All categories

3 years ago

What is the sum of the geometric sequence 1,3,9, ... if there are 13 terms

Mathematics

1 answer:

Kruka [31]3 years ago

3 0

Answer:

The answer is 797,161

Step-by-step explanation:

This one is fairly easy if tedious.

How do you get from to 3 from 1? (multiply 1 by 3).

How do you get to 9 from 3? (multiply 3 by 3).

Then simply multiply each successive result by 3 until you have 13 results. Then add those 13 results.

You might be interested in

11pts BTW PLZ HELP ASAP AM NOT TO GOOD AT MATH

dedylja [7]

First, set up the percent proportion, cross multiply and divide. Finally, subtract the answer you get from the original number.
You should get, $1,425.50.

6 0

4 years ago

Read 2 more answers

A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the

Murljashka [212]

Answer:

Step-by-step explanation: The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed (a cylinder and two cones). The silo is made up of a cylinder (with height 10 feet and base radius 5 feet) and two cones (each with height 5 ft and base radius 5 ft). The formulas given at the beginning of the SAT Math section:

Volume of a Cone:

$V=\frac{1}{3} \pi r^2h$

Volume of a Cylinder:

$V=\pi r^2h$

can be used to determine the total volume of the silo. Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is given by

$V_{silo} =\pi (5^2)(10)+(2)(\frac{1}{3})\pi (5^2)(5)=(\frac{4}{3})(250)\pi$

which is approximately equal to 1,047.2 cubic feet.

The final answer is D.

6 0

3 years ago

The Nellie Mae organization conducts an extensive annual study of credit card usage by college students. For their 2004 study, t

Masja [62]

Answer:

1. Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1=p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

2. Test statistics = 4.63

P-value = 0.00001

3. We conclude that the proportion of undergraduate students who held a credit card differed between these two years.

Step-by-step explanation:

We are given that the Nellie Mae organization conducts an extensive annual study of credit card usage by college students.

For their 2004 study, they analyzed credit bureau data for a random sample of 1,413 undergraduate students between the ages of 18 and 24. They found that 76% of the students sampled held a credit card. Three years earlier they had found that 83% of undergraduates sampled held a credit card.

Let $p_1$ = population proportion of undergraduate students who held a credit card in year 2001

$p_2$ = population proportion of undergraduate students who held a credit card in year 2004

1. Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1=p_2$ {means that the proportion of undergraduate students who held a credit card does not differed between these two years}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that the proportion of undergraduate students who held a credit card differed between these two years}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of undergraduate students who held a credit card in 2001 = 83%

$\hat p_2$ = sample proportion of undergraduate students who held a credit card in 2004 = 76%

$n_1$ = sample of students surveyed in 2001 = 1,413

$n_2$ = sample of students surveyed in 2004 = 1,413

So, test statistics = $\frac{(0.83-0.76)-(0)}{\sqrt{\frac{0.83(1-0.83)}{1,413} +\frac{0.76(1-0.76)}{1,413}} }$

= 4.63

2. Hence, the value of test statistics is 4.63.

Also, P-value is given by the following formula;

P-value = P(Z > 4.63) = 1 - P(Z $\leq$ 4.63)

= 1 - 0.99999 = 0.00001

3. Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics is does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of undergraduate students who held a credit card differed between these two years.

6 0

3 years ago

Given f of x is equal to the quantity x minus 4 end quantity divided by the quantity x squared plus 13x plus 36 end quantity, wh

gavmur [86]

The simplified expression of the function $f(x) =\dfrac{x-4}{x^2+13x+36}$ is

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$ . f(x) is increasing for all x > –4.The correct answer is option C.

<h3>What is a function?</h3>

A function is defined as a relation between the set of inputs having exactly one output each.

The function expression is given as:

$f(x) =\dfrac{x-4}{x^2+13x+36}$

Expand the denominator

$f(x) =\dfrac{x-4}{x^2+4x +9x+36}$

Factorize the denominator

$f(x) =\dfrac{x-4}{x(x+4)+9(x+4)}$

Factor out x + 9

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$

The simplified expression of the function $f(x) =\dfrac{x-4}{x^2+13x+36}$ is

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$ . f(x) is increasing for all x > –4

What is the sum of the geometric sequence 1,3,9, ... if there are 13 terms​

What is the sum of the geometric sequence 1,3,9, ... if there are 13 terms