geno3141

The area of the triangle is:  A  =  ½ · (base) · (height)  =  ½ · ( 7 ) · ( 3 )   =  21/2

The equation of line(BA) is:  y  =  (3/10)(x + 6).

The line  x = k  is a vertical line that passes through the x-intercept  (k, 0).

It also passes through the point  ( k, (3/10)(k + 6) )  on the line(BA).

The region of the triangle to the left of the line  x = k  is a triangle with base length = k + 6

and whose height is  (3/10)(k  + 6).

The area of this triangle is:  ½ · (k + 6) · (3/10)(k + 6)

Since this area = one-half of the total area of the triangle:

     ½ · (k + 6) · (3/10)(k + 6)  =  ½ · (21/2)

                        (3/10)(k + 6)²  =  21/2

                                  (k + 6)²  =  35

                                    k + 6  =  sqrt(35)                       (you can ignore the other answer)

                                          k  =  sqrt(35) - 6                  (a point slightly to the left of the axis)

Since the median is ten and there are ten distinct numbers, the median must be found by finding the mean between the two "middle" numbers.

This could be done by having the integers 9 and 11 in the group.

The four smallest numbers less than 9 are 1, 2, 3, and 4.

The four smallest numbers more than 11 are 12, 13, 14, and 15.

My guess is that the set consists of 1, 2, 3, 4 9, 11, 12, 13, 14, and 15.

There are 6 choices for the shirt,

there are 3 choices for the pants,

there are 2 choices for the shoes,

and there are 5 choices for the tie (4 ties plus no tie)

for a total of 6 x 3 x 2 x 5 choices for the outfit.

There are 4 choices for the left-most digit (1, 2, 3, or 4; 5 can't be chosen)

then there are 4 choices for the middle digit and 3 choices for the right-most digit.

This means that there are 4 x 4 x 3 = 48 choices.

If the word "boys" only refers to male children and the word "girls" only refers to female children,

then 80% of 30% = 24% of the people were girls.

Let's see:

100 = 2 x 2 x 25  or 4 x 5 x 5 so it works

101 is prime so it is excluded

102 = 2 x 3 x 17 so it works

103 is prime so it is excluded

104 = 2 x 2 x 26 or 2 x 4 x 13 so it works

105 = 3 x 5 x 7 so it works

106 = 2 x 53 ============ this can't be encoded; so the answer is 106

Since  2⁰ = 1

           2² = 4

           2³ = 8

           2⁴ = 16

           2⁵ = 32

           2⁶ = 64

I would expect that  g(x) = 2^x.

If so,  2⁰ = 1

To find the inverse of  f(x)  =  2x³ + 5  follow these steps:

1)  Replace  'f(x)'  with  'y':  y  =  2x³ + 5 

2)  Interchance  'x'  and  'y':  x  =  2y³ + 5

3)  Solve this equation for y:  x  =  2y³ + 5

                                          x - 5  =  2y³  

                                  (x - 5) / 2  =  y³

                          [ (x - 5) / 2 ]^1/3  =  y

4)  Replace  'y'  with  'f^-1(x)'  indicating that this equation is the inverse:  f^-1(x)  =   [ (x - 5) / 2 ]^1/3 

This shows that  g(x)  is the inverse of  f(x). 

If you want to, you can follow these steps to find the inverse of  g(x), showing that  f(x)  is the inverse of  g(x).

The first card can be any suit so we don't need to include it into the calculation.

Because each card is replaced after it is drawn, there is a 1/4^th chance that the second card will match the first.

It is also true that the third card has a 1/4^th chance that it will match the first two.

Lastly, the fourth card has a 1/4^th chance that it will match the first three.

Multiplying together these possibilities, we get a probability of (1/4) x (1/4) x (1/4)  =  1/64.

The total area = 9 x 10 = 90 sq in

The shaded area = 78 sq in

Subtracting, the central area = 12 sq in

Since the height is 2 in, the width must = 6 in