Answer:
Height of vertical post relative to the horizontal is 6.3 ft
Height of vertical post above the roof (roofing sheets) is 4.0 ft
Step-by-step explanation:
Given the roof is 20° relative to the horizontal and the solar panel should be 38° relative to the horizontal, then finding the vertical support holding the back of the panel relative to the horizontal will be;
Apply the formula for sine of an angle as;
Sin of angle theta = opposite side length/hypotenuse
Sin 38° = O/8 where O is the length of opposite side of the angle
8*sin 38°=O
4.93 ft = O
Applying Pythagorean relationship to find the length from the bottom part of the panel to the vertical support relative to the horizontal will be;
a²+b²=c² where a=?, b=4.93 and c = 8
a²+4.93²=8²
a²=8²-4.93²
a=6.3 ft
Finding the height of the roof from the horizontal at 20° angle
Tan 20°= O/6.3
6.3 tan 20° = O
2.3 ft =O
Now finding the length of vertical post above the roof will be;
6.3-2.3=4.0 ft
Answer:
g(x) = -9(x + 1)2 - 7
Step-by-step explanation:
Answer:
x = 5.5
Step-by-step explanation:
Since the shape is a parallelogram, the opposite angles are congruent. Angle A is opposite Angle Y so we can set their values equal to each other to solve for x:
3x + 10 = 2x + 15.5
Bring the variables to one side and the constants to the other:
<u>x = 5.5</u>
Answer:
a) P(X>825)
b) This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.
Step-by-step explanation:
We know a priori that 60% of the eligible voters did vote.
From this proportion and a sample size n=1309, we can construct a normal distribution probabilty, that is the approximation of the binomial distribution for large samples.
Its mean and standard deviation are:
Now, we have to calculate the probabilty that, in the sample of 1309 voters, at least 825 actually did vote. This is P(X>825).
This can be calculated using the z-score for X=825 for the sampling distribution we calculated prerviously:
This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.