Answer: 0.6065
Step-by-step explanation:
Given : The machine's output is normally distributed with
Let x be the random variable that represents the output of machine .
z-score : 
For x= 21 ounces
For x= 28 ounces
Using the standard normal distribution table , we have
The p-value : 
Hence, the probability of filling a cup between 21 and 28 ounces= 0.6065
In the Figure below is shown the graph of this function. We have the following function:
The 
occurs when 
, so:
Therefore, the is the given by the point:
From the figure we have three 
:
So, the occur when 
. Thus, proving this:
Answer:
Independent Variable: Number of hours
Dependent Variable: Cost
Equation: C = 2x + 6
Step-by-step explanation:
The independent variable (x) is the variable that is manipulated. In this instance, that would be the number of hours a person rents out the bike.
The dependent variable (C) is the variable that is manipulated depending on the value of the independent variable. In this instance, that would be the total cost for renting the bike.
The total equation would be C = 2x + 6. The coefficient, 2, represents the charge of $2 per hour and the 6 represents the starting charge of $6.
We are asked to determine what happens to the values of
as
approaches
using values of
less than
AND using values of
greater than
.
<span>Observe from the graph that as </span>
approaches
from the left or the right, the values of
increase without bound.
Therefore, we know the following. 
Answer:
42
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Step-by-step explanation:
<u>Step 1: Define</u>
2x³ - x² - 4x + 9
x = 3
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em>: 2(3)³ - 3² - 4(3) + 9
- Exponents: 2(27) - 9 - 12 + 9
- Multiply: 54 - 9 - 12 + 9
- Subtract: 45 - 12 + 9
- Subtract: 33 + 9
- Add: 42
