m < 1 = 130°
m < 1 = 130°m < 2 = 50°
We know this is a linear pair, therefore the two angles must add up to 180°
Combine like terms
Isolate the variable
Plug in 26 for x in both of the individual angle equations.
A good way to check if we did this correctly, is to add up the two angles. Because 180 + 50 = 180, we did this correctly.
I hope this helped. Let me know if you have any questions!
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)
0.5^6 = 0.0156
Assuming an unbiased coin.
Answer:
Step-by-step explanation:
Function f(x)=|x| is transformed to create function g(x)=|x+4|+3. What transformations are performed to function f to get function g? Select each correct answer.
Function f is translated 4 units to the right.
Function f is translated 3 units to the left.
Function f is translated 4 units down.
(this one is correct) Function f is translated 3 units up.
Function f is translated 4 units up.
(this one is correct) Function f is translated 4 units to the left.
Function f is translated 3 units to the right.
Function f is translated 3 units down.
