Lance the wizard has been informed that tomorrow there will be a 40% chance of encountering the evil myrmidons and a 30% chance of meeting up with the dreadful balrog. moreover, hugo the elf has predicted that there is a 10% chance of encountering both tomorrow. what is the probability that lance will be lucky tomorrow and encounter neither the myrmidons nor the balrog?

There is a 40% probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog.

Step-by-step explanation:

We can solve this problem using the Venn's Diagram of these probabilities.

I am going to say that:

A is the probability that he encounters evil Myrmidons.

B is the probability that he encounters dreadful Balrog.

C is the probability that he does not encounter any of them.

We have that:

In which a is the probability that he only encounter evil Myrmidons and is the probability that he encounters both.

By the same logic, we also have:

The sum of all the probabilities is decimal 1, so:

We start finding these values from the intersection of both sets:

Hugo the Elf has predicted that there is a 10% chance of encountering both tomorrow.

This means that .

30% chance of meeting up with the dreadful Balrog.

This means that

40% chance of encountering the evil Myrmidons

This means that

What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog?

This probability is the value of C. So:

There is a 40% probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog.

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

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation: