If 64ᵃ⁺ᵇ = 32 ᵃ⁺²ᵇ, then a=?
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Answer: The margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.
Step-by-step explanation:
Since we have given that
Sample size = 400
Mean = $357.75
Standard deviation = $37.89
At 95% confidence level, z = 1.96
We first find the margin of error.
Margin of error is given by
95% confidence interval would be
Hence, the margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.
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).