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zloy xaker [14]
3 years ago
15

Solve, need an explanation as well. Please

Mathematics
1 answer:
Aliun [14]3 years ago
7 0

Step-by-step explanation:

.05N + .10D = 1.65

.05 is the value of the nickel and .10 is the value of the dime.

N + D = 21 because you have some combination of them that total 21

solve for N: N = 21- D

substitute into the first equation

0.5 (21-D) + .10D = 1.65

1.05 - .05D + .10D = 1.65

.05D = .6

D = 12 you have 12 dimes

21-12 = 9 nickels

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The sum of the series \sum_{k=1}^{4}\left(2 k^{2}-4\right) is 44.

Step-by-step explanation:

The given series is \sum_{k=1}^{4}\left(2 k^{2}-4\right)=44

To find the sum of the series, we need to substitute the values for k in the series.

\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right]

Now, simplifying the square terms, we get,

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Multiplying the terms,

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Subtracting the values within the bracket term, we get,

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\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44

Thus, the sum of the series is \sum_{k=1}^{4}\left(2 k^{2}-4\right)=44

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