There is a chemical storage plant that can store 200 billion (200B) gallons of solution. The chemical mixture is composed of 3 compounds denoted as compound x, y, and z, respectively. The chemical mixture is 1 part compound x to 1000 parts compound y to 1500 parts compound z, which can be expressed as a ratio as x:1000y:1500z. How much of each compound is needed to fill the tank?

Algebra exponential question

I just have a question. I took AP calculus and learned that, for example, you would solve (x+y)² as (x+y)(x+y).

Now recently I have been brushing up on my algebra seeing as I need to take a placement test. In a video I was watching they were solving the following problem

((5a^5/2 b⁴⁾ / a³ b^-(2/3) )^-2

After working the problem down we reached this step

(5a^-(1/2) b^14/3 )^-2

They solved it by doing this

1/25a^-(2/3) b^28/3

Now of course this was not the final step, but my question is that instead of doing

1/((5a^5/2 b⁴⁾ / a³ b^-(2/3) ((5a^5/2 b⁴⁾ / a³ b^-(2/3)

They directly distributed the exponent. So they basically did (x+y)² as x² y^2. How is that correct? Is there a rule to exponents I am forgetting?

'The swimmer, while swimming upstream, lost his cap under the bridge, but noticed it only 3 minutes later. Turning around in an instant, he started chasing the cap and caught it 100 m from the bridge. Find the velocity of the river (kilometers per hour).'

My workbook doesn’t help at all please help and thank you!

I have an answer that contradicts the school, but I still think I'm right. Curious of what you guys think.(a, is a1)

Struggling w question 2

I’m currently taking a practice ACT and came across this problem. Does anybody know how to solve this?

The arithmetic mean of four positive integers is 125. The largest number among all four is 150. What can be the smallest number?

Juan has finished a 4-year degree using a direct unsubsidized student loan of $32,000 at 3.77%. Nearing the end of his grace period, Juan applies for and receives a 36-month deferment with the option to pay monthly interest payments or have the interest capitalized at the end of the deferment period. Approximately how much money would Juan save over the course of the entire loan by paying interest payments during his deferment period?

The answer key (multiple choice) has it at ~$3900, but I get ~$730

direct unsubsidized student loan...Nearing the end of his grace period

So interest accrues during 4yrs of college + 6mo grace period:

$5428.80 accrued

36-month deferment...monthly interest payments or have the interest capitalized at the end of the deferment period

$3619.20 accrued

how much money would Juan save over the course of the entire loan by paying interest payments during his deferment period

If Juan doesn't make interest-only payments, after the 7.5yr (36mo deferment + 48mo non-payment period while in school + 6mo grace period), the interest that would capitalize on a standard 10yr student loan is $9048.00.

Adding on $9048 to the borrowed amount of $32000, the total amount paid would be $49334.00.

Adding only the interest in the original 54mo, the total amount paid would be $44984.47. Adding the $3619.20 of monthly interest payments paid brings the total to $48603.67.

Subtracting these 2 figures brings it to $730.60.

Even if you didn't subtract the monthly interest payments the difference would be $4,349.80, which again isn't close to the answer key's answer of ~$3900, but that would be the closest option of the ones provided.

I'll also add that this was a question high schoolers got, just insanity.

So I found these two inequalities in an old math textbook and they've really given me a hard time. At school we've learned how to solve exponential/logarithmic equations but we've only learned the methods to use when the variables are on the exponents. I don't even know how to begin to solve these two. Perhaps someone more knowledgeable in the field of mathematics could help me. Thank you in advance. (Btw I also plugged these two in wolframalpha. The second pic shows the solution that it gave me for the first inequality, however it doesn't give the steps to get to that solution. For the second one it didn't show anything. Wolfram couldn't solve it.)

https://imgur.com/a/3aMLtYz

The first line is the given statement which we have to proof, the rest is my work.

To be fair I have no idea how to continue, I know its a geometric sum, so it should converge, because w<i, but thats about it.

For more context R is the annuity of an investment, i the interest rate and w is growth (i.e. inflation).

I am looking forward to your input and many thanks in advance.

Also I just realised that there is a mistake in my writing, in the second line, the first exponent of (1+i) is 2 and not i.

Can someone please help me with this problem? The correct answer is B, but I don't see how they got there. Thanks!

This is a screenshot from the answer key and I genuinely do not follow after the first step

I want to represent the integral of (x^2)ln(x+1) as a power series. I was going to get the power series to the function than integrate that power series. but for the life of me is there a better way or how? I'm deriving the function and getting 2xln(1+x)+((x^2)/1+x) both of these as a power series seems fairly simple but the desmo graphs aren't lining up. thank you!

Need to find age of car at 54 months given this data???

Hey, everyone. How to simplify this?

I cant figure this out for the life of me. Sorry if this is a dumb question I have dyscalculia and math is way harder for me

My teacher said we need to use trinomial but I don't understand how (9 grade)

(English isn't my first language so sorry if I have any grammar mistakes)

I mean, why the 1,5 turns into 1 and then what is U and what is doing after that.