Use Euler’s formula to answer question.
1 answer:
Answer: The correct option is (C) 38.
Step-by-step explanation: Given that a polyhedron has 20 vertices and 20 faces.
We are to find the number of edges of the polyhedron using Euler's formula.
<em><u>Euler's formula :</u></em>
For any polyhedron, the number of vertices and faces together is exactly two more than the number of edges.
Mathematically, V − E + F = 2, where V, E and F represents the number of vertices, number of edges and number of faces of the polyhedron.
For the given polyhedron, we have
number of vertices, V = 20,
number of faces, F = 20
and
number of edges, E = ?
Therefore, from Euler's formula
.
Thus, the required number of edges of the given polyhedron is 38.
Option (C) is CORRECT.
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Derek will pay $625.25 less than the original prize
<u>Step-by-step explanation:</u>
The selling price of the computer=$610
The selling prize is 1/5 of its original prize
Derek has a 10% off coupon
Let the original prize of the computer=x
selling prize=x-x/5
4x/5=610
4x=3050
x=3050/4=762.5
the difference in the original prize and the prize at which Derek bought the computer=x-9x/50
=41x/50
Derek will pay $625.25 less than the original price for the computer.
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!