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3 years ago

Given the following set of data: 3, 4, 5, 6, 8, 9, 9, which measures below have a value of 6? (Check all that apply.)

Mathematics

1 answer:

barxatty [35]3 years ago

8 0

Range - 6
Mode - 9
High value - 9
Median - 5

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Let R = [ 0 , 1 ] × [ 0 , 1 ] R=[0,1]×[0,1]. Find the volume of the region above R R and below the plane which passes through th

Bond [772]

The three vectors $\langle0,0,1\rangle$ , $\langle1,0,8\rangle$ , and $\langle0,1,9\rangle$ each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,

$\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle$

$\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle$

Then the cross product of these two results is normal to the plane:

$\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle$

Let $(x,y,z)$ be a point on the plane. Then the vector connecting $(x,y,z)$ to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that

$\langle-7,-8,1\rangle\cdot(\langle x,y,z\rangle-\langle0,0,1\rangle)=0$

which reduces to the equation of the plane,

$-7x-8y+z-1=0\implies z=7x+8y+1$

Let $z=f(x,y)$ . Then the volume of the region above $R$ and below the plane is

$\displaystyle\int_0^1\int_0^1(7x+8y+1)\,\mathrm dx\,\mathrm dy=\boxed{\frac{17}2}$

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2 years ago

Edwina measured the length of this swimming pool by drawing similar triangles as shown. What is the best estimate of p, the leng

Paraphin [41]

Answer:

Option C. $p=33\ ft$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

Using proportion

$\frac{p}{12}=\frac{22}{8}\\ \\p=12*22/8\\ \\p=33\ ft$

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2 years ago

Read 2 more answers

The product of n and 14

professor190 [17]

Answer:

14n

Step-by-step explanation:

You multiply 14 by n, which is 14n.

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2 years ago

For a biology assignment, Christopher records the height of a plant

aivan3 [116]

What is your question???

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2 years ago

For the function y = f(x) = 3x -5<br> What is the y intersection

Jobisdone [24]

Answer:

The y-intercept is -5.

Step-by-step explanation:

In algebra, "y=" and "f(x)=" is basically the same thing. You don't have to write them both. Also, $y=3x-5$ is in slope-intercept form, which is: $y=mx+b$ , where $b$ is the y-intercept. That means "-5" is the y-intercept.

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2 years ago