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3 years ago

Make b the subject of the formula a = sqrt(b+6)

Mathematics

2 answers:

balu736 [363]3 years ago

7 0

Answer:

a = √(b+ 6)

a² = b + 6 (Square both sides)

b = a² - 6 (subtract 6 from both sides)

KonstantinChe [14]3 years ago

4 0

Answer:

b = a^2 - 6

Step-by-step explanation:

a = sqrt(b+6)

Find the square of both sides

a^2 = (b+6). Open brackets

a^2 = b+6

Subtract 6 from both sides

a^2 - 6 = b + 6 -6

b = a^2 - 6

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Suppose that the times required for a cable company to fix cable problems in its customers’ homes are uniformly distributed betw

vampirchik [111]

Answer:

a) 60% probability that a randomly selected cable repair visit will take at least 50 minutes

b) 60% probability that a randomly selected cable repair visit will take at most 55 minutes.

c) The expected length of the repair visit is 52.5 minutes.

d) The standard deviation is 7.22 minutes.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

For this problem, we have that:

Uniformly distributed between 40 and 65 minutes, so $a = 40, b = 65$

(a) What is the probability that a randomly selected cable repair visit will take at least 50 minutes?

Either it takes less than 50 minutes, or it takes at least 50 minutes. The sum of the probabilities of these events is decimal 1. So

$P(X < 50) + P(X \geq 50) = 1$

The intervals can be open or closed, so

$P(X < 50) = P(X \leq 50)$

We have that

$P(X \geq 50) = 1 - P(X < 50)$

$P(X < x) = \frac{50 - 40}{65 - 40} = 0.4$

$P(X \geq 50) = 1 - P(X < 50) = 1 - 0.4 = 0.6$

60% probability that a randomly selected cable repair visit will take at least 50 minutes

(b) What is the probability that a randomly selected cable repair visit will take at most 55 minutes?

This is $P(X \leq 55)$

$P(X \leq 55) = \frac{55 - 40}{65 - 40} = 0.6$

60% probability that a randomly selected cable repair visit will take at most 55 minutes.

(c) What is the expected length of the repair visit?

The mean of the uniform distribution is:

$M = \frac{a+b}{2}$

$M = \frac{40+65}{2} = 52.5$

The expected length of the repair visit is 52.5 minutes.

(d) What is the standard deviation?

The standard deviation of the uniform distribution is

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

$S = \sqrt{\frac{(65-40)^{2}}{12}}$

$S = 7.22$

The standard deviation is 7.22 minutes.

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3 years ago

An astronaut who weighs 126 lb on earth weighs 21 lb on the moon. How much would a person who weighs 234 lbs on the moon weigh o

ivann1987 [24]

Answer:

$1,404\ lb$

Step-by-step explanation:

we know that

using proportion

$\frac{126}{21}\frac{earth}{moon} =\frac{x}{234}\frac{earth}{moon}\\ \\x=126*234/21\\ \\x=1,404\ lb$

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4 years ago

Read 2 more answers

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maks197457 [2]

Step-by-step explanation:

step 1. let's call the line in the middle y.

step 2. y = sqrt(5^2 + 7^2) = sqrt(74). pythagorean theorem.

step 3. x^2 + y^2 =100 (pythagorean theorem))

step 4. x^2 + (sqrt(74))^2 = 100.

step 5. x^2 = 100 - 74

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step 7. x = sqrt(26). note: sqrt is the square root.

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3 years ago

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nirvana33 [79]

The answer is D. 486 i<span>n²</span>

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3 years ago

Read 2 more answers

PLZ HELP ASAP

Alexxandr [17]

Answer:

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Step-by-step explanation:

Plot the points. The result is shown in the attachment.

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3 years ago