Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
Answer:
b. A binomial variable with 25 independent trials
Step-by-step explanation:
The conducted experiment is binomial experiment because outcome can be divided into success or failure. The success would be the people who read novel in the past year and also responses are independent of each other. We have to find the number of trials n in the given problem.
we are given that variance of R=6 and p=probability of success=0.4.
We know that variance of binomial distribution is
Variance=npq
where q=1-p=1-0.4=0.6.
By putting the values in variance formula, we can get the value of n.
6=n*0.4*0.6
6=0.24*n
n=6/0.24
n=25
Hence, random variable R is a binomial variable with 25 independent trials.
Answer:
x < -8
Step-by-step explanation:
Step 1: Translate
Product = multiplication = -8(x)
More than = >
64 = 64
Step 2: Write out inequality
-8x > 64
Step 3: Solve
x < -8
The answer would be C. When you calculate the mean, it includes every number for a certain period of time into things and averages it out. The median does not average out all the numbers.
115.9%
1.159
rounded is 1.159 still
