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)
Jackets = 3
Shirt = 6
Ties = 8
Pants = 4
Number of combination = 3 x 6 x 8 x 4 = 576
Answer: There are 576 possible combinations.
Answer:
X is 50
Step-by-step explanation:
Answer:
Option B
Step-by-step explanation:
![(q + p)q = (s + r)s](https://tex.z-dn.net/?f=%28q%20%2B%20p%29q%20%3D%20%28s%20%2B%20r%29s)
Lets open the brackets of L.H.S.
![=> q^2 + pq = (s+ r)s](https://tex.z-dn.net/?f=%3D%3E%20q%5E2%20%2B%20pq%20%3D%20%28s%2B%20r%29s)
Lets substract q² from both the sides.
![=> q^2 + pq - q^2 = (s + r)s - q^2](https://tex.z-dn.net/?f=%3D%3E%20q%5E2%20%2B%20pq%20-%20q%5E2%20%3D%20%28s%20%2B%20r%29s%20-%20q%5E2)
![=> pq = (s + r)s - q^2](https://tex.z-dn.net/?f=%3D%3E%20pq%20%3D%20%28s%20%2B%20r%29s%20-%20q%5E2)
Lets divide both the sides by q.
![=> \frac{pq}{q} = \frac{(s + r)s - q^2}{q}](https://tex.z-dn.net/?f=%3D%3E%20%5Cfrac%7Bpq%7D%7Bq%7D%20%3D%20%5Cfrac%7B%28s%20%2B%20r%29s%20-%20q%5E2%7D%7Bq%7D)
![=> p = \frac{(s + r)s }{q} - \frac{q^2}{q} = \frac{(s + r)s}{q} - q](https://tex.z-dn.net/?f=%3D%3E%20p%20%3D%20%5Cfrac%7B%28s%20%2B%20r%29s%20%7D%7Bq%7D%20-%20%5Cfrac%7Bq%5E2%7D%7Bq%7D%20%3D%20%5Cfrac%7B%28s%20%2B%20r%29s%7D%7Bq%7D%20-%20q)
Answer: me + u is us
Step-by-step explanation: