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nordsb [41]
3 years ago
11

You bought a large container of fruit punch. The label on the container says there are 128 fluid ounces of fruit punch in the co

ntainer. How many cups is that?
Mathematics
2 answers:
coldgirl [10]3 years ago
7 0
1 cup=8oz
ratio
1:8=x:128
1/8=x/128
multiply both sides by 128
128/8=x
16=x

16 cups
Sedbober [7]3 years ago
7 0

Answer:

16 cups.

Step-by-step explanation:

It is given that a large container of fruit punch contains 128 fluid ounces of fruit punch in it.

We know that

8 fluid ounces = 1 cup

Divide both sides by 8.

1 fluid ounces = 1/8 cup

Now multiply both sides by 128

128× 1 fluid ounces = 128\times \frac{1}{8} cup

128 fluid ounces = 16 cup

Since container of fruit punch contains 128 fluid ounces of fruit punch in it, therefore there 16 cups of fruit punch in the container.

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The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i
kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.


Recall the formula for the sum of consecutive positive integers,

\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2

Now,

1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224

numbers, and their sum is

\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of 1+9\times2=19.

So, the sum of the first 1234 terms in the sequence is 2419.

8 0
2 years ago
A bookstore sold 25 books in 5 days. At this rate
Sonbull [250]

Answer:

20 days

Step-by-step explanation:

We multiply 25 by 4 to get 100, then multiply 5 by 4 to get 20.

5 0
3 years ago
Read 2 more answers
What is the square root of 5x^2 = 300
vesna_86 [32]

So, values of x are: x=2\sqrt{15},\,\,x=-2\sqrt{15}

Step-by-step explanation:

We need to find the square root of 5x^2 = 300

Writing in mathematical form:

5x^2=300

Divide both sides by 5

\frac{5x^2}{5}=\frac{300}{5}

x^2=60

Taking square root on both sides

\sqrt{x^2}=\sqrt{60}

x=\pm (\sqrt{2\times 2\times 3\times 5})

x=\pm (\sqrt{2^2 \times 3\times 5})

x=\pm (2\sqrt{3\times 5})

x=\pm (2\sqrt{15})

x=2\sqrt{15},\,\,x=-2\sqrt{15}

So, values of x are: x=2\sqrt{15},\,\,x=-2\sqrt{15}

Keywords: Square root

Learn more about square root at:

  • brainly.com/question/3511750
  • brainly.com/question/4034547

#learnwithBrainly

7 0
3 years ago
Use the equation p = 831 where p = pressure and
Inga [223]

Answer:

The lower the volume, the higher the pressure.

Step-by-step explanation:

Volume and pressure are inverse to each other -- so the more pressure, the less volume, and vice versa. Think of it like this: if you were squished into a tiny room, there would be a lot of pressure on you, and not a lot of volume to move in!

You can also think of it numerically. The higher the V in that equation (the higher the denominator) the lower the p in the equation.

6 0
3 years ago
Read 2 more answers
How many solutions does the system have? 2x+3y=-6 3x-4y=-12. A) exactly one solution b) no solution c) infinity many solutions
katovenus [111]

Answer:

a.

Step-by-step explanation:

by elimanation,cimparison or substitution you wull get the value of x=-60/17 and y=6/17

8 0
3 years ago
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