4 (x-2) + 2 ( x + 1 )

3. (5 + 2) = (3 . 5) + (3 . 2) *

UNO [17]

Answer:

C) Distributive Property

Step-by-step explanation:

You're distributing in the 3 when you multiply it by the 5 and the 2 in the algebraic process:

➦ ➦

3•(5 + 2) = (3 • 5) + (3 • 2)

So, the 3 was distributed between the 5 and 2 when you multiplied.

Hence, this is the distributive property.

8 0

3 years ago

What is the value of y

pashok25 [27]

y = 3

The opposite sides of a rectangle are equal thus

2y + 4 = 10

subtract 4 from both sides

2y = 10 - 4 = 6

divide both sides by 2

y = $\frac{6}{2}$ = 3

6 0

3 years ago

Brenda has a circular garden of radius 21 m . She ran round the garden twice .what distance did she cover

Pavlova-9 [17]

Answer:

Brenda ran 263.76 metres.

Step-by-step explanation:

The circumference of a circle is two times pi times its radius. Brenda rand that twice, so we need:

2 × 2πr

= 4πr

= 4 × 3.14 × 21m

= 263.73m

4 0

3 years ago

In October 1945, the Gallup organization asked 1,487 randomly sampled Americans, "Do you think we can develop a way to protect o

GalinKa [24]

Answer:

Yes. There is enough evidence to support the claim that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.

Step-by-step explanation:

The question is incomplete:

In October 1945, the Gallup organization asked 1487 randomly sampled Americans, "Do you think we can develop a way to protect ourselves from atomic bombs in case other countries tried to use them against us?" with 788 responding yes. Did a majority of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945? Use the α=0.05 level of significance.

This is a hypothesis test for a proportion.

The claim is that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.

Then, the null and alternative hypothesis are:

H_0: \pi=0.5\\\\H_a:\pi>0.5

The significance level is 0.05.

The sample has a size n=1487.

The sample proportion is p=0.53.

$p=X/n=788/1487=0.53$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1487}}\\\\\\ \sigma_p=\sqrt{0.000168}=0.013$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.53-0.5-0.5/1487}{0.013}=\dfrac{0.03}{0.013}=2.288$

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

$\text{P-value}=P(z>2.288)=0.011$

As the P-value (0.011) 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 the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.

8 0

3 years ago

Kyle has three short straws, four medium straws, and six long straws. If he randomly draws two straws, one at a time without rep

ipn [44]

Before the first straw is drawn, there are three short straws and $3+4+6=13$ straws in all. Thus, the probability of drawing a short straw first is $\frac{3}{13}$ .

After a short straw is drawn, there are two short straws and twelve total straws, a probability of $\frac{2}{12} = \frac{1}{6}$ .

Thus, the probability of both of these events occurring is $\frac{3}{13} \cdot \frac{1}{6} = \boxed{\frac{1}{26}}$ .

6 0

3 years ago

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