2 Answers:
- Choice B) angle R and angle U
- Choice D) angle K and angle L
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Explanation:
There are a lot of lines here, so it's easy to get a bit lost if you're not careful. I recommend starting with a blank piece of paper. On it, draw two lines that intersect any way you want. An "X" shape forms. The angles that are opposite one another (eg: top and bottom angles) are known as vertical angles, and they are always congruent.
Going back to your diagram, angle R and angle U fit the description of vertical angles. We used two lines to form these vertical angles. Despite the name, the angles do not have to be aligned vertically. Unfortunately it's a misnomer in my opinion. Angle R is opposite angle U, and both are formed by the two slanted lines that go in both directions. It might help to copy the diagram your teacher has given to you, and then erase the portions that seem extra (eg: erase the ray that helps form angle S, and also erase angle S as well) and it might help show why angle R is a vertical angle pair with angle U.
Similarly, angle K and angle L fit the description as well, so this is the second pair of vertical angles.
Something like "angle E and angle N" is not an answer because we used 3 lines to help form these angles, instead of two only. We can rule out "angle S and angle J" for similar reasons.
As for when you see vertical angles in everyday life, it depends on what the context is. For example, if you're drawing out a floorplan, then knowing the angles may be very handy. You could use a protractor to measure the angles, or you could use geometric properties such as the vertical angle theorem to quickly determine the angle values (if you know some angles already).
Answer:
a) Mean = 382.3 psi
Standard deviation = 20.8 psi
b) 392.7 psi
c) P(X<400)=0.8026
Step-by-step explanation:
a) The population mean can be estimated as equal to the mean of the sample, and the population standard deviation can be estimated from the sample standard deviation:
b) We start by searching for the z-value for the 95th percentile. This value is
z=1.645:
Then, the strength value below which 95% of all welds will have their strengths is:
c) We calculate the probability of X being equal or less than 400 as:
Answer: what are steps 1-2? may i have the question?
Step-by-step explanation:
Answer: each of the students took 1/4 of an eraser home.
Step-by-step explanation:
On the last period our teacher had 1/2 of an eraser left. She gave it equally to 2 students. This means that the amount of eraser that each student takes home would be
(1/2)/2 = 1/2 × 1/2 = 1/4 of an eraser. Converting to decimal, it becomes 0.25 of an eraser.
