If P=(-2,5) and (x,-27), find all numbers x such that the vector represented by PQ has length -40
1 answer:
Answer:
x ∈ {-26, 22}
Step-by-step explanation:
A graph shows that the points (-26, -27) and (22, -27) lie on a circle of radius 40 centered at (-2, 5). That is, if Q is either one of these points, the vector PQ will have a length of 40:
- √((-26-(-2))^2 +(-27-5)^2) = √((-24)^2 +(-32)^2) = √1600 = 40
- √((22 -(-2))^2 +(-27 -5)^2) = √(24^2 +(-32)^2) = √1600 = 40
You can call it -40 if you like, but you have to define what negative length means when you do that.
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Answer:
The probability that the mean monitor life would be greater than 96.3 months in a sample of 84 monitors
P(X⁻ ≥ 96.3) = 0.0087
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the mean of the Population = 95
Given that the standard deviation of the Population = 5
Let 'X' be the random variable in a normal distribution
Let X⁻ = 96.3
Given that the size 'n' = 84 monitors
<u><em>Step(ii):-</em></u>
<u><em>The Empirical rule</em></u>
Z = 2.383
The probability that the mean monitor life would be greater than 96.3 months in a sample of 84 monitors
P(X⁻ ≥ 96.3) = P(Z≥2.383)
= 1- P( Z<2.383)
= 1-( 0.5 -+A(2.38))
= 0.5 - A(2.38)
= 0.5 -0.4913
= 0.0087
<u><em>Final answer:-</em></u>
The probability that the mean monitor life would be greater than 96.3 months in a sample of 84 monitors
P(X⁻ ≥ 96.3) = 0.0087