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Use the Pythagorean theorem to find the unknown side of the right triangle.

Nesterboy [21]

The length of hypotenuse is 39.

Step-by-step explanation:

Given,

Vertical side = a = 15

Horizontal side = b = 36

Hypotenuse = c

Using pythagorean theorem

$a^2+b^2=c^2\\(15)^2+(36)^2=c^2\\225+1296=c^2\\1521=c^2\\c^2=1521$

Taking square root on both sides

$\sqrt{c^2}=\sqrt{1521}\\c=39$

The length of hypotenuse is 39.

Keywords: square root, addition

Learn more about square roots at:

#LearnwithBrainly

8 0

3 years ago

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time coll

ICE Princess25 [194]

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.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

The margin of error is:

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

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

(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.

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

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

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

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

$(\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}$

$n = 1036.03$

Rounding up

n = 1037.

(b) Assume prior studies have shown that about 55% of full-time students earn bachelor's degrees in four years or less.

$\pi = 0.55$

So

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

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

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

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

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

$n = 1025.7$

Rounding up

n = 1026.

6 0

3 years ago

Find the Quetion of the line that passes through the points (1,6) and (5,2)

NemiM [27]

Answer:

$y=-x+7$

Step-by-step explanation:

Equation of straight line is given as

$y-y_1=m(x-x_1)$

where slope m is calculated as

$m=\frac{y_2-y_1}{x_2-x_1}$

Here 

$(x_1, y_1)=(1, 6) \ \ and \ \ (x_21, y_2) = (5, 2)$

$m = \frac{2 - 6}{5 - 1}\\m=\frac{- 4}{4} \\m=-1$

Equation of line that passes through the points (1,6) and (5,2)

$y-6=-1(x-1)\\y=-x+7$

5 0

2 years ago

Gabriela Mistral was a poet, diplomat, teacher and humanitarian. Each week she worked a certain amount of days as a poet diploma

Ipatiy [6.2K]

Answer:

Gabriela Mistral works as a humanitarian for $8$ days.

Step-by-step explanation:

Gabriela Mistral was a poet, diplomat, teacher and humanitarian such that each week she worked a certain amount of days as a poet diplomat teacher and humanitarian.

Ratio is $1:1:3:2$