What is 87 over 62 in simplest form?

Identify the segments that are parallel, if any, if ∠DCB and ∠CDA are supplementary.

Triss [41]

Answer:

C

Step-by-step explanation:

We are given that

$\angle$ DCB and $\angle$ CDA are supplementary.

We have to identify the parallel segments if $\angle$ DCB and $\angle$ CDA are supplementary.

Supplementary angles: If the angles are supplementary then the sum of two angles is 180 degrees.

Therefore,

$\angle DCB+\angle CDA=180^{\circ}$

Therefore, angle DCB and angle CDA are interior angles .

Because CA is a transversal line and sum of interior angles is 180 degrees.

When the sum of interior angles formed between two lines and on same side of transversal line is 180 degrees. Then the lines are parallel.

Therefore, angle DCB and angle CDA are formed between line AD and BC.

Hence, AD is parallel to BC.

Option C is correct.

8 0

3 years ago

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.65$ estimated proportion.

$p$ true population

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

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

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.64$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.06$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.65(1-0.65)}{(\frac{0.06}{1.64})^2}=169.968$

And rounded up we have that n=170

6 0

4 years ago

The graph of y=f(x) is shown below. find all the values of x where f(x)=8

Tcecarenko [31]

Answer:

x = 4

Step-by-step explanation:

Find 8 on the y-axis. Draw a horizontal line through y =8. Determine the x value for which the graph intersects this horizontal line y = 8. It is x = 4

7 0

3 years ago

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Amanda lives in Fairbanks Alaska she records the low temperature for five days, which days low temperature was 9c colder than th

Brrunno [24]

Answer: all of them they are negitive numbers

Step-by-step explanation:

3 0

3 years ago

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A (not necessarily convex) 11-sided polygon can have at most how many right interior

EastWind [94]