First, we distribute the 2 through the parenthesis.
3x+2x+8=5(x+1)+3
Then we distribute the 5 through the parenthesis
3x+2x+8=5x+5+3
Collect the like terms
5x+8=5x+5+3
Add the numbers
5x+8=5x+8
The statement is true for any value of x, because both sides are identical
1. Each shelf holds 5 hermit-crab cages. There are 23 hermit crab cages to be displayed. Divide the number of hermit crab cages to be displayed by the number of hermit crab cages that can be displayed on each shelf:

This means that you need 5 shelves (4 shelves is not enough, because 3 hermit crab cages will be not displayed).
2. Each shelf holds 3 hermit-crab care booklets. There are 12 hermit-crab care booklets to be displayed. Divide the number of hermit-crab care booklets to be displayed by the number of hermit-crab care booklets that can be displayed on each shelf:

This means that you need 4 shelves.
Answer: first, you have to divide 23 by 5 and find the quotient and remainder and divide 12 by 3 and find the quotient and remainder. Then you have to determine the number of shelves needed. You need 5 shelves.
5 times -3 = -15
17 - (-15) = 32
B.32
P/90 = 4/18
18P = 90*4 [cross-multiplication]
P = 360/18
P = 20
So, answer is P equals to 20
Using the binomial distribution, it is found that the expected values are given by:
a) 120.
b) 150.
<h3>What is the binomial probability distribution?</h3>
It is the probability of <u>exactly x successes on n repeated trials, with p probability</u> of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
In this problem, for both items, we consider that the number cube is rolled 180 times, hence n = 180.
Item a:
4 of the 6 possible values are greater than 2, hence p = 4/6 = 2/3.
The expected value is given by:
E(X) = 180 x 2/3 = 120.
Item b:
5 of the 6 values are less than 6, hence p = 5/6.
The expected value is given by:
E(X) = 180 x 5/6 = 150.
More can be learned about the binomial distribution at brainly.com/question/24863377