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3 years ago

What are the values of r and a1 for 1/4(2)k-1

Mathematics

2 answers:

Kipish [7]3 years ago

7 0

Answer:

Step-by-step explanation:

Rasek [7]3 years ago

3 0

Given:

$\sum_{k=1}^{6}\dfrac{1}{4}(2)^{k-1}$

To find:

The values of r and $a_1$ .

Solution:

We have,

$\sum_{k=1}^{6}\dfrac{1}{4}(2)^{k-1}$

Here,

$a_k=\dfrac{1}{4}(2)^{k-1}$ ...(i)

We know that, kth term of a GP is

$a_k=a_1(r)^{k-1}$ ...(ii)

From (i) and (ii), we get

$a_1=\dfrac{1}{4}$ and $r=2$

Therefore, the correct option is C.

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Tina mailed a package in a container shaped like a

tamaranim1 [39]

Answer: the answer is 293 1/4. 3

Step-by-step explanation:

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2 years ago

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Sales of a new line of athletic footwear are crucial to the success of a company. The company wishes to estimate the average wee

MariettaO [177]

Answer:

188 weeks of data must be sampled.

Step-by-step explanation:

From the information given, we can deduce that:

The Margin of error is within = 200

The confidence interval = 95%

The level of significance = 1 - C.I

= 1 - 0.95

= 0.05

The standard deviation = 1400

The number of weeks the data must be sampled can be determined by using the formula for sample size which is:

$n =( \dfrac{Z_{\alpha/2} \times \sigma}{E} )^2$

$n =( \dfrac{Z_{0.05/2} \times 1400}{200} )^2$

$n =( \dfrac{1.96 \times 1400}{200} )^2$

$n =( \dfrac{2744}{200} )^2$

$n =( 13.72)^2$

n = 188.24

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Thus, 188 weeks of data must be sampled.

6 0

3 years ago

Answer this question to get marked as brainliest!!!!

allsm [11]

Answer:

62.8319 ≈ 62.8 inches

Step-by-step explanation:

$c = 2\pi *r\\r = 10 in\\\\c =(2\pi )*(10)\\= 62.8318530718\\62.8$

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3 years ago

Suppose you read online that children first count to 10 successfully when they are 32 months old, on average. You perform a hypo

creativ13 [48]

Answer:

$p_v =2*P(t_{(35)}$

Step-by-step explanation:

Assuming this info from R

hist(gifted$count)

## Min. 1st Qu. Median Mean 3rd Qu. Max.

## 21.00 28.00 31.00 30.69 34.25 39.00

## Sd

## [1] 4.314887

Data given and notation

$\bar X=30.69$ represent the mean

$s=4.3149$ represent the sample standard deviation

$n=36$ sample size

$\mu_o =32$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different than 32, the system of hypothesis would be:

Null hypothesis: $\mu = 32$

Alternative hypothesis: $\mu \neq 32$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{30.69-32}{\frac{4.3149}{\sqrt{36}}}=-1.822$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=36-1=35$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(35)}$

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3 years ago

ILL MARK BRAINLIEST ASAP IF CORRECT Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -

Oduvanchick [21]

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h. k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 6, - 1), thus

y = a(x + 6)² - 1

To find a substitute one of the roots into the equation

Using (- 3, 0), then

0 = a(- 3 +6)² - 1

0 = 9a - 1 ( add 1 to both sides )

1 = 9a ( divide both sides by 9 )

a = $\frac{1}{9}$ , thus

y = $\frac{1}{9}$ (x + 6)² - 1 ← in vertex form

Expand factor and simplify

y = $\frac{1}{9}$ (x² + 12x + 36) - 1 ← distribute

y = $\frac{1}{9}$ x² + $\frac{4}{3}$ x + 4 - 1

= $\frac{1}{9}$ x² + $\frac{4}{3}$ x + 3 ← in standard form

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3 years ago