Step-by-step explanation:
3(p2q + pq2 - pq) - 6pq + 3pq2 =
3[-20 × 2 + (-20) × 2 - (-20)] - 6 × (-20) + 3 × 2 × (-20) =
3[-40 + (-40) + 20] - 6 × (-20) + 3 × 2 × (-20) =
3(-40 - 40 + 20) - 6 × (-20) + 3 × 2 × (-20) =
3(-80 + 20) - 6 × (-20) + 3 × 2 × (-20) =
3 × (-60) - 6 × (-20) + 3 × 2 × (-20) =
-180 + 120 + 6 × (-20) =
-180 + 120 + (-120) =
-180 + 120 - 120 =
-60 - 120 = -180
Answer:
A 99% confidence interval will be wider than a 95% confidence interval
Step-by-step explanation:
From the question we are told that
The 95% confidence interval for for the mean foot length for students at the college is found to be 21.709 to 25.091 cm
Generally the width of a confidence interval is dependent on the margin of error.
Generally the margin of error is mathematically represented as
From the above equation we see that
Here is the critical value of the half of the level of significance and this value increase as the confidence level increase
Now if a 99% confidence level is used , it then means that the value of
will increase, this in turn will increase the margin of error and in turn this will increase the width of the confidence interval
Hence a 99% confidence interval will be wider than a 95% confidence interval
Answer:
The function touches the damping factor
at x= and x=
The x-intercept of f(x) is
at x=
Step-by-step explanation:
Given function is f(x)= and damping factor as y=
and y=
To find when function touches the damping factor:
For f(x)= and y=
Equating the both the equation,
x=
For f(x)= and y=
Equating the both the equation,
x=
Therefore, The function touches the damping factor x= and x=
To find x-intercept of f(x):
For x-intercept, y=0
f(x)=
y=
Hence, is always greater than zero.
Therefore,
x=
Thus,
The x-intercept of f(x) is at x=
