80%, 1000-200 = 800/1000 or 80%
The coordinates of point B that divides the line in the ratio 1:3 is: ( C )(3.25, 2.75)
<h3>What is a line segment?</h3>
A line segment is formed by joining two points by a straight line.
Analysis:
The coordinates of point B(x,y) are gotten by the formula
x = 
y = 
where, x1 and y1 are coordinates of A and x2 and y2 are coordinates of B
are the values of the ratio p:q.
x1 = 4, x2 = 1 y1 = 5, y2 = 2, p = 1, q = 3
x = 
= 3.25
y = 
= 2.75
coordinates of B are ( 3.25, 2.75)
In conclusion, the coordinates of point B are (3.25, 2.75)
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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.
The value of the expression is one eight
<h3>How to solve the expression?</h3>
The expression is given as:
negative one fifth times the quantity 4 minus 14 times the quantity one fourth squared end quantity
Rewrite properly as:
-1/5 * (4 - 14) * (1/4)^2
Evaluate the difference
-1/5 * (-10) * (1/4)^2
Evaluate the exponent
-1/5 * (-10) * 1/16
This gives
2 * 1/16
Further, evaluate
1/8
Hence, the value of the expression is one eight
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<h3><u>
Proportional.</u></h3>
The corresponding sides of similar figures can be equal, but if they are different in any way, they will always be proportional.
Corresponding angles, however, will always be equal.
