Mr. Wells runs a telecommunications company. While going through the company's project records, he found that there were 8 engineers under every team leader and 5 project managers for every 50 engineers. Mr. Wells currently employs 15 team leaders. How many project managers are employed by Mr. Wells?
The total number of engineers employed by Mr. Wells is 8 engineers/team leader * 15 team leaders = <<8*15=120>>120 engineers.
Therefore, the number of project managers employed by Mr. Wells is 5 project managers/50 engineers * 120 engineers = <<5/50*120=12>>12 project managers. Answer: \boxed{12}.
In a flower garden, there are 3 tulips for every 8 daisies. If there are 15 tulips, how many daisies are there?
If there are 3 tulips for every 8 daisies, that means there are 8/3 daisies for every tulip.
So, if there are 15 tulips, then there are 15 * (8/3) = 40 daisies.
Therefore, there are 40 daisies in the flower garden. Answer: \boxed{40}.
A paper company produces 3,220 notebooks in 4 days. How many notebooks can it produce in 12 days?
To solve this problem, we can use the following proportion:
number of notebooks produced / number of days = constant rate
Let's call the constant rate "r". Then we have:
3,220 notebooks / 4 days = r
To find out how many notebooks can be produced in 12 days, we can set up the same proportion using this new number of days:
number of notebooks produced / 12 days = r
To solve for the number of notebooks, we can cross-multiply and solve for the unknown:
3,220 notebooks / 4 days = number of notebooks / 12 days
(3,220 notebooks / 4 days) x 12 days = number of notebooks
9,660 notebooks = number of notebooks
Therefore, the paper company can produce 9,660 notebooks in 12 days. Answer: \boxed{9,660}.
Rachel is training for a cycling tournament. She can bike 2 1/4 miles in 1/5 of an hour. At this rate, how many miles can she bike in 1 1/3 hours?
Rachel's rate is 2 1/4 miles in 1/5 hour. We can convert this to a rate per hour by multiplying both the numerator and denominator of the fraction by 5 (to get rid of the fraction in the denominator):
2 1/4 miles / 1/5 hour = 2 1/4 miles x 5/1 hour = 11 1/4 miles per hour
Therefore, Rachel can bike 11 1/4 miles in one hour.
To find out how far she can bike in 1 1/3 hours, we can multiply her rate per hour by the number of hours:
11 1/4 miles per hour x 4/3 hours = (45/4) x (4/3) miles = 15 miles
Therefore, Rachel can bike 15 miles in 1 1/3 hours. Answer: \boxed{15}.
David used 14 1/4 pounds of clay to make 3 pots. At this rate, how many pounds of clay would he need to make 10 pots?
To find out how much clay David needs for 10 pots, we can set up a proportion:
pounds of clay used / number of pots = constant rate
Let's call the constant rate "r". Then we have:
14 1/4 pounds / 3 pots = r
To find out how much clay is needed for 10 pots, we can set up the same proportion using this new number of pots:
pounds of clay used / 10 pots = r
To solve for the pounds of clay needed, we can cross-multiply and solve for the unknown:
14 1/4 pounds / 3 pots = pounds of clay / 10 pots
(14 1/4 pounds / 3 pots) x 10 pots = pounds of clay
47 1/2 pounds = pounds of clay
Therefore, David would need 47 1/2 pounds of clay to make 10 pots. Answer: \boxed{47 \frac{1}{2}}.
Willie runs 4 miles in 16 minutes. If Willie runs at the same rate, how many miles can he run in 36 minutes?
Willie runs 4 miles in 16 minutes, which means he runs 4/16 = 1/4 mile per minute.
To find out how far he can run in 36 minutes, we can multiply his rate by the number of minutes:
1/4 mile per minute x 36 minutes = 9 miles
Therefore, Willie can run 9 miles in 36 minutes if he runs at the same rate. Answer: \boxed{9}.
Amanda is making pastry dough. She mixes 1/3 of a cup of flour and 1/5 of a cup of sugar. If she wants to mix flour and sugar in the same ratio to make 16 cups of pastry dough, how many cups of flour and sugar will she need?
Let's call the total amount of flour and sugar Amanda needs "x".
According to the problem, the ratio of flour to sugar in the mixture is the same as the ratio of 1/3 to 1/5.
We can find the equivalent ratio with a common denominator:
1/3 = 5/15
1/5 = 3/15
So the ratio of flour to sugar is 5:3.
