You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you wont be a hobbit or use an umbrella

Answer:

Stationary matrix S = [ 0.6   0.4 ]

limiting matrix  P = [tex]\left[\begin{array}{ccc}0.6&0.4\\0.6&0.4\\\end{array}\right][/tex]

Step-by-step explanation:

Transition matrix

[tex]p = \left[\begin{array}{ccc}0.8&0.2\\0.3&0.7\\\end{array}\right][/tex]

solving the equation SP = S ( using Markova chain with 2 states )

stationary matrix,  S = [ a , 1 - a ]

given that  SP  = S

[ a , 1 - a ] * [tex]\left[\begin{array}{ccc}0.8&0.2\\0.3&0.7\\\end{array}\right][/tex] =  [ a , 1 - a ]

= a*(0.8) + ( 1 - a ) ( 0.3 ) = a

∴ a = 0.6

hence;  stationary matrix S = [ 0.6   0.4 ]

             limiting matrix  P = [tex]\left[\begin{array}{ccc}0.6&0.4\\0.6&0.4\\\end{array}\right][/tex]

Answer:

[tex]-4p^3-3p^2-17p[/tex]

Step-by-step explanation:

Adding a negative number is the same as subtracting a number. Using this logic, we can change the equation to equal this:

[tex]-3p^3+5p^2-2p-p^3-8p^2-15p[/tex]

Combining like terms, we have negative 3p cubed minus another p cubed, which equals negative 4p cubed, we have 5p squared minus 8p squared, which equals negative 3p squared, and we have negative 2p minus 15p, which is negative 17p.

Answer:

19. 11

21. 119

Step-by-step explanation:

19.

(-5)² - [4(-3 ∙ 2 + 4)² + 3] + 5 =

= (-5)² - [4(-6 + 4)² + 3] + 5

= (-5)² - [4(-2)² + 3] + 5

= (-5)² - [4(4) + 3] + 5

= (-5)² - [16 + 3] + 5

= 25 - 19 + 5

= 6 + 5

= 11

21.

5 - 8[6 - (3 ∙ 2 - 8 + 2|4 ÷ -2 + (-3)| - 4) - 7 · 2] - 3² · (-2) =

= 5 - 8[6 - (3 ∙ 2 - 8 + 2|-2 + (-3)| - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (3 ∙ 2 - 8 + 2|-5| - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (3 ∙ 2 - 8 + 2(5) - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (6 - 8 + 10 - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (-2 + 10 - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - (8 - 4) - 7 · 2] - 3² · (-2)

= 5 - 8[6 - 4 - 7 · 2] - 3² · (-2)

= 5 - 8[6 - 4 - 14] - 3² · (-2)

= 5 - 8[2 - 14] - 3² · (-2)

= 5 - 8[-12] - 3² · (-2)

= 5 - (-96) - 9 · (-2)

= 5 + 96 + 18

= 101 + 18

= 119

Answer:

D and C

Step-by-step explanation:

1) You can cross check using desmos.

2) cos(120) is - 0.5

Answer:

SEE BELOW

Step-by-step explanation:

1. find value of m

a^2 + b^2 = c^2

7.5^2+10^2=c^2

15+100=c^2

115=c^2

square it

=10.7 (not answer)

a^2+b^2=c^2

10.7^2+30^2=c^2

114.49+900=c^2

1014.49=c^2

square it

m=31.9

2.20^2 + 21^2 = 841

29^2=841

yes the triangle is right angled !!!

hope this helps :)

Answer:

y=2x-1

Step-by-step explanation:

The slope is 2/1=2 and the y-intercept is -1.

Answer:

Slope = 2, Y intercept = -1

Step-by-step explanation:

For the Slope use Rise/Run to calculate (you go two up and 1 over which means 2/1 which equals 2).

For the Y intercept find where the line intersects the Y Axis which is -1.

Answer:

Download gauthmath it will help Jesus loves you

that's a point slope form so

y +5 = 2(x -4)

steAnswer:

Step-by-step explanation:

step1 5(9x-8)=4(x+2)

step2 45x -40=4x +8

step3 41x=48

step 4 x=48/41

Start with the answer format we want, and work your way toward forming a single fraction like so

[tex]a + \frac{b}{x+2}\\\\a*1+\frac{b}{x+2}\\\\a*\frac{x+2}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)+b}{x+2}\\\\\frac{ax+2a+b}{x+2}\\\\\frac{ax+(2a+b)}{x+2}\\\\[/tex]

Compare that last expression to (2x+1)/(x+2). Notice how the ax and 2x match up, so a = 2 must be the case.

Then we have 2a+b as the remaining portion in the numerator. Plugging in a = 2 leads to 2a+b = 2*2+b = 4+b. Set this equal to the +1 found in (2x+1)/(x+2) to have the terms match.

So, 4+b = 1 leads to b = -3

Therefore, a = 2 and b = -3

------------------------------------------------

An alternative route:

[tex]\frac{2x+1}{x+2}\\\\\frac{2x+1+0}{x+2}\\\\\frac{2x+1+4-4}{x+2}\\\\\frac{(2x+4)+1-4}{x+2}\\\\\frac{2(x+2)-3}{x+2}\\\\\frac{2(x+2)}{x+2}+\frac{-3}{x+2}\\\\2-\frac{3}{x+2}\\\\[/tex]

I added and subtracted 4 in the third step so that I could form 2x+4, which then factors to 2(x+2). That way I could cancel out a pair of (x+2) terms toward the very end.

------------------------------------------------

Other alternative methods involve synthetic division or polynomial long division. They are slightly separate but related concepts.

