Answer:
To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.
Step-by-step explanation:
As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.
To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:
dfdx=4x−3
f(b)−f(a)b−a=f'(c)
f(x)x=0=1
f(x)x=2=3
Hence:
3−12=4c−3
and c=1.
Answer:
The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
An experimenter flips a coin 100 times and gets 59 heads.
This means that 
98% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).
The unit rate for the nearest cent per once for each size is 0.24 : 0.19
Answer:
mass=180kg and the volume=6m³.
then the formula to find density is= mass/volume
using this formula,180kg/6m³=30kg/m³
A geometric figure enclosed by a circle is called an inscribed figure.
