At the first time, it bounces: 80 x 3/4 = 60 (feet)

At the second time, it bounces: 60 x 3/4 = 45(feet)

At the third time, it bounces: 45 x 3/4 = 33,75 (feet)

There are 200 children in the study

There are 60% of girls of 100 girls in the study

So the girls enjoy Quirk is 60

=> The percent is: 60 : 200 = 30%

The intersection of AC and BD is both the middle of AC and BD

Call it is H

=> AH = HC = 3 ( units)

=> \(S_{AHC}=\dfrac{3.5}{2}=7.5\left(units^2\right)\)

=> \(S_{ABCD}=7,5.4=30\left(units^2\right)\)

Call three numbers is a,b,c

Suppose a < b < c

=> b = 8

Call \(\dfrac{a+b+c}{3}=x\)

=> a = x - 6

c = x + 7 

=> a + b + c = x - 6 + 8 + x + 7 = 2/3 ( a+ b + c) + 9 

=> 9 = 1/3 ( a + b + c)

=> a + b + c = 27 

Call the hypotenuse of the triangle is a

Two sides is b and c.

We have: b = a x sin 30 = 40 x sin30 = 40 x 1/2 = 20( units)

=> c = a x sin 60 = 40 x sin60 = \(40\dfrac{\sqrt{3}}{2}=20\sqrt{3}\) (units)

=> \(S_{ABC}=\dfrac{20\sqrt{3}.20}{2}=200\sqrt{3}\left(areaunit\right)\)

Because 2009 and 2010 aren't leap year 

=> Each year has 365 days

=> Two years have: 830 days = 19920 ( hours) = 1195200 ( mins)

So there are: 1195200 x 60 = 71712000 = 71712 x 10^3 ( beats)

We have:

The area of the circle is: \(2,5^2\Pi\approx19,63\left(cm^2\right)\)

The diameter of the circle is 2,5 x 2 = 5 cm

=> The side of the square is also 5 cm

So the area of the square is 5 x 5 = 25\(\left(cm^2\right)\)

So the stripe's area is: 25 - 19,63 \(\approx5,38\left(cm^2\right)\)

Call the number of students is x

We have:

x = 6n (1)

x - 3 = 7m

x - 4 = 5n (2)

From (1) and (2) we have: 

x - ( x - 4 ) = 6n - 5n

<=> 4 = n

=> x = 6.4 = 24 (students)

After 1 days that Jerry has worked, there has left project is:

1 - 1/9 = 8/9(project)

After 3 days worked alone, Jerry will work:

1/9 x 3 = 1/3(project)

So the work that Bill work in these days is:

8/9 - 1/3 = 5/9(project)

Call the Sammy's first pennies is 100k

After giving Becky half of his pennies, he has:

100k : 2 = 50k

After giving Janie one-fourth of his remaining pennies, he has: 

50k - 50k x 1/4 = 37,5k

After giving Mary Beth half the pennies that Sammy had left, he has:

37,5k - 37,5k : 2 = 18,75k

=> 18,75k = 12 

=> k = 0,64

Sammy had given Becky 50k pennies

So he had given : 

50 x 0,64 = 32 (pennies)

We have: JK = AB - A - B = 9A 

We also see: 

The multiples of 9 which have two-digit always have the sum of two digits = 9

=> 9A has the total of two digit = 9

So JK also has the total of two digit = 9

=> J+K = 9

Takes lots of time :) 

The ratio of the original is: 

Red : Yellow : Blue = 12 : 2,5 : 0,5 = 24 : 5 : 1

So the red = 24k 

Yellow = 5k

Blue = k 

The main batch use:

5k = 30 (gallons)

=> k = 6

=> Red = 24 x 6 = 144(gallons)

Blue = 6 (gallons)

So the total of gallons is: 144 + 30 + 6 = 180 ( gallons)

When sale 20% off first, she will sale the number of cents larger. 

So when she sale 20% off last, she will sale the number of cents smaller.

So for the more money she spend, she must sale the smallest.

=> She will sale 4,00 first and 20% in the second.

In case 1, she will sale: 

25 x 20% + 4 = 9 (cents)

In case 2, she will sale:

( 25 - 4 ) x 20% + 4 = 8,2 (cents)

So in case 2, she will spend:

9 - 8,2 = 0,8 (cents)

This question is old 

In the first 240 miles, the car travel at the time:

240 : 60 = 4 (hrs)

In the next 160 miles, the car travel at the time:

160 : 80 = 2 (hrs)

The time remaining is: 9 - 4 - 2 = 3 (hrs)

The distance remaining is: 616 - 240 - 160 = 216 (miles)

The average speed of the car before the remainder of the trip in order for the car to arrive on schedule is: 216 : 3 = 72 (mph)

According to the title, we have: a = 9

b = 8

So b + a : 0,5 = 8 + 9 : 0,5 = 8 + 18 = 26 :) 

Call the other leg is: x

So the hypotenuse is x + 1 

We have: \(29^2+x^2=\left(x+1\right)^2\)( Pythagorean theorem)

\(\Leftrightarrow841+x^2=x^2+2x+1\)

\(\Leftrightarrow841=2x+1\)

\(\Leftrightarrow x=420\)

=> The sum of two sides is: 420 + 29 = 449

The positive square root of 200 is \(\approx14\)

The positive square root of 121 is 11

The percent that 14 larger than 11 is: 

\(14\times\dfrac{100}{14}-11\times\dfrac{100}{14}\approx21,5\%\)

In the first 240 miles, the car travel at the time:

240 : 60 = 4 (hrs)

In the next 160 miles, the car travel at the time:

160 : 80 = 2 (hrs)

The time remaining is: 9 - 4 - 2 = 3 (hrs)

The distance remaining is: 616 - 240 - 160 = 216 (miles)

The average speed of the car before the remainder of the trip in order for the car to arrive on schedule is: 216 : 3 = 72 (mph)

He has gone the number of miles is:

74592 - 74568 = 24 (miles)

He has gone the number of gallons is:

24 : 28 = \(\dfrac{6}{7}\)(gallons)

The cost of gas that was used for Ryosuke to drive his friend home from work is:

\(4.05\times\dfrac{6}{7}\approx3.5\)($)

Error, sr