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At Glenridge High School, 20 percent of the students are seniors. If all of the seniors attended the school play, and 60 percent of all the students attended the play, what percent of the non-seniors attended the play?

This question is very  t r i c k y

100%   -   all students at Glenridge High School

20%    -    seniors, and all of them attended the play

Out  of  80% of non-seniors, only one half of them  attended the play.

Answer:    50% of non-seniors attended the play.    

Part 1:  Yes.

f(x)  =  a(x +3)(x - 4)(x - 8)             g(x)  =  b(x + 5)(x + 3)(x - 2)(x - 4)(x - 8)

g(x) / (x)  =  [ b(x + 5)(x + 3)(x - 2)(x - 4)(x - 8) ] / [ a(x + 3)(x - 4)(x - 8) ]  =  (a/b)(x + 5)(x - 2)

Part 2: Each of the x-term factors of f(x) must be x-term factors of g(x).

The vertex is (2,1) and it has no expansion or contraction, so its equaiton is:  y - 1  =  (x - 2)²

Multiplying out and simplifying:  y  =  x² - 4x + 5

a = 1,     b = -4,     c = 5

Let A be the point (2,0) 

and B be the point (4,3).

The slope is:  (3 - 0) / (4 - 2)  =  3/2.

If the roots are  3 + sqrt(5)  and  3 - sqrt(5), then the equation is:

    y  =  [x - ( 3 + sqrt(5) ) ] · [x - ( 3 - sqrt(5) ) ]

If you expand the above equation, you will end with:  y  =  x² - 6x + 4

Now, to find the vertex:           y  =  x² - 6x + 4

                                          y - 4  =  x² - 6x

Complete the square:  y - 4 + 9  =  x² - 6x + 9

                                          y + 5  =  (x - 3)²

So, the vertex is:  (3, -5)

As you can see....only one number, 26 is in the intersection

   even numbers above 20  and less than 50...     22 24  26 .....48   14 numbers         1 out of 14   = 1/14

Please Help Electric Pavlov!

Please Help Electric Pavlov!

.22 (5)  +  .90 (12)  =  x ( 5 +12)     solve for 'x' the decimal percentage of the resulting alloy

100% is the number of people in the survey

-10% = 90%

70% - 4000    +    60% - 4000    + 4000 = 90

130% - 4000 = 90%

-4000 = -40%

100% = 10 000 people

A. P = 2 · 3 x        if this is actually    2 * 3^x

B. P = 2 · x 3

C. P = 3 · x 2

D. P = 3 · 2 x

First of all, the upside down "U" means the intersection of sets, therefore (I don't know the Latex of symbol for the upside down "U" but it is called cap) A cap B is the number that appears in both sets. The only one that does this is 26, therefore A cap B is 26. So all you have to do is find the probability that 26 is chosen from the even numbers above 20 and less than 50. There are 14 even numbers, and 26 is one of them, so the probability that the number is in the set A cap B is \(\frac{1}{14}.\)

w or p      x      s p k n      x  c s r m n

    2          x           4         x    5            =  ......

there are 13 or 14 

a. The probability is 1/12.

The equation is y = x^2 - 5x + 8, so a + b + c = 1 + (-5) + 8 = 4.

The area of the polygon is 25.

A scientist studied the population growth of a certain type of bacteria. He concluded that if you start with 2 bacteria, then the population, P, would triple with each passing day, x. Which of these equations represents the population growth of this bacteria?

A.

P=2·3xP=2·3x

B.

P=2·x3P=2·x3

C.

P=3·x2P=3·x2

D.

P=3·2x

p=2x+p

First find the temperature

sqrt (10^2 +(-4)^2 = 10.77

cos = adj/hypotenuse

       = 10/10.77 = .92847          sec = 1/cos = 1/.92847 = 1.077

Think of each number in terms of their remainder when divided by 3.

1 has rem 1

2 has rem 2

3 has rem 0

4 has rem 1

5 has rem 2

6 has rem 0

7 has rem 1

8 has rem 2

9 has rem 0

10 has rem 1

11 has rem 2

12 has rem 0

In order that each column sums to a number divisible by three we must have combinations such that each number with remainder 0 is combined with one of the numbers with remainder 1 and one with remainder 2.

There are 4*4*4 = 64 ways of doing this. This is the result if the columns are distinguishable. If they aren't distinguishable this number should be divided by 4 (I think!).

here is one

1  2  3

5  4  6

7  8  9

11 10 12       there are many more....see Alan's answer below:

2 j + 6a = 12

5j  + 3a = 15     Multiply by -2

-10j - 6a = -30    add to first equation

-8j = -18       solve for j      then use this value of ' j' to calculate 'a ' with one of the equations....

Thanks for the help!