what is the probability that the difference between the largest and the smallest numbers is k in a subset of four different numbers chosen from 1 through 20 (3 ≤ k ≤ 19)?

Answers

Answer 1

The probability subset of four is:

Σ(x=1 to 10) (x-1)(20-x-k)C(2) + Σ(x=11 to 17) (20-x)(x+k-2)C(2) / C(20,4)

How to find the probability that difference the largest and smallest numbers in a subset of four different numbers?

To find the probability that the difference between the largest and smallest numbers in a subset of four different numbers chosen from 1 through 20 is k, we need to count the number of ways we can choose four numbers such that their difference is k, and then divide by the total number of ways to choose four numbers.

Let's first count the number of ways to choose four numbers such that their difference is k. We can do this by fixing the smallest number, and then counting the number of ways to choose the other three numbers such that their difference is k.

If the smallest number is x, then the largest number must be x+k, and we need to choose two numbers from the remaining numbers (1 through x-1 and x+k+1 through 20) such that their difference is also k.

If x ≤ 10, then there are x-1 numbers less than x, and 20-(x+k+1)+1 = 20-x-k numbers greater than x+k. So the number of ways to choose two numbers with a difference of k is (x-1)(20-x-k).

Therefore, the total number of ways to choose four numbers with a difference of k when the smallest number is x and x ≤ 10 is (x-1)(20-x-k)C(2).

If x > 10, then there are 20-x numbers greater than x, and (x+k-1)-1 = x+k-2 numbers less than x+k. So the number of ways to choose two numbers with a difference of k is (20-x)(x+k-2).

Therefore, the total number of ways to choose four numbers with a difference of k when the smallest number is x and x > 10 is (20-x)(x+k-2)C(2).

Therefore, the total number of ways to choose four numbers with a difference of k is:

Σ(x=1 to 10) (x-1)(20-x-k)C(2) + Σ(x=11 to 17) (20-x)(x+k-2)C(2)

The total number of ways to choose four different numbers from 1 through 20 is C(20,4) = 4845.

So the probability that the difference between the largest and smallest numbers is k in a subset of four different numbers chosen from 1 through 20 is:

Σ(x=1 to 10) (x-1)(20-x-k)C(2) + Σ(x=11 to 17) (20-x)(x+k-2)C(2) / C(20,4)

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Related Questions

Use a property of equality to solve this equation 4.5x=18

Answers

Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

hope this helps l:-)

Consider the division expression LaTeX: 7\frac{1}{2}\div27 1 2 ÷ 2. Select all multiplication equations that correspond to this division expression.

Answers

Answer:

2 x ? = 7 1/2 and ? x 2 = 7 1/2

Step-by-step explanation:

This is the answer because it didn't show the answer so all you have to figure out is the multiplication problem that goes with the division problem. So 2 x ? = 7 1/2 and ? x 2 = 7 1/2 you don't have to include the answer all you have to include is where the answer will do if you DID have the answer. These two are correct because the multiplication number can go in any order.

I know this might not be the best step-by-step explanation ever but I truly tried but the answer is correct.

Denise buys a tote bag at a gift shop for $12. The same bag is available at Denise's pharmacy for 2/3 the price she paid at the gift shop. Let's say you have enough money to buy 10 bags from the gift shop. How many bags can you buy from the pharmacy with the same amount of money? A.3 B.12 C.15 D.18

Answers

Answer:

15

Step-by-step explanation:

The price of the bag at the pharmacy is

2/3 * 12 = 8 dollars

You have enough for 10 at the gift shop

10 * 12 = 120

Take 120 dollars and divide by 8 dollars to see how many you can get at the pharmacy

120/8 =15

Answer:

the answer is C. it was on my mid-term

Step-by-step explanation:

Please Answer Quickly!!!!!
Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of x. Do not include parentheses in your answer.

(x^5 + y^5) ÷ (x + y)

Answers

Factor the numerator and denominator and cancel the common factors.

x^5/x+y + y^5/x+y

Answer:

x^4 + x^4 or x^4 - x^3 + x^2y^2 - xy^3 + y^4

Step-by-step explanation:

Please Answer Quickly!!!!!Divide the following polynomials. Then place the answer in the proper location

Given the following scatterplot, if a point was added in the upper left corner with an x-value of 10 and ay-value of 20, what would happen to the value of the correlation coefficient, r?

Answers

The upper left corner with an x-value of 10 and a y-value of 20 to the given scatterplot would likely decrease the value of the correlation coefficient, r.

