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Amanda [17]
3 years ago
5

A scientists has a container of %2 acid solution and a container of 5% acid solution. How many fluid ounces of each concentratio

n should be combined to make 25fl oz of 3.2% acid solution?
Mathematics
1 answer:
sergij07 [2.7K]3 years ago
7 0

Answer: 15 oz of 2% solution and 10 oz of 5% solution

<u>Step-by-step explanation:</u>

Set up a table with the given information. <em>Multiply across and add down</em>. The bottom row (Total) will provide the equation. Then, solve the equation for the variable (2% solution) and substitute that value into the quantity for the 5% solution to find that value.

\begin {array}{l|c|c||l}&Quantity&Percent&Qty\times Percent\\ Solution\ A&x&2\%=0.02&\qquad 0.02(x)=0.02x\\Solution\ B&25-x&5\%=0.05&0.05(25-x)=1.25-0.05x\\Total&25&3.2\%=0.032&0.02x+1.25-0.05x\\\end{array}  \\\\\\.\qquad 25(0.32) = 1.25-0.03x\\.\qquad \qquad -0.8 = 1.25 - 0.03x\\.\qquad \quad \ -0.45 = -.03x\\.\qquad \qquad \ 15 = x\\\\Solution\ A: x = 15\\Solution\ B: 25 - x = 25 - (15) = 10

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The two rectangular prisms are similar. What is the volume of the larger rectangular prism?
Brums [2.3K]

The question is missing the figure which is attached below.

Answer:

1620 cm³

Step-by-step explanation:

Given:

The two prisms are similar.

Volume of the smaller prism (V₁) = 60 cm³

Length of the smaller prism (l₁) = 5 cm

Length of the larger prism (l₂) = 15 cm

Now, we know that, for similar figures, the dimensions of the figure are in proportion to each other. Therefore,

\frac{l_2}{l_1}=\frac{b_2}{b_1}=\frac{h_2}{h_1}=k(constant)\\\\Where,\\b_1,b_2\to\ widths\ of smaller\ and\ larger\ prisms\ respectively\\\\h_1,h_2\to\ heights\ of\ smaller\ and\ larger\ prisms\ respectively

\frac{l_2}{l_1}=\frac{15\ cm}{5\ cm}=3\\\\\therefore\ k=3

This means that, the smaller figure is dilated by a scale factor of 3.

Hence, l_2=3l_1,b_2=3b_1,h_2=3h_1

Volume of smaller prism is given as:

V_1=l_1b_1h_1\\\\l_1b_1h_1=60\ cm^3

Volume of larger prism is given as;

V_2=l_2b_2h_2\\\\V_2=3l_1\times 3b_1\times 3h_1\\\\V_2=27(l_1 b_1h_1)\\\\V_2=27\times 60=1620\ cm^3\ \ \ \ [\because\ l_1b_1h_1=60\ cm^3]

Therefore, the volume of the larger rectangular prism is 1620 cm³.

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