a communication system consists of n components, each of which will, independently, function with probability p. the total system will be able to operate effectively if at least one-half of its components function. (a) let x denote the number of functioning components out of the n components. what is the distribution of x? (b) what is the probability that a 5-component system will function? (c) for what values of p is a 5-component system more likely to operate effectively than a 3-component system?

Answers

Answer 1

A Communication system consists of n components.

a) Binomial distribution,

P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾

b) For 5-component system,

P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5

c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.

Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .

(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.

(b) Now , 5-component system is function . That is n=5

Probability that 5-components system will function is P(X= 5)

= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)

(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is

⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵

Whereas the corresponding probability for a 3-components system

³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3

³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³

5-Component system is better than 3-Components system if

10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³

=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²

Which reduce to

3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0

either p> ½ or p <1

=> p belongs to ( 0.5, 1)

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Related Questions

Bob is planning to start an it business, servicing computers that are infected with viruses. to start his new enterprise, bob estimates that he will need to spend $5,000 on equipment $6,000 on premises, $4,000 on advertising. all of these costs are fixed. he is planning on charging his customers $250 each to fix an infected computer. for each computer that he fixes, he must spend $25 on parts and software. suppose we let x be the number of computers that bob fixes. if bob only fixes 50 computers, what is his total loss?

Answers

If Bob only fixes 50 computers, his total loss is $3,750.

What is the total loss?

The total loss results from the negative difference between the total revenue and the total costs.

The total costs consist of variable and fixed costs.

The result is a loss when the total costs exceed the total revenue.  This result becomes a profit or income when the total revenue exceeds the total costs.

Fixed Costs:

Equipment = $5,000

Premises = $6,000

Advertising = $4,000

Total fixed costs = $15,000

Variable cost per unit = $25

Selling price per unit = $250

Total number of computers fixed = 50

The total variable cost for 50 units = $1,250 (50 x $25)

The total costs (fixed and variable) = $16,250

The sales revenue for 50 units = $12,500 (50 x $250)

Loss = $3,750 ($12,500 - $16,250)

Thus, Bob will incur a total loss of $3,750 if he fixes only 50 computers based on his fixed and variable costs.

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Please tell me what is 1,359 divided by 45 is ??

Answers

30.2 is the answer to this question

What is the Answer to 7 1/2 / 9

Answers

Answer:

7.5/9 = 0.83333

0.83333 = 5/6

7 1/2 / 9 = 5/6

Please help me solve this problem

Answers

The following table justifies the reasons of each step of the solution by stating the algebraic property that is used to get to each steps

What are algebraic equations?

Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of a variable, a coefficients and a constants.

          Statement                                                           Reason

4.5(8-x)+36=102-2.5(3x+24)                                           Given

4.5(8-x)=66-2.5(3x+24)                           Subtracting 36 from the both sides

36-4.5x=66-7.5x-60                       Opening the brackets on the both sides

36-4.5x=-7.5x+6                                       Subtracting the constants on RHS

36+3x=6                                                         Adding -7.5x on the both sides

3x=-30                                                    Subtracting 36 from the both sides.

x=-10                                                             Dividing by 3 on the both sides.

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X=
//////////////////////////////

Answers

Answer: [tex]x=90[/tex]

Step-by-step explanation:

Using the alternate exterior angles theorem,

[tex]180-x=x\\\\180=2x\\\\x=90[/tex]

In Exercises 1-3, graph AABC and its image after a reflection in the given line.
1. A(0, 2), B(1, -3), C(2, 4); x-axis
1.
2. A(-2,-4), B(6,2), C(3. – 5); y-axis
3. A(4, -1), B(3, 8), C(-1, 1); y = -2

Answers

The figures after each reflection are given at the end of the answer.

Reflection over the x-axis


The rule for the reflection over the x-axis is:

(x,y) -> (x, -y)

Hence the signal of the y-coordinate is changed.

Then the coordinates of the image of triangle ABC are given as follows:

A'(0,-2), B'(1,3) and C(2,-4)

Reflection over the y-axis


The rule for the reflection over the x-axis is:

(x,y) -> (-x, y)

Hence the signal of the x-coordinate is changed.

Then the coordinates of the image of triangle ABC are given as follows:

A'(2,-4), B'(-6,2) and C'(-3,-5)

Reflection over y = -2

The rule for the reflection over the line y = -2 is:

(x,y) -> (x, y +/- constant)

The constants for each point are given as follows:

A': -3, hence point (4,-3), as -1 is one unit above y = -2, hence the reflected coordinate will be one unit below.B': -12, hence point (3,-12), as 8 is 10 units above y = -2, hence the reflected coordinate will be ten units below.C': -5, hence point (-1, -5), as 1 is 3 units above y = -2, hence the reflected coordinate will be three units below at y = -5.

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find a number of ways in which 4 algebra books, 5 geometry and 2 chemistry books can be placed on a shelf so that the arrangement begins and ends with a chemistry book

Answers

4 algebra books, 5 geometry and 2 chemistry books can be arranged in 5760 ways.

What is permutation?A permutation of a set is a loosely defined arrangement of its members into a sequence or linear order, or a rearrangement of its elements if the set is already ordered. The act or process of changing the linear order of an ordered set is also referred to as "permutation." A permutation is a specific arrangement of objects. Set members or elements are arranged in a sequence or linear order here. For example, the permutation of set A=1,6 is 2, as in 1,6,1. There are no other ways to arrange the elements of set A, as you can see.

Given ,

4 algebra books , 5 geometry , 2 chemistry books,

The number of permutations =

2! x 5! x 4!

= (1 x 2) x (5 x 4 x 3 x 2) x (4 x 3 x 2)

= 2 x (120) x (24)

= 5760 ways.

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Solve 2x + 32 + x = 17.

x = 5
x = 0.2
x = −0.2
x = −5
Please and thank you.

Answers

2x+32+x = 17

Combine 2x and X to get 3x.

3x+32 = 17

Subtract 32 on both sides.

3x = 17−32

Remains 32 of 17 to obtain −15.

3x = −15

Divide both sides by 3.

x = -15/3

Divide −15 by 3 to get −5.

x = −5

The last option is correct.

The value of x after solving the given equation 2x + 32 + x = 17, is x = -5, which is the last option.

Given an equation:

2x + 32 + x = 17

It is required to find the value of x after solving or simplifying the equation.

In order to get the value of x, the equation has to be solved in such a way that the terms with the variable have to be placed on one side and the constant terms on the other side.

Consider:

2x + 32 + x = 17

Add x and 2x since they are like terms in variables.

3x + 32 = 17

Subtract 32 from both sides of the equation.

3x = 17 - 32

3x = -15

Divide both sides of the equation by 3.

x = -5

Hence, the value of x is -5.

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Which of the following describes the graph of y 3 -3 in a coordinate plane?

Answers

ANSWER

The boundary line is a solid horizontal line that passes through (0, -3). The half-plane that does not contan the origin is shaded.

(the answer is the second option)

EXPLANATION

The graph is

first answer will be brainliest

You decide to use a scale of 1 in: 7 ft to make a scale drawing of your classroom. If the actual length of your classroom is 49 feet, what should the length of the classroom in the drawing be?

Answers

The dimension of the length of the classroom in the drawing is calculated to be 7 ft

What is scale of a map?

The scale of a map represents by how much a map is reduced or increased. Most of the times the map is smaller than what is being represented hence the scale is usually a reduction.

How to find the length of the classroom in the drawing

Give that

1 in in drawing represent 7 ft in actual length

If the actual length of your classroom is 49 feet then we solve as follows to get the dimension in the drawing:

1 in = 7 ft

? in = 49 ft

cross multiplying gives

7 * ? = 49 * 1

? = 49 / 7

? = 7 in

Hence, the conclusion is that the unknown dimension in the drawing represented as ? is equal to 7 in.

