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SpyIntel [72]
3 years ago
11

The image shows the construction of two tangent lines from a point outside the circle to the circle. Given that drawing the tang

ent lines JP and KP is step 5 in the construction and the answer choices represent steps 1 through 4, which is step 1?
A) Construct the perpendicular bisector of OP.
B) Draw a circle and a point outside the circle.
C) Draw two arcs on the circumference of the circle.
D) Draw line OP, to join the center O to point P.

Mathematics
1 answer:
Dahasolnce [82]3 years ago
6 0

Answer: (<em>Draw a circle and a point outside the circle.)</em>

Step-by-step explanation:

Step 1: Draw a circle and a point outside the circle.

Step 2: Draw line OP, to join the center O to point P.

Step 3: Construct the perpendicular bisector of OP.

Step 4: Draw two arcs on the circumference of the circle.

Step 5: Draw tangent lines JP and KP.

Proof:

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Step-by-step explanation:

2cm loss from 5cm.

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A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.95. Assuming indep
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Answer:

a) There is a 99.99997% probability that at least one valve opens.

b) There is a 22.62% probability that at least one valve fails to open.

Step-by-step explanation:

For each valve, there are only two possible outcomes. Either it open, or it does not. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

p = 0.95, n = 5

(a) What is the probability that at least one valve opens?

Either no valves open, or at least one opens. The sum of the probabilities of these events is decimal 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1)

So

P(X \geq 1) = 1 - P(X = 0)

P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} = 0.0000003

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000003 = 0.9999997

There is a 99.99997% probability that at least one valve opens.

(b) What is the probability that at least one valve fails to open?

Either all valves open, or at least one does not open. The sum of the probabilities of these events is decimal 1. So

P(X = 5) + P(X \leq 4) = 1

We want P(X \leq 4)

So

P(X \leq 4) = 1 - P(X = 5)

P(X = 5) = C_{5,5}.(0.95)^{5}.(0.05)^{0} = 0.7738

P(X \leq 4) = 1 - P(X = 5) = 1 - 0.7738 = 0.2262

There is a 22.62% probability that at least one valve fails to open.

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3 years ago
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