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3 years ago

Find the volume of a sphere that has a diameter of 30 feet. Use 3.14 for pi.

Mathematics

1 answer:

NemiM [27]3 years ago

5 0

Umm the answer I’m pretty sure is the diameter 5.346 and 30 feet divide that by 30

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2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

insens350 [35]

The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400

The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

(a) The books in any order

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

The number of arrangement is n!:

So, we have:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

(b) The mathematics book, not together

There are 2 mathematics books.

If the mathematics books, must be together

The number of arrangements is:

$\mathbf{Maths\ together = 2 \times 9!}$

Using the complement rule, we have:

$\mathbf{Maths\ not\ together = Total - Maths\ together}$

This gives

$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

(c) The novels must be together and the chemistry books, together

We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

$\mathbf{Arrangements = n! \times 3! \times 5!}$

$\mathbf{Arrangements = 4! \times 3! \times 5!}$

$\mathbf{Arrangements = 17280}$

(d) The mathematics must be together and the chemistry books, not together

We have:

$\mathbf{Mathematics = 2}$

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

$\mathbf{Mathematics = 2!}$

Literally, the number of chemistry and mathematics now is:

$\mathbf{n =Chemistry + 1}$

$\mathbf{n =5 + 1}$

$\mathbf{n =6}$

So, the number of arrangements of these books is:

$\mathbf{Arrangements = n! \times 2!}$

$\mathbf{Arrangements = 6! \times 2!}$

Now, there are 7 spaces between the chemistry and mathematics books.

For the 3 novels not to be together, the number of arrangement is:

$\mathbf{Arrangements = ^7P_3}$

So, the total arrangement is:

$\mathbf{Total = 6! \times 2!\times ^7P_3}$

$\mathbf{Total = 6! \times 2!\times 210}$

$\mathbf{Total = 302400}$

Read more about permutations at:

brainly.com/question/1216161

8 0

2 years ago

The owners of a golf course hired a company to determine how many squirrels were living on their property. First, the company pu

muminat

Answer:

Squirrel population is 440 squirrels.

Step-by-step explanation:

It is given that there are 22 squirrels are marked.

Later the company returned and counted a total of 220 squirrels of which are marked were 11.

So, we can set up proportional equation to find the squirrel population.

Let squirrel population is x.

We can set up proportional equation as

$\frac{11}{220}=\frac{22}{x}$

Cross multiply

11 x=4840

Divide both sides by 11

x=440

Best estimate is 440.

6 0

3 years ago

Will give brainliest to the 1st right answer!!!!

monitta

Step-by-step explanation:

c is the answer

can i have brainliest

3 0

3 years ago

What is x-y explain ?????????

maksim [4K]

Answer:

An x-y axis, also known as a cartesian coordinate system or a coordinate plane, is a two-dimensional plane of points defined uniquely by a pair of coordinates. ... The horizontal line, then, is known as the x axis and measures the distance left or right from the vertical line.

8 0

2 years ago

question says Miranda is thinking of a number. She says, "If I multiply it by 5 and then subtract 3 and then multiply the result

OlgaM077 [116]

Answer:

Step-by-step explanation:

To make your equation, you basically write all the steps down with x as your number and then set it equal to 34 (wow, that was very confusing, sorry!). This means that your equation would be (5x-3)2=34. Now, you'll solve this by starting with distributing the 2 (2*5x and 2*-3), which will give you the equation 10x-6=34. Next, add six to both sides (10x-6+6=10x and 34+6=40), so you should get 10x=40. Lastly, divide both sides by 10 (10x/10=x and 40/10=4) to get x=4. I'd also advise checking your answer by multiplying 4 by 5 (20), then subtracting 3 (20-3=17), and multiplying it by 2 (2*17=34). :)

8 0

3 years ago