Answer:
Option a) 50% of output expected to be less than or equal to the mean.
Step-by-step explanation:
We are given the following in the question:
The output of a process is stable and normally distributed.
Mean = 23.5
We have to find the percentage of output expected to be less than or equal to the mean.
Mean of a normal distribution.
- The mean of normal distribution divides the data into exactly two equal parts.
- 50% of data lies to the right of the mean.
- 50% of data lies to the right of the mean
Thus, by property of normal distribution 50% of output expected to be less than or equal to the mean.
According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
<h3>How to apply translations on a given function</h3>
<em>Rigid</em> transformations are transformation such that the <em>Euclidean</em> distance of every point of a function is conserved. Translations are a kind of <em>rigid</em> transformations and there are two basic forms of translations:
Horizontal translation
g(x) = f(x - k), k ∈
(1)
Where the translation goes <em>rightwards</em> for k > 0.
Vertical translation
g(x) = f(x) + k, k ∈
(2)
Where the translation goes <em>upwards</em> for k > 0.
According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
To learn more on translations: brainly.com/question/17485121
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You can use the sum and difference identities which for cosine is cos(a+b)= cosacosb-sinasinb
Answer:
no 2. cube a' will be smaller because it was multiplied by a fraction
no 3. c