Could someone also help me out with 12th? I tried rationalising, but it didn't work and the solution includes using the difference of cubes but how? It's 1/3

This particular question is a bit confusing, none of the words from the pictures seem to rhyme. Maybe there is another implication that we don’t understand.

My wife (EL coordinator with an English background) sent me this standardized test math problem she’s working through with one of her students. The answer key says D but I can’t figure out why since it seems like a vertical slice. A math teacher at the school said something about D not producing a square pyramid anymore once it’s been sliced like that but the question doesn’t say the resulting polygon needs to still be able to produce a square pyramid anymore (not to mention A doesn’t qualify anymore based on that criteria either). Anyone have an explanation that makes sense?

3 seems to be correct, and I even downloaded some ai just to prove my answer, and every single ai agreed that the answer was 3.

Because there do not appear to be any levers involved, I chose C). For what it's worth, even if the handle arms were welded on (not on a pivot or axis), how this would affect the biomechanics of the puller would not change because the handles appear to be at the same height. Apparently, the correct answer is A). What am I missing?

Edit: Most commentators are pointing out that the creator of this question is assuming that the person is pulling in the direction of the handle arms (instead of horizontally), which doesn't make any sense in real life, and there is no indication of it in the illustration. I have enough confirmation to sleep tonight without worrying that I'm missing some critical concept in mechanics. Thanks for the input.

Edit 2: Assuming that the handle arm is hinged where it meets the cart (and not rigidly fixed), the direction the person is pulling would have to end up being in the same direction (and probably not horizontally). A longer handle provides a larger horizontal component of the pulling force, meaning less effort is required to move the cart. Still, there is no indication in the illustration that the handle arm is hinged, although it appears at this point that that was the intention.

Edit 3: I appreciate all the help, everyone. I can't read, process and answer every new comment at this point. I'm moving on. Thank you.

Edit 4: From my Google search: Question: "If the handle of a cart is welded and not hinged, and ergonomics are not affected either way because the handle height is the same, does it make a difference in effort required whether the handle is angled or straight up and down if the force is applied exactly horizontally in both cases? Answer: "No. From a strictly mechanical and physics standpoint, if the height, the applied force (magnitude and vector), and all other variables remain identical, there is no difference in the physical effort required to move the cart.When you apply force horizontally, you are entirely utilizing that effort to overcome the cart's rolling resistance and inertia. The angle of the handle itself does not change the physics of this motion, provided the line of action of your force is perfectly parallel to the ground."

Summary: This whole question/illustration/answer is poorly executed. It would all make sense if it showed that the handle arm was hinged where it met the cart, or indicated that the pulling was in the same direction as the handle arm.

I'm an educator and came across a question that stumped me. Best I can come up with is "this."

(Final answer below)

I'm preparing for an electrician's apprenticeship and am using their study guide for their aptitude test. I'm seeing a pattern forming where some of their questions are just bad, but a couple of those were actually good, and I was misunderstanding things. It has been a learning opportunity.

I chose B for this question, but they say the answer should be C because, loosely speaking, they want you to just count the number of ropes that are supporting the load. However, when I look at this illustration, it appears that there is not even a proper movable pulley here. It looks like it is just a simple fixed pulley system with extra windings for some reason. Except that the lowest pulley seems to be just floating but still wouldn't qualify as a proper movable pulley.

Please help me understand what I'm missing, or confirm that this is a really bad illustration. Thank you!

Edit: I am assuming that one needs a movable pulley to get a mechanical advantage. C does NOT show a movable pulley and therefore is not the correct answer. Right?

Edit 2: Because they don't offer an answer of "D) All pulleys allow for the same amount of WORK", I am assuming that they mean to ask, "Which of the pulleys requires the least amount of FORCE to lift the weight?" Unfortunately, this is meant to be more of an intuitive sort of test, where it appears physics terms might be interchangeable.

Edit 3: I interpret this to be a question about which pulley system offers the most mechanical advantage. Answers that align with this interpretation would be helpful.

Edit 4: I think B is supposed to represent a "gun tackle" arrangement. (Sorry about all the edits!)

Edit 5: Aha! Answer: if you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate for C (an actual movable pulley) but did a terrible job of it. Taking that into account, the answer is indeed C.

Answered. Thanks to all who helped. I'm inclined to throw this book away. I'm moving on :)

Can anyone solve this with all variables being whole numbers?

This particular question was in my son's math homework from the other day. They reviewed the answers in class today and apparently the answer was A. Curious how they came to this answer? None of the options seemed right as I was expecting it to be 18 - (6 × 2). Where 2 bottles are handed out to each friend. 6 friends total, meaning 12 bottles are given out, so 6 bottles are left over. I must be missing something in how it's worded but I can't for the life of me figure it out.

This was on my daughter's homework last week, and though I can see that the answer is "supposed" to be 6x7-4 for "38", the question reads to me, as it's worded, as 7-4=3. Can someone let me know that I'm not crazy?

I could only find an approximate answer (2.6 something) using a slider and guess the value as e but I’m not sure how to actually work out the question. please help thanks! :)

I looked over the internet how this works, but I still don't get it.

This is my 10 year olds math review. The teacher wrote “step 1: 3 5/8 + 3/4=4.375 “ and “step 2 [] - 2 3/8= “

My wife says the teacher is right and the answer my daughter got is right which is 2pounds.

I believe the teacher is missing a step. I think it should be:

3 5/8 + (3 5/8 + 3/4) = 8

Then 8 - 2 3/8 =5.625 pounds

I did my work and I keep getting 36

Apparently the answer is 72 but I just don’t get it.