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3 years ago

Find the 15th term in the geometric sequence shown below. 1, 3, 9...

Mathematics

2 answers:

Alex73 [517]3 years ago

8 0

Answer:'3^14

Step-by-step explanation:

This geometric sequence has common ratio 3 and first term 1.

Thus, the general formula for the nth term is a(n) = 1*3(n - 1).

The 15th term is thus a(15) = 1*3^(n -1) = 3^14.

serious [3.7K]3 years ago

6 0

Answer:

Step-by-step explanation:

a₁ = 1

r = 3/1 = 3

an = a₁rⁿ⁻¹

a₁₅ = 1*(3)¹⁴

a₁₅ = 4782969

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Anna is saving to buy a new cell phone. Her mother is helping Anna by contributing money each month. What is the ratio between t

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Answer:

Option D. 3:1, $120

Step-by-step explanation:

The complete question in the attached figure

Part 1) What is the ratio between the amount of money contributed by Anna and the amount contributed by her mother?

Let

x -----> the amount of money contributed by Anna

y ----> the amount of money contributed by her mother

we know that

Looking at the table

The value of x is equal to $x=\$30+\$60+\$90+\$120=\$300$

The value of y is equal to $y=\$10+\$20+\$30+\$40=\$100$

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substitute the values

$\frac{x}{y}=\frac{300}{100}=\frac{3}{1}$

Part 2) What was the total amount saved in April?

we know that

To find out the total amount saved in April, adds Mon's contribution in April plus Anna's contribution in April

$(\$30+\$90)=\$120$

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3 years ago

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Answer:

The answer is 25

Step-by-step explanation:

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3 years ago

Question 6 of 25 What is sin 45°?

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2 years ago

A personnel director in a particular state claims that the mean annual income is the same in one of the state's counties (Coun

Shalnov [3]

Answer:

a) The hypothesis that the mean annual income is the same could not be rejected. There is no enough evidence to claim they are different.

b) The critical values for this two-sided test are t=±1.711.

Step-by-step explanation:

The question is incomplete:

(a) Identify the claim and state H0 and Ha.

Which is the correct claim below?

(b) Find the critical value(s) and identify the rejection region(s).

Enter the critical value(s) below.

We have an hypothesis test on the difference of two means.

The null and alternative hypothesis are:

$H_0: \mu_a-\mu_b=0\\\\H_a: \mu_a-\mu_b\neq 0$

The claim of the alternative hypothesis is that the mean annual income is different in County A and County B.

The null hypothesis is that the mean annual income is equal in both counties.

The significance level is α=0.10.

The sample from County A has a mean of S40,400, a s.d. of $8,700 and a sample size of 18 residents.

The sample from County B has a mean of S39,200, a s.d. of $6,000 and a sample size of 8 residents.

The standard error of the difference of means is:

$\sigma_d=\sqrt{\frac{\sigma_a^2}{n_a}+\frac{\sigma_b^2}{n_b}}=\sqrt{\frac{8700^2}{18}+\frac{6000^2}{8}}=\sqrt{8705000}=2950$

The degrees of freedom are:

$df=n_a+n_b-2=18+8-2=24$

Then, the test statistic is:

$t=\frac{\Delta M-\Delta \mu}{\sigma_d} =\frac{(40,400-39,200)-0}{2950} =\frac{1200}{2950}=0.407$

For a statistic t=0.407, and df=24, the P-value is P=0.69. As the P-value is bigger than the significance level, the null hypothesis failed to be rejected.

If we would use the critial value approach, we would have to calculate the critical values for t, for df=24, two sided test and α=0.10.

The critical values, looking in a table, are t=1.711.

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2 years ago