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3 years ago

Help please, kind of confused

Mathematics

1 answer:

Anvisha [2.4K]3 years ago

3 0

Answer:

Step-by-step explanation:

Yikes. This is quite a doozy, so pay attention. We will begin by factoring by grouping. Group the first 2 terms together into a set of parenthesis, and likewise with the last 2 terms:

$(2d^4+6d^3)-(18d^2-54d)$ and factor out what's common in each set of parenthesis:

$2d^3(d+3)-18d(d+3)$ . Now you can what's common is the (d + 3), so factor that out now:

$(d+3)(2d^3-18d)$ BUT in that second set of parenthesis, we can still find things common in both terms, so we continue to factor that set of parenthesis, carrying with us the (d + 3):

$(d+3)2d(d^2-9)$ BUT that second set of parenthesis is the difference of perfect squares, so we continue factoring, carrying with us all the other stuff we have already factored:

$(d+3)2d(d+3)(d-3)$ . That's completely factored, but it's not completely simplified. Notice we have 2 terms that are identical: (d + 3):

$2d(d+3)^2(d-3)$ is the completely factored and simplified answer, choice 3)

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If outliers are discarded, then the retirement savings by residents of Econistan is normally distributed with a mean of $100,000

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Answer:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

Step-by-step explanation:

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".

Solution to the problem

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

$X \sim N(100000,20000)$

Where $\mu=100000$ and $\sigma=20000$

We are interested on this probability

$P(X>117000)$

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

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

If we apply this formula to our probability we got this:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

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Answer:

D. The player skates 12 m forward and then skates 12 m in the opposite direction.

Step-by-step explanation:

The player skates 12 m forward then back 12 m which means he is back to his starting point. :)

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Step-by-step explanation:

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Step-by-step explanation:

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The volume of this cube is 27 cubic meters. What is the value of m?

ladessa [460]

Hey ! there

Answer:

n is equal to 3 meters

Step-by-step explanation:

In this question we are provided with a cube having volume 27 cubic meters . And we are asked to find the value of n that is basically its edge .

For finding the value of n we need to know the volume of cube. So ,

$\: \qquad \: \qquad \: \underline{ \boxed{ \frak{Volume_{(Cube)} = a {}^{3} }}}$

Where ,

a refers to edge of cube

SOLUTION : -

Substituting given volume that is 27 m³ and value of a as n in formula :

$\quad \longrightarrow \qquad \: n {}^{3} = 27$

Applying cube root on both sides :

$\quad \longrightarrow \qquad \: \sqrt[3]{n {}^{3} } = \sqrt[3]{27}$

We get ,

$\quad \longrightarrow \qquad \:n= \sqrt[3]{27}$

We know that 3 × 3 × 3 is equal to 27 that means cube root of 27 is 3 . So ,

$\quad \longrightarrow \qquad \: \blue{\underline{\boxed{\frak{ n = 3 \: m}}}} \quad \bigstar$

Henceforth , value of n is ❝ 3 meters ❞

Verifying : -

Now we are checking our answer whether it is wrong or right by substituting value of n and equating it with given volume that is 27 cubic meters . So ,

a³ = 27 ( where a is equal to n )

Substituting values :

( 3 )³ = 27

3 × 3 × 3 = 27

9 × 3 = 27

27 = 27

L.H.S = R.H.S

Hence, Verified .

Therefore, our answer is correct .

<h2>#Keep Learning</h2>

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