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solong [7]
3 years ago
13

An arithmetic series begins 29+25+21+... find the maximum value that the series could have

Mathematics
1 answer:
Fittoniya [83]3 years ago
5 0

The series' value is maximized if the sum only consists of positive terms. Notice that each term in the sum takes the form 4<em>n</em> + 1 for integer <em>n</em>. This means the smallest positive integer that the sum can involve is 1, so the maximum value is

<em>S</em> = 29 + 25 + 21 + … + 9 + 5 + 1

Reversing the order of terms gives the same sum,

<em>S</em> = 1 + 5 + 9 + … + 21 + 25 + 29

Adding terms in the same positions gives us twice this sum,

2<em>S</em> = (29 + 1) + (25 + 5) + (21 + 9) + … + (1 + 29)

Notice how each grouped sum adds to 30. There are 8 terms in the sum, since 4<em>n</em> + 1 = 29 when <em>n</em> = 8. So

2<em>S</em> = 8 × 30 = 240   ===>   <em>S</em> = 120

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6 0
3 years ago
Read 2 more answers
the demand for a product for the last six years has been 15, 15, 17, 18, 20, and 19. The manager wants to predict the demand for
Marta_Voda [28]

Answer and explanation:

Given : The demand for a product for the last six years has been 15, 15, 17, 18, 20, and 19. The manager wants to predict the demand for this time series using the following simple linear trend equation : tr_t = 12 + 2t

To find : What are the forecast errors for the 5th and 6th years?

Solution :

Data : 15, 15, 17, 18, 20, and 19.

The simple linear trend equation is given as, tr_t = 12 + 2t

For t = 5 years

tr_t = 12 + 2(5)

tr_t = 12 +10

tr_t = 22

Observed tr_t = 20

Predicted tr_t = 22

Forecast error = Observed – Predicted = 20 – 22 = -2

Absolute forecast error = |-2| = 2 .

For t = 6 years

tr_t = 12 + 2(6)

tr_t = 12 +12

tr_t = 24

Observed tr_t = 19

Predicted tr_t = 24

Forecast error = Observed – Predicted = 19 – 24 = -5

Absolute forecast error = |-5| = 5.

7 0
4 years ago
To determine customer opinion of their​ pricing, Greyhound Lines randomly selects 90 busses during a certain week and surveys al
joja [24]

Answer: Cluster sampling.

Step-by-step explanation:

  • Cluster sampling is a sampling technique in statistics in which the  researcher splits the entire population into different groups called clusters.
  • After that he randomly select a sample from the clusters from the population and survey all elements of sampled clusters.
  • Researcher performs his analysis on data from the sampled clusters.

In the given situation Greyhound Lines randomly selects 90 buses during a certain week and surveys all passengers on the buses.

Here, week= Cluster

Buses = Elements

Therefore , the type of sampling is​ used = Cluster sampling.

6 0
3 years ago
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Vedmedyk [2.9K]

Step-by-step explanation:

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7 0
3 years ago
Given:g(x)=x^3-2x^2+x-3.Findg(-2)
inna [77]

Answer:

Step-by-step explanation:

g(-2) = (-2)³ - 2*(-2)²+ (-2) - 3

= -8 -2*4 - 2 - 3 = -8 - 8 -2 -3 = - 21

4 0
4 years ago
Read 2 more answers
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