Answer:
x = -1
Step-by-step explanation:
Given the point, (-1, 2), and that the slope is <u><em>undefined</em></u>.
The standard linear equation of vertical lines is <em>x</em> =<em> a</em>, where the x-intercept is (<em>a</em>, 0), and the slope is undefined because all points on the line have the same x-coordinate. Attempting to solve for the slope of a vertical line using the slope formula, m = (y₂ - y₁)/(x₂ - x₁), will result in a mathematical operation of <u>division by zero</u> (which is an <em>undefined operation</em>).
Since the slope is <u>undefined</u>, then it is <u>not possible</u> to create a linear equation in either the slope-intercept form, or point-slope form.
Therefore, the equation of a vertical line given the point, (-1, 2) is <em>x</em> = -1.
Answer:
A) The relative frequencies in the table are reasonably close; C) The relative frequency of rolling an even number is 0.51.
Step-by-step explanation:
The relative frequencies given are at most 0.02 apart. This means they are reasonably close.
The theoretical probability for each outcome would be 1/4, or 0.25; this means the theoretical probability of rolling an even number would be 0.50, not 0.51.
However, the relative frequency of rolling an even number would be 0.24+0.27 = 0.51.
Since the relative frequencies are reasonably close, the number cube is likely to be fair.
Answer:
B and D
Step-by-step explanation:
B:
Anything to a negative power means that it is 1/that to the positive power.
E.g. x^-1 = 1/x^1
In other words, anything to the power of a negative switches sides of a fraction (i.e. if in numerator moves to denominator and vice versa.)
1/x^-1 = 1/1/x^1 which is just equal to x, because there are x number of 1/xs in one (1/x * x =1) Therefore Option B is equal to just x.
D: (assuming the first given term is x^1/3 and not X1/3 (?) Correct me if I'm wrong).
x^1/3 * x^1/3 * x^1/3 is also equal to just x.
This is because when multiplying together terms with the same base (x in this case) the exponents just add together, so:
x^1/3 * x^1/3 * x^1/3 = x^(1/3 +1/3 +1/3) = x^1 = x.
Therefore B and D are equivalent because they both equal x.
Hope this helped!
Answer:
The statement, (1- <em>α</em>)% confidence interval for (μ₁ - μ₂) does not contain zero is TRUE.
Step-by-step explanation:
The hypothesis for a test is defined as follows:
<em>H</em>₀: μ₁ = μ₂ vs. <em>H</em>ₐ: μ₁ ≠ μ₂
It is provided that the test was rejected st the significance level <em>α</em>%.
If a decision is to made using the confidence interval the conditions are:
If the null hypothesis value is not included in the (1 - <em>α</em>)% confidence interval then the null hypothesis will be rejected and vice versa.
In this case the null hypothesis value is:
<em>H</em>₀: μ₁ - μ₂ = 0.
If the value 0 is not included in the (1 - <em>α</em>)% confidence interval for the difference between two means, then the null hypothesis will be rejected.
Thus the statement, (1- <em>α</em>)% confidence interval for (μ1- μ2) does not contain zero is TRUE.
