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2 years ago

Order these numbers from least to greatest.0.85,1/4,5/8,20%,0.3

1 answer:

4 0

1/4 = 0.25
5/8 = 0.625
20% = 0.20
So now we have: 0.20 < 0.25 < 0.3 < 0.625 < 0.85
So the solution is 20%, 1/4, 0.3, 5/8, 0.85

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3 years ago

Read 2 more answers

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

drek231 [11]

Answer:

The probability that X is less than 42 is 0.1271.

Step-by-step explanation:

The random variable X follows a Normal distribution.

The mean and standard deviation are:

E (X) = μ = 50.

SD (X) = σ = 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 z-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 z-table for the probability.

Thus, the probability that X is less than 42 is 0.1271.

The normal curve is shown below.

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3 years ago

John had 2/3 of his homework complete, Sarah had 5/10, Alex 7/8, and Michelle 1/2. Who competed the most of the homework assignm

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3 years ago

Read 2 more answers

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

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