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rewona [7]
3 years ago
14

gabriel has 6 2/3 of almond flour to make macaroons. he plans to make a recipe that uses 3/4 of a cup of almond flour. what is t

he greatest number recipes he can make?
Mathematics
1 answer:
harina [27]3 years ago
6 0

Answer:

8 cups max

Step-by-step explanation:

3/4 cup = 1 recipe

6 2/3(20/3) cup =  <u>20/3 x 1 </u>

                                  3/4

= <u>20</u> / <u>3</u>

   3     4

= <u>20</u> x<u> 4</u>

   3     3

= 80/9

= 8 cups max

the 9th cup will not be enough.

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1 over the square root of 8 = 4^(m − 2)?
andrew11 [14]

Answer:

5.5

Step-by-step explanation:

\frac{1}{ \sqrt{8} }  =  {4}^{(m - 2)}  \\

Squaring both sides

\frac{1}{8}  =  {4}^{2(m - 2)} \\   \frac{1}{8} =   {4}^{2}   \times  {4}^{(m - 2)}  \\  \frac{1}{8 \times  {4}^{2} }  =  {4}^{(m - 2)}  \\   \frac{1}{8 \times 16}  =  {4}^{(m - 2)}  \\  \frac{1}{128}  =  {4}^{(m - 2)}  \\  log_{4}(128)  = (m - 2) \\  \frac{7}{2}  = m - 2 \\ m =  \frac{11}{2}  = 5.5

7 0
4 years ago
Evaluate 1^3 + 2^3 +3^3 +.......+ n^3
Molodets [167]

Notice that

(n+1)^4-n^4=4n^3+6n^2+4n+1

so that

\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)

We have

\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)

\implies\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(n+1)^4-1

so that

\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)

You might already know that

\displaystyle\sum_{i=1}^n1=n

\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2

\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6

so from these formulas we get

\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n

\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4

\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}

If you don't know the formulas mentioned above:

  • The first one should be obvious; if you add n copies of 1 together, you end up with n.
  • The second one is easily derived: If S=1+2+3+\cdots+n, then S=n+(n-1)+(n-2)+\cdots+1, so that 2S=n(n+1) or S=\dfrac{n(n+1)}2.
  • The third can be derived using a similar strategy to the one used here. Consider the expression (n+1)^3-n^3=3n^2+3n+1, and so on.
7 0
4 years ago
Find all the the real square roots of 144
Zanzabum

Answer:

12 and -12

Step-by-step explanation:

Just square root 144

3 0
4 years ago
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