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nordsb [41]
3 years ago
7

Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house. The length

of his patio, the side along the house, is 6 feet longer than twice its width. Find the length and width of the patio.

Mathematics
1 answer:
podryga [215]3 years ago
3 0

Answer:

The length of the patio is 32 ft and the width is 13 ft

Step-by-step explanation:

see the attached figure to better understand the problem

Let

L ----> the length of his patio

W ---> the width of his patio

we know that

L+2W=58 ----> equation A

L=2W+6 ----> equation B

substitute equation B in equation A and solve for W

2W+6+2W=58

4W+6=58

4W=58-6

4W=52

W=13\ ft

Find the value of L

L=2W+6  ----> L=2(13)+6=32\ ft

therefore

The length of the patio is 32 ft and the width is 13 ft

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There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3
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Answer:

0.4 ; 0.6125

Step-by-step explanation:

Given the following :

Bag 1 : 75 red ; 25 blue

Bag 2: 60 red ; 40 blue

Bag 3: 45 red ; 55 blue

Probability = (required outcome / Total possible outcomes)

A) since the probability of choosing each bag is equal :

BAG A:

P(choosing bag A) = 1 / total number of bags = 1/3 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (1/3 × 75/100) = 25/300

BAG B:

P(choosing bag B) = 1/3 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (1/3 × 40/100) = 40/300

BAG C:

P(choosing bag C) = 1/3

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (1/3 × 55/100) = 55/300

= (25/300) × (40/300) × (55/300) = (25 + 40 + 55)/300 = 120/300 = 0.4

2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each?

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P(choosing bag A) = 0.5 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (0.5 × 75/100) = (0.5 * 0.75) = 0.375

BAG B:

P(choosing bag B) = (1-0.5) / 2 = 0.25 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (0.25 × 40/100) = (0.25 × 0.4) = 0.1

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P(choosing bag C) = (1 - (0.5+0.25)) = 0.25

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

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