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3 years ago

What is the first quartile of the data displayed in this box-and-whisker plot?

Mathematics

2 answers:

Lana71 [14]3 years ago

5 0

The answer is C. 37. To get this, look at the line that makes up to left side of the box.

Mekhanik [1.2K]3 years ago

4 0

Answer:

Step-by-step explanation:

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The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai

sammy [17]

The Lagrangian is

$L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)$

with partial derivatives (set equal to 0)

$L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0$

$L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0$

$L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0$

$L_\lambda=4x^2+4y^2-z^2=0$

$L_\mu=2x+4z-2=0\implies x+2z=1$

Case 1: If $y=0$ , then

$4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|$

Then

$x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23$

$\implies x=\dfrac15\text{ or }x=-\dfrac13$

So we have two critical points, $\left(\dfrac15,0,\dfrac25\right)$ and $\left(-\dfrac13,0,\dfrac23\right)$

Case 2: If $\lambda=-\dfrac14$ , then in the first equation we get

$x(1+4\lambda)+\mu=\mu=0$

and from the third equation,

$z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0$

Then

$x+2z=1\implies x=1$

$4x^2+4y^2-z^2=0\implies1+y^2=0$

but there are no real solutions for $y$ , so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

$f\left(\dfrac15,0,\dfrac25\right)=\dfrac15$ (min)

and

$f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59$ (max)

5 0

3 years ago

What is the value of x in the figure? A. 40 B. 70 C. 80 D. 120 E. 150

Marizza181 [45]

Answer:

E) 150°

Step-by-step explanation:

angle adjacent to 70° angle is 110°

the angle supplemental to 'x' must be 180-(40+110) or 30°

this means 'x' must be 150°

7 0

3 years ago

Read 2 more answers

What equation is equal to 2y= 2x + 2?

VMariaS [17]

Answer:

y = x+1

Step-by-step explanation:

2y = 2x+2 ( divide both sides of the equation with 2)

y = x + 1

4 0

3 years ago

Find the equation of this line

Elena-2011 [213]

Answer:

y = 2x + 4

Step-by-step explanation:

The slope is 2/1 (or just 2) and the 4 is the y-intercept

5 0

3 years ago

Read 2 more answers

I just need one more answer to this. Please someone help!

den301095 [7]

Answer:

(1,0)

(-2,3)

(5,24)

Step-by-step explanation:

To solve this you can can just plug in the x and y values and see which work

y = x²-1

Lets test (0,1):

1 = 0²-1

1 = -1

This pair does not work, because 1 does not equal -1

Lets test (1,0):

0 = 1²-1

0 = 0

This does work, because 0 equals 0

Lets test (3,5):

5 = 3²-1

5 = 9 - 1

5 = 8

This pair does not work, because 5 does not equal 8

Lets test (5,24):

24 = 5²-1

24 = 25 -1

24 = 24

This pair does work, because 24 equals 24

Lets test (-2,3):

3 = (-2)²-1

3 = 4-1

3 = 3

This pair does work, because 3 equals 3

Lets test (-4,-17):

-17 = (-4)²-1

-17 = 16 - 1

-17 = 15

This pair does not work, because -17 does not equal 15

So the pairs that are on the graph are:

(1,0)

(-2,3)

(5,24)

4 0

3 years ago