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Answer:
The probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525
Step-by-step explanation:
Standard deviation =
We are supposed to determine the probability that a randomly chosen part has diameter of 3.5 inches or more
Refer the z table for p value
Hence the probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525
Answer:
The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]
The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]
The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]
The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]
Step-by-step explanation:
For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:
Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:
Given: 27x³ - 64y³
[3x - 4y][9x² + 12xy + 16y²]
↑ ↑ ↑
same as opposite ALWAYS POSITIVE
given of given
Given: 27x³ - 8y³
[3x - 2y][9x² + 6xy + 4y²]
↑ ↑ ↘
same as opposite ALWAYS POSITIVE
given of given
Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:
Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:
Given: 27x³ + 64y³
[3x + 4y][9x² - 12xy + 16y²]
↑ ↑ ↘
same as opposite ALWAYS POSITIVE
given of given
Given: 27x³ + 8y³
[3x + 2y][9x² - 6xy + 4y²]
↑ ↑ ↘
same as opposite ALWAYS POSITIVE
given of given
I am delighted to assist you anytime!
* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.
Answer:
$1753.13
Step-by-step explanation:
Kane's Annual Salary = $42,500
Gross Pay = $42,500
Net Pay = Gross Pay - 1% of Gross Pay
=42500 - (0.01 X 42500)
=$42,075
Since he is paid twice a month with paychecks being of equal amounts.
Number of Payments in a Year =12 X 2= 24
Therefore, Kane's Take Home pay after Medicare taxes