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3 years ago

What is the first quartile, Q1, of the following distribution?

Mathematics

1 answer:

rusak2 [61]3 years ago

3 0

Answer:

26.5

Step-by-step explanation:

the median is 37 due to there being 17 data points in the set. So the first quartile wouldn't contain 37 so you find the other point. The point is in between 26 and 27, so you add those 2 points together and divide it by 2 to get your answer.

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago

What is the factored form of 64g^3+8

vivado [14]

$\bf \textit{difference and sum of cubes}
\\\\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
(a+b)(a^2-ab+b^2)= a^3+b^3 
\\\\
a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad
(a-b)(a^2+ab+b^2)= a^3-b^3\\\\
-------------------------------\\\\
64g^3+8\implies 4^3g^3+8\implies (4g)^3+2^3
\\\\\\
(4g+2)[(4g)^2-(4g)(2)+2^2]\implies (4g+2)[(4^2g^2)-8g+4]
\\\\\\
(4g+2)(16g^2-8g+4)$

3 0

3 years ago

Write the first six terms in the number pattern. Start with 83 and subtract 9 repeatedly.

Mila [183]

83, 74, 65, 56,47,38,29,20,11,2,etc

hope this helps

5 0

3 years ago

4 2/9 as a decimal work shown

Xelga [282]

The Answer Is:4.222222

4 2/9 = 4 + 2/9

= 4/1 + 2/9

= (4/1 * 9/9) + 2/9

= 36/9 + 2/9

= 38/9

= 38 ÷ 9 = 4.222222

4 0

2 years ago

Determine whether quadrilateral ABCD is a rhombus, a rectangle, a square, a parallelogram, or none. List all that apply. Explain

svlad2 [7]

Answer:

ABCD is a rhombus, and a parallelogram

==================================

<h3>Given </h3>

Points A(-6, - 1), B(4, - 6), C(2, 5), D(- 8, 10)

First, plot the points (see attached picture).

Then, connect all the points.

Opposite sides are parallel,
Diagonals are perpendicular.

From our observation the figure is rhombus.

Let's confirm it with the following.

1) Find midpoints of diagonals and compare.

AC → x = (- 6 + 2)/2 = - 2, y = (- 1 + 5)/2 = 2
BD → x = (4 - 8)/2 = - 2, y = (- 6 + 10)/2 = 2

The midpoint of both diagonals is same (- 2, 2).

2) Find slopes of diagonals and check if their product is -1, this will confirm they are perpendicular.

m(AC) = (5 - (-1))/(2 - (-6)) = 6/8 = 3/4
m(BD) = (10 - (-6))/(-8 - 4) = - 16/12 = - 4/3

m(AC) × m(BD) = 3/4 * (- 4/3) = - 1

Confirmed.

So this is a rhombus and also a parallelogram but not rectangle or square, since opposite angles are not right angles.

5 0

11 months ago