A local gym offers its members the opportunity to choose between two fitness classes: weight lifting and Pilates. Of the 350350350350 gym members, 175175175175 regularly attend weight lifting, 200200200200 regularly attend Pilates, and 100100100100 regularly attend weight lifting and Pilates. Using this information, answer each of the following questions.
Let be the event that a randomly selected gym member regularly attends weight lifting and be the event that a randomly selected gym member regularly attends Pilates.
What is P(W)P(W)P(W)P, left parenthesis, W, right parenthesis, the probability that a gym member attends weight lifting?
What is P(P)P(P)P(P)P, left parenthesis, P, right parenthesis, the probability that a gym member attends Pilates?
What is P(W and P)P(W\text{ and }P)P(W and P)P, left parenthesis, W, start text, space, a, n, d, space, end text, P, right parenthesis, the probability that a gym member attends weight lifting and Pilates?
What is P(W or P)P(W\text{ or }P)P(W or P)P, left parenthesis, W, start text, space, o, r, space, end text, P, right parenthesis, the probability that a gym member attends weight lifting or Pilates?

their is no graph showing

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

answer: b

step-by-step explanation: