yaytomath

We can set the group of freshmen as one object. So, we are ordering one group and 3 sophomores, which is 4!=24 ways. However, to order the freshment inside the group, we also have 4!=24 ways. Therefore, there are 24*24=576 ways to order all of them.

We have one choice for A and three for R. After that, no matter which R we choose, we'll have 3 C's to choose from. After that, we'll have three H's to choose from. Therefore, the answer is 3^3 = 27. :D

grogg's dad's age = D

Grogg's age = G

We can create equations:

(D-7)=9(G-7)

and

(D-4)=6(G-4)

These simplify into 

D-7=9G-63

D-4=6G-24

or

D=9G-56

D=6G-20

Because D equals both of these, we know that 

9G-56=6G-20

We solve this and get 

3G=36

G=12. 

We can subsitute this into any of the equations.

6(12)-20 = 52

9(12)-56= 52

So Grogg's dad is 52 years old.

Happy new Year btw :D

common ratio = r

first term = t

Because we have two consecutive terms, we know that the common difference is just the 2nd one divided by the first one. Therefore, the common difference is 14/16=7/8.

The 32nd term is also t(7/8)^31 and the 24th term is t(7/8)^23. Dividing, you get (7/8)^8. That means that (the 32nd term)/14=(7/8)^8. You can use a calculator to see what this is, and it is 

14(7/8)^8 which is about 4.81. :D

common difference = d

first term = t

The common difference would just be (5-4)/2 because there is one term in between the 23rd and 25th term. That means that the common difference is 0.5. We can say that the 25th term is t+24(0.5) and the 48th term is t+47(0.5). That means that the difference of the two terms is t+47(0.5)-t-24(0.5)= 23(0.5)=11.5. Because this is the difference, that means that the 48th term - 5 = 11.5. That means that the 48th term = 16.5.

So the answer is 16.5:)

If you arrange the small triangles with the medium size ones, you can create a right triangle. If you draw a line connecting C and G, you can divide the quadrilateral into 4 triangles. You can now see that the yellow triangle and the combined red triangle are equal, so the answer is 1/2.

For example, let us set the intersection of AE and BH to X. if you move XAH to the bottom of XHG, you can create triangle XAG. Lets set the intersection of lines CG and AE to Y. XYG will equal to XHG. so yea i think. 1/2.

Ok, so we can start off by expanding each side:

6c+3=84c-9

Add 9 to both sides:

6c+12=84c

Subtract 6c on both sides:

12=72c

Finally, you can divide 72 on both sides to isolate c:

1/6=c

So the answer I think is just 1/6

No,because using the triangle inequality, 12+30 is less than 43, so there is no way it could make a triangle

ok so we break it down 

12! has 4 "3" factors and 1 "9" factor

so that's 1+4=5

15! has 5 "3's" and 1 "9"

so that's 5+1=6

18! has 6 "3's" and 2 "9's"

so that's 6+2=8

21! has 7 "3's" and 2 "9's"

so that's 7+2=9

24! has 8 "3's" and 2 "9's"

so that's 8+2=10 factors of 3

so its basicaly 3^5 + 3^6 + 3^8 + 3^9 + 3^10 

simplify that to (3^5)(1 + 3 + 3^3 + 3^4 + 3^5)

1 + 3 + 3^3 + 3^4 + 3^5 is not divisible by 3

so it's 3^5

I think

x^2 +7x -44

ax^2+bx+c

we already know a is 1, for it's given

x^2+bx+c

b is just sum of roots which is just 11+(-4)=7

x^2+7x+c

c is just the product of the roots which is 11x(-4)=-44

so it's just x^2 + 7x - 44