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Dmitry_Shevchenko [17]
3 years ago
5

The common ratio in a geometric series is 0.5 and the first term is 256.

Mathematics
1 answer:
Anastaziya [24]3 years ago
5 0

Answer:

504

Step-by-step explanation:

Given,

common ratio (r) = 0.5

first term (a_1) is 256

Sum of first n terms in geometric series is given by the formula (r < 1):

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

Hence, sum of first 6 terms mean:

r = 0.5

a = 256

n = 6

Substituting, we get the answer to be:

S_n=\frac{a(1-r^n)}{1-r}\\S_6=\frac{256(1-(0.5)^6)}{1-0.5}\\S_6=504

The sum of first 6 terms is 504

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Answer:

We conclude that the actual percentage of households is equal to 30%.

Step-by-step explanation:

We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.

Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Let p = <u><em>proportion of households that have three cell phones NOT known.</em></u>

So, Null Hypothesis, H_0 : p = 30%      {means that the actual percentage of households is equal to 30%}

Alternate Hypothesis, H_A : p \neq 30%     {means that the actual percentage of households different from 30%}

The test statistics that would be used here <u>One-sample z-test for proportions;</u>

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where, \hat p = sample proportion of households having three cell phones = \frac{43}{150} = 0.29

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So, <u><em>the test statistics</em></u>  =  \frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }  

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The value of z test statistic is -0.27.

<u>Also, P-value of the test statistics is given by;</u>

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                            = 1 - 0.6064 = <u>0.3936</u>

<u>Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.</u>

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.

Therefore, we conclude that the actual percentage of households is equal to 30%.

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Answer:

Description

Step-by-step explanation:

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