sat explanations

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1

can someone help me with these questions from old sats?

1- in a volleybal league with 4 teams, each team plays exactly 2 games with each of other 3 teams in the league. What is the total number of games played in this league?

2-the graph of a function in the xy plane is a parabola that opens upward and has its vertex at point (c,d) if the line l is tangent to the parabola at its vertex, which of the following must be another point on line l?
(-5,d)
(-5,-d)
(0,0)
(c,-5)
(-5,-c)

2
  1. There are 4C2 = 6 possible combinations of 2 teams (or just (1,2), (1,3), (1,4), (2,3), (2,4), (3,4)). But for each combination, two games are played so the # of games is 6*2 = 12.
  2. The slope of line l is 0 because l is the tangent line of the parabola at its vertex (I.e. derivative is 0). So the y-coordinate on all points on l is constant and equal to d, so A is correct.
3
  1. Answer is 12. The easy way to solve this is to write it out logically. Assign each team a variable (A through D).

A plays B, C, and D (3 games)
B must still play C and D (2 games)
C must still play D (1 game)
D has now played each team once (0 games).

Add these up and you have 6 games, after each has played each one time. 6 x 2 = 12.

4

thank you very much!

5

thank you!

6

I have more questions, could someone please help me?

1- the integers 1 through 6 appear on the six faces of a cube, one on each face. if three such cubes are rolled, what is the probability that the sum of the numbers on the top faces is 17 or 18?

2- single color tokens of blue, red, green, or yellow are placed in a single line so that the pattern of blue, red, green, yellow, blue, red, green, yellow repears throughout. if the first token in the line is blue, which of the following tokens is green?

3- five different bands have been selected to march in a parade. one band has been chosen to lead the parade. in how many different orders can the reimaining four bands be placed in the parade?

4- the function f is defined by f(x)=2x^2 -5. what are all possible values of f(x) where -2<x<2?

5- Each of the 75 children in a line was assigned one of the integers from 1 through 75 by counting off in order. then, standing in the same order, the children counted off in the opposite direction, so that the child who was assigned the number 75 the first time was assigned the number 1 the second time. which of the following is a pair of numbers assigned to the same child?
50 and 25
49 and 24
48 and 26
47 and 29
45 and 32