Afootball coach is trying to decide: when a team is ahead late in the game, which strategy is better?

play the "regular" defense.

play a "prevent" defense that guards against long gains but makes short gains easier.

the coach reviews the outcomes of 100 games.

compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. draw a conclusion based on your results.

You are more likely to win by playing regular defense.

Step-by-step explanation:

Assume out of 100 reviewed games, there were 50 regular defense games and 50 prevent defense games. And out of 50 regular defense games, 38 were win, 12 were lose. And out of 50 prevent defense game, 29 were win, 21 were lose.

Probability to win the game by playing regular defense is:

P(win | regular) = 38/50 = 0.76

Probability to win the game by playing prevent defense is:

P(win | prevent) = 29/50 = 0.58

Since the probability of winning by regular defense game is more than prevent defense game (0.76 > 0.58), you are more likely to win by playing regular defense.

The probability of winning when playing regular defense is higher than the probability of winning with *prevent* defence.

Step-by-step explanation:

Let us assume that a total of 100 games were reviewed, 50 games were using regular defense method while the remaining 50 games were using the prevent defense method.

Out of the 50 regular defense games, 38 were win while 12 games were lose.

Out of 50 prevent defense game, 29 were win, while 21 games were lose.

The Probability of winning by regular defense is:

P(win by regular) = 38/50 = 0.76

Probability of winning by playing prevent defense is:

P(win by prevent) = 29/50 = 0.58

From the above analysis we observe that the probability of winning by using the regular defense method is greater than the probability of winning by prevent defense method.

That is 0.76 > 0.58.

Therefore, the team is more likely to win by using the regular defense method.

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

table 3 represents a direct variation function. : )