A radar antenna, making one revolution every 5 seconds, is located on a ship that is 6 km from a straight shoreline. How fast is
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Answer:
(D)The midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of RP is 7, and the slope of SQ is Negative one-sevenths.
Step-by-step explanation:
- Point P is at (4, 2),
- Point Q is at (8, 5),
- Point R is at (5, 9), and
- Point S is at (1, 6)
Midpoint of SQ
Midpoint of PR
Now, we have established that the midpoints (point of bisection) are at the same point.
Two lines are perpendicular if the slope of one is the negative reciprocal of the other.
In option D
- Slope of RP =7
- Slope of SQ
Therefore, lines RP and SQ are perpendicular.
Option D is the correct option.
Answer:
1. A Venn diagram is attached. The amount of people that have health insurance and is confident about the economy is 287.
2. The amount of people that have health insurance and is not confident about the economy is 116.
3. The amount of people that have health insurance or is confident about the economy is 437.
Step-by-step explanation:
1) Using sets theory, we know:
U: 500 people surveyed
A: people who is confident in the economy
B: people that have health insurance
A' and B': people who is not confident in the economy and don't have health insurance.
A=321
B=403
A' and B' =63
In the attached picture we can see a Venn diagram that represents the situation. In order to obtain the intersection of both sets A∩B, we calculate:
(321 - x) + (403 - x) + x + 63 = 500
321 - x + 403 - x + x + 63 +x -500 = 500 +x - 500
321 + 403 + 63 -500 = x
x= 287
2) The amount of people that have health insurance and is not confident about the economy is given by the intersection of the complement of set A and set B:
A' ∩ B can be calculated as:
B - (A ∩ B)= 403 - 287= 116
3) The amount of people that have health insurance or is confident about the economy is given by:
(A∪B) = (A) + (B) - (A ∩ B)
(A∪B) = 321 + 403 - 287= 437