This means that if Amanda needs x total cups of flour and sugar, 5/8 of that amount should be flour and 3/8 should be sugar.
We know that x = 16 (since she needs 16 cups of pastry dough). So we can set up an equation:
5/8 x = cups of flour
3/8 x = cups of sugar
We can substitute x = 16 into the equation:
5/8 x 16 = cups of flour
3/8 x 16 = cups of sugar
Simplifying:
10 cups of flour = cups of flour
6 cups of sugar = cups of sugar
Therefore, Amanda needs 10 cups of flour and 6 cups of sugar to make 16 cups of pastry dough while maintaining the same ratio of flour to sugar as in her original recipe. Answer: \boxed{10 \text{ cups of flour}, 6 \text{ cups of sugar}}.
Brian randomly surveyed a group of 180 boys at his middle school to learn what sport students thought should be played at the next middle school event.
The results of the survey are as shown below.
Baseball: 50
Rugby: 5
Badminton: 20
Basketball: 35
Soccer: 70
Determine the population, the sample, and the conclusion of the survey.
A.
Population: a group of students in the college
Sample: a group of 180 boys
Conclusion: Baseball should be played at next middle school event.
B.
Population: all the boys in the college
Sample: a group of 180 boys
Conclusion: Rugby should be played at the next middle school event.
C.
Population: all the girls in the college
Sample: a group of 180 girls
Conclusion: Badminton should be played at the next middle school event.
D.
Population: all of the students in the middle school
Sample: a group of 180 boys
Conclusion: Soccer should be played at the next middle school event.
D.
Population: all of the students in the middle school
Sample: a group of 180 boys
Conclusion: Soccer should be played at the next middle school event.
Type the correct answer in each box. Use numerals instead of words. A representative sample of 60 students from a middle school is surveyed. Each student is asked what transportation method they use to get to school. The table below shows the responses. Transportation Method Number of Students Ride a bike 7 Ride a bus 20 Ride in a car 18 Ride a scooter 6 Walk 9 Complete the statements about all the middle school students based on the sample results. It is expected that blank times as many students at the middle school ride in a car as walk to school. It is expected that blank % of the middle school students ride a scooter to school. In a random sample of 45 students at the middle school, it is expected that blank students ride a bus to school. In a random sample of 360 students at the middle school, it is expected that blank students ride a bike to school.
It is expected that 2 times as many students at the middle school ride in a car as walk to school. (18 car riders divided by 9 walkers)
It is expected that 15% of the middle school students ride a scooter to school. (6 scooter riders divided by total sample of 60 students, then multiplied by 100 to convert to a percentage)
In a random sample of 45 students at the middle school, it is expected that 15 students ride a bus to school. (20 bus riders in the original sample of 60 students, multiplied by 45/60 to adjust for the smaller sample size)
In a random sample of 360 students at the middle school, it is expected that 42 students ride a bike to school. (7 bike riders in the original sample of 60 students, multiplied by 360/60 to adjust for the larger sample size)
A survey was conducted to find the favorite sport of two high schools, St. Johns City School and St. David Charter School. To carry out this survey, two groups of 200 students were randomly selected from 1,000 students from each school. The results obtained are given in the table shown below.
Sports St. Johns City School St. David Charter School
Baseball 52 58
Basketball 53 45
Football 65 69
Volleyball 30 28
Which of the following statements about the data above is true?
A.
The estimated number of students who chose volleyball as their favorite sport is higher at St. Johns City School than at St. David Charter School.
B.
The estimated number of students who chose basketball as their favorite sport is higher at St. David Charter School than at St. Johns City School.
C.
The estimated number of students who chose football as their favorite sport is higher at St. Johns City School than at St. David Charter School.
D.
The estimated number of students who chose volleyball as their favorite sport is higher at St. David Charter School than at St. Johns City School.
A.
The estimated number of students who chose volleyball as their favorite sport is higher at St. Johns City School than at St. David Charter School. (30 volleyball players at St. Johns City School, compared to 28 at St. David Charter School)
Three students from Milton Middle School are running for class president. A preliminary poll was taken in three homeroom classes, each with the same number of students. The results are shown in the table below.
Poll Results
Students Class A % Class B % Class C %
Ian 46 37 45
Jessie 27 29 9
Jeremy 27 34 46
Based on these preliminary results, who could be predicted to win class president?
