Answer:
1. Distributive property
2. Combine like terms
3. Addition property of equality
4. Division property of equality
Step-by-step explanation:
7x - ½ ( 8x+ 2 ) = 6 Distribute the -½
7x - 4x - 1 = 6 Combine like terms
3x - 1 = 6 Add 1 on both sides
3x = 7 Divide 3 on both sides
x = 7/3
Hello!
Given the rule of V(x, y) = (x, y - 1), we can determine that it might be a horizontal or vertical shift.
Since we know that x-values are domain and y-values are range, we know that the range of the function is decreasing by 1 (y - 1), so, the entire function is shifting down one unit.
Therefore, the type of transformation given by the rule is a vertical shift/translation downwards by one unit.
<u>Answer:</u>
The correct answer option is: True.
<u>Step-by-step explanation:</u>
Its true that if there is no linear equation to start with, you can isolate and substitute a variable that is squared in both the equation.
For example, for the given non linear equation, start by dividing both sides by coefficient of the variable.
Once you do that and isolate a variable, continue solving by substituting that variable into the other equation.
Answer: 4
<u>Step-by-step explanation:</u>
f(x) = 4x³ - x² + 1 g(x) = x - 1
g(2) = (2) - 1
= 1
f(1) = 4(1)³ - (1)² + 1
= 4 - 1 + 1
<h2> = 4</h2>
Answer: a. CI for the mean: 17.327 < μ < 26.473
b. CI for variance: 29.7532 ≤
≤ 170.9093
Step-by-step explanation:
a. To construct a 95% confidence interval for the mean:
The given data are:
mean = 21.9
s = 7.7
n = 12
df = 12 - 1 = 11
1 - α = 0.05
= 0.025
t-score =
= 2.2001
Note: since the sample population is less than 30, it is used a t-score.
The formula for interval:
mean ± 
Substituing values:
21.9 ± 2.200.
21.9 ± 4.573
The interval is: 17.327 < μ < 26.473
b. A 95% confidence interval for the variance:
The given values are:
= 
= 59.29
α = 0.05
= 0.025
= 0.975
= 21.92
= 3.816
Note: To find the values for
and
, look for them at the chi-square table
The formula to calculate interval:
(
)
are the lower and upper limits, respectively.
Substituing values:
(
)
(29.7532, 170.9093)
The interval for variance is: 29.7532 ≤
≤ 170.9093