The table shows the results of randomly selecting a colored cube from a bag 80 times. The cube was returned to the bag after each selection.Blue Orange Purple Red Yellow Number of Times Selected 14 8 16 24 18Based on these results, what is the expected probability of randomly selecting a red cube from the bag in one attempt?
The expected probability of randomly selecting a red cube from the bag in one attempt can be calculated by dividing the number of times the red cube was selected by the total number of selections:
Probability of selecting a red cube = Number of times selected red cube / Total number of selections
Probability of selecting a red cube = 24 / 80
Probability of selecting a red cube = 0.3
Therefore, the expected probability of randomly selecting a red cube from the bag in one attempt is 0.3 or 30%.
Jasmine is planning water balloon activities for the end-of-season team party. She already has 250 water balloons and plans to order "bundles" of 36 auto-fill water balloons. Jasmine wants at least 1,200 water balloons for the water games and water balloon fight.
Which inequality correctly represents the minimum number of bundles of 36 water balloons, x, that Jasmine should order to have at least 1,200 balloons?
Responses
A 36x – 250 ≥ 1,200; minimum number of bundles is 4136 x – 250 ≥ 1,200; minimum number of bundles is 41
B 36(x + 250) ≥ 1,200; minimum number of bundles is 2836( x + 250) ≥ 1,200 span widget ; minimum number of bundles is 28
C 36x + 250 ≥ 1,200; minimum number of bundles is 2736 x + 250 ≥ 1,200 span widget ; minimum number of bundles is 27
D 36x + 250 ≥ 1,200; minimum number of bundles is 26
To find the minimum number of bundles, x, that Jasmine should order to have at least 1,200 balloons, we need to set up the inequality based on the information provided.
Jasmine already has 250 water balloons, so the total number of water balloons she needs must be at least 1,200. Since she plans to order bundles of 36 auto-fill water balloons, the number of bundles required can be represented by x.
The inequality would be as follows:
36x + 250 ≥ 1,200
Therefore, the correct inequality representing the minimum number of bundles of 36 water balloons Jasmine should order is:
36x + 250 ≥ 1,200
Minimum number of bundles is 27
Hence, the correct answer is:
C 36x + 250 ≥ 1,200; minimum number of bundles is 27.
Clinton and Stacy want to buy a trampoline for their kids. They are considering two trampolines.
Trampoline A has a diameter of 14 feet.
Trampoline B has a diameter of 20 feet.
Approximately how much greater, in square feet and rounded to the nearest hundredth, is the area of Trampoline B than the area of Trampoline A?
To find the difference in the area of the two trampolines, we need to calculate the area of each trampoline first.
The formula to calculate the area of a circle is A = πr^2, where r is the radius of the circle. Since we are given the diameter, we need to divide it by 2 to get the radius.
For Trampoline A:
Diameter = 14 feet
Radius = 14 feet / 2 = 7 feet
Area of Trampoline A = π(7)^2 = 49π square feet
For Trampoline B:
Diameter = 20 feet
Radius = 20 feet / 2 = 10 feet
Area of Trampoline B = π(10)^2 = 100π square feet
Now, we can find the difference in the area of Trampoline B compared to Trampoline A:
Area of Trampoline B - Area of Trampoline A = 100π - 49π = 51π square feet
Approximately, when we substitute the value of π as 3.14, we get:
51π ≈ 51 * 3.14 ≈ 160.14 square feet
Therefore, the area of Trampoline B is approximately 160.14 square feet greater than the area of Trampoline A.
Your favorite breakfast cereal contains a fidget toy in each box. There are three different fidget toys in the complete collection (spinner, pop strip, squishy ball) and each toy has an equal chance of being in each box.
You want to figure out what the probability is that you will get more than one squishy ball if you buy four boxes of the cereal. Which experiment could be used to simulate this situation?
Responses
A You flip a coin 4 times and record the number of times you get tails. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more tails.You flip a coin 4 times and record the number of times you get tails. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more tails.
B You put 10 each of 4 different colored marbles in a bag for a total of 40 marbles. You draw 3 marbles out without replacing them and record how many are red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red marbles.You put 10 each of 4 different colored marbles in a bag for a total of 40 marbles. You draw 3 marbles out without replacing them and record how many are red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red marbles.
C You have a spinner equally divided into 3 sections, with each section colored red, blue, or green. You spin the spinner 4 times and record how many times you get a red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red spins.You have a spinner equally divided into 3 sections, with each section colored red, blue, or green. You spin the spinner 4 times and record how many times you get a red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red spins.
D You draw 4 cards from a standard deck of cards and record how many hearts you get. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more hearts.
The situation described involves selecting items from a set with replacement and recording the results. The best experiment to simulate this situation is one where you draw items multiple times and record the number of times a specific outcome occurs.
Option D: You draw 4 cards from a standard deck of cards and record how many hearts you get. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more hearts.
In this experiment, drawing cards from a standard deck with hearts representing the "squishy balls" in the cereal boxes is similar to the scenario described. The experiment involves selecting items (cards) multiple times and recording the occurrence of a specific outcome (getting hearts). By repeating the experiment multiple times and calculating the percentage of trials resulting in 2 or more hearts, you are simulating the scenario where you buy multiple cereal boxes and record the number of squishy balls (specific outcome) you receive.
Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
The distance from their home to Yellowstone National Park is 1,701 miles.
On average the RV gets 10.5 miles per gallon.
On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
Responses
To calculate the total cost of gasoline for the round trip to Yellowstone National Park and back home, we first need to find out how many gallons of gasoline will be needed for the entire trip.
The total distance of the round trip is twice the distance from home to Yellowstone National Park:
Total distance = 2 * 1,701 miles = 3,402 miles
To determine how many gallons of gasoline will be needed:
Gallons of gasoline = Total distance / Average miles per gallon
Gallons of gasoline = 3,402 miles / 10.5 miles per gallon ≈ 324 gallons
Next, we calculate the total cost of gasoline:
Total cost = Gallons of gasoline * Cost per gallon
Total cost = 324 gallons * $3.60 per gallon = $1,166.40
Therefore, Clinton and Stacy will spend approximately $1,166.40 on gasoline for the round trip to Yellowstone National Park and back home.
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
Responses
A purchase price: $117, advertised price: $293purchase price: $117, advertised price: $293
B purchase price: $120, advertised price: $300purchase price: $120, advertised price: $300
C purchase price: $130, advertised price: $325purchase price: $130, advertised price: $325
D purchase price: $108, advertised price: $270purchase price: $108, advertised price: $270