If a student wanted to immediately eliminate (get rid of) the fraction in this problem, they should:

What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 3?

meriva

Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

In this case a=5, and d=-2 so

a(n)=5-2(n-1) which can be simplified...

a(n)=5-2n+2

a(n)=7-2n

The domain is restricted to integers from 1 to +oo.

3 0

3 years ago

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For a given IQ test, an individual is considered a genius if their score falls more than three standard deviations from the mean

ki77a [65]

Answer:

$P(Z>3) = 1-P(Z$

So then the probability that an individual present and IQ higher than 3 deviation from the mean is 0.00135

And if we find the number of individuals that can be considered as genius we got: 0.00135*1500=2.025

And we can say that the answer is a.2

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Solution to the problem

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu=?,\sigma=?)$

We are interested on this probability

$P(X>X+3\mu)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

And we can find the following probablity:

$P(Z>3) = 1-P(Z$

So then the probability that an individual present and IQ higher than 3 deviation from the mean is 0.00135

And if we find the number of individuals that can be considered as genius we got: 0.00135*1500=2.025

And we can say that the answer is a/2.0

3 0

3 years ago

Nine hundred ninety two hundred thousandths wrote in decimal form

uranmaximum [27]

Answer:

I think the answer is 9.920 please be careful with your answer I think it 9.920 because it says nine hundred and ninety two thousands so therefor the decimal need to be in between 9 and 9 I hope you get this correct!

step-by-step explanation:

3 0

2 years ago

What's the equation of this line ?

Gennadij [26K]

Y = -3x + 7

good luck!

5 0

3 years ago

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Show work

nika2105 [10]

Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.

Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

There are three right triangles we can work with.

Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation $x^{2} + 48^{2} = z^{2}$

Triangle with sides 27, x and y. Here y is the hypotenuse so we get $27^{2} + x^{2} = y^{2}$

Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get $y^{2} + z^{2} = (27+48)^{2}$ . That is, $y^{2} + z^{2} = 5625$

We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation: $y^{2} + z^{2} = 5625$ and replace $z^{2}$ and $y^{2}$ using expressions that contain an expression in terms of x from the first two equations we came up with.

That gives us: $48^{2} + x^{2} + x^{2} + 27^{2} =5625$ which we solve for x as follows:

$2 x^{2} + 3033 =5625
2x^{2} =2592
 x^{2} =1296
x=36$

Now that we know x we can substitute 36 for x into the equation $48^{2} + x^{2} = z^{2}$ and solve for z as follows:
$48^{2} + 36^{2} = z^{2} 
2304+1296=z^{2} 
3600=z^{2} 
z=60$

This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.

4 0

3 years ago

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