Help on math questions?
1. Heather's school is switching from block scheduling to a more traditional schedule. She is trying to determine how the parents and students feel about this. What is the population of her study?
A) All of the students at her high school
B) All of the families that attend her high school
C) 500 randomly chosen families from her high school
D) The parents of all of the students at her high school
2. In ΔMNO m∠O < m∠M < m∠N. List the side lengths in order from shortest to longest
A) MN, NO, MO
B) MN, MO, NO
C) MO, NO, MN
D) NO, MN, MO
3. On the coordinate grid of a map, Josie's house is located at (2,7). Her school is located at (-5,5). If each map unit equals one mile, what is the approximate distance from her house to school?
A) 2.83 miles
B) 4.79 miles
C) 7.28 miles
D) 12.37 miles
4. In ΔMNO NM = 3 cm, NO = 4 cm and MO = 5 cm. List the angles in order from smallest to largest
A) ∠O, ∠N,∠M
B) ∠N, ∠M, ∠O
C) ∠O, ∠M, ∠N
D) ∠N, ∠O, ∠M
5. State the range of the function f(x) = square x
A) [0, ∞)
B) [1, ∞)
C) [-1, ∞)
D) (-∞, ∞)
You have several Questions to answer here.
1. The best gauge of both the parents and Students opinions of the change in the scheduling would logically be Answer B, but if the High School has 1,000+ students that could become impractical. It would be better to take just a sampling of the families that would be representative of all the students and their families. Answer C gives a decent portion of the likely number of families at the school, and the random choice ensures it would be representative of the entire student body and their families.
2. In a triangle, there is a correlation between the relative measures of the angles and the lengths of the opposite sides. The smallest angle `/_O` is opposite side `MN` so MN is the shortest. `/_ M` is opposite side `ON` so that would be the second longest side. The largest angle is `/_N` which is opposite side `MO` making that the longest side.
3. The School and Josie's house represent two points of a right triangle, and the distance between them is the hypotenuse (H). The vertical leg is the difference in y coordinates `7-5=2` and the Horizontal leg is the difference in x coordinates `2-(-5)=7` According to Pythagorean theorem `2^2 + 7^2 = H^2` so that means that the distance between the School and Josie's house is `sqrt(4+49)=sqrt(53)~~7.28`
4. This is the reverse of Problem 2. The same relationship between angle measures and the lengths of opposite sides. The shortest side (NM) would be opposite the smallest angle `/_O` The second shortest side (NO) would be opposite the second smallest angle `/_M` And the longest side (MO) would be opposite the largest angle `/_N`
5. What is the Range of `f(x)=x^2` ?
The range of a function is the set of values that the Function answer could be in. Since the function squares x, and no square number can be less than zero, the bottom value has to be 0. And there is no upper limit to square numbers, so the maximum value is `oo` That gives a range of `[0,oo]`