1. A weather station in a major city in the Northwest kept data about the weather conditions over the past year. The probabilities are displayed in the table below:

Hot Mild Cold
Sunny 0.15 0.30 0.10
Cloudy 0.10 0.25 0.10

If a random day is chosen from this data, what is the probability that the day was hot or sunny?
0.10
0.15
0.30
0.65

2. A local university wanted to understand what students prefer to eat during finals. They asked 1,000 students, "Do you prefer chicken, burgers, or pizza?" The results of the survey are shown in the two-way table below:

Chicken Burgers Pizza
Male 127 218 125
Female 219 192 119

What is the probability that a person chosen at random from this survey prefers pizza, given that they are female? Round your answer to the nearest tenth.
11.9%
12.5%
22.5%
48.8%

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

900 degrees

step-by-step explanation:

step-by-step explanation:

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