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2 years ago

Find the sum of the first 8 terms of the sequence: -5. 15, -45, 135, .......

1 answer:

7 0

Sum of geometric sequence

for the sum where the initial value is a₁ and the common ratio is r and the term is n

$S_n= \frac{a_1(1-r^n)}{1-r}$

common ratio is -3
-5 times -3 is 15, -15 times -3=-45 etc
first term is -5
and we want the 8th term

$S_8= \frac{-5(1-(-3)^8)}{1-(-3)}$
$S_8= \frac{-5(1-6561)}{1+3}$
$S_8= \frac{-5(-6560)}{4}$
$S_8= \frac{32800}{4}$
$S_8= 8200$

the sum is 8200

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What is −34, 0.5, 23,−73, 1.2 in order from least to greatest?

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Answer:

-73, -34, 0.5, 1.2, 23

Step-by-step explanation:

In Mathematics, the set of numbers are arranged in two ways. It means that the numbers can be arranged either in ascending order or descending order. If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number.

If the numbers are arranged from the greatest to the least, then it is called descending order. In this form, the numbers are in decreasing form. The first number should be greater than the second number.

Also, read: Descending Order

Standard Form

The standard form to represent the least to the greatest arrangement of numbers is given by:

a < b < c < d < …..

Here,

a, b, c, d represent the numbers

Example: 2 < 5 < 7 < 8

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2 years ago

A report states the average selling price is almost $520,000. Which measure of center was most likely used for the report?

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Answer:

Mean

Step-by-step explanation:

None

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A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find

lyudmila [28]

Answer:

$f(x)=120000 \times (1.055)^{x}$

Step-by-step explanation:

We are given that the present value for the home is $120,000 and the rate of interest is 5.5% i.e. 0.055.

We will use the following formula:

$f(x)=P \times (1+r)^{x}$

where $P$ is the present value, $r$ is the rate of interest and $x$ is the number of years.

Substituting the values in the above formula to get:

$f(x)=120000 \times (1+0.055)^{x}$

$f ( x ) = 120000 \times ( 1.055 ) ^ { x }$

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Jerry's Fish Shack claims that 16% of its employees are late to work once a week. The manager surveyed 25 employees and found th

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Answer:

We need to conduct a hypothesis in order to test the claim that the true proportion of employess are late to work is 0.16, so we need to apply a one sample proportion test:

Null hypothesis: $p=0.16$

Alternative hypothesis: $p \neq 0.16$

$z=\frac{0.20 -0.16}{\sqrt{\frac{0.16(1-0.16)}{25}}}=0.546$

$p_v =2*P(z>0.546)=0.585$

Step-by-step explanation:

Data given and notation

n=25 represent the random sample taken

$\hat p=0.2$ estimated proportion

$p_o=0.16$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of employess are late to work is 0.16, so we need to apply a one sample proportion test:

Null hypothesis: $p=0.16$

Alternative hypothesis: $p \neq 0.16$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.20 -0.16}{\sqrt{\frac{0.16(1-0.16)}{25}}}=0.546$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>0.546)=0.585$

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Answer:

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Step-by-step explanation:

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