Analyze the polynomial function f(x)equalsnegative 4 (x plus 3 )(x minus 4 )cubed using parts (a) through (e).a) Determine th
1 answer:
Answer:
a) f(x) tends to minus infinity
b) (0,768) is the y-intercept, (4,0) and (-3,0) are the x-intercepts.
Step-by-step explanation:
Our function is a polynomial of degree 4.
a) The monomial with highest degree determines the behavior of f(x) when x tends to infinity and when x tends to -infinity. This monomial is -4x⁴. Without expanding completely, (x-4)³ has x³ as a summand, which multiplies with -4x from the first factor, to give -4x⁴. When x goes to infinity (or minus infinitive), x²=(x²)² is positive (nonzero squares are always positive) thus -4x² is negative, and f(x) tends to minus infinity.
b). To find the y-intercept, we compute (0,f(0)). Since f(0)=-4(3)(-4)³=768, then (0,768) is the point of the y-intercept.
For the x-intercept, solve f(x)=0. f(x)=0 has the solutions x=-3 and x=4. In this case, the x-intercept is in both x=0 and x=4. Then (-3,0) and (4,0) are x-intercepts.
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Answer:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.
Step-by-step explanation:
Data given and notation
represent the number with no defects in sample 1
represent the number with no defects in sample 1
sample 1
sample 2
represent the proportion of number with no defects in sample 1
represent the proportion of number with no defects in sample 2
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference in the the two proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
Since is a two sided test the p value would be:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.