4 is the greatest common factor of 32 and 44
Answer:
Step-by-step explanation:
The angles (2x- 10) and (4x+ 16) are consecutive interior angles and therefore are corresponding
<u>Corresponding angles sum to 180</u>
- (2x - 10) + (4x + 16) = 180
- 6x + 6 = 180
- 6x = 174
- x = 174/6
- x = 29
Answers:
- (a) Independent
- (b) Dependent
- (c) Dependent
- (d) Independent
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Explanation:
If events A and B are independent, then the two following equations must both be true
- P(A | B) = P(A)
- P(B | A) = P(B)
This is because the conditional probability P(A|B) means "P(A) when B has happened". If B were to happen, then P(A) must be the same as before. In other words, event B does not affect A, and vice versa.
For part (a), we have P(B) = 1/4 and P(B|A) = 1/4 showing that P(B|A) = P(B) is true, and therefore we can say the events are independent. We don't need the info that P(A) = 1/8.
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Unlike part (a), part (b) has the answer "dependent" because P(A) = 1/8 and P(A | B) = 1/3 differ in value. Event A starts off at probability 1/8, but then event B occurring means P(A) gets increased to 1/3. The prior knowledge about B changes the chances of A. The P(B) = 1/5 is unneeded.
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If A and B were independent, then,
P(A and B) = P(A)*P(B)
However,
P(A)*P(B) = (1/4)*(1/5) = 1/20
which is not the same as P(A and B) = 1/6. Therefore the two events are dependent.
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Refer back to part (a)
P(A) = 1/4 and P(A|B) = 1/4 are identical in value, so P(A|B) = P(A) which leads to the events being independent. Whether we know event B happened or not, it does not affect the outcome of event A. P(B) = 1/9 is unneeded.
Answer:
a/c=2/7 u are welcome thanks for ur help
Answer: 2.325 meters
Step-by-step explanation:
The roof of a lean-to-garden shed has a gradient of 0.35.find the height....they have given the base as 1.5m and a shorter height 1.8m its like a house
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It sounds like you have a right triangle with base = 1.5,
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Use a proportion to get:
(height of that triangle)/1.5 = 35/100
height of that triangle = 1.5*0.35 = 0.5250
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greater height of the lean-to = 1.8 + 0.5250 = 2.325 meters
