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Also, I think they wrote the solution wrong. B is the best answer.

I think it's B, but we can have a debate. 

Okay, let's narrow this down:

First, read the problem carefully. 

Now, we eliminate.

Choice D is wrong since it reflects of the whole U.S., not New Jersey.

Choice C is wrong since it reflects on STUDENTS at this public university in New Jersey.

Now we are down to A and B.

To me, I think it's B since it has a larger sample size, and it will have more accurate results. 

I don't know why, either. I got B.

Angle(E) of the triangle has 180 - 2x degrees.

Angle(F) of the triangle has 180 - 4x degrees.

The three angles of the triangle equal 180 degrees, so (180 - 2x) + (180 - 4x) + (x)  =  180

                                                                                                                      360 - 5x  =  180

                                                                                                                              -5x  =  - 180

                                                                                                                                 x  =  36 degrees

[180 - 4x] + [180 - 2x] + x =180, solve for x

x = 36,    2x =2 x 36 =72,   4x =4 x 36 =144

I think that your answer is better than their's. Having 1500 randomly selected persons is (almost always) more accurate than just 300; but, their answer seems to assume that the reaction of New Jersey residents will reflect the same attitudes as those of the country as a whole; an assumption that, I feel, is not warranted.

By entering -2, you made the y-component to be (y - 5)² which would make the circle tangent to the x-axis --

and the circle will be above the x-axis (center at (6,5)  -- however, you were instructed to translate the circle

downwards -- by making a = 5, you translated the circle upwards.

You will need the y-component to be (y + 5)²  --  which will make the circle tangent to the x-axis -- it will

be tangent below the x-axis.

A triangle has 180 degrees. A straight angle has 180 degrees. 

The straight line is 6x. Also, a triangle has 180. So, x=30. 

(I don't know your level, so I don't know how to explain it. I don't think you have learned too much about triangles yet, so I'm super sorry if you don't get my explanation.)

-tigernathan

n = 207

[2 + 7] x 23 =207

7 - 2 = 5

2x+60+3x+20=180 (because BEF equals the angle that is with angle EFD)

Solve 5x=100 --> x=20

You can do the rest

A pair = 2 cubes

So if we need to ensure that at least one pair of each color has been removed, we want the worse-case scenario:

First we select red, then blue, then green (this is worse-case, because we haven't gotten a pair yet). Then we select one of the three colors (aha! one pair since all of the colors have already been selected) then we select another same color (this is worst-case because we haven't hit two pairs yet). Then we select another same color and another and another until we use up all of the red (this is worst-case because red has the most). We do that for 14 times (since there are 15 and the first red was already selected.) Now we move on to green (this is worst-case because green is the second most), we do that for 12 times (same logic). You get it. Now we select our last one which is blue (since the others are already all used up). And now you're finished. Hopefully, you can add up those cubes.

c=0;a=1;b=(2^a - 1);if(b%7==0, goto4, goto6);printb;c=c+1;a++;if(a<=1000, goto2, 0);printc

OUTPUT =333  positive integers.

10 digit numbers go something like this: _ _ _ _ _ _ _ _ _ _ 

If number 2 is in the first place, it's kind of set so you basically only need to find 9 digit numbers now: _ _ _ _ _ _ _ _ _

If repition is not allowed, the first digit has 9 (no 0) choices the second also has 9 (because any number except the first chosen) the third has 8, and so on. That's basically going to be 9*9! (without the 1 but anything times 1 does nothing)

Try figuring that out!

thanks

Thank you for the hint! It helped

There are 9 choices for the first (left-hand) digit and 10 choices for the second digit, giving 9 x 10 = 90 

choices for the first two digits.

The last two digits, starting with 00 must be divisible by 4; such as 00, 04, 08, 12, etc.

How many choices are there for the last two digits?

Multiply this answer by 90 to get the final answer for the number of numbers that are divisible by 4.

To find the number that are divisible by 4, subtract that answer from 9999.

By a geometric theorem (involving similar triangles):  CB · CA  =  CD · CL

--->     (7) · (7 + 2x + 3)  =  (9) · (9 + x + 1)

--->          (7) · (10 + 2x)  =  (9) · (10 + x)

--->                  70 + 14x  =  90 + 9x

...

find x; then find AB ...

xxxxxxxxxxx

sumfor(k, 1, 1000, (k / (2^k))) = it converges to 2

Have you gotten the answer, or do you need more help?

Thanks understood completely.

Hint:     12y³ - 6y²  =  6y²(2y - 1)

If x= 1, y = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 12,13,14,15

If x = 2, y = 1, 2, 3, 4, 5, 6, 7

If x = 3, y = 1, 2, 3, 4, 5

If x = 4, y = 1, 2, 3

If x = 5, y =

...

Hint, you shouldn't be lazy and let other people do the work for you, mathematicions like Albert Einstein took years to figure out one question.
 

anyways, you should simplify x(x+5)=-n which will be x^2+5x+n=0, then make a chart with two columns and 10 rows and you plug in 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 into x^2+5x+n=0, then if the discriminant (b^2-4ac) is negative, it has unreal roots, 

I'll do one for you, for example if we have 7 as n, then 

a=1

b=5

c=7

then plug these into b^2-4ac and you will get (5)^2 -- (4)(1)(7), this will equal to 

25-28 which is [-3] this means that if n is 7, then the quadratic has no real roots, if b^2-4ac is equal to something positive then it has real roots.