The normal form of a line is given by the equation x * cos theta + y * sin theta = p where theta is the angle of the normal line from the positive x-axis and p is the length of the normal line. Converting to normal line form, the equation must first be converted into standard form: 2x + 7y = 4. Then dividing the whole equation by sqrt(a^2 + b^2): sqrt(2^2 + 7^2) = sqrt(53). Hence, the equation becomes 2 / sqrt(53) * x + 7 / sqrt(53) * y = 4 / sqrt(53). Therefore, the length of the normal line is 4 / sqrt(53), and the angle is arctan(7/2) = 74.05 degrees.
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The value of g across from angle G is 5feet
According to sine rule
Given the following
∠G = 45°
∠F = 82°
f = 7feet
Required
side g
Substitute the given values into the formula
Hence the value of g across from angle G is 5feet
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Answer:
Answer:
Both centres are best described by the median.
Step-by-step explanation:
Here is a summary of the statistics from your data.
City Min Q1 IQR Q3 Max Median Mean σ
Rome 0 3.60 8.65 12.25 16 8.25 7.99 5.20
NY 1 2.25 4.69 6.64 20 5.45 6.39 5.91
The box plots below show that both centres are best described by the median.
The outlier in the New York data greatly distorts the mean but does not affect the median. The mean without the outlier would have been 4.45.
Answer:
28, 56
56
Step-by-step explanation:
a
To solve this, we use the combination rule.
nCk = n!/k!(n-k)! where
n is the number of options (8) k is the number of slots (2).
Assuming the order doesn't matter, then
8C2 = 8! / 2!(8-2)!
8C2 = 8! / 2! 6!
8C2 = 40320 / 2 * 720
8C2 = 40320 / 1440
8C2 = 28
If the order does matter, then we use permutation instead.
nPk = n!/(n-k!) where n = 8 and k =2 8P2 = 8! / 6!
8P2 = 40320 / 720
8P2 = 56
b
We are told that there exist 8 ways to choose a president and a vice president. This means that, after choosing a president from 8 people, there remains 7 people to choose his vice from. Thus, the number of ways to choose a president and his vice are 8 * 7 = 56
