System of Equations
Solve the following system of equations:
y=2
3x+2y=6
Substitute y=2 into the other equation:
2x+2(2)=6
2x+4=6
Subtract 4 from both sides -> 2x=2
Divide both sides by 2. -> x=1
Therefore the solution is (1,2)
Dot Plots show __(how many?)_ piece of data.
EVERY
Solve the following equation: 3x=27
3x=27
Divide both sides by 3. -> x=9
Answer: x=9
What are the two main measures of center?
Mean and Median
What are the two main measures of spread?
Interquartile Range and Standard Deviation
Solve the following system:
y=2x-1
2x+3y=-19
Distribute the 3 -> 2x+6x-3=-19
Combine like terms -> 8x-3=-19
Add 3 to both sides -> 8x=-16
Divide both sides by 8 -> x=-2
Substitute the x=-2 into one of the original equations: -> y=2(-2)-1
y=-4-1
y=-5
The solution is (-2,-5) Check by graphing.
What is frequency?
The amount of times something happens / how often something occurs.
Solve the following equation.
-4x+7=15
-4x+7=15
Subtract 7 from both sides. -> -4x=8
Divide both sides by -4 -> x=-2
Answer: x=-2
How do you calculate the median?
Arrange numbers from smallest to largest, then find the middle number.
The shape of the data can be described different ways. What are three ways we describe the shape of the data?
Bell-Shaped
Symmetric
Bimodal
Skewed
Uniform
Solve the following system of equations:
-6x+4y=-28
6x-7y= 13
Using elimination - Add the two equations
0x-3y=-15
-3y=-15
Divide both sides by -3 -> y=5.
Substitute the y=5 into one of the original equations.
-6x+4(5)=-28
Simplify -> -6x+20=-28
Subtract 20 to both sides -> -6x=-48
Divide both sides by -6 -> x=-48/-6 -> x=8
The solution is (8, 5)
What is the 5-number summary?
Minimum, First Quartile, Median, Third Quartile, Maximum
A decal sticker costs $6 with no letters. Every letter you want to add costs $2 each. Write an equation that represents the total cost, y of the decal sticker for x amount of letters.
y=6+2x
How do you calculate the mean?
Add up all the numbers and divide by how many data values you have
How do you find the first and third quartile?
Find the medians of the upper and lower half.
Solve the system of equation:
2x-5y=18
2x+3y=2
0x-8y=16
-8y=16
Divide both sides by -8 ->y=-2
Substitute the y=-2 into one of the original equations:
2x-5(-2)=18
Simplify -> 2x+10=18
Subtract 10 from both sides -> 2x=8
Divide both sides by 2 -> x=4
The solution is (4, -2)
How much % of the data is in 1 quartile?
25%
An ice cream cone costs $4. Each topping,x, you add costs $0.50 each. Write an equation that represents the total cost, y, of an ice cream cone with x amount of toppings.
y=4+0.50x
Which measure of center is LEAST affected by outliers?
The median.
How do you calculate the interquartile range?
Q3 - Q1
Solve the following system:
9x+6y=18
3x-2y=6
Using graphing.
Graph both equations and look for the intersection point.
The solution is (2,0)
What is the difference between a histogram and a bar graph?
Histograms show the frequency of data values in ranges in quantitative data where bar graphs show the values in categorical data.
Histograms bars are adjacent and bar graphs are not (typically)
Sally is saving money in her bank account. She initially puts $120 in her savings account and adds $40 each week. How many weeks will it take Sally to have $760 in her account?
Write an equation from the situation -> 120+40x=760
Subtract 120 from both sides -> 40x=640
Divide both sides by 40. x=16
It will take Sally 16 weeks to have $760 in her account.
Which measure of center is used for symmetrically distributed data?
Mean
Which measure of spread is used for symmetrically distributed data?
The Standard Deviation