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A surveyor needs to find the distance across a pond. He measures a triangle with side $A = 40$ m, side $B = 50$ m, and the angle between them is $60^\circ$. Using the Cosine Law ($c^2 = a^2 + b^2 - 2ab\cos(C)$), what is the distance across the pond?
Answer: 45.8 m
Solution: $c^2 = 40^2 + 50^2 - 2(40)(50)\cos(60)$. $c^2 = 1600 + 2500 - 4000(0.5)$. $c^2 = 2100$. $\sqrt{2100} \approx 45.8$.
The odds against a snowstorm tomorrow are 3:1. What is the probability that it will snow?
Answer: $25\%$ or $\frac{1}{4}$.
Which number is the outlier in this set: $\{12, 14, 13, 15, 85, 12\}$? How does it affect the mean?
Answer: 85 is the outlier. It skews the mean significantly higher (drags the average up).
A plumber charges a $\$60$ service fee plus $\$40$ per hour. What is the rate of change?
Answer: $\$40$/hour.
On a distance-time graph, what does a horizontal line represent?
Answer: The object has stopped moving (distance is not changing as time passes).
A triangle has sides of length 8 cm, 9 cm, and 12 cm. Which law would you use to find the largest angle?
Answer: The Cosine Law.
You buy a raffle ticket for $\$5$. There is a $1/100$ chance to win $\$200$ and a $99/100$ chance to win nothing. What is the expected value of the ticket?
Answer: $-\$3.00$ (A loss of 3 dollars).
If a scatter plot shows points rising from left to right, what kind of correlation is this?
Answer: Positive correlation.
Write an equation for the plumber in Question 16, where $C$ is total cost and $h$ is hours worked.
Answer: $C = 40h + 60$
You have data for years 2010 to 2020. You use the trend to predict the value for 2025. Is this interpolation or extrapolation?
Answer: Extrapolation (predicting outside the known data range).
A carpenter measures a board as 12.5 cm. The true length is 12.52 cm. Is the measurement accurate, precise, or both?
Answer: It is fairly accurate (close to the true value) but has low precision (limited to one decimal place).
Find the mean, median, and mode of this data set: $\{4, 8, 8, 10, 15\}$.
Answer: Mean = 9, Median = 8, Mode = 8.
A study shows that ice cream sales and drowning incidents both increase in July. Does ice cream cause drowning?
Answer: No. This is correlation, not causation. Both are caused by a third variable: hot weather.
Using the equation $C = 40h + 60$, if the total bill was $\$260$, how many hours did the plumber work?
Answer: 5 hours.
You are starting a food truck. Is the cost of the truck insurance a fixed cost or a variable cost?
Answer: Fixed cost (you pay it regardless of how many burgers you sell).
A machine part must be $5.00$ inches $\pm 0.02$ inches. What is the maximum and minimum allowable width?
Answer: Max: 5.02 inches; Min: 4.98 inches.
A student’s course grade is calculated as follows: Assignments (20%), Tests (30%), Final Exam (50%). If the student scores 80 on assignments, 70 on tests, and 60 on the final, what is their final grade?
Answer: 67%
You want to know the favourite music of students in your high school. You ask 50 students leaving the Band Room. Why is this data biased?
Answer: Sampling bias. Students in the band are more likely to prefer instrumental or classical music than the general student population.
Does the equation $y = 50x$ represent direct variation or partial variation?
Answer: Direct variation (because the y-intercept is 0).
You sell handmade chairs. Materials cost $\$20$ per chair. Rent for your workshop is $\$500$/month. If you sell 10 chairs for $\$100$ each, what is your profit (or loss)?
Answer: $\$300$ Profit.
The probability of winning a specific raffle is $\frac{1}{20}$. What are the odds in favor of winning?
Answer: 1:19
If you scored in the 85th percentile on a standardized test, what does that mean?
Answer: You scored higher than 85% of the people who took the test.
Calculate the slope of a line passing through $(2, 4)$ and $(6, 12)$.
Answer: 2
Plan A costs $\$10$/month + $\$0.10$/text. Plan B costs $\$30$/month for unlimited texts. At how many texts do the plans cost the same?
Answer: 200 texts.
A car consumes 8.5 L/100 km. How much fuel is needed for a 400 km trip?
Answer: 34 Litres.