Answer correctly and 40 points. Thx. Will report if wrong. ASAP plz! Thx!

Answer Correctly And 40 Points. Thx. Will Report If Wrong. ASAP Plz! Thx!

Answers

Answer 1

Answer:

-7

Step-by-step explanation:

if you multiply by 7 positive it wont work because u cant cancel 7x out and a fraction wont work because theres no fraction involved in this so ur answer is A


Related Questions

The sum of two numbers is 8 and their difference is half of the sum. Find the
two numbers.

Answers

Answer:

6 and 2

Step-by-step explanation:

6+2= 8, so they can combine to equal 8. First box checked. Then, they can also be subtracted to get 4, half of 8. 8/2= 4 and 6-2=4. Second box checked.

Hope this helped :D

Step-by-step explanation:

Let's take the numbers as m and n and classify the info

m+n=8

m-n=4

So solving the sums Simultaneously you can get

2n=4

n=2

Substituting this value gives

2+m=8

m=6

Inorder to check if your answers are valid add them to the equations

6+2=8✅

6-2=4✅

Therefore the answers are valid

the expression when b=3 and y= -3
5b-y​

Answers

Answer:

18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Step-by-step explanation:

Step 1: Define

Identify

b = 3

y = -3

5b - y

Step 2: Evaluate

Substitute in variables:                                                                                     5(3) - -3Multiply:                                                                                                             15 - - 3Subtract:                                                                                                            18

Need help please I don’t get it

Answers

the e-function stuff can be confusing sometimes, but notices that g(x) / the blue line, is just somewhat lower, rest is the same.

how much lower? look at the y-intercepts

f(0)= "about 5"

g(0)= "about -3"

with this y-intercept only option c can work

Solve the system of linear equations below.

6x + 3y = 33
4x + y = 15

A.
x = 2, y = 7
B.
x = -13, y = 7
C.
x = - 2/3, y = 12 2/3
D.
x = 5, y = 1

Answers

Answer:

A. x=2 y=7

Step-by-step explanation:

-12x -3 = 3y

6x + 3y = 33

sooo you add them up...

so its

-6x = -12

x=2

and then you plug in the x value into one of the equations

6x + 3y = 33

6(2) + 3y = 33

12 + 3y = 33

3y = 33 - 12

3y = 21

21/3=7

y=7


Find the volume
h=9cm

8cm

8cm

Answers

Answer: (8x8x9)/3=192

If a number is added to the numerator of 5/6 and twice as much is added to the denominator the result is 3/5 find the number

Answers

Answer:

"(5+x)/(6+2x) = 3/5" is the answer

A rectangle's length is three times as long as it is wide. Which expression represents the change in area if the width of the rectangle is increased by 1?
1. 3x^2
2. 3x
3. 3x^2+3x
4. the area increases by 3

Answers

Step-by-step explanation:

Let's say the rectangle's width is equal to y. We know that the length is three times the width, so the length = 3 * y. We also know that the area for a rectangle is equal to length * width, so the area, z, is equal to

(3*y) * y = z

3 * y² = z

Now, let's increase the width of the rectangle by 1. We can replace y with y+1 (as y+1 is 1 greater than y), and 3 * y with 3 * (y+1) to get

3*(y+1) * (y+1) = new area

(3y+3)*(y+1) = new area

3y²+3y +3 y + 3 = new area

3y² + 6y + 3 = new area

The difference in area is equal to the new area subtracted by the old area, or

3y²+6y+3 - 3y² = 6y +3. The variable for x is not given, so if x = (2y+1), the answer would be the second choice. However, solely using the information given, it is impossible to determine a solution outside of saying that it is not option 4, as 6y + 3 ≠ 3

Solve the given system by the substitution method
5x + y 19
7x-2y = 13​

Answers

Answer:

x = 3 , y = 4

Step-by-step explanation:

5x + y = 19 --------- ( 1 )

=> y = 19 - 5x

7x - 2y = 13 ------------ ( 2 )

Substitute y in ( 2 ) :

                        7x - 2( 19 - 5x ) = 13

                        7x - 38 + 10x = 13

                        17x = 13 + 38

                        17x = 51

                           x = 3

Substitute x in ( 1 ) :

                           5x + y = 19

                           5( 3 ) + y = 19

                            15 + y = 19

                              y = 19 - 15

                               y = 4

2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the formula for trapezium = 0.5x b+axh

Given:

Base=

Top (a) =

Height =

3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.

