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The smallest number that satisfies both conditions is 28, so when divided among 7 people, there are 0 coins left.

To find the smallest number you'll need to know something called modular arithmetic which is something I cannot explain so you may have to look that up yourself.

Hope this helps!

Thanks!

Yep 

Excellent!

That's what I got too.

This problem seems tricky at first, if you plug in any positive integer, you will always get an even number. There is only one even prime which is 2. When n=16,19, p=2 which are the only values that work. So 16*19= 304 which is your answer.

Hope it helps!

Four grapes, since that is the largest possible remainder.

Thank you so much. The image definitely helped with the confusion I had. I didn't know that the U was union or the upside-down was intersect. My teacher is trying to teach from home so it is just a mess. Thank you again!

For f(g(x)) you'll get 3ax+3b+2 and for g(f(x)) you'll get 3ax+2a+b. The equation 3ax+3b+2=3ax+2a+b can be simplified to b+1=a. We also know that ab=20 so the only value where ab=20 and b+1=a is where b=4 and a=5. So your answer is 5.

Find 3/4 of the volume of the cylinders (How to find the volume of it is shown in my answer above), then find the volume of the rectangular prism!

Oops... it is not a rectangular prism. My bad! I will try again.

Ok, it is a volume but it still is not quite right.   

Can you see why it is not the correct volume?

Draw the front bit on some paper, that might help.

If you didn't know, the "U" means Union and the upside-down "U" means intersect.

Cal you have messed that up. Can you see why?

I got this image fromo online, I hope this can clarify some of your confusion.

What area?  It is a 3-dimensional object.  

It has a volume. The sides have area.  What area do you want?

If the average cost of the plane ticket for 5 days was $67, that means the sum of the costs is 5*67= $335. The first four days are given at $40, $44, $50, and $60. The sum of those is $194. The cost of the ticket on the last day would be $335-$194= $141.

Hope it helps!

If two dice are rolled, there are 6*6=36 number of possibe outcomes. If a number is less than 4 on a dice, that means it can be 1,2, or 3 giving you 3 choices. That makes 3*3=9 number of possible outcomes of both numbers being less than 3. For the probability, it would be 9/36=1/4.

Hope it helps!

Thanks