In each round of a game show, a contestant answers a multiple-choice question that has three answer choices. the contestant advances to the next round by answering the question correctly. what is the probability of advancing to the seventh round if the contestant randomly guesses the answer to each question? write your answer as a fraction in simplest form.

The probability of advancing to the seventh round is:

Step-by-step explanation:

It is given that:

In each round of a game show, a contestant answers a multiple-choice question that has three answer choices.

Also, the contestant advances to the next round by answering the question correctly.

Hence, in order to reach the seventh round he has to correctly answer in all of the preceding rounds (i.e. round 1 to round 6)

Now, as we know that the event of answering in each round is independent of the other rounds.

Hence, the probability of advancing to the seventh round is product of probability of answering correctly in all the preceding rounds.

Let P denotes the probability of an event.

P( answering round 1 correctly)=P(1)=1/3

( since, we know that out of three choices only one is correct)

P( answering round 2 correctly)=P(2)=1/3

Similarly,

P( answering round 3 correctly)=P(3)=1/3

P( answering round 4 correctly)=P(4)=1/3

P( answering round 5 correctly)=P(5)=1/3

P( answering round 6 correctly)=P(6)=1/3

Hence,

Hence, the probability is:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

y/x=18

step-by-step explanation: