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The distance between line y = -2x + 5  and y = -2x - 5 is  2 √5 unit.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given lines are,

y = -2x + 5       (1),

y = -2x - 5        (2)

The lines can be written as

2x + y -5 = 0,

2x + y + 5 = 0

Since, the slope of the line (1) and line (2) is -2, which implies that lines are parallel.

To find the distance between line y = -2x + 5  and y = -2x - 5

Use formula,

Distance = \(\frac{ |c_1 - c_2|}{\sqrt{a^2+b^2}}\)

Compare the lines with standard equations of line,

ax + by + c =0.

a = 2, b = 1 , c₁ = -5, c₂ = 5.

Distance = |(-5) - 5| / √(2² + 1²)

               = 10 / √5

               = 2 √5

The distance between lines is  2 √5 unit.

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To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer:

9+(-14)=-5

Step-by-step explanation:

9+(-14)

9-14

=-5

Answer:

-5

Step-by-step explanation:

the answer is negative 5

Answer:

yes

Step-by-step explanation:

6x-3x-3x=-2+2

you put all same numbers in the same side

that makes 0 on both sides

The differential equation describing the relationship between the balance B of Rachel's car loan and time t is given by dB/dt = 0.045B - 375.

The equation represents the change in the balance of Rachel's car loan over time. The term dB/dt represents the rate of change of the balance with respect to time. The right-hand side of the equation consists of two terms. The first term, 0.045B, represents the increase in the balance by 4.5% per month. This term accounts for the growth of the loan balance due to accrued interest.

The second term, -375, represents the decrease in the balance by $375.00 each month, which could be the monthly payment towards the loan principal. By subtracting this payment from the growth, the equation captures the net change in the balance. The equation allows us to model and analyze the behavior of the loan balance as time progresses.

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Using mathematical induction, it can be proven that \(\( \sum_{k=0}^{n} r^{k}=\frac{1-r^{n+1}}{1-r} \)\) holds for all positive integers n.

To prove the given equation using induction, we will follow the steps of a proof by mathematical induction.

Step 1: Base Case

Let's verify the equation for the base case, where n = 0.

When n = 0, the equation becomes:

\(\( \sum_{k=0}^{0} r^{k} = \frac{1-r^{0+1}}{1-r} \)\)

Simplifying the equation on both sides, we have:

\(\( r^0 = \frac{1-r}{1-r} \)\( 1 = \frac{1-r}{1-r} \)\( 1 = 1 \)\)

The equation holds true for the base case.

Step 2: Inductive Hypothesis

Assume that the equation holds for some arbitrary positive integer k, i.e.,

\(\( \sum_{k=0}^{k} r^{k} = \frac{1-r^{k+1}}{1-r} \)\)

Step 3: Inductive Step

We need to prove that the equation holds for k+1 using the inductive hypothesis.

Starting with the left-hand side (LHS) of the equation:

\(\( \sum_{k=0}^{k+1} r^{k} = \sum_{k=0}^{k} r^{k} + r^{k+1} \)\)

Using the inductive hypothesis, we can substitute the expression:

\(\( = \frac{1-r^{k+1}}{1-r} + r^{k+1} \)\( = \frac{1-r^{k+1} + (1-r)r^{k+1}}{1-r} \)\( = \frac{1-r^{k+1} + r^{k+1} - r^{k+2}}{1-r} \)\( = \frac{1-r^{k+2}}{1-r} \)\)

This matches the right-hand side (RHS) of the equation, completing the inductive step.

Step 4: Conclusion

By completing the base case and proving the inductive step, we have shown that the equation holds true for all positive integers. Therefore, \(\( \sum_{k=0}^{n} r^{k} = \frac{1-r^{n+1}}{1-r} \)\) is proved using induction.

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Therefore, the 99% confidence interval for the proportion of unemployed heads of households in the population is approximately 0.063 to 0.129.

To compute a 99% confidence interval for the proportion of unemployed heads of households in the population, we can use the formula for a confidence interval for a proportion:

P ± Z * sqrt(P(1 - P) / n)

Where:

P is the sample proportion of unemployed heads of households (48/500 = 0.096)

Z is the Z-score corresponding to a 99% confidence level (approximately 2.576 for a 99% confidence level)

n is the sample size (500)

Plugging in the values, we can calculate the confidence interval:

Lower Limit = 0.096 - 2.576 * sqrt((0.096 * (1 - 0.096)) / 500) ≈ 0.063

Upper Limit = 0.096 + 2.576 * sqrt((0.096 * (1 - 0.096)) / 500) ≈ 0.129

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Answer:

1.25

Step-by-step explanation:

B

8/10=5/5+x

C

8/10=5/5+x

40+8x=50

      8x=10

        x=5/4

        x=1.25

Answer: answer

Step-by-step explanation: Answer:1. Circle with center X had radius r ; Given

Circle with center Y had radius Y has radius S ; Given

Translate X to Y ; Translation is a similarity transformation

Dilate circle X by s/r ; Dilation is a similarity transformation

Circle X ~ Circle Y ; a composition of similarity transformation maps circle X to circle Y

Answer:

view attachment

Two Hills in Roswell is 1.173 miles apart in real life.

