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I'm sorry, my formatting was wrong. On number two, the last sentence should be, "What is the probability that the sum of the two rolls is 5?"

You answer was wrong, but only because I wrote the question wrong. Sorry about that, but thank you very much for trying!

okay, ty!

Groan!!

Use speed = distance/time to find her initial speed = 100/5 = 20 mph

Hence speed in last part of the trip = v2 = 40 mph

Distance travelled in first part of trip = 100 miles

Distance travelled in second part of trip d2 = 300 - 100 = 200 miles.

Time taken for second part of trip = distance/speed = d2/v2 = 200/40 = 5 hours.

b/g = 4  or  b = 4g  (1)

b = g + 33   (2)

Can you use these two equations to find b and g and hence the total, b + g?

When x is 3 then sqrt(3+1) = 2, so f(2) = 1/3.

If f(x) = a then we have:  x² + 4x -31 = a

Rewrite as x² + 4x - 31 - a =0

For this to have a single root we must have  4² - 4*(-31 - a) = 0 or a = -35

If smaller even integer is x then the next consecutive even integer is x + 2, so:

3x = -146 - 4(x + 2)

Solving this results in x being an integer (150/7 is not an integer).

Ron = R

Harry = H

1 / 2 - 1 / R = 1 / H

1 / 2 - 1 /3 = 1 / H, solve for H

H = 6 Hours it takes Harry to clean the room by himself.

Side length ???

Maybe you were out in the sun too long ....

Thanks Alan,

I was wondering how to do that one formally.

Thanks Coolstuff too :)

Let me out!  Let me out!  Chris was not kidding! 

It is so daaaaark and stuffy in here!  

And ....

I think Chris put a pair of his smelly socks in here just to torture me!

1+2+3+4+5+6+7+8+9+10 = 55

55/2 = 27.5

So I want 27*28

(10 +9+1+3+4)*(7+8+2 +6+5) = 756    biggest maybe

(10+9+8+7+6)*(5+4+3+2+1) = 600       smallest maybe

No problem  It happens to all of us!

Systematic way as follows:

(However, CoolStuffYT's way works as well!)

How many liters of a 32 % alcohol solution must be mixed with 15 liters of a 81% alcohol solution to get a 46% alcohol in the entire solution?

rom i dont think thats right

In triangle STU, we have ST = SU = 22 and TU = 8. Let M be the midpoint of  and N be on  such that  is an altitude of triangle STU. If  and  intersect at X, then what is SX?

SX = 15.087 units 

5^0 has 1

5^1 has 2

etc 

so

5^(6^9) has 6^9+1  digits when written is base 5

by the way, 5^(6^9) is a base 10 number, not a base 5 number. Base 5 can only use the digits 0,1,2,3,4 

The link does not work.

\(\text{The number of components that fail has a binomial distribution, $n=12,~p=0.2$}\\ P[k>3]=1-P[0]-P[1]-P[2]-P[3] = \\ 1 - \sum \limits_{k=0}^3 \dbinom{12}{k}(0.2)^k(0.8)^{12-k} = 0.205431\\ \)

\(P[E]=2P[O]\\ P[E]+P[O]=1\\ P[E]=\dfrac 2 3,~P[O]=\dfrac 1 3\\ P[1]=P[3]=P[5]=\dfrac 1 3 \cdot \dfrac 1 3 =\dfrac 1 9\\ P[2]=P[4]=P[6]=\dfrac 1 3 \cdot \dfrac 2 3 = \dfrac 2 9\\ P[roll < 4]=P[1]+P[2]+P[3] = \dfrac 1 9 + \dfrac 2 9 + \dfrac 1 9 = \dfrac 4 9\)

By the angle bisector theorem, AI/ID = 7/12.