The Kims are hosting a catered dinner. The cost for 3 servings is $18. The cost for 10 servings is $60. What is the cost per serving?(1 point)

Question

$ (response area) per serving

Answer 1

To find the cost per serving, we can calculate it using the total cost and the number of servings.

1. For 3 servings:
   \[ \text{Cost per serving} = \frac{\text{Total cost}}{\text{Number of servings}} = \frac{18}{3} = 6 \text{ dollars per serving} \]

2. For 10 servings:
   \[ \text{Cost per serving} = \frac{\text{Total cost}}{\text{Number of servings}} = \frac{60}{10} = 6 \text{ dollars per serving} \]

In both cases, the cost per serving is the same.

Therefore, the cost per serving is $6.

Answer 2

A graph of the cost of gas purchased depending on the number of gallons pumped has the points (4,15)
and (8,30)
. What is the rate of change in the cost of the gas as each gallon is pumped?(1 point)
$
per gallon

Answer 3

To find the rate of change (which represents the cost per gallon of gas), we can use the formula for the slope between two points on a graph, which is given by:

\[ \text{Rate of Change} = \frac{\text{Change in Cost}}{\text{Change in Gallons}} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \((4, 15)\) and \((8, 30)\):

• \( (x_1, y_1) = (4, 15) \)
• \( (x_2, y_2) = (8, 30) \)

Calculating the change in cost and the change in gallons:

\[ \text{Change in Cost} = y_2 - y_1 = 30 - 15 = 15 \] \[ \text{Change in Gallons} = x_2 - x_1 = 8 - 4 = 4 \]

Now, substituting these values into the rate of change formula:

\[ \text{Rate of Change} = \frac{15}{4} = 3.75 \]

Thus, the rate of change in the cost of gas is $3.75 per gallon.

Answer 4

A linear graph of the cost of broccoli in dollars per pound has the points (3,8.25)
and (6,16.50)
. What is the rate of change in the purchase price in dollars per pound?(1 point)
$
per pound

Answer 5

To determine the rate of change in the purchase price of broccoli in dollars per pound, we will similarly use the formula for the slope between two points. The formula is:

\[ \text{Rate of Change} = \frac{\text{Change in Price}}{\text{Change in Pounds}} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the given points \((3, 8.25)\) and \((6, 16.50)\):

• \( (x_1, y_1) = (3, 8.25) \)
• \( (x_2, y_2) = (6, 16.50) \)

Now we can calculate the change in price and the change in pounds:

\[ \text{Change in Price} = y_2 - y_1 = 16.50 - 8.25 = 8.25 \] \[ \text{Change in Pounds} = x_2 - x_1 = 6 - 3 = 3 \]

Now, substituting these values into the rate of change formula:

\[ \text{Rate of Change} = \frac{8.25}{3} = 2.75 \]

Thus, the rate of change in the purchase price of broccoli is $2.75 per pound.

Answer 6

Use the table to answer the question.

Height Above Canyon Floor Time (minutes)
360 0
280 3
160 10
80 14
Which statement best interprets the rate of change of the linear model shown in the table?

(1 point)
Responses

The elevation of a hiker who is hiking up from canyon floor changes at a rate of −20
feet per minute.
The elevation of a hiker who is hiking up from canyon floor changes at a rate of negative 20 feet per minute.

The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute.
The elevation of a hiker who is hiking up from a canyon floor changes at a rate of 20 feet per minute.

The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of 20 feet per minute.

The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20
feet per minute.
The elevation of a hiker who is hiking down to a canyon floor changes at a rate of negative 20 feet per minute.
Skip to navigation

Answer 7

To determine the correct interpretation of the rate of change of the linear model represented in the table, we need to analyze the height and time data provided:

1. Data from the table:

   • At 0 minutes, the height is 360 feet.
   • At 3 minutes, the height is 280 feet.
   • At 10 minutes, the height is 160 feet.
   • At 14 minutes, the height is 80 feet.

