Unit 4.5 (Linear Regressions)
Figure A:
Is this
a) positive correlation
b) negative correlation
c) no correlation
Answer: A
Which of the following is a solution to x+3>15?
5
10
16
-4
Answer: 3
Solve the following system of equations:
y = 2x + 1
3x + y = 11
(desmos)
(2,5)
5x<7
Is this point a solution for this Inequality
(-3,2)
YES
In the exponential equation y = 500(0.82)^x, identify the initial value and the percentage rate of decay.
Answer: Initial = 500, Decay = 18%
Figure B:
Which statement is the best description of the association between these variables?
A. Driving at higher speeds always resulted in less fuel being used.
B.The amount of fuel used was lowest at speeds around 60
C. None of the above
Answer: B
Solve for x:
3x+2<18+5
Answer:
x<7
Solve the following system of equations:
4x + 3y = 14
2x - y = 2
(No desmos)
(2,2)
Graph the following systems of inequalities:
y<5/6x+5
7x+2y<_-4
And select which of the following are solutions to the system:
(0,3)
(0,7)
(-3,5)
(-2,5)
(-2,5)
The Missing Slope
A line passes through the points (0, 5) and (2, 13). Find the value of m and b.
Answer: m = 4, b = 5
Figure C:
Interpret this slope in context of the problem.
Answer: for every 1$ increase in price, there is an average increase of 5 points on rating.
What is the solution to the following inequality?
3(x−4)+2<5x+103
Answer:
x>-20
Elimination Method
Solve the following system of equations:
3x + 2y = 16
7x + y = 19
(No desmos)
(2,5)
Billy's lemonade stand sells small cups of lemonade for $3 and large cups of lemonade for $5. Billy wants to raise more than $150. If he is projected to sell 20 small cups of lemonade, how many large cups will he need to sell to meet his goal? (set up a system of equations,2: graph the system to get your answer)
18 Large cups
An exponential graph has a starting value of 7 and passes through the point (2, 28). What is the growth factor (b)?
Answer: b = 2 (Equation: y = 7(2)^x)
Figure D:
Which of the following is the best estimate of the average score change associated with a 1 hour increase in study time?
A.20 points
B.5 points
C. 2 points
D. 1 point
Answer: A
You are at the store buying individual candies for your friends,
Chocolates are $1 and gummies are 50 cents, you have $15
Write a system of equations to represent the situation.
Answer:
1x+0.5y<15.25
At a local theater, the cost of 2 adult tickets and 5 child tickets is $67. The cost of 3 adult tickets and 2 child tickets is $62.
Write a system of equations to represent this situation, where "a" is the price of an adult ticket and "c" is the price of a child ticket.
Part B: Solve the system to find the individual price of one adult ticket and one child ticket.
Answer: Equations: 2a + 5c = 67 and 3a + 2c = 62
Solution: Adult ticket (a) = $16, Child ticket (c) = $7
At the movies you have $40 . To pay for your movie ticket it costs $15. Each snack at the movies is $8. How many snacks will you be able to buy?
x<_3.125 or 3 snacks total
Find the linear equation for a line where the rate of change is -3 and it passes through the point (2, 10).
Answer: y = -3x + 16
Figure E:
Which equation best represents the line of best fit for this set of data?
1) y = 15x
2) y = 0.07x
3) y = 0.1x − 0.4
4) y = 14.1x + 5.8
Answer: 4
Maya is buying snacks in bulk for a school fundraiser. There are 2 companies selling bulk snacks,
Company A sells each box for $10 with a discount of $8 for buying in bulk
Company B sells each box for $8 with an extra fee of $4 for buying in bulk.
Write an inequality to determine when Company A costs more than Company B?
Answer: 10x-8>8x+4
x>2
After buying 2 boxes
Find the intersection point (x, y) for this system:
y = 2x
x + y = 12
(4, 8) (Since x + 2x = 12, then 3x = 12, so x = 4)
Bob got fired and is packing up his plants from his office in boxes. He really liked succulents, and needed to take all 150 home with him. Management gave him small boxes, which will hold 15 plants, and large boxes, which will hold 30 plants.
However, they only gave him 4 of each. If he wants to carry the least amount of boxes possible, how many of each should he fill.
4 large boxes and 2 small boxes
An exponential function has a growth factor of 5. The graph passes through the point (2, 500). What is the initial value (a) of this function?
Answer: 20