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3 years ago

In the figure below, determine the perimeter of triangle EFG

Mathematics

1 answer:

Airida [17]3 years ago

3 0

Answer:

82 units

Step-by-step explanation:

From the image, we can see that the 2 triangles are similar triangles.

Thus:

BC = EF

BD = EG

CD = FG

Now, BD = 4x - 9 and EG = 2x + 15

Thus;

4x - 9 = 2x + 15

4x - 2x = 15 + 9

2x = 24

x = 24/2

x = 12

Thus, in triangle EFG where EG = 2x + 15, then EG = 2(12) + 15 = 39

Also, EF = BC = 17

FG = 26

Thus, perimeter of triangle EFG is;

P = 26 + 17 + 39

P = 82 units

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3 years ago

A random sample of medical files is used to estimate the proportion p of all people who have blood type B. (a) If you have no pr

GaryK [48]

Answer:

a) 752 medical files should be included.

b) 372 medical files should be included.

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.

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

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

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

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

Question a:

This is n for which M = 0.03. We have no estimate, so we use $\pi = 0.5$ . So

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

$0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}$

$0.03\sqrt{n} = 1.645*0.5$

$\sqrt{n} = \frac{1.645*0.5}{0.03}$

$(\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2$

$n = 751.67$

Rounding up:

752 medical files should be included.

Question b:

Now we have that:

$\pi = \frac{13}{90} = 0.1444$

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

$0.03 = 1.645\sqrt{\frac{0.1444*0.8556}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.1444*0.8556}$

$\sqrt{n} = \frac{1.645\sqrt{0.1444*0.8556}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.645\sqrt{0.1444*0.8556}}{0.03})^2$

$n = 371.5$

Rounding up:

372 medical files should be included.

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3 years ago