geno3141

If the ratios are 1:3:5, write them as:  1x, 3x, and 5x.

Since they are the three angles of a triangle, their sum is 180:   --->   1x + 3x + 5x  = 180°

--->   9x  =  180°

--->    x  =  20°

--->   x  =  20°     and     3x  =  60°     and     5x  =  100°

The quotient of a number and three is:  x/3

If  x/3  =  -4,  then multiply both sides by 3:

--->   x  =  -12

If  27  is divided by  2, the quotient will be  13, with a remainder of 1.

This is  13 1/2  or  13.5.

0.35  =  35/100  =  7/20

To find out, replace x with -3:

Left side:     4x - 3 + 2x  =  4(-3) - 3 + 2(-3)  =  ?

Right side:   4 + x - 8  =  4 + (-3) - 8  =  ??

Does the answer for  ?  match the answer for  ?? 

If they match, -3 is an answer; if they don't match, then -3 isn't an answer.

When she enters the water, f(x) = 0.

0 = -4.9t² + 4t + 10

Solve for t by using the quadratic formula:  t =  [ -4 ± √(4² - 4 · -4.9 · 10) ] / [2 · -4.9 ]    --->  t = 1.89 sec.

The area of the square is so large that it completely encloses rectangle R. So, let's just create a rectangle with one endpoint on the line  y = -3x and placed horizontally.

From a point (x, -3x), create a rectangle to the right and up. The distance from this point to the right end of rectangle R is: 8 - x; the distance from this point up to the top of rectangle R is:  12 - -3x).

The total area is:  (8 - x)(12 - -3x)  =  (8 - x)(12 + 3x)  =  96 + 12x - 3x².

The first derivative is:  12 - 6x

Setting this equal to zero:  12 - 6x  = 0  --->   12  =  6x   --->   2 = x   

If  x = 2,  y = -6

The horizontal length is 8 - 2  =  6, the vertical length is 12 - -6  =  18     --->   Area  =  108

The standard error of the mean is the value found by dividing the standard deviation by the square root of the number in the sample.

SEM  =  16/√36  =  2.667

z-score  =  [x-bar  -  mean(x-bar)] / [ std dev x-bar ]

            =  [40 - 39] / [2/√30]  

            =  0.0913

Now, you will need to find the normalcdf for a z-score of this size or greater.

If the number is greater than 1, count the number of places from the right-end of the number to the location immediately after the first digit; in this problem, there are 10 places.

Answer:  5.8 x 10^10.