This implies that 7 in in the drawing represents actual distance of 49 ft and this is a reduction

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5. Which expression does not have a value of 3?
å
O
O
-16-(-11)
19-16
-13-(-16)
1-(-2)

Answers

The first one.

-16 - (-11)

Would be -16 + 11,

Which is equal to -4

a potter forms a piece of clay into a right circular cylinder. as she rolls it, the height of the cylinder increases and the radius decreases. assume that no clay is lost in the process. suppose the height of the cylinder is increasing by centimeters per second. what is the rate at which the radius is changing when the radius is centimeters and the height is centimeters?

Answers

The radius of the cylinder is decreasing at the rate of 0.22 cm per second.

One of the most important and fundamental curvilinear of a geometric shapes, a right circular cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.The radius of the cylinder is the length of the line joining the circumference and the center of the circle.The derivative of the logarithm,  dx /dt, is also the growth rate. The fractional change, must be used to represent a minor change in the logarithm. if the variable grows at the constant fixed rate g.

Volume of a right circular cylinder = π r² h

Now we differentiate w.r.t to get :

[tex]\frac{dV}{dT} =2 \pi r h\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]

Taking the values we get :

[tex]-34.3 = 154 \frac{dr}{dt}[/tex]

[tex]\frac{dr}{dt} = -0.22[/tex]

Hence the radius is decreasing at the rate of -0.22 cm per second.

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Find the measure of each angle in the diagram

Answers

The measure of each angle in the diagram is as follows:

3y + 11 = 50 degrees10y = 130 degrees(4x - 22) = 50 degrees7x + 4 = 130 degrees

How to find the angles in intersecting lines?

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, the measure of each angle in the diagram can be calculated as follows:

10y = 7x + 4 (vertically opposite angles)

3y + 11  = 4x -22(vertically opposite angles)

Therefore,

10y - 7x = 4

3y - 4x = -22 - 11

10y - 7x = 4

3y - 4x = -33

multiply equation(ii) by 1.75

10y - 7x = 4

5.25y - 7x = - 57.75

subtract equation(ii) from equation(i)

Hence,

4.75y = 61.75

y = 61.75 / 4.75

y = 13

Therefore,

10(13) - 7x = 4

130 - 7x = 4

130 - 4 = 7x

7x = 126

x = 126 / 7

x = 18

Therefore, the unknown angles are as follows;

3y + 11 = 3(13) + 11 = 50 degrees10y = 10(13) = 130 degrees(4x - 22) = 4(18) - 22 = 50 degrees7x + 4 = 7(18) + 4 = 130 degrees

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(9-7)2+4*3(2-4)2. By gtsggggy

Answers

Answer: it

Step-by-step explanation:

!!!

can someone help me really quick please

Answers

The value of p is $ 6.75.

It is given in the figure that the price of 6 apples in the grocery store is $ 4.50.

We have to find the value of p which is the price of 9 apples.

By unitary method, we can write,

Price of 1 apple = 4.5/6 = 3/4 =  $ 0.75.

Hence,

Price of 9 apples = 0.75*9 = 6.75 dollars  

Hence, the value of p is $ 6.75.

Unitary method

The unitary method is generally a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.

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How far up a wall will an 11-meter ladder reach, if the foot of the ladder is 4 meters away from the base of the wall?
A. 11 m
B. 4 m
C.
D.

Answers

Answer:

√105 meters, or about 10.25 meters

Step-by-step explanation:

[tex] {x}^{2} + {4}^{2} = {11}^{2} [/tex]

[tex] {x}^{2} + 16 = 121[/tex]

[tex] {x}^{2} = 105[/tex]

[tex]x = \sqrt{105} = 10.25[/tex]

Answer:

10.246 or sqrt(105)

Step-by-step explanation:

Given,

length of the ladder = 11 m

distance of the foot of the ladder from the base of the wall = 4 m

According to Pythagoras' theorem,

(hypotenuse)^2 = (side1)^2 + (side2)^2

As per the problem,

hypotenuse = 11m

side1 = distance from wall = 4 m

side2 = height reached by the ladder on the wall

that is, (11)^2 = (4)^2 + (side2)^2

              121 = 16 + (side2)^2

               121 - 16 = (side2)^2

                (side2)^2 = 105

                  (side2) = sqrt(105) = 10.246 m

Hence, the ladder can reach up to 10.246 m height on the wall.

