Answer:
When x = 72, the z score is:
The average is 58
This z-score indicates that x= 72 is 1.273 standard deviations above the mean.
Step-by-step explanation:
Let’s consider the following details for this question: John's typing speed on a test is assumed to follow a normal distribution. Let X denote the number of words he can type in a minute. Hence, X ~ N(58, 11). It’s important to round the result to three decimal points if needed.
Provide your response below for words per minute on a typing test conducted on Sunday. The z score when x = 72 is
In this scenario, we acknowledge that the variable under consideration is represented by a normal distribution:
The formula for the z score is as follows:
By substituting values, we derive:
The mean is 58
This z-score indicates that x= 72 is 1.273 standard deviations higher than the mean.
It's known that
When two lines are parallel, their slopes are identical.
The slope between any two points can be calculated using the following formula:
We will calculate the slope for each case to find the solution to the problem.
Case A) Point 
Determine the slope of BC
Insert the values into the formula:
Thus,
The equation 
is parallel to the line that goes through the points
Therefore,
the result for Part A) is
------>
Case B) Point 
Calculate the slope of DE
Plug the values into the formula:
Thus,
The equation 
is parallel to the line that goes through the points
Therefore,
the result for Part B) is
------>
Case C) Point 
Determine the slope of FG
Insert the values into the formula:
Thus,
Any linear equation with slope will be parallel to the line through the points
Case D) Point 
Calculate the slope of HI
Substitute the values in the formula:
Thus,
The equation 
is parallel to the line through the points
Therefore,
the result for Part D) is
------>
Case E) Point 
Determine the slope of JK
Insert the values into the formula:
Thus,
Any linear equation characterized by slope will be parallel to the line that runs through the points
Case F) Point 
Find the slope of LM
Substitute the values in the formula:
Thus,
The equation 
is parallel to the line connecting the points
Therefore,
the result for Part F) is
------>
Greetings:
<span>(4y-3)²=72
4y-3 = </span>±√72
thus, y= (3+√72) /4 or y= (3 - √72) /4
To simplify the expression:
-(6 x^3 - 2 x + 3) - 3 x^3 + 5 x^2 + 4 x - 7
Start with - (6 x^3 - 2 x + 3) = -6 x^3 + 2 x - 3:
-6 x^3 + 2 x - 3 - 3 x^3 + 5 x^2 + 4 x - 7
Next, combine similar terms: -3 x^3 - 6 x^3 + 5 x^2 + 4 x + 2 x - 7 - 3 = (-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3):
(-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3)
-3 x^3 - 6 x^3 results in -9 x^3:
-9 x^3 + 5 x^2 + (4 x + 2 x) + (-7 - 3)
Combine 4 x and 2 x to get 6 x:
-9 x^3 + 5 x^2 + 6 x + (-7 - 3)
The operation -7 - 3 yields -10:
-9 x^3 + 5 x^2 + 6 x - 10
Factoring out -1 from -9 x^3 + 5 x^2 + 6 x - 10 leads to:
Final Answer: - (9 x^3 - 5 x^2 - 6 x + 10)
1. "The limit on John's credit card is defined by the function f(x)=15,000+1.5x," indicating that if John's monthly income is $5,000, he can spend a maximum of f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22,500 (dollars). As another example, if John's monthly income is $8,000, then he can spend up to f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars). 2. If we consider the maximum amount John can spend as y, it can be represented as y=15,000+1.5x. To express x, the monthly income, in terms of y, we rearrange this equation: y=15,000+1.5x results in 1.5x = y-15,000. Therefore, in functional notation, x is a function, referred to as g, based upon y, the maximum sum. Generally, we denote the variable of a function by x, so we redefine g as: This tells us that if the maximum amount that John can spend is $50,000, then his monthly income would be $23,333. 3. If John's limit is $60,000, his monthly income equals $30,000. Note: g is deemed as the inverse function of f because it reverses the actions of f.
