Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
2 answers:
Step-by-step explanation:
Refer to the attached graph that illustrates the axis of symmetry.
We need to identify the graph that represents the axis of symmetry for the function:
This function describes a parabola.
The axis of symmetry is defined as a vertical line that bisects the parabola into two equal halves. It intersects the parabola at its vertex.
To determine the vertex of the parabola, we can utilize the formula: , where:
a = coefficient of
b = coefficient of x.
We will express our parabola as the quadratic equation as:
By substituting a= 1 and b= -4 into the formula, we obtain:
Thus, the vertical line at x = 2 serves as the axis of symmetry for our function, making graph B the correct option.
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Answer:
The chance of completing the entire package installation in under 12 minutes is 0.1271.
Step-by-step explanation:
We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.
To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.
Utilizing , we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.
Given the symmetry of the standard normal distribution density function, we ascertain .
Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.