All Answers 355967 Answers

To find what percent of money the salesman buys the coat for, we can say that the original price is 100% of the value.

If 12.5% is discounted, 87.5% is left to pay for.

87.5% is the same as 7/8, so we multiply 64*(7/8), which equals 56.

If he sold the coat for a profit of 30%, the amount he profited is 130% of 56
130% is also equal to 1.3, so 56*1.3=72.8

We know that a 15% discount was given, so 72.8 is only 85% of the marked price. 

we can use the equation 72.8/x=85/100, which simplifies to 72.8/x=17/20

By cross multiplying, we get 17x=72.8*20, which is also 17x=1456

By dividing both sides by 17, we get x≈$85.65

As AD=EG, the diagram shown above must be a rectangle.
The area of a rectangle is defined as length*width.

AD*DC must be equal to EG*FH, since EG and FH are also perpendicular to sides AD and DC.

We know that AD=18, DC=27, and EG=18.

By setting FH=x, we get the equation

18*27=18x.

By dividing both sides by 18, we get x=27.

A + B + C = 863           A => x          B => 4y         C => 3y

1/3(A) + 1/3(C) = 863 - 674

x/3 + y = 189

x = 3(189 - y) 

x = 567 - 3y

(567 - 3y) + 7y = 863

y = 74

x = 345      This is your answer  

If the numbers are ordered from least to greatest, they would go as follows:
0.0123, 0.10203, 0.112233, 0.1223, 0.123, 0.123, 0.13.

The second and sixth numbers are then circled and added together. The second and sixth numbers are 0.10203 and 0.123.
0.10203+0.123=0.22503

Daniel,
0.75 is what is left of 60 from the original rectangle.

To find the percent decrease, you must subtract .75 from 1. The answer is then .25, or 25%.

 If BD:CD = 1:2, then find AD.

\(\overline {AD}=h\)

\((10^2-h^2):(17^2-h^2)=1:4\\ 400-4h^2=289-h^2\\ -3h^2=-111\\ h=\sqrt{37}\)

\(h=\overline{AD}=6.08\)

  !

Only in the case of a rectangle or a square, AD = EG

Let us consider the area of this parallelogram. The area of this paralleogram is EG * DC = 18*27 = 486. Another way to calculate the area of this paralleogram is BC * FH. We know that BC = AD = 18. Therefore, 18 * FH = 486, or FH = 27. 

The area of the original figure is 6*10 = 60. The area of the new figure is 5*9 = 45. Let x be the percentage decrease. Then, we know that 60x = 45. Therefore, x = 0.75 = 3/4

i think the answer is 9. 

since the 1.5 cups of flour is for 2 pound cakes, then you can just multiply 2x6= 12 and 1.5x6=9, so there are 9 cups of flour in 12 ONE pound cakes 

another way to solve it is you can divde 1.5 by 2. you will get 0.75. then you multiply 0.75 (aka value of one pound cake) by 12 and you get 9. 

other person had a different answer but this is just my explaination of the problem 

hey so i belive the answer is 28

since 5 of the fish are sold and there are 9 fish left, that means there were 14 fish. 

since there are twice as many snakes as fish, that would be 14x2=28 

not sure if the answer is correct though

thanks! 

35 cups are needed.

Using the formulas:  1 + 2 + ... + n  =  (n(n + 1)/2  and  1² + 2² + ... + n²  =  n(n + 1)(2n + 1)/6

to find the value of:  21² + 22² + ... + 41² + 42²:

Note that there are 22 addends.

21² + 22² + ... + 41² + 42²  =

(20 + 1)²  +  (20 + 2)²  +  (20 + 21)²  + (20 + 22)²

Using the binomial expansion:

=  ( 20² + 2·20·1 + 1² )  +  ( 20² + 2·20·2 + 2²​ )  +  ...  +  ( 20² + 2·20·21 + 21²​ )  +  ( 20² + 2·20·22 + 22²​ )

Rearranging:

=  [ 20² + 20² + ... + 20² + 20² ]  +  [ 2·20·1 + 2·20·2 + ... + 2·20·21 + 2·20·22 ]  +  [ 1² + 2²​ + ... + 21²​ + 22²​ ]

=   22[ 20² ]  +  [ 2·20·1 + 2·20·2 + ... + 2·20·21 + 2·20·22 ]  +  [ 1² + 2²​ + ... + 21²​ + 22²​ ]

=  8800  +   [ 2·20·1 + 2·20·2 + ... + 2·20·21 + 2·20·22 ]  +  [ 1² + 2²​ + ... + 21²​ + 22²​ ]

=  8800  +  40 · [ 1 + 2 + ... + 21 + 22 ]  +  [ 1² + 2²​ + ... + 21²​ + 22²​ ]

=  8800  +  40 · [ 22(1 + 22)/2 ]  +  [ 1² + 2²​ + ... + 21²​ + 22²​ ]

=  8800  +  40 · [ 253 ]  +  [ 1² + 2²​ + ... + 21²​ + 22²​ ]

=  8800  +  10120  +  [ 1² + 2²​ + ... + 21²​ + 22²​ ]

=  8800  + 10120  +  [ 22(22 + 1)(2·22 + 1)/6 ]

=  8800  +  10120  +  3795

=  22715

If BD:CD = 2:3, then find AD.

Hello Guest!

\((10^2-h^2):(17^2-h^2)=4:9\\ 900-9h^2=1156-4h^2\\ -5h^2=256\)

The specified ratio BD: CD = 2: 3 is not possible.

  !

What is the value of 21^2 + 22^2 + 23^2 + ... + 40^2 + 41^2 + 42^2==22,715

85 more than the square of a number:     85 + x2

22 times the number:                                22x

85 + x2  =  22x    --->     x2 - 22x + 85  =  0    --->     (x - 17)(x - 5)  =  0

                                                                       --->     Either  x = 17  or  x = 5

Let what Billy had ==B

Ahmad had ==B + 160

Ahmad gave ==0.20[B + 160]==0.20B + 32

B + 0.2B + 32 ==1.2B + 32 - what Billy got.

0.50[1.2B + 32]==0.6B + 16 - what Billy had left

[B + 160] - [0.2B + 32] + [0.6B + 16]==180 + 0.6B + 16

1.4B + 144 ==180 + 0.6B + 16, solve for B

B==65 - what Billy started with.

65 + 160 ==225 - what Ahmad started with.

0.6B + 16 ==39 + 16 ==55 - What Billy ended up with.

1.4B + 144 ==91 + 144 ==235 - What Ahmad ended up with.

235 - 55 ==180 - difference in what they ended up with.

100 throu 999 would be 900 of them

   10 000 would be the next one .....10 099 would be the 1000th one

Multiplying by a constant does not change the degree of a polynomial  ( unless the constant = 0 )    ( the addition of the two COULD change)

  degree 8 would be the largest possible ...

There should be 1 small bus and 8 large busses.