helperid1839321

This post does not appear to contain a math-related question, could you mark it as off topic?

To plug it in, we can assume that the scale factor is just for one dimension (a.k.a. just length of the lines). For volume, area is usually in units cubed, and for surface area, it's usually squared. We can apply this modification to the scale factor. So the new surface area would be multiplied by 9 (3²), and the new volume would be the old one times 27 (3³).

(Just making it easier to understand, sorry if I made it more complicated.)

Lets start by multiplying it all out.

\(4(x+5)(x+6)(x+10)(x+12) - 3x^2 = 4(x^4+[5+6+10+12]x^3+[5*6+5*10+5*12+6*10+6*12+10*12]x^{2}+[5*6*10+5*6*12+5*10*12+6*10*12]x+[5*6*10*12]\)(Sorry it's so long, I wanted to be complete.)

That simplifies to the more manageable, \(4(x^4+33x^3+200x^2+1980x+3600)-3x^2=4x^4+132x^3+800x^2-3x^2+7920x+14400=4x^4+132x^3+797x^2+7920x+14400\)

As for factoring it... you need to use a calculator (maybe this one?) Let's see how:

solve(4x^4+132x^3+797x^2+7920x+14400=0) = {x=-((sqrt(33*sqrt(193)+(901/4))/2))-((sqrt(193)/2))-((33/4)), x=(sqrt(33*sqrt(193)+(901/4))/2)-((sqrt(193)/2))-((33/4)), x=(sqrt(193)/2)-((sqrt((901/4)-(33*sqrt(193)))/2))-((33/4)), x=(sqrt(193)/2)+(sqrt((901/4)-(33*sqrt(193)))/2)-((33/4))}

That's your answer if you want the roots, but honestly, I doubt whoever gave you this problem was looking for this sort of answer (at least, I hope not )

Hope this helped!

Most probability problems are easier to solve when solving for the chance something won't happen, for some reason, although trying to do that with 5 appears to give me -8%, so I'm going to do the longer route.

We can start by first listing all ways that Beta can win. Namely, B-B-A, B-B-B, B-A-B, and A-B-B. BAB and ABB are technically the same thing because the order doesn't affect the outcome, so I will solve them once and double the chance. Similarly, the final game has no effect on the outcome if Beta wins the first 2 games, so we can simplify BBA + BBB to BB_ (the blank is there to represent the unplayed final game).

BB: The chance of Beta winning the first 2 games is equal to their chance of winning one game squared (chance of B winning * chance of B winning = chance of B winning in any 2 given times, a.k.a. the first 2 times now.) 40% * 40% = 16%, so BB = 16%.

ABB and BAB: We can assume Alpha won the first game, as the order doesn't matter (it's just who won more games, not who won which game when). Therefore, ABB = 60% * 40% * 40% = 9.6%.

Now that we have all of the outcomes covered, we can add them. BB + BAB + ABB = 16% + 9.6% + 9.6% = 35.2% chance that team Beta wins the championship.

Hope this helped! 

We can start by taking the 2 smaller fractions and turning them into one bigger fraction! (I'm sorry if you don't like fractions, but making fractions makes everything a whole lot easier.) Like this: \(\frac{x(x+2)}{(x+1)(x+2)}+\frac{x(x+1)}{(x+1)(x+2)}\). This doesn't seem like it gets us anywhere but now we can make only one fraction. \(\frac{x([x+1]+[x+2])}{x^2+3x+2}=kx\) Before we divide by x, we have to solve for x=0. (I'm going to skip all of the math, you end up with 0 = 0, so there is nothing to be gained.) Now we can divide by x. \(\frac{x+1+x+2}{x^2+3x+2}\) We can simplify this: \(\frac{2x+3}{(x+1)(x+2)}\).

Honestly, from here, I'm stumped. Hey, CPhill, Pavlov, or Omi, could you finish this one? 

Oops, I think you forgot to put in the equation. Might want to take another look at that 

Let's start by eliminating some choices. A and C can't be correct. For A, 8 socks were chosen 4 times, which means that the proportion was met at least once. Therefore, because the reasoning is invalid, A can't be the right answer. For C, white socks were picked far more often than half the time. Because of this we can eliminate C as a possible answer, leaving only B and D.

Think this one through. We know that 80% of the socks are white socks, so it is fair to say that there are 8 white socks out of 10 total socks. It appears this trial was run 10 times. I think a regular, "add and divide" average should suffice here. So \(\frac{7 \times 3 + 8 \times 4 + 9 \times 3}{10}\) is the long form of our average. The convinient part is that this equals exactly 8, so if we assume that there were 10 socks, the average perfectly matches. Therefore, we can say that D is the right answer. The reason behind C is true, but the 9-sock outcomes were counterbalanced by 3 seven-sock outcomes.

Complementary angles - also known as angles that add up to 90 degrees.
Angle A - a degrees (for simplicity)
Angle B - b degrees, we will assume angle b is larger.
a + b = 90
b = 3a (a is now 3 times less than b)
4a = 90
a = 22.5 degrees
b = 67.5 degrees

I'm pretty sure all of my fellow helpers are working through the "unanswered" questions as fast as possible, we're trying our best. Thanks for letting us know 

To factor, we need to find 2 numbers that add to 2 and multiply to -15.
5 seems like it could fit with -3 to match the requirements.
Ima go wtih d here.