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that is what i did but it might be wrong let me find out,

csc(10) = -1.8381639608909151

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Doubling does not all ways work, ur wrong and so am i

Yes, since you double it... right?

The volume of a cylinder =  pi r^2 h

                           432 pi = pi r^2 h    divide both sides by pi

                           432 = r^2 h            Now since the ball touches the bottom and top    and the sides

                                                               h must be equal to diameter    and thus r = h/2   put this into the equation

                            432 = (h/2)^2 h   and solve for h = 12

Now you know the diameter of the sphere = 12    and the radius of the sphere = 6

sub this in to the volume of a sphere = 4/3  pi  r^3       and you will have your answer !

Nice, Chris! That's a hard one!!!

Ax  + By  =  3

The slope of this line =  -A/B

And

Since  this line passes through  (-7, 2)  it must be that

A(-7) + B(2)  =  3

-7A + 2B  =  3

2B = 3 + 7A

B  =  [ 3 + 7A ] / 2

And

x + 3y  =  - 5

3y = -x  - 5      divide  both sides  by  3

y = (-1/3)  - 5/3

The slope of this line  =  (-1/3)   and since  this line is parallel to the first line we have  that

-A/ B  = -1/3

A  / B   =  1 / 3

A / [ (3 + 7A)/ 2 ] =   1 / 3

2A / ( 3 + 7A )  = 1/3     cross-multiply

3 * 2A =  1 ( 3 + 7A)

6A  = 3  + 7A

-A  = 3

A = -3

B = (3 + 7A) / 2  =  ( 3 + 7(-3)) / 2 =  -18/2  =   -9

So

A = -3

B = -9

B - A   =    -9 -  (-3)  =    -6

There isn't any graphs to choose from in your Q submission....

     However the graph should be a slanted line getting higher to the right.....

the first three terms are found by substituting   n = 1      n= 2     and n = 3 into the equation

n² + 20    put in  n = 1     1^2 + 20 = 21

   I think you can do the  n=2  and n=3 versions

How many terms are less than 50?

n^2 + 20  < 50

n^2  <   30

n   <  5.47   ( taking the positive root only)  

                         the answer would be 5                  5^2 + 20 = 45                but 6 would not work  6^2 + 20 = 56

We  have that

a1 + a2   = a3

a2 + a3  = a4  ⇒  a2 + (a1 + a2)  =  a1  + 2a2

a3  + a4 =  a5  ⇒   (a1 + a2) + ( a1 + 2a2)  = 2a1  + 3a2

a4 + a5 = a6  ⇒   (a1 + 2a2) + ( 2a1 + 3a2)   = 3a1 + 5a2

a5 + a6 = a7  ⇒   (2a1 + 3a2) + ( 3a1 + 5a2)  =  5a1 + 8a2  =  120 

a1  =  [ 120 - 8a2 ]   /  5

a1 =  120 / 5  -  8a2 / 5

a1  = 24  -  8a2  / 5

a1 will be an integer  and < a2    when  a2  = 10

Then a1 =  24 - 8(10)/5  =  24  - 80/5  =  24 -  16  =  8

So

a1 = 8

a2 = 10

a3 = 18

a4 = 28

a5 = 46

a6 = 74

a7 = 120

a8=  194

1. The angles in the dilation are the exact same, as they are both similar since their corresponding sides are all proportional to each other in a scale factor of 2.

2. I'd imagine there's some kind of tool to measure angle. Use that on both of these triangles, and you should find that they have the same angle measurements

3. That would be true for any angles in dilation, since dilating these triangles are just "stretching them", or magnifying their sides by a certain factor, leaving the same proportion between the original and the dilated triangle, meaning they remain similar, and thus, have the same angle measurements.

The INTEREST on that amount for 7 years would just be       $ 875 * t * rate     where rate is in decimal form (.04)

$ 875 * 7 * .04 = $  ..........

Nice,Chris!!!!

Thank you for the hints and help guys!!!!

1. if you don't live, what else do you do? You need to use your life wisely so that you can do stuff.

2. You need to be there for your future wife, children, etc. They will need you!

3. God bless you, and you need to bless him back.

...as explained fully above

to divide fraction by a fraction      take the denominator, flip it and multiply by the numerator

-5/13   /  1/5    =   -5/13  *  5/1 =  -25 / 13      or     -1  12/13

Nice, jfan!!!!

My advice would be to use complementary counting. In otherwords, you take the total number of ways to form a 3 senator committee, and subtract from it the number of ways that a single party can hold all 3 seats. That simplifies the problem immensely.

We then have:

100 * 99 * 98 ways to form a 3 member senate. If we had a committe with all 3 seats belonging to one party, there are two cases:

Democrats occupy all of them, of which there are:

47*46*45 ways to do this

Republicans occupy all of them, of which there are:

53*52*51

We add these two cases up, and then subtract it from the total number of ways to form a 3 member senate.

970200- 237846= 732354 ways(check me if I'm wrong)

Here is my shot at this:

You can choose 2 democrats and one repub   or    two repub and 1 dem.

47 c 2   x  53      +    53 c 2 x 47   =......       

No worries!  :)

The formula for volume of a cylinder is as follows:

given r as the area of one of its circular bases, and H as the height, 

the volume of the cylinder = \(\pi*r^2*h\)

The volume of the cylinder given in this problem has an 18 inch diameter, meaning the radius is 9

The volume is then:

\(\pi * 9^2 * 15 = 1215\pi\) in.³

Next, to calculate how much total water is within the cylinder, we just need to subtract the volume of the 6 inch diameter ball from the cylinder(since that ball takes up volume).

The volume of a sphere is as follows:

given r as its radius, its volume is then:

\(\frac43 * \pi * r^3\)

We are given that the diameter of this ball is 6 inches, so the radius is then 6/2 = 3 inches

The volume is then:

\(\frac43 * \pi * 3^3 = \frac43 * 27 * \pi = 36\pi\) in.³

Our total volume of water is then:

\(1215\pi - 36\pi = 1179\pi\)in.³

the '4' is in the 'ten thousands' position and represents  forty thousand.

Oh right, oops on my part! The problem didn't say whether we have to find the smallest one tho, but I'm assuming it does :)

Sorry. I'm a bit brain-dead today.

What is -5/13 divided by one-fifth?

We will find how many cubes there are to find the volume. Since there are 16 cubes in one face, you can multiply that by two to get 32.

Hence, the volume of the cuboid is 32cm^3