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3 years ago

PLEASE ANSWER TODAY! THANK YOU! :)

Mathematics

2 answers:

makkiz [27]3 years ago

6 0

Answer:

1/3

Step-by-step explanation:

Gnoma [55]3 years ago

4 0

Answer:

The 2nd is 1/3,

and the third one is 3.

Step-by-step explanation:

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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

What its the exact and estimate of -3.7 +(-6.8) and i need work

hodyreva [135]

Exact:

-3.7 - 6.8 = -10.5

Estimate:

-4 - 7 = -11

6 0

3 years ago

Read 2 more answers

Miguel is making smoothies out of yogurt and juice to serve to his friends, and he needs to make 12 cups. The ratio of yogurt to

tester [92]

12 divided by 2 is 6. So he will need a 6 cups of yogurt

6 0

3 years ago

Read 2 more answers

Which series of transformations shows that rectangle A is similar to rectangle B?

Brut [27]

Answer:

D. Dilate rectangle A by a scale factor of 3 with the center of dilation at the origin and rotate it 90° clockwise about the origin.

Step-by-step explanation:

The coordinates of triangle A are (-2,1) , (1,1), (1,-1) and (-2, -1) while that of triangle B are (-3, 6), (3, 6), (3, -3) and (-3, 3).

To transform A to be we need a combination of two transformations, and that is dilation and rotation.

If A is dilated by a scale factor three through the origin as the center of dilation and then rotated through 90° clockwise with the origin as the center of origin, then rectangle B will be obtained.

8 0

3 years ago

Read 2 more answers

What is y<-x+5 and y≤ 2x-1??

olga nikolaevna [1]

9514 1404 393

Answer:

see attached

Step-by-step explanation:

The pair of inequalities is graphed in the attachment.

The first inequality graphs as a shaded area below the dashed line y=-x+5.

The second inequality graphs as a shaded area below the solid line y=2x-1.

The solution set is the doubly-shaded area below the point where the lines intersect.

3 0

3 years ago