21. Which two ratios can be represented by a ratio of 7 to 12? A the ratio of shells to rocks if there are 7 rocks and 12 shells
B the ratio of shoes to dresses if there are 7 dresses and 12 shoes
c the ratio of shots made to shots taken if 7 out of 12 shots taken are made
D the ratio of sick patients to total patients if there are 7 sick patients and 12 healthy patients
E the ratio of small dogs to big dogs if there are 7 small dogs and 12 big dogs
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c the ratio of shots made to shots taken if 7 out of 12 shots taken are made

E the ratio of small dogs to big dogs if there are 7 small dogs and 12 big dogs

Step-by-step explanation:

Ratio of a to b:

The ratio of a to b is given by a divided by b.

A the ratio of shells to rocks if there are 7 rocks and 12 shells

12 shells and 7 rocks, so this ratio is 12 to 7.

B the ratio of shoes to dresses if there are 7 dresses and 12 shoes

12 shoes and 7 dresses, so this ratio is 12 to 7.

c the ratio of shots made to shots taken if 7 out of 12 shots taken are made

7 shots made out of 12 taken, so this ratio is 7 to 12, and c is one of the correct options.

D the ratio of sick patients to total patients if there are 7 sick patients and 12 healthy patients

7 sick patients

7 + 12 = 19 total patients

So this ratio is 7 to 19

E the ratio of small dogs to big dogs if there are 7 small dogs and 12 big dogs

7 small dogs and 12 big dogs, so this ratio is 7 to 12, and e is the other correct option.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24