If x = ‐3, evaluate x + 7

The length of a rectangular patio is 4 feet less than three times it's width. The area of the patio is 160 square feet. Find the

Levart [38]

Step-by-step explanation:

The length of a rectangular patio is 4 feet less than three times it's width. The area of the patio is 160 square feet. Find the dimensions of the patio.

3 0

3 years ago

Will give brainless ⭐️!!!

maria [59]

Answer:

It's the second on, 4 units up and 8 units to the left

5 0

3 years ago

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Find the perimeter of the following shape, rounded to the nearest tenth:

muminat

So will be 5+5 + 2sqrt2 +2sqrt2 = 10 + 3 +3 = 16 rounded

hope helped

6 0

4 years ago

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For a large supermarket chain in a particularâ state, aâ women's group claimed that female employees were passed over for manage

PolarNik [594]

Answer:

1) As the P-value (0.097) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the women's claim that female employees were passed over for management training in favor of their male colleagues.

2) The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that female employees were passed over for management training in favor of their male colleagues.

We use the women's part for sample and population proportions.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.4\\\\H_a:\pi$

The significance level is 0.05.

The sample has a size n=50 persons.

The sample proportion is p=0.3.

$p=X/n=15/50=0.3$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.4*0.6}{50}}\\\\\\ \sigma_p=\sqrt{0.0048}=0.069$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.3-0.4+0.5/50}{0.069}=\dfrac{-0.09}{0.069}=-1.299$

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 (0.097) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that female employees were passed over for management training in favor of their male colleagues.

b) We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.3.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.3*0.7}{50}}\\\\\\ \sigma_p=\sqrt{0.0042}=0.0648$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0648=0.127$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.3-0.127=0.173\\\\UL=p+z \cdot \sigma_p = 0.3+0.127=0.427$

The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

5 0

3 years ago

All 231 students in math club went on a field trip some rode in vans that held 7 people and some rode on buses that held 25 peop

MariettaO [177]

Answer:

8 vans

7 buses

Step-by-step explanation:

Let there be "b" buses

and "v" vans

Since 7 people is the capacity of vans, the total capacity is

7v

Also, since 25 people is the capacity of 1 bus, the total capacity is

25b

In total 231 people, so we can write our first equation as:

7v + 25b = 231

Now, we know there are 15 vehicles (bus + vans) in total, so we can write our 2nd equation as:

v + b = 15

Now, we solve for v and b. Let's solve the 2nd equation for v and substitute that into 1st and solve for b first:

v + b = 15

v = 15 - b

Now,

$7v + 25b = 231\\7(15-b) + 25b = 231\\105-7b+25b=231\\18b=126\\b=7$

Hence, there are 7 buses

Since 15 vehicles in total, the number of vans is:

15 - 7 = 8 vans

So,

8 vans

7 buses

8 0

4 years ago