1.The number of plastic straws produced by a machine varies directly as the amount of time the machine is operating. If the machine produces 20,000 straws in 8 hours, how many straws can it produce in 50 hours?
2.The time required to empty a tank varies inversely as the rate of pumping. If a pump can empty a tank in 45 minutes at the rate of 600 gallons per minute, how long will it take the pump to empty the same tank at the rate of 1000 gallons per minute?
3.The mean rounded to the nearest tenth of the following data set is:
15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15, 19
4.The mode of the following data set is:
15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15, 19
5.The median (rounded to the nearest tenth if needed) of the following data set is:
15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15
6.The first quartile (rounded to the nearest tenth if needed) of the following data set is:
15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15
7.If the local lunch shop offers chicken, tuna, and vegetable sandwiches on plain, onion, or garlic bagels, how many possible sandwiches can be served?
8.How many committees of 3 people are possible from a group of 12?
How many different seating arrangements are possible for 6 people in 4 chairs?
What is the probability of rolling a 4 on a die?
idk that’s why i was asking for help.
1. To find the number of straws the machine can produce in 50 hours, we can set up a proportion. Since the number of straws produced varies directly with the amount of time the machine is operating, we can write the proportion as:
20,000 straws / 8 hours = x straws / 50 hours
To solve for x, we can cross-multiply and solve for x:
20,000 * 50 = 8 * x
1,000,000 = 8x
Dividing both sides by 8, we get:
x = 125,000
Therefore, the machine can produce 125,000 straws in 50 hours.
2. The time required to empty a tank varies inversely with the rate of pumping. We can set up the equation:
Time * Rate = constant
Given that the tank is emptied in 45 minutes at a rate of 600 gallons per minute, we can write the equation as:
45 minutes * 600 gallons/minute = T minutes * 1000 gallons/minute
To find T, we can set up a proportion:
45 * 600 = T * 1000
Simplifying, we get:
27,000 = 1000T
Dividing both sides by 1000, we get:
T = 27
Therefore, it will take the pump 27 minutes to empty the same tank at a rate of 1000 gallons per minute.
3. To find the mean of the given data set, we need to add up all the numbers and divide by the total count. So, adding up the numbers, we get:
15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210
Dividing by the count of numbers (12 in this case), we get:
210 / 12 = 17.5
Therefore, the mean of the data set rounded to the nearest tenth is 17.5.
4. The mode of a data set is the value(s) that appears most frequently. In the given data set, the number 15 appears most frequently (3 times), which makes it the mode.
5. To find the median of a data set, we need to arrange the numbers in ascending order and find the middle value. In this case, when we arrange the numbers in ascending order, we get:
11, 15, 15, 15, 16, 17, 18, 19, 20, 22, 23
Since we have 11 numbers, the middle value is the 6th number, which is 17. Therefore, the median of the data set is 17.
6. The first quartile is the median of the lower half of the data set. To find the first quartile, we need to arrange the numbers in ascending order:
11, 15, 15, 15, 16, 17, 18, 19, 20, 22, 23
Since we have 11 numbers, the first quartile is the median of the first 5 numbers. The 3rd number in the sorted list is 15, so the first quartile is 15.
7. To find the number of possible sandwiches that can be served, we multiply the number of options for each category together. In this case, we have 3 types of sandwiches (chicken, tuna, and vegetable) and 3 types of bagels (plain, onion, and garlic). So, the number of possible sandwiches is:
3 options for sandwiches * 3 options for bagels = 9 possible sandwiches
Therefore, there are 9 possible sandwiches that can be served.
8. To find the number of committees of 3 people possible from a group of 12, we use the combination formula. The formula for combinations is:
nCr = n! / (r!(n-r)!)
For a group of 12, the possible number of 3-person committees is:
12! / (3!(12-3)!) = 12! / (3!9!)
Simplifying, we get:
12! / (3!9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Therefore, there are 220 different committees of 3 people possible from a group of 12.
For the next two questions, we can use the probability formula.
9. The probability of rolling a 4 on a die can be calculated by dividing the number of favorable outcomes (rolling a 4) by the total number of possible outcomes (numbers 1 to 6). Since the die has 6 sides, the probability of rolling a 4 is:
1 favorable outcome (rolling a 4) / 6 total possible outcomes = 1/6
Therefore, the probability of rolling a 4 on a die is 1/6.
1. To solve this problem, we can set up a proportion. Since the number of straws produced varies directly with the amount of time the machine is operating, we can write the proportion as:
Straws produced / Time operating = Straws produced / Time operating
We know that the machine produces 20,000 straws in 8 hours, so we can write:
20,000 / 8 = x / 50
To find the value of x (the number of straws produced in 50 hours), we can cross-multiply and solve for x:
20,000 * 50 = 8 * x
1,000,000 = 8x
x = 1,000,000 / 8
x = 125,000
Therefore, the machine can produce 125,000 straws in 50 hours.
2. Similar to the first problem, we can use the concept of inverse variation to solve this problem. The time required to empty the tank is inversely proportional to the rate of pumping. We can write the proportion as:
Time required / Rate of pumping = Time required / Rate of pumping
We know that the pump can empty the tank in 45 minutes at the rate of 600 gallons per minute. We can write:
45 / 600 = x / 1000
To find the value of x (the time required to empty the tank at the rate of 1000 gallons per minute), we can cross-multiply and solve for x:
45 * 1000 = 600 * x
45,000 = 600x
x = 45,000 / 600
x = 75
Therefore, it will take the pump 75 minutes to empty the tank at the rate of 1000 gallons per minute.
3. To find the mean of a data set, you need to add up all the numbers in the set and then divide by the total count of numbers.
For this data set: 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15, 19
Add up all the numbers: 15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 230
Then divide by the total count of numbers, which is 12: 230 / 12 = 19.17
Rounded to the nearest tenth, the mean of this data set is 19.2.
4. The mode of a data set is the number(s) that appear(s) most frequently. In this data set: 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15, 19, the number 15 appears three times, which is more frequently than any other number. Therefore, the mode of this data set is 15.
5. To find the median of a data set, you need to arrange the numbers in ascending order and then find the middle value.
For this data set: 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15
Arrange the numbers in ascending order: 11, 15, 15, 15, 16, 17, 18, 19, 20, 22, 23
Since there are 11 numbers in total, the middle value is the 6th number, which is 17. Therefore, the median of this data set is 17.
6. To find the first quartile of a data set, you need to arrange the numbers in ascending order and then find the median of the lower half of the data.
For this data set: 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15
Arrange the numbers in ascending order: 11, 15, 15, 15, 16, 17, 18, 19, 20, 22, 23
Since there are 11 numbers in total, the lower half of the data set goes from the 1st number to the 6th number (inclusive). The median of this lower half is the average of the 3rd and 4th numbers, which are both 15. Therefore, the first quartile of this data set is 15.
7. To find the number of possible sandwiches that can be served, you need to multiply the number of options for each choice together.
In this case, for each choice (type of sandwich and type of bagel), you have 3 options. Therefore, the total number of possible sandwiches is 3 (types of sandwich) multiplied by 3 (types of bagel), which equals 9.
Therefore, there are 9 possible sandwiches that can be served.
8. To find the number of committees of 3 people possible from a group of 12, you need to use the concept of combinations.
The formula for finding combinations is C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items chosen.
In this case, we have 12 people and we want to choose 3 for the committee. Substituting into the formula, we have:
C(12, 3) = 12! / (3! * (12-3)!)
Calculating this, we get:
C(12, 3) = 12! / (3! * 9!)
Since 9! can be canceled out in the numerator and denominator, we have:
C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1)
Calculating further, we get:
C(12, 3) = 220
Therefore, there are 220 possible committees of 3 people that can be formed from a group of 12.
The number of different seating arrangements for 6 people in 4 chairs can be calculated using the concept of permutations.
The formula for finding permutations is P(n, r) = n! / (n-r)!, where n is the total number of items and r is the number of items chosen.
In this case, we have 6 people and 4 chairs. Since each chair can only be occupied by one person, we need to find the number of permutations by choosing 4 people out of the total 6.
Substituting into the formula, we have:
P(6, 4) = 6! / (6-4)!
Calculating this, we get:
P(6, 4) = 6! / 2!
Since 2! can be canceled out in the numerator and denominator, we have:
P(6, 4) = 6 * 5 * 4 * 3
Calculating further, we get:
P(6, 4) = 360
Therefore, there are 360 different seating arrangements possible for 6 people in 4 chairs.
The probability of rolling a 4 on a six-sided die can be calculated by dividing the number of favorable outcomes (getting a 4) by the total number of possible outcomes (6, since there are 6 faces on the die).
Since there is only one face on the die that has a 4, the number of favorable outcomes is 1.
So, the probability of rolling a 4 is:
P(4) = Number of favorable outcomes / Total number of possible outcomes
P(4) = 1 / 6
Therefore, the probability of rolling a 4 on a die is 1/6.
#1. x/50 = 20000/8
What ideas do you have on the others?