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3 years ago

Find p+q, given that (q+4)(p+3)-(q+2)(p+1)=44.

Mathematics

1 answer:

Fofino [41]3 years ago

5 0

Q = -p + 17
or
p = -q + 17
Not sure if this is correct

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1 Add or subtract and simplify. * (3d + 5) + (40 – 1)

aksik [14]

3d +4

How to:
Combine like terms

7 0

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:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

(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

Simplify 6 - 3(4 - 3x) -3x - 6 9x + 18 9x - 6

svet-max [94.6K]

Answer:

6 (19 x - 2)

Step-by-step explanation:

Simplify the following:

6 - 3 (4 - 3 x) - 3 x - 6×9 x + 18×9 x - 6

-6×9 = -54:

6 - 3 (4 - 3 x) - 3 x + -54 x + 18×9 x - 6

18×9 = 162:

6 - 3 (4 - 3 x) - 3 x - 54 x + 162 x - 6

Grouping like terms, 6 - 3 (4 - 3 x) - 3 x - 54 x + 162 x - 6 = (-3 x - 54 x + 162 x) - 3 (4 - 3 x) + (6 - 6):

(-3 x - 54 x + 162 x) - 3 (4 - 3 x) + (6 - 6)

-3 x - 54 x + 162 x = 105 x:

105 x - 3 (4 - 3 x) + (6 - 6)

6 - 6 = 0:

105 x - 3 (4 - 3 x)

-3 (4 - 3 x) = 9 x - 12:

9 x - 12 + 105 x

Grouping like terms, 105 x + 9 x - 12 = (105 x + 9 x) - 12:

(105 x + 9 x) - 12

105 x + 9 x = 114 x:

114 x - 12

Factor 6 out of 114 x - 12:

Answer: 6 (19 x - 2)

7 0

3 years ago

The following function is probability Distribution function.

Rina8888 [55]

Answer:

9.60 ; - 60.96

Step-by-step explanation:

Given the function :

F(x)=6(x+1) /25, x=0, 1, 2, 3, 4.

x = 0

F(0)=6(0+1)/25 = 6/25 = 0.24

x = 1

F(1)=6(1+1)/25 = 12/25 = 0.48

x = 2

F(2)=6(2+1)/25 = 18/25 = 0.72

x = 3

F(2)=6(3+1)/25 = 24/25 = 0.96

x = 4

F(2)=6(4+1)/25 = 30/25 = 1.2

X ______0 _____ 1 ______ 2 ______ 3 ____ 4

P(x) ___ 0.24 __ 0.48 ___ 0.72 ____ 0.96 __ 1.2

Mean, μ = Σx*p(x) :

(0*0.24) + (1*0.48) + (2*0.72) + (3*0.96) + (4*1.2)

= 9.60

Variance : Σx²*p(x) - μ²

(0^2*0.24) + (1^2*0.48) + (2^2*0.72) + (3^2*0.96) + (4^2*1.2) - 9.6^2

= 31.2 - 92.16

= - 60.96

4 0

2 years ago

G(t)=t³+5t²; Find g(-1)

erik [133]

Answer:

I need points sorry bbh

Step-by-step explanation:

6 0

2 years ago