Please use " ^ " to denote exponentiation: <span>f(x) = 4x^2 + 2x -5. To find the vertex form of this equation, complete the square:
f(x) = 4x^2 + 2x - 5
= 4(x^2 + (2/4)x) - 5
= 4(x^2 + (1/2)x ) -5
= 4(x^2 + (1/2)x + 1/16 ) - 4/16 - 5
= 4(x+1/4) - 21/4 <= in vertex form
Here h= -1/4 and k = -21/4. The vertex is at (-1/4, -21/4)</span>
The square root of 100 and of 0.25 are both rational as they are finite numbers, the square root of 100 being 10 and the square root of 0.25 being 0.5.
Answer:
Step-by-step explanation:
Let x be the random variable representing the lifespan of laptops. Since the lifespans are normally distributed and population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
n = number of samples
From the information given,
µ = 24.5
σ = 2.6
n = 33
the probability that the mean lifespan of these laptops will be less 23.8 months is expressed as
P(x ≤ 23.8)
For x = 23.8
z = (23.8 - 24.5)/(2.6/√33) = - 1.55
Looking at the normal distribution table, the probability corresponding to area on the left of the z score is 0.061
P(x ≤ 23.8) = 0.061
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