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5 s / 3 b  * 6 b /3 h   * 3 h  =   10 stars

Five friends live on the same street.

Their houses are at points A, B, C, D, and E, with the distances shown.

The five friends decide to meet at point P so that the total walking distance

for all five friends is minimized.
What is AP?

\(\begin{array}{|ccccc|c|c|r|} \hline A & B&C&D&E &\text{Meet at} & \text{walking distance} &AP \\ & & & & & & \text{for all} \\ & & & & & & \text{five friends} \\ \hline 0&5&9&11&14&A&39&0\\ \hline 5&0&4&6&9&B&24&5 \\ \hline 9&4&0&2&5&C&\color{red}20&9 \\ \hline 11&6&2&0&3&D&22&11 \\ \hline 14&9&5&3&0&E&31&14 \\ \hline \end{array}\)

The total walking distance
for all five friends is minimized at Point C and AP = 9

Gavin said that he had more books than anyone in his class. Jacob said that he had more books. Peter said that he had even more books. Jacob has 20 books. Gavin has 3 more books than Jacob. Peter has 8 fewer books than Gavin. How many books does Peter have?

Hello Whayousayy!

The children are lying.

Jacob has 20 books. Gavin has 23 books. Peter has 15 books.

  !

AP = AC = 9

Total walking distance = 20

Set total cost of present = x

Ali = 15+3/8x

Ben = 25

That means 40+3/8x = x, 40 = 5/8x, simplifying gets us x = 64, which is the cost of the present.

What is the smallest positive integer \(n\) such that
\(3n\) is a perfect square and
\(2n\) is a perfect cube?

My attempt:

\( \begin{array}{|rcll|} \hline 3n &=& 3*&3*2*3*2*3 =2^2(3^2)^2=324=18^2 \\ 2n &=& 2*&3*2*3*2*3 =2^33^3=216=6^3 \\ \hline n &=& & 3*2*3*2*3 = 108 \\ \hline \end{array}\)

 If \(n \equiv 2 \pmod{7}\),
 then find the remainder when
 \((n + 2)(n + 4)(n + 6)\) is divided by \(7\).

\(\begin{array}{|rcll|} \hline \mathbf{(n + 2)(n + 4)(n + 6) \pmod{7}} &\equiv& (2 + 2)(2 + 4)(2 + 6) \pmod{7} \\ &\equiv& 4*6*8 \pmod{7} \\ &\equiv& 192 \pmod{7} \\ &\equiv& {\color{red}3} \pmod{7} \\ \hline \end{array}\)

7 white rice: 3 wild rice for 10 total

then by multiplying all by 3, it's now

7*3 cups of white rice: 3*3 cups of wild wice for 10*3 total cups.

Which ends up to be 21 cup white rice and 9 cup wild rice

If I expand
\(25*24*23* \dotsm *12*11*10\),
how many zeros are there at the end of the number I get?

\(25*24*23* \dotsm *12*11*10 = 25!-9!\)

\(\begin{array}{|rcll|} \hline \text{zeros} &=& \lfloor\frac{25}{5}\rfloor +\lfloor\frac{25}{25}\rfloor -\lfloor\frac{9}{5}\rfloor \\ &=& 5+1-1 \\ \mathbf{\text{zeros}} &=& \mathbf{5} \\ \hline \end{array}\)

Since it's obvious there's more 2's than 5's in this string of numbers, we just count the number of 5's to get the answer/

5's: 10,15,20,25(25has 5^2), so there is 5^5 in total

from that we know there's 100000 that can be combined in this number which leaves us with 5 0's at the end

set total cookies as x

3/8x=coconut cookies

2/5*5/8 = 1/4x=peanut cookies

(rest) x-3/8x-1/4x = 3/8x accounts for chocolate cookies, so 3/8 is the fraction we're looking for

since 5 stars is 3 balloons, 10 stars is 6 balloons, so we know 3 hearts is 10 stars.

A father is 9 times as old as his son. In three years, the father will be 6 times as old as his son.
How old is the son?

Son = x       Father = 9x

x + 3                9x + 3

(9x + 3) / (x + 3) = 6

x = 5

sorry man

3+2+2+4=11

If he eats one per day it will take 11 days to finish.

AAAOOOBBSSSS

One way to do it is as follows

11!/(3!*2!*2!*4!)

Which would be

69300

Yay!

7+11-5 =   13     out of 30 play basketball or baseball

That's wrong. Someone give me the correct ansawer please. 

doing it

The number of ways is C(11,4)*C(10,4) = 69300.

2x^2 + 6x + 11

2 (x^2+3x) + 11

2 ( x+ 1.5)^2  - 4.5 + 11

2(x+ 1.5)^2  + 6.5                 h = - 1.5

f(-2) =  -1/2 +  (-1/2 / (1-1/2) )

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

for the second part sub in   -2/3    for     x^-1   

What answers did you get so far?

2x^4 * 3x^10    results in    6 x^14         (x^2+5)^7   results in  (1) x^14        subtracted from the first term results in 5 x¹⁴      Degree 14

= 2 ^{(10 + 40+120)}                 n = 10+40+120