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3 years ago

Tính : a) (a+b+c)^2b) (a-b-c)^2c) (a+b-c)^2d) (a-b+c)^2

Mathematics

1 answer:

LiRa [457]3 years ago

3 0

Answer:

a.) a² + b² + c ² + 2ab + 2ac + 2bc

b.) a² + b² + c² - 2ab - 2 ac + 2bc

c ) a² + b² + c² + 2ab - 2ac - 2bc

d.) a² + b² + c² - 2ab + 2ac - 2bc

Step-by-step explanation:

Use ( a + b + c )² = a² + b² + c² + 2 × ab + 2 × ac + 2 × bc to expand all these expression

a) ( a + b + c )²

= a² + b² + c² + 2 × ab + 2 × ac + 2 × bc

= a² + b² + c ² + 2ab + 2ac + 2bc

b.) ( a - b - c )

= a² + ( - b )² + ( - c)² + 2a ( -b ) + 2a(-c) + 2(-b)(-c)

= a² + b² + c² - 2ab - 2 ac + 2bc

c.) ( a + b - c )²

= a² + b² + ( -c)² + 2ab + 2a ( - c) + 2 b( -c)

= a² + b² + c² + 2ab - 2ac - 2bc

d.) (a - b + c ) ²

= a² + ( -b)² + c² + 2a(-b) + 2ac + 2c( -b)

= a² + b² + c² - 2ab + 2ac - 2bc

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3 years ago

Please help me<br> Show your work

GrogVix [38]

<u>ANSWER TO PART A</u>

The given triangle has vertices $J(-4,1), K(-4,-2),L(-3,-1)$

The mapping for rotation through $90\degree$ counterclockwise has the mapping

$(x,y)\rightarrow (-y,x)$

Therefore

$J(-4,1)\rightarrow J'(-1,-4)$

$K(-4,-2)\rightarrow K'(2,-4)$

$L(-3,-1)\rightarrow L'(1,-3)$

We plot all this point and connect them with straight lines.

ANSWER TO PART B

For a reflection across the y-axis we negate the x coordinates.

The mapping is

$(x,y)\rightarrow (-x,y)$

Therefore

$J(-4,1)\rightarrow J''(4,1)$

$K(-4,-2)\rightarrow K''(4,-2)$

$L(-3,-1)\rightarrow L''(3,-1)$

We plot all this point and connect them with straight lines.

See graph in attachment

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3 years ago

Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible cho

yaroslaw [1]

Answer:

a) attached below

b) ( T,T )

c) The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

d) The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 )

Step-by-step explanation:

A) write down the game in matrix form

let: E = exit at the industry immediately

T = exit at the end of the quarter

N = exit at the end of the next quarter

matrix is attached below

B) weakly dominated strategies is ( T,T )

C) Find the pure-strategy Nash equilibria

The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

D ) Find the unique mixed-strategy Nash equilibrium

The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 ) since T is weakly dominated then the mixed strategy will be NE

Assume that P is the probability of firm 1 exiting immediately ( E )

and q is the probability of firm 1 staying till next term ( N ) ∴ q = 1 - P.

hence the expected utility of firm 2 choosing E = 0 while the expected utility of choosing N = 4p - 2q .

The expected utilities of E and N to firm 2 =

0 = 4p - 2q = 4p - 2 ( 1-p) = 6p -2 which means : p = 1/3 , q = 2/3

4 0

3 years ago

Which of the following measures cannot be determined from a box plot?

ad-work [718]

<h3>3 Answers:</h3>

B) Mean
C) Mean absolute deviation
E) Mode

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

Explanation:

The box plot, aka "box-and-whisker plot", visually represents five things. These things are:

Minimum
Q1 = first quartile
Median (sometimes referred to as Q2 or second quartile)
Q3 = third quartile
Maximum

This list of five items is known as the five number summary.

The min is the tip of the left most whisker, assuming there aren't any small outliers. The max is the opposite side, being the tip of the right most whisker (assuming no large outliers). If there are any outliers, then they'll be shown as "island" dots on their own separated from the main box plot. The left and right edges of the box are Q1 and Q3 respectively. The median is the vertical line inside the box. The vertical line does not have to be at the midpoint of the left and right edges of the box. It simply needs to be somewhere in the box.

--------

Since the box plot lets us know the min and max, we can compute the range because

range = max - min

and we can also calculate the interquartile range (IQR) because

IQR = Q3 - Q1

--------

So to summarize so far, the five number summary is visually represented as the box plot. The range and IQR can be computed using items from the five number summary.

We cannot compute the mean because we would need the actual data set of values, rather than the summary data. The same goes for the mean absolute deviation (MAD) and the mode. Since your teacher is looking for things that cannot be determined from a box plot, we'll go for answers B, C and E.

In other words, we rule out choices A, D, and F because we can compute or determine those values from a box plot.

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