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kolbaska11 [484]
3 years ago
8

The summation expression in the following series has an absolute value in it. Expand and evaluate the summation notation. What i

s the sum of the series?

Mathematics
1 answer:
nikitadnepr [17]3 years ago
4 0
|3i-10|=\begin{cases}3i-10&\text{for }3i-10\ge0\\-(3i-10)&\text{for }3i-10

We have that 3, which means |3i-10| reduces to 3i-10 when i\ge4, or reduces to 10-3i when i\le3.

So we can expand the summation as

\displaystyle\sum_{i=1}^6|3i-10|=\sum_{i=1}^3(10-3i)+\sum_{i=4}^6(3i-10)

Notice that the 10 contributes a total of 30 from the first sum, and -30 from the second sum, so those terms cancel, leaving us with

\displaystyle3\left(\sum_{i=4}^6i-\sum_{i=1}^3i\right)=3((4+5+6)-(1+2+3))=3(15-6)=3(9)=27
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OleMash [197]

Answer:

Step-by-step explanation:

\frac{57}{40.3}=\frac{23}{QR}  \\

cross multiply

57(QR)=926.9

QR=16.26...

round to nearest tenth

QR=16.3

4 0
3 years ago
The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting.
puteri [66]

Using concepts of the normal and of the uniform distribution, it is found that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

  • In an uniform distribution, all outcomes are equally as likely, thus they have the same height.
  • In the normal distribution, the outcomes with the highest likelihood are those closest to the mean, thus they have the highest height. This means that the mean of this distribution is 8.
  • The standard deviation cannot be a negative value, so in this problem, it is 1.2, which means that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

A similar problem is given at brainly.com/question/25128186

7 0
3 years ago
Find the volume. Round your answer to one decimal place.<br> (PLZ SOMEBODY HELP ASAP)
den301095 [7]

Answer:

32.738ft³

32.7ft³

Step-by-step explanation:

This is half a sphere therefore volume=4/3πr³×1/2

4/3×22/7×2.5³×1/2

=32.738ft³

3 0
4 years ago
(13x^3-13x^4)+(6xy^3-9x^3)-(x^4+12xy^3)
Anestetic [448]

Answer:

-14x^4+4x^3-6xy^3

Step-by-step explanation:

8 0
3 years ago
Solve (2/3)-(1/x)=5/6
Keith_Richards [23]
\frac{2}{3} - \frac{1}{x} = \frac{5}{6}   Multiply both sides by 3
2 - \frac{1(3)}{x} = \frac{5(3)}{6}   Simplify the numerators
2 - \frac{3}{x} = \frac{15}{6}   Multiply both sides by 6
12 - \frac{3(6)}{x} = 15   Simplify the numerator
12 - \frac{18}{x} = 15   Multiply both sides by x
12x - 18 = 15x   Subtract 12x from both sides
       -18 = 3x    Divide both sides by 3
        -6 = x      Switch the sides to make it easier to read
         x = -6

Check your answer by plugging -6 in for the x in the original problem:

\frac{2}{3} - \frac{1}{x} = \frac{5}{6}   Plug in -6 for x
\frac{2}{3} - \frac{1}{-6} = \frac{5}{6}   Change \frac{2}{3} to \frac{4}{6} so all denominators are the same
\frac{4}{6} - \frac{1}{-6} = \frac{5}{6}   Change \frac{1}{-6} to  \frac{-1}{6} for easier work
\frac{4}{6} - \frac{-1}{6} = \frac{5}{6}   Subtract the numerators (4 - (-1) )
\frac{5}{6} = \frac{5}{6}

So, x = -6 .
5 0
3 years ago
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