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3 years ago

A rectangle has a perimeter of 48 cm and a width of 6 cm. Use the formula P=2ℓ+2w to find the length.

Mathematics

2 answers:

mr Goodwill [35]3 years ago

6 0

Answer:

a.ℓ=(P/2)-w, b.ℓ=18 cm

Step-by-step explanation:

Hello

I can help you with this one

Let

perimeter=2ℓ+2w

perimeter=48 cm

width=6 cm

Step one

a. Write the formula in terms of ℓ, it means that ℓ must be isolated

P=2ℓ+2w

subtract 2w in both sides

P-2w=2ℓ+2w-2w

P-2w=2ℓ

divide both sides by 2

(P-2w)/2=2ℓ/2

(P/2)-w=ℓ

ℓ=(P/2)-w

Step two

b.Substitute the clues you are given into the rearranged formula.

replace the values

ℓ=(P/2)-w

ℓ=(48 cm /2)-6 cm

ℓ=24 cm - 6 cm

ℓ=18 cm

Have a good day

Vinil7 [7]3 years ago

5 0

Answer:the length is equal to 18. 2l+2w= 12+?=48. 48-12=36, 36/2=18

Step-by-step explanation:

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Answer:

a) n = 1037.

b) n = 1026.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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(a) Assume that nothing is known about the percentage to be estimated.

We need to find n when M = 0.04.

We dont know the percentage to be estimated, so we use $\pi = 0.5$ , which is when we are going to need the largest sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 2.575*0.5$

$(\sqrt{n}) = \frac{2.575*0.5}{0.04}$

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$n = 1036.03$

Rounding up

n = 1037.

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$\pi = 0.55$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 2.575\sqrt{\frac{0.55*0.45}{n}}$

$0.04\sqrt{n} = 2.575*\sqrt{0.55*0.45}$

$(\sqrt{n}) = \frac{2.575*\sqrt{0.55*0.45}}{0.04}$

$(\sqrt{n})^{2} = (\frac{2.575*\sqrt{0.55*0.45}}{0.04})^{2}$

$n = 1025.7$

Rounding up

n = 1026.

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