Answer:
the rate of change in volume is dV/dt = 4π mm³/s = 12.56 mm³/s
Step-by-step explanation:
since the volume V of a cylinder is related with the height H and the radius R through:
V = πR²*H
then the change in time is given by the derivative with respect to time t
dV/dt = (∂V/∂R)*(dR/dt) + (∂V/∂H)*(dH/dt)
the change in volume with radius at constant height is
(∂V/∂R) = 2*πR*H
the change in volume with height at constant radius is
(∂V/∂H) = πR²
then
dV/dt = 2π*R*H *(dR/dt) + πR²*(dH/dt)
replacing values
dV/dt = 2π* 2 mm * 20 mm * (-0.1 mm/s) + π (2 mm) ²* 3 mm/s = 4π mm³/s
dV/dt = 4π mm³/s = 12.56 mm³/s
Answer:
The 95 percent confidence interval for the mean of the population from which the study subjects may be presumed to have been drawn is (19.1269, 32.6730).
Step-by-step explanation:
Intern No. of Breast
Number Exams Performed X²
1 30 900
2 40 1600
3 8 64
4 20 400
5 26 676
6 35 1225
7 35 1225
8 20 400
9 25 625
<u>10 20 400 </u>
<u> </u><u> ∑ 259 ∑ 7515</u>
Mean= X`= ∑x/n= 259/10= 25.9
Variance = s²= 1/n-1[∑X²- (∑x)²/n]
= 1/0[7515- (259)²/10]= 1/9[7515- 6708.1]
= 806.9/9=89.655= 89.66
Standard Deviation= √89.655= 9.4687
Hence
The value of t with significance level alpha= 0.05 and 9 degrees of freedom is t(0.025,9)= 2.262
The 95 % Confidence interval is given by
x`±t(∝,n-1) s/√n
So Putting the values
25.9± 2.262( 9.4687/√10)
= 25.9 ±2.262 (2.9943)
= 25.9 ± 6.7730
= 25.9 +6.7730=32.6730
25.9 -6.7730= 19.1269
= 19.1269, 32.6730
The 95 percent confidence interval for the mean of the population from which the study subjects may be presumed to have been drawn is (19.1269, 32.6730).
Answer:
1.99385kg of chicken was eaten.
Step-by-step explanation:
We first need to know how many grams were left in kilograms, so we can find the difference.
Unit conversion: 6.15g x 1kg/1000g = 0.00615kg
Eaten amount of chicken: 2kg - 0.00615kg = 1.99385kg
Hungry family, I suppose...