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The sum of the interior angles of a quadrilateral equals 360°.

miss Akunina [59]

True this is because of the number of angles a quadrilateral has which is 4

5 0

3 years ago

Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute in

stiks02 [169]

Answer:

a) The null and alternative hypothesis are:

$H_0: \pi=0.53\\\\H_a:\pi$

b) If 300 families were sampled, for a significance level of 5%, there is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago (P-value = 0.001).

Step-by-step explanation:

The claim that we want to have evidence to support is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

The hypothesis for this test should state:

- For the null hypothesis, that the population proportion is not significantly different from 53%.

$H_0:\pi=0.53$

- For the alternative hypothesis, that the population proportion is significantly less than 53%.

$H_a: \pi$

If 300 families are sampled, we can perform a hypothesis test for a proportion.

The claim is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.53\\\\H_a:\pi$

The significance level is 0.05.

The sample has a size n=300.

The sample proportion is p=0.44.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.53*0.47}{300}}\\\\\\ \sigma_p=\sqrt{0.00083}=0.029$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.44-0.53+0.5/300}{0.029}=\dfrac{-0.088}{0.029}=-3.065$

This test is a left-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=P(z$

As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

3 0

3 years ago

Points A, B, C, and D lie on the circle. Solve for the value of X

aliina [53]

Answer:

A 65

Step-by-step explanation:

The angle formed by two chords is 1/2 the sum of intercepted arcs

x = 1/2 (51+79)

x = 1/2(130)

x =65

4 0

3 years ago

Read 2 more answers

Select all ratios equivalent to 15:5.<br> 9:3<br> 6:2<br> 3:1

natali 33 [55]

Answer:

All three.

Step-by-step explanation:

All three of these ratios are equivalent to 15:5. Here's how:

Let's look at the first ratio, 9:3. Did you notice something common? 3 x 3 = 9. 9/3 = 3. 5 x 3 = 15. 15/3 = 5. Both of these numbers are divisible by 3, so these ratios are equivalent.

Second. 6:2. 2 x 3 = 6. 6/3 = 2. 5 x 3 = 15. 15/3 = 5. See the similarity? The same applies to the next problem, number three, although it does slightly differentiate.

Third, 3:1. See, here, since the ratio is smaller than the problem, we can't multiply, since this ratio is smaller than the original number. But, it's still the same thing. A ratio is a number that compares a value to another value. This means that 3:1 is 3 compared to one. Now, let me clarify. 15:5. 3:1. These are the exact same values, except they are just written in a different form, and simplified. Since 5 x 3 = 15, we know that we can divide 15 evenly by 5, which makes it 3, and divide 5 evenly by 5, which equals one. So here we have our answer for the third problem. 5:1.

Ratios are basically division, except simplified. Every single ratio problem works this way. Once you get the hang of it, it's immensely easy. Hope this helped!

6 0

3 years ago

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 5 sin2 t, y = 5 cos2 t

rodikova [14]

$\begin{cases}x(t)=5\sin2t\\y(t)=5\cos2t\end{cases}\implies\begin{cases}\frac{\mathrm dx}{\mathrm dt}=10\cos2t\\\frac{\mathrm dy}{\mathrm dt}=-10\sin2t\end{cases}$

The distance traveled by the particle is given by the definite integral

$\displaystyle\int_C\mathrm dS=\int_0^{3\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt$

where $C$ is the path of the particle. The distance is then

$\displaystyle\int_0^{3\pi}\sqrt{100\cos^22t+100\sin^22t}\,\mathrm dt=10\int_0^{3\pi}\mathrm dt=30\pi$

6 0

3 years ago

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