Geometry
What is the area of a trapezoid with bases 3 and 8 and height 6?
33
There are 5 blue tokens and 1 black token in a basket. Two tokens are selected from the basket without replacement.
What is the probability that both tokens will be black?
0
Find the mean of the data set below.
38, 6, 22, 17, 31, 2, 14, 42, 8, 34
21.4
The mean of a sample is recorded to be 8.32. Find an unbiased estimate for the population mean.
8.32
Find the 100th term of the sequence 1, 4, 7, ...
298
Find the length of an arc in a circle with radius 5 and base angle 75 degrees. Give your answer correct to 3 s.f.
6.54
In a group of 30 students, 17 study biology, 19 study chemistry, and 9 study neither. Find the probability that a randomly chosen student studies both biology and chemistry.
0.5
What is the name of the sampling method in which you select every nth entry?
Systematic sampling
The standard deviation of a sample with 15 entries is 1.14. Find an unbiased estimator for the population
1.18
Find the 20th term of the sequence 182, 91, 45.5, 22.75, ...
3.47*10-4
The area of a sector with base angle 60 degrees is 42. Find the radius of the sector. Give your answer correct to 4 decimal places.
8.9562
The weight of bags of sugar is normally distributed with mean 0.975 kg and standard deviation 5g.
A bag that weights less than k kg is considered underweight. This happens with 5% of the bags of sugar.
Find the value of k.
0.967 kg
Consider a data set in which Q1 is 15 and Q3 is 20.
A certain integer is an outlier and smaller than 15.
Find the largest possible value of this number.
7
Annie thinks the bags of rice she buys in a local grocery store have a mean weight of 1.5 kg.
She collects a sample of 10 bags and finds the following data.
mean: 1.43, Sx = 0.478
By finding a suitable 90% confidence interval, state if Annie is correct.
(1.1529,1.7071)
The mean of 1.5 kg is inside the confidence interval, it is possible that Annie is correct.
Kathy invests 10 000 USD into a savings account with 2.1% interest, compounded quarterly.
Find the value of Kathy's investment after 7 years.
Give your answer correct to 2 decimal places.
11579.09 USD
In a right-angled triangle, the hypothenuse has length 8 and one the angles has measure 30 degress. Find the length of the side opposite to that angle.
4
Sandy tosses a biased coin 10 times. The coin is weighed is such a manner, that the probability of throwing tails is 0.57.
Find the probability that Sandy throws exactly 4 heads in her 10 throws.
0.246
What are the 5 values required to build a box-and-whisker plot?
Min, Q1, Med, Q3, Max
Mark has 25 students in his class. He believes that on any given day, the probability that a student will come to class is 0.8.
He decides to test his hypothesis and formulates the following hypotheses:
H0: p=0.8
H1: p>0.8
Mark decides he will reject his null hypothesis if more than 20 students come to class today.
Find the probability of a type I error.
0.421
Roland took out to loan of $650 000 to buy a house.
The loan is for 20 years, at a 1.8% rate.
Find the value of Roland's monthly payments. Give your answer correct to the nearest dollar.
$3227
In the triangle ABC, side BC has length 7, side AB has length 5 and angle C has measure 42 degrees.
Find both possible measures of angle A.
A=69.5 degrees or A=110.5 degrees.
Joan believes that the number of visitors in her cafe in an hour can be modelled with a Poisson distribution with mean 32.
Considering Joan's cafe is open from 10am to 8pm, find the probability that at most 300 people will visit her cafe on a given day.
0.137
The mean grade of 9 students is recorded to be 5.48.
A tenth student with grade 6 joins the group and a new mean is recorded.
Find the value of the new mean.
5.532
Mark has 25 students in his class. He believes that on any given day, the probability that a student will come to class is 0.8.
He decides to test his hypothesis and formulates the following hypotheses:
H0: p=0.8
H1: p>0.8
Mark decides he will reject his null hypothesis if more than 20 students come to class today.
As it turns out, the probability a student will come to class is actually 0.85.
Find the probability of a Type II error.
0.318
Consider the arithmetic sequence 2, 6, 10, 14, ... , 250
Kelly decides to add every 3rd term of this sequence, starting with the first term. Find Kelly's result.
2562