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 18
Based on these results, what is the expected probability of randomly selecting a red cube from the bag in one attempt?
Responses
A 0.24
B 0.20
C 0.04
D 0.30
The total number of times a cube was selected from the bag is 80.
The number of times a red cube was selected is 24.
Therefore, the probability of selecting a red cube in one attempt can be calculated as:
P(Red) = Number of times Red was selected / Total number of selections
P(Red) = 24 / 80
P(Red) = 0.30
Therefore, the expected probability of randomly selecting a red cube from the bag in one attempt is 0.30.
So, the correct answer is:
D. 0.30
Jeremiah volunteered to bring a smoked brisket to the family reunion. During cooking in a smoker, a brisket loses 35% of its uncooked weight.
If Jeremiah wants to have 12 1/2 lbs of cooked brisket, then what should the weight of the uncooked brisket be that he starts with?
Round the answer to the nearest tenth of a pound.
responses
35.7
20.6
19.2
16.9
8.1
4.4
Let x be the weight of the uncooked brisket that Jeremiah starts with.
After losing 35%, the cooked brisket weighs 100% - 35% = 65% of the uncooked weight.
So, the weight of the cooked brisket will be 0.65x.
Given that Jeremiah wants to have 12 1/2 lbs of cooked brisket, we can set up the equation as:
0.65x = 12.5
Solving for x:
x = 12.5 / 0.65
x ≈ 19.2
Therefore, the weight of the uncooked brisket that Jeremiah should start with is approximately 19.2 lbs.
The closest response is:
C. 19.2.
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
Let x represent the number of bundles of 36 auto-fill water balloons that Jasmine should order. Each bundle contains 36 water balloons.
Jasmine already has 250 water balloons, and she needs at least 1,200 water balloons. So, the total number of water balloons she needs can be represented by the equation:
250 + 36x ≥ 1200
Subtracting 250 from both sides:
36x ≥ 950
Dividing by 36 on both sides to solve for x:
x ≥ 950 / 36
x ≥ 26.3888 (approximately)
Thus, the minimum number of bundles that Jasmine should order is 27 to have at least 1,200 water balloons for the water games and water balloon fight.
The correct inequality representing this is:
36x + 250 ≥ 1,200, with the minimum number of bundles being 27.
Therefore, 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?
Use 3.14 for n.
Responses
A 640.56 ft2
B 18.84 ft2
C 241.86 ft2
D 160.14 ft2
To calculate the area of a circle, we use the formula: Area = π * r^2, where r is the radius of the circle.
For Trampoline A with a diameter of 14 feet, the radius (r) is half the diameter: r = 14/2 = 7 feet.
The area of Trampoline A = π * 7^2 = 3.14 * 49 ≈ 153.86 square feet.
For Trampoline B with a diameter of 20 feet, the radius is half the diameter: r = 20/2 = 10 feet.
The area of Trampoline B = π * 10^2 = 3.14 * 100 = 314 square feet.
To find the difference in area between Trampoline B and Trampoline A:
Area of B - Area of A = 314 - 153.86 ≈ 160.14 square feet.
Therefore, the area of Trampoline B is approximately 160.14 square feet greater than the area of Trampoline A.
The correct answer is:
D. 160.14 ft^2
A new event in the Buck-Up Rodeo circuit is the Quarter Horse Mile, which is four laps around a racetrack. Colten entered his quarter horse, Jasper, in this race in three consecutive rodeos.
Jasper completed his first race in exactly 4 1/2 minutes, with an average lap time of 1.125 minutes per lap.
In Jasper's second race, he changed his average lap time from the first race by -0.075 minutes.
In Jasper's third race, he changed his total race time from the first race by -1.00 minute.
Use the drop-down menus to correctly complete the statements.
In Jasper's second race, his total time from the first race changed by response area
minutes; his total race time was responses area
minutes.
In Jasper's third race, his average lap time from his first race changed by response area
minutes; his average lap time was response area
minutes.
In Jasper's first race, his total time for 4 laps was 4.5 minutes.
Therefore, his average lap time in the first race was 1.125 minutes per lap.
1. In Jasper's second race, his total time changed by -0.075 minutes per lap compared to the first race.
So, his total time in the second race would be:
Total time in the second race = Total time in the first race + (-0.075 * 4)
Total time in the second race = 4.5 + (-0.075 * 4)
Total time in the second race = 4.5 - 0.3 = 4.2 minutes
Therefore, Jasper's total time from the first race changed by 0.3 minutes; his total race time was 4.2 minutes.
2. In Jasper's third race, his total race time changed by -1.00 minute compared to the first race.
So, his total time in the third race would be:
Total time in the third race = Total time in the first race - 1
Total time in the third race = 4.5 - 1 = 3.5 minutes
Using the average lap time of 1.125 minutes per lap from the first race:
1. In Jasper's third race, his average lap time changed by 0. after the first race.
Thus, his average lap time in the third race would be 1.125 - 0 = 1.125 minutes per lap.
Therefore, in Jasper's second race, his total time from the first race changed by 0.3 minutes; his total race time was 4.2 minutes.
In Jasper's third race, his average lap time from the first race changed by 0 minutes; his average lap time was 1.125 minutes.