Eric reflected parallelogram ABCD across the x-axis. If angle A is 125° and angle B is 55°, what is the degree measurement of an
1 answer:
The measures of the angles don't change when you translate a figure, because the entire figure is moving as a whole. Imagine having a paper parallelogram, moving it around and flipping it over. Not even dilations would change these angles (for reasons that can be pretty easily visualed but not really proven until geometry)
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Answer:
99.38%
Step-by-step explanation:
We have that the mean (m) is equal to 124, the standard deviation (sd) 6.4 and the sample size (n) = 64
They ask us for P (x <126)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (126 - 124) / (6.4 / (64 ^ 1/2))
z = 2.5
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <2.5) = 0.9938
The probability is 99.38%
Answer: Distance between parent and coach = 24.05m
Step-by-step explanation:
Angle of sight between the coach and the ground(θ) = 38°
Angle of sight between the parent and the ground (θ) = 30°
Height of diving platform = 10m
The horizontal distance(x) between the coach and Melanie :
Tanθ = opp / adj
Tan 38° = 10 / x
x = 10 / 0.7812856
x = 12.79m
The horizontal distance (y) between the parent and Melanie :
Tanθ = opp / adj
Tan 30° = 10 / y
y = 10 / 0.5773502
y = 17.32m
Angle at base of platform between Melanie's coach and her parent = 105°
Distance (a) between coach and parent can be calculated using the cosine rule.
a^2 = x^2 + y^2 - 2bcCosA
Where a, b, c are side lengths and A is the included angle
Therefore,
a^2 = 12.79^2 + 17.32^2 - 2(12.79)(17.32)Cos105°
a^2 = 163.5841 + 299.9824 − (-114.6686)
a^2 = 163.5841 + 299.9824 + 114.6686
a^2 = 578.2351
a = √578.2351
a = 24.046519
a = 24.05m
