A horse trainer is putting up a fence for the horse she trains. the trainer has purchased enough wood to build 1,500 feet of fence . to give the horses room to run , the trainer wants the lenght of the fence to be at least twice its width.

Which system of linear equalities describes the conditions in this problem?

a) 2w + 2l ≤ 1500 , l ≤ 2w

b) 2w + 2l ≥ 1500 , l ≤ 2w

c) 2w+2l ≤ 1500, l ≥ 2w

d) 2w + 2l ≥1500, l ≥2w

Horse trainer would put a fence in the rectangular shape as given in the below diagram:

As given in the first condition that fence length can be maximum 1500 foot as that is maximum wood available.

Length of the fence from the above diagram = 2 (length) + 2 (width)

= 2l + 2w

So, 2l+2w (length of fence) should be less than or equal to 1500 foot. This can be written in equation form:

2w + 2l ≤ 1500------First Equation.

In second condition, it is given that length should be at least twice of the width i.e. in other words length (l) is equal to or greater than twice of width (w). This can be written in equation form as below:

l ≥ 2w ------Second Equation

So from first and second equation, we can say system of linear equalities describes the conditions in this problem are

2w+2l ≤ 1500, l ≥ 2w Answer is (c)

Question-2

The theoretical probability of undesirable side effects resulting from taking Pyrene is 1 in 15. If 210 people take Pyrene to relieve congestion, theoretically how many will encounter undesirable side effects?

Probability of side effects resulting from taking Pyrene = 1/15

So, number of people who theoretically encounter undesirable side effects are

= Probability * Number of people

= (1/15) * 210

= 14 Answer

So, 14 people are expected to encounter undesirable side effects out of 210.

Question-3

Q A bag contains 5 yellow marbles, 16 green marbles, and 2 red marbles. What is the chance of drawing a yellow marble? If a red marble is drawn the first time and then a second marble is drawn without replacement, what is the probability of drawing a green marble? Give solutions exactly in reduced fraction form, separated by a comma.

ANSWERS

Yellow Marbles = 5;

Green Marbles = 16;

Red Marbles = 2

Total Marbles = 5+16+2 = 23

Chance of drawing a yellow marble:

Probability of drawing a yellow marble = favorable outcomes/ total outcomes

= 5 / 23

Probability of drawing a green marble, when a red marble has been already withdrawn without replacement:

After red marble is drawn, remaining total marbles are 22.

Drawing a green marble, so favorable outcomes = 16

So, probability of drawing a green marble = 16/22 = 8/11

So, answers are 5/23, 8/11