Alan

Notice that the curve goes through the following three points (you could choose any three, but these are easy ones):

 (0, 5)   (2, 1)  and  (4, 5)

This allows you to set up the following three equations:

5 = a*0²  +  b*0 + c     or simply  c = 5

1 = a*1² + b*1 + c     or   a + b = -4         ...(1)

5 = a*4² + b*4 + c    or    16a + 4b = 0    ...(2)

You could solve equations (1) and (2) for a and b if you wish; however, since you are only asked for a + b + c you could simply use the value of a + b from (1) together with the value for c.

This question seems to occur frequently!  Have a look here: https://web2.0calc.com/questions/i-m-really-stumped-polynomials 

The common ratio is simply r = -2/7, so the infinite sum is given by 1/(1 - (-2/7))  or 7/9

For the product to be even there must be at least one even integer.

Probability of no even integers p0 = (10/20)*(9/19)*(8/18)

Hence probability of at least one even integer = probability of even product    p = 1 - (10/20)*(9/19)*(8/18)

(Edited to make more sense!  Thanks EP).

In general, when you have the complex number a + bi the angle is given by \(\theta =tan^{-1}(\frac{b}{a})\)

A rectangular page is designed to contain 64 square inches of print. The margins at the top and bottom of the page are each 2 inches deep. The margins on each side are 1½ inches wide. What should the dimensions of the page be so that the least amount of paper is used?

This graph should help you answer the question:

Probability of selecting all males: pm = (8/16)*(7/15)*(6/14)*(5/13) = 1/26

Similarly, probability of choosing all females: pf = 1/26

Hence probability of not having all males or all females (i.e. at least one male/female pair): p = 1 - pm - pf = 12/13

2^2x+3 = 2^2x.2³ = 8.2^2x = 8.(2^x)²

So  8.(2^x)² = 14

(2^x)² = 14/8

2^x = sqrt(14/8)

As follows: