comparing these values.

Explanation:

In order to find the absolute maximum and absolute minimum values of a function on a given interval, you must first find the critical points of the function within the interval. Critical points occur where the derivative of the function is equal to zero or is undefined. In this case, the derivative of f(t) = 9t + 9 cot(t/2) is f'(t) = 9 - (9/2) csc2(t/2). Set this to zero and solve for t to find the critical points. Additionally, the endpoints of the interval, π/4 and 7π/4, could be the absolute maximum or minimum, so these should be evaluated as well. Once you have found the values of the function at these points and the endpoints, compare them to determine the absolute maximum and minimum values.

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Final answer:

To find the absolute maximum and minimum values of a function, we find the critical points and endpoints. Evaluating the function at these points gives the maximum and minimum values.

Explanation:

To find the absolute maximum and absolute minimum values of a function on a given interval, we need to find the critical points and endpoints of the interval.

To find the critical points of f, we need to find where the derivative of f is equal to zero or undefined. The derivative of f(t) = 9t + 9cot(t/2) is f'(t) = 9 - 9csc^2(t/2).

Setting f'(t) = 0, we have 9 - 9csc^2(t/2) = 0. Solving this equation, we get csc^2(t/2) = 1, which means sin^2(t/2) = 1. This gives us sin(t/2) = ±1. The critical points occur when t/2 = π/2 or t/2 = 3π/2. Solving for t, we get t = π or t = 3π as the critical points.

The endpoints of the interval are π/4 and 7π/4.

Now we evaluate the function f at the critical points and endpoints:

f(π/4) = 9(π/4) + 9cot(π/8) ≈ 6.566
f(π) = 9π + 9cot(π/2) = 9π
f(3π) = 9(3π) + 9cot(3π/2) = 27π
f(7π/4) = 9(7π/4) + 9cot(7π/8) ≈ 46.607

From these evaluations, we can see that the absolute maximum value occurs at t = 7π/4 and is approximately 46.607, while the absolute minimum value occurs at t = π/4 and is approximately 6.566.

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1. Write a function rule for finding the amount of daily pay, p, in the following situation: A bus drivergets paid $100 each day plus $0.20 per kilometer, k. (1 point)
100 = 0.20 × k
p = 0.20 × 100 × k
p = 0.20k + 100
0.20k = 100 + p
Use the table below to answer the following question.
2. Do the values in the table represent a linear function? If so, what is the function rule?
(1 point)
The values do not show a linear function.
Yes, the values show a linear function: y = x + 4.
Yes, the values show a linear function: y = 2x + 2.
Yes, the values show a linear function: y = 2x.
Use the following graph to answer the question.
3. Write an equation for the line shown in the graph.
(1 point)2/20/2015 Writing Rules for Linear Functions
https://www.connexus.com/content/render.aspx?disableAssessment=true&printpreview=true&printpopup=true&idSection=504591&idCourse=31343&idWebus… 2/2
10 = 4x
y = 2x + 10
y = 10x – 2
y = –x + 10
Write a function rule for the total cost.
4. One frozen yogurt store sells frozen yogurt for $3.00 per cup and $1.25 per topping. Write a linear
equation to show the total cost of a cup of frozen yogurt. Then calculate the total price for one cup of
frozen yogurt with 4 toppings. (1 point)
y = 1.25x + 3; $5.00
y = 3x + 1.25; $13.25
y = 1.25x + 3; $8.00
y = 5x + 3; $8.00

Answers

1.
To figure out how much the bus driver gets paid everyday you will need this function.
P = 0.20K + 100

2.
the table:(x)(-2,0,2,4 (y)-4,0,4,8
The values in the table do represent a linear function.

Y = 2X

Plug in values from the table

-4 = 2(-2)
-4 = -4

3.
Connexus login?

4.
The equation that shows the total cost of a cup of frozen yogurt is Y = 1.25X + 3; $8.00.

Which shows a correct order to solve this story problem? Gina used 3.2 ounces of strawberry jelly and 4.7 ounces of raspberry jelly in her recipe. She made the same recipe 4 times.

How much jelly did Gina use altogether?

A.
Step 1: Add the weights of the two jellies.
Step 2: Divide that sum by 4.

B.
Step 1: Subtract the weight of the strawberry jelly from the raspberry jelly.
Step 2: Multiply that difference by 4.

C.
Step 1: Add the weights of the two jellies.
Step 2: Multiply that sum by 4.

D.
Step 1: Subtract the weight of the strawberry jelly from the raspberry jelly.
Step 2: Divide that difference by 4.