Combine these radicals. –66

Micah is buying items for a birthday party. If he wants to have the same amount of each item, what is the least number of packag

Zolol [24]

For us to be able to answer this question the number of the items that Micah is buying.
....and any important information concerning this problem.

8 0

2 years ago

Read 2 more answers

Given: EFGH inscribed in k(O) m∠FHE = 45°, m∠EGH = 49° Find: m∠FEH

hodyreva [135]

Answer:

$m$

Step-by-step explanation:

we know that

The inscribed angle measures half that of the arc comprising

step 1

Find the measure of arc EF

$m$

we have

$m$

substitute

$45\°=\frac{1}{2}(arc\ EF)$

$arc\ EF=90\°$

step 2

Find the measure of arc EH

$m$

we have

$m$

substitute

$49\°=\frac{1}{2}(arc\ EH)$

$arc\ EH=98\°$

step 3

Find the measure of arc FGH

$arc\ FGH=360\°-(arc\ EH+arc\ EF)$

substitute the values

$arc\ FGH=360\°-(98\°+90\°)$

$arc\ FGH=172\°$

step 4

Find the measure of angle FEH

$m$

we have

$arc\ FGH=172\°$

substitute

$m$

7 0

2 years ago

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

Step-by-step explanation:

Previous concepts

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".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Part 1

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 $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

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 $ME =\pm 0.1$ 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)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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 $ME =\pm 0.04$ 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)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.96})^2}=425.22$

And rounded up we have that n=426

3 0

2 years ago

Jeanine’s swimming pool has a diameter of 27 feet. Surrounding the pool is a

Anuta_ua [19.1K]

Answer:

It will cost $427.04 to paint deck and it will cost 958.485 to add fencing around deck

Step-by-step explanation:

Diameter of swimming pool = 27 feet

Radius of pool r= $\frac{27}{2}=13.5 feet$

Surrounding the pool is a deck that extends 5 feet from the edges of the pool

Outer radius R = 13.5+5=18.5

Area of deck = Outer area - Inner area

Area of deck = $\pi R^2 -\pi r^2$

Area of deck = $3.14(18.5^2-13.5^2)$

Area of deck = $502.4 ft^2$

Cost of painting 1 sq.feet = $0.85

Cost of painting 502.4 sq.feet = $502.4 \times 0.85=427.04$

Perimeter of deck = $2 \pi R = 2 \times 3.14 \times 18.5 =116.18 feet$

Cost of fencing 1 foot = $8.25

Cost of fencing 116.18 foot = $116.18 \times 8.25=958.485$

Hence it will cost $427.04 to paint deck and it will cost 958.485 to add fencing around deck

6 0

2 years ago

Which of these statements best describes the relation shown in Item 1?

Oksi-84 [34.3K]

Answer:

The relation is 'a function that is one-to-many'.

Step-by-step explanation:

From the table, we can see that element 10 i.e. y=10 in the range, corresponds to two elements i.e. x=-5, and x=5 in the domain.

In other words, the given table represents the many-to-one function as an element of the range y = 10 corresponds to more than one element in the domain.

Therefore, the relation is 'a function that is one-to-many'.

3 0

2 years ago

Combine these radicals. –66 –54