A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.(1 point)

Question

Responses

The quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 0.52 meters/second.

The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 1.08 meters/second.

The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.

The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.(1 point)
Responses

The quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 0.52 meters/second.

The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 1.08 meters/second.

The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.

The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.

Answer 1

To determine the average rate of change in the dolphin's position, we need to calculate the difference in position (displacement) and divide it by the time taken.

1. Calculate the displacement:

   • The dolphin reaches a height of 3.5 meters above the water and then dives to 10 meters below the water.
   • To represent the position relative to the water surface:
     • The height above the water is positive, so it's +3.5 meters.
     • The depth below the water is negative, so it's -10 meters.
   • The total displacement from the highest point to the lowest point is: \[ \text{Displacement} = -10 - 3.5 = -13.5 \text{ meters} \]

2. Calculate the time taken:

   • The time taken for this change in position is 12.5 seconds.

3. Calculate the average rate of change: \[ \text{Average Rate of Change} = \frac{\text{Displacement}}{\text{Time}} = \frac{-13.5 \text{ meters}}{12.5 \text{ seconds}} = -1.08 \text{ meters/second} \]

Thus, the quotient that describes the rate of change in the dolphin’s position is -1.08 meters/second.

The correct response is: The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.

Answer 2

A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.(1 point)
Responses

The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second.

The quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 3.47 meters/second.

The quotient that describes the average rate of change for the diver’s depth is −0.49 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.49 meters/second.

The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.

Answer 3

To calculate the average rate of change in the scuba diver's depth, we will find the total change in depth (displacement) and then divide that by the time taken for the change.

1. Calculate the initial and final depth:

   • The diver starts at a depth of 15 meters below the surface.
   • She descends 10 meters lower, which means her final depth is: \[ \text{Final Depth} = -15 - 10 = -25 \text{ meters} \]

2. Calculate the displacement:

   • The displacement is calculated as the difference between the final depth and the initial depth: \[ \text{Displacement} = \text{Final Depth} - \text{Initial Depth} = -25 - (-15) = -25 + 15 = -10 \text{ meters} \]

3. Calculate the time taken:

   • The time taken for the descent is 10.1 seconds.

4. Calculate the average rate of change: \[ \text{Average Rate of Change} = \frac{\text{Displacement}}{\text{Time}} = \frac{-10 \text{ meters}}{10.1 \text{ seconds}} \approx -0.9901 \text{ meters/second} \]

Rounding to the nearest hundredth: \[ \text{Average Rate of Change} \approx -0.99 \text{ meters/second} \]

Thus, the correct response is: The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.

Answer 4

Solve using division of rational numbers. If a car’s value decreases by $4,000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)(1 point)
Responses

0.003
0.003

−0.003
negative 0.003

−$333.33
negative 333.33 dollars

$333.33

Answer 5

To find the monthly decrease in the car's value, we need to divide the total decrease in value by the number of months.

1. Total decrease in value: \(-4000\) dollars (the negative sign indicates a decrease).
2. Total time period: 12 months.

Now, we can perform the division:

\[ \text{Monthly decrease} = \frac{-4000}{12} \]

Calculating this gives:

\[ \text{Monthly decrease} \approx -333.33 \text{ dollars} \]

Thus, the value of the car decreases by approximately \(-333.33\) dollars each month.

The correct response is: −$333.33 (negative 333.33 dollars)

Answer 6

It is recommended that hikers drink 24 ounces of water an hour. If a canteen has 24 ounces of water, how much should the amount of water in the canteen change every 10 minutes?(1 point)
Responses

−4 ounces
negative 4 ounces

4 ounces
4 ounces

0.4 ounces
0.4 ounces

−0.4 ounces
negative 0.4 ounces

Answer 7

To determine how much the amount of water in the canteen should change every 10 minutes, we need to find out how much water is recommended to be consumed in that time frame based on the hourly recommendation.

1. Water intake recommendation: 24 ounces per hour.
2. Time period for consumption: 10 minutes.

First, we need to convert 10 minutes into hours since the recommendation is given on an hourly basis:

\[ 10 \text{ minutes} = \frac{10}{60} \text{ hours} = \frac{1}{6} \text{ hours} \]

Now we can calculate how much water should be consumed in that \( \frac{1}{6} \) of an hour:

\[ \text{Water change in 10 minutes} = 24 \text{ ounces/hour} \times \frac{1}{6} \text{ hour} = 4 \text{ ounces} \]

Since the water is being consumed, this represents a decrease in the amount of water in the canteen. Therefore, the amount of water in the canteen should change by:

\[ -4 \text{ ounces} \]

Thus, the correct response is: −4 ounces (negative 4 ounces).