Short Answer x = - 6
Remark
You gave the second best answer.
The trick here is not to divide both sides by 2. Solve the problem this way.
log_5(x + 1)^2 = 2 Take the antilog of both sides
(x + 1)^2 = 5^2 Expand the equation
x^2 + 2x + 1 = 25 Subtract 25 from both sides.
x^2 + 2x - 24 = 0 Factor
(x + 6)(x - 4) = 0 Find the zeros.
x + 6 = 0
x = - 6 <<<<<<<< Answer. This is the extraneous root.
The reason this is an extraneous root is that x<=0 do not have a logarithem
x - 4 = 0
x = 4 This is a legitimate result to the original equation.
Answer: u= ( 4342.08, 5145.92).
Step-by-step explanation: the population mean is estimated using the sample by the formulae assuming a 95% confidence level
u = x' + Zα/2 * (√σ/n) or x' - Zα/2 * (√σ/n)
u = estimated population mean
x' = sample mean = 4744
n = sample size =8
σ = sample standard deviation. = 580
α = level of significance = 1- confidence level = 1-0.95= 0.05
Zα/2 = z score from the normal distribution table for a 2 tailed test = 1.96
First boundary value for interval
u = 4744 + 1.96 ( 580/√8)
u = 4744 + 1.96 * (205.0609)
u = 4744 + 401.92
u = 5145.92
Second boundary value for interval
u = 4744 - 1.96 ( 580/√8)
u = 4744 - 1.96 * (205.0609)
u = 4744 - 401.92
u = 4342.08
Thus the confidence interval for population mean is
u= ( 4342.08, 5145.92).
Less than 3 is about 10.75% and greater than 13 is about 6.18%.
To find these percents, you need to find the z-score for each value. Then, use your table to find the correct percent. Be sure to find the side above 13 when you use your chart.
For less than 3:
(3 - 7.45) / 3.6 = -1.24 = The percent below this is 0.1075
For greater than 13:
(13 - 7.45) / 3.6 = 1.54 = The percent above this is 0.0618
Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well.
<span>When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6, and so forth. Since we know angle 1 = angle 5, so from that you can see that r and s are parallel</span>