The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative correlation) to 1 (perfect positive correlation), with 0 indicating no correlation. In a scatterplot, points that are closer to forming a straight line indicate a stronger linear relationship, while points that are more scattered indicate a weaker linear relationship.

In the given scatterplot, adding a point in the upper left corner with an x-value of 10 and a y-value of 20 would likely introduce an outlier that deviates from the overall pattern of the data. This outlier would be located far away from the other points, potentially causing the scatterplot to become more scattered and less linear. As a result, the linear relationship between the two variables, as measured by the correlation coefficient, r, would likely decrease. This is because the outlier would have a disproportionate influence on the calculation of the correlation coefficient, pulling it closer to 0 or even changing the direction of the correlation, if the outlier introduces a different pattern to the data.

Therefore, adding a point in the upper left corner with an x-value of 10 and a y-value of 20 to the given scatterplot would likely decrease the value of the correlation coefficient, r.

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Suppose two firms are deciding how much of a good to produce. The inverse demand function is p(y1 + y2) = 100 − 2(y1 + y2). Suppose further that the two firms have production costs of c1(y1) = 2y1 and c2(y2) = 4y2, respectively.
1. Suppose that Firm 1 gets to choose output y1 first, and then Firm 2 gets to decide y2 after observing y1 (the Stackelberg case). What are the equilibrium production choices yˆ , yˆ ? What profit does each firm make?
2. Suppose now that Firm 1 and Firm 2 choose outputs simultaneously. What are the equilibrium production choices yˆ , yˆ ? What profit does each firm make? Which firm is better off, and which firm is worse off in this setup than the Stackelberg case above?

Answers

In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78) and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case.

1. In the Stackelberg case, let Firm 1 choose output y1 first, and then Firm 2 decides y2 after observing y1. Firm 1 is the leader and Firm 2 is the follower. Thus, the optimization problem for Firm 2 is as follows:

Max p(y1 + y2) * y2 - c2(y2), where y1 is chosen by Firm 1.

Thus, the profit function of Firm 2 is Π2(y1, y2) = (100 − 2(y1 + y2))y2 − 4y2

                                                                              = (100 − 2y1 − 2y2)y2

Differentiating with respect to y2, we obtain:

∂Π2(y1, y2) / ∂y2 = 100 − 2y1 − 4y2

Setting this equal to zero, we obtain:

50 − y1 = 2y2

Thus, Firm 2's best response function is: yˆ2(y1) = (50 − y1)/2

Now, Firm 1 knows that Firm 2 will choose yˆ2 given that it already chose y1.

Firm 1 chooses y1 to maximize its own profit, which is:

Π1(y1) = (100 − 2(y1 + yˆ2(y1)))y1 − 2y1

= (100 − 2y1 − 25 + 0.5y1)y1

= (75 − 1.5y1)y1

Differentiating with respect to y1, we obtain:

∂Π1(y1) / ∂y1 = 75 − 3y1

Setting this equal to zero, we obtain:

y1 = 25

Thus, yˆ1 = 25, and yˆ2 = (50 − y1)/2 = 12.5.

The profit of Firm 1 is Π1(y1) = (75 − 1.5y1)y1 = 562.5, and the profit of Firm 2 is

= Π2(y1, y2)

= (100 − 2y1 − 2y2)y2

= 156.25.2.

In the simultaneous-move case, the optimization problem for Firm 1 is as follows:

Max p(y1 + y2) * y1 - c1(y1) - c2(y2)

Similarly, the optimization problem for Firm 2 is: Max p(y1 + y2) * y2 - c1(y1) - c2(y2)

These two problems can be combined into a single problem by substituting

p(y1 + y2) = 100 − 2(y1 + y2) and

c1(y1) = 2y1 and c2(y2) = 4y2.

Thus, the profit function of each firm is:

Π1(y1, y2) = (50 − y1 − y2)y1Π2(y1, y2) = (50 − y1 − y2)y2

The first-order conditions for maximizing these profit functions are:

= ∂Π1(y1, y2) / ∂y1

= 50 − 2y1 − y2

= 0

∂Π2(y1, y2) / ∂y2 = 50 − y1 − 2y2 = 0

Solving these equations simultaneously, we obtain:

y1 = 16.67, y2 = 16.67, and Π1(y1, y2) = Π2(y1, y2) = 277.78.

