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3 years ago

A rectangular park is 150 yards on one side and 125 yards on the other.

1 answer:

4 0

So, there is a rectangular park with longer side (length) 150 yards and shorter side (width) 125 yards.

so walking around the rectangular park once is like covering the Perimeter (p) of the rectangular park.

So, lets find the perimeter of the park.
Perimeter of rectangle = 2 ( l + w)
= 2 ( 150 + 125 )
= 2 * 275
= 550 yards

Now, walking around the park two times is like doubling the Perimeter of the rectangle. So, when Debbie walks around the park 2 times, he covers the perimeter of the rectangular field twice.

i.e. Debbie walked 2 * Perimeter
= 2 * 550
= 1100 yards

Now, If Debbie wanted to walk 1,000,000 yards, she has to walk the rectangular park (1,000,000 / the Perimeter of the park)
i.e. 1,000,000 / 550
= 1818.18 times

So,
(a) she walks 1100 yards
(b) She have to walk 1818.18 times

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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

A recipe calls for 2/5 cup of chicken broth and 1/6 cup of vegetable broth. What is the total amount of broth need for the recip

Bess [88]

Answer:

I may not be correct, depending on what you were taught, but it would be...

17/30

Step-by-step explanation:

(2/5×6/6)+(1/6×5/5)

12/30 + 5/30

17/30

keep in mind you don't add the denominators at all ( the numbers at the bottom half of the fraction)

3 0

3 years ago

Is -7 rational Helppppppp

Finger [1]

Answer:

Rational numbers are fractions composed of integers. An integer is a number with no fractional part. So 7/8 is a ratio of whole numbers, which makes it rational. Negative or positive does not matter.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the domain of a graph

Vika [28.1K]

Answer:

refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

7 0

3 years ago

If you travel 540 miles on 18 gallons of gas how far can you travel on 6 gallons of gas

Anika [276]

The answer is 180 since 18/3 = 6 divide 540/3

5 0

3 years ago