PLEASE HELP 100 PTS!

4.
(07.05 MC)

An equation is shown below:

5x + 3(x − 5) = 6x + 2x − 15

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points)

infinite solutions

Distributive Property

Step-by-step explanation:

5x + 3(x − 5) = 6x + 2x − 15

Distribute

5x+3x -15 = 6x+2x -15

Combine like terms

8x -15 = 8x-15

Subtract 8x from each side

8x-8x-15 = 8x-8x-15

-15=-15

This is always true so there are infinite solutions

We used the Distributive Property

And the Subtraction Property of Equality

A) all real values of x

B) distributive property

Step-by-step explanation:

A)

5x + 3(x − 5) = 6x + 2x − 15

5x + 3x - 15 = 8x - 15

8x - 15 = 8x - 15

-15 = -15

This is an identity, true for all real values of x

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560