Answer:

a = 2

b = -3

Step-by-step explanation:

the secret is seeing that the numerator (top part of the division) contains 2x. that means 2 times the factor of x in the denominator (bottom part of the division).

so, we want to change the numerator that we can simply say the result is 2 and some rest (remainder).

2×(x+2) would be 2x + 4

aha !

and we have 2x+1 up there. so, what had to happen to get from 2x+4 to 2x+1 ? we had to subtract 3. it to get to 2x+4 we have to add 3.

but if we add 3, we need also to subtract 3 to keep the value of the whole expression the same.

therefore we get

(2x+1)/(x+2) = (2x+4)/(x+2) - 3/(x+2) =

= 2×(x+2)/(x+2) - 3/(x+2) = 2 - 3/(x+2)

Answer:

Height of the house = 3 meter (Approx.)

Step-by-step explanation:

Given:

Scale model;

1 centimeter = 0.6 meter

According to graph

Height of cube = 5 cube = 5 centimeter

Find:

Height of the house

Computation:

Height of the house = height of the house in scale model x Scale model

Height of the house = 5 x 0.6

Height of the house = 3

Height of the house = 3 meter (Approx.)

Answer:

d

Step-by-step explanation:

trust me gang

Answer:

the degree is the value of the highest exponent... 4x^3 the exponent is a three

answer "D"

Step-by-step explanation:

Answer:

5^1

Step-by-step explanation:

[tex]\sqrt{5} =5^{\frac{1}{2} }[/tex] (law of indices - fractional powers)

after converting all the numbers to this form:

[tex]\frac{5^{{\frac{2}{3} } } * 5^{\frac{1}{2} } }{5^{\frac{1}{6} } } \\[/tex]

combine using law of indices:

5^(2/3+1/2-1/6) = 5^1

Answer:

7

Step-by-step explanation:

[tex]s = {a}^{2} \: thus \: a = \sqrt{s } = \sqrt{49} = 7[/tex]

Answer:

Step-by-step explanation:

I would begin by distributing the L. It will be easier in the end to do it this way. There are a couple of ways you can do this, but distribution is the easiest. After you distribute the L you have

T = 2L + LRS

Next subtract the 2L to get

T - 2L = LRS. Lastly, to isolate the R, divide away the LS to get

[tex]\frac{T}{LS}-\frac{2L}{LS}[/tex] = R  In that second term, the L's cancel each other out, leaving us with

[tex]\frac{T}{LS}-\frac{2}{S}[/tex] = R

Area of a circle: pi x r^2

---r is the radius of the circle

A = pi x 20^2

A = 3.14 x 400

A = 1256 square miles

Hope this helps!

Answer:

Letter B. Hyperbole is your answer

7/8 = x/56

x = 7 x 7

so, 49/56 = rod

so, 49 pieces will be made

hope it helps :)

Answer:

30.

Step-by-step explanation:

x^2 = 24^2 + 18^2

x^2 = 576 + 324 = 900

x = sqrt900 = 30.

Answer:

2nd is the correct answer for your question

Answer:

1/3^4

1/81

Step-by-step explanation:

(3^2)^-2

We know that a^b^c = a^(b*c)

3 ^(2*-2)

3^-4

We know that a^-b = 1/a^b

1/3^4

1/81

Answer:

4/3

Step-by-step explanation:

To find the slope, we can use the slope formula

m= (y2-y1)/(x2-x1)

   = ( -1 - -13)/( 3 - -6)

    = (-1+13)/( 3+6)

   = 12/9

   = 4/3

Answer:

G. [tex]\displaystyle \frac{4}{3}[/tex]

Step-by-step explanation:

Hi there!

[tex]slope=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]  where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-6,-13) and (3,-1)

[tex]slope=\displaystyle \frac{-1-(-13)}{3-(-6)}\\\\slope=\displaystyle \frac{-1+13}{3+6}\\\\slope=\displaystyle \frac{12}{9}\\\\slope=\displaystyle \frac{4}{3}[/tex]

Therefore, the slope of the line is [tex]\displaystyle \frac{4}{3}[/tex].

I hope this helps!

Answer:

Step-by-step explanation:

Step 1

Find the height:

Step 2

Find the area:

Answer:

16 degrees

Step-by-step explanation:

Tan(?) = perpendicular/base

Tan(?) = 13/46

?=arctan(13/46)=16

Answer:

Step-by-step explanation:

Total people:

Probabilities of men:

Required probability is:

Answer:

c =4 4/9 minutes

Step-by-step explanation:

The formula is

1/a + 1/b = 1/c  where a and b is the time for each working alone and c is the time working together

1/8 + 1/10 = 1/c

Multiply by 40c to clear the fractions  ( 40c is the least common multiple)

40c(1/8 + 1/10 = 1/c)

5c + 4c = 40)

9c = 40

Divide by 9

9c/9 = 40/9

c =4 4/9 minutes

Answer:

780

Step-by-step explanation:

Let x be the original price

x - x*72% is the new price

x - .72x = 218.40

.28x = 218.40

Divide each side by .28

.28x/.28 = 218.40/.28

x =780

Answer: 27

Step-by-step explanation:

[tex]Mean=\frac{16 + 25 + 23 + 12 + 17 + x}{6}=20 \\16 + 25 + 23 + 12 + 17 + x=20(6)\\93+x=120\\x=120-93=27[/tex]

Answer:

27 years old

Step-by-step explanation:

There are originally 5 people in the room.

Their ages are: 16, 25, 23, 12, 17

The sum of their ages is: 93

One person enters the room. That person's age is unknown, so we call it x.

The sum of the ages of the 6 people is:

x + 93

There are 6 people in the room now, so the mean age is (total age divided by number of people):

(x + 93)/6

We are told the mean age is 20.

(x + 93)/6 = 20

x + 93 = 120

x = 27

Answer: 27 years old