Write y=2x+3 using function notation
2 answers:
Answer:
Step-by-step explanation:
The function f(x) is the another way of representing the y-values in the function
i.e
Then y-axis be labeled with f(x)
Also; the ordered pair is written as: (x, f(x)) instead of (x, y)
Given the equation:
replace y = f(x)
then;
therefore, the equation y=2x+3 using function notation is,
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Answer:
a) We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.
b) There is a 15.97% probability that x will be between 54 and 55.
c) The 47th percentile of x is .
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11.
This means that .
We have to find the standard deviation of the sample, that is:
(a) Is it appropriate to use the normal distribution to find probabilities for x?
We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.
(b) Find the probability that x will be between 54 and 55.
This is the pvalue of the Z score when X = 55 subtracted by the pvalue of the Z score when X = 54.
X = 55
has a pvalue of 0.88877.
X = 54
has a pvalue of 0.72907.
So, there is a 0.88877 - 0.72907 = 0.1597 = 15.97% probability that x will be between 54 and 55.
(c) Find the 47th percentile of x. Round the answer to at least two decimal places.
This is the value of X when Z has a pvalue of 0.47;
This is between and
. So we use
.
The 47th percentile of x is .
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
3
Using (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 3, 6)
m = =
= - 2
Since the line passes through the origin (0, 0) then y- intercept is 0
y = - 2x ← equation of line
4
let (x₁, y₁ ) = (6, 0) and (x₂, y₂ ) = (0, 3)
m = =
= -
note the line crosses the y- axis at (0, 3) ⇒ c = 3
y = - x + 3 ← equation of line
5
let (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (-2, - 3)
m = =
= 3
note the line crosses the y- axis at (0, 3) ⇒ c = 3
y = 3x + 3 ← equation of line