Probability (7DSP1, 7DSP4, 7DSP5)
A bag contains 5 identical marbles: 1 purple, 1 orange, 1 black, 1 white, and 1 pink. What is the sample space and the probability of picking the orange marble?
Sample Space = {purple, orange, black, white, pink}
P(orange) = 1/5 or 20%
Two different 7th-grade classes (Ousley's and Leininger's) took a 10-point quiz. A random sample of 5 students from each class was taken:
Ousley's class scores: 6, 7, 8, 8, 10
Leininger's class scores: 7, 8, 8, 9, 9
Calculate the MEAN and MEDIAN for both classes. Which class performed better on average?
OUSLEY'S Mean: 39/5 = 7.8
OUSLEY'S Median: 8
LEININGER'S Mean: 41/5 = 8.2
LEININGER'S Median: 8
LEININGER's class did better overall.
A standard soda can has a radius of 3 cm and a height of 12 cm. Using 3.14 for pi, what is the volume of the can?
V=pi(radius2)height
V = 339.12 cm3
Maya has $40 in her wallet. She goes to the store and buys a notebook for $5.75 and a set of pens for $12.50. How much money does she have left after her purchases?
$21.75
You are looking at a line on a graph. It passes perfectly through the points (0, -1) and (2, 3). What is the slope of this line?
The slope is 2.
You have a spinner divided into 8 equal sections: 3 are blue, 2 are red, 2 are green, and 1 is yellow. If you spin the spinner 400 times, how many times would you expect to land on blue?
3/8 = x/400
150 times
A scientist measures the heights (in inches) of two different types of tomato plants.
TYPE 1: 10, 12, 14, 15, 22 (Range: 12; IQR: 4)
TYPE 2: 14, 15, 15, 16, 17 (Range: 3; IQR: 1.5)
Interpret the RANGE and IQR to compare the two populations. Which plant type is more predictable in its growth?
TYPE 1 has a higher variablility (more spread out).
TYPE 2 is more predictable and consistent because RANGE and IQR are are much smaller.
A wooden garden planter is shaped like an "L." It is made of two joined rectangular prisms.
PRISM A: 4 ft long, 2 ft wide, 1 ft high
PRISM B: 2 ft long, 2 ft wide, 1 ft high
What is the total volume of soil needed to fill the planter?
PLANTER A: 4 x 2 x 1 = 8 ft3
PLANTER B: 2 x 2 x 1 = 4 ft3
TOTAL VOLUME: 8 + 4 = 12 ft3
6x + 7
Graph the line that passes through the point (1,2) and has a slope of 2/3. List three other points that lie on this line.
POSSIBLE POINTS: (-2, 0), (4,4), (7, 6), (10, 8)
A city council wants to know if the residents of the city support building a new park. They mail a survey to 500 randomly selected households in the city. Identify the population and the sample.
Sample: The 500 specific households that were selected to receive the survey. This is the smaller group being studied to represent the whole.
Two groups of students recorded how many hours they slept last night.
GROUP A: 6, 7, 7, 8, 8, 8, 9, 9
GROUP B: 8, 8, 9, 9, 9, 10, 10, 11
Describe the visual overlap of these two distributions.
If you picked a student who slept 7 hours, which group do they likely belong to?
VISUAL OVERLAP: There is a small overlap at 8 and 9 hours.
INFERENCE: A student who slept 7 hours almost certainly belongs to GROUP A, as there is no overlap at the 7-hour mark.
A rectangular fish tank has a volume of 3000 inches3. The base of the tank is 20 inches long and 10 inches wide. How tall is the fish tank?
Volume = l x w x h
3000 = 20 x 10 x h
h = 15 inches
Create an equivalent expression for 12x - 18 by factoring out the Greatest Common Factor (GCF).
6(2x - 3)
A family goes out to dinner and the bill comes to $60. The restaurant applies a 6% sales tax to the bill. After the tax is added, the family decides to leave a 20% tip based on the NEW total. What is the final amount they pay?
