A whale is swimming at a current depth of 15 meters below the surface. It swims up toward the surface and arrives there 9.5 seconds later. Find the quotient that best describes the rate of change in the whale’s depth. Give your answer to the nearest hundredth.

Question

The quotient that best represents the rate of change in the whale’s depth is
meters/second.

Answer 1

To find the rate of change in the whale's depth, we first need to determine how much the whale ascended and then divide that by the time taken.

1. Initial depth: \( -15 \) meters (below the surface, we can take this as negative).
2. Final depth at the surface: \( 0 \) meters.
3. Change in depth:

\[ \text{Change in depth} = \text{Final depth} - \text{Initial depth} \] \[ = 0 - (-15) = 15 \text{ meters} \]

4. Time taken: \( 9.5 \) seconds.

5. Rate of change in depth:

\[ \text{Rate of change} = \frac{\text{Change in depth}}{\text{Time}} = \frac{15 \text{ meters}}{9.5 \text{ seconds}} \]

Now we perform the division:

\[ \frac{15}{9.5} \approx 1.5789473684210527 \]

Rounding to the nearest hundredth:

\[ \approx 1.58 \]

Thus, the quotient that best represents the rate of change in the whale’s depth is \( \boxed{1.58} \) meters/second.

Answer 2

Solve using division of rational numbers. If a car’s value decreases by $2,500 in the first 6 months, how much does the value decrease per month? (Round to the nearest hundredth.)

Answer 3

To find the amount by which the car's value decreases per month, we need to divide the total decrease in value by the number of months.

Given:

• Total decrease in value = $2,500
• Time period = 6 months

Now, we perform the division:

\[ \text{Decrease per month} = \frac{\text{Total decrease}}{\text{Number of months}} = \frac{2500}{6} \]

Calculating the division:

\[ \frac{2500}{6} \approx 416.6666666666667 \]

Now, rounding to the nearest hundredth:

\[ \approx 416.67 \]

Thus, the value of the car decreases by approximately \( \boxed{416.67} \) dollars per month.

Answer 4

A restaurant uses a 15-pound bag of flour in 4 days. Each day, the bag of flour gets lighter as more flour is used. How much does the average amount of flour in the bag change each day? (Round to the nearest hundredth.)
pounds

Answer 5

To calculate the average amount of flour used each day, we need to divide the total amount of flour in the bag by the number of days it lasts.

Given:

• Total amount of flour = 15 pounds
• Duration = 4 days

Now, we perform the calculation:

\[ \text{Average amount of flour used per day} = \frac{\text{Total amount of flour}}{\text{Number of days}} = \frac{15 \text{ pounds}}{4 \text{ days}} \]

Calculating the division:

\[ \frac{15}{4} = 3.75 \]

Thus, the average amount of flour in the bag that gets lighter each day is approximately \( \boxed{3.75} \) pounds.