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Stells [14]
3 years ago
8

The formula below gives T, the approximate time in years it takes a population to double if the annual growth rate is r percent.

Mathematics
1 answer:
matrenka [14]3 years ago
4 0
The answer is 
T=70/r=70/<span> 24/100=100*70/24=7000/24=291.6
</span>T=<span>291.6</span>
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The average cost of tuition plus room and board at small private liberal arts colleges is reported to be less than $18,500 per t
lys-0071 [83]

Answer:

The null and alternative hypothesis for this study are:

H_0: \mu=18500\\\\H_a:\mu< 18500

The null hypothesis is rejected (P-value=0.004).

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

Then, the null and alternative hypothesis are:

H_0: \mu=18500\\\\H_a:\mu< 18500

The significance level is 0.05.

The sample has a size n=150.

The sample mean is M=18200.

The standard deviation of the population is known and has a value of σ=1400.

We can calculate the standard error as:

\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31

Then, we can calculate the z-statistic as:

z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624

This test is a left-tailed test, so the P-value for this test is calculated as:

P-value=P(z

As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

3 0
3 years ago
2)<br> Solve the quadratic equation by taking square roots.<br> 4x^2 = 24
Veronika [31]

Answer:

4x²=24

or,x²=24÷4

or,x=root 6

8 0
3 years ago
The population of deer forest is currently 800 individuals. Scientists predict that this population will grow at a rate of 20 pe
jonny [76]

Answer:

<em>C. 3.8 years</em>

Step-by-step explanation:

<u>Exponential Growth </u>

The natural growth of some magnitudes can be modeled by the equation:

P(t)=P_o(1+r)^t

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The actual population of deer in a forest is Po=800 individuals. It's been predicted the population will grow at a rate of 20% per year (r=0.2).

We have enough information to write the exponential model:

P(t)=800(1+0.2)^t

P(t)=800(1.2)^t

It's required to find the number of years required for the population of deers to double, that is, P = 2*Po = 1600. We need to solve for t:

800(1.2)^t=1600

Dividing by 800:

(1.2)^t=1600/800=2

Taking logarithms:

t\log 1.2=\log 2

Dividing by log 1.2:

t=\frac{\log 2}{ \log 1.2}

Calculating:

t = 3.8 years

Answer: C. 3.8 years

6 0
3 years ago
Find the value of the series
jekas [21]

Step-by-step explanation:

that is

sum(2^r) for r=1 to n, plus sum(1/2) for r=1 to n.

and that is

sum(2^r) + n/2 for r=1 to n.

2^r is a geometric sequence with 2 being the common ratio (every new term is created by multiplying the previous term by 2).

and since r is starting at 1, the first term a1 = 2.

the formula for the sum of a finite geometric sequence is

Sn = a1×(1 - r^n) / (1 - r)

with r being the common ratio .

so, in our case

Sn = 2×(1 - 2^n) / (1 - 2)

Sn = (2 - 2^(n+1)) / -1 = 2^(n+1) - 2

and so, in total we get

2^(n+1) - 2 + n/2 = 2^(n+1) + (n - 4)/2

3 0
2 years ago
Express the area of each square as a monomial.<br> 8g^3h
jek_recluse [69]
The area of a square with a side of 8g^3h is:

\bf{Area = 8g^3h \times 8g^3h}\\\\\bf{Area = (8g^3h)^2}\\\\\boxed{\bf{Area = 64g^6h^2}}}
3 0
3 years ago
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