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Answer:
The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.
Step-by-step explanation:
Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. )
Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:
(3,5)-(1,1) and (0, 2)-(5, 12)
To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate. That will give us a valid Δx and Δy to get the slope.
In the first pair, 3 > 1, so we'll subtract the second point from the first:
So the first pair of vectors describe a line with a slope of 2. Let's look at the other pair:
That also gives us a slope of 2, meaning that the two lines are parallel.
This same process will need to be done for the other three questions. We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image. For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.
The missing part of the question is show in bold format.
Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for rolling it
once. Your probability model shows a probable outcome of 1/6 for each of the numbers on the cube, 1 chance for all any of the 6 numbers.
You roll it 500 times and get the following data:
Outcome 1 2 3 4 5 6
Frequency 77 92 75 90 76 90
Exercises 1–2
1. If the equality model was correct, about how many of each outcome
would you expect to see if the cube is rolled 500 times
2. Based on the data from the 500 rolls, how often were odd numbers observed? How often were even numbers observed?
Answer:
Step-by-step explanation:
1.
If the equally likely model was correct, about how many of each outcome
would you expect to see if the cube is rolled 500 times.
The probability of rolling any of the numbers from 1 to 6 is p(1/6)
The number of each of the outcomes expected to be seen in 500 rolls of the number cube is
2. From the given data in the roll;
The odd numbers 1, 3 and 5, were obtained at 77, 75 and 76 times respectively.
Thus, the total number of times odd number were rolled = 77 + 75 + 76 = 228
Probability of an odd number turning up =
=
= 0.456
= 45.6%
The even numbers, 2, 4 and 6, were obtained 92, 90 and 90 times respectively.
The total number of times even number were rolled = 92 + 90 + 90 = 272
Probability of an even number turning up =
=
= 0.544
= 54.4%