3) A car can travel 442 miles on 26 gallons of gasoline. How much gasoline will it need to go 102 miles?

Answers

Answer:

The car will need 6 gallons of gasoline to travel 102 miles

Explanation:

Given that the car travels 442 miles on 26 gallons of gasoline.

Because the more the distance, the more the volume of gasoline used, this is a direct proportion.

So, we have:

[tex]\begin{gathered} V=\frac{102\times26}{442} \\ \\ =6 \end{gathered}[/tex]

It will need 6 gallons.

At a high school, students can choose between three art electives, four history electives, and five computer electives.
Fach student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
O
7C2
1202
С
.?
122
O (G) 4401)
12Cz
12P2
Mark this and return
Save and Exit
Next
Submit

Answers

Expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.

As given in the question,

Number of art electives students = 3

Number of history electives students = 4

Number of computer electives students = 5

Choosing an art electives students = ³C₁

Choosing an history electives students = ⁴C₁

Expression represents the probability that a student chooses an art elective and a history elective

= (³C₁⁴C₁) / ¹²C₂

Therefore, expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.

The complete question is:

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.

Which expression represents the probability that a student chooses an art elective and a history elective?

a. ⁷C₂ / ¹²C₂

b. ⁷P₂ / ¹²P₂

c. (³C₁⁴C₁) / ¹²C₂

d. (³P₁⁴P₁) / ¹²P₂

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A square has approximately 300 square feet . The length of each side of the square is between which two whole numbers?

Answers

Area = 300 ft^2

Formula

Area = length of a side x length of a side

Substitution

300 = length of a side ^2

[tex]\sqrt{300}[/tex][tex]\sqrt{300}\text{ = 17.32}[/tex]

The length of a side is between 17 and 18

Answer:

The length of the side of the square is approximately [tex]17.32[/tex] feet, which lies between the whole numbers [tex]17[/tex] and [tex]18[/tex].

Step-by-step explanation:

Step 1: Assume your variable

Since all the sides of a square are the same, let's consider the side to be the variable: [tex]x[/tex].

Step 2: Create an equation

The formula for the area of a square is:

[tex]\text{Area}=\text{Side}^{2}[/tex]

We have assumed the side to be [tex]x[/tex], and the area is said to be [tex]300[/tex], so substitute these values into the formula:

[tex]\text{Area}=\text{Side}^{2}\\300=x^{2}[/tex]

Step 3: Solve the equation

Using the formula for the area of a square, we came to find an equation:

[tex]x^{2}=300[/tex]

Now, let's find the value of [tex]x[/tex]:

[tex]x^{2}=300\\\\\text{Square root both sides of the equation:}\\\sqrt{x^{2}}=\sqrt{300}\\\\\text{Simplify:}\\x=\sqrt{300}\\\\\text{Calculate:}\\x\approx 17.32[/tex]

The length of the side of the square is approximately [tex]17.32[/tex] feet.

As we know, this number lies between [tex]17[/tex] and [tex]18[/tex].

