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2 years ago

At the theater, tickets for adults cost $4.75

1 answer:

7 0

X+y= 26 and 4.75x + 2.25y= 83.50

y=26-x( substitute this into second equation for y and solve for x)

4.75x + 2.25(26-x)= 83.50

4.75x + 58.5-2.25x= 83.50

x= 10

Now solve for y by substituting your answer for x

10+ y= 26

y=16

Therefore, 16 tickets were purchased for kids and 10 for adults.

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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

1b) Answer the following: * If arc WX = 40' and arc Y Z = 92, find m23.

spin [16.1K]

Answer:

m<3 = 66°

Step-by-step explanation:

<3 is an angle with its vertex inside the circle shown in the diagram. This, it's an internal angle.

The measure of an internal angle is equal to half the sum of the measure of the arcs intercepted.

Thus, the equation that shows relationship between <3 and arc WX and arc YZ is shown below:

m<3 = ½(40 + 92)

m<3 = ½(132)

m<3 = 66°

5 0

3 years ago

Please Help Me I Need Finish This Tonight

vladimir2022 [97]

1) a- rectangle
b- same place you started, facing west
2) a- right triangle
b- parallelogram
c- not sure the specific name they are looking for...
* also have no clue what a recipe is in terms of this lol
3) a- square
b- rectangle, depending on the length of the segments and their distance
apart
4) not sure

5 0

3 years ago

a recipe for one pumpkin pie calls for 1 1/4 cups of sugar Elena only has 1/2 cup of sugar and she needs to make for pumpkin pie

seraphim [82]

Answer: she would need four and a half cups more of sugar.

Step-by-step explanation:

You have to add together all of them sugar she would have needed so (1 1/4 times 4) and then subtract what she already had and that gives you 4 and 1/2 cups she would need. Hope this helps

7 0

2 years ago

strojnjashka [21]

Answer:

2500 pence (C = 2500)

Step-by-step explanation:

$C = 10t + 20m$

From the given information, t is the number of texts so essentially you will plug in the number of texts provided (150) in the place of the variable t.

$C = 10(150) + 20m$

Apply the same thing to minutes, plug in the number of minutes (50) in the place of the variable m.

$C = 10(150) + 20(50)$

Now multiply the substitutes with the co-efficient.

$C = 1500 + 1000$ (10*150=1500 & 20*50=1000)

Add the addends

C = 2500

7 0

2 years ago