A.
Ian
B.
Jessie
C.
Jeremy
D.
cannot predict from these results
A.
Ian. (He received the highest percentage of votes in each of the three classes.)
There are 1,500 apples in a cold storage room. Some are green apples, and the rest are red apples. The manager of the cold storage facility wants to estimate the number of green apples in the room. He takes a random sample of 20 apples and records the number of green apples. He repeats this 15 times and records the data as shown. Percentage of Green Apples in a Sample Number of Times Percentage Occurred 25% 1 35% 2 40% 3 45% 3 50% 3 55% 1 60% 2 Total 15 The dot plot for the data is shown. From the data, what is the best prediction for the percentage of green apples in the room? A. The percentage of green apples in the room is 40%. B. The percentage of green apples in the room is 45%. C. The percentage of green apples in the room is 50%. D. The percentage of green apples in the room is 60%. the data plot shows 25 has one dot 30 has none 35 has 2 40 has 3 45 also has 3 50 has 3 55 has 1 and 60 has 2
The best prediction for the percentage of green apples in the room is 45%. (This percentage occurred 3 times, which was tied for the most of any percentage, and it is also closer to the middle of the range of percentages.) Answer: \boxed{45\%}.
A survey was carried out to find the favorite beverage of a particular telemarketing company having 2,000 employees. To carry out this survey, two groups of 100 employees each were randomly selected and asked to vote for their favorite beverage. The results obtained are given in the table shown below.
Beverage Group A Group B
Coffee 42 44
Green Tea 9 11
Soft Drinks 28 22
Energy Drinks 21 23
Which of the following statements about the data above is true?
A.
The estimates for both groups show an equal number of employees would have voted for coffee.
B.
The estimated number of employees who would have voted for green tea is higher when based on the results of Group A rather than Group B.
C.
The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.
D.
The estimated number of employees who would have voted for coffee is higher when based on the results of Group A rather than Group B.
C.
The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A. (Group B had 44 coffee voters, compared to 42 in Group A.)
Becca and Carmen are doing research for their school newspaper.
Becca surveyed a sample of 40 students buying lunch in the school cafeteria last Tuesday about their favorite items on the cafeteria menu.
Carmen asked the school secretary to randomly select 40 students from the student registry and emailed them a survey about their favorite school-sponsored activities.
Whose data can be used to draw conclusions and make generalizations about the school's student population?
A.
only Becca's
B.
only Carmen's
C.
both Becca's and Carmen's
D.
neither Becca's nor Carmen's
C.
Both Becca's and Carmen's data can be used to draw conclusions and make generalizations about the school's student population. Combining the results from both surveys can provide a more comprehensive view of the student population's interests and preferences.
Select the correct answer from each drop-down menu. The students at Jillian and Kayla's school will be voting next week to select the theme for the next school dance. Jillian and Kayla have been asked by the student council to survey random groups of students to predict the outcome of the vote. They each randomly selected 40 students and asked which theme was preferred. The results of the surveys are given below. Under the Sea Tropical Islands The Wild West Dragons and Castles Jillian's Survey 11 8 6 15 Kayla's Survey 14 9 4 13 Complete the statements to make them true. "Dragons and Castles" is predicted by blank to be the winning theme when the whole school votes. Both surveys predict that blank will receive the fewest votes from the overall student population. Using larger samples would blank predictors of which theme will win the school-wide vote.
"Dragons and Castles" is predicted by both surveys to be the winning theme when the whole school votes.
Both surveys predict that "The Wild West" will receive the fewest votes from the overall student population.
Using larger samples would improve the predictors of which theme will win the school-wide vote.
Three random samples of 50 middle school students were asked what hobby they would like to take up during summer break. The data gathered from the three samples is shown in the table below.
Sample Writing Gardening Drawing/Painting Total
#1 13 10 27 50
#2 12 9 29 50
#3 16 8 26 50
Which inference is supported by the data in the table?
A.
Most middle school students would want to take up writing or gardening during summer break.
B.
Most middle school students would want to take up drawing or painting during summer break.
C.
Most school students would want to take up writing or gardening during summer break.
D.
Most school students would want to take up drawing or painting during summer break.
B.
Most middle school students would want to take up drawing or painting during summer break. (This is the hobby that received the most votes in each of the three samples.)