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lakkis [162]
3 years ago
10

The line plot shows the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the pre

vious week. Select from the drop-down menus to complete each statement. The range . The mean . Two line plots one above the other, both are labeled from zero to twelve by ones. The top line plot is labeled Boys with four Xs over five and one X over zero, two, three, four, ten, and twelve. The bottom line plot is labeled Girls with three Xs above eight, two Xs above three and four, and one X above two, six and seven.

Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
8 0
10 students per gender:

Boys:  <span>four Xs over five and one X over zero, two, three, four, ten, and twelve. 
5, 5, 5, 5, 0, 2, 3, 4, 10, 12 </span>→ 0, 2, 3, 4, 5, 5, 5, 5, 10, 12<span>
mean: 5.1
range: 12

</span><span>Girls: three Xs above eight, two Xs above three and four, and one X above two, six and seven.
8, 8, 8, 3, 3, 4, 4, 2, 6, 7 </span>→ 2, 3, 3, 4, 4, 6, 7, 8, 8, 8 
<span>mean: 5.3
range: 6

The boys have the higher range while the girls have the higher mean value.


</span><span>
</span>
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Answer:

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Step-by-step explanation:

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Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

y = 10000 * 1.04^x

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

y = 12000* 0.97^x

<h3>The similarities in the equations</h3>

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In (a) and (b), we have:

y = 10000 * 1.04^x ---- city A

y = 12000* 0.97^x --- city B

When city A exceeds city B, we have the following inequality

10000 * 1.04^x > 12000 * 0.97^x

Divide both sides by 10000

1.04^x > 1.2 * 0.97^x

Divide both sides by 0.97^x

(\frac{1.04}{0.97})^x > 1.2

1.07^x > 1.2

Take the natural logarithm of both sides

\ln(1.07)^x > \ln(1.2)

This gives

x\ln(1.07) > \ln(1.2)

Solve for x

x > \frac{\ln(1.2)}{\ln(1.07)}

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<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

y = 10000 * 1.04^x ---- city A

y = 12000* 0.97^x --- city B

When city A is at least twice city B, we have the following inequality

10000 * 1.04^x \ge 2 * 12000 * 0.97^x

10000 * 1.04^x \ge 24000 * 0.97^x

Divide both sides by 10000

1.04^x \ge 2.4 * 0.97^x

Divide both sides by 0.97^x

(\frac{1.04}{ 0.97})^x \ge 2.4

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Take the natural logarithm of both sides

\ln(1.07)^x \ge \ln(2.4)

This gives

x\ln(1.07) \ge \ln(2.4)

Solve for x

x\ge \frac{\ln(2.4)}{\ln(1.07) }

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This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

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