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Citrus2011 [14]
3 years ago
7

If tñ=2ñ+3, find S10​

Mathematics
1 answer:
Allisa [31]3 years ago
3 0

Answer:

S_{10}=280

Step-by-step explanation:

Given that,

t_n=2n+3 ...(1)

We need to find the value of S_{10}.

Put n = 1 to find the first term.

t_1=2(1)+3=5

Put n = 2 to find the second term.

t_2=2(2)+3=7

Put n = 3 to find the third term.

t_3=2(3)+3=9

Put n = 10 to find the tenth term.

t_{10}=2(10)+3=23

It means we need to find the sum of 5,7,9,.....,23.

The formula for the sum of n terms is given by :

S_=\dfrac{n}{2}(a+a_n)

We have, n = 10, a = 5 and a_n=23

So,

S=\dfrac{10}{2}(5+23)\\\\S_{10}=10\times 28\\\\=280

So, the value of S_{10} is equal to 280.

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2. When a large truckload of mangoes arrives at a packing plant, a random sample of 150 is selected and examined for
kirza4 [7]

a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).

b) The margin of error is: 2.45%.

c) The 90% confidence is the level of confidence that the true population percentage is in the interval.

d) The needed sample size is: 271.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions has the bounds given by the rule presented as follows:

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

The margin of error is given by:

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

The variables are listed as follows:

  • \pi is the sample proportion, which is also the estimate of the parameter.
  • z is the critical value.
  • n is the sample size.

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of \frac{1+0.90}{2} = 0.95, so the critical value is z = 1.645.

The sample size and the estimate are given as follows:

n = 150, \pi = \frac{15}{150} = 0.1

The margin of error is of:

M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%

The interval is given by the estimate plus/minus the margin of error, hence:

  • The lower bound is: 10 - 2.45 = 7.55%.
  • The upper bound is: 10 + 2.45 = 12.45%.

For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:

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

0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}

0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}

\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}

(\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2

n = 271 (rounded up).

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

3 0
1 year ago
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