<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis
(???, 0): 0 = - ln (x - 4)

0 = ln (x - 4)

1 = x - 4
<u> +4 </u> <u> +4 </u>
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)

1 = ln (x - 4)

e = x - 4
<u> +4 </u> <u> +4 </u>
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
<u> +4 </u> <u>+4 </u>
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
*************************************************************************
transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
f(x) = - 3ˣ⁺⁵
= - 3⁰⁺⁵
= - 3⁵
= -243
Horizontal Asymptote: y = 0 <em>(explanation above)</em>
Answer:
a. Z = 2.6667
b.
c. Upper limit = 3.39
Step-by-step explanation:
Part a
We are given
Population mean = 3
Population standard deviation = 0.3
Sample mean = 3.2
Sample size = n = 16
Level of significance = 0.05
Null hypothesis: H0: µ = 3
Alternative hypothesis: Ha: µ > 3
The test statistic formula is given as below:
Z = (sample mean – population mean) / [SD / sqrt(n)]
Z = (3.2 – 3)/[0.3/sqrt(16)]
Z = 2.6667
Part b
Type I error is the probability of rejecting the null hypothesis that the population mean is 3 ppm when actually it is 3 ppm. Type II error is the probability of do not rejecting the null hypothesis that the population mean is 3 ppm when actually it is exceeding 3 ppm. Type II error is the serious in this scenario.
Part c
We are given
Population mean = 3
Population standard deviation = 0.3
Sample mean = 3.2
Sample size = n = 16
Confidence level = 90%
Critical z value = 2.3263
Formula is given as below:
Lower limit =sample mean – z*SD/sqrt(n)
Upper limit = sample mean + z*SD/sqrt(n)
Lower limit = 3.2 – 2.5758*0.3/sqrt(16)
Lower limit = 3.01
Upper limit = 3.2 + 2.5758*0.3/sqrt(16)
Upper limit = 3.39
JGL,LGJ, GJ, GL are the four angles
Answer:
36
Step-by-step explanation: