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3 years ago

Find the volume of a sphere with a surface area of 576 in.

Mathematics

1 answer:

Kitty [74]3 years ago

4 0

Answer:

Since we have given that

Surface area of sphere = 576 pi cm. sq.

As we know the formula,

Surface area of sphere is given by

So, the volume of a sphere would be

Hence, the required volume is 7241.14 cm³.

Step-by-step explanation:

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Use fundamental identities to fully simply the expression.

gtnhenbr [62]

$\bf \stackrel{\textit{pythagorean identities}}{sin^2(\theta)+cos^2(\theta)=1}\qquad \qquad \stackrel{\textit{symmetry identities}}{cos(-\theta)=cos(\theta ) } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{array}{llrll} 3sin^3(t)csc(t)\qquad &+cos^2(t)&\qquad +2cos(-t)cos(t)\\\\ 3sin^3(t)\cdot \cfrac{1}{sin(t)}&&+2[cos(t)]cos(t)\\\\ 3sin^2(t)&&+2cos^2(t) \end{array} \\\\[-0.35em] ~\dotfill\\\\ 3sin^2(t)+cos^2(t)+2cos^2(t)\implies 3sin^2(t)+3cos^2(t) \\\\\\ 3[sin^2(t)+cos^2(t)]\implies 3[1]\implies 3$

5 0

4 years ago

In the last election, a state representative received 52% of the votes cast. One year after the election, the representative org

butalik [34]

Answer:

The probability that more than half of the sample would vote for him is P=0.7549.

Step-by-step explanation:

With a sample size of n=300, we can approximate this to the normal distribution.

The parameters will be

$\mu=p\cdot n=0.52\cdot 300=156\\\\\sigma=\sqrt{np(1-p)} =\sqrt{300\cdot 0.52(1-0.52)} =\sqrt{74.88}= 8.65$

We have to calculate the probability that half or more of the sample vote for him. This is P(x>150).

To calculate this probability, first we calculate the z-value:

$z=\frac{x-\mu}{\sigma}=\frac{150-156}{8.65}=\frac{-6}{8.65}=-0.69$

Then

$P(x>150)=P(z>-0.69)=0.7549$

The probability that more than half of the sample would vote for him is P=0.7549.

5 0

3 years ago

Misaki cut some wood for a bookcase she is building.She needs to find how many 1/3 ft boards she can make from a 5 ft board.Expl

N76 [4]

Answer: There are 15 boards that she can make from a 5 ft board.

Step-by-step explanation:

Since we have given that

Length of a board = 5 ft

Length of board she can make from the above board is given by

$\frac{1}{3}\ ft$

We need to find the number of boards she can make from a 5 ft board.

According to question,

$\text{Number of boards}=\frac{5}{\frac{1}{3}}\\\\\text{Number of boards}=5\times 3\\\\\text{Number of boards}=15$

Hence, there are 15 boards that she can make from a 5 ft board.

6 0

3 years ago

Read 2 more answers

The average (arithmetic mean) of k scores

denis23 [38]

Answer:

(E) (20k - 150)/(k - 10)

Step-by-step explanation:

Sum of all scores = average × number of scores = 20 × k = 20k

Sum of 10 scores = 15 × 10 =150

Sum of remaining scores = 20k - 150

Number of remaining scores = k -10

Average of remaining scores = sum of remaining/no. remaining

= (20 k -150)/(k-10)

6 0

4 years ago

How many ways can a cook arrange 9 of her 12 spice jars on a spice rack?

pshichka [43]

It depends if the 12 spice jars are all different.

If they are:

_ _ _ _ _ _ _ _ _ (9 spaces)

12*11*10*9*8*7*6*5*4

12 possibilities for first one, 11 for second, etc...

Multiply out to get:
79833600

5 0

4 years ago

Read 2 more answers