Answer:
0.9
Step-by-step explanation:
took the test
Answer:
the rotation angle is double the angle between the lines
Step-by-step explanation:
The Reflections in Intersecting Lines Theorem will tell you that the effective angle of rotation is double the angle between the intersecting lines. Here, the figure is effectively rotated 144°, not 72°. If a 72° rotation is desired, the lines need to intersect at an angle of 36°.
Answer:
17 m² or 17 square meters
Step-by-step explanation:
A trapezoid has base lengths of 5 meters and 3.5 meters. If the height of the trapezoid is 4 meters, what is the area of the trapezoid?
Area of a trapezoid =1/2(b1 + b2)h
Where
b1 = First base length = 5m
b2 = Second base length = 3.5 m
Height = 4m
= 1/2(5m + 3.5m) × 4m
= 1/2(8.5m) × 4m
= 1/2 × 8.5m × 4m
= 17 m²
Therefore, the area of the trapezoid is 17 m² or 17 square meters
Answer:
The expected revenue of the tour operator is 985.
Step-by-step explanation:
There are two outcomes:
Either less than 21 tourists show up and the operator does not have to pay anything. Or 21 tourists show up and the operator has to repay 100.
Anyways, initially he gets the price of all the tickets sold. That is 21 each at 50, so 
.
Then, we need to find the probability that all of the 21 tourists show up. In this case, we have to subtract 100 from the revenue.
Each tourist has a 0.02 probability of not showing up. This means that each has a 1-0.02 = 0.98 probability of showing up. So the probability P that all 21 tourists show up is 
.
So, the expected revenue of the tour operator is
Rounded up, the expected revenue of the tour operator is 985.
Label the 3 distinct sides of the box. I arbitrarily chose the letters a, b and c.
Use the info about areas as follows:
ab=54 in^2
ac=90 in^2
bc=60 in^2
Here you have 3 equations in 3 unknowns (a, b and c), which is enough info to use to determine a, b and c. Then the volume of the box is a*b*c.
Example: bc = 90, but c = 60/b. You could subst. 60/b for c in the 2nd and 3rd equation, which will eliminate c completely and leave you with 2 equations in 2 unknowns.
Continuing this procedure, I determined that a=9, b=6 and c=10. Thus, the volume of the box is V = 9*6*10 = 540 cubic inches (answer)