The mile, sometimes called the international mile or statutory mile to distinguish it from others, is an imperial unit in the United Kingdom and a common unit of distance in the United States. Both are based on old English units that are 5,280 British feet or 1,760 yards long. The legal mile was standardized in 1959 by an international agreement between the British Commonwealth and the United States and formally redefined in SI units to be exactly 1,609.344 meters.

With the modifier, the mile is also used to describe or convert a wide range of units derived from or roughly equivalent to the Roman mile, such as the Chinese mile (now exactly 500 m). will be The Romans divided the mile into 5,000 Roman feet, but the furlong was so important in Elizabethan England that in 1593 the legal mile was equal to 8 furlongs, or 5,280 feet. This form of the mile has since spread partially to the successor states of the British Empire, where they continue to use the mile.

According to the question:

The scale is 1 inch : 0.51 miles. It means 1 inch on the map represents 0.51 miles in real life.

If we have 2.3 inches on the map, then in real life

in real life = 2.3 × 0.51

in real life = 1.173 miles.

Two hills in Roswell is 1.173 miles apart in real life

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Answer:

B = 10

I hope this helps!

Considering concepts of divisibility, the amount of numbers in the set that are divisible by 2 but not by 10 is:

(C) 19.

The data-set has (55 - 10) + 1 = 46 numbers, hence 23 are divisible by 2. 20, 30, 40 and 50 are also divisible by 10, that is, 4 numbers have to be removed, hence the amount is:

23 - 4 = 19.

Which means that option C is correct.

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The relation "a-b a mod 4 = b mod 4" means that for any two numbers a and b, if their difference is divisible by 4, then they belong to the same equivalence class. To find the equivalence class of -, we need to find all the numbers that have the same modulus as - when divided by 4.

We can start by listing out some numbers with the same modulus as -. For example, we have {-9, -5, -1, 3, 7, ...}, since these numbers are all congruent to -1 mod 4. Similarly, we have {0, 4, 8, 12, ...} for numbers that are congruent to 0 mod 4, and {1, 5, 9, 13, ...} for numbers that are congruent to 1 mod 4.

Therefore, the equivalence class of - is {-9, -5, -1, 3, 7, ...}, which contains all the negative numbers that are congruent to -1 mod 4.

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E) 10 minutes. At the local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes, which is equivalent to a rate of 0.4 cars per minute (12 arrivals / 30 minutes). The service time for each car averages 2 minutes per arrival and follows an exponential distribution.

To find the average time in the queue for each arrival, we can use Little's Law. Little's Law states that the average number of customers in a system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In other words, L = λW.

In this scenario, we are given the arrival rate (λ) and the service time (μ), but we want to find the average time a customer spends in the system (W). To do this, we can use the formula for the average time in an M/M/1 queue: W = 1 / (μ - λ).

Plugging in the values, we get W = 1 / (0.5 cars/minute - 0.4 cars/minute) = 1 / 0.1 cars/minute = 10 minutes. Thus, the average time in the queue for each arrival is 10 minutes.

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Answer:

1/4

Step-by-step explanation:

The answer would be one fourth because the amount of red is 5/20 which is equal to 1 fourth.

Hope this helps

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Answer:

\(\sf -\dfrac{7}{4}\)

Step-by-step explanation:

  (1, -5)    ⇒ x₁ = 1    ; y₁ = -5

  (-3, 2)  ⇒ x₂ = -3  ; y₂ = 2

\(\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}\)

            \(\sf =\dfrac{2-[-5]}{-3-1}\\\\= \dfrac{2+5}{-4}\\\\=\dfrac{7}{-4}\\\\= -\dfrac{7}{4}\)

The lengths of a,b,c, and d have been derived and expressed in terms of trigonometric ratios below.

As we can see from the figure itself, the value of a = sin θ

This can be written as such because = sin θ = Perpendicular / Hypotenuse

Here, the perpendicular = a and hypotenuse = radius = 1

= sin θ = a

The value of b = tan θ

This is because tan θ = perpendicular/base

Here, the base = radius = 1

= tan θ = b  

The value of c = sec θ

This is because sec θ = Hypotenuse / Base

= sec θ = c

The value of d = cos θ

This is because cos θ = Base / Hypotenuse

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Question:

The graph represents the two companies' prices. What is the linear equation that represents each T-shirt company?

Answer:

1.) Shirt Box: y = 7.5x + 30

2.) Just Tees: y = 10.5x

Step-by-step explanation:

For Number -One- We do - 7.5 + 30 = 37.5

For Number -Two- We do -  10.5  ×  "X"

You See We have to solve for "X"

This is just to give the idea, and Kinda help Explain it. . .

(Yes i know im 4 days late - & Yes i know its already answered, But I just explained it To get the Understanding of the Two answers.)

Answer:

Shirt box : y=7.5x+30

Just tees: y=10.5x

Step-by-step explanation:

Prisms and pyramids are  geometric shapes that have flat sides, flat bases and angles. So those are some similarities. However, the bases and side faces on prisms and pyramids differ. Prisms have two bases while pyramids only have one. There are a variety of pyramids and prisms, so not all shapes in each category look the same.

