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Nady [450]
2 years ago
12

6. Karla keeps a log to determine how many minutes she spends on daily tasks. She makes a table to

Mathematics
1 answer:
IRINA_888 [86]2 years ago
6 0

Answer:

60 seconds greater

Step-by-step explanation:

1 = 60

2 = 120

3 = 180

4 = 240

5 = 300

6 = 360

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A camera manufacturer spends $2,250 each day for overhead expenses plus $6 per camera for labor and materials. The cameras sell
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Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66
Ipatiy [6.2K]

Answer:

Summation notation is:

\sum_{n=1}^{16}[5(x-1)-9]

If you prefer it a little more simplified:

\sum_{n=1}^{16}(5x-14)

Step-by-step explanation:

First my favorite part, finding a pattern between the consecutive terms.

This is an arithmetic series because the terms are going up by 5 each time.

So arithmetic sequence, think linear equations:

x     |      y

1            -9

2           -4

3             1

4             6

..................

n             66

We are going to have to find that n but will will eventually...

The equation for a line in point slope form is y-y_1=m(x_x_1) where (x_1,y_1) is a point on the line and m is the slope.

We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).

I'm going to use the first point (1,-9).

So the equation in point slope form is y-(-9)=5(x-1)

Subtract 9 on both sides:

y=5(x-1)-9

Now we need to know how many terms we are adding so what is x if y=66.

66=5(x-1)-9

Add 9 on both sides:

75=5(x-1)

Divide both sides by 5:

15=x-1

Add 1 on both sides:

16=x

We have 16 terms in this sequence where the 16th term is 66.

Summation notation is:

\sum_{n=1}^{16}[5(x-1)-9]

You could simplify the 5(x-1)-9.

Distribute:  5x-5-9

Add like terms:  5x-14

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2 years ago
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