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3 years ago

In the following diagram, HI is parallel to JK. What is the measure of x?

Mathematics

2 answers:

Vilka [71]3 years ago

8 0

Answer:

Step-by-step explanation:

find the missing angle in triangle HAI =60.

VERTICALLY OPPOSITE ANGLES ARE EQUAL.=60

Angle x is alternating with the angle.

Degger [83]3 years ago

5 0

Answer:

$x = 60 \: \: degrees$

Step-by-step explanation:

<h3>Lets take LAH angle as 'y'</h3>

$61 + 59 + y = 180 \\ 120 + y = 180 \\ y = 180 - 120 \\ y = 60 \: \: degrees$

$y = x(corresponding \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: angles) \\ 60 = 60 \\ \\$

$x = 60 \: \: degrees$

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Answer:

Step-by-step explanation:

2 •(3(5+2)-1)

2 ·(3(7)-1)

2·(21-1)

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=40

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3 years ago

Is 15/20 a half or a whole?

Arte-miy333 [17]

Answer:

15/20 is neither its 3-quarters

Step-by-step explanation:

15/20 is 3/4 which is 75% therefore...

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3 years ago

Read 2 more answers

Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increas

polet [3.4K]

Answer:

a) The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

Step-by-step explanation:

a) Develop a 90% confidence interval estimate of the population mean monthly rent.

Our sample size is 120.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 120-1 = 119$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 119 and 0.05 in the t-distribution table, we have $T = 1.6578$ .

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{650}{\sqrt{120}} = 59.34$

Now, we multiply T and s

$M = T*s = 59.34*1.6578 = 98.37$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 98.37 = $3387.63.

The upper end of the interval is the mean added to M. So it is 3486 + 98.37 = $3584.37.

The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) Develop a 95% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.95$

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

With 119 and 0.025 in the t-distribution table, we have $T = 1.9801$ .

$M = T*s = 59.34*1.9801 = 117.50$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 117.50 = $3368.5.

The upper end of the interval is the mean added to M. So it is 3486 + 117.50 = $3603.5.

The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) Develop a 99% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.99$

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.005$

With 119 and 0.025 in the t-distribution table, we have $T = 2.6178$ .

$M = T*s = 59.34*2.6178 = 155.34$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 155.34 = $3330.66.

The upper end of the interval is the mean added to M. So it is 3486 + 155.34 = $3641.34.

The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

4 0

3 years ago

The sum of A and B is 171 and their difference is 35. What are the numbers?

antoniya [11.8K]

Answer:

103 and 68

Step-by-step explanation:

since the difference has to be 35 subtract 35 from 171 (equals 136) then divide it by 2, you get 68 which is your first number, then add 35 back and get 103 for the second number, I hope this helped

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4 years ago

Read 2 more answers

Can someone please explain how to do this!!!

DedPeter [7]

Hi there!

So we are given that:-

tan theta = 7/24 and is on the third Quadrant.

In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.

Since we want to find the value of cos theta. cos must be less than 0 or in negative.

To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.

Using the Identity

$\large \displaystyle{ {tan}^{2} \theta + 1 = {sec}^{2} \theta}$

Substitute tan theta = 7/24 in.

$\large \displaystyle{ {( \frac{7}{24}) }^{2} + 1 = {sec}^{2} \theta }$

Evaluate.

$\large \displaystyle{ \frac{49}{576} + 1 = {sec}^{2} \theta} \\ \large \displaystyle{ \frac{625}{576} = {sec}^{2} \theta}$

Reminder -:

$\large \displaystyle{ sec \theta = \frac{1}{cos \theta} }$

Hence,

$\large \displaystyle{ \frac{576}{625} = {cos}^{2} \theta} \\ \large \displaystyle{ \sqrt{ \frac{576}{625} } = cos \theta} \\ \large \displaystyle{ \frac{24}{25} = cos \theta}$

Because in QIII, cos<0. Hence,

$\large \displaystyle \boxed{ \blue{cos \theta = - \frac{24}{25} }}$

Using the Pythagorean Theorem

$\large \displaystyle{ {a}^{2} + {b}^{2} = {c}^{2} }$

Define c as our hypotenuse while a or b can be adjacent or opposite.

Because tan theta = opposite/adjacent. Therefore:-

$\large \displaystyle{ {7}^{2} + {24}^{2} = {c}^{2} } \\ \large \displaystyle{49 + 576 = {c}^{2} } \\ \large \displaystyle{625 = {c}^{2} } \\ \large \displaystyle{25 = c}$

Thus, the hypotenuse side is 25. Using the cosine ratio:-

$\large \displaystyle{cos \theta = \frac{adjacent}{hypotenuse}}$

Therefore:-

$\large \displaystyle{cos \theta = \frac{24}{25} }$

Because cos<0 in Q3.

$\large \displaystyle \boxed{ \red{cos \theta = - \frac{24}{25} }}$

Hence, the value of cos theta is -24/25.

Let me know if you have any questions!

8 0

3 years ago