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2 years ago

If y varies inversely as x, and y = 23 when x 8, find y when x 4.

Mathematics

1 answer:

Virty [35]2 years ago

7 0

Answer:

y = 46

Step-by-step explanation:

Given y varies inversely as x then the equation relating them is

y = $\frac{k}{x}$ ← k is the constant of variation

To find k use the condition y = 23 when x = 8 , then

23 = $\frac{k}{8}$ ( multiply both sides by 8 )

184 = k

y = $\frac{184}{x}$ ← equation of variation

When x = 4 , then

y = $\frac{184}{4}$ = 46

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Considering the Central Limit Theorem, we have that:

a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.

b) The probability can be calculated, as the sample size is greater than 30.

<h3>What does the Central Limit Theorem state?</h3>

It states that the sampling distribution of sample means of size n is approximately normal has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ , as long as the underlying distribution is normal or the sample size is greater than 30.

In this problem, the underlying distribution is skewed right, that is, not normal, hence:

For item a, the probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.

For item b, the probability can be calculated, as the sample size is greater than 30.

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2 years ago

A blind man wanders under a door into an empty room. After running into the walls repeatedly for a while, it stops to think and

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From the side where the man is located in the 10' by 12' rectangular room, we have;

A) 0.046

B) The average time to escape in first attempt is approximately 605.02 seconds

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A) From The given diagram, we have;

Width of the door = 10 - 6 - 2 = 2

Therefore, the door is 2 feet wide

Distance, d1, from the man to the side of the door closer to him is given by Pythagorean theorem as follows;

d1 = √(6² + 7²) = √(85)

From the furthest side of the door to the man, we have;

d2 = √(7² + 8²) = √(113)

According to the law of cosines, we have;

2² = 85+113 - 2×√(85)×√(113) cos(A)

Where angle <em>A </em>is the angle formed by the lines from the man to the closer and farther sides of the door.

2×√(85)×√(113) cos(A) = 85+113 - 2²

A = arccos((85+113 - 2²)/(2×√(85)×√(113)))

A = arccos (194/(2×√(9605)) ≈ 8.213°

The angle of the possible directions in which the man can turn is 180°.

Therefore;

The probability, <em>P(</em><em>E)</em>, of escaping in the first move is therefore;

P(E) = 8.213°/180° ≈ 0.046

B) Given that the man escapes in the first move, the shortest and longest distances the man moves are;

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Speed of the man, <em>v </em>= 0.5 cm/sec

Therefore by unit conversion function of a graphing calculator;

v = (25/1524) ft./sec

The times taken are;

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Average time, <em>t </em>= (t1 + t2)/2

Which gives;

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1 year ago

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