60 x 0.06 = 3.60 tax
60 + 3.60 = 63.60 new total
63.20 x 0.20 = 12.72 tip
63.20 + 12.72 = 76.32
TOTAL BILLS WITH TIP AND TAX = $76.32
Match each of the following scenarios to the most appropriate probability term: impossible, unlikely, equally likely, likely, or certain.
SCENARIO A: Flipping a fair coin and landing on "heads."
SCENARIO B: Rolling a standard six-sided die and getting a number less than 10.
SCENARIO C: Winning a lottery where you have 1 ticket out of 10 million sold.
SCENARIO D: Picking a blue marble from a bag that only contains red marbles.
SCENARIO E: Choosing a red card from a standard deck of cards (which are 50% red and 50% black).
SCENARIO A: Equally Likely
SCENARIO B: Certain
SCENARIO C: Unlikely
SCENARIO D: Impossible
SCENARIO E: Equally Likely
A small business have 5 employees with the following annual salaries:
$30k, $32k, $35k, $38k, $40k
The owner hres a new executive with a salary of $150k (an outlier). How does this outlier affect the MEAN and MEDIAN?
MEAN BEFORE OUTLIER: 175/5 = $35k
MEAN WITH OUTLIER: 325/6 = $54.2k
* The mean increased significantly.
MEDIAN BEFORE OUTLIER: $35k
MEDIAN WITH OUTLIER: $36.5k
* The median was relatively stable.
A circular jogging track has a diameter of 50 meters. If a runner laps the track one time, how far did they run? (Use 3.14 for pi.)
C = pi x diameter
A = pi x r2
C = pi x diameter
C = 3.14 x 50
C = 157 meters
A recipe for one batch of cookies requires 2 1/2 cups of flour. Leo wants to make 3 batches. He opens a new bag of flour that contains 10 cups. After making his 3 batches, how much flour will be left in the bag?
2 1/2 cups left
2 1/2 x 3 = 7 1/2 cups used
10 - 7 1/2 = 2 1/2 cups left
A store owner buys a bicycle for $100. He marks it up by 40% to sell it in his shop. After a month, the bike has not sold, so he offers a 15% discount (markdown) on the retail price. What is the final sale price of the bike?
Markup: 100 x 1.40 = $140 original retail price
Markdown: 140 x 0.85 = $119 sale price
A factory produces 5000 lightbulbs a day. A quality control manager selects a random sample of 100 bulbs and finds that 2 of them are defective. Based on this sample, how many defective bulbs should the manager expect in the total daily production of 5000?
100 bulbs
2 defective/100 total = x defective/5000 total
Two basketball players recorded their points over 5 games. Both have a mean of 10 points.
PLAYER 1 points: 8, 9, 10, 11, 12
PLAYER 2 points: 2, 5, 10, 15, 18
Calculate the MAD for both players. Who is the more consistent scorer?
PLAYER 1: 6/5 = 1.2
PLAYER 2: 26/5 = 5.2
PLAYER 1 is more consistent since the MAD score is lower.
A pizza restaurant sells a large pizza with a radius of 8 inches. What is the total area of the pizza in square inches?
C = pi x diameter
A = pi x r2
A = pi x r2
A = 3.14 x 82
A = 200.96 inches2
A music streaming service charges a flat monthly fee of $5.50, plus $0.75 for every song downloaded. Last month, Marcus was charged a total of $14.50. Write and solve an equation to find x, the number of songs Marcus downloaded.
x = number of songs downloaded
0.75x + 5.50 = 14.50
x = 12 songs
A factory machine fills bottled water at a constant rate. It can fill 15 bottles every 3 minutes.
1. Find the unit rate.
2. Write an equation to represet the total bottles filled (y) in x minutes.
1. 15 bottles/3 minutes = 5 bottles per minute
2. y = 5x