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2 years ago

The sum of the first n consecutive even numbers can be found using S = n2 + n, where n ≥ 2.

Mathematics

2 answers:

riadik2000 [5.3K]2 years ago

7 0

Answer:

Value of n when sum is 156 is 12

Step-by-step explanation:

Given: function to find sum of first n consecutive even numbers, S = n² + n where n ≥ 2

To find: value of n when Sum = 156

Consider, the function

S = n² + n

156 = n² + n

n² + n - 156 = 0

n² + 13n - 12n - 156 = 0

n ( n + 13 ) - 12 ( n + 13 ) = 0

( n + 13 )( n - 12 ) = 0

So, n + 13 = 0 nd n - 12 = 0

⇒ n = -13 and n = 12

n cannot be less than 2, So, value of n = 12

Therefore, Value of n when sum is 156 is 12

viktelen [127]2 years ago

3 0

The following are the choices on this question:
A.6
B. 39
C. 26
D. 12
The answer is option D. 12.

Check this out:
S=n² + n
S= 12² + 12
(you can get the square of 12 by multiplying 12 by itself: 12 × 12)
S=144 +12
S=156

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And we can find this probability using the complement rule, the normal standard table or excel and we got:

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And we can find this probability with this difference:

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And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the velocities of a population, and for this case we know the distribution for X is given by:

$X \sim N(46.8,1.75)$

Where $\mu=46.8$ and $\sigma=1.75$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel and we got:

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Part b

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And we can find this probability using the complement rule, the normal standard table or excel and we got:

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And we can find this probability with this difference:

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And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

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