2. Finding the rate of change:

   To find the rate of change in height (elevation) over time, we can calculate the change in height divided by the change in time between the first and the last entries in the table.

   • Change in height from 360 feet to 80 feet: \[ \text{Change in Height} = 80 - 360 = -280 \text{ feet} \]

   • Change in time from 0 minutes to 14 minutes: \[ \text{Change in Time} = 14 - 0 = 14 \text{ minutes} \]

   • Rate of Change: \[ \text{Rate of Change} = \frac{-280 \text{ feet}}{14 \text{ minutes}} = -20 \text{ feet per minute} \]

3. Interpretation: The negative sign indicates that the height is decreasing, meaning the hiker is moving down towards the canyon floor.

From the options provided, the correct interpretation of the rate of change would be:

The elevation of a hiker who is hiking down to a canyon floor changes at a rate of −20 feet per minute.

This statement accurately reflects that the hiker is descending, as indicated by the negative rate of change.

Answer 8

Use the table to answer the question.

Number of Months Cost ($)
1 74
2 99
3 124
4 149
The table below shows the cost for a gym membership at the local fitness center with an initial start-up fee charged in the first month. Find the slope, or monthly cost.

(1 point)
Responses

$25
$25

$49
$49

$74
$74

$37.25
$37.25
Skip to navigation

Answer 9

To determine the monthly cost (slope) of the gym membership from the given table, we can analyze the change in cost over the change in months.

Data from the table:

• Month 1: Cost = $74
• Month 2: Cost = $99
• Month 3: Cost = $124
• Month 4: Cost = $149

Finding the slope (monthly cost):

The slope can be calculated using the formula:

\[ \text{Slope} = \frac{\text{Change in Cost}}{\text{Change in Months}} \]

To find the slope, we can take any two consecutive points. Let's use the first two points as an example:

• From Month 1 to Month 2:
  • Change in Cost = \(99 - 74 = 25\)
  • Change in Months = \(2 - 1 = 1\)

So the slope for these two points is:

\[ \text{Slope} = \frac{25}{1} = 25 \]

To confirm, we can check the slope between the other points as well:

• From Month 2 to Month 3:
  • Change in Cost = \(124 - 99 = 25\)
  • Change in Months = \(3 - 2 = 1\)

\[ \text{Slope} = \frac{25}{1} = 25 \]

• From Month 3 to Month 4:
  • Change in Cost = \(149 - 124 = 25\)
  • Change in Months = \(4 - 3 = 1\)

\[ \text{Slope} = \frac{25}{1} = 25 \]

Conclusion:

The monthly cost (slope) for the gym membership is consistently $25.

The correct answer is:

$25.

Answer 10

A linear graph of parking fees in dollars based on hours parked has the points (2,20)
and (6,44)
. How would you interpret the slope of the graph as the rate of change in the parking fee for each additional hour of parking?(1 point)
Responses

The parking fee rises by $10 with each additional hour.
The parking fee rises by $10 with each additional hour.

The parking fee rises by $8 with each additional hour.
The parking fee rises by $8 with each additional hour.

The parking fee rises by $6 with each additional hour.
The parking fee rises by $6 with each additional hour.

The parking fee rises by $7.33 with each additional hour.
The parking fee rises by $7.33 with each additional hour.

Answer 11

To determine how to interpret the slope of the graph as the rate of change in the parking fee per hour, we need to calculate the slope using the given points \((2, 20)\) and \((6, 44)\).

Finding the Slope:

The formula for the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points:

• \( (x_1, y_1) = (2, 20) \)
• \( (x_2, y_2) = (6, 44) \)

Calculate the changes:

1. Change in Parking Fee: \[ y_2 - y_1 = 44 - 20 = 24 \]

2. Change in Hours: \[ x_2 - x_1 = 6 - 2 = 4 \]

Calculate the slope:

\[ \text{Slope} = \frac{24}{4} = 6 \]

Interpretation:

The slope of \(6\) means that the parking fee rises by $6 for each additional hour of parking.

Conclusion:

The correct interpretation is:

The parking fee rises by $6 with each additional hour.