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Law Incorporation [45]
3 years ago
5

A rectangle is twice as long as it is wide. if its length is increase by 4 cm and its width is decreased by 3 cm, the new rectan

gle formed has an area of 100 cm2 . find the dimensions of the original rectangle.
Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0
Now the width is w.
It's twice as long as wide, so now the length is 2w.

If the length is increased by 4 cm, the length will be 2w + 4.
The width is decreased by 3 cm, so the width will be w - 3.

The are of the new rectangle is 100 cm^2.

area = length * width

area = (2w + 4)(w - 3)

The area of the new rectangle is 100, so we get

(2w + 4)((w - 3) = 100

2w^2 - 6w + 4w - 12 = 100

2w^2 - 2w - 112 = 0

w^2 - w - 56 = 0

(w - 8)(w + 7) = 0

w - 8 = 0   or   w + 7 = 0

w = 8   or   w = -7

A width cannot be negative, so discard w = -7.

w = 8

The width is 8 cm.
The length is twice the width, so the length is 16 cm.
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Answer:5in

Step-by-step explanation:

1. Identify the triangle

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2. solve (if not done with 3,4,5 triple)

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1 year ago
g 78% of all Millennials drink Starbucks coffee at least once a week. Suppose a random sample of 50 Millennials will be selected
Tatiana [17]

Answer:

We know that n = 50 and p =0.78.

We need to check the conditions in order to use the normal approximation.

np=50*0.78=39  \geq 10

n(1-p)=50*(1-0.78)=11 \geq 10

Since both conditions are satisfied we can use the normal approximation and the distribution for the proportion is given by:

p \sim N (p, \sqrt{\frac{p(1-p)}{n}})

With the following parameters:

\mu_ p = 0.78

\sigma_p = \sqrt{\frac{0.78*(1-0.78)}{50}}= 0.0586

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

We know that n = 50 and p =0.78.

We need to check the conditions in order to use the normal approximation.

np=50*0.78=39  \geq 10

n(1-p)=50*(1-0.78)=11 \geq 10

Since both conditions are satisfied we can use the normal approximation and the distribution for the proportion is given by:

p \sim N (p, \sqrt{\frac{p(1-p)}{n}})

With the following parameters:

\mu_ p = 0.78

\sigma_p = \sqrt{\frac{0.78*(1-0.78)}{50}}= 0.0586

6 0
3 years ago
Can anyone help me pls. Show your work.
nekit [7.7K]

Answer:Do you have a pic of the map? It would  make it easier to solve if I could see the map. Its basic area. A=base times height. If the park is 50 m long and is a square, you would do 50 times 50=2500

tep-by-step explanation:

4 0
3 years ago
Read 2 more answers
If julie needs 3 14_ cups of oatmeal, how many 1_ 4 cups of oatmeal will she use?
nydimaria [60]
She will use 13  there are four 1/4 per cup 4 times 3 plus 1 =13
3 0
3 years ago
What is the answers to this problem? Please help!!
Allushta [10]

Answer:

a = 31.7

c = 39.1

Step-by-step explanation:

tan54 = a / 23

a = 23 * tg54

a = 31.7

sin54 = 31.7 / c

c = 31.7 / sin54

c = 39.1

:)

5 0
2 years ago
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