Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, -2 is the only other
1 answer:
Answer:
Step-by-step explanation:
we know that
2 is a zero of multiplicity 3 of the polynomial
so
we have that
x=2 is a solution of the polynomial
A factor of the polynomial is
----> is elevated to the cube because is a multiplicity 3
and the other solution is x=-2
since the polynomial is fifth degree, x=-2 must have a multiplicity 2
so
the other factor of the polynomial is
----> is squared because is a multiplicity 2
therefore
The polynomial is equal to multiply the factors by the leading coefficient
so
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Answer:
The confidence interval for the difference in proportions is
No. As the 95% CI include both negative and positive values, no proportion is significantly different from the other to conclude there is a difference between them.
Step-by-step explanation:
We have to construct a confidence interval for the difference of proportions.
The difference in the sample proportions is:
The estimated standard error is:
The z-value for a 95% confidence interval is z=1.96.
Then, the lower and upper bounds are:
The confidence interval for the difference in proportions is
<em>Can it be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group?</em>
No. It can not be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group, as the confidence interval include both positive and negative values.
This means that we are not confident that the actual difference of proportions is positive or negative. No proportion is significantly different from the other to conclude there is a difference.
Given that:
Parent equation :
Transformed function :
Solution:
Let Parent equation be . Then,
...(1)
The translation is defined as
.... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
, So graph of parent function compressed vertically by factor
.
, so the graph of parent function shifts 32 units right.
, so there is no vertical shift.
Therefore, the graph of parent function compressed vertically by factor and shifts 32 units right to get the graph of c(x).