Question

A quiz consists of 3 true-or-false questions and 2 multiple choice questions. The multiple choice questions have 3 options each. How many ways can a student complete the quiz?

a) 18

b) 48

c) 54

d) 72

Answer 1

@Vocaloid

Answer 2

"3 true-or-false questions"

each T or F only has 2 possibilities
for three questions we multiply 2 by itself 3 times

so 2*2*2

"2 multiple choice questions with three options each"
so multiply 3 by itself two times

3 *3

Answer 3

putting it all together = 2*2*2*3*3 = ?

Answer 4

Oh sorry, I didn't see that you were asking me a question. I was on another tab. So okay... the answer would be 72 then?

Answer 5

yeah

Answer 6

A secret code consists of 2 digits, followed by 2 letters, followed by 1 of the following symbols: @, #, %, and &. Digits and letters cannot repeat. How many secret codes are possible?


a) 234,000


b) 243,360


c) 260,000


d) 270,400

Answer 7

2 digits: 9 * 9 since there are 9 digits

2 letters: 26 * 26 since there are 26 letters in the alphabet

1 of 4 possible symbols, so * 4

therefore 9 * 9 * 26 * 26 * 4 *

Answer 8

hm lemme double check something

Answer 9

alright

Answer 10

oh, there are 10 digits not 9 whoops

Answer 11

therefore 10 * 10 * 26 * 26 * 4

Answer 12

Okay so that would be 270,400

Answer 13

right?

Answer 14

yes

Answer 15

How many distinct arrangements can you make using the letters in the word EXPERIMENT?

a) 604,800


b) 725,760


c) 1,209,600


d) 3,628,800

Answer 16

there are 9 total letters with three repeated E's

so 9!/3!

note: this is 9 factorial over 3 factorial, not 9/3

Answer 17

wait okay so it's a) 604,800

Answer 18

yes

Answer 19

How many ways can a dance instructor send 4 of her 11 students to a summer dance program?


a) 7920


b) 1980


c) 720


d) 330

Answer 20

n is the total set (11 students) and r is the set being chosen (4 students)

plugging them in gives us

11! / (4!(11-4)!)

Answer 21

Eh I'm not really sure for this one. So, I'm just gonna take an educated guess. 1980?

Answer 22

I've given you the formula and the substitution, you just need to plug 11! / (4!(11-4)!) into a calculator.

Answer 23

That came out to be 13 when I used a calculator e.e

Answer 24

you can make it easier by simplifying first

Answer 25

so in the end that's (11*10*9*8)/(4*3*2*1) see what that gives you

Answer 26

330

Answer 27

yup that's what i got too

Answer 28

I have 3 more questions left. Will you be able to help with the rest?

Answer 29

i'll give it my best try

Answer 30

There are 5 keys on a keychain. One of the keys starts a car. If a key is randomly chosen, what is the probability that it starts the car?


a) 5%


b) 15%


c) 20%


d) 25%

Answer 31

1 good key/5 total keys

1/5 = what as a percent?

Answer 32

20%

Answer 33

awesome so 20% = your sol'n

Answer 34

sol'n?

Answer 35

solution

Answer 36

20%, not 25%

Answer 37

have to be careful with the wording on this one

"probability that a randomly chosen female runs sprints"

so we want

(females who run sprints)/(total females)

any ideas what that might be, based on the numbers in the table?

Answer 38

http://prntscr.com/l2aic2

Answer 39

so, looking at the table

how many females run sprints? and how many total females are there?

Answer 40

12 females run sprints and there are 31 females in total.

Answer 41

well done

so 12/31 = ?

Answer 42

So that would be, 0.39?

Answer 43

yup

Answer 44

Okay I'm gonna post the last question

Answer 45

The probability of choosing a winning card from a stack of cards is 2.9%. What is the probability of choosing a losing card?


a) 99.71%


b) 97.1%


c) 92.9%


d) 87.1%

Answer 46

b right?

Answer 47

assuming there are only two types of cards (winning and losing)

winning + losing = 1

so 100% - 2.9% will give you the losing probability

Answer 48

so 0.971

Answer 49

your pretty smart vocaloid but I think I was right on that one

Answer 50

good, which is also 97.1%

Answer 51

great job envision:)

Answer 52

Thank you so much for helping, Vocaloid! Your explanations are very helpful!