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3 years ago

14

A rose garden is formed by folning a rectangle and a semicircle, as shown below. The rectangle is 21 ft long and 17 ft wide. If

the gardener wants to build a
fence around the garden, how many feet of fence are required? (Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in
your answer.)

2 answers:

VLD [36.1K]3 years ago

6 0

Answer:

76 ft of fence is required.

Step-by-step explanation:

21 ft + 17 ft + 21 ft + 17 ft = 76 ft

Tju [1.3M]3 years ago

5 0

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Find the reference angle for -369°

Gwar [14]

Answer:

351°

Step-by-step explanation:

-369° + 360° = -9°. This is in Quadrant IV. If you want a reference angle in Quadrant I, find the positive angle between 0 and 360° that has the same terminal point at does -9°. It is 360° - 9° = 351°

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3 years ago

Round 98984 to 1 significant figure

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Answer:

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Step-by-step explanation:

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3 years ago

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On a 50 question test, Erick missed 10 questions. What is the exact grade he got on the test?

Bogdan [553]

Answer

He got an 80

Step-by-step explanation:

50 - 10 = 40

40/50 as a whole number is 80

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3 years ago

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:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

<u />

<u>(a) The books in any order</u>

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:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

<u>(b) The mathematics book, not together</u>

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

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

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

<u>(c) The novels must be together and the chemistry books, together</u>

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:

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

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

$\mathbf{Arrangements = 17280}$

<u>(d) The mathematics must be together and the chemistry books, not together</u>

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

3 years ago

Find the slope of the line that passes through the ordered pairs (3,5) and (-3,-5)

bija089 [108]

Answer:

5/3

Step-by-step explanation:

In this question, we are trying to find the slope of the line with the given points.

To find the slope, we would use the slope equation: m = y2-y1/x2-x1

Plug in the coordinates and solve:

-5 - 5/-3 - 3

-10/-6

Simplify further while canceling out the negative.

5/3

The slope of the line would be 5/3

6 0

3 years ago