Answer:
- complement: 32.8°
- supplement: 122.8°
Step-by-step explanation:
The sum of an angle A and its complement C is 90°:
A + C = 90°
C = 90° -A . . . . . subtract A from both sides.
That is, the complement of an angle is found by subtracting the angle from 90°.
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The sum of an angle and its supplement is 180°. This means the supplement of an angle is found by subtracting the angle from 180°. You may notice the supplement is 90° more than the complement.
A + S = 180°
S = 180° -A = 90° +(90° -A)
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For the given angle, the complement is ...
C = 90° -57.2° = 32.8°
And the supplement is ...
S = 180° -57.2° = 122.8°
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<em>Additional comment</em>
We generally like angle measures to be positive (as with all measures in geometry). Hence, we might say that the complement of an angle greater than 90° does not exist. YMMV
Answer:
409 i would say
Step-by-step explanation:
very sorry is its wrong!!! :(
Answer: Choice A)
x = 11*sqrt(2)/2
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Work Shown:
You can use the sine rule to find the value of x
sin(angle) = opposite/hypotenuse
sin(45) = x/11
x = 11*sin(45)
x = 11*sqrt(2)/2
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Or you could use the 45-45-90 triangle template
hypotenuse = sqrt(2)*short leg
11 = sqrt(2)*x
x = 11/sqrt(2)
x = 11*sqrt(2)/2 after rationalizing the denominator
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Or you could use the pythagorean theorem
For a 45-45-90 triangle, the legs are the same length. They are both x for now.
a^2+b^2 = c^2
x^2+x^2 = 11^2
2x^2 = 121
x^2 = 121/2
x = sqrt(121/2)
x = sqrt(121)/sqrt(2)
x = 11/sqrt(2)
x = 11*sqrt(2)/2
Answer:
0.9699 = 96.99% probability of a bulb lasting for at most 637 hours.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
![\mu = 590, \sigma = 25](https://tex.z-dn.net/?f=%5Cmu%20%3D%20590%2C%20%5Csigma%20%3D%2025)
Find the probability of a bulb lasting for at most 637 hours.
This is the pvalue of Z when X = 637. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{637 - 590}{25}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B637%20-%20590%7D%7B25%7D)
![Z = 1.88](https://tex.z-dn.net/?f=Z%20%3D%201.88)
has a pvalue of 0.9699
0.9699 = 96.99% probability of a bulb lasting for at most 637 hours.