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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Answer:
There is a possibility that Darius is 138 inches.
Step-by-step explanation:
Imagine william is 67 (Close integer less than 68)
d can be equal to 4 + 2(67)
D is less than or equal to 138 inches.
The answer for this question is 138
Answer:
a) 10.6; 48.7; within
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 29.6
Standard deviation = 6.35
"According to the Empirical Rule, the ages of nearly all lead actresses will be between______________and_____________ years.
Nearly all(99.7%) will be within 3 standard deviations from the mean.
So from 29.6 - 3*6.35 = 10.6 years to 29.6 + 3*6.35 = 48.7 years.
Anna was 11-years old, so she was within this range.
So the correct answer is
a) 10.6; 48.7; within
