Answer:
99% confidence interval for the population average examination score is between a lower limit of 69.2872 and an upper limit of 82.7128.
Step-by-step explanation:
Confidence interval = mean +/- margin of error (E)
mean = 76
variance = 144
sd = sqrt(variance) = sqrt(144) = 12
n = 25
degree of freedom (df) = n - 1 = 25 - 1 = 24
confidence level (C) = 99% = 0.99
significance level = 1 - C = 1 - 0.99 = 0.01 = 1%
t-value corresponding to 24 df and 1% significance level is 2.797
E = t×sd/√n = 2.797×12/√25 = 6.7128
Lower limit = mean - E = 76 - 6.7128 = 69.2872
Upper limit = mean + E = 76 + 6.7128 = 82.7128
99% confidence interval is (69.2872, 82.7128)
12k-1 is the simplified answer
Answer:

Step-by-step explanation:
Given

Let the roots be
and 
So:

Required
Determine the relationship between d, c and p

Divide through by d


A quadratic equation has the form:

So:


So, we have:
-- (1)
and
-- (2)
Make
the subject in (1)


Substitute
in (2)


Multiply both sides by d


Cross Multiply

or

Hence, the relationship between d, c and p is: 
Answer:
2/3 > x
Step-by-step explanation:
0.5 > 0.75x
2/3 > x