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3 years ago

Find Sn for the given geometric series. Round answers to the nearest hundredth, if necessary.

Mathematics

1 answer:

ololo11 [35]3 years ago

4 0

Answer:

a. 435.4

Step-by-step explanation:

We are given a geometric sequence with first term, firth term and the common ratio. We are asked to find the sum of first 5 terms of the geometric series.

The formula to calculate the sum of finite geometric series is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

Since we need to find the sum of first 5 terms, n will be 5. Using these values in the above formula, we get:

$S_{5}=\frac{0.28(1-6^{5})}{1-6}\\\\ S_{5}=435.4$

Therefore, the sum of first 5 terms of the given geometric series would be 435.4

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How to write 0.038383838 in bar notation?

Annette [7]

Answer:

I think it would be 0.038

with a line over the 38

Step-by-step explanation:

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2 years ago

ms. rochelle wants to put her 29 student in a group of 6b how may groups of six can she make if she pust the remaining students

lubasha [3.4K]

4 groups of 6 and 5 students left over to eat

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2 years ago

4. The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation

sergey [27]

Answer:

Function $f(x)$ is shifted 1 unit left and 1 unit up.

$f(x)\rightarrow f(x+1)+1$

Transformed function $f(x+1)+1=\log(x+1)+1$

Step-by-step explanation:

Given:

Red graph (Parent function):

$f(x)=\log(x)$

Blue graph (Transformed function)

From the graph we can see that the red graph is shifted 1 units left and 1 units up.

Translation Rules:

$f(x)\rightarrow f(x+c)$

If $c>0$ the function shifts $c$ units to the left.

If $c$ the function shifts $c$ units to the right.

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

Applying the rules to $f(x)$

The transformation statement is thus given by:

$f(x)\rightarrow f(x+1)+1$

As function $f(x)$ is shifted 1 unit left and 1 unit up.

Transformed function is given by:

$f(x+1)+1=\log(x+1)+1$

5 0

3 years ago

The difference between a number x and 3 is at least nine Write an inequality for the following sentence.

dybincka [34]

Answer:

3 - x ≥ 9

Step-by-step explanation:

At least in inequality means greater than or equal to (≥)

Difference in mathematics means subtraction

The difference between a number x and 3

3 - x

is at least nine

3 - x ≥ 9

The inequality for the sentence is

3 - x ≥ 9

6 0

3 years ago

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

Katyanochek1 [597]

Answer: $(0.367,\ 0.473)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ is the sample proportion, n is the sample size , $z_{\alpha/2}$ is the critical z-value.

Given : Significance level : $\alpha:1-0.99=0.01$

Sample size : n= 85

Critical value : $z_{\alpha/2}=2.576$

Sample proportion: $\hat{p}=\dfrac{36}{85}\approx0.42$

Now, the 99% confidence level will be :

$\hat{p}\pmz_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.42\pm(2.576)\sqrt{\dfrac{0.42(1-0.42)}{85}}\\\\\approx0.42\pm0.053\\\\=(0.42-0.053,\ 0.42+0.053)=(0.367,\ 0.473)$

Hence, the 99% confidence interval estimate of the true proportion of families who own at least one DVD player is $(0.367,\ 0.473)$

3 0

2 years ago