Abaseball team played 32 games and lost 8 katy was the catcher in 5/8 of the winning games and 1/4 of the losing games

a. Fraction of games won by team is .

b. Total games played by Katy as catcher is 17.

Step-by-step explanation:

Here is the complete question: A baseball team played 32 games and lost 8 Katy was the catcher in 5/8 of the winning games and 1/4 of the losing games.

a. What fraction of the games did the team win?

b. In how many games did Katy play catcher?

Given: Total number of games= 32

           Total games lost= 8.

           Katy was the catcher in 5/8 of the winning games.

           Katy was the catcher in 1/4 of the losing games.

Now, finding total number games that team won.

Winning total=

∴ Total number of games that team won is 24.

Next finding fraction of the games did the team win.

Fraction of games won by team is

∴ Fraction of games won by team =

Fraction of games won by team is

Lets find out numbers of games Katy play chatcher.

We know, Katy was the catcher in 5/8 of the winning games.

∴ Katy was catcher=

Katy was catcher in 15 of the wining games.

We also know, Katy was the catcher in 1/4 of the losing games.

∴ Katy was catcher=

Katy was the catcher in 2 of the losing games.

Total games played by Katy as catcher= Catcher in wining games+ catcher in losing games.

∴ Total games played by Katy as catcher=

Hence, total games played by Katy as catcher is 17.

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

the f

last graph i believe

step-by-step explanation:

worked it out i believe