Question

The number of sports drinks in a cooler during practice is modeled by the equation y=648-24x where y is the number of ounces in the cooler after practice and x is the number of players at the practice who take drinks from the cooler.

Part A
Based on the information in the equation, press the hotspots of three statements that are true.
Hint: 648 is the starting point.
-24 is the slope (rate of change).

Answer 1

A,C,C,E

Explanation:

Answer 2

Hello!

The answers are:

B. Before practice, there are 648 ounces of sports drink in the cooler.

C. Each plater drinks approximately 24 ounces of sports drink at practice.

E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.

Why?

We are given the equation:

`y=f(x)=648-24x`

Let's discard each of the given options in order to find the three correct options.

A. The cooler is meant to be used only by 24 players: False.

If we want to calculate how many players can use the cooler, we need to isolate "x" (rate of change) from the given equation, so, isolating we have:

`f(x)=648-24x`

`0=648-24x`

`648=24x\\\\24x=648\\\\x=(648)/(24)=27`

We have that the cooler can be used by 27 players, so, the first option that states that "The cooler is meant to be used only by 24 players" is false.

B. Before practice, there are 648 ounces of sports drink in the cooler: True.

We have that before the practice when the cooler is not being used by any player (or there is no any player) has 648 ounces (full), we can calculate it making the variable "x" equal to 0, so, calculating we have:

`f(x)=648-24x`

`f(0)=648-24*(0)=648`

Therefore, we have that the statement "Before practice, there are 648 ounces of sports drink in the cooler." is true.

C. Each plater drinks approximately 24 ounces of sports drink at practice: True.

From the statement, we know that the rate of change is equal to (-24), and it's equal to the number of ounces that each player drinks.

Hence, we have that the statement "Each plater drinks approximately 24 ounces of sports drink at practice." is true.

D. If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink: False.

If we want to calculate the number of ounces that 24 players will drink, we need to use the slope value. If we know that each player drinks 24 ounces, so, to calculate how many ounces of sports drink will 24 players drink, we need to use the following equation:

`DrankOunces=24oz*Players\\\\DrankOunces=24oz*24=576oz`

We have that 24 players will drink a total of 576 ounces, so, the statement "If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink." is false.

E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice: True.

From the statement and the equation, we know that the slope (rate of change) is negative, meaning that for each player (x) it will be 24 fewer ounces of sports drink after practice, for example, calculating for 1 and 2 players, we have:

`f(1)=648-24*1=624`

`f(x)=648-24*2=600`

We can see that for each player, it will be 24 fewer ounces of sports drink after practice.

Hence, we have that the statement "For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice." is true.

Therefore, the correct options are:

B. Before practice, there are 648 ounces of sports drink in the cooler.

C. Each plater drinks approximately 24 ounces of sports drink at practice.

E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.

Have a nice day!