ONE VARIABLE STATISTICS
Identify the sample and the population
Liam Hemsworth observed that many middle school students at his local park were playing soccer after school. He proposed to the school sports committee that they organize an after-school soccer tournament.
Sample: The middle school students who observed playing soccer at the local park.
Population: All middle school students at Liam’s school.
SOHCAHTOA
Standing on a cliff, louis Vuitton observes a boat on the water at an angle of depression of 30°. If Mia is 50 meters above the water level, how far away is the boat from the base of the cliff? Round your answer to the nearest meter.
86.43 meters
Expand and Simplify (x+ 5)(x- 7)
use F.O.I.L. method
x2- 2x - 35 .
A survey by Fitness Canada has shown that, by age 18, one in five teenagers have tried a diet program. Of those who try a diet program, 40% continue to follow the diet.
(a) What is the probability that a person has not tried a diet program by age 18?
the probability that a person has not tried a diet program by age 18 is 0.80 or 80%.
Calculate how much interest is earned if $4000 is invested at 4% simple interest for 1 year.
$ 160
Identity the population and sample
Maya is the owner of a coffee shop. She asks customers who visit the shop on Saturday morning if they prefer adding new vegan options to the menu.
Population: All customers of the coffee shop.
Sample: The customers who visit the coffee shop on Saturday morning.
SOHCAHTOA
2. Sitting atop a tower, Abcdefg spots a bird on the ground below at an angle of depression of 45°. If Sarah is 80 meters above the ground, how far is the bird from the base of the tower? Round your answer to the nearest meter.
80
Expand and simplify the expression (2x - 3)(3x + 4)
6x2- x - 12 .
A study by the OVO's has shown that, by age 16, one in six teenagers have taken a computer programming course. Of those who take a computer programming course, 50% pursue a career in technology.
(a) What is the probability that a person has not taken a computer programming course by age 16?
probability that a person has not taken a computer programming course by age 16 is approximately 0.833 or 83.3%.
Calculate how much interest is earned if $5000 is invested at 9% simple interest for 26 weeks.
$225
Mr. Thompson’s grade 7 students want to participate in a math competition. Mr. Thompson writes each student’s name on a slip of paper, puts all the slips in a hat, and randomly draws names to form the team. What sampling technique Mr. Thompson used to select the participants.
simple random sampling
3. Standing on a hill, David Blaine sees a lighthouse beacon shining at an angle of depression of 20°. If David is 60 meters above sea level, how far away is the lighthouse from the base of the hill? Round your answer to the nearest meter.
164.84
Convert the quadratic equation y = 3(x - 5)2 from vertex form to standard form by expanding and simplifying.
y = 3x2 - 30x + 75
In the month of June 2021, at least some snowfall was recorded on 8 different days at the Banff Mountain weather station.
(a) Suppose one day in June 2021 is selected at random. What is the probability of choosing a day on which it snowed?
probability of choosing a day on which it snowed is approximately 0.267 or 26.7%.
Matt invested $4000 at 4% per year, compound annually. How much money does he have at the end of 2 years?
$4161.60
Alex wants to find out the favorite sport among university students in California. Alex’s friend Jordan attends a different university, so they each survey students at their respective universities. Alex combines the results from both universities to draw conclusions.
(a) Identify the population and the sample.
(b) Is the sample representative of the population? If it is, explain why. If it isn't, suggest how the sample could be improved.
(a) University students in California.
- Sample:The students surveyed by Alex and Jordan at their respective universities.
(b) Is the sample representative? no
- Explanation: The sample only includes students from two universities
- Suggested Improvement: To make the sample more representative, surveys should be conducted at a larger number of universities across different regions of California
Cosine Law
Given a triangle with side lengths a = 18 , b = 24 , and an angle C = 105° , use the Law of Cosines to find the length of the third side, c .
c2 = a2+ b2 - 2ab * cos(C)
28.09
State the x-intercepts of the quadratic function
y = (x - 2)(x + 4)
the x-intercepts of the quadratic function are x = 2 and x = -4
In the month of October 2022, at least some snowfall was recorded on 9 different days at the Anchorage weather station.
(a) Suppose one day in October 2022 is selected at random. What is the probability of choosing a day on which it snowed?
(b) Refer to the probability of precipitation you calculated in part (a). Describe how to make a spinner to simulate this situation.
(a)probability of choosing a day on which it snowed is approximately 0.290 or 29.0%.
for (b) either:
Draw a Circle:drawing a circle, which will represent the spinner.
Divide the Circle: Divide the circle into 31 equal sections because there are 31 days in October
John Drevenestiscis leviticus Johnson borrowed $3000 from his friend for Vbucks. The interest rate on the borrowed money was 10% per year, compound monthly. His friend is expecting John Drevenestiscis leviticus Johnson to repay him full after 2 years.
(a) How much would John Drevenestiscis leviticus Johnson repay?
(b) How much of the amount John Drevenestiscis leviticus Johnson repays will be in interest?
(a) 3661.20
(b) 661.20
Mrs. Chen’s grade 8 students want to participate in a science quiz. Mrs. Chen divides the class into two groups based on their seating arrangement, numbering students in each group from 1 to 15. She then selects participants by choosing even-numbered students from one group and odd-numbered students from the other. What sampling technique Mrs. Chen used to select the participants.
Stratified Random sampling
Given a triangle with side lengths a = 18 , b = 24 , and an angle C = 105° , use the Law of Cosines to find the length of the third side, c .
10.7
Factor the polynomial 3y2 - 27 . Provide the answer.
3(y+3)(y-3)
In a month-long survey conducted at a local library, it was found that 18 out of 30 people borrowed a fiction book.
(a) Suppose one person from the survey is selected at random. What is the probability that this person borrowed a fiction book?
probability that this person borrowed a fiction book is 0.60 or 60%.
Drake has a loan for $7000 must be paid in 3 years. He wants pay it early. Kendrick (creditor) nodded and demanded 20% per year, compounded monthly. How much will Kendrick be willing to accept today?
3,860.73