Unit 1:Integers, Rational Numbers, Fractions, Decimals
A. -4 + (-8)
B. 3 + (-3)
C. -2 + 2
D. - 6 + (-6)
B and C
Solve y + 3 < - 8
y < -11
Julie sells fresh apples at the farmers market for 5 dollars per pound. If you have 28 dollars, how many pounds of apples can you purchase?
5.6 Pounds
What are the definitions and formulas of the following angle relationships?
Complementary
Supplementary
Vertical
1. Complementary Angles
Definition: Two angles are complementary if the sum of their measures is 90°.
Example: If one angle is 30°, the other must be 60° to be complementary.
Formula:
Angle 1+Angle 2=90∘2. Supplementary Angles
Definition: Two angles are supplementary if the sum of their measures is 180°.
Example: If one angle is 110°, the other must be 70° to be supplementary.
Formula:
Angle 1+Angle 2=180∘3. Vertical Angles
Definition: Vertical angles are formed when two straight lines intersect. They are opposite angles and are always equal.
Example: If two intersecting lines form an angle of 40°, the vertical angle will also be 40°.
Key Property: Vertical angles are congruent (equal in measure).
Formula:
Angle 1=Angle 2What do the following numbers mean in terms of probability? (impossible, unlikely, equally likely, likely, certain)
0.5
0.77
0
1
.23
0.5 = equally likely
0.77 = likely
0 = impossible
1 = certain
.23 = unlikely
NO CALCULATOR
-125 ÷ 5
Solve 15x + 3 = 8
x = 1/3
A map uses a scale where 1 inch represents 20 miles. If the distance between two cities on the map is 4.5 inches, what is the actual distance between the two cities?
90 Miles
DOUBLE JEOPARDY!!!
Solve the following complementary angle:
Angles A and B make up complementary angle C.
Angle A is 72° and Angle B is 3x + 3°
What is the value of x?
x = 5
A spinner has 8 equal sections numbered 1 through 8.
What is the probability of spinning an even number?
NO CALCULATOR
-2/3 ÷ -3/4
8/9
Simplify: 2x +3 -4(8x +2)
−30x−5
DOUBLE JEOPARDY!!Carol has a copy of a painting, the dimensions of her copy are 1.75 in by 5.25 in. The scale of the copy are 0.5 inches: 12 centimeters.
What is the area of the original painting? (In cm2)
42×126=5,292 cm2
A circular garden has a diameter of 12 meters. How much fencing would you need to go around the garden to enclose it?
37.68 meters
DOUBLE JEOPARDY!!!
Jar: 4 yellow, 6 purple, 5 orange candies.
What is the probability that the first candy is yellow, and the second is purple, if you do not replace the first?
4/35
A hiker climbs a mountain and reaches a height of 1,250 meters. On the way down, the hiker descends at a rate of 75 meters per hour for 4 hours. What is the hiker's final elevation, in meters, after the descent?
950 meters
(4/11)x = -16/55
x = -4/5
A random sample of students at New Hampstead K8 were asked if they prefer Takis, Hot Cheetos, or Doritos. 14 said they prefer Takis, 12 said they prefer Hot Cheetos, and 3 said they prefer Doritos.
What percentage of those sampled preferred Hot Cheetos? Round the percentage to two decimal places.
41.38%
Solve the following supplementary angle:
Angles A and B make up supplementary angle C.
Angle A is 6x +13° and Angle B is 14x -33°
What is the value of x?
x = 10
The test scores from a class are:
72, 85, 90, 72, 88, 94, 85, 90, 100, 76, 85, 92, 90, 88, 72
a) What is the mean of the scores?
b) What is the median?
c) What is the mode?
Mean: 83.93
Median:
Median = 88
Mode = 72, 85, 90
NO CALCULATOR
-6 + 14 - 8 + (-2) - 13 = ?
-15
Simplify: -9x(-9 +6x) -5x(7 +4x)
46x - 74x2
A store sold 120 shirts last month. This month, the store had an increase in sales and sold 15% more shirts than last month. However, the next month, they had a 10% decrease in sales compared to this month.
How many shirts did the store sell this month?
How many shirts did the store sell next month after the decrease?
The store sold 138 shirts this month.
The store sold 124 shirts next month after the decrease.
Two lines intersect, forming vertical angles. One angle is represented by the expression 5x + 7°, and the vertical angle across from it is represented by 3x + 23°.
What is the value of x?
x = 8
Side 1: Frequency 19
Side 2: Frequency 16
Side 3: Frequency 12
Side 4: Frequency 8
What is the theoretical and experimental probability of side 3?
Theoretical: 1/4 or .25 or 25%
Experimental: Side 3: 12/55 ≈ 0.218 or 21.8%