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8 days ago

A scientist has two kinds of solutions. The first solution is Solution A, which is an $80\%$ acid solution. The second solution

is Solution B, which is a $30\%$ acid solution. (a) Find the amount of Solution A (in mL) that must be added to $500$ mL of Solution B in order to produce a $70\%$ acid solution. (b) Find the amount of Solution A and Solution B (in mL) that can be combined in order to form a $100$ mL solution that is $50\%$ acid. (c) Does there exist a combination of Solution A and Solution B that is $90\%$ acid?

Mathematics

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Monica reads 7 1/2 pages of a mystery book in 9 minutes. What is her average rate in pages per minute

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The answer is found by dividing the total pages by the total time in minutes.

Calculating 7.5 divided by 9 equals approximately 0.8333, so Monica reads around 0.83 pages each minute on average.

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Explain how u would use the integer tiles to find the quotient of -15 and 3

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Calculating (-15)/3 gives -5.

The operation (-15)/3 can be visualized using red tiles for negatives and yellow for positives. The problem asks how many tiles remain when dividing 15 negative tiles among three groups equally. Using red tiles signifies the negative value involved. The division yields 5 red tiles in each group, establishing that the overall answer is negative.

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1. The following are the number of hours that 10 police officers have spent being trained in how to handle encounters with peopl

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Answer:

$Range = 16$

$Inter\ Quartile\ Range = 6.75$

$Variance = 20.44$

$Standard\ Deviation = 4.52$

Step-by-step explanation:

Provided

4, 17, 12, 9, 6, 10, 1, 5, 9, 3

Calculating the range;

$Range = Highest - Lowest$

From the data provided;

The highest value is 17 and the lowest is 1

Thus;

$Range = 17 - 1$

$Range = 16$

Calculating the inter-quartile range

The inter-quartile range (IQR) is computed as follows

$IQR = Q_3 - Q_1$

Where

Q3 = Upper Quartile and Q1 = Lower Quartile

Start by sorting the data in ascending order

1, 3, 4, 5, 6, 9, 9, 10, 12, 17

N = Total data points; N = 10

---------------------------------------------------------------------------------

Calculating Q3

$Q_3 = \frac{3}{4}(N+1) th\ item$

Substituting 10 for N

$Q_3 = \frac{3}{4}(10+1) th\ item$

$Q_3 = \frac{3}{4}(11) th\ item$

Expressing 8.25 as 8 + 0.25 $Q_3 = \frac{33}{4} th\ item$

$Q_3 = 8.25 th\ item$

Converting 0.25 into fractions

$Q_3 = (8 + 0.25) th\ item$

$Q_3 = 8th\ item + 0.25 th\ item$

From the ordered dataset;

$Q_3 = 8th\ item +\frac{1}{4} th\ item$ and

$Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)$

$8th\ item = 10$ $9th\ item = 12$

$Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)$

$Q_3 = 10 +\frac{1}{4} (12 - 10)$

$Q_3 = 10 +\frac{1}{4} (2)$

$Q_3 = 10 +0.5$

$Q_3 = 10.5$

Calculating Q1

Substituting 10 for N

$Q_1 = \frac{1}{4}(N+1) th\ item$

Expressing 2.75 as 2 + 0.75

$Q_1 = \frac{1}{4}(10+1) th\ item$

$Q_1 = \frac{1}{4}(11) th\ item$

$Q_1 = \frac{11}{4} th\ item$

$Q_1 = 2.75 th\ item$

Converting 0.75 into fractions

$Q_1 = (2 + 0.75) th\ item$

$Q_1 = 2nd\ item + 0.75 th\ item$

From the arranged dataset;

and $Q_1 = 2nd\ item +\frac{3}{4} th\ item$

$Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)$

$2nd\ item = 3$ $3rd\ item = 4$

$Q_1 = 3 +\frac{3}{4} (4 - 3)$

$Q_1 = 3 +\frac{3}{4} (1)$

$Q_1 = 3 +0.75$

$Q_1 = 3.75$

---------------------------------------------------------------------------------

Remember that

$IQR = Q_3 - Q_1$

$IQR = 10.5 - 3.75$

$IQR = 6.75$

Calculating Variance

Begin by determining the mean

$Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}$

$Mean = \frac{76}{10}$

$Mean = 7.6$

Then subtract the mean from each value and square the differences

$(1 - 7.6)^2 = (-6.6)^2 = 43.56$

$(3 - 7.6)^2 = (-4.6)^2 = 21.16$

$(4 - 7.6)^2 = (-3.6)^2 = 12.96$

$(5 - 7.6)^2 = (-2.6)^2 = 6.76$

$(6 - 7.6)^2 = (-1.6)^2 = 2.56$

$(9 - 7.6)^2 = (1.4)^2 = 1.96$

$(10 - 7.6)^2 = (2.4)^2 = 5.76$

$(12 - 7.6)^2 = (4.4)^2 = 19.36$

$(17 - 7.6)^2 = (9.4)^2 = 88.36$

Sum up the squared results

$43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4$

Then divide that sum by the total number of observations;

$Variance = \frac{204.4}{10}$

$Variance = 20.44$

Calculating Standard Deviation (SD)

$SD = \sqrt{Variance}$

$SD = \sqrt{20.44}$

$SD = 4.52$ (Approximated)

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2 months ago

Find the 45th term of the arithmetic sequence: −9, −2, 5, 12, ...

Leona [12618]

You can determine your result by adding +7 to every value.

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