CPhill

Express the values of x that satisfy the inequality -3 ≤ x < 7 as an interval.

[-3, 7)

Find all values of s (s + 4)(s - 3) ≤ 0   Give your answer as an interval.

Let's solve this

s(s + 4)(s -3)  = 0      the three solutions are s =0, s = -4 and s = 3

Then, the solutions to this inequality  will occur on one or more of these possible intervals (-infinity, -4] , [-4, 0], [0,3] or [3, ifinity)

The intervals  (-infinity, -4]   and [0, 3]  will satify the inequality.....here's a graph : 

1/5 + 4 + 4/5     we can arrange this as :

1/5 + 4/5 + 4  =

5/5 + 4   =

1 + 4   = 

5

Hey, JillyBean....try downloading GoogleChrome.......it does the same thing to me at my local library until I download Chrome......then....it seems to work fine........

 0.0065 = 

6.5   x   10^-3

11 and 11/64   inches

4. In how many ways can 7 people be seated in a row of chairs if two of the people, Wilma and Paul, refuse to sit next to each other?

[ I learned  this trick from Melody......]

Let us consider the number of arrangements where Wilma  and Paul are sitting together

We can seat them in any of 6 positions and arrange the other people in 5! ways......but.....we can also arrange Wilma and Paul in two different ways in each of the 6 positions.....so.......the total arrangements where they sit together = 6 * 2 * 5!  =  1440 ways

And the total number of ways to seat all 7 people = 7!  = 5040 ways

So.......the total number of ways to seat all 7 people  minus the arrangements where Wilma and Paul sit togeher  = the number of arrangements where they don't sit together

5040 - 1440  =  3600 arrangements where they are not sitting together.......

3. I have 6 shirts, 6 pairs of pants, and 6 hats. Each item comes in the same 6 colors ( so that I have 1 item of each color). I refuse to wear an outfit in which all 3 items are the same color. How many choices for outfits do I have?

Assuming that two of the items can be the same color.......

We have  6*6*6   = 216 possible outfits if we can wear any color that we'd like........however....only 6 of these are all the same color......

So.....the total number of outfits you could wear, but avoiding all the same colors  =  216 - 6  = 210

There are  99,999 - 10,000 + 1  = 90,000 five digit numbers

Let's just consider how many of them have no zeroes.......

We have 9 ways to select a non-zero digit for each of the positions, so this must be  9^5  = 59049  five digit numbers that have no zeroes........then  90,000 - 59,049   = 30,951 of them must contain at least one zero