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2 years ago

If two angles are supplementary and congruent, what is the measure of each angle?

Mathematics

2 answers:

matrenka [14]2 years ago

8 0

Answer:

Step-by-step explanation:

supplementary angles equal 180 degrees and 90+90=180

VikaD [51]2 years ago

4 0

Answer:

90°

Step-by-step explanation:

Supplementary angles are angles that add up to 180°.

Congruent means the angles are equal to each other.

Since there are two angles, and they have to be equal to each other, we can divide 180° by 2 to find the measure of each angle.

180° / 2 = 90°

Both angles have a measure of 90°.

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Consider the statement | x − 4 | < 0.5 |x-4|<0.5. What is the meaning of this statement? Select all that apply. a. All val

stich3 [128]

Answer:

Option D.

Step-by-step explanation:

The given statement is

$|x-4|$

x-4 is difference between x and 4.

|x-4| distance from x because distance can not be negative.

Inequality sign "<" means less than.

$|x-4|$ represent all values of x whose distance from 4 is less than 0.5.

Therefore, the correct option is D.

8 0

3 years ago

Can someone help me with this question please?

blagie [28]

Not sure but i guess 25 %ile is 55/4=13.75 and 80%ile=80*55/100=44

6 0

3 years ago

In a random sample of 150 customers of a high-speed Internetprovider, 63 said that their service had been interrupted one ormore

erastovalidia [21]

Answer:

a) The 95% confidence interval would be given by (0.341;0.499)

b) The 99% confidence interval would be given by (0.316;0.524)

c) n=335

d)n=649

Step-by-step explanation:

1) Notation and definitions

$X_{IS}=63$ number of high speed internet users that had been interrupted one or more times in the past month.

$n=150$ random sample taken

$\hat p_{IS}=\frac{63}{150}=0.42$ estimated proportion of high speed internet users that had been interrupted one or more times in the past month.

$p_{IS}$ true population proportion of high speed internet users that had been interrupted one or more times in the past month.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

1) Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.42 - 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.341$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.499$

The 95% confidence interval would be given by (0.341;0.499)

2) Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by: