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3 years ago

A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses:

Mathematics

2 answers:

Stella [2.4K]3 years ago

8 0

Answer:

Average = 11.2

Median = 11

Step-by-step explanation:

Mean = Average

Average = Sum of the numbers divided by how many numbers are there.

5 + 10 + 12 + 15 + 16 + 9 = 67

There are 6 numbers.

Average rounded to the nearest tenth = 67/6 = 11.2

Median = middle of the numbers in ascending order.

Put the numbers in order and you would get: 5, 9, 10, 12, 15, 16

When there is two medians, find the average of the two.

The average of 10 and 12 is 11.

Median is 11.

Hope this helps :)

Have a spectacular day!

vaieri [72.5K]3 years ago

3 0

Answer:

Mean: 11.2

Median: 11

Mode: There is none

Step-by-step explanation:

mean -you add all the numbers and divide by the number of numbers

median- you arrange the data set by numerical value (increasing) and it is basically the "middle number" for example 1, 2, 3, (2 would be the "middle" number" )

mode- is the number that appears most often. in this scenario, all numbers appear the same amount of times (1) so there is no mode.

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Compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = 2xy (x2 +

blsea [12.9K]

Answer with step-by-step explanation:

We are given that a function

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

Differentiate partially w.r.t x

Then, we get

$\frac{\delta f}{\delta x}=2y(x^2+y^2)^2+8x^2y(x^2+y^2)=(x^2+y^2)(2x^2y+2y^3+8x^2y)=2(5x^2y+y^3)(x^2+y^2)$

Differentiate again w.r.t x

$\frac{\delta^2f}{\delta x^2}=2(10xy)(x^2+y^2)+4x(5x^2y+y^3)=20x^3y+20xy^3+20x^3y+4xy^3=40x^3y+24xy^3$

Differentiate function w.r.t y

$\frac{\delta f}{\delta y}=2x(x^2+y^2)^2+2xy\times 2(x^2+y^2)\times 2y$

$\frac{\delta f}{\delta y}=(x^2+y^2)(2x^3+2xy^2+8xy^2)=2(x^2+y^2)(x^3+5xy^2)$

Again differentiate w.r.t y

$\frac{\delta^2f}{\delta x^2}=2(2y)(x^3+5xy^2)+20xy(x^2+y^2)=4x^3y+20xy^3+20x^3y+20xy^3=24x^3y+40xy^3$

Differentiate partially w.r.t y

$\frac{\delta^2f}{\delta y\delta x}=2(2y(5x^2y+y^3)+(x^2+y^2)(5x^2+3y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta y\delta x}=10x^4+36x^2y^2+10y^4$ $\frac{\delta^2f}{\delta x\delat y}=2(2x(x^3+5xy^2)+(3x^2+5y^2)(x^2+y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta x\delat y}=10x^4+36x^2y^2+10y^4$

Hence, if f(x,y) is of class $C^2$ (is twice continuously differentiable), then the mixed partial derivatives are equal.

i.e $\frac{\delta^2f}{\delta y\delta x}=\frac{\delta^2f}{\delta x\delta y}$

8 0

4 years ago

Jake needs 8 cups of milk to make a chocolate shake for his family. His measuring device measures liquids by the pint. If 1 pint

zvonat [6]

If you would like to know how many pints should Jake measure, you can calculate this using the following step:

1 pint ... 2 cups
x pints = ? ... 8 cups

1 * 8 = 2 * x
8 = 2 * x /2
x = 8/2 = 4 pints

The correct result would be 4 pints.

8 0

3 years ago

Read 2 more answers

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irina [24]

Answer is -7 because -15+8=-7

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4 years ago

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Answer:

here