Printer A and Printer B complete the same printing task. Printer A completes the task in 40 minutes. Printer B can print 4 more pages per minute than printer A and takes 16 fewer minutes to complete the task.
How many pages were in the printing task?

The duration of the bond is approximately 7.7472 years.

A bond is a debt security issued by a company, government, or other organization to raise capital. When an entity issues a bond, it is essentially borrowing money from investors, who buy the bond with the expectation of receiving interest payments over a set period of time, and then receiving the principal back at the bond's maturity date.

In the given question,

Given information:

Settlement date = June 13, 2018

Maturity date = December 19, 2027

Coupon rate = 6% (semi-annual payments)

Yield to maturity = 7%

Face value of the bond = $1000

First, let's calculate the present value of the bond's cash flows:

PV of coupon payments =

(0.06/2) x $1000 / (1 + 0.07/2)^1 + (0.06/2) x $1000 / (1 + 0.07/2)^2 + ... + (0.06/2) x $1000 / (1 + 0.07/2)^18 = $687.58

PV of principal = $1000 / (1 + 0.07/2)^18 = $412.04

Total present value of the bond = $687.58 + $412.04 = $1099.62

Next, let's find the time-weighted average of the cash flows to calculate the duration:

Time to receive each cash flow:

June 13, 2018 (settlement date): 0

December 19, 2018: 0.5

June 19, 2019: 1

December 19, 2019: 1.5

June 19, 2020: 2

December 21, 2020: 2.5

June 21, 2021: 3

December 20, 2021: 3.5

June 20, 2022: 4

December 19, 2022: 4.5

June 19, 2023: 5

December 19, 2023: 5.5

June 19, 2024: 6

December 19, 2024: 6.5

June 19, 2025: 7

December 19, 2025: 7.5

June 19, 2026: 8

December 21, 2026: 8.5

June 21, 2027: 9

December 19, 2027 (maturity date): 9.5

Using the formula for duration:

Duration = (PV of future cash flows x time to receive each cash flow) / PV of all cash flows

We get:

Duration = ($687.58 x 0 + $34.28 x 0.5 + $34.28 x 1 + $34.28 x 1.5 + $34.28 x 2 + $34.28 x 2.5 + $34.28 x 3 + $34.28 x 3.5 + $34.28 x 4 + $34.28 x 4.5 + $34.28 x 5 + $34.28 x 5.5 + $34.28 x 6 + $34.28 x 6.5 + $34.28 x 7 + $34.28 x 7.5 + $34.28 x 8 + $34.28 x 8.5 + $1034.28 x 9.5) / $1099.62

Duration = 7.7472 (rounded to 4 decimal places)

Therefore, the duration of the bond is approximately 7.7472 years.

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The largest possible value for f(4) applying the mean value theorem is 10

According to the Mean Value Theorem, there exists a value c between 0 and 4 such that:

f'(c) = (f(4) - f(0)) / (4 - 0)

Simplifying this equation, we get:

f(4) - f(0) = 4f'(c)

Since f'(x) ≤ 3 for all x, we can substitute 3 for f'(c) to obtain:

f(4) - (-2) ≤ 4(3)

f(4) + 2 ≤ 12

Therefore, we have:

f(4) ≤ 10

So the largest possible value for f(4) is 10.

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The best graphical representation for the data on the number of hours 14-year-olds slept each night, gathered from a random sample of 130 athletic programs in the state, would be a histogram or a line plot.

A histogram is a graphical representation that uses bars to display the frequency or proportion of data in different intervals or bins. It is