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Let  there  be  100  contestants  and let  each  question  be  worth  1 point  for a correct answer 

The total points possible of correct answers =  100  * 44  = 4400

Let  x  be  the average  number of questions  that  were  answered correctly by the bottom  25%

So   we  have

75 peolple with 48 correct answers each + 25 people with x correct answers each =  4400

75( 48)   +   25 (x)    =   4400

3600  +  25x  =  4400

25x =  4400 - 3600

25x = 800

x = 32   =  the  avg no.  of  questions answered correctly  by the  bottom 25%

So     60  -  32   =   28  = avg no. of  questions answerd incorrectly by the bottom 25%

Surface of cube   2 x 2  x 6  = 24 units²

The surface of a sphere with TWICE this surface area (since we are painting only 1/2 of the sphere ) = 4 pi r2 = 48 units²

    4 pi r² = 48

        r =  sqrt( 48/4pi) = sqrt (12/pi)  = 2 sqrt (3/pi)

The rate of change of the height is 12.75 inches/s.

$100\cdot(x-4)+10\cdot{x}=100x-400+10x=700$

$110x=1100$

$x=10$

$10+(10-4)=\boxed{16}$

The rate of change of the surface area of the sphere is 40.428 cm^2/s.

4 * $1 = $4

$7 + $4 = $11 (Cost of same number of each

                         type of coins)

$1 + $0.10 = $1.10 (Value of 1 pair)

$11 ÷ $ 1.10 = 10 (pairs)

10 * 2 = 20

20 - 4 = 16

Lucas has 16 coins in all.

Actually 76 was right :)

2x2x6=24

total amount of paint = 24

4$\pi$r$^2$=surface of sphere

2$\pi$r$^2$+$\pi$r$^2$=surface of hemisphere=24

$\pi$r$^2$=8

r$^2$=$\dfrac{8}{\pi}$

r=$\boxed{\frac{2\sqrt2}{\sqrt{\pi}}}$

The fron of the train enters tunnel at 120 km/hr   and   15 s later the tail-end enters the tunnel

The train length will be how far the train travels in 15 s   @   120 k/hr

15 s =   15/3600 hr

rate * time = distance   ( or length in this case)

15 / 3600 hr  *  120 k/hr = .5 km     or  500 meters long

1 group --> 2 wins + 1 draw 

Points for a group of 2 wins and 1 draw

--> 2 * 3 + 1 * 1

= 7

No points were scored for any loses, so all the 70 points must be due to the wins and draws, which were in groups of 2 wins and 1 draw.

70 ÷ 7 = 10 (Number of groups)

3 * 10 = 30 (Total wins and draws)

38 - 30 = 8

The team lost 8 games.

r = 10    theta = 11 pi /6

Hmm... you could be right...

A = 96   B = - 80     difference = 176

Smallest A --> 8 * 2 = 16

Largest A --> 8 * 12 = 96

Smallest B --> 20 * 1 = 20

Largest B --> 20 * 4 = 80

Difference between Largest A and Smallest B 

= 96 - 20

= 76

Difference between Largest B and Smallest A

= 80 - 16

= 64

Largest possible difference = 76.

The largest possible difference is 12x8-1x20=96-20=76, not 4x20-2x8=64, which is less than 76.

$12x+14y\ge1200$

we can think of this as a timeline, where our point is x units away from 12:00, and 99 units the other direction, there is a point 2x units away from 8:00

this turns into an equation:3x+99=240 we will just solve for x:

3x=240-99=141

x=$\boxed{47}$minutes away from 12 P.M.

careful with the expression sqrt(a)/b*pi. some people could thing it's $\dfrac{\sqrt{a}}{b\pi}$.

we can say that the length of one side of the yard is 2 meters(ignore how small it is). With numbers, it is much easier to calculate.

We can draw lines from the center of the triangle to the midpoints of the sides, to get 3 quadrilaterals. we can cut those in half so that there are lines going from the center to the vertices, so we have 6 congruent 30-60-90 triangles. We know that the long leg of the triangles is 1, so the radius of the area Fido's leash is able to reach is $\dfrac1{\sqrt3}$. So, the area Fido is able to go in is

$(\dfrac{1}{\sqrt3})^2\cdot\pi=\dfrac13\pi$

the area of the triangle is height x base / 2 = 2 $\sqrt3$ x 2 / 2 = 2$\sqrt3$

so the fraction of the yard Fido is able to cross is

$\dfrac{\dfrac13}{2\sqrt3}\pi=\dfrac{\sqrt3}{18}\pi$

so a=3 and b=18. therefore: ab=$\boxed{54}$

75/100 = 3/4 

44 * 4 = 176

176 - 3 * 48 = 32

32 was the average number 

8x + 3 = 27

     - 3    - 3

      8x = 24 

       x = 3

8x + 3 = 59

     - 3  = -3

      4x     56

       x = 7

160-2w≤145

the answer is 42

The height should be increased by 30%.