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3 years ago

How many ounces of a 35% alcohol solution must be mixed with 10ounces of 40% alcohol solution to make a 37% alcohol solution?

1 answer:

5 0

First off, let's change the format of the percentage to decimal.. so 35% is just 35/100 or 0.35 and 40% is 40/100 or 0.4 and so on.

$\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{35\% sol'n}&x&0.35&0.35x\\
\textit{40\% sol'n}&10&0.40&4.00\\
-----&-----&-------&-------\\
mixture&y&0.37&0.37y
\end{array}$

now, whatever "x" amount is, we know that x + 10 must add up to "y". x + 10 = y, because both quantities added will give the mixture amount.

and whatever 0.35x + 4 = 0.37y, because both concentrated amounts must give the 37% of the mixture.

$\bf \begin{cases}
x+10=\boxed{y}\\
0.35x+4=0.37y\\
----------\\
0.35x+4=0.37\left( \boxed{x+10} \right)
\end{cases}$

solve for "x", to see how much of the 35% solution will be needed.

what about "y"? well, x + 10 = y.

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5=1/2x - 3 please help me out

liq [111]

Answer:

x = 16

Step-by-step explanation:

5 = 1/2(x) - 3

Add 3 to both sides.

8 = 1/2(x)

Rewrite for clarity.

1/2(x) = 8

x/2 = 8

Multiply both sides by 2.

x = 16.

Proof:

5 = 1/2(x) - 3

Substitute variable.

5 = 1/2(16) - 3

Multiply 1/2 and 16.

5 = 8 - 3

Subtract 3 from 8.

5 = 5

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3 years ago

Consider the functions below. f(x, y, z) = x i − z j + y k r(t) = 4t i + 6t j − t2 k (a) evaluate the line integral c f · dr, wh

fredd [130]

With

$\vec r(t)=4t\,\vec\imath+6t\,\vec\jmath-t^2\,\vec k$

we have

$\mathrm d\vec r=(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt$

The vector field evaluated over this parameterization is

$\vec f(x,y,z)=\vec f(x(t),y(t),z(t))=4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k$

so the line integral is

$\displaystyle\int_{-1}^1(4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k)\cdot(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt$

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3 years ago

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3 years ago

I need the answer ASAP :( really struggling

pashok25 [27]

<h3>Answer: Choice A $-4 \le x \le -2$ </h3>

Explanation:

Ask yourself this: "When is the graph completely horizontally flat?" The answer to this question is when x is between -4 and -2. This is where the graph is constant. All other intervals are either increasing or decreasing.

Saying "The graph is constant" basically means "constant rate of change", which is another way of saying that the graph isn't changing. Constant means it stays the same.

So this is why the answer is $-4 \le x \le -2$

Note how only choice A has both endpoints in the negative region, so it is a quick way to spot the answer.

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3 years ago