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Marat540 [252]
2 years ago
5

Find the gradient of the line joining the points P(2,5) and Q(4,-2).​

Mathematics
1 answer:
liq [111]2 years ago
6 0
Answer is -7/2

Gradient or slope is found by change in y over change in x.
Or
(y2 - y1) over (x2 - x1)

So
(-2 -5) over (4-2)
= -7/2
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The temperature readings from a thermocouple in a furnace fluctuate according to a cumulative distribution function,
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Answer:

P(x

P(x

P(x>808.40) = 0.58

P(x\le805.40\ or\ x\ge 808.40) = 0.85

Step-by-step explanation:

Given:

F(x) = \left\{\begin{array}{ll}{0} &; {x

Solving (a): P(x < 810)

To solve this, we make use of:

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F(x) = 0.05 * 810 -40

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P(x

Solving (b): P(x < 800)

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P(x

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x < 800^\circ C

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P(x

Solving (c): P(x > 808.40)

Here, we make use of complement rule:

P(x>808.40) = 1 - P(x \le 808.40)

Where:

P(x\le808.40) = 0.05x - 40

P(x\le808.40) = 0.05*808.40 - 40

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So:

P(x>808.40) = 1 - 0.42

P(x>808.40) = 0.58

Solving (d) The probability that the temperature lies outside 805.60 and 808.40

First, we calculate the probability that it lies within.

This is represented as:

P(805.40 < x < 808.40)

This is calculated using:

P(805.40 < x < 808.40) = F(808.40) - F(805.40)

P(805.40 < x < 808.40) = 0.05*808.40-40 - (0.05*805.40-40)

P(805.40 < x < 808.40) = 0.42 - (0.27)

P(805.40 < x < 808.40) = 0.42 - 0.27

P(805.40 < x < 808.40) = 0.15

Using complement rule, the required probability is:

P(x\le805.40\ or\ x\ge 808.40) = 1 - 0.15

P(x\le805.40\ or\ x\ge 808.40) = 0.85

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3 years ago
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