geno3141

Assuming that all machines are functioning independently:

a) If the probability of failing is p, then the probability of working is (1 - p).

    The probability that all will keep working is (1 - p)^n; thus, the probability that at least one will fail is 

             1 - (1 - p)^n

b) The probability that exactly k machines will fail is n nCr k ·p^k·(1 - p)^(n- k)

c) Part b gives the individual probabilities, their sum will be the sum found in part a.

The clarification that I would make is that the slope of a line is not found by using exponents:  rather,

m  = (y2 - y1) / (x2 - x1)  =  (-7 - -1) / (-7 - 14) =  -6 / -21  =  2/7.

So, I agree with your calculations, just not how the formula was stated.

To find the equation of the line, use the point-slope form:  y - y1  =  m(x - x1)

--->   y - -1  =  (2/7)(x - 14)   --->   y + 1  +  (2/7)(x - 14)

--->   7y + 7  =  2(x - 14)   --->  7y + 7  =  2x - 28   --->   -2x + 7y  =  -35  --->  2x - 7y  =  35

Did you mean:       2x^7 < 18?

If so:  divide by 2:   x^7 < 9

Find the 7th root:        x < (9)^(1/7)

Approximately:            x < 1.3687

I would approach this a little differently.

It is an absolute value equation, so its general form is:  y - k  =  a|x - h| 

where the vertex is located at the point (h, k) and its slope is a:

In function form, this becomes:  f(x)  = a|x - h| + k                  (notice the change-in-sign of the k-term)

For this problem, h = 6 and k = -1.

To find a, which is the slope, use the formula:  (y2 - y1)/(x2 - x1).

We can use (0, 11) for (x1, y1) and (6, -1) for (x2, y2), so  a  =  (-1 - 11)/(6 - 0)  =  -12/6  =  -2.

However, being an absolute value graph, the slope will be negative if it opens downward, positive if it opens upward; so we have to change the -2 to a +2. (We got the negative because we used a point where the line fell downward to the vertex; if we used a point to the right of the vertex, where the line went upward, we would have gotten a +2.) 

This makes our function:  f(x)  =  2|x - 6| - 1

Thus, a = 2 and b = 6. 

I think that when  7x² - 3xy - 4y²  is factored, the factors are  (x-y)(7x + 4y), giving:

[(x + y)(x + y)]/[(x + y)(x - y)] · [(x - y)(7x + 4y)]/[(x + y)(4x - 7y)]

=  (7x + 4y) / (4x - 7y)

What is the equation?

Do you mean:  31/4 ?

To get the numerator:  7x4 + 3  =  31

5x  =  25

Divide both sides by 5:

5x/5  =  25/5

   x    =  5

I'm going to assume that the first equation is:  -5x + y  =  -2

I will try to eliminate the y-terms by multiplying the first equation by -6:

-5x + y  =  -2          --->   multiply x -6   --->     30x - 6y  =  12

-3x + 6y  =  -12      --->                                   -3x + 6y  =  -12

       Adding down the columns:                          27x         =  0

                                                                                x  =  0

IF x = 0, (first equation) -5x + y  =  -2     --->     -5(0) + y  =  -2     --->     y  =  -2.

Answer:  x = 0,  y = -2

To divide fractions, multiply by the reciprocal:

5/7 ÷ -8/14  =  5/7 x -14/8  =  -70/56  =  -35/28  =  -5/4