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)
F should be -1, 6
E should be -4, 2
D should be -4, 9
Answer:
f(-1) = 3
General Formulas and Concepts;
<u>Pre-Alg</u>
- Order of Operations: BPEMDAS
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 9(3)ˣ
x = -1
<u>Step 2: Solve</u>
- Substitute: f(-1) = 9(3)⁻¹
- Evaluate: f(-1) = 9(1/3)
- Multiply: f(-1) = 9/3
- Divide: f(-1) = 3
Answer:
x=45
Step-by-step explanation:
add (3x-9)+30+24=180
subtract 30 and 24 from both sides
(3x-9) = 126
+9 on both sides
3x=135
divide by 3 on both sides
x=45
Answer:
f(x) has moved:
4 units in the positive y direction i.e upwards
3 units in the positive x direction
Step-by-step explanation:
to get g(x), f(x) has undergone the following transformations
f(x) = x³
f1(x) = x³ + 4 (translation of 4 units in the positive y direction i.e upwards)
f2(x) = g(x) = (x-3)³ + 4 (translation of 3 units in the positive x direction i.e towards the right)