Hit the heart if this was helpful

Answer:

x - y = -4

Step-by-step explanation:

Standard Form: Ax + By = C

A is non-negative

Step 1: Define equation

y - 3 = (x + 1)

Step 2: Solve to Standard Form

The resultant of these two forces is 780.31N

If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

The formula for the resultant force is expressed as:

\(R =\sqrt{(\sum F_x)^2+(\sum F_y)^2}\)

Take the sum of force along the horizontal

\(\sum F_x = 450cos10^0+380cos30^0\\\sum F_x =443.16 + 329.09\\\sum F_x = 772.25N\)

Take the sum of force along the vertical

\(\sum F_y = 450sin10^0-380sin30^0\\\sum F_y=78.14 - 190\\\sum F_y= -111.86N\)

Get the resultant force:

\(R =\sqrt{(772.25)^2+(-111.86)^2}\\R = \sqrt{596,370.0625 +12,512.6596}\\R = \sqrt{608,882.7221}\\R = 780.31N\)

Hence the resultant of these two forces is 780.31N

b) According to Newton's second law of motion;

\(R =ma\\a=\frac{R}{m} \\a=\frac{780.31}{3200}\\a = 0.244m/s^2\)

Hence If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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Answer:

13,000

_____

4%

I'm sorry if this is incorrect

Answer:

Option (B)

Step-by-step explanation:

From the graph attached,

x-intercepts of the graphed function are,

x = -3 and x = 4

Therefore, zero factors of the function will be,

(x + 3) and (x - 4)

So the quadratic function given in the graph will be in the form of,

f(x) = (x + 3)(x - 4)

Option (B) will be the correct option.

Total number of cases possible when 3 Dice roll= 6^3=216

Now we have to find the number of cases when values shown on two of the dice sum to the value shown on the remaining, probability is 0.28

Now we need to count the instances where the values on two dice add up to the value on the other die, which is one. If a die shows 6, the remaining two dice must either show (5,1) or (4,2), or (3,3)

Total number of scenarios that could occur in this situation: 3!+3!+3!/2!=15

2. If a die shows 5, the other two dice must either display (4,1) or (3,2)

The total cases that could occur in this scenario are 3!+3! =12.

3. If a die shows 4, the other two dice must either display (3,1) or (2,2)

Total number of scenarios that could occur in this situation: 3!+3!/2!=9

4. If a die shows 3, the other two dice must also show 3. (2,1)

The total number of cases possible in this scenario= is 3!/2! =3

Total cases possible= 15+12+9+6+3=45

Probability= 45/216=5/24= 0.208

probability is 0.208

correct option is (D).

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The question was incomplete. Check below the complete question.

Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die?

(A) 1/6

(B) 13/72

(C) 7/36

(D) 5/24

(E) 2/9

No, it is not reasonable to conclude that the assumption that the error term has a normal probability distribution is not violated based on the normal probability plot of the armand's pizza data.

The normal probability plot is a graphical tool used to assess whether a set of data follows a normal distribution. In this case, if the points on the plot approximately fall along a straight line, it suggests that the data is normally distributed. Conversely, deviations from a straight line indicate a departure from normality.

Upon examining the normal probability plot for the armand's pizza data, it is crucial to assess whether the points form a relatively straight line. If the points deviate significantly from a straight line, it would suggest that the assumption of a normal distribution for the error term is violated.

However, without further details or a visual representation of the plot, it is not possible to provide a specific analysis of the armand's pizza data. It is essential to evaluate the distribution of the residuals or errors, which represent the differences between the observed and predicted values in a statistical model. If these residuals deviate noticeably from normality, it would indicate a violation of the assumption of a normal error term distribution.

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Yes, it is reasonable to conclude that the assumption that the error term has a normal probability distribution is not violated based on the normal probability plot for the Armand's Pizza data.

The normal probability plot is a graphical tool used to assess the normality assumption of a dataset. It plots the observed data against the expected quantiles of a normal distribution.

If the points on the plot roughly follow a straight line, it suggests that the data can be reasonably modeled by a normal distribution.

In this case, if the normal probability plot for the Armand's Pizza data shows a linear trend, it indicates that the error term has a normal distribution and the assumption is not violated.

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Answer:

AAS Postulate.

Step-by-step explanation:

The AAS Postulate states that if 2 angles and a non-included side are congruent on both triangles, then the two triangles are equivalent.

In this case, the first Angle is: ∠B ≅ ∠D (Given, both are 90° in measurement)

For the side: Line BE ≅ line DE (Given)

∡BEA ≅ ∡DEC (Definition of Vertical Angles)

AAS Postulate is therefore used.

~

Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.

In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.

19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:

4.8² + 7.2² = 12²

74.88 = 144 [not true} Therefore, AB is not tangent to circle C.

20. Also, we will have the following:

15² + 11.2² = 6.8²

350.44 = 46.24 [not true].

AB is not tangent to circle C.

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