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3 years ago

Factor the polynomial.3x^6y^2+81y^2

Mathematics

2 answers:

Elan Coil [88]3 years ago

6 0

3x⁶y²+81y² =
3y²(x⁶+27) =
3y²((x²)³+3³)=
3y²(x²+3)(x⁴-3x²+9)

Answer: D.

Zarrin [17]3 years ago

3 0

Answer is choice D

The reason why is...
3x^6y^2 + 81y^2 = 3y^2(x^6 + 27)
3x^6y^2 + 81y^2 = 3y^2((x^2)^3 + 3^3)
3x^6y^2 + 81y^2 = 3y^2(x^2 + 3)((x^2)^2 - (x^2)*3 + 3^2)
3x^6y^2 + 81y^2 = 3y^2(x^2 + 3)(x^4 - 3x^2 + 9)

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Answer:

8 units by 10 units

Step-by-step explanation:

$150 \div 15 = 10 \\ 120 \div 15 = 8$

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2 years ago

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tensa zangetsu [6.8K]

0.63 is the correct answer

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2 years ago

Vail Resorts pays part-time seasonal employees at ski resorts on an hourly basis. At a certain mountain, the hourly rates have a

notsponge [240]

Answer:

$z=0.842$

And if we solve for a we got

$\mu=13.16 +0.842*3=15.69$

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 hourly rates of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,3)$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>13.16)=0.20$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.842$

And if we solve for a we got

$\mu=13.16 +0.842*3=15.69$

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2 years ago

everyday Penelope jogs three laps around the playground to keep in shape the playground is rectangular with the width of 163 m a

Veronika [31]

Answer:

The total amount of meters in one lap is 966

Step-by-step explanation:

we know that

The total amount of meters in one lap is the same that the perimeter of the rectangular playground

The perimeter of the rectangular playground is equal to

$P=2(L+W)$

we have

$L=320\ m\\W=163\ m$

substitute

$P=2(320+163)$

$P=966\ m$

3 0

2 years ago

Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =

irga5000 [103]

Answer: The required solution is $y=50e^{0.1386t}.$

Step-by-step explanation:

We are given to solve the following differential equation :

$\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

$\dfrac{dy}{y}=kdt.$

Integrating both sides, we get

$\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]$

Also, the conditions are

$y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50$

and

$y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.$

Thus, the required solution is $y=50e^{0.1386t}.$

8 0

2 years ago

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