Write the equation of the line that passes through the points (3,1)(3,1) and (-7,-1)(−7,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answers

Answer:

[tex]\textsf{Point-slope form}: \quad y-1=\dfrac{1}{5}(x-3)[/tex]

Step-by-step explanation:

Define the given points:

(x₁, y₁) = (3, 1)(x₂, y₂) = (-7, -1)

Substitute the defined points into the slope formula to find the slope of the line:

[tex]\implies \textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{-7-3}-\dfrac{-2}{-10}=\dfrac{1}{5}[/tex]

Substitute the found slope and one of the points into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=\dfrac{1}{5}(x-3)[/tex]

Simplify to slope-intercept form, if necessary:

[tex]\implies y-1=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]

[tex]\implies y=\dfrac{1}{5}x+\dfrac{2}{5}[/tex]

Solve. (−7x−14)−(x−5)

Answers

Step-by-step explanation:

-7x(x-5)-(-14)(x-5)

-7x²+35+14x-70

-7x²-14x-35

Hope this is correct

Have a good day

the life of light bulbs is distributed normally. the variance of the lifetime is 225225 and the mean lifetime of a bulb is 520520 hours. find the probability of a bulb lasting for at most 533533 hours. round your answer to four decimal places.

Answers

The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225. The probability that a light bulb will survive at most 533 hours is 0.86.

Given that,

The lifespan of light bulbs is generally distributed. The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225.

We have to calculate the probability that a light bulb will survive at most 533 hours.

We would use the normal distribution formula, which is stated as, because the lifespan of light bulbs is distributed regularly,

z = (x - µ)/σ

Where

x = life of light bulbs.

µ = mean lifetime

σ = standard deviation

From the information given,

µ = 520 hours

Variance = 225

σ = √variance = √225

σ = 15

The probability that a light bulb will last for no more than 560 hours is given by

P(x ≤ 533)

For x = 533

z = (533 - 520)/15 = 0.86

According to the normal distribution table, 0.86 represents the probability for the z score.

Therefore, the probability that a light bulb will survive at most 533 hours is 0.86.

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Which of the following represents the dimensions of the room

Answers

Given:

The length of the rectangular room is 6 more than the width.

The area of the room, A = 27 square units.

Required:

We need to find the dimensions of the given rectangular room.

Explanation:

Let w be the width of the rectangle.

6 more than means add 6.

The length of the rectangle, l= w+6.

Consider the area of the rectangle formula.

[tex]A=lw[/tex]

Substitute A = 27, and l=w+6 in the formula.

[tex]27=(w+6)w[/tex]

[tex]27=w^2+6w[/tex]

Subtract 27 from both sides of the equation.

[tex]27-27=w^2+6w-27[/tex]

[tex]0=w^2+6w-27[/tex]

[tex]w^2+6w-27=0[/tex][tex]Use\text{ }6w=9w-3w.[/tex]

[tex]w^2+9w-3w-27=0[/tex]

Take out the common multiple.

[tex]w(w+9)-3(w+9)=0[/tex]

[tex](w+9)(w-3)=0[/tex]

[tex](w+9)=0,(w-3)=0[/tex][tex]w=-9,3[/tex]

The measure is always positive.

[tex]w=3\text{ units,}[/tex]

Substitute w =3 in the equation l =w+6.

[tex]l=3+6=9\text{ units.}[/tex]

We get l =9 units and w =3 units.

Final answer:

The dimensions of the room are 3 and 9.

In trIangle OPQ, p = 3.4 cm, q = 3.2 cm and angle 0=99º. Find the area of Triangle OPQ, to the nearest10th of a square centimeter.

Answers

we know that

The area of a triangle applying the law of sines is equal to

[tex]A=\frac{1}{2}\cdot p\cdot q\cdot\sin (O)[/tex]

substitute the given values

[tex]\begin{gathered} A=\frac{1}{2}\cdot3.4\cdot3.2\cdot\sin (99^o) \\ A=5.37\text{ cm\textasciicircum{}2} \end{gathered}[/tex]

the answer is

5.37 square centimeters

You type 41 words per minute. How many minutes does it take you to type 615 words?

Answers

Given:

Type 41 words per min.

Find-:

How many min. take you to type 615 words

Explanation-:

1 min words type = 41

For 615 words,

41 words typed in 1 min.

For 1 words type it take min is:

[tex]1\text{ Words take time=}\frac{1}{41}\text{ min.}[/tex]

For 615 words:

[tex]\begin{gathered} \text{ Time}=\frac{1}{41}\times615 \\ \\ =\frac{615}{41} \\ \\ =15 \end{gathered}[/tex]

For type 615 words take time is 15 min.

