Answer:
95% confidence interval for the difference between the average mass of eggs in small and large nest is between a lower limit of 0.81 and an upper limit of 2.39.
Step-by-step explanation:
Confidence interval is given by mean +/- margin of error (E)
Eggs from small nest
Sample size (n1) = 60
Mean = 37.2
Sample variance = 24.7
Eggs from large nest
Sample size (n2) = 159
Mean = 35.6
Sample variance = 39
Pooled variance = [(60-1)24.7 + (159-1)39] ÷ (60+159-2) = 7619.3 ÷ 217 = 35.11
Standard deviation = sqrt(pooled variance) = sqrt(35.11) = 5.93
Difference in mean = 37.2 - 35.6 = 1.6
Degree of freedom = n1+n2 - 2 = 60+159-2 = 217
Confidence level = 95%
Critical value (t) corresponding to 217 degrees of freedom and 95% confidence level is 1.97132
E = t×sd/√(n1+n2) = 1.97132×5.93/√219 = 0.79
Lower limit = mean - E = 1.6 - 0.79 = 0.81
Upper limit = mean + E = 1.6 + 0.79 = 2.39
95% confidence interval for the difference in average mass is (0.81, 2.39)
Answer:
scale factor 3 is the answer.
Step-by-step explanation:
Length = 18 in
Breadth = 3 in
height = 10 in
Volume of cuboid = l × b × h
V = 18 × 3 × 10
V = 540 in³
540 in³ is the original volume. The volume needs to be tripled, so multiply the original volume with 3
V = 540 × 3 = 1620 in³
∴ 1620 in³ will be the new volume if it's tripled and the scale factor is 3.
Part a: Option D 18 feet per second
Part b: increasing
Solution:
Height 
Part a: To find the average rate of change for h(t) between t = 0 and t = 2.
Substitute t = 0 in h(t).
h(0) = 3
Substitute t = 2 in h(t).
h(2) = 39
Average rate of change formula:
Here, a = 0 and b = 2.
= 18
Average rate of change = 18 feet per second
Option D is the correct answer.
Part b:
This means height of the ball is increasing for 0 < x < 2.
X2+y2–x–2y–11/4=x2−x+14−14+y2−2y+4−4−11/4=(x−12)2+(y−2)2−14−4−114=(x−12)2+(y−2)2−7=0(x−12)2+(y−2)2=(7√)2
Center(1/2 ,2)
radius = \sqrt 7
Answer:
64000
Step-by-step explanation:
