Answer:
Factorizing as the Difference of Two Squares
1. 144x2 - 49
Step-by-step explanation:
Where is the picture?
Answer:
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- <u><em>Yes, it is reasonable to expect that more than one subject will experience headaches</em></u>
Explanation:
Notice that where it says "assume that 55 subjects are randomly selected ..." there is a typo. The correct statement is "assume that 5 subjects are randomly selected ..."
You are given the table with the probability distribution, assuming, correctly, the binomial distribution with n = 5 and p = 0.732.
- p = 0.732 is the probability of success (an individual experiences headaches).
- n = 5 is the number of trials (number of subjects in the sample).
The meaning of the table of the distribution probability is:
The probability that 0 subjects experience headaches is 0.0014; the probability that 1 subject experience headaches is 0.0189, and so on.
To answer whether it <em>is reasonable to expect that more than one subject will experience headaches</em>, you must find the probability that:
- X = 2 or X = 3 or X = 4 or X = 5
That is:
- P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5).
That is also the complement of P(X = 0) or P(X = 1)
From the table:
- P(X = 0) = 0.0014
- P(X = 1) = 0.0189
Hence:
- 1 - P(X = 0) - P(X = 1) = 1 - 0.0014 - 0.0189 = 0.9797
That is very close to 1; thus, it is highly likely that more than 1 subject will experience headaches.
In conclusion, <em>yes, it is reasonable to expect that more than one subject will experience headaches</em>
Length of the rectangular patio = 12 1/2 feet
= 25/2 feet
Area of the rectangular patio = 103 1/8 square feet
= 825/8 square feet
Let us assume the width of the rectangular patio = x feet
Then
Area of the rectangular patio = Length * Width
825/8 = (25/2) * x
25x/2 = 825/8
25x = (825 * 2)/8 feet
25x = 825/4 feet
x = 825/(4 * 25) feet
= 33/4 feet
= 8 1/4 feet
So the width of the rectangular patio is 8 1/4 feet. I hope the procedure is clear enough for you to understand.
If the two triangles are congruent it means that their side lengths are equal, so we can assume that x = 3x - 8 and so 2x = 8 and x = 4. Hope that helps :)
Answer: D. (4,3)
The x coordinates of A and B are 9 and -1 in that order. Add them up to get 9+(-1) = 9-1 = 8. Then divide by two to end up with 8/2 = 4. The midpoint has an x coordinate of 4.
Repeat for the y coordinates. Add them up: 8+(-2) = 8-2 = 6. Then divide by two: 6/2 = 3. The midpoint has an y coordinate of 3.
Those two coordinates pair up to get (x,y) = (4,3) which is the midpoint of segment AB.
