Answer:
m = 18
Step-by-step explanation:
Given :
=> -15 is a root of the polynomial
=> It is a zero to the solution.
Process :
Substitute -15 in place of x.
=> (-15)² + (-15)m + 45 = 0
=> 225 + 45 - 15m = 0
=> 15m = 270
=> m = 270/15
=> m = 18
Answer:
1. 8.19, 2. 25.96, 3. 3.95
Step-by-step explanation:
use soh cah toa
1. cos is adjacent/hypotenuse
cos73=x/28
multiply both sides by 28
28cos73=x=8.186
2. sin is opposite over hypotenuse
sin68=x/28
multiply both sides by 28
28sin68=x=25.961
3. sin is opposite over hypotenuse
sin26=x/9
myltiply both sides by 9
9sin26=x=3.945
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)
