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John     50 000 (1 + .04)^2 = 54080.00

Patricia 50000  (1+.01)^8 = 54142.84                You can finish......

-x^2+8x       max will occcur at  x   =   -b/2a   =  - 8 / (-2) = 4

                           value of the function will be     - (4^2) + 8(4) = 16  

Are u asking for the odds or for the fraction the fraction is 1/6188

Now, for negative EXPONENTS, I counted 11 of them from x^-44, x^-40, x^-36.........x^-4.

Your expression is written like this:  (x^2 + 1/x^2)^22 . So both terms are +. Therefore, there is NO minus sign in the expansion of the 23 terms.

Here is the summary of the sum of the DIGITS of the product of 2001 "8s"   x   2001  "9s"

Total Sum = 18009
Total Num = 4002
Total 8's: SUM =16,000. NUMBER=2,000
Total 7's: SUM =7. NUMBER =1
Total 2's: SUM =2. NUMBER =1
Total 1's: SUM =2,000. NUMBER=2,000

Hello! This factors to (3x-11)(x+2)! LMK if that is right! 

PQ is larger than QR. I don't think that's right. It is my fault too. I sent the diagram! 

< ...havent found anything online to help me with this > 

The measure of an inscribed angle is half the measure of the intercepted arc.

See https://www.varsitytutors.com/hotmath/hotmath_help/topics/inscribed-angles

First, we choose the two girls to stand next to each other.  We can do this in 5*4/2 = 10 ways.  There are then 8 ways to choose the two places where they stand next to each other.  There are 7 other people on the soccer team, so there are 10*8*7! ways to arrange the team members.  Answer = 403200.

You draw cards from a deck of 52 cards until you get two cards of the same rank
What is the probability that you will end up with no more than three cards?

What is the probability of rolling a die 3 times and never getting a 6? What is the probability of getting a 6 at least once?

Let p(x) = ax + b.  Then you can prove the result.

b = boys

g = girls = 325-b

b+25      +    .95(325-b)  =341      solve for b

d = distance           r = rate      d/r = time

d/40  +    d /70   =  5.5

110d = 5.5 *70*40

d= 140 km

Just add 1 to the M of the last term and keep k the same: [m C k-1] + [m C k]=[m+1 C k].

Example: [10 C 4-1] + [10 C 4] =330 =[10+1 C 4] =11 C 4 =330.

y is proportional to x^2, and y = 8 when x = 8.  What is y equal to when x = 6?

y =k * x^2, where k = proportionality constant
8 =k * 8^2
k =8
y =8 * 6^2
y = 288

A =5 + 1 =6

B =7 -2 = 5

C =6 x 3 =18

D =4 and 8

So, the remaining card is 9

Let  T  represent the time going from A to B.

The distance =  rate x time   --->   distance  =  40·T

Since the total time was 5.5 hrs, the time returning from B to A was  5.5 - T  hours.

The distance returning  --->   distance  =  70·(5.5 - T)

Since the distance going is the distance returning:  40·T  =  70·(5.5 - T)

Solving:                                                                      40T  =  385 - 70T

                                                                                 110T  =  385

                                                                                       T  =  3.5 hours

The distance going     =  40·3.5  =  140 km

The distance returning  =  70·2  =  140 km