geno3141

The central angle measures  5pi/12.

The full circle measures  2pi.

Finding the portion of the circle:  (5pi/12) / 2pi  =  5/24^th  of the circle.

The area of the circle is:  pi · (5 in)²   =  25pi in²

Finding  5/24^th  of the circle:  (5/24) · (25pi in²)  =  125/24 pi in² 

This is an isosceles triangle.

Drop a perpendicular from Z to side XY; call the point of intersection P.

Since the triangle is isosceles, P will be the midpoint of side XY.

Consider triangle(XZP).

It is a right triangle.

Its hypotenuse is 7, one of its sides is 3.

Using the Pythagorean Theorem to find the other side:  3² + ZP²  =  7² 

   --->   9 + ZP²  =  49   --->   ZP²  =  40   --->   ZP  =  sqrt(40)   --->   ZP  =  2 · sqrt(10)

The base of the triangle is XY; the height is ZP.

Its area is  ½ · 6 · 2 sqrt(10)  =  6 · sqrt(10)

The mean is found by the formula:                      (a + b) / 2  

The standard deviation is found by the formula:  sqrt[ (a - b)²  12 ]

For  U(4, 13):     a = 4     b = 13

--->   mean  =  (4 + 13) / 2  =  17/2  =  8.5

--->  standard deviation  =  sqrt[ (13 - 4)² / 12 ]  =  sqrt[ 81 / 12 ]  =  2.598

If the probability of making the shot is 3/4, then the probability of missing the shot is 1/4.

Th probability of missing twice in a row is:  (1/4) x (1/4)  =  1/16

9 1/16 is not a whole number ...

Do you mean "decimal number" or "common fraction"?

You can draw a vertial line that divides this picture into two parts:

-- on the left, a rectangle that is 60m x 120m

-- on the right, a triangle whose two bases are 80m and 140 m

Find the area of the rectangle and the area of the triangle and add them together:

  Area  =  (60m · 120m) + (½ · 80m · 140m)  =  

"at least eight" means "eight or more":

The probability of getting 

--  exactly 8 is:    ₁₀C₈ · (0.85)⁸ · (0.15)²  =  0.73153125

--  exactly 9 is:    ₁₀C₉ · (0.85)⁹ · (0.15)¹  = 

--  exactly 10 is:  ₁₀C₁₀ · (0.85)¹⁰ · (0.15)⁰  =  

Can you find the other two answers?

To get the final answer, you will need to add these three answers together.

3mn - 6m + 5n + ?

Factoring "3mn - 6m"

  3m(n - 2) + 5n + ?

We need to have it look like this:

  3m(n - 2) + 5(n - 2)

So:  ?  =  -10

Checking:

 3mn - 6m + 5n - 10

  3m(n - 2) + 5(n - 2)

  (3m + 5)(n - 2)

The equation   y = x   is its own inverse.

The two triangles are similar by AA -- both have a right angle and the angle of incidence equals the angle

of reflection.

Therefore,      (the height of the triangle) / 20'  =  6'/3'