According to the Central Limit Theorem, the distribution of the sample means is approximately normal, with the mean equal to the population mean (1.4 flaws per square yard) and standard deviation given by:
The z-score for 1.5 flaws per square yard is:
The cumulative probability for a z-score of 1.11 is 0.8665. Therefore the probability that the mean number of flaws exceeds 1.5 per square yard is
1 - 0.8665 = 0.1335.
The table of values that could be used to graph g(x), a reflection of f(x) across the x-axis is table (c)
<h3>How to determine the table of values?</h3>
From the question, we have the following equation that can be used in our computation:
f(x) = One-third(6)x
When this statement is represented as an equation, we have the following representation
f(x)= 1/3(6)ˣ
The transformation is given as
A reflection of f(x) across the x-axis
This means that
g(x) = -f(x)
So, we have
g(x) = -1/3(6)ˣ
What this means is that the values of f(x) are negated to get g(x)
The table that represents this is table (c)
Hence, the table of values is table (c)
Read more about transformation at
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Part A:
The first step of completing the square is writing the expression
as
which expands to
.
We have the first two terms exactly the same with the function we start with:
and
but we need to add/subtract from the last term, 49, to obtain 41.
So the second step is to subtract -8 from the expression
The function in completing the square form is
Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function
can either make U-shape or ∩-shape depends on the value of the constant
that goes with
. When
is (+), the curve is U-shape. When
(-), the curve is ∩-shape
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is
This function is shown in the diagram below
Answer:
Step-by-step explanation:
For that transformation you just have to use polar coordinates, notice that when you use polar coordinates the radius is constant when the angles varies and the angle is constant when the radius varies. Therefore your transformation would be just
.
