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adelina 88 [10]
3 years ago
14

Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the p

robability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Mathematics
1 answer:
drek231 [11]3 years ago
6 0

Answer:

The probability that <em>X</em> is less than 42 is 0.1271.

Step-by-step explanation:

The random variable <em>X </em>follows a Normal distribution.

The mean and standard deviation are:

E (X) = <em>μ</em> = 50.

SD (X) = <em>σ</em> = 7.

A normal distribution is continuous probability distribution.

The Normal probability distribution with mean µ and standard deviation σ is given by,

f_{X}(\mu, \sigma)=\frac{1}{\sigma\sqrt{2\pi}}e^{-(x-\mu)^{2}/2\sigma^{2}};\ -\infty

To compute the probability of a Normal random variable we first standardize the raw score.

The raw scores are standardized using the formula:

z=\frac{x-\mu}{\sigma}

These standardized scores are known as <em>z</em>-scores and they follow normal distribution with mean 0 and standard deviation 1.

Compute the probability of (X < 42) as follows:

P(X

*Use a <em>z</em>-table for the probability.

Thus, the probability that <em>X</em> is less than 42 is 0.1271.

The normal curve is shown below.

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A ratio that is equivalent to 8/3 is 16/6.

Because:-  8*2= 16
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16/6 is equivalent to 8/3

Writing a proportion:-

8/3=16/6
8 0
3 years ago
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Math help please please ​
Vika [28.1K]

Answer:

3(3x+1) (2x-1)

Step-by-step explanation:

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Factor out a 3

3(6x^2 -x-1)

3(3x+1) (2x-1)

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3 years ago
Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li
krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years

First, let us calculate the decay constant (k)

75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036

Next, let us calculate the half-life as follows:

\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2}  \approx 669\ years

Therefore the half-life is between 600 and 700 years

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Triangle IJK has the coordinates listed:
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Point j’ is at (-10, -8)
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8x=-4(x+3)<br> I would really appreciate some help
olganol [36]

Answer:

x = -1

Step-by-step explanation:

8x = - 4(x + 3)

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+4x  +4x

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12       12

x = -1

  • Remember, a negative times a positive equals a negative
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Hope this helps you!!! :)

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