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lara [203]
2 years ago
6

it takes someone 15 minutes to prepare 3 1/4 cups of juice how many hours would it take to prepare 32 1/2 cups of juice​

Mathematics
1 answer:
wariber [46]2 years ago
4 0

\bf \begin{array}{ccll} minutes&\stackrel{juice}{cups}\\ \cline{1-2} 15&3\frac{1}{4}\\\\ x&32\frac{1}{2} \end{array}\implies \cfrac{15}{x}=\cfrac{3\frac{1}{4}}{32\frac{1}{2}}\implies \cfrac{15}{x}=\cfrac{\frac{3\cdot 4+1}{4}}{\frac{32\cdot 2+1}{2}}\implies \cfrac{15}{x}=\cfrac{\frac{13}{4}}{\frac{65}{2}}

\bf \cfrac{15}{x}=\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{5}{~~\begin{matrix} 65 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{15}{x}=\cfrac{1}{10}\implies 150=x\leftarrow \begin{array}{llll} \textit{150 minutes or}\\\\ \textit{2 hours and a half} \end{array}

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There are 12 boys and 16 girls in a classroom. Which represents the simplified ratio of girls to students in the classroom?
dedylja [7]

We know that there are 16 girls. That is the first part of the ratio. Now, it says girls to students, which mean you have to add up the total of girls and boys together. 12+16=28. There are 28 students in total. Now, you have the ratio of 16:28. But, it says simplified...so we need to divide both sides of the ratio by a number. Let's choose 4 because 4 can go both into 16 and 28. 16/4=4. 28/4=7. So, the simplified ratio of girls to students in the classroom is 4:7.

Hope this helped!

4 0
2 years ago
you fill up 40 gallon pool putting in 2 gallons water every minute, if someone scoops out 1 gallon every 8 minutes, how long wou
Sav [38]
There's a catch here, and I don't really want to go into full detail.  Because of
this catch, I think it would be unusually tough to write a simple equation for this
situation. If you wouldn't mind, let's just list it instead:

<u>After</u> . . <u>water added</u> . . <u>total in pool</u>

7 min . . . 14 gallons . . . 14 gallons
1 more . . 1 gallon . . . . . 15 gallons
7 more . . 14 gallons . . . 29 gallons
1 more . . 1 gallon . . . . . 30 gallons
5 more . . 10 gallons . . . 40 gallons, the pool is full

Add up all the minutes: <u>21 minutes</u>
5 0
2 years ago
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Kobotan [32]
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4 0
2 years ago
-3•e^(2m-5)-3=-27 how to solve
zzz [600]

Answer:

m = 3.53972077085

Step-by-step explanation:

-3 × e^{2m - 5} - 3 = -27

Subtracting -3 from both sides of the equation gives;

-3 × e^{2m - 5}  = -24

Dividing by -3 on both sides of the equation gives;

e^{2m - 5} = 8

Let 2m - 5 = x

xloge = 3log2

x = \frac{3log2}{loge} = 2.0794415417

So,

2m - 5 = 2.0794415417

2m = 2.0794415417  + 5

2m = 7.0794415417

Dividing by 2 on both sides of the equation gives:

m = 3.53972077085

3 0
3 years ago
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hram777 [196]
<h2>Answer:</h2>

All the answers have been attached in the file below.

Download pdf
3 0
3 years ago
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