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Vinvika [58]
3 years ago
9

the sum of the first twelve terms of arithmetic progression [AP] is 168. if the third term is 7. find the value of the common di

fference and the first term ​
Mathematics
1 answer:
34kurt3 years ago
3 0

Answer:

Common difference = 2

First term = 3.

Step-by-step explanation:

3rd term = a1 + (3 - 1)d  = 7    where a1 = first term and d = the common difference.

Sum of the first 12 terms = (12/2)[2a1 + (12-1)d] = 168

so 6(2a1 + 11d) = 168

So simplifying, we have the following system:

 a1 + 2d = 7  ..................(A)

12a1 + 66d = 168

2a1 + 11d = 28.................(B)   Multiplying equation A by - 2:

-2a1 - 4d =- -14                      Adding this to equation B

7d = 14

d = 2

Now plug this into equation A:

a1 + 2(2) = 7

a1 = 7-4

a1 = 3.

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3 years ago
Calculate the annual return percentage
const2013 [10]
The annual returns will be calculated as follows:
a] Here we use the formula:
A=p(1+r/100)^n
A=future amount
p=principle
r=returns
n=time
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7 0
3 years ago
It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportat
katrin2010 [14]

Answer: H_0:\mu=120

H_A:\mu\neq120

Step-by-step explanation:

Let \mu denotes the average braking distance for a population of small car.

Given : It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet.

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Objective of test : Whether the statement made in the advertisement is false

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Since '=' signs is contained by Null hypothesis and alternative hypothesis is against it.

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Which expression corresponds to this graph?
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5 0
2 years ago
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