Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion. Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1
Choose 1

(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75

(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75

(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10

(Choice D)
D
18+0.08B \geq 1018+0.08B≥1018, plus, 0, point, 08, B, is greater than or equal to, 10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs

Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.

The inequality that represents the scenario is, and the smallest number of balls Carolina can buy is 713

Given that:

per ball

Let:

The amount (A) Carolina can spend on B balls is:

A = Entrance Fee + Rate * B

This gives:

To get $10, Carolina must spend $75 or more.

This means:

So, the inequality is:

The smallest number of balls is calculated as follows:

Collect like terms

Divide both sides by 0.08

Round up

Hence, the inequality is and the smallest number of balls is 713

Learn more about inequalities at:

link

Using a linear function, it is found that:

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The linear function for the cost of B paintballs has the following format:

In which

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Question 1:

Thus:

, given by option B.

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Question 2:

Rounding up, she has to buy at least 713 paintballs.

A similar problem is given at link

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week