All Answers 354657 Answers

I will go and answer it now!

180 - (84+43) = x

Try it out!

I hope this helps!

We have $3x+7 \equiv 2 \pmod{16}$, so $3x \equiv -5 \equiv 11 \pmod{16}$.
This solves to $x \equiv 9 \pmod{16}$.

Thus, $2x+11 \equiv 2\cdot 9+11\equiv 13 \pmod{16}$.

There are 9 possible numbers for the first ball, then 8 possible numbers for the second number, then 7 possible numbers.  There are 9 possible outcomes for the SuperBall, so the answer is (1200 - 9*8*7 - 9)/1200 = 687/1200.

Case 1: Superball

The probability is 1/10, because you choose 1 out of 10.

Case 2: 2 whites

The probability is 1/C(10,2) = 1/45, because you choose 2 out of 10.

Case 3: 3 whites

The probability is 1/C(10,3) = 1/120, because you choose 3 out of 10.

Adding these, you get 1/10 + 1/45 + 1/120 = 47/360.

a^3 + b^3 = 42

(a+b)(a^2 - ab + b^2) = 42

a^2 - ab + b^2 = 6

(a+b)^2 - 3ab = 6

49 - 3ab = 6

ab = 43/3

a^2 - ab + b^2 = 6

a^2 - 43/3 + b^2 = 6

a^2 + b^2 = 20 1/3

=^._.^=

(1) The probability is 1/C(20,3) = 1/1140.

(2)

Case 1: Superball

The probability is 1/10, because you choose 1 out of 10.

Case 2: 2 whites

The probability is 1/C(10,2) = 1/45, because you choose 2 out of 10.

Case 3: 3 whites

The probability is 1/C(10,3) = 1/120, because you choose 3 out of 10.

Adding these, you get 1/10 + 1/45 + 1/120 = 47/360.

y = k / sqrt(x)

4 = k / (sqrt 2)           k, the proprtionality constant = 4 sqrt 2

16 = 4 sqrt 2    / sqrt x

4 sqrt 2 / 16 = sqrt x

16 * 2  / 256  = x

x = 1/8

Need some angle iformation to complete this ....  

Guest is correct....I did not quite read the question corectly.....

   Largest exterior angle would have the smallest interior angle

     largest exterior angle is  7 x 24 = 168 degrees

        Interior + exterior = 180 degrees             180 - 168 = 12 degrees for the smallest INTERIOR angle !     THANX < guest !

We can use power of a point to find XY. 

8^2 = 4 * xy

xy = 16

Now we have a right triangle with legs 20 and 8. 

sqrt(20^2 + 8^2) = sqrt(464) = 4sqrt(29)

=^._.^=

The sum of the squares of two nonnegative numbers is 327. The product of the two numbers is 101. What is the sum of the two numbers?    

I don't think this will work.  The only factors of 101 are 1 and 101.  If you square 101 you're already larger than 10,000 so the "sum of the squares" part of the problem isn't satisfied. 

I claim that the $n=m=15$, so $n-m=0$.  To see that $15!$ is a common multiple of 4125 and 2816000, just check that $15!$ is a multiple of both $4125=3\cdot 5^3\cdot 11$  and $2816000=2^{11}\cdot 5^3\cdot 11$.  To see that $15!$ is the smallest common multiple of 4125 and 2816000, note that $14!$ is not a common multiple of 4125 and 2816000 (because $5^3$ does not divide $14!$ so it can't divide any $x!$ where $x \le 14$).

What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the ratio of 3:5:7?

360/15 = 24

7 * 24 = 168

Smallest interior angle = 180 - 168 = 12º

Shortly after 10 'o clock, the hands of a clock made a 90-degree angle. What's the time?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Here's another way to solve this problem.

Arc from 10 to 12 = 60º

Let x be the arc-path of minute hand in degrees.

60 + x - (x/12) = 90

x = 360/11 = 32.72727272º     (minute hand arc)

x/12 = 30/11 = 2.72727272º     (hour hand arc)

The original mixture is 16 quarts ammonia and 4 quarts water.  So, to make it 50% ammonia, you take out 4 quarts of ammonia.  So you need to take out 4*0.8 = 3.2 quarts of the mixture.

The sum of the two numbers is 25.

The solution to the first inequality is w <= 2 and the solution to the second inequality is w <= -6, so the interval is [-6,2].

All of the exterior angles sum to 360 

360 / ( 3+ 5 + 7) = 24

   the exterior angles are then   3 * 24           5 * 24        and     7 * 24

    24 * 3 = 72 degrees would be the smallest

At 10:00 the hour hand is at 300 degrees   .....  it moves 1/2 degree per minute

    so the angle it forms with the 12 : oo position is

       360 - 300 - 1/2 x

     the minute hand moves 6 degrees per minute

     the angle it forms with 12:00   is      6 x

summed they = 90 degrees

360-300-1/2 x     +     6x     = 90

60 + 5.5 x = 90

5.5x  = 30

x = 5.45 minutes   ( 5 min 27 sec)                       so at   10:05:27   the hands form a 90 degree angle