geno3141

To find the percent of increase:

     first, find the amount of increase:     164 - 151 = 13 pounds

     then, divide by the original amount:  13 / 151  =  0.0861

     to turn into a percentage, multiply that answer by 100:  0.0861 x 100  =  8.6%

To find the payment:     P  =  i·A / [1 - (1 + i)^(-N) ]

For one year:

     i = interest rate, as a decimal, per period:  0.072 / 3  =  0.024

    A = amount borrowed:  3000

    N = number of payments:  3

    P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-3) ]   =  $1048.38

For three years:    If it's three equal installments per year:      N = 9

    P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-9) ]   =  $374.60

For five years:       If it's three equal installments per year:      N = 15

    P  =  (0.024)(3000) / [ 1 - (1 + 0.024)^(-15) ]   =  $240.52

I lost the question towards the end ...

Perhaps you mean:   2 x 2 x 2 x 2 x 2 x 2 x 2   =   2 ^ 7

(I got the 7 by counting the number of 2's in the problem.)

Growth and decay problems:  By how much will a population grow or decline? What is the half-life of an element?

Using logarithms to solve problems in which the variable is an exponent.

Solving those problems taht arise using calculus.

Solving problems in probability that use the normal curve of distribution, whose function is described in terms of e.

This is a volume problem:  volume  =  area of base x height  

                  which is also:  volume  =  area of base x depth

(However, the 0.6 sqm of material must actually be 0.6 cubic meters of material.)

volume = 0.6 cubic meters          area of base = 6.0 square meters         depth = unknown

----->     0.6  =  6.0 x depth

Dividing by 6.0:     ----->     0.6 / 6.0  =  depth     ----->     0.1 meters  =  depth

If you want a point that is one-third of the way from (2, 3) to (5, 9), it will have to be one-third of the way in the x-direction and one-third of the way in the y-direction.

In the x-direction:  the distance from 2 to 5 is 3; one-third of 3 is 1; adding 1 to 2 (the beginning x-value), answer = 3.

In the y-direction:  the distance from 3 to 9 is 6; one-third of 6 is 2; adding 2 to 3 (the beginning y-value), answer = 5.

The location of the point on-third of the way from (2, 3) to (5, 9) is (3, 5).

tan(32°)  =  x/6.5

0.6249  =  x/6.5

x  =  -.6249 x 6.5

x  =  4.062

Another way to get CPhill's answer:

Still using his idea of subtracting the probability of getting no kings from 1, the total possible probability.

The only way that you can get no kings is:

to get no king for the first card:  probability = 48/52    

to get no king for the second card:  probability = 47/51

to get no king for the third card:  probability = 46/50

to get no king for the fourth card:  probability = 45/49

and, finally:

to get no king for the fifth, and last, card:  probability = 44/48

Multiplying all these probabilities together:  48/52 x 47/51 x 46/50 x 45/49 x 44/ 48  =  0.6588

Subtracting this from 1.000:  1.000 - 0.6588  =  0.341

There are two ways that I can think of:

1)  Graphing:  answers  =  1.0897554  and  3.9102446

2)  Quadratic formula:    ((7+(4*(3^(1/2))))^(t^2-5 t+5))+((7-(4*(3^(1/2))))^(t^2-5 t+5))=14

      Notice that, on the left side, you have two equal terms, the equation can be reduced to:

       2*((7-(4*(3^(1/2))))^(t^2-5 t+5))=14

      which becomes:  (7-(4*(3^(1/2)))^(t^2-5 t+5)=7

      Take the log of both sides:  log(7-(4*(3^(1/2)))^(t^2-5 t+5)  =  log(7)

       --->   (t^2-5 t+5) * log(7-(4*(3^(1/2)))  =  log(7)

       --->  (t^2-5 t+5)  =  log(7) / log(7-(4*(3^(1/2)))

       --->  t^2-5 t+5  =  0.9774385152

       --->  t^2-5 t+ (5 - 0.9774385152)  =  0

       --->  a = 1,  b = -5,  c = (5 - 0.9774385152)

       Placing these values into the quadratic formula gives the same results.

sin(A)^4 - cos(A)^4

=   ( sin²(A) - cos²(A) )( sin²(A) + cos²(A) )            Since  sin²(A) - cos²(A) = 1:

=   ( sin²(A) - cos²(A) )(1)

=   sin²(A) - cos²(A)