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vesna_86 [32]
3 years ago
14

Liam's bottle had 2 and 1/2 cups of juice in it. He drank 1/3 of the juice in his bottle. How many cups of juice did Liam drink.

Mathematics
2 answers:
bekas [8.4K]3 years ago
6 0

liam drank 2/6 cups of juice

Ann [662]3 years ago
6 0

Answer:

Liam drank five sixths of a cup of juice.


Step-by-step explanation:

Here we want (1/3) of (2 1/2 cups); that's how much Liam drank.

Re-writing this, we get:

1         5

----- * ----- = 5/6.

 3       2

Liam drank five sixths of a cup of juice.

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Find the area of the shaded region ​
o-na [289]

so hmmm let's get the area of the whole hexagon, and then get the area of the circle inside it, then <u>subtract the area of the circle from that of the hexagon's</u>, what's leftover is what we didn't subtract, namely the shaded part.

\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\cot\stackrel{\stackrel{degrees}{\downarrow }}{\left( \frac{180}{n} \right)}~ \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\[-0.5em] \hrulefill\\ n=\stackrel{hexagon}{6}\\ s=\frac{9}{2} \end{cases}\implies A=\cfrac{1}{4}(6)\left( \cfrac{9}{2} \right)^2 \cot\left( \cfrac{180}{6} \right)

A=\cfrac{1}{4}(6)\cfrac{9^2}{2^2} \cot(30^o)\implies A=\cfrac{243}{8}\cot(30^o)\implies A=\cfrac{243\sqrt{3}}{8} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{4}{5} \end{cases}\implies A=\pi \left( \cfrac{4}{5} \right)^2\implies A=\cfrac{16\pi }{25} \\\\[-0.35em] ~\dotfill

\stackrel{\textit{area of the hexagon}}{\cfrac{243\sqrt{3}}{8}}~~ - ~~\stackrel{\textit{area of the circle}}{\cfrac{16\pi }{25}}\implies \cfrac{6075\sqrt{3}-128\pi }{200}

5 0
2 years ago
Michael reads 12 pages of a book in 18 minutes, 8 pages in 12 minutes,and 20 pages in 30 minutes. Is this a proportional relatio
maria [59]

Answer:

  • y = 2/3x

Step-by-step explanation:

<u>Reading rate is y pages per x minutes and proportional relationship formula is:</u>

  • y = kx

<u>The coefficient is:</u>

  • k = y/x

<u>Let's verify if the given numbers fit into the same relationship:</u>

  • 12/18 = 2/3
  • 8/12 = 2/3
  • 20/30 = 2/3

We confirm all same and it means k = 2/3

<u>Required equation is:</u>

  • y = 2/3x

This represents that Michael reads 2 pages per 3 minutes and for x minutes he reads 2/3x pages

7 0
3 years ago
Ns of
motikmotik

Answer:

y=3x2^x

Step-by-step explanation:

5 0
3 years ago
Which number completes the inequality?
aliya0001 [1]
The answer to it would be C.
5 0
3 years ago
Mathematical induction of 3k-1 ≥ 4k ( 3k = k power of 3 )
tresset_1 [31]

For making mathematical induction, we need:

  • a base case

An n_0 for which the relation holds true

  • the induction step

if its true for n_i, then, is true for n_{i+1}

<h3>base case</h3>

the relationship is not true for 1 or 2

1^3-1 = 0 < 4*1

2^3-1 = 8 -1 = 7 < 4*2 = 8

but, is true for 3

3^3-1 = 27 -1 = 26 > 4*3 = 12

<h3>induction step</h3>

lets say that the relationship is true for n, this is

n^3 -1 \ge 4 n

lets add 4 on each side, this is

n^3 -1 + 4 \ge 4 n + 4

n^3 + 3 \ge 4 (n + 1)

now

(n+1)^3 = n^3 +3 n^2 + 3 n + 1

(n+1)^3 \ge n^3 + 3 n

if n \ge 1 then 3 n \ge 3 , so

(n+1)^3 \ge n^3 + 3 n \ge n^3 + 3

(n+1)^3 \ge  n^3 + 3 \ge 4 (n + 1)

(n+1)^3  \ge 4 (n + 1)

and this is what we were looking for!

So, for any natural equal or greater than 3, the relationship is true.

4 0
3 years ago
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