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Answer:
The store can be 90% confident that the interval from 0.293 to 0.355 captures the proportion of all customers of this store who have moved in the past 5 years.
Step-by-step explanation:
The confidence interval provides a range of values (lower and upper bound) based on a certain confidence level at which the true proportion or mean value of a given sample mean or proportion exists. In the scenario above, the confidence level is 90% and the confidence interval is 0.293 to 0.355. Hence, we can be 90% confident that the true proportion of all customers of the store who have moved within the last five years exists within this interval.
These are a huge pain. First set up your initial triangle with A and B as your base angles and C as your vertex angle. Now drop an altitude and call it h. You need to solve for h. Use sin 56 = h/13 to get that h = 10.8. The rule is that if the side length of a is greater than the height but less than the side length of b, you have 2 triangles. h<a<b --> 10.8<12<13. Those are true statements so we have 2 triangles. Side a is the side that swings, this is the one we "move", forming the second triangle. First we have to solve the first triangle using the Law of Sines, then we can solve the second. 
to get that angle B is 64 degrees. Now find C: 180-56-64=60. And now for side c: 
and c=12.5. That's your first triangle. In the second triangle, side a is the swinging side and that length doesn't change. Neither does the angle measure. Angle B has a supplement of 180-64 which is 116. So the new angle B in the second triangle is 116, but the length of b doesn't change, either. I'll show you how you know you're right about that in just a sec. The only angle AND side that both change are C and c. If our new triangle has angles 56 and 116, then C has to be 8 degrees. Using the Law of Sines again, we can solve for c:
and c = 2.0. We can look at this new triangle and determine the side measures are correct because the longest side will always be across from the largest angle, and the shortest side will always be across from the smallest angle. The new angle B is 116, which is across from the longest side of 13. These are hard. Ugh.
Answer:
Step-by-step explanation:
The maximum volume the shipping container can have is 10 cubic yards.
The volume of a rectangular prism is given as:
V = L * W * H
where L is length, W is width and H is height.
To find the maximum height of the container, make H the subject of formula:
We have been given the length and width of the container as 2 1/2 yards and 3 1/2 yards respectively.
Hence, the maximum height is:
The maximum height of the container is .