CPhill

I'll see what I can do......

We need to find the number in the intersection, first....and we have

P(M or E)  = P(M) + P(E)  - P(M and E)

300  = 250 + 220  - P(M and E)

P(M and E)  = 250 + 220 - 300   = 170

Here's the Venn diagram :

b).    the student takes Math 128, given that the student takes only one class

130 students only take  one class.......and 80 of these take Math 128 only....so 80/130  = 8/13

c).    the student takes English, given that the student takes Math 128

250 students take Math 128......and of these 170 also take English......so  170/250  = 17/25

d).    the student takes Math 128, given that the student takes English

220 take English.....and of these 170 also take Math 128 ......so    170/220  = 17/22

e).    the student takes neither, given that the student does not take Math 128

The number not taking Math 128   = 50 plus the 20 taking neither  = 70  ........and there are 20 taking neither [none].....so 20/70  = 2/7

[Melody or Alan.....could you check these answers???......I'm not totally confident about these]

Very impressive, Hayley.......a BIG 5 points from me........

P(Face card / Red)  =  [Probability of a Face Card and Probability of a Red Card] / [Probability of a Red Card}   = [12/52 * 1/2] / [ 1/2]   =  [ 6/52] /[ 1/2]  =  12/52  = 6/26 = 3/13

P(Red Card / Face Card)  = [ [Probability of a Face Card and Probability of a Red Card] / [Probability of a Face Card]  =   [ 12/52 * 1/2] / [12/52] =  1/2

In 5 minutes, the plane travels 450/12 = 37.5 miles

And we can use the sine to calculate this

sin13 = a / 37.5      where a is the gain in altitude.........rearrange

37.5(sin13) =  a  = about 8.4  miles

We can use a proportion to solve this

196ft  x (1/3)in / 1ft   =  about 65.3333   inches

12 / .90  = 

12 / [90 / 100]  =

12 *  100  / 90

1200/90  =   13.3333......girls   ?????

Ther are infinite possibilities......200  +  40  is one

OK......I guess we have 

2^(t + 3)   = 7^(t - 1)    ????    if so........take the log of both sides

log2^(t +3)  = log7^(t - 1)      and we can write

(t +3) log2  = (t - 1) log 7     simplify

t log2  + 3log2  = tlog7 - log 7

3log2 + log7  = tlog7 - t log2

3log2 + log 7  = t [ log 7 - log2]       divide both sides by log 7 - log2

[3log2 + log 7 ] / [ log7 - log2]  = t  = about 3.2132

Here's a graphical solution :  https://www.desmos.com/calculator/hvjfai7rfa

The solution occurs at about t = 0.91

-61=d+(-18)  add 18 to both sides

-43  = d