List the possible rational zeros for each function.
2 answers:
9514 1404 393
Answer:
- {±1/2, ±1, ±3/2, ±2, ±3, ±9/2, ±6, ±9, ±18}
- {±1, ±2, ±3, ±4, ±6, ±8, ±12 ±24}
- -2, -1, 2
- -4, 1, 2
Step-by-step explanation:
Possible rational zeros are of the form ...
±{divisor of the constant term}/{divisor of the leading coefficient}
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1. Rational zeros will be one of ±{1, 2, 3, 6, 9, 18}/{1, 2}, so will be ...
{±1/2, ±1, ±3/2, ±2, ±3, ±9/2, ±6, ±9, ±18}
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2. Rational zeros will be one of {±1, ±2, ±3, ±4, ±6, ±8, ±12 ±24}.
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3. The pairs of coefficients suggest factoring by pairs:
f(x) = (2x^3 +2x^2) -(8x +8) = 2x^2(x +1) -8(x +1) = 2(x^2 -4)(x +1)
f(x) = 2(x -2)(x +2)(x +1)
Zeros of f(x) are 2, -2, -1, values of x that make the factors zero.
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4. The sum of coefficients is zero, so x=1 is a zero. Factoring that out by any of several means, you find ...
f(x) = (x -1)(x^2 +2x -8)
The quadratic is factored by looking for factors of -8 that have a sum of 2. (4 and -2 are those)
f(x) = (x -1)(x +4)(x -2)
Zeros of f(x) are 1, -4, 2.
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The attached graph confirms our factoring of the polynomials of questions 3 and 4. For cubic and higher degree, I find a graphing calculator to be quite helpful finding zeros.
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Answer:
a) The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
b) The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
c) The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
d) A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.
Step-by-step explanation:
<em>a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000?</em>
For college graduates in business, the salary distributes normally with mean salary of $53,901 and standard deviation of $15,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
<em>b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000?</em>
<em />
For college graduates in health sciences, the salary distributes normally with mean salary of $51,541 and standard deviation of $11,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
<em>c. What is the probability that a new college graduate in health sciences will earn a starting salary less than $40,000?</em>
To calculate the probability of earning less than $40,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
<em />
<em>d. How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences?</em>
The z-value for the 1% higher salaries (P>0.99) is z=2.3265.
The cut-off salary for this z-value can be calculated as:
A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.
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