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3 years ago

Fill in the blanks.

Mathematics

1 answer:

Anna [14]3 years ago

4 0

Answer:

In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Also:

The normal distribution is symmetric, which means that 50% of the data is above the mean and 50% is below.

Then:

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The population of a town doubled approximately every 5 years during the first several decades after it was founded. If the origi

zzz [600]

Answer:

624 people

(I put two ways to look at the problem.)

Step-by-step explanation:

What is describe here is an exponential function of the form:

$P=P_0 e^{kt}$

$t$ is the number of years after 1761.

$P_0$ is the initial population.

So t=0 represents year 1761.

t=1 represents year 1762

t=2 represents year 1763

....

t=20 represents year 1781.

So we have the doubling time is 5 years. This means the population will be twice what it was in 5 years. Let's plug this into:

$P=P_0e^{kt}$

$2P_0=P_0e^{k\cdot 5}$

Divide both sides by $P_0$ :

$2=e^{5k}$

Convert to logarithm form:

$5k=\ln(2)$

Multiply both sides by 1/5:

$k=\frac{1}{5}\ln(2)$

$k=\ln(2^{\frac{1}{5}})$ By power rule.

So in the next sentence they actually give us the initial population and we just found k so this is our function for P:

$P=39e^{\ln(2^{\frac{1}{5}})t}$

So now we plug in 20 to find how many residents there were in 1761:

$P=39e^{\ln(2^{\frac{1}{5}})(20)}$

This is surely going to the calculator:

$P=624$

Now if you don't like that, let's try this:

Year 0 we have 39 people.

Year 5 we have 39(2)=78 people.

Year 10 we have 78(2)=156 people.

Year 15 we have 156(2)=312 people.

Year 20 we have 312(2)=624 people.

7 0

3 years ago

Does this graph represent a function? Why or why not?

Harlamova29_29 [7]

The answer would be D.
Curve of the function can't be cut by vertical line more than once at different points.

4 0

3 years ago

Use the translation (x, y)→(x−4, y+2) to find the preimage of (7, 2)

Bess [88]

Answer:

(11 , 0)

Step-by-step explanation:

x - 4 = 7

x = 7 +4

x = 11

y + 2 = 2

y = 2 - 2

y = 0

6 0

2 years ago

What are the solutions to the equation?

olga2289 [7]

Answer:

x = −10 and x = 4

Step-by-step explanation:

x2 + 6x = 40

Subtract 40 from each side

x^2 + 6x -40 =0

Factor, what 2 numbers multiply to -40 and add to 6

10 * -4 = -40 10+-4 = 6

(x+10) (x-4) = 0

Using the zero product property

x+10 =0 x-4=0

x=-10 x=4

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3 years ago

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How many milliliters are equal to 4 liters

iren2701 [21]

Answer:

$4,000 ml = 4 liters$

Hope this helps!

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4 years ago

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