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bonufazy [111]
1 year ago
8

I need to find the surface area. it's a cut sphere with a diameter of 14.

Mathematics
1 answer:
alex41 [277]1 year ago
6 0

Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

\begin{gathered} r=\frac{D}{2} \\ r=\frac{14}{2} \\ r=7\text{ in} \end{gathered}

The cut sphere is called a hemisphere.

The surface area of a sphere is

A_1=4\pi r^2

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

\begin{gathered} A_2=\frac{4\pi r^2}{2} \\ A_2=2\pi r^2 \end{gathered}

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

A_3=\pi r^2

Therefore, the total area of the hemisphere is,

\begin{gathered} A=A_2+A_3 \\ A=2\text{ }\pi r^2+\pi r^2 \\ A=3\text{ }\pi r^2 \end{gathered}

The total surface area of a hemisphere is,

\begin{gathered} A_{}=3\text{ }\pi r^2 \\ A=3\text{ }\pi\times7^2 \\ A=461.8in^2 \end{gathered}

Therefore, the total surface area of the cut sphere is 461.8 square inches.

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Sam spent a total of $90 at the grocery store. of this amount, he spent $72 on fruit. What percentage of the total did he spend
mylen [45]

Answer:

80%!

you can put the amount spent on fruit over the total and compare it to a percentage table!

4 0
3 years ago
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Omar has 2 3/4 cups of dough to make Dumplings. If he uses 3/16 cup of dough for each dumpling,how many whole dumplings can Omar
Brrunno [24]

Omar can make 14 whole dumplings. You change 2 3/4 cups to an improper fraction ( multiply the denominator and add the numerator ) and you get 11/4. Since you need 3/16 cups for one dumpling you have to find the greatest common denominator which is 16. You multiply 4 by 11 to get the numerator and end up with 44/16. Since you need 3/16 for one whole dumping you divide 44 by 3 and get 14.6 repeating. You cannot have a fraction of a dumpling so you round down and get the answer 14.



5 0
4 years ago
Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement
Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.173, n = 120. So

\mu = E(X) = np = 120*0.173 = 20.76

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

Z = \frac{X - \mu}{\sigma}

Z = \frac{34 - 20.76}{4.14}

Z = 3.2

Z = 3.2 has a pvalue of 0.9993

X = 21

Z = \frac{X - \mu}{\sigma}

Z = \frac{21 - 20.76}{4.14}

Z = 0.06

Z = 0.06 has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0
3 years ago
What is the second step to solve this equation?<br> 5X-8=27
vesna_86 [32]

Answer:

The next step is to Divide 35 by 5  then solve for x

Step-by-step explanation:

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olga2289 [7]

Answer:

k= 1316/117

Step-by-step explanation:

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