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barxatty [35]
2 years ago
7

Evaluate the summation of 3 n plus 2, from n equals 1 to 14. 39 49 340 343.

Mathematics
1 answer:
lord [1]2 years ago
5 0

The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

<h3>How to find the sum of consecutive integers?</h3>

1 + 2 + 3 + ... + n = \dfrac{n(n+1)}{2}

<h3>
What are the properties of summation?</h3>

\sum_{i=r}^s  (a \times f(i) + b) = a \times [\: \sum_{i=r}^s f(i)] + (s-r)b

where a, b, r, and s are constants, f(i) is function of i, i ranging from r to s (integral assuming).

For the given case, the considered summation can be written symbolically as:

\sum_{n=1}^{14}  (3n + 2)

It is evaluated as;

\sum_{n=1}^{14}  (3n + 2) = 3 \times [ \: \sum_{n=1}^{14} n ] + \sum_{n=1}^{14} 2\\\\\sum_{n=1}^{14}  (3n + 2) = 3 \times \dfrac{(14)(14 + 1)}{2} + (2 + 2 + .. + 2(\text{14 times}))\\\\\sum_{n=1}^{14}  (3n + 2) = 3 \times 105 + 28 = 343\\

Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

Learn more about summation here:

brainly.com/question/14322177

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1) The total cost is 329.00 (or 329). The parts are 125.00 (or 125), and the labor is 68 per hour.

2) If we say h is the number of hours of labor, then we can create this equation --> 68h (or 68 multiplied by "h") 68h would be the cost of labor, and we need to find the number of hours (h) as a number.

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--> This equation can be made as the total cost (329) is equal to the parts (125) and the labor (68h)

4) Subtract 125 from both sides to get 68h by itself

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--> This means that h is 3.

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