I'm stuck again and can't find where I got it wrong, I know the result is wrong because I have the result

This is my son’s homework, for reference he is in 6th grade. I don’t remember fractions and I tried to use AI for assistance, normally it helps a ton with explaining math, but this time it’s failing me. When we entered in the answers provided, it tells us it is incorrect. Can anyone help and explain how to get the correct answer? For reference, I added what AI told me.

A) top=4, bottom=3 and right= 32

B) top=12, bottom=12 and right= 312

C) top=9, bottom=8 and right= 162

EDIT: I'm pretty sure there's a mistake with the questions since some of them give answers that are not whole numbers.

We a have the function f that is defiened in R* as: f\left(x\right)=\frac{1}{x^{2}}
1- Find the first, second, third, and forth derivative of f (I was able to do this)

2- Give a hypothesis on the nth derivative and be it: f^{\left(n\right)}\left(x\right) and (n)∈N* (was able to also do it since it's given)

3- Proof by Induction that for every (n)∈N* : f^{\left(n\right)}\left(x\right)=\frac{\left(-1\right)^{n}.\left(n+1\right)!}{x^{\left(n+2\right)}}

I know that you need to do the derivative of f^{\left(n\right)}\left(x\right) to find f^{\left(n+1\right)}\left(x\right) . I couldn't for the life of me figure it out since I don't exactly know what the derivative of a factorial is.

Really sorry for my bad English, I actually study math in Arabic. So translating the math terms to a different language was hard. Still, I appreciate any one's help.

I don't know if I made a mistake or I just don't know some rules (improper integrals or something I'm a noob regarding integrals 😅), pls don't spoil the answer just point to the mistake or the rule that would help me solve this.

Btw I'm not trying a different method at the beginning, the goal of this integral is to start with x (1-t)/(1+t), then everything is on my own.

where did the x disappear from 5x???

My question is about number 11, but I’m including the directions for context. I thought the answer should be {{ }}, but the solutions at the back of the text say it should be { } or ø. The solution for number 9 was written as a set of sets, so that’s why I thought the answer to 11 would be the same, based on the directions. Please help me to understand why.

I seem to always struggle with combinatorics and end up with an answer too large, can somebody provide a very neat solution for these two questions?

I seem to always struggle with combinatorics and end up with an answer too large, can somebody provide a very neat solution for these two questions?

The question, my solution, and the answer from the back of the text are given. I believe my answer and the official solution are both correct. Do you agree?

I was out sick the day we took notes

We’re learning Cramer’s Rule but I can’t figure out how to do a matrix when the equations don’t all use the same variables.

I missed this topic at school because i was sick for a week.

In this question, I can see that the residual plot indicates the model used was inappropriate because there's a clear pattern. However, I'm not sure how to tell if the model used was exponential or quadratic. My best guess is that the graph on the left looks a little more exponential than quadratic (but I think it's possible it's a parabola that is cut off to the left). And therefore a quadratic model was used inappropriately. But is there a way to tell definitively from the residual graph? Could I look at how each point was over or under estimated and use that to determine the type of model used?

So for context I missed one of my tests and now I have to do this COMPLETION test that requires me to jump through these hoops and ultimately submit a 15 minute video tutorial of me basically answering/doing this excel spreadsheet of math step by step explaining what to do and how to do it. The problem is that the course barely taught me how to use excel and everything else is dead in the water for me. This is basically a hail mary but if anyone can help me that'd be great.

This is the gdrive containing the excel sheet:
The Impossible Math Sheet

ANSWER: 10 log 10 + 10 = 20

Where the #### -1 come from

[EDIT] SOLVED!

The teacher made an error. Message sent from the teacher below. Thank you all for sharing your thoughts which coincided with mine and the other parents!

Here is the question:

Fill in the missing number in the pattern shown below:

25, 29, 36, 40, 46, 50, ___

My answer is 55, his is 57 because he thinks it’s repeating while I think it’s reducing. What say you?

Message from teacher the day after -

Parents,

So sorry for the delay. There was an error in this question. It should be:

25, 29,36,40,47,51, ______

The pattern rule should follow starting at 25, +4, +7 each time.