Comparing this to the Stackelberg case, we see that both firms are worse off in the simultaneous-move case. In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78), and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case. Thus, Firm 1 is better off in the Stackelberg case, and Firm 2 is worse off.

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here is the 4rth one to do

here is the 4rth one to do

Answers

The correct option is; Yes, all the three expressions are equivalent to each other.

What is meany by the term exponent?A number's exponent signifies how many times a number has been multiplied by itself. For instance, 2×2×2×2 can be written as 2⁴, because 2 is multiplied on its own four times. In this case, 2 is referred to as the "base," and 4 is referred to as the "exponent" as well as "power." In general, xⁿ denotes that x has been multiplied by itself n times.

For the given question;

The three expressions are given as;

a: 20(1.1ˣ)   ...1

b: 20(1.1⁻¹)⁻¹ˣ

Simplifying as;

= 20(1.1⁻¹⁽⁻¹ˣ⁾)

= 20(1.1ˣ) ....2

c: 20(1.1¹/⁵)⁵ˣ

Simplifying.

= 20(1.1¹/⁵⁽⁵ˣ⁾)

= 20(1.1ˣ) ....3

So, a = b = c

Thus, all three expressions are equivalent to each other.

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i need to find the value of X

i need to find the value of X

Answers

Answer:

62°

Step-by-step explanation:

180°-68.5°-49.5°=62°

Answer:

x=62

Step-by-step explanation:-

In a triangle, angle sum property(ASP) is 180

x+68.5+49.5=180

x+118=180

x=180-118

x=62

Hope it helps you!

Some please help you will get brainiest if it’s right

Some please help you will get brainiest if its right

Answers

Answer:

Step-by-step explanation:

a=graph

b= x=2

Some please help you will get brainiest if its right

The sum of 32 and 48 can be expressed in different ways using the Distributive Property.

Answers

The sum of 32 and 48 can be expressed in different ways using the Distributive Property as 8(4 + 6).

What is Distributive property?

The distributive property of multiplication is that when two numbers are added such as (a+b) and multiplied by a third number such as x, then the result will be the sum of multiplication of the third number with the first number (xa) and the third number with the second number (xb).

x(a+b) = xa + xb,

The sum of 32 and 48 can be expressed in different ways using the Distributive Property as,

8(4 + 6)4(8 + 12)2(16 + 24)

Hence, the sum of 32 and 48 can be expressed in different ways using the Distributive Property as 8(4 + 6).

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Please help me with my Geometry HW! I need to get it done.

Please help me with my Geometry HW! I need to get it done.

Answers

The volume of the given cuboid will be 11.34 m³.

The volume V of a cuboid is given by the formula:

V = l x w x h

where l, w, and h are the length, width, and height of the cuboid, respectively.

In this case, the length is 1.5 m, the width is 2.1 m, and the height is 3.6 m. So we have:

V = 1.5 x 2.1 x 3.6

Simplifying the right-hand side, we get:

V = 11.34 cubic meters

Therefore, the volume of the cuboid is 11.34 cubic meters.

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What is the y-intercept of 2x y =- 3?

Answers

The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

What is the y-intercept of the given equation?

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation in the question

2x - y = -3

First, we solve form for y and reorder in slope intercept form.

2x - y = -3

Subtract 2x from both sides

2x - 2x- y = -3 - 2x

- y = -3 - 2x

Divide each term by -1

y = 3 + 2x

Reorder in slope intercept form

y = 2x + 3

To find the y-intercept, replace x with zero and solve for y

y = 2(0) + 3

y = 3

Therefore, the y-intercept is 3.

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Write an equation in point slope form of the line graphed below. (Use the right hand point)

Write an equation in point slope form of the line graphed below. (Use the right hand point)

Answers

Answer:

y+1=1/2(x-1)

Step-by-step explanation:

The point is (1,-1) and the slope is 1/2, so you plug in the number in the blanks y-___=___(x-___).  The y in the first the slope in the second and the x in the third.

The equation is in slope-intercept form y = -x/4 -3/4

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A graph of the line.

Assuming the graph measurement is 1 unit.

Then we interpreted two points (-1, 1) and (3, 0).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

y - 1 = (-1/4)(x + 1)

y - 1 = -x/4 -1/4

y = -x/4 -3/4

Therefore, the equation is y = -x/4 -3/4

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Raise to the power:
\((-2abx)^{4}\)

Answers

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\(( { - 2abx})^{4} = ({ - 2})^{4} \times ( {a})^{4} \times ({b})^{4} \times ({x})^{4} = \\ \)

\(16 {a}^{4} {b}^{4} {x}^{4} \)

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use the same regression results where you already found r square and other results for this regression. what is the standard error for the estimated slope of the regression line? answer to four decimal places.

