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It would take 1 hour for each member if there are 45 members to paint a wall, so it's 45 hours in total.

Let \(x\) represent how many hours 12 members need to paint the same wall.

\(12x=45 \times 1\)

\(x=\frac{45}{12}=\frac{15}{4}\)hrs

In minutes, it would be \(3 \times \frac{15}{4}=225 \) minutes.

Solve by multiplying the first two polynomials first.

This gets you \(3a^3-2a^2-12a+6a^2-4a-24\) which simplifies down to \(3a^3+4a^2-16a-24\)

Now you do \((a^2-2a+1)(3a^3+4a^2-16a+24)\)

After multiplying, you get \(3a^5+4a^4-16a^3-24a^2-6a^4-8a^3+32a^2+48a+3a^3+4a^2-16a-24\)

\(3a^5+4a^4-16a^3-24a^2-6a^4-8a^3+32a^2+48a+3a^3+4a^2-16a-24\) simplifies down to \(3a^5-2a^4-21a^3+12a^2+32a-24 \)

So the answer is \(3a^5-2a^4-21a^3+12a^2+32a-24\)

Simplify as

4x^2 -10x -6  =  0 

2x^2 - 5x - 3  = 0

Product of roots =  -3/2  =  ab

Sum of roots  = 5/2  = a + b

1 / a  + 1 / b   =    (a + b)  / (ab)   = ( 5/2)  /(-3/2) =  - 5 / 3 

Simplify as

3x^2 -3x + 20   =    0 

Product of roots =  ab  = 20/3

2ab = 40/3

Sum of  roots =   a + b  =   - (-3) / 3  = 1

Square both sides

a^2 + 2ab + b^2 = 1

a^2 + b^2  + 40/3 = 1

a^2 + b^2  = -37/3               square both sides

a^4 + 2(ab)^2  + b^4  =  1369 /  9

a^4 + b^4  + 2(20/3)^2  = 1369 /  9

a^4 + b^4 + 800/9  = 1369/9

a^4 + b^4  = 569 / 9

Simplify as

6x^2  - 21x  - 31     =   0

x =   [ 21 + sqrt  [ 441  + 744 ] ] / 12  =  [ 21 + sqrt (1185)  ]  / 12 

( x - 5)  (x + 5)  = x^2   - 25   =  x^2 + 0x  - 25

\(\frac{a + 2}{a + 1} = \frac{b}{8} \)

8(a + 2)  / ( a + 1)   =  b

a         b

-9       7

-5       6

-3       4

-2       0

0       16

1       12

3       10

7         9

\(\because \triangle TSU \sim \triangle TPM\)

\(\therefore \angle TMP = \angle TUS = {89}^{\circ}\)

\(\because \angle STU = {29}^{\circ}, \angle TZU = {90}^{\circ}\)

\(\therefore \angle TUZ = 180-29-90={61}^{\circ}\)

\(\therefore \angle TMZ + \angle TUZ = {160}^{\circ}\).

All the children and all the adults sit together, so suppose on one side there sits 4 children, on the other sides sits 4 adults.

Suppose one of the children is Johnny.

We must always rotate the table so that Johnny is at the bottom of any orientation. 

Therefore, the children must always be the bottom of the table, in the orientation.

The children have 4! ways and the adults have 4! ways.

Therefore, there are 576 ways to be seated. 

\(\sqrt{200} = 10\sqrt2\), so \(a^2 + b^2 = 200\) 

Assuming that a and b are both integer side lengths, \(10^2+10^2=200\), so the sides are 10 and 10.

10 times 10 is 100, so the area of the rectangle is \(\bf100\)

I would assume that DX = 3.

If CX, AX, and BX all equal three, the point X will have to be the center of the rectangle, so DX = 3.

C                                                                                                                               D

                                                            .x                                                                   

A                                                                                                                               B

I would assume that DX = 3.

If CX, AX, and BX all equal three, the point X will have to be the center of the rectangle, so DX = 3.

C                                                                                                                               D

A                                                                                                                               B

6*24*4=576

6*16*4=384

https://web2.0calc.com/questions/counting_81244

https://web2.0calc.com/questions/altitudes_39

The ones that aren't cozy

11,13,15,17,19

31,33,35,27,39

51,53,55,57,59

71,73,75,77,79

91,93,95,97,99  =    25 numbers

Number of two-dgit numbers  =  99 - 10 + 1 =  90

So

90  - 25  =  65  are cozy

The answer is 0.

Billy purchased 100 shirts at a cost of $15 each and planned to resell them. The first week he sold some of them for $25 each. The second week he sold the rest for $20 each. If his total profit was $600, how many shirts did he sell the first week?  

            n  =  number of shirts sold the 1^st week at $10 profit  

(100 – n)  =  number of shirts sold the 2^nd week at $5 profit  

            [ 10 • (n) ]  +  [ 5 • (100 – n) ]  =  600    

                        10n + 500 – 5n  =  600  

                                            5n  =  100  

                                              n  =  20  shirts sold the first week  

check answer  

                                        20 shirts • 10 profit  =  200  

                                        80 shirts •   5 profit  =  400  

                                                      total profit  =  600  

_.