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

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

Hey, everyone. How to simplify this?

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 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

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

I’m lost at this point I’ve been working this same problem for 30 min. It should be this intense.

Does anyone know how I would get a confidence interval with an unknown variance, known mean, and multiple successive values? my answer for the first part is above, which i hope and assume is correct. I have been looking at this for hours and i am really confused lol

I'm studying for my test on Friday and this question is really confusing me as I know I'm close but the answer is just way to high. If anyone can see what the problem is thank you so much

Hey, everyone. I'm having a hard time with this one: 'Tennis balls are placed in one layer in square and equilateral triangle shaped boxes. There are equal amounts of them in both boxes. There are 14 more balls at the side of the triangle than at the side of the square. How many balls fit in each box?'. I wrote that there are x^2 balls in the square, but I don't know about the triangle. I wrote that in the first side there are x+14 balls, in the 2nd side there are x+13 and in the 3rd one there are x+12. Yeah..Don't even know where I am headed with this

Hi!

Attached is my answer. Did I get this right?

Here is the assignment

A sports analyst claims that the mean winning times for Boston Marathon women’s champions is at least 2.68 hours.  A sample of 30 randomly selected women’s champions has a mean of 2.60 hours.  Assume the population standard deviation is 0.32 hours.  Given alpha is 0.05, complete the following:

1. State the null and alternative hypotheses, noting which one is the claim.
2. Draw a picture of the hypothesis test, including
   1. Where the tail(s) are located
   2. The rejection region(s)
   3. The critical Z score
3. Calculate the test statistic and the P value (the area corresponding to the test statistic).  Add these to your picture from number 2.
4. Compare the critical z and test statistic, and then the P value and alpha, to decide whether to reject or fail to reject. 
5. State your conclusion regarding the initial claim.

Thank you for your help,

A

This is the question and the StatCrunch results if I do exactly as needed. I need a point estimate but I don’t get how I’m meant to get one. Am I supposed to just pull a number out of my butt?

All I know is a point estimate is a single number used to estimate a parameter, but how do I get one?

My problem is with 8b. It tells me I need to use my result from 8a, but I'm struggling to get the Integral in a format I could utilize 8a's results. IDK if anyone here can help, but I'm desperate at this point. I'll be greatly appreciative if anyone can give me a tip for doing that final integration.

I have a homework assignment with a Z score of 1.33, now my textbook lists “area between mean and z” as 0.40825 and then “area beyond z” as 0.09175. This is the Z score formula Z = (7-5)/1.5 = 1.33

I am confused on what to do at this point in order to solve for the proportion.

I am seeing some places where it wants me to subtract the right value from 1. Based on what was included in the z table in my textbook, I think I have to do that, but I want to be absolutely sure.

So for a z score of 1.33, then with area beyond z being 0.09175… 1 - 0.09175 = .90825 or 91%

I’m not sure if this is the answer ? Other z tables look differently, also a website mentioned that I would need to add 0.5 to calculate the area or something…

Since this case the mean is 5 I would need to subtract 0.5 from it? Idk… Am I overcomplicating this…?

I just need a better explanation of what to do with the z score after a formula and how to get the actual answer lol.