Indices - Quiz 2


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University of Sydney
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Indices - Quiz 2 Question

Question 1

Which of the following simpliﬁes $45a2 ÷ 9a6?$

Not correct. Choice (a) is false.

Try again, you have not found $a2 ÷a6 .$

Not correct. Choice (b) is false.

Try again, remember $45 a2 45a2 ÷ 9a6 = 9-× a6 .$

Not correct. Choice (c) is false.

Try again, remember $2 6 45 a2 45a ÷9a = 9 × a6 .$

Your answer is correct.

$2 6 45 a2 2-6 -4 45a ÷ 9a = 9 × a6 = 5a = 5a .$

Question 2

Which of the following gives the correct value of $a-1 + b-2$ where $a = 3$ and $b = 2.$

Not correct. Choice (a) is false.

Try again, recall $-1 1 a = a-,$ not $- a .$

Your answer is correct.

$-1 - 2 1 1- 4+-3- -7 a + b = 3 + 22 = 12 = 12 .$

Not correct. Choice (c) is false.

Try again, recall $a-1$ means $1. a$

Not correct. Choice (d) is false.

Try again, recall to add fractions you must ﬁnd a common denominator.

Question 3

Which of the following correctly simpliﬁes $-- x10√ x5 --x---?$

Your answer is correct.

$x10√x5- x10x 52 10+5- 1 23 √ --- ---x---= --x--= x 2 = x 2 = x23.$

Not correct. Choice (b) is false.

Try again, remember $√x5-= x 52 .$

Not correct. Choice (c) is false.

Try again, you cannot cancel out $x$ ’s

Not correct. Choice (d) is false.

Try again, you have forgotten the $x$ in the denominator.

Question 4

Suppose the geometric mean of ${X1 ,X2 ,...,Xn}$ is deﬁned by $XG- = (X × X × ...×X )1n . 1 2 n$
Which of the following is the geometric mean, $XG-,$ of ${5 ,3 ,2,5},$ correct to 2 decimal places?

Not correct. Choice (a) is false.

Try again, you have divided by 4, not taken the 4th root.

Not correct. Choice (b) is false.

Try again, you have only taken the 4th root of one of the numbers, not the product.

Not correct. Choice (c) is false.

Try again, you have found the average.

Your answer is correct.

$√45-×-3-×-2×-5 = 3.4996 = 3.50$ correct to 2 decimal places.

Question 5

The Poisson Variable $X$ is used to model rare events where $e-λλX- P(X) = X!$ is the probability of $X$ occurrences of the event in a given time frame. Which of the following represents $P (3)$ correct to 3 decimal places where $λ = 1.5$ in the given time frame?

Your answer is correct.

$- 1.5 3 P(3) = e---1.5--= 0.75306-= 0.12551 3× 2× 1 6$ which is $0.126$ correct to 3 decimal places.

Not correct. Choice (b) is false.

Try again, did you divide by $3! = 3× 2 ×1$ or just 3?

Not correct. Choice (c) is false.

Try again, remember a probability must be between 0 and 1.
Did you input $e1.5$ instead of $e-1.5?$

Not correct. Choice (d) is false.

Try again, you seem to have your $X$ and your $λ$ the wrong way around.