Answers:
- a) The sample is the set of students Ms. Lee selects from the box.
- b) The population is the set of all students in Ms. Lee's classroom.
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Explanation:
The first sentence tells us what the population is: it's the set of all her students. She's not concerned with any other students in any other classroom. So her "universe", so to speak, is solely focused on this classroom only. Once the population is set up, a sample of it would be a subset of the population.
If set A is a subset of set B, then everything in A is also in B, but not vice versa. For example, the set of humans is a subset of the set of mammals because all humans are mammals. However, a dog is a mammal but not a human. This shows that A is a subset of B, but not the other way around. In this example, A = humans and B = mammals.
Going back to the classroom problem, we have A = sample and B = population. If Ms. Lee has 30 students, and she randomly selects 5 of them, then those 30 students make up set B and the 5 selected make up set A. Selecting the names randomly should generate an unbiased sample. This sample should represent the population overall. If the population is small enough, the teacher could do a census and not need a sample. Though there may be scenarios that it's still effective to draw a sample.
Answer:
D.lines that lie in the same plane but will never intersect
Step-by-step explanation:
parallel lie in the same plane but never meet
Answer:
-40%
Step-by-step explanation:
NV = new value
OV = old value
percent change = (NV - OV)/(OV) × 100%
percent change = (30 - 50)/(50) × 100%
percent change = -20/50 × 100%
percent change = -40%
Given: an n-gon
Prove: The sum of the measures of the interior angles is 180(n – 2)°.
Complete the missing parts of the paragraph proof.
We are given an n-gon, which has n sides and n vertices.
Answers:
1. If we choose one of the vertices, we can draw <u>n-3</u> diagonals.
2. These diagonals form <u>n-2</u> triangles.
3. The sum of the interior angle measures of a triangle is <u>180</u> degrees.
4. <u>n – 2</u> triangles would have an interior angle measure sum of <u>180</u> degrees.
5. Therefore, the sum of the measures of the interior angles of an n-gon is 180(n – 2)°.