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3 years ago

The perimeter of a semi circle is 5.14 km. What is the semi circles diameter.

Mathematics

1 answer:

White raven [17]3 years ago

6 0

Diameter of semicircle is equal to 2 km.

<h3>Explanation:</h3>

Given: Perimeter of semicircle = P = 5.14 km

d=?

Perimeter of semicircle is given by

$P = (\pi \times r ) + d\\5.14 = (\pi \times r ) + d\\\\Since \ d=2r; \ r=\frac{d}{2} \\5.14 = (\pi \times \frac{d}{2}) + d\\$

Simplifying the above equation

$5.14 = ( \frac{(\pi \times d) + 2d}{2}) \\\\5.14 \times 2 = d(\pi +2)\\\\d=\frac{5.14 \times 2}{\pi +2 }\\$

As value of pi = 3.14, equation becomes

$d=\frac{5.14 \times 2}{\ 3.14 +2} = \frac{10.28}{5.14} =2 \ km$

Diameter of semicircle is equal to 2 km.

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The American Bankers Association reported that, in a sample of 120 consumer purchases in France, 48 were made with cash, compare

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Step-by-step explanation:

Hello!

You have the information for two variables

X₁: Number of consumer purchases in France that were made with cash, in a sample of 120.

n₁= 120 consumer purchases

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p'₁= 48/120= 0.4

X₂: Number of consumer purchases in the US that were made with cash, in a sample of 55.

n₂= 55 consumer purchases

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p'₂= 24/55= 0.4364

You need to construct a 90% CI for the difference of proportions p₁-p₂

Using the central limit theorem you can approximate the distribution of both sample proportions p'₁ and p'₂ to normal, so the statistic to use to estimate the difference of proportions is an approximate standard normal:

[(p'₁-p'₂) ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'_1(1-p'_1)}{n_1} +\frac{p'_2(1-p'_2)}{n_2} }$ ]

$Z_{0.95}= 1.648$

[(0.4-0.4364)±1.648 * $\sqrt{\frac{0.4(1-0.4)}{120} +\frac{0.4364(1-0.4364)}{55} }$ ]

[-0.1689;0.0961]

The interval has a negative bond, it is ok, keep in mind that even tough proportions take values between 0 and 1, in this case, the confidence interval estimates the difference between the two proportions. It is valid for one of the bonds or the two bonds of the CI for the difference between population proportions to be negative.

I hope this helps!

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3 years ago

00:36:46

miskamm [114]

Question:

In some code, letters a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. We just do not know which letter represents which number. Consider the following relationships:

a + c = e,

b – d = d and

e + a = b

Which of the following statements is true?

(A) b = 4, d = 2

(B) a = 4, e = 6

(D) a = 4, c = 6

Answer:

(B) a = 4, e = 6 is the correct answer.

Explanation:

(A) b = 4, d = 2

a + c = e => a + c = e

b – d = d => 4 - 2 = 2

e + a = b => e + a = 4

We are not able to find out what will be at place of a , c , e by which all other relationships are not getting satisfied. And if we apply numbers by hit and trial they are not getting satisfied.

(B) a = 4, e = 6

a + c = e => 4 + c = 6 => 4 + 2 = 6

b – d = d => b - d = d => 10 - 5 = 5

e + a = b => 6 + 4 = 10

We were able to find all a , b , c , d , e and it satisfies all relationships given.

a + c = e => a + c = 2

b – d = d => 6 - d = d

e + a = b => e + a = 6

We are not able to find out what will be at place of a , c , d by which all other relationships are not getting satisfied. And if we apply numbers by hit and trial they are not getting satisfied.

(D) a = 4, c = 6

a + c = e => 4 + 6 = 10

b – d = d => b - d = d

e + a = b => e + 4 = b => 10 + 4 = 14(this is not from the numbers as given in question so b can't be equal to 14)

We got stuck at the value of b which was 14 and not given in question so, we can leave this option in between as it is not satisfying the relationships.

Therefore, (B) a = 4, e = 6 is the correct answer.

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3 years ago