Question

1. an aquarium is being filled at a rate of 2.5 inches per second. the equation ( y = 2.5x ) is used to determine the height after ( x ) seconds. find the domain and range of the situation if it takes 60 seconds to fill the aquarium.
2. the total cost for buying new sneakers for the basketball team can be found by using the function ( y = 25x + 85 ), where ( x ) is the number of players. if between 9 and 16 players need new sneakers, find the domain and range of this situation.
3. the total cost for attending the state fair can be found using the function ( y = 15 + 2.5x ), where ( x ) is the number of food tickets purchased. if a family purchases between 5 and 10 food tickets, what is the domain and range of this situation?
4. student council is selling candy grams. they are using the formula ( y = 2.5x ) to determine ( y ), the profit earned, for ( x ) candy grams. they have to sell between 55 and 60 candy grams to meet their goal. find the domain and range of the situation.
5. the formula ( x + y = 180 ) can be used to find the degrees of supplementary angles, where ( x ) is the smaller angle. find the domain and range of this situation.
6. a local carpenter uses the function ( y = 180x ) to determine the amount earned, ( y ), for each bookcase sold. he has to sell between 5 and 10 bookcases each month in order to meet his sales goal. find the domain and range of this situation.
7. the height in inches of concrete being poured for a foundation can be found using the function ( y = 15 + 2.5x ), where ( x ) is the number of minutes. if the concrete is poured between 5 and 10 minutes, find the domain and range of this situation.
8. the total distance for traveling to a local conference can be found by using the function ( y = 25x + 85 ), where ( x ) is the number of miles driven. if most employees drive between 9 and 16 miles, find the domain and range of this situation.

options:
a. domain: ( 0 < x < 180 ), range: ( 0 < y < 180 );
b. domain: ( 9 leq x leq 16 ), range: ( 290 leq y leq 485 );
c. domain: ( {55, 56, 57, 58, 59, 60} ), range: ( {137.5, 140, 142.5, 145, 147.5, 150} );
d. domain: ( 5 leq x leq 10 ), range: ( 27.5 leq y leq 40 );
e. domain: ( 0 leq x leq 60 ), range: ( 0 leq y leq 150 );
f. domain: ( {5, 6, 7, 8, 9, 10} ), range: ( {900, 1080, 1260, 1440, 1620, 1800} );
g. domain: ( {9, 10, 11, 12, 13, 14, 15, 16} ), range: ( {290, 315, 340, 365, 415, 440, 465} );
h. domain: ( {5, 6, 7, 8, 9, 10} ), range: ( {27.5, 30, 32.5, 35, 37.5, 40} )

Explanation:

Problem 1:

Step1: Determine domain

The aquarium fills in 60 seconds, so \( x \) (time in seconds) ranges from \( 0 \) to \( 60 \), inclusive. So domain: \( 0 \leq x \leq 60 \).

Step2: Determine range

The function is \( y = 2.5x \). When \( x = 0 \), \( y = 0 \); when \( x = 60 \), \( y = 2.5\times60 = 150 \). So range: \( 0 \leq y \leq 150 \).

Step1: Determine domain

Number of players \( x \) is between \( 9 \) and \( 16 \), inclusive. So domain: \( 9 \leq x \leq 16 \).

Step2: Determine range

Function \( y = 25x + 85 \). When \( x = 9 \), \( y = 25\times9 + 85 = 225 + 85 = 310 \)? Wait, no, maybe typo? Wait, if \( x \) is 9 to 16, when \( x = 9 \), \( y = 25(9)+85 = 225 + 85 = 310 \)? But option B has range \( 290 \leq y \leq 485 \). Wait, maybe \( x \) is 9 to 16, \( y = 25x + 85 \). When \( x = 9 \), \( y = 25*9 + 85 = 225 + 85 = 310 \)? No, maybe the function is \( y = 25x + 85 \), if \( x \) is 9 to 16: \( x = 9 \), \( y = 25*9+85 = 310 \); \( x = 16 \), \( y = 25*16 + 85 = 400 + 85 = 485 \). But option B has domain \( 9 \leq x \leq 16 \), range \( 290 \leq y \leq 485 \). Maybe a miscalculation. Anyway, matching domain \( 9 \leq x \leq 16 \) with option B.

Step1: Determine domain

Number of food tickets \( x \) is between \( 5 \) and \( 10 \), inclusive (integers, since tickets are whole). So domain: \( \{5,6,7,8,9,10\} \).

Step2: Determine range

Function \( y = 15 + 2.5x \). For \( x = 5 \): \( y = 15 + 12.5 = 27.5 \); \( x = 6 \): \( 15 + 15 = 30 \); \( x = 7 \): \( 15 + 17.5 = 32.5 \); \( x = 8 \): \( 15 + 20 = 35 \); \( x = 9 \): \( 15 + 22.5 = 37.5 \); \( x = 10 \): \( 15 + 25 = 40 \). So range: \( \{27.5,30,32.5,35,37.5,40\} \), which matches option H.

Answer:

E (Domain: \( 0 \leq x \leq 60 \), Range: \( 0 \leq y \leq 150 \))

Problem 2: