Question
A number cube that has sides numbered 1 through 6 is rolled 210 times.
How many times would you expect the result to be a number greater than 4?
How many times would you expect the result to be a number greater than 4?
Answers
GPT 3.5
Since there are 6 possible outcomes when rolling a number cube, each outcome has an equal probability of 1/6.
To find the expected number of times the result is greater than 4, we can calculate the probability of rolling a number greater than 4 and then multiply it by the total number of rolls:
Probability of rolling a number greater than 4 = 2/6 (rolling a 5 or 6)
Expected number of times rolling a number greater than 4 = (2/6) * 210 = 70
Therefore, we would expect the result to be a number greater than 4 approximately 70 times out of 210 rolls.
To find the expected number of times the result is greater than 4, we can calculate the probability of rolling a number greater than 4 and then multiply it by the total number of rolls:
Probability of rolling a number greater than 4 = 2/6 (rolling a 5 or 6)
Expected number of times rolling a number greater than 4 = (2/6) * 210 = 70
Therefore, we would expect the result to be a number greater than 4 approximately 70 times out of 210 rolls.
A circular play mat has a diameter of 6 feet.
Part A What is the circumference, in feet, of the play mat rounded to the nearest hundredth?
Part A What is the circumference, in feet, of the play mat rounded to the nearest hundredth?
GPT 3.5
To calculate the circumference of a circle, we use the formula:
Circumference = π * diameter
Given that the diameter of the play mat is 6 feet, we can plug this value into the formula:
Circumference = π * 6
Circumference = 18.8495559... (approximating π to be 3.14159)
Rounded to the nearest hundredth, the circumference of the play mat is approximately 18.85 feet.
Circumference = π * diameter
Given that the diameter of the play mat is 6 feet, we can plug this value into the formula:
Circumference = π * 6
Circumference = 18.8495559... (approximating π to be 3.14159)
Rounded to the nearest hundredth, the circumference of the play mat is approximately 18.85 feet.
What is the area in square feet, of the play mat rounded to the nearest hundredth?
GPT 3.5
To calculate the area of a circle, we use the formula:
Area = π * (radius)^2
Given that the diameter of the play mat is 6 feet, the radius is half of the diameter, so radius = 6/2 = 3 feet.
Now we can plug the radius into the formula to calculate the area:
Area = π * (3)^2
Area = π * 9
Area = 28.2743338... (approximating π to be 3.14159)
Rounded to the nearest hundredth, the area of the play mat is approximately 28.27 square feet.
Area = π * (radius)^2
Given that the diameter of the play mat is 6 feet, the radius is half of the diameter, so radius = 6/2 = 3 feet.
Now we can plug the radius into the formula to calculate the area:
Area = π * (3)^2
Area = π * 9
Area = 28.2743338... (approximating π to be 3.14159)
Rounded to the nearest hundredth, the area of the play mat is approximately 28.27 square feet.
Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.
The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)
Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?
The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)
Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?
GPT 3.5
To find the constant of proportionality, we can use the formula y = kx with any pair of values from the table.
Let's use the pair (4, 33.60):
33.60 = k * 4
Now we solve for k:
k = 33.60 / 4
k = 8.40
Therefore, the constant of proportionality in this situation is k = 8.40.
Let's use the pair (4, 33.60):
33.60 = k * 4
Now we solve for k:
k = 33.60 / 4
k = 8.40
Therefore, the constant of proportionality in this situation is k = 8.40.
Bella's Boutique is having their annual three-day Bella's Blowout Sale.
On the first day of the sale, all merchandise with a red tag is reduced by 25% from its regular price.
On the second day of the sale, the price of each sale item is reduced to 80% of its price from the previous day.
On the third day of the sale, the price of each sale item is reduced to 50% of its price from the previous day.
One sale item has a regular price of $40.
Plot 3 points on the number line to show the price of this item on each of the three days of the sale.
Do NOT plot a point for the regular price of the item.
On the first day of the sale, all merchandise with a red tag is reduced by 25% from its regular price.
On the second day of the sale, the price of each sale item is reduced to 80% of its price from the previous day.
On the third day of the sale, the price of each sale item is reduced to 50% of its price from the previous day.
One sale item has a regular price of $40.
Plot 3 points on the number line to show the price of this item on each of the three days of the sale.
Do NOT plot a point for the regular price of the item.
GPT 3.5
To determine the prices of the item on each of the three days of the sale, we can calculate the reductions step by step.
1. On the first day, the item with a regular price of $40 is reduced by 25%. The price after the reduction is:
$40 - ($40 * 0.25) = $40 - $10 = $30
2. On the second day, the reduced price from the first day is further reduced to 80%. The price after this reduction is:
$30 * 0.80 = $24
3. On the third day, the reduced price from the second day is further reduced to 50%. The price after this reduction is:
$24 * 0.50 = $12
Plotting these points on a number line:
- Day 1: $30
- Day 2: $24
- Day 3: $12
1. On the first day, the item with a regular price of $40 is reduced by 25%. The price after the reduction is:
$40 - ($40 * 0.25) = $40 - $10 = $30
2. On the second day, the reduced price from the first day is further reduced to 80%. The price after this reduction is:
$30 * 0.80 = $24
3. On the third day, the reduced price from the second day is further reduced to 50%. The price after this reduction is:
$24 * 0.50 = $12
Plotting these points on a number line:
- Day 1: $30
- Day 2: $24
- Day 3: $12