Answer:
12 the answer
Step-by-step explanation:
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:
A.
Step-by-step explanation:
(9x + 5) - (4x+3) = 0
9x - 4x + 5 - 3 = 0
5x + 2 = 0
5x = -2
5x/5 = -2/5
x= -2/5
solution is (x, y ) → (- 1, 4 )
y + 2x = 2 → (1)
y + 4x = 0 → (2)
subtract equation (1) from (2) to eliminate term in y
(y - y ) + (4x - 2x ) = (0 - 2 )
2x = - 2 ( divide both sides by 2 )
x = - 1
substitute x = - 1 in either (1) or (2) and solve for y
(1) → y - 2 = 2 ( add 2 to both sides )
y = 4
solution is (x, y ) → (- 1, 4 )
