Answer:
Step-by-step explanation:

(One tailed test at 5% significance level)
Sample size =200 and sample proportion =
Std error of p = 
Test statistic = p diff/std error = -2.89
p value = 0.001926
So we reject H0 and accept alternate hypothesis.
Got your answer.
I drew it out on a digital drawing software I have.
Answer:
see explanation
Step-by-step explanation:
The vertex form of f(x) is
f(x) = (x - h)² + k
where (h, k) are the coordinates of the vertex
To obtain this form use the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 14x
f(x) = x² + 2(7)x + 49 - 49 + 36
= (x + 7)² - 13
The minimum value of f(x) is the y- coordinate of the vertex
vertex = (- 7, - 13), that is minimum value = - 13
Answer:
4
Step-by-step explanation:
Given that 


Now,


This can be written as
[as
]

[ by using equation (i)]
=4
Hence, 
Answer:
12+4x
Step-by-step explanation: