This is a true statement.
Consider two events A and B. We say they are complementary if P(A)+P(B) = 1
This means that either event A or event B must happen, since the "1" represents 100% probability. Having a probability of 100% means absolute certainty.
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Example:
A = the event it rains
B = the event it does not rain
P(A) = 0.30 = 30% chance of rain
P(B) = 0.70 = 70% chance it does not rain
P(A)+P(B) = 0.30+0.70 = 1
So this shows the two events are complementary.
The solution to the algebraic equation, −0.4x − 3.1 = 5.9, is:<u> x = -22.5</u>
Given the algebraic equation, −0.4x−3.1 = 5.9, to solve for x, follow the steps below:
−0.4x − 3.1 = 5.9
−0.4x − 3.1 + 3.1 = 5.9 + 3.1
-0.4x = 9
- Divide both sides by -0.4
-0.4x/-0.4 = 9/-0.4
x = -22.5
Therefore, the solution to the algebraic equation, −0.4x − 3.1 = 5.9, is:<u> x = -22.5</u>
<u></u>
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Answer:
The18th term of the given sequence is -128
Explanation:
To find the 18th term of the sequence:
42, 32, 22, 12, ..., we need to find the nth term of the sequence first.
The nth term of a sequence is given be the formula:

Where a is the first term, and d is the common difference.
Here, a = 42, d = 32 - 42 = -10

To find the 18th terem, substitute n = 18 into the nth term
Answer:
Plot the line y = 2x - 3 and the portion above the line will satisfy the inequality.
Given:
Consider the pentagon MVEDR is dilated with the origin as the center of dilation using the rule
to create pentagon M'V'E'D'R'.
To find:
The correct statement.
Solution:
If a figure dilated by factor k, then the rule of dilation is

Here,
If k>1, then the image is larger than the original figure.
If k<1, then the image is smaller than the original figure.
We have,

Here, M'V'E'D'R' is image and MVEDR is original figure. The scale factor is

Pentagon M'V'E'D'R' is smaller than pentagon MVEDR because the scale factor is less than 1.
Therefore, the correct option is B.