A least squares line of the form
For this set of bivariate data,
The slope of the least squares line,
- 0.44
- 0.45
- 0.58
- 0.59
- 0.76
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A least squares line of the form
For this set of bivariate data,
The slope of the least squares line,
The variables recovery time after exercise (in minutes) and fitness level (below average, average, above average) are
The birth weights of a large population of babies are approximately normally distributed with a mean of 3300 g and a standard deviation of 550 g.
Part 1
A baby selected at random from this population has a standardised weight of
Which one of the following calculations will result in the actual birth weight of this baby?
Part 2
Using the 68–95–99.7% rule, the percentage of babies with a birth weight of less than 1650 g is closest to
Part 3
A sample of 600 babies was drawn at random from this population.
Using the 68–95–99.7% rule, the number of these babies with a birth weight between 2200 g and 3850 g is closest to
If
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The graph of
Let
The value of
At the start of a particular week, Kim has three red apples and two green apples. She eats one apple everyday. On Monday, Tuesday and Wednesday of that week, she randomly selects an apple to eat. In this three-day period, the probability that Kim does not eat an apple of the same colour on any two consecutive days is
The simultaneous linear equations
Let
The equation
Consider the probability distribution for the discrete random variable
The value of
The graph of the function
A fair standard die is rolled 50 times. Let
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a.
b. | ||
Jacinta tosses a coin five times.
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Albin observes a total of 12 heads from the 18 tosses.
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a.
b.
Given the function
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Given the function
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ii. On the axes below, sketch the graph of the function
Also draw the tangent to the graph of
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ii.
Find
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Let
Find
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Let
Find
A fair standard die is rolled 50 times. Let
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a.
b. | ||
c.
The shaded region in the diagram below is bounded by the vertical axis, the graph of the function with rule
Let
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a.
b.
c.i.
c.ii.
Jacinta tosses a coin five times.
Assuming that the coin is fair and given that Jacinta observes a head on the first two tosses, find the probability that she observes a total of either four or five heads. (2 marks)
Let
Find the domain and the rule of the inverse function
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A function
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ii. On the axes below, sketch the graph of the function
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a. | ||
b. | ||
c. | ||
Find
The proportion of a population that have brown eyes is 0.35.
Using
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A light manufacturer knows that 6% of the light bulbs it produces are defective.
Light bulbs are supplied in boxes of 20 bulbs. Boxes are supplied in pallets of 120 boxes.
Calculate the probability that
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i.
ii. | ||
iii.
It is known that 43% of voters in a city voted for Labor in the election.
If 250 voters from the city are selected at random, use a suitable approximation and the attached probability table to find the probability that at least 120 of those chosen voted for Labor. (3 marks)
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Netball Australia records show that 10% of all registered players are over the age of 25.
Assuming the sample proportion is normally distributed, calculate the expected mean and standard deviation of this group. (2 marks)
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i. | ||
ii.
A biased coin has a 0.6 chance of landing on heads. The coin is tossed 15 times.
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i. | ||
ii.
iii.
A delivery company has 1095 packages to deliver on a given day.
It has 17 delivery vans that will deliver all packages. If one van delivers more packages than all other vans, the company pays the driver a $100 bonus.
What is the minimum number of packages a van could deliver and still win the $100 bonus. (2 marks)
A sock drawer contains blue, white and green socks.
If individual socks are randomly chosen from the drawer, what is the minimum number that must be selected to ensure there are at least three pairs? (2 marks)
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Eleven numbers are randomly chosen from the set of integers,
Prove that the sum of two of the eleven numbers randomly selected must equal 21. (2 marks)
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A multiple choice quiz asks students 4 questions. Each question has three possible answers, a, b or c, and students must attempt each question.
How many students must do the quiz to ensure that at least two sets of answers are identical? (2 marks)
A paint company claims that the mean time taken for its paint to dry when motor vehicles are repaired is 3.55 hours, with a standard deviation of 0.66 hours.
Assume that the drying time for the paint follows a normal distribution and that the claimed standard deviation value is accurate.
Write down the mean and standard deviation of
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At a car crash repair centre, it was found that the mean time taken for the paint company's paint to dry on randomly selected vehicles was 3.85 hours. The management of this crash repair centre was not happy and believed that the claim regarding the mean time taken for the paint to dry was too low. To test the paint company's claim, a statistical test was carried out.
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a. |
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b.
c. |
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d.
e.
f. |
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A pallet of bricks weighing 500 kg sits on a rough plane inclined at an angle of
Suddenly the water is completely emptied from the container and the pallet of bricks begins to slide down the plane. The frictional resistance force of 50
The vertical cross-section of a barrel is shown above. The radius of the circular base (along the
a. i. Show that the volume of the barrel is given by
ii. Find the volume of the barrel in cubic centimetres. (1 marks)
The barrel is initially full of water. Water begins to leak from the bottom of the barrel such that
b. Show that
c. Find
d. Using a definite integral in terms of
a. i.
ii.
b.
c.
d.
a.i. | ||
a.ii. | ||
b.
c.
d.
Consider the function
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Consider the function
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On average, batsmen playing cricket in a T20 competition play a scoring shot two out of every three balls.
In a regular season, a total of 1200 overs that each contain six balls, are bowled.
Estimate how many overs would have at least five scoring shots. (3 marks)
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A manufacturer of pool cue tips knows that 4% of pool cue tips produced in its factory need to be scrapped.
A random sample of 10 cue tips produced in the factory is examined.
Give your answer correct to 3 decimal places. (1 mark)
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Give your answer correct to 3 decimal places. (2 marks)
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i.
ii. | ||
A snowboarder at the Winter Olympics leaves a ski jump at an angle of
Let the origin
The position vector of the snowboarder
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a.
b. | |
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c.
d.
A snowboarder at the Winter Olympics leaves a ski jump at an angle of
Let the origin
The position vector of the snowboarder
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a.
b. | |
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c.
d.
e.
In the complex plane,
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Find
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Consider a random variable
If a large number of samples, each of size 100, is taken from his distribution, then the distribution of the sample means,
The position vector
The force, in newtons, acting on the mass when
For the vectors
The vector resolute of
Euler's method, with a step size of 0.1, is used to approximate the solution of the differential equation
When
With a suitable substitution,
The total area enclosed between the
The gradient of the line that is perpendicular to the graph of a relation at any point
The relation satisfies the differential equation
The maximal domain and range of the function
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A circle with centre
The values of
A. −3 and 38
B. 3 and 12
C. −3 and −8
D. 3 and 18
The curve given by
A projectile is fired from a canon at ground level with initial velocity
The equations of motion are
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