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raketka [301]
3 years ago
8

If angle PQR and angle RQS form a linear pair and angle PQR =5x+5 and angle RQS =11x-65 then angle PQR=?

Mathematics
1 answer:
Mama L [17]3 years ago
3 0

Answer:

m<PQR = 80°

Step-by-step explanation:

<u>Points to remember</u>

Sum angles in a linear pair is 180

<u>To find the value of x</u>

It is given that, angle PQR and angle RQS are linear pairs, and

m< PQR =5x+5 and m<RQS =11x-65

m<PQR + m<RQS = 180

5x + 5 + 11x - 65 = 180

16x -60 = 180

16x = 180 + 60

16x = 240

x = 15

<u>To find the value of angle PQR</u>

m<PQR = 5x + 5

 = 5*15 + 5

 = 75 + 5 = 80

Therefore m<PQR = 80°

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Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a
tigry1 [53]

Answer:

SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58

ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073

\bar X - ME = 237- 14.073 = 222.927

\bar X + ME = 237+ 14.073 = 251.073

n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238

So the answer for this case would be n=238 rounded up to the nearest integer

Null hypothesis:\mu \geq 247  

Alternative hypothesis:\mu  

z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165  

p_v =P(z  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

Step-by-step explanation:

For this case we have the following data given:

\bar X =237 represent the sample mean

\sigma = 47 represent the population deviation

n =30 represent the sample size selected

\mu_0 = 247 represent the value that we want to test.

The standard error for this case is given by:

SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58

For the 90% confidence the value of the significance is given by \alpha=1-0.9 = 0.1 and \alpha/2 = 0.05 so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:

z_{\alpha/2}= 1.64

And the margin of error would be:

ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073

The confidence interval for this case would be given by:

\bar X - ME = 237- 14.073 = 222.927

\bar X + ME = 237+ 14.073 = 251.073

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

Replacing into formula (b) we got:

n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238

So the answer for this case would be n=238 rounded up to the nearest integer

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:  

Null hypothesis:\mu \geq 247  

Alternative hypothesis:\mu  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165  

P-value  

Since is a left tailed test the p value would be:  

p_v =P(z  

Conclusion  

If we compare the p value and the significance level given \alpha=0.1 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

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Relative max on (2)
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mrs Moore worked 42 hours and 35 minutes last week. How many hours and minutes did she average in each of the five days?
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Answer:

6.08333333 hours

Step-by-step explanation:

((42 hours) + (35 minutes)) / 7 = 6.08333333 hours

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3 years ago
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Mr. Suárez wants to paint his storage shed. He needs to calculate the lateral surface area of the shed so
astraxan [27]

Answer:

Lateral surface area of the storage shed = 336 ft²

Step-by-step explanation:

The shed is in the shape of a rectangular prism. The lateral surface area of the storage shed can be calculated below. The lateral area is the sides of the prism.

lateral area of a rectangular prism = 2h (l + w)

where

l = length

h = height

w = width

h = 8 ft

l = 14 ft

w = 7 ft

lateral area of a rectangular prism = 2h (l + w)

lateral area of a rectangular prism = 2 × 8 × (14 + 7)

lateral area of a rectangular prism = 16 (21)

lateral area of a rectangular prism = 336 ft²

Lateral surface area of the storage shed = 336 ft²

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2 years ago
Jennifer is playing with a die that has six faces. What is the likelihood that she will roll a four?
Ymorist [56]
The likely hood would be1 out of 6
7 0
3 years ago
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