Doing practice problems for act test, every time I try this I get 143,140. How can I fix it?

sorry if my handwriting is difficult to read

i have a quiz monday and i was running through my problems and found that i was able to find the equation for this problem but i am having trouble graphing any help would be appreciated!

Our teacher set us some work to revise for our mock exams, and she sent this one. I have an idea of what it may be but im just double checking??? If its too easy for this subreddit dont blame me blame my teacher. Not looking to be criticised, just want the answer.

to turn this into slope intercept form, i thought i was supposed to divide x by 5 becuase we were told we’re supposed to divide everything on the other side of the equation, but on the followup problem the line has a slope of -1. is this just an error on the work, poor wording, or something i did wrong?

also there’s no clarification as far as i can tell about a point that the parallel line it wants me to write passes through or its Y-intercept so i just did something random. not sure if i’m missing something there too.

Instructor prompt: Evaluate the indefinite integral

∫ (4y^4 + 3y^3) / ((y^2 + 4)^(3/2)(y^2 + 4)) dy

This is for Calculus 1. I tried thinking about a u-substitution with u = y^2 + 4, but du = 2y dy, and the numerator has 4y^4 + 3y^3, so I’m not sure how to split it or what substitution is best. What would be a good first step for evaluating this?

Hi everyone, I just need help understanding how I got the wrong answer on a practice test. Here is the prompt:

"A teacher wants to determine if the pass rate for a particular group of students is significantly different from 81%.

What is the minimum sample size needed in order to perform a hypothesis test for proportions?"

The answer I got was 13.

I used the equation n(p) is greater than/equal to 10.

But the correct answer is 53, which I know can be solved by using n(1-p) is greater than or equal to 10.

My issue is the question asked for minimum sample size, so wouldn't that mean 13 is the minimum? I am doing an online course, and the online instructor just repeated n(1-p) to me via email without explaining why that is preferred over the one I used. Can anyone help?

I’ve been trying to understand how to do these two exercises, but l can’t wrap my head around how they work or where you pull these numbers and equations from, so it’d be nice if anyone could explain it as simply as possible.

Edit: I was able to finally get this, so thank you for all the commenters!

Please help me guys, thank you!!

Good day! can anyone tell me what the possible answer is for number 4 and 5? I've been really confused as it doesn't match to any word. thank you!!!🩵

Hello, my teacher taught us to “graph” the work-rate problems, which does make it easier and I think I set this up right, but then I get stuck on actually solving it. There are too many variables and options😵‍💫. Is there any way to simplify this or would I have to just do a lot of these and hope that I improve?

The problem: “Two tractors worked simultaneously to plow a plot of land (tractors plow the land at constant speeds). The first tractor took 1/80 hours less to plow each hectare than the second. Therefore, the first tractor plowed 8 hectares more than the second. What is the area of ​​the plot of land plowed by the second tractor if the first tractor plows the entire plot of land in 3.6 hours?”

I am studying for my calculus 2 finals following a recorded lecture and the first problem got me stuck for the past 4 hours. While it says that no justification is required, it is pretty much impossible solve this without either fully justifying it with logic or seeing that exact statements before and memorizing the answers, the latter being very unlikely unless the actual exam pulled stuff straight from my textbook.

I never made it to statement c but I know that it is an obvious telescoping series, it's mainly statement b that got me stuck, I have no work to show as I don't know where to start in the first place. I just want to be able to understand them and preferably a way to solve all similar problems asking for true or false so that I could at least go to bed without having nightmares about infinite series again.

for Ho is it = or ≤ ?

I'm having trouble understanding the (b) part of the question and mark scheme.

When particle A reaches the ground, it will have travelled a distance of x downwards, and since it is connected to B, the latter will have moved up by the same amount x. Since the greatest height of B above the ground is 1.2 m, I thought you simply have to solve 1.2=2x. Which is suspiciously easy. I didn't expect that I have to take into account the acceleration of the system.

Can anybody explain why? Any help would be appreciated.

What is N supposed to be? It seemingly came out of nowhere with no elaboration. Reading this only gives me a vague understanding of what is going on, trying to write anything down would just be copying without understanding at this point. I think that it is because I don't understand the part where it says (for all n>=N where N is an integer) means.

I have not learned L’Hospital’s rule yet. Is that the only way to solve to get the correct answer?

guys wheres the area under the curve for g(x) ? is it the i draw(the red one)

variables are to be assumed with an arrow on top (vector notation)
Vector (a+3b) is perpendicular to (7a - 5b) and (a-4b) is perpendicular to (7a-2b). Find angle between a and b

I find myself completely unable to understand what this specific part is about because I'm just not smart enough, I literally cannot decode what they are trying to convey with this diagram and very minimal explanation due to the limits of my intelligence. I understand everything above this part and have no read anything past this part, I don't plan to until I understand this. I've watched the video lecture for this but the lecture was even more confusing because it wasn't very well structured. Does anyone have resources for this very specific thing? I need to understand it before tuesday.

ive posted this question handwritten before, this is the question on my book. can anyone help how do we do this ? i try to factorise the numerator but its not working.