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4 years ago

1. Solve for p

Mathematics

1 answer:

DerKrebs [107]4 years ago

6 0

Answer:

$1. \quad p=\dfrac{-3q}{2}\\\\2. \quad b=\dfrac{4a+7}{2}, b=\dfrac{19}{2}\\\\3. \quad r=\dfrac{d}{t}\\\\4. \quad \text{D. 30}$

Step-by-step explanation:

1. Subtract p:

3p +3q -p = 0

2p +3q = 0 . . . . collect terms

2p = -3q . . . . . . subtract 3q

p = -3q/2 . . . . . . divide by the coefficient of p

2. Add 7 and divide by the coefficient of b:

4a +7 = 2b

(4a +7)/2 = b

Substitute for a to find the value of b.

(4(3) +7)/2 = b = 19/2

3. Divide by the coefficient of r:

r = d/t

4. The sum of length and width is half the perimeter:

15 + w = 90/2 = 45

w = 30 . . . . . . . subtract the length; the width is 30 units

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Answer:

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Step-by-step explanation:

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Read 2 more answers

Let x denote the lifetime of a mcchine component with an exponential distribution. The mean time for the component failure is 25

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Answer:

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The mean time for the component failure is 2500 hours.

This means that $m = \frac{2500}, \mu = \frac{1}{2500} = 0.0004$

What is the probability that the lifetime exceeds the mean time by more than 1 standard deviations?

The standard deviation of the exponential distribution is the same as the mean, so this is P(X > 5000).

$P(X > x) = e^{-0.0004*5000} = 0.1353$

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

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3 years ago

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3 years ago

W is the midpoint of VX and Z is the midpoint of VY . If XY=p and WZ=p–30, what is WZ?

juin [17]

$\large{ \tt{❃ \: EXPLANATION}} :$

You'll have to know : Mid-point theorem states that A straight line segment joining the mid-points of any two triangle is parallel to the third side and it is equal to half of the length of the third side.

We're provided : XY = p , WZ = p - 30 & we're asked to find out the value of WZ. For that , firstly we have to find out the value of p.

$\large{ \tt{❁ \: LET'S \: START }: }$

Set up an equation & solve for p :

$\large{ \bf{☄ \: p - 30 = \frac{1}{2} p }}$

$\large{ \tt{↦ \frac{1}{2} p = p - 30}}$

$\large{ \tt{↦ \frac{1}{2} p - p = - 30}}$

$\large{ \tt{↦ \frac{p - 2p}{2} = - 30 }}$

$\large{ \tt{↦p - 2p = - 60}}$

$\large{ \tt{ ↦ \: - p = - 60}}$

$\large{ \tt{↦p = 60}}$

The value of p is 60

$\large{ \tt{❇ \: REPLACING \: VALUE}} :$

$\large{ \tt{↬ \: wz = p - 30 = 60 - 30 = \boxed{\boxed{ \tt{30 }} }✔}}$

Hence , WZ = 30 .

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3 years ago