Simplify (3xy^6)^2(x^3y^2)^4
1 answer:
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Answer:
- The answer or forecast for temperature using a three-day moving average =
- The answer or forecast for temperature using a three-day moving average =
- 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 = (∑||)/
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:
- 91.50-91.17=0.33
- 91.50-91.17= 0.33
- 91.00-91.17= -0.17
- 91.00-91.17= -0.17
- 89.00-91.17= -2.17
- 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!
<h2>○=> <u>Correct option</u> :</h2>
Selling price of a car = $19,000
Percentage of sales tax in the city = 8.3%
Sales tax :
Thus, the sales tax on the car = $1577
Cost of license and title = $75
Total price of car :
= Cost price of car + Sales tax + cost of license/title
Thus, the total purchase price of the car = $20,652.00
Therefore, the correct option is <em>(C) $20,652.00</em>
Answer:
(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
(B) f(x + h) - f(x) = 8xh + 4h² - 6h
(C)
Step-by-step explanation:
* Lets explain how to solve the problem
- The function f(x) = 4x² - 6x + 6
- To find f(x + h) substitute x in the function by (x + h)
∵ f(x) = 4x² - 6x + 6
∴ f(x + h) = 4(x + h)² - 6(x + h) + 6
- Lets simplify 4(x + h)²
∵ (x + h)² = (x)(x) + 2(x)(h) + (h)(h) = x² + 2xh + h²
∴ 4(x + h)² = 4(x² + 2xh + h²) = 4x² + 8xh + 4h²
- Lets simplify 6(x + h)
∵ 6(x + h) = 6(x) + 6(h)
∴ 6(x + h) = 6x + 6h
∴ f(x + h) = 4x² + 8xh + 4h² - (6x + 6h) + 6
- Remember (-)(+) = (-)
∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
- Lets find f(x + h) - f(x)
∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
∵ f(x) = 4x² - 6x + 6
∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)
- Remember (-)(-) = (+)
∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6
- Simplify by adding the like terms
∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)
∴ f(x + h) - f(x) = 8xh + 4h² - 6h
* (B) f(x + h) - f(x) = 8xh + 4h² - 6h
- Lets find
∵ f(x + h) - f(x) = 8xh + 4h² - 6h
∴
- Simplify by separate the three terms
∴
∴
* (C)