Ron needed to buy a new jacket for his upcoming ski trip. The ticket price of the jacket was $199.00. After the sales tax was ad
1 answer:
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Answer:
61,239,550
Step-by-step explanation:
We let the random variable X denote the IQ scores. This would imply that X is normal with a mean of 100 and standard deviation of 17. We proceed to determine the probability that an individual chosen at random from the population would be a genius, that is;
Pr( X>140)
The next step is to evaluate the z-score associated with the IQ score of 140 by standardizing the random variable X;
The area to the right of 2.3529 will be the required probability. This area from the standard normal tables is 0.009314
From a population of 6,575,000,000 the number of geniuses would be;
6,575,000,000*0.009314 = 61,239,550
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:
a) (0, ∞)
b) (-∞, ∞)
c) x = 0
Step-by-step explanation:
It helps to have some idea what the log function is.
__
a) The domain is all positive numbers: (0, ∞).
b) The range is all real numbers: (-∞, ∞). (The vertical translation downward by 5 units does not change that.)
c) There is a vertical asymptote where the argument of the log function is zero: at x=0.
