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3 years ago

Two quantities, x and y, are directly proportional. If you take a third of x, what happens to y?

Mathematics

2 answers:

crimeas [40]3 years ago

7 0

D. if something is directly proportional then if something happens to X the exact same thing needs to happen to Y

zimovet [89]3 years ago

6 0

The answer would be D
Since what you do on one side has to be done by the other side

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A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108

Morgarella [4.7K]

Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

$4x+L=108$

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

$V=x^2L$

If we express L in function of x using the restriction equation, we get:

$4x+L=108\\\\L=108-4x$

We replace L in the volume formula and we get

$V=x^2L=x^2*(108-4x)=-4x^3+108x^2$

To maximize the volume we derive and equal to 0

$\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18$

We can replace x to calculate L:

$L=108-4x=108-4*18=108-72=36$

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

4 0

3 years ago

Read 2 more answers

1.What is the y-intercept of the plane whose equation is 4x + 5y – z = 20?

Katena32 [7]

In case of plane, for y intercept, x and z are o .

So we will get

4(0)+5y-0=20

5y=20

Dividing both sides by 5

y = 4

So the y intercept is (0,4,0).

In second question, x intercept is 1, y intercept is -1 and z intercept is 2 .

So the correct option is the third equation , that is x-y+2z=4 .

8 0

3 years ago

Read 2 more answers

I don't understand linear relationships. Can someone explain how it works

Vesna [10]

Linear relationships can be expressed in a graphical format where the variable and the constant are connected via a straight line or in a mathematical format where the independent variable is multiplied by the slope coefficient, added by a constant, which determines the dependent variable.

5 0

2 years ago

How many solutions does this linear system have?

Tanya [424]

Answer:

B (2.5, 0)

Step-by-step explanation:

2x - y = 5 (multiply all by 4)

8x- 4y = 20

-8x - 4y = - 20

eliminate the 4y

8x- 4y = 20

-8x - 4y = - 20

-------------------- –

16x = 40

x = 40/16 = 2.5

now we substitute x with 2.5

2x - y = 5

2(2.5) - y = 5

y = 0

8 0

3 years ago

HELPPP ASAPP Bernie's Bars has determined that a granola bar measuring 3 inches long has a z-score of +1 and a granola bar measu

Len [333]

Answer:

Standard deviation of the length of granola bars produced at Bernie's Bars is 0.50

Step-by-step explanation:

We are given the following information in the question:

Formula:

$z_{score} = \displaystyle\frac{x - \mu}{\sigma}$

where,

μ is the mean and σ is the standard deviation.

Putting the values we get:

$\displaystyle\frac{ 3- \mu}{\sigma} = 1\\\\3 = \sigma + \mu\\\\\displaystyle\frac{ 3.5- \mu}{\sigma} = 2\\\\3.5 = 2\sigma + \mu$

Solving the two obtained equations:

Subtracting the two obtained equation, we have:

$3.5-3 = \mu + 2\sigma - \mu -\sigma\\\sigma = 0.5$

Hence, standard deviation of the length of granola bars produced at Bernie's Bars is 0.50

3 0

3 years ago

Read 2 more answers