(- 5, - 6 )
for x- coordinate x + 5 = 0 ⇒ x = - 5
given f(x) ± c , the value of c translates the graph vertically up/down by ± c
here c = - 6 , thus graph is shifted down by - 6
thus the vertex = (- 5, - 6)
Answer:
f(x) = 3x(x-1)(x-3)
Step-by-step explanation:
f(x) = 3x³-12x²+9x = 3x(x²-4x+3) =
= 3x(x²-x-3x+3) = 3x[x(x-1)-3(x-1)] =
= 3x[(x-1)(x-3)] = 3x(x-1)(x-3)
Answer:
(a) The sampling distribution of
= Population mean = 79
(b) P (
greater than 81.2 ) = 0.1357
(c) P (
less than or equals 74.4 ) = .0107
(d) P (77.6 less than
less than 83.2 ) = .7401
Step-by-step explanation:
Given -
Sample size ( n ) = 81
Population mean
= 79
Standard deviation
= 18
(a) Describe the sampling distribution of ![\overline{X}](https://tex.z-dn.net/?f=%5Coverline%7BX%7D)
For large sample using central limit theorem
the sampling distribution of
= Population mean = 79
(b) What is Upper P (
greater than 81.2 ) =
= ![P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}> \frac{81.2 - 79}{\frac{18}{\sqrt{81}}})](https://tex.z-dn.net/?f=P%28%5Cfrac%7B%5Coverline%7BX%7D%20-%20%5Cnu%20%7D%7B%5Cfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D%7D%3E%20%5Cfrac%7B81.2%20-%2079%7D%7B%5Cfrac%7B18%7D%7B%5Csqrt%7B81%7D%7D%7D%29)
= ![P(Z> 1.1)](https://tex.z-dn.net/?f=P%28Z%3E%201.1%29)
= ![1 - P(Z< 1.1)](https://tex.z-dn.net/?f=1%20-%20P%28Z%3C%20%20%201.1%29)
= 1 - .8643 =
= 0.1357
(c) What is Upper P (
less than or equals 74.4 ) =
= ![P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{74.4- 79}{\frac{18}{\sqrt{81}}})](https://tex.z-dn.net/?f=P%28%5Cfrac%7B%5Coverline%7BX%7D%20-%20%5Cnu%20%7D%7B%5Cfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D%7D%5Cleq%20%20%5Cfrac%7B74.4-%2079%7D%7B%5Cfrac%7B18%7D%7B%5Csqrt%7B81%7D%7D%7D%29)
= ![P(Z\leq -2.3)](https://tex.z-dn.net/?f=P%28Z%5Cleq%20%20-2.3%29)
= .0107
(d) What is Upper P (77.6 less than
less than 83.2 ) =
= ![P(\frac{77.6- 79}{\frac{18}{\sqrt{81}}})< P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{83.2- 79}{\frac{18}{\sqrt{81}}})](https://tex.z-dn.net/?f=P%28%5Cfrac%7B77.6-%2079%7D%7B%5Cfrac%7B18%7D%7B%5Csqrt%7B81%7D%7D%7D%29%3C%20P%28%5Cfrac%7B%5Coverline%7BX%7D%20-%20%5Cnu%20%7D%7B%5Cfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D%7D%5Cleq%20%20%5Cfrac%7B83.2-%2079%7D%7B%5Cfrac%7B18%7D%7B%5Csqrt%7B81%7D%7D%7D%29)
= ![P(- 0.7< Z< 2.1)](https://tex.z-dn.net/?f=P%28-%200.7%3C%20Z%3C%20%20%202.1%29)
= ![(Z< 2.1) - (Z< -0.7)](https://tex.z-dn.net/?f=%28Z%3C%20%20%202.1%29%20-%20%28Z%3C%20%20%20-0.7%29)
= 0.9821 - .2420
= 0.7401
The total number of ribbons is 8 because 4 + 3 + 1 is 8
The number of green ribbons is 3
That means that 3 out of the 8 ribbons are green
Answer: 3/8