supremecheetah

toast = t

bagels = b

muffins = m

Use systems of equations. I'll help on the first part. Try finishing the rest yourself!

    t+2b+3m = 8.15

-  2t+b = 3.15

        b + m  = 3.50

---------------------------

   -t    +    2m = 1.50

Assume:

the # of yellow marbles is x

the # of green marbles is 2x

the # of blue marbles is 3x

the # of white marbles is 4x

x+2x+3x+4x=180

10x = 180 

x = 18

the # of blue marbles = 3x = 3(18) = 54 marbles

Credit to https://web2.0calc.com/questions/help-pls_10673 for inspiring my solution. :)

Let 3x be the number of juniors and 2x be the number of seniors.

Six more juniors join the class: the number of girls is now  3x + 6

One senior drop the class: rhe number of boys is now  2x - 1

The ratio of juniors to seniors is now 2:3  --->   (3x + 6) : (2x - 1)  =  2 : 3

(3x + 6)/(2x - 1) = 2/3

3(3x+6) = 2(2x-1)

9x+18 = 4x-2

5x  = -20

x = -4

I don't understand it now; the answer is negative??

Can someone help? Thanks!

We can apply the binomial formula here; it would be row 5 of the pascal's triangle. 

I would write the expansion, and I did, but I deleted it accidently. :(

You would get 1920 as your answer.

Hello! I'm going to help with the first part so that you can finish the rest of this problem yorself. I suggest using system of equations.

toast = t

bagel = b

muffin = m

     t+2b+3m = 8.15  

-   3t+b        = 3.15

         b + m = 3.50

--------------------------

   -2t   + 2m = 1.5

Now, we have eliminated one variable. Find two equations to eliminate the second variable so you can easily find the answer.

Here are two solutions: https://web2.0calc.com/questions/help-pls_10673

Hello! I'm not going to give a full solution but instead hints. I would suggest starting of with casework or trying this with smaller numbers. E.g. if Magnus only had 2 freinds and 4 stickers how many ways can Magnus give out the 4 stickers. Think about how many stickers the 1st freind can get at first then same for the 2nd freind and add your results up. Do you have any questions how to do this?

Consider looking at these solutions here: https://web2.0calc.com/questions/counting_35794#:~:text=Therefore%2C%20there%20are%20564%20ways,in%20front%20of%20their%20sibling.

Hello! Let me know if you find any errors in my solution.

The volume of a cylinder = $\pi r^2h$

We know:

$v = 780 cm^3$

$h = 12cm$

Now we plug in those values:
$780 cm^3 = \pi r^2 12$

And isolate the variable r:

$\frac{780 cm^3}{12cm} = \pi r^2 \\\frac{65cm^2}{\pi} = r^2 \\r = \frac{\sqrt{65}cm}{\pi}$

And round the radius to the nearest tenth:

$r = \frac{\sqrt{65}}{\pi} \\r \approx \frac{8.1}{\pi} \\\pi \approx 3.1 \\r \approx \frac{8.1}{3.1} \approx \boxed{2.6 cm}$

Therefore, the answer is $\boxed{2.6 cm}$