8x - 3y = 24
y-intercept ⇒ x = 0
subtitute
8 · 0 - 3y = 24
-3y = 24 |divide both sides by (-3)
y = -8
The volume of the cylinder is 4710 cubic inches
Step-by-step explanation:
Volume of the cone = 1570 cubic inches
Volume of cone = 1/3(volume of the cylinder)
So,
Volume of the cylinder = 3(volume of the cone)
Volume of the cylinder = 3(1570)
= 4710 cubic inches
The volume of the cylinder is 4710 cubic inches
Answer:
95% confidence interval for the mean number of months is between a lower limit of 6.67 months and an upper limit of 25.73 months.
Step-by-step explanation:
Confidence interval is given as mean +/- margin of error (E)
Data: 5, 15, 12, 22, 27
mean = (5+15+12+22+27)/5 = 81/5 = 16.2 months
sd = sqrt[((5-16.2)^2 + (15-16.2)^2 + (12-16.2)^2 + (22-16.2)^2 + (27-16.2)^2) ÷ 5] = sqrt(58.96) = 7.68 months
n = 5
degree of freedom = n-1 = 5-1 = 4
confidence level (C) = 95% = 0.95
significance level = 1 - C = 1 - 0.95 = 0.05 = 5%
critical value (t) corresponding to 4 degrees of freedom and 5% significance level is 2.776
E = t×sd/√n = 2.776×7.68/√5 = 9.53 months
Lower limit of mean = mean - E = 16.2 - 9.53 = 6.67 months
Upper limit of mean = mean + E = 16.2 + 9.53 = 25.73 months
95% confidence interval is (6.67, 25.73)
Answer:
<R = 158
Step-by-step explanation:
Supplementary angles equal 180 degrees.
<Q + <R =180
22 + <R = 180
Subtract 22 from each side
22-22 + <R = 180-22
R = 158
