Distance and Midpoint
What is the distance formula?
d=√(x₂-x₁)²+(y₂-y₁)²
To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.
4(2)(4)(3) = 96 possible systems
Based on this equation, (x-3)2+(y-4)2=80, the center and radius of this circle are...
center: (3, 4), radius: 4√5
Daniel had a bag of marbles. There were 20 marbles in the bag: 6 red, 5 orange, 3 brown, 2 yellow, and 4 blue. Without looking, he chose a marble, recorded the color, and returned the marble to the bag. He performed this experiment 100 times and found that he chose a red marble 22 times. What was the experimental probability of choosing a red marble?
11/50
What is the distance between (8,11) and (8,4)?
7 units
There are 12 yes or no questions. How many ways can these be answered?
212 = 4096 ways
What is the corresponding general form of the equation of the circle (x+1)2+(y+4)2=9?
x2 + y2 + 2x + 8y + 8 = 0
What is the probability of getting a sum 7 from 3 throws of a dice?
1/36
Given the points A and B where A is at coordinates ( 2, -5 ) and B is at coordinates ( -3, -7 ) on the line segment AB, find the length of AB in simplest radical form.
√29 units
A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players.
How many different selections can be made?
10C5 x 5C1 = 1260 different selections
Find the equation of a circle whose center is (0,-3) and radius is √14.
x2+(y+3)2=14
In a bag you have 11 red,4 blue and 9 orange balls. Suppose you picked up 1 ball randomly. Find the probability that it is neither red nor orange?
1/6
Joshwyn just got out of school and he can either go to the library or to the mall. If the two places are equidistant from the school, the mall is at (9,2) and the school is at (3,4), where is the library located at?
(-3,6)
Police use photographs of various facial features to help witnesses identify suspects. One basic identification kit contains 195 hairlines, 99 eyes and eyebrows, 89 noses, 105 mouths, and 74 chins and cheeks. A witness can clearly remember the hairline and the eyes and eyebrows of a suspect. How many different faces can be produced with this information?
Number of faces = 1 • 1 • 89 • 105 • 74 = 691,530 different faces
Find the standard form of the equation for the circle centered at (–5, 12)
and passing through the point (–2, 8).
(x+5)2 + (y–12)2 = 25
Find the probability of getting a non-face card or a 7 card from an ordinary deck of 52 playing cards?
10/13
Leanne is standing at (5,8) when two cars from the same distance is driving towards her. One of the car is located at (-1, 3), where is the other car located at?
(11,13)
How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
3x5x5x5= 375 integers
What is the standard form of the equation x2 + y2 - 8x + 4y - 9 = 0
(x–4)2 + (y+2)2 = 29
A family has 3 children, if the probability of giving birth to a boy is same as the giving birth to a girl. Find the probability getting at least two boys?
1/2