What is the LCM of 8 and 14 using prime factorization

kodGreya [7K]

1,060 hope this helped !

6 0

4 years ago

A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes a) are there in total?

attashe74 [19]

Answer:

There are 256 ways in total.

There are 56 possible outcomes contain exactly three heads.

The possible outcomes contain at least three heads is 219.

The possible outcomes contain the same number of heads and tails are 70.

Step-by-step explanation:

Consider the provided information.

A coin is flipped eight times where each flip comes up either heads or tails.

Part (a) How many possible outcomes are there in total?

Each time we flip a coin it comes up either heads or tail.

Therefore the total number of ways are:

$2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^8=256$

Hence, there are 256 ways in total.

Part (b) contain exactly three heads?

We want exactly 3 heads, therefore,

n=8 and r=3

According to the definition of combination: $\binom{n}{r}=\frac{n!}{r!(n-r)!}$

$\binom{8}{3}=\frac{8!}{3!(5)!}=56$

Hence, there are 56 possible outcomes contain exactly three heads.

Part (c) contain at least three heads?

For 3 heads: $\binom{8}{3}=\frac{8!}{3!(5)!}=56$

For 4 heads: $\binom{8}{4}=\frac{8!}{4!(4)!}=70$

For 5 heads: $\binom{8}{5}=\frac{8!}{5!(3)!}=56$

For 6 heads: $\binom{8}{6}=\frac{8!}{6!(2)!}=28$

For 7 heads: $\binom{8}{7}=\frac{8!}{7!(1)!}=8$

For 8 heads: $\binom{8}{8}=1$

Now add them as shown:

56+70+56+28+8+1=219

Hence, the possible outcomes contain at least three heads is 219.

Part (d) contain the same number of heads and tails?

Same number of heads and tails means that the value of r=4.

Therefore,

$\binom{8}{4}=\frac{8!}{4!(4)!}=70$

Hence, the possible outcomes contain the same number of heads and tails are 70.

6 0

3 years ago

PLEASE HELP I need to answer the question quick .

Finger [1]

Answer:

D. y+3 = 6(x-1)

Step-by-step explanation:

i just wrote it out and i think thats the answer but not sure. hopefully this helps :)

8 0

3 years ago

Which expression makes the equation true for all values of x?

Ugo [173]

A. 4x-4

We want the expressions to be equal, and:

4(4x-4)= 16x-16

So, A is the answer

7 0

3 years ago

Read 2 more answers

Complete the following proof Given: is the midpoint of , is the midpoint of Prove: =2

Vesnalui [34]

Answer:

Step-by-step explanation:

Statements Reasons

1). M is the midpoint of segment AB 1). Given

B is the midpoint of segment MD

2). AM = MB and MB = BD 2). Definition of midpoint

3). MD = MB + BD 3). Segment Addition Postulate

4). MD = MB + MB 4). Substitution property of of Equality

5). MD = 2MB 5). Simplify

Therefore, if M is the midpoint of segment AB, B is the midpoint of MD then MD = 2MB

5 0

3 years ago