Answer:
The water level rising when the water is 4 inches deep is .
Step-by-step explanation:
Rate of water pouring out in the cone = R=
Height of the cup = h = 6 inches
Radius of the cup = r = 3 inches
r = h/2
Volume of the cone =
h = 4 inches
The water level rising when the water is 4 inches deep is .
Answer:
a) Failed to reject the null hypothesis (P-value=0.09).
b) The 95% CI for the difference in proportions is:
Step-by-step explanation:
a) We have to perform a hypothesis test for the difference of proportions.
The null and alternative hypothesis are:
The significance level is 0.05.
The proportion of the passenger cars owners is:
The proportion of commercial truck owners is:
The weigthed average p is
The estimated standard deviation is
We can calculate the z-value as:
The P-value for z=-1.362 is P=0.0866.
The P-value (0.09) is greater than the significance level (0.05), so it failed to reject the null hypothesis. There is no enough evidence to prove that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
b) We can construct a 95% CI, according to the significance level of 0.05.
The z-value for this CI is 1.96.
We have to recalculate the standard deviation:
The lower limit is then:
The upper limit is:
The 95% CI for the difference in proportions is:
In this case, we can conclude that the difference between the proportions, with 95% confidence, can still be equal or greater than zero, meaning that it is possible passenger car owners violate laws more than truck owners.
The student's statement about area is incorrect because by joining suitable lines, we can divide the region into 3 rectangles and we can find its area.
Please check the attached figure.
From the figure, we can easily observe that the area of the shaded region = Area of the rectangle A + Area of the rectangle B - Area of the rectangle C.
