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3 years ago

Find the value of a and b

Mathematics

1 answer:

andriy [413]3 years ago

4 0

Answer:

a = 133 degrees

b = 78 degrees

Step-by-step explanation:

the top and bottom lines are parallel.

the two sidelines are lines that intercept the top and bottom lines.

as they intercept parallel lines, they actually must have the same angles with them.

so, the 47 degrees inner angle at the bottom line, must be also somewhere at the interception point with the top line. and right, it must be now mirrored the outward angle at the top line. and that means a (the inward angle at the top line) is also the outward angle at the bottom line.

the sum of inward and outward angles at a point must always be 180 degrees.

so, the outward angle of 47 = the inward angle a =

= 180 - 47 = 133 degrees.

similar in the other side.

102 is the inward angle.

the outward angle of that is 180 - 102 = 78 degrees.

and that is also the inward angle b.

b = 78 degrees

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ASHA 777 [7]

Answer:

Original data: 21 29 32 38 38 45 50 64 72 100

$\bar X = \frac{21+29+32+38+38+45+50+64+72+100}{10}=48.9$

Mode =38.

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Change 1: 2 29 32 38 38 45 50 64 72 100

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Mode =38.

$Median = \frac{38+45}{2}=41.5$

Change 2: 29 32 38 38 45 50 64 72 100

$\bar X = \frac{29+32+38+38+45+50+64+72+100}{9}=52$

Mode =38.

$Median = 45$

Step-by-step explanation:

Original data: 21 29 32 38 38 45 50 64 72 100

The mean is calculated with the following formula:

$\bar X = \frac{\sum_{i=1}^{10} X_i}{10}$

And if we replace we got:

$\bar X = \frac{21+29+32+38+38+45+50+64+72+100}{10}=48.9$

The mode is the most repeated value in the sample and on this case is Mode =38.

Since we have an even number of points the median is calculated as the average between the observations 5 and 6 from the dataset ordered.

$Median = \frac{38+45}{2}=41.5$

Change 1: 2 29 32 38 38 45 50 64 72 100

The mean is calculated with the following formula:

$\bar X = \frac{\sum_{i=1}^{10} X_i}{10}$

And if we replace we got:

$\bar X = \frac{2+29+32+38+38+45+50+64+72+100}{10}=47$

The mode is the most repeated value in the sample and on this case is Mode =38.

Since we have an even number of points the median is calculated as the average between the observations 5 and 6 from the dataset ordered.

$Median = \frac{38+45}{2}=41.5$

Change 2: 29 32 38 38 45 50 64 72 100

Now the sample size is 9 instead of 10

The mean is calculated with the following formula:

$\bar X = \frac{\sum_{i=1}^{9} X_i}{9}$

And if we replace we got:

$\bar X = \frac{29+32+38+38+45+50+64+72+100}{9}=52$

The mode is the most repeated value in the sample and on this case is Mode =38.

Since we have odd number of points the median is calculated from the 5 position of the dataset ordered.

$Median = 45$

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