Answers

A regression model can only predict values that are lower or higher than the actual value. As a result, the only way to determine the model's accuracy is through residuals.

What is regression ?

Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the relationship between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).

The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).

Based on a line of best fit, linear regression determines the linear relationship between two variables.

The slope of a straight line used to represent linear regression thus indicates how changing one variable affects changing another..

In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept. Regression without linearity.

Hence, A regression model can only predict values that are lower or higher than the actual value.

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please help???????? ASAP​

please help???????? ASAP

Answers

Answer:

The answer is 9

Step-by-step explanation:

You each exponent to get 81/9. You simplify and it gives you 9.

Answer:

The answer is 9

Step-by-step explanation:

if u multiply by the exponents

3^4=81

3^2=9

then divide 81÷9=9

Which is a correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” when n = 4?
The correct expression is StartFraction n cubed Over 16 EndFraction minus 2 + 8.
The correct expression is 2 minus StartFraction n cubed Over 16 EndFraction + 8.
One of the steps to determining the value when n = 4 is 1 minus 2 + 8.
One of the steps to determining the value when n = 4 is 2 minus 1 + 8.
The value when n = 4 is 6.
The value when n = 4 is 7.
The value when n = 4 is 9.
The value when n = 4 is 10.

Answers

Answer:

A and H are correct

Step-by-step explanation:

I took the quiz

The expression for the given statement is n³/16-2+8. Therefore, the options A and H are correct answer.

What is an expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given statement is “two less than the quotient of a number cubed and sixteen, increased by eight”

"Two less than x" describes "x- 2"

"Quotient of x and y" describes  x/y

"x increased by y" describes x+y

n³/16 is the quotient and 2 is subtracted and 8 is increased which means 8 is added.

So, the expression is n³/16-2+8

= n³/16 +6

When n=4, we get

4³/16 +6

= 4+6

= 10

Therefore, the options A and H are correct answer.

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Please help I need the answer

Please help I need the answer

Answers

Step-by-step explanation:

(i) Here in ∆ AED and ∆ CEB ,

ang . DAE = ang. BCE AD = BC ang. AED = ang. BEC

Hence by AAS congruence congruence condition ,

∆AED \(\cong \) ∆CEB

Also ,

AE = CE . . . . . (i) BE = DE . . . . . (ii)

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

(ii) In ∆ AEB and ∆CED ,

AE = CE BE = DE ang. DEC = ang. AEB ( vertically opposite angles)

Hence by SAS condition ,

∆AEB \(\cong \) ∆CED

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

(iii) Here ,

ang BAC = ang. DCA

Since these two angles are alternate interior Angles and equal . Hence the lines will be parallel . Also since ∆AEB is congruent to ∆CED , the corresponding sides will be equal . Hence AB = CD .

Hence Proved !

The cost of a call was $1.00

Answers

I want chicken nuggets

Before you can multiply two matrices together, the number of ___ in the first matrix must equal the number of rows in the second matrix.

Answers

Before you can multiply two matrices together, the number of COLUMN in the first matrix must equal the number of rows in the second matrix.

What is matrix ?

The entries of a matrix are a rectangular array of numbers (or other mathematical objects). Standard operations like addition and multiplication can be performed on matrices. A matrix over a field F is often just a rectangular array of F's constituent elements.  Real and complex matrices are those whose entries are real or complex numbers, respectively.

The entries or elements of the matrix are its numbers, symbols, or phrases. In a matrix, the terms "rows" and "columns" refer to the horizontal and vertical rows of entries, respectively.

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50 point! Look at the picture attached. I will mark brainliest!

50 point! Look at the picture attached. I will mark brainliest!

Answers

Answer:

22°

Step-by-step explanation:

Triangle KJL ≅ Triangle MJL (RHS)

[JL = JL(common), KL = LM(given), angle KLJ = angle MLJ(given)]

we come up to the conclusion that 4x + 6 = 3x + 10

x = 4

∴angle KJL = 4(4) + 6 = 22°

22 degrees is the right answer

Consider function g. Which function could be the inverse of function g? PLEASE HELP !

Consider function g. Which function could be the inverse of function g? PLEASE HELP !

Answers

Answer:

Step-by-step explanation:

The correct answer is B .

