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Answer:

The value is  [tex]P(X > 500 ) = 0.011942[/tex]

Step-by-step explanation:

From the question we are told that

       The mean is  [tex]\mu = 430[/tex]

       The standard deviation is  [tex]\sigma = 120[/tex]

       The sample size is  n  =  15

Generally  the probability that the sample mean is above 500

Gnerally the standard error of mean is mathematically represented as

             [tex]s = \frac{\sigma }{ \sqrt{n} }[/tex]

=>          [tex]s = \frac{ 120 }{ \sqrt{15} }[/tex]

=>           [tex]s = 30.984[/tex]

Generally  the probability that the sample mean is above 500

     [tex]P(X > 500 ) = P( \frac{X - \mu }{\sigma_x} > \frac{500 - 430 }{ 30.984 } )[/tex]

[tex]\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )[/tex]

       [tex]P(X > 500 ) = P( Z > 2.259 )[/tex]

=>     [tex]P(X > 500 ) = P( Z > 2.259 )[/tex]

From the z table  the area under the normal curve to the right  corresponding to  2.259  is

          [tex]P( Z > 2.259 ) = 0.011942[/tex]

=>       [tex]P(X > 500 ) = 0.011942[/tex]

Answer:

E: The study was not comparative—only one treatment was used.

Step-by-step explanation:

Well-designed experiments should involve comparisons of at least two treatment groups, one of which could be a control group.

A well-designed experiment investigates design features that achieve the research to rule out sources of variation as reasons for the observed relationship between both the independent variable(s) and the predictor variables.

Therefore, the final answer is "Option E".

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Answer:

2x - 1

Step-by-step explanation:

Equivalent Algebraic Expressions

One algebraic expression can be written in several ways by applying known rules and theorems that modify expressions without changing its final value.

The expression:

1 + 2(x - 1)

Can be modified by applying the following operations:

Multiplying the constant by the contents in parentheses:

1 + 2x - 2

Collecting like terms:

-1 + 2x

Or, equivalently:

2x - 1

Answer:

Step-by-step explanation:

The answer is C

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Hope it helps

Answer:

[tex]\frac{47}{330}[/tex]

Step-by-step explanation:

We require to create 2 equations with the recurring part (42) placed after the decimal point.

let x = 0.14242 ( multiply both sides by 10 and 1000 )

10x = 1.4242... → (1)

1000x = 142.4242... → (2)

Subtract (1) from (2) thus eliminating the recurring decimal

990x = 141 ( divide both sides by 990 )

x = [tex]\frac{141}{990}[/tex] = [tex]\frac{47}{330}[/tex]

The fractional form of the recurring decimal 0.142 is 47/330.

A number whose digits are periodic and the indefinitely repeated component is not zero is represented as a repeating decimal or recurring decimal. If and only if a number's decimal representation repeats or terminates, it is possible to demonstrate that the number is rational.

Given, A recurring decimal 0.142 where 4 and 2 are repeating.

In the denominator, we'll write as many 9's as there are recurring digits after the decimal and after as many zeros as there are digits after the decimal which are not repeating, and in the numerator, we'll subtract the nonrecurring digits from the total digits after the decimal.

Therefore, 0.142 where 4 and 2 are repeating can be written in fraction form as,

(142 - 1)/990.

= 141/990.

= 47/330.

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Answer:

4/9 is the answer

Step-by-step explanation:

you're welcome

Answer:

The value of f(g(-2)) is 12.

Step-by-step explanation:

We'll start by solving g(-2):

[tex]g(-2)\\= (-2)^2 + 2\\= 4 + 2\\= 6[/tex]

Now we can take that value and plug it into function f:

[tex]f(6)\\= \frac{-1}{2}6^2 + 5 * 6\\= -36/2 + 30\\= -18 + 30\\= 12[/tex]

Alternatively, you can work out a new single function that in itself describes f(g())

[tex]f(g(x)) = -\frac{1}{2}g(x)^2 + 5g(x)\\= -\frac{1}{2}(x^2 + 2)^2 + 5(x^2 + 2)\\= -\frac{1}{2}(x^4 + 4x^2 + 4) + 5x^2 + 10\\= -\frac{1}{2}x^4 - 2x^2 - 2 + 5x^2 + 10\\= -\frac{x^4}{2} + 3x^2 + 8[/tex]

and try plugging -2 into the new function

[tex]= - \frac{-2^4}{2} + 3(-2)^2 + 8\\= -16 / 2 + 3 * 4 + 8\\= -8 + 12 + 8\\= 12[/tex]

The value of f(g(-2)) for the given expression will be 12.

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

We have,

f(x) = [tex]\frac{-1}{2} x^2[/tex]  + 5x

And,

g(x) = x² + 2

Now,

For, x = -2,

i.e.

g(x) = x² + 2

Now,

Substituting the value of x = -2,

g(-2) = (-2)² + 2

On solving,

We get,

g(-2) =  6

Now,

For, f(g(-2)),

f(x) = [tex]\frac{-1}{2} x^2[/tex]  + 5x

i.e.

Substituting the value of g(-2) =  6,

i.e.

f(g(-2)) = [tex]\frac{-1}{2} (g(-2)^2)[/tex] + 5(g(-2))

i.e.

f(g(-2)) = [tex]\frac{-1}{2} *6^2[/tex]  + 5 * 6

On solving,

We get,

f(g(-2)) = -18 + 30

i.e.

f(g(-2)) = 12

So, the value of f(g(-2)) for the given expression is 12.

Hence, we can say that the value of f(g(-2)) for the given expression will be 12.

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Answer:

It's the last one

I hoped that helped