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klemol [59]
3 years ago
6

Solve for n in the literal equation a(n-2)+5=bn

Mathematics
1 answer:
Helga [31]3 years ago
7 0

Answer:

<u><em>Answer is below</em></u>

Step-by-step explanation:

<em><u>a(n-2)+5=bn</u></em>

<em><u>Add -bn to both sides</u></em>

<em><u>an-2a+5+(-bn)=bn+(-bn)</u></em>

<em><u>an-bn-2a+5=0</u></em>

<em><u>add two a to both sides</u></em>

<em><u>an−bn−2a+5+(2a)=0+(2a)</u></em>

<em><u>an−bn+5=2a</u></em>

<em><u>Add -5 to both sides</u></em>

<em><u>an−bn+5+(-5)=2a+(-5)</u></em>

<em><u>an−bn=2a−5</u></em>

<em><u>Factor out our variable</u></em>

<em><u>n(a−b)=2a−5</u></em>

<em><u>Divide both sides by a-b</u></em>

<em><u>n(a-b)/a-b=2a-5/a-b</u></em>

<em><u>n=2a-5/a-b</u></em>

<em><u>Hope this helps</u></em>

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The missing number is 29

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3 years ago
Daily high temperatures in the city of Houston for the last week have been: 90, 93, 90 92, 90, 88, 98 (yesterday).
vesna_86 [32]

Answer:

  1. The answer or forecast for temperature using a three-day moving average =
  2. The answer or forecast for temperature using a three-day moving average =
  3. The mean absolute deviation based on a two-day moving average, covering all days =  

Step-by-step explanation:

1. Three-point averages are calculated by taking a number in the series with the previous and next numbers and averaging the three of them.

Step I - Calculate the three series of succession of numbers form the data and find the average of each of them:

A) (90 + 93 +90)/3 = 91.00

B) (93 + 92 + 90)/3 = 91.67

C) (90 + 92 +90)/3 = 90.67

D) (92 + 90 + 88)/3 = 90.00

E) (90 + 88 + 98)/3 = 92.00

So our series approximated to the nearest whole number is:

91, 92, 91, 90, 92

STEP II

 

From the series above the highest temperature today is unpredictable because the series is irregular. It went from 91 to 92, then it dropped to 90 and came back to 92.

             

2. Using a two day moving average we have

STEP I .  

Calculate the moving averages

           

A) (90+93)/2 = 91.50

B) (93 + 90)/2 = 91.50

C) (90 + 92)/2 = 91.00

D) (92 +90)/2 = 91.00

E) (90 + 88)/2 = 89.00

F) (88 + 98)/2 = 93.00

STEP II

The temperature also cannot be predicted because of the irregular series.

3. Calculating the Mean Absolute Deviation based on a two-day moving average

The formula for MAD = (∑|x_{i} - \frac{}{x}|)/n

STEP I

To find the mean absolute deviation of the data, start by finding the mean of the data set.

Mean of the data set =

(91.50 + 91.50 + 91.00 +  91.00 + 89.00 +93.00)/6

Mean = 91.17

STEP II

Get the distance between the data point and the mean:

  1. 91.50-91.17=0.33
  2. 91.50-91.17= 0.33
  3. 91.00-91.17= -0.17
  4. 91.00-91.17= -0.17
  5. 89.00-91.17= -2.17
  6. 90.00-91.17= -1.17

STEP II

Add all the distances together

0.33 + 0.33 - 0.17 - 0.17 - 2.17 - 1.17 = -3.02

STEP III

Divide the the sum by data points

-3.02/6

= -0.50

So on average the temperatures were <em>-0.50</em> from the mean.

Cheers!

3 0
3 years ago
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tresset_1 [31]
3x^2 - 7x + 12 = 0 ....subtract 12 from both sides
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x^2 - 7/3x = -4

His work is not accurate because he divided the second term by 4 instead of 3.
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Aleks04 [339]

√(t + u)

√(21 + 4)

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5

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JulsSmile [24]

Answer:

x = 2            x = -6

Step-by-step explanation:

2 (x+2) ^2-4=28

Add 4 to each side

2 (x+2) ^2-4+4=28+4

2 (x+2) ^2= 32

Divide by 2

2/2 (x+2) ^2=32/2

(x+2)^2 = 16

Take the square root of each side

sqrt((x+2)^2) =±sqrt( 16)

x+2 = ±4

Subtract 2 from each side

x+2-2 = -2±4

x = -2±4

x = -2+4      and x = -2-4

x = 2            x = -6

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