Your job is to sort and stack marblesfor sale. A bag contains 44 marbles, and some green. If there are 11 red marbles, what is the ratio of green to red marbles

Answers

Answer:

3 : 1

Step-by-step explanation:

Given that :

Total Marbles in bag = 44

Color of marbles in bag : red, green

Number of red marbles = 11

The ratio of green to red marbles :

Number of green marbles :

(Total marbles in bag - number of red marbles)

(44 - 11) = 33 green marbles

Hence, ratio of green to red Marbles:

Number of green marbles : number of red marbles

33 : 11

3 : 1

Answer:

The correct answer is 2:1.

Step-by-step explanation:

I did the K12 assignment and is said this was the right answer.  

+ -/7 points SPreCalc7 2.4.039 + Ask Your Teacher My Notes 13. An object is dropped from a high cliff, and the distance (in feet) it has fallen after t seconds is given by the function d(t) = 16t2. Complete the table to find the average speed during the given time intervals. d(b) - d(a) t = a Average speed t = b 9 9.5 9.1 9 9.01 9.001 9.0001 9 Use the table to determine what value the average speed approaches as the time intervals get smaller and smaller. Is it reasonable to say that this value is the speed of the object at the instant t = 9? Explain. From the table it appears that the average speed approaches ft/s (rounded to the nearest whole number) as the time intervals get smaller and smaller. It reasonable to say that this number is the --Select-- speed of the object at the instant t = 9. Submit Answer

Answers

The average speed during a given time interval can be found by calculating the change in distance over the change in time, or (d(b) - d(a))/(b-a). In this case, we can use the given function d(t) = 16t^2 to find the distance at each given time.  It is reasonable to say that this value is the speed of the object at the instant t = 9 because as the time interval approaches zero, the average speed approaches the instantaneous speed at that moment.

For the first time interval, t = a = 9 and t = b = 9.5:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.5)^2 = 1444
Average speed = (1444 - 1296)/(9.5 - 9) = 148/0.5 = 296 ft/s

For the second time interval, t = a = 9 and t = b = 9.1:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.1)^2 = 1324.96
Average speed = (1324.96 - 1296)/(9.1 - 9) = 28.96/0.1 = 289.6 ft/s

For the third time interval, t = a = 9 and t = b = 9.01:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.01)^2 = 1300.9616
Average speed = (1300.9616 - 1296)/(9.01 - 9) = 4.9616/0.01 = 496.16 ft/s

For the fourth time interval, t = a = 9 and t = b = 9.001:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.001)^2 = 1296.288016
Average speed = (1296.288016 - 1296)/(9.001 - 9) = 0.288016/0.001 = 288.016 ft/s

For the fifth time interval, t = a = 9 and t = b = 9.0001:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.0001)^2 = 1296.0288016
Average speed = (1296.0288016 - 1296)/(9.0001 - 9) = 0.0288016/0.0001 = 288.016 ft/s

As the time intervals get smaller and smaller, the average speed approaches 288 ft/s.

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PQ= RQ and PS= RS a=?

PQ= RQ and PS= RS a=?

Answers

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

What are interior angles?

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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How much time will it take for the laptop to receive one mtu-size (1500 byte) packet?

Answers

The correct answer is it would take approximately 0.000012 seconds (or 12 microseconds) for the laptop to receive a packet of MTU size (1500 bytes) with a network speed of 1 Gbps.

To determine the time it will take for a laptop to receive a packet of MTU size (1500 bytes), we need to consider the data transfer rate or network speed.

Let's assume the network speed is given in bits per second (bps). We'll need to convert the packet size from bytes to bits and then divide it by the network speed to calculate the time.

First, let's convert the packet size from bytes to bits:

Packet size = 1500 bytes

1 byte = 8 bits

1500 bytes * 8 bits/byte = 12000 bits

Now, we need to divide the packet size by the network speed to calculate the time:

Time = Packet size / Network speed

For example, if the network speed is 1 Gbps (1 gigabit per second), the calculation would be:

Time = 12000 bits / (1 Gbps) = 12000 / (10^9) seconds = 0.000012 seconds

Therefore, it would take approximately 0.000012 seconds (or 12 microseconds) for the laptop to receive a packet of MTU size (1500 bytes) with a network speed of 1 Gbps.

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How do I even do this...

How do I even do this...