Applying the formula for parallelogram=bxh

Given:

Base=

Height=

pahelp po thanks​

Answers

Answer:

2. 2200 m²

3. 703 m²

Step-by-step explanation:

2. Given,

Base (b) = 45m

Top (a) = 35m

Height (h) = 55m

Area = (a+b)*h/2

= (45+35)*55/2

= 85*55/2 = 2200 m²

3. Given,

Base (b) = 19m

Height (h) = 37m

Area = b*h

= 19*37

= 703 m²

(The * sign represents the multiplication sign)

Answered by GAUTHMATH

Answer:

2. area = 2200 m²

3. area = 703 m²

Step-by-step explanation:

2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the

formula for trapezium = 0.5 * (b+a) * h

Given:

Base= 45 m

Top (a) = 35 m

Height = 55 m

area = 0.5 * (b+a) * h

area = 0.5 * (45 m + 35 m) * 55 m

area = 2200 m²

3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.

Applying the formula for parallelogram = b * h

Given:

Base= 19 m

Height= 37 m

area = b * h

area = 19 m * 37 m

area = 703 m²

Seth and Ted can paint a room in 5 hours if they work together. If Ted were to work by himself, it would take him 2 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick?

Answers

Answer:

9 hours

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x/x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.Answer:

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x / x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

Cross product

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

Cross product

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.0990195135927

Approximately,

x = 9 hours or -1 hour

It can't take Seth negative hours to work

Therefore,

x = number of hours it would take Seth to work by himself = 9 hours

Express these system specifications using the propositions p “The user enters
a valid password,” q “Access is granted,” and r “The user has paid the
subscription fee” and logical connectives (including negations).
a) “The user has paid the subscription fee, but does not enter a valid
password.”
b) “Access is granted whenever the user has paid the subscription fee and
enters a valid password.”
c) “Access is denied if the user has not paid the subscription fee.”
d) “If the user has not entered a valid password but has paid the subscription
fee, then access is granted.”

Answers

Answer:

a) r ⋀~p

b)(r⋀p)⟶q

c) ~r ⟶ ~q

d) (~p ⋀r) ⟶q

Step-by-step explanation:

To solve this question we will make use of logic symbols in truth table.

We are told that;

p means "The user enters

a valid password,”

q means “Access is granted,”

r means “The user has paid the

subscription fee”

A) The user has paid the subscription fee, but does not enter a valid

password.”

Fist part of the statement is correct and so it will be "r". Second part of the statement is a negation and will be denoted by ~p. Since both statements are joined together in conjunction, we will use the conjuction symbol in between them which is "⋀" Thus, we have; r ⋀~p

B) Still using logic symbols, we have;

(r⋀p)⟶q

⟶ means q is true when r and p are true.

C) correct symbol is ~r ⟶ ~q

Since both statements are negation of the question. And also, if ~r is true then ~q is also true.

D) Similar to answer A to C above, applying similar conditions, we have (~p ⋀r) ⟶q

Create a circle such that its center is point A and B is a point on the circle.

Answers

Answer:

The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.

Find the range of the data.
Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88

Answers

Answer:

24

Step-by-step explanation:

To find the range, you must subtract the lowest value from the highest value in the data set. If you organize the set from least to greatest, 72 is the lowest, and 96 is the highest.

So, 96 - 72 = 24, which is the range.

The population of a colony of 300 bacteria grows exponentially. After 2 hours, the population reaches 500. How much time will it take for the population to reach 9,600

Answers

Answer:

t = 13.56915448 hrs.

Step-by-step explanation:

500 = 300 [tex]e^{2k}[/tex]

5/3 = [tex]e^{2k}[/tex]

ln(5/3) = 2k ln(e)

k = ln(5/3)/2

k= 0.255412812

~~~~~~~~~~~~

9600 = 300 [tex]e^{0.255412812 t}[/tex]

32= [tex]e^{0.255412812 t}[/tex]

ln(32) = [tex]0.255412812 t[/tex] ln(e)

t = ln(32)/0.255412812

t = 13.56915448 hrs.

Consider the function f(x) = x2 and the function g(x) = 3x2. How will the graph of g(x) differ from the graph of f(x)?

Select the correct answer

The graph of g(x) is the graph of f(x) shifted to the left 3 units.

The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3.

The graph of g(x) is the graph of f(x) compressed vertically by a factor of

The graph of g(x) is the graph of f(x) shifted up 3 units. ​

Answers

Answer:

Third Choice - The graph of g(x) is the graph of f(x) compressed vertically by a factor of 3

Step-by-step explanation:

x^2 is the the parent function, so it opens up with a normal compression.

Any number > (greater than) 1 as a coefficient of x will lead to a vertical compression (narrower parabola), while any number < (less than) 1 as a coefficient of x will lead to a vertical stretch (wider parabola).

So, 3x^2 would have to have to be a compressed parabola.

I hope this helps!

Answer:

The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3.

Step-by-step explanation:

A vertical stretch or shrink of a function, kf(x), results from multiplying the entire function by a constant, k.

In this case, g(x) equals 3 times f(x). If k > 1, then the graph will be stretched vertically (along the direction of the y-axis) by a factor of k.

So, the graph of g(x) is the graph of f(x) stretched vertically by a factor of 3.

A basketball team is to play two games in a tournament. The probability of winning the first game is .10.1 the first game is won, the probability of winning the second game is 15. If the first game is lost, the probability of winning the second game is 25. What is the probability the first game was won if the second game is lost? Express the answer with FOUR decimal points.

Answers

Answer:

[tex]P(\frac{A}{B'})[/tex]=0.111

Step-by-step explanation:

Given:

The probability of winning the first game is 10.1

The first game is won

The probability of winning the second game is 15

If the first is lost, the probability of winning the second game is 25

Solution:

[tex]P(B)=P(A)P(\frac{B}{A})+P(A')P(\frac{B}{A'})\\ =0.1(0.15)+(0.3)*0.25)\\P(B)=0.24 ------(1)\\P(\frac{A}{B})=\frac{P(\frac{B}{A})P(A) }{P(B)}\\ =\frac{0.15(0.1)}{0.24}\\ =0.0625 ------(2)\\P(B')=1-P(B)=0.76 ------(3)\\P(A)=P(B)P(\frac{A}{B})+P(B')P(\frac{A}{B'})\\0.1=0.24(0.0625)+0.76(p(\frac{A}{B'} ))\\P(\frac{A}{B'})=0.111[/tex]

Answer:

[tex]P(W_1/W_2')=0.1110[/tex]

Step-by-step explanation:

Probability of winning the first game be considering the given factors be, [tex]W_1=0.1[/tex]

Probability of winning the second game be considering the given factors be, [tex]W_2[/tex]= probability of winning the second game when the first game is won + probability of winning the second game when the first game is lost:

[tex]P(W_2)=P(W_1).P(W_2/W_1)+P(W_1').P(W_2/W_1')[/tex]

[tex]P(W_2)=0.1\times 0.15+0.9\times 0.25[/tex]

[tex]P(W_2)=0.24[/tex]

Hence the probability of losing the second game:

[tex]P(W_2')=1-P(W_2)[/tex]

[tex]P(W_2')=0.76[/tex]

Probability of winning the first game when the second game is won:

[tex]P(W_1/W_2)=\frac{P(W_2/W_1).P(W_1)}{P(W_2)}[/tex]

[tex]P(W_1/W_2)=\frac{0.15\times 0.1}{0.24}[/tex]

[tex]P(W_1/W_2)=0.0625[/tex]

Probability of winning the first game be considering the given factors, [tex]W_1[/tex]= probability of winning the first game when the second game is won + probability of winning the first game when the second game is lost:

[tex]P(W_1)=P(W_2).P(W_1/W_2)+P(W_2').P(W_1/W_2')[/tex]

[tex]0.1=0.24\times0.0625+0.76\times P(W_1/W_2')[/tex]

[tex]P(W_1/W_2')=0.1110[/tex]

What does y equal in the solution of the system of equations below? 5y-3x-4z=22 2z-2x=-6 2z+3x=-6

Answers

9514 1404 393

Answer:

  y = 2

Step-by-step explanation:

Subtracting the second equation from the third gives ...

  (2z +3x) -(2z -2x) = (-6) -(-6)

  5x = 0

  x = 0

Using this in the third equation, we have ...

  2z +0 = -6

  z = -3

And substituting these values into the first equation, we have ...

  5y -3(0) -4(-3) = 22

  5y = 10 . . . . . subtract 12

  y = 2

__

The solution to the system is (x, y, z) = (0, 2, -3).

Nikola thinks that the model that reflects the growth of smartphones shipped from manufacturers to stores around the world may be logistic rather than exponential. Do you agree with Nikola

Answers

Answer:

When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.

Step-by-step explanation:

Exponential model:

The variable keeps growing consistently, at a fixed rate.

Logistic model:

The variable starts growing, but as it approaches a limit, for example, the carry capacity of an environment, the growth rate starts to decrease, until the variable stabilizes at a fixed value.

Growth of smartphones shipped from manufacturers to stores around the world.

When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.

Find the measure of ∠C in the image below. 60+55+m∠C=180

Answers

Answer:

angle C= 65 degree

Step-by-step explanation:

60+55+x= 180

115+x= 180

x= 180-115

x= 65

angle C= 65 degree

Please mark me as brainliest.


51
What is the inverse of the function f(x) = 2x + 1?
Oh(x) =
1
2x-
o h«x)= kx +
- 3x-2
Oh(x) =
Oh(x) =
Mark this and return
Save and Exit
Next
Submit
Type here to search
81
O
10:49 AM
^ D 0x
mamman

Answers

Answer:

let inverse f(x) be m:

[tex]m = \frac{1}{2x + 1} \\ 2x + 1 = \frac{1}{m} \\ 2x = \frac{1 - m}{m} \\ x = \frac{1 - m}{2m} [/tex]

substitute x in place of m:

[tex]{ \bf{ {f}^{ - 1}(x) = \frac{1 - x}{2x } }}[/tex]

a) Read section 1.5 in the Yakir textbook. If you were a teacher and had 30 students in your class and wanted to know the class average on the first quiz, would you use a parameter or a statistic

Answers

Answer:

Parameter

Step-by-step explanation:

Required

Parameter of Statistic

From the question, we understand that the teacher is to calculate the class average.

To calculate the class average, the teacher will use the mean function/formula, which is calculated as:

[tex]Mean = \frac{\sum x}{n}[/tex]

Generally, mean is an example of a parameter.

So, we can conclude that the teacher will use parameer

help please i don’t understand it at this moment

Answers

Answer:

it's H. 1/2 in.=1,000 ft

F. 1 in.= 100ft

[tex]{hope 8 helps}}[/tex]

Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
Ox45)
0 - 6x - 5 < 10 - x
0 -6x + 15 < 10 - 5
E

-
3
5
2
-1
0
1
2
3

Answers

Answer:

45.9

Step-by-step explanation:

1). A population of 20 rabbits is released into a wildlife region. The population is growing at a rate of 60% per year.
A) the General Equation from the Video was: P(x) = (blank)


What is the population of rabbits after 5 years?

B) the Evaluated equation I used to get the following answer is (blank)
and After five years there will be(blank)
rabbits.

And What is the population of rabbits after 8 years?

c) the Evaluated equation I used to get the following answer is(blank)
and After eight years there will be(blank)
rabbits.

Answers

Answer:

(a) A = 20(1.6)^t

(b) 210 rabbits

Step-by-step explanation:

Initial number of rabbits = 20

rate of growth, R = 60 % annually

(A) The general equation is  

[tex]A = P \left ( 1+\frac{R}{100} \right )^t\\\\A = 20\left ( 1+\frac{60}{100} \right )^t\\\\A = 20 (1.6)^t[/tex]

(B) Let the time, t = 5 years

So, the population after 5 years is

[tex]A = 20 (1.6)^5\\\\A = 209.7 = 210 rabbits[/tex]

The volume of a pyramid is 240 cubic centimeters. The pyramid has a rectangular base with sides 6cm by 4cm. Find the altitude and lateral surface area of the pyramid if the pyramid has equal lateral edges​

Answers

Answer:

altitude = 30 cm

lateral surface area = 301 cm² (approximately)

Step-by-step explanation:

let the altitude be x,

240=6*4*x/3

or, x=30 cm

Lateral surface area,

=l×√(w/2)²+h²]+w×√[(l/2)²+h²]

=6×√[(4/2)²+30²]+4×√[(6/2)²+30²]

≈300.99806

≈ 301 cm²

Answered by GAUTHMATH

Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative​ frequency?Complete the table below. Use the minimum data entry as the lower limit of the first class.Class Frequency, f Relative frequencyx-x x xx-x x xx-x x xx-x x xx-x x x sumf= X?​(Type integers or decimals. Round to the nearest thousandth as​ needed.)DATA:Triglyceride levels of 26 patients​ (in milligrams per deciliter of​ blood)138 199 240 143 294 175 240 216 223180 138 266 161 175 402 172 459 147391 152 199 294 188 320 421 161

Answers

Answer:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

Step-by-step explanation:

Solving (a): The frequency distribution

Given that:

[tex]Lowest = 138[/tex] --- i.e. the lowest class value

[tex]Class = 5[/tex] --- Number of classes

From the given dataset is:

[tex]Highest = 459[/tex]

So, the range is:

[tex]Range = Highest - Lowest[/tex]

[tex]Range = 459 - 138[/tex]

[tex]Range = 321[/tex]

Divide by the number of class (5) to get the class width

[tex]Width = 321 \div 5[/tex]

[tex]Width = 64.2[/tex]

Approximate

[tex]Width = 64[/tex]

So, we have a class width of 64 in each class;

The frequency table is as follows:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

Solving (b) The relative frequency histogram

First, we calculate the relative frequency by dividing the frequency of each class by the total frequency

So, we have:

[tex]\begin{array}{ccc}{Class}& {Frequency} & {Relative\ Frequency} & 138 - 202 & 14 & 0.53 & 203 - 267 & 5 & 0.19 & 268 - 332 & 3 & 0.12 & 333 - 397 & 1 & 0.04 & 398 - 462 & 3 & 0.12 \ \end{array}[/tex]

See attachment for histogram

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

What is net cash flow

Answers

Net cash flow is a profitability metric that represents the amount of money produced or lost by a business during a given period.

-10 degrees Celsius is what Fahrenheit

Answers

Answer:

Step-by-step explanation:

i think if its -10 degrees i think the fahrenheit would be 50 degrees

If the domain of a function that is reflected over the x-axis is (1, 5), (2, 1), (-1, -7), what is the range?
A. (1, -5), (2, -1), (-1, 7)

B. (5, 1), (1, 2), (-7, -1)

C. (-5, -1), (-1, -2), (7, 1)

D. (-1, 5), (-2, 1), (1, -7)

Answers

Answer:

A. (1, -5), (2, -1), (-1, 7)

Step-by-step explanation:

Reflecting a function over the x-axis:

When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:

[tex](x,y) \rightarrow (x,-y)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,5) \rightarrow (1,-5)[/tex]

[tex](2,1) \rightarrow (2,-1)[/tex]

[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]

Thus the correct answer is given by option a.

Answer:

It is letter A and please give me brainliest

Step-by-step explanation:

The thickness X of aluminum sheets is distributed according to the probability density function f(x) = 450 (x2 - x) if 6 < x < 12 0 otherwise 5-1 Derive the cumulative distribution function F(x) for 6 < x < 12. The answer is a function of x and is NOT 1! Show the antiderivative in your solution. 5-2 What is E(X) = {the mean of all sheet thicknesses)? Show the antiderivative in your solution.

Answers

Solution :

Given :

[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]

1. Cumulative distribution function

[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]

              [tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]

             [tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]

             [tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]

             [tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]

            [tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]

2.  Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]

                       [tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]

                     [tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]

                     [tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]

                     [tex]$=\frac{1}{450} [4608 - 252]$[/tex]

                    = 17.2857

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