No the corresponding angles are not congruent, because the angle measures on the smaller figure are 90, 90, 137, and 43, while the larger figure has angle measures of 90, 90, 136, 44. that is why the following figures are not congruent.

3 0

3 years ago

The additional cost per month of a sunroof, spoiler and stereo is represented by three consecutive even integers, respectfully.

lesya [120]

Answer:

Step-by-step explanation:

First of all, I think it was "respectively", not "respecfully", =))). A noticeable point.

From the problem, three item's costs are represented by three consecutive even integer.

Thus, we can call cost of spoiler is x, sunroof is x-2, stereo is x + 2. It is conditioned that x is an even number.

Since the sum of the three is 48, we have

(x-2) + x + (x+2) = 48

x+x+x -2 +2 = 48

3x =48

x=16

So the spoiler is 16; thus, the sunroof is 14 and the stereo is 18

3 0

3 years ago

The proportion of left handed people in the population is about 0.10. Suppose a random sample of 300 people is observed. (a) Wha

pantera1 [17]

Answer: $(\hat{p})\sim N(0.10,\ 0.017)$

Step-by-step explanation:

Sampling distribution of the sample proportion $(\hat{p})$ :

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

The sampling distribution of the sample proportion $(\hat{p})$ has mean = $\mu_{\hat{p}}=p$ and standard deviation = $\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}$ .

Given : The proportion of left handed people in the population is about 0.10.

i.e. p=0.10

sample size : n= 300

Then , the sampling distribution of the sample proportion $(\hat{p})$ will be :-

$(\hat{p})\sim N(0.10,\ \sqrt{\dfrac{0.10(1-0.10)}{300}})$

$(\hat{p})\sim N(0.10,\ \sqrt{0.0003})$

$(\hat{p})\sim N(0.10,\ 0.017)$ (approx)

Hence, the sampling distribution of the sample proportion $(\hat{p})$ is $(\hat{p})\sim N(0.10,\ 0.017)$

8 0

3 years ago