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Vikki [24]
3 years ago
10

Which of the following represents the sum of 3+10+......+87+94 if the arithmetic series has 14 terms

Mathematics
2 answers:
AleksandrR [38]3 years ago
7 0

Answer:

679

Step-by-step explanation:

The formula for calculating the sum of an arithmetic progression which contains the first and the last term is expressed as;

Sn = n/2(a+l) where:

n is the number of terms in the series

a is the first term of the series

l is the last term of the series.

Given the series 3+10+......+87+94 which has 14terms,

a = 3

n = 14

l = 94

S3 = 14/2(3+94)

S3 = 7(97)

S3 = 679

nirvana33 [79]3 years ago
5 0
Here is a trick that not a lot of people know

(# of terms)*(first+last)/2
(in case you don't know, * means multiply and / means divide)


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Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of
anyanavicka [17]

Answer:

The 99% confidence interval for the true percentage of all adults in the town that smoke is (0.1159, 0.2841).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

Of 150 adults selected randomly from one town, 30 of them smoke. This means that n = 150, p = \frac{30}{150} = 0.2

99% confidence interval

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.20 - 2.575\sqrt{\frac{0.20*0.80}{150}} = 0.1159

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.20 + 2.575\sqrt{\frac{0.20*0.80}{150}}{119}} = 0.2841

The 99% confidence interval for the true percentage of all adults in the town that smoke is (0.1159, 0.2841).

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