Answers

Answer:

x = 2 ± \(\sqrt{15}\)

Step-by-step explanation:

x² - 4x - 11 = 0 ( add 11 to both sides )

x² - 4x = 11

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2)x + 4 = 11 + 4

(x - 2)² = 15 ( take square root of both sides )

x - 2 = ± \(\sqrt{15}\) ( add 2 to both sides )

x = 2 ± \(\sqrt{15}\)

prime, incorporated, purchases $100,000 in construction machinery on january 1, year 1. the useful life is estimated to be 8 years, and the residual value is estimated to be $20,000. if the company uses the double-declining-balance method, the asset will reach its residual value in the ____ year.

Answers

If the company uses the double-declining-balance method, the asset will reach its residual value in the 9th year. We can find the solution in the following manner.

Under the double-declining-balance method of depreciation, the depreciation rate is twice the straight-line rate, and the book value is multiplied by the depreciation rate each year. The formula for calculating the depreciation expense is:

Depreciation expense = (2 / Useful life) x Book value at the beginning of the year.

In this case, the construction machinery has a useful life of 8 years and a cost of $100,000 with a residual value of $20,000. Therefore, the depreciable base is $80,000 ($100,000 - $20,000).

To calculate the depreciation expense for the first year, we use the formula:

Depreciation expense = (2 / 8) x $100,000 = $25,000

The book value at the beginning of year 2 is:

Book value = Cost - Accumulated depreciation

Book value = $100,000 - $25,000 = $75,000

To calculate the depreciation expense for year 2, we use the same formula:

Depreciation expense = (2 / 8) x $75,000 = $18,750

We continue to calculate the book value and depreciation expense for each year until the book value reaches the residual value of $20,000.

Year 1:

Book value = $100,000 - $25,000 = $75,000

Year 2:

Book value = $75,000 - $18,750 = $56,250

Year 3:

Book value = $56,250 - $14,063 = $42,187

Year 4:

Book value = $42,187 - $10,547 = $31,640

Year 5:

Book value = $31,640 - $7,910 = $23,730

Year 6:

Book value = $23,730 - $5,932 = $17,798

Year 7:

Book value = $17,798 - $4,450 = $13,348

Year 8:

Book value = $13,348 - $2,337 = $11,011

Year 9:

Book value = $11,011 - $1,674 = $9,337

Therefore, the asset will reach its residual value in Year 9.

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Sophie needed to get her computer fixed she took it to the repair store the technician at the store worked on the computer for four hours, and charged her $
127 for parts the total was $227 write and Solve an equation which can be used to determine X the cost of labor per hour

Answers

Answer:

Equation: 

4x + 127 = 227

The per-hour cost for labor, x, was $25 per hour.

Step-by-step explanation:

We want to find the cost of labor for each hour. They worked on her computer for 4 hours. The per hour cost of labor we don't know, so we can call it x.

The repair shop charges x dollars per hour.

So the total LABOR charge is 4x.

The whole cost is:

Whole_Cost

= LABOR + PARTS

We know the whole cost, $227.

We know the parts, $127.

227 = 4x + 127

To solve, subtract 127

100 = 4x

divide by 4

25 = x

The cost per hour for labor is $25per hour.


Line x is parallel to line y. Line z intersects lines x and y.
1/2
4/3
5/6
8/7
Determine whether each statement is Always True, Sometimes True, or Never True.
Always True Sometimes True Never True
m2 1 + m 24 = 180°
m2 5 - m2 7 = 0°
ZIY
22 28
m22-23= m_1-m24
ооооо
OOOOO
ооооо

Line x is parallel to line y. Line z intersects lines x and y.1/24/35/68/7Determine whether each statement

Answers

The ∠1+∠4=180 degree is always true, ∠5-∠7=0 is always true , z⊥y is sometimes true, ∠2≅∠8 is always true and ∠2-∠3=∠1-∠4 be sometimes true.

What is Coordinate System?

Arrangement of reference lines or curves used to identify the location of points in space is called coordinate system.

Line x is parallel to line y.

Line z intersects lines x and y.

∠1+∠4=180 degree is always true.

∠5-∠7=0 is always true because the two angles are true.

z⊥y is sometimes true.

∠2≅∠8 is always true because the two angles are congruent.

∠2-∠3=∠1-∠4 will be sometimes true.

Hence, the ∠1+∠4=180 degree is always true, ∠5-∠7=0 is always true , z⊥y is sometimes true, ∠2≅∠8 is always true and ∠2-∠3=∠1-∠4 be sometimes true.

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