Need help on 41-44 please

In ∆PQR, PQ = 39 cm and PN is an altitude. Find PR if QN = 36 cm and RN = 8 cm.

OLEGan [10]

Use the Pythagorean theorem two times:

$NQ^2+NP^2=QP^2\\\\36^2+h^2=39^2\\\\1296+h^2=1521\qquad\text{subtract 1521 from both sides}\\\\h^2=225\to h=\sqrt{225}\\\\\boxed{h=15\ cm}$

second time:

$PR^2=RN^2+NP^2\\\\x^2=8^2+15^2\\\\x^2=64+225\\\\x^2=289\to x=\sqrt{289}\\\\\boxed{x=17\ cm}$

<h3>Answer: PR = 17 cm.</h3>

8 0

3 years ago

Read 2 more answers

Total tax: 0.05(50 + 40)

Elenna [48]

Answer:

i think it's 4.5

7 0

3 years ago

What is the sum of all exterior angles of a megagon

EastWind [94]

Step-by-step explanation:

A regular megagon is repr {1,000,000} and can be constructed as a truncated 500,000-gon, t{500,000}, a twice-truncated 250,000-gon, tt{250,000}, a thrice-truncated 125,000-gon, ttt{125,000}, or a four-fold-truncated 62,500-gon, tttt{62,500}, a five-fold-truncated 31,250-gon, ttttt{31,250}, or a six-fold-truncated 15,625-gon, tttttt{15,625}. A regular megagon has an interior angle of 179.99964°. The area of a regular megagon with sides of length a is given by

Please Give Brainliest!One of my brainliest Answers were deleted since the question got deleted!

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4 0

3 years ago

A directed line segment starts at (1.0) and ends at (4.6), Point R partitions the segment

MrRissso [65]

9514 1404 393

Answer:

(3.4)

Step-by-step explanation:

The length of the given segment is 4.6 -1.0 = 3.6. The first portion of the division will be 2/(2+1) = 2/3 of that length, or (2/3)(3.6) = 2.4.

Then the coordinates of point R are ...

(1.0) +(2.4) = (3.4)

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<em>Additional comment</em>

We cannot tell if your coordinates are supposed to be Cartesian coordinates (1, 0) and (4, 6), or if they are points on a number line. As it happens, it makes no difference. The final answer is interpreted the same way the given coordinate points are interpreted: 3.4 on a number line or (3, 4) on a plane.

6 0

3 years ago

According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY

wel

Answer:

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

Step-by-step explanation:

Proportion of all children in the United States who currently live with at least one grandparent is higher than 11%

This means that the null hypothesis is:

$H_0: p = 0.11$

And the alternate hypothesis is:

$H_a: p > 0.11$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.11 is tested at the null hypothesis:

This means that $\mu = 0.11, \sigma = \sqrt{0.11*0.89}$

Suppose that in a recent sample of 1550 children, 214 were found to be living with at least one grandparent.

This means that:

$n = 1550, X = \frac{214}{1550} = 0.1381$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.1381 - 0.11}{\frac{\sqrt{0.11*0.89}}{\sqrt{1550}}}$

$z = 3.54$

Pvalue of the test and decision:

This is the probability of finding a sample proportion above 0.1381, which is 1 subtracted by the pvalue of Z = 3.54.

$z = 3.54$ has a pvalue of 0.9999

1 - 0.9999 = 0.0001

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

8 0

3 years ago