Answer:
- zeros are {-2, 3, 7} as verified by graphing
- end behavior: f(x) tends toward infinity with the same sign as x
Step-by-step explanation:
A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.
<h3>Zeros</h3>
The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.
<h3>End behavior</h3>
The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.
- x → -∞; f(x) → -∞
- x → ∞; f(x) → ∞
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<em>Additional comment</em>
The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.
We know the x^2 coefficient is the opposite of the sum of the zeros:
-(7 +(-2) +3) = -8 . . . . x^2 coefficient
And we know the constant is the opposite of the product of the zeros:
-(7)(-2)(3) = 42 . . . . . constant
These checks lend further confidence that the zeros are those given.
(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)
( x - a)^2 + (y - b)^2 = r^2
where (a,b) is the center of the circle and r = radius.
so the answer is
( x - 2)^2 + (y - 3)^2 = 16
Answer:
d. -Sample selection was random
-Individual observations are independent of each other
np≥10
Step-by-step explanation:
a. The point estimate of a sample proportion is obtained using the formula;
Hence, the point estimate of the proportion of the population is 0.2877
b. The desired margin of error is the calculated using the point estimate value as follows:
Hence, the desired margin of error for the sample proportion is 0.0263
c. Given a confidence level of 95%, the confidence interval can be calculated as:
Hence, the confidence interval at 95% confidence level is 0.2614<p<0.3140
#We are 95% confident that the interval estimate contains the desired proportion.
d. The assumptions are:
-The sample size is is more than 10 or equal to 10:
-The selection was from a randomized experiment.
-The individual observations were independent of each other.
Well, you distribute the 8 to both terms since it is being multiplied.
8 * y = 8y
8 * 3 = 24
so the ending equation should be 8y + 24