Indices - Quiz 1

Question 1

Which of the following simplifies $x12× x8÷ x3 ?$

Not correct. Choice (a) is false.

Try again, you have added all of the indices, remember that $xa ÷ xb = xa-b.$

Not correct. Choice (b) is false.

Try again, you have multiplied and divided by the indices, not added and subtracted.

Not correct. Choice (c) is false.

Try again, you have subtracted both 8 and 3 from 12.

Your answer is correct.

This is $x12+8-3 = x17.$

Question 2

Which of the following gives the correct value of $ab- 1 + bc- 1$ where $a = 3,b = 2$ and $c = 12 ?$

Your answer is correct.

$ab- 1 + bc- 1 = 3× 12 + 2×-11= 32 + 4 = 112-. 2$

Not correct. Choice (b) is false.

Try again, $1 2 × 1-= 4, 2$ not $1.$

Not correct. Choice (c) is false.

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

Not correct. Choice (d) is false.

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

Question 3

Which of the following represents $1 x 3 ?$

Not correct. Choice (a) is false.

Try again, this is $x -3.$

Not correct. Choice (b) is false.

Try again, this is $x-13 .$

Your answer is correct.

$x1n = V~ nx-$ for all $n.$

Not correct. Choice (d) is false.

Try again, this is $- 3 x .$

Question 4

Is the following expression True or False? $V~ - sum n--------- sum n --i=1(Xi---X)2-= --i=1 V~ (Xi---X)-. n - 1 n- 1$

Not correct. Choice (a) is false.

The statement is false since $V~ -------------- V~ -------------------------- sum n (X - X)2 (X -X)2 + ...+ (X - X)2 --i=1---i------= --1---------------n------ n - 1 n - 1$
so the square root and the square do not cancel out.

Your answer is correct.

$V~ sum n---------- V~ -------------------------- --i=1(Xi--X)2-= (X1---X)2-+-...+-(Xn---X)2 n- 1 n- 1$
so the square root and the square do not cancel out.

Question 5

The Binomial Variable $X$ is used to model the number of successes in $n$ trials where

$n! P (X) = ----------pX(1- p)n-X X!(n -X)!$

is the probability of $X$ successes in $n$ trials, where the probability of a single success is $p .$

Which of the following is the probability $P(3),$ that is 3 successes out of 4 trials, correct to 3 decimal places, where the probability of a single success is 0.7?