Answer:

15 minutes.

Step-by-step explanation:

615 / 41

= 15

For a set of five numbers,
the mode is 8
the median is 12
Work out one possible set of five numbers.

Answers

Step-by-step explanation:

mode = the number appearing the most often in the list of data.

median = the middle number. half of the other numbers are smaller, and the other half is larger.

so, we know one number already : 12 in the middle.

that gives us

_ _ 12 _ _

a good mode is when it has a real majority (e.g. every other number appears only once, but the mode number appears twice).

so, 8 should appear twice.

as 8 is smaller than 12, it can only be on the left side of 12.

that gives us

8 8 12 _ _

note we need 2 numbers larger than 12, but each appearing only once.

so, e.g.

8 8 12 13 14

The total weight of three bean bags is 6.8 kg. Bag A weighs 1.5 kg more than Bag B. Bag C weighs 500 g more than Bag A. Calculate the weight of Bag B (will give brainliest and 50 points​

Answers

Answer: 1.6 kg

Step-by-step explanation:

Let the weight of bag B in kg be B.

Then, Bag A weights B+1.5 and bag C weighs B+0.5.

[tex]B+1.5+B+0.5+B=6.8\\\\3B+2=6.8\\ \\ 3B=4.8\\\\B=1.6[/tex]

Determine the relationship between lines a, b, and c line a y=5x -3 line b X + 5y=2 line c -10y - 2x =0

Answers

Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.

Write the given lines in standard form

Line a -5x + y = -3

Line b x + 5y = 2

Line c -2x - 10y = 0

a1 = -5, b1 = 1, c1 = -3

a2 = 1, b2 = 5, c2 = 2

a3 = -2, b3 = -10, c3 = 0

a1/a2 = -5/1

b1/b2 = 1/5

c1/c2 = -3/2

As we see that

a1/a2 ≠ b1/b2

Hence, lines a and b are intersecting.

a1/a3 = -5/-2

b1/b3 = 1/-10

As we see that

a1/a3 ≠ b1/b3

Hence, lines a and c are intersecting.

a2/a3 = 1/-2

b2/b3 = 5/-10 = 1/-2

c2/c3 = 2/0

As we see that

a2/a3 = b2/b3 ≠ c2/c3

Hence, lines b and c are parallel.

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Rewrite x4y2 − 3x3y3 using a common factor. 3xy(x3y − x2y) 3xy2(x2 − x2y) x2y(xy − 3xy2) x2y2(x2 − 3xy)

Answers

Answer:

  (d)  x²y²(x² − 3xy)

Step-by-step explanation:

You want to identify a rewrite of x⁴y² − 3x³y³ using a common factor among ...

3xy(x³y − x²y) 3xy²(x² − x²y) x²y(xy − 3xy²) x²y²(x² − 3xy)

Simplified

Here, we write the expanded form of the answer choices to see if any is a fit for the given expression.

3xy(x³y − x²y) = 3x⁴y² -3x³y²3xy²(x² − x²y) = 3x³y² -3x³y³x²y(xy − 3xy²) = x³y² -3x³y³x²y²(x² − 3xy) = x⁴y² -3x³y³ . . . . . . . matches the given expression

__

Additional comment

The relevant rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

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Mr. Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long. If each DVD is 11⁄20 inches wide, how many DVDs can he put side-by-side on the shelf?
DVDs

Answers

The number of DVDs that he can put side-by-side on the shelf is 19.

How to calculate the value?

From the information, Mr Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long and each DVD is 11⁄20 inches wide.

The number of DVDs that can be put will be the division of the numbers that are given. This will be:

= Length of shelf / Width of each DVD

= 10 2/3 ÷ 11/20

= 32/3 ÷ 11/20

= 32/3 × 20/11

= 640 / 33

= 19 13/33

= 19 approximately

He can put 19 DVD.

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