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Three boys have the same number of blue toy cars. 1/4 of Nelson's toy cars and 4/5 of Ted's toy cars and of 2/3 Kieran's toy cars are blue. The total number of toy cars that are not blue is 75. How many toy cars does Ted have?

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3x + x/4 + x/2 = 75

x = 20           (Each boy has 20 blue toy cars)

Ted has 25 toy cars 

This one's quite tough. 

From the 2 equations, a - b = -1

So 2008a - 2008b = -2008

so 4007a = -1

so a = \(-{1 \over 4007}\), so b = \(4016 \over 4017\)

Let us assume that Caleb had x marbles. As Ben had five times as many marbles as Caleb, therefore, Ben had 5x marbles with him.

It is given that Ben gave away 87 marbles, therefore, the number of marbles remaining

with Ben was:
                      M_B = 5x - 87

It is also given that Caleb won 13 new marbles. Therefore, the number of marbles remaining with 

Caleb was:
                 M_C = x + 13

It is given that in the end, both Caleb and Ben had the same number of marbles. Therefore, equate the expressions obtained for the number of marbles left with Ben and Caleb and

 solve for x.

                     M_B = M_C

               5x - 87 = x + 13

                5x - x  = 13 + 87

                     4x  = 100

                       x  = 100/4 

                       x  = 25

Therefore, the number of marbles left

with Ben and Caleb were:

                        M_B = 5x - 87

                              = 5 (25) - 87

                              = 38

Answer - Each of them had 38 marbles in the end.

\(q = 3*8 - 3 = 21\)

25% of students chose Basketball.

The diagonal :    sqrt ( 3^2 + 4^2 + 5^2 ) =__________

The range of the function g(x) = 2/(4 + 2x^2) can be written as an interval (a,b]. What is a + b?

Hello Guest!

\(g(x) = \dfrac{2}{4+2x^2}\)

\(R=b-a\\ b=0.5\\ a\approx 0\ |\ a>0\\ a+b\approx 0.5\ |\ >0.5\)

  !

(a)  How many chickens are there on Simon's farm?

(b)  Each duck on Thiru's farm lays an average of 6 eggs per week. How many duck eggs are produced on Thiru's farm per week?

Hello KourageKowardlyDog!

\(Simon:\\ (d-84):d=1:7\\ d=7d-7\cdot84\\ 6d=588\)

\(d=98\\ c=14\)

\(Thiru:\\ (d-84):d=2:3\\ 2d=3d-3\cdot 84 \)

\(d=252,\ e=252\cdot 6=1512\\ c=168\)

(a) 14 chickens are there on Simon's farm.

(b) 1512 duck eggs are produced on Thiru's farm per week?

  !

$BI = 2 \sqrt{14}$

\({1 \over {1 + {1 \over {\sqrt{2} + 1}}}} = {1 \over {1 + {\sqrt{2} - 1}}} = {\sqrt{2} \over 2}\)

The degree of f is 3.

Let 'b' be Ben's amount at first, and 'c' be Caleb's amount at first. 

We can form 2 equations: b = 5c and b - 87 = c + 13, so 5c - 87 = c + 13, so 4c = 100, so c = 25, b = 125. 

BUT THE QUESTION ASKS FOR HOW MANY MARBLES THEY HAVE AT THE END.

Since they both have the same amount left, 125 - 87 = 25 + 13 = 38.

\(\sqrt{3 \over 28} = {\sqrt{3} \over \sqrt{28}} = {{\sqrt{3}*\sqrt{28}} \over 28}\), you can finish it :)     (√a * √b = √(ab))

Perimeter = 2*(l + w)

so l + w of this rectangle = 282/2 = 141. So the w (width) = 141 - 59 = 82

Any vlue of 'y' that makes the denominator will result in an 'undefined' situation

y^2 -8y+2 = 0

    The sum of the roots can be found by  -b/a   =   8 

....or you can use the quadratic formula to find roots    x = 4 +- sqrt(14)      sum = 8

1st bank: \(3^0\)

2nd bank: \(3^1\)

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.

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6th bank: \(3^5 = 243\)

 5/8x = 65

      x = 104

104 x 6 = 624

624 pages

Convert to base 10, multiply, and convert back again. :)

Area = 1/2 *  x  * 12        total area =  2 * 1/2 x * 12 = x * 12

area = 28

12x = 28

x = 28/12 = 7/3

hyp^2 =  12^2   + (7/3)^2

          = 144 + 49/9

hyp = sqrt (1345/9)

then  circumference   =  2 * sqrt ( 1345/9)   + 2 * 7/3         you can finish ....

15

base 2: 1111

base 4: 33

I meant paperbacks to be P, not B  

a = 2.5 b      

b = g-7           so   a = 2.5 (g-7)

g                         summed = 142

2.5(g-7)     +    g-7    +    g   = 142      solve for g...                 *** edited ***

Paperbacks books => B             Hardcover books => H = B+36

B+36 - 3/4(B) = B - 1/2(B+36)

B = 216

H = B + 36

It says it's wrong can someone else help?

Should be:  a  -  b ==770

                      a + b ==1010