15. Suppose a car gas tank holds 21 gallons of gas. On a trip it uses 2/3 of a tank of gas on a trip. Then it uses 1/3 of what i
1 answer:
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<h2>Steps:</h2>
So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:
Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:
Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:
Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:
Now you can rewrite it as:
Next, multiply:
Next, divide:
And lastly, simplify:
- A good tip:
<u>The correct option is C. x² + 4x + 4.</u>
Answer:
And we can use the following excel code to find the answer: "=NORM.DIST(-0.704,0,1,TRUE)"
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable of interest for a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
And we can use the following excel code to find the answer: "=NORM.DIST(-0.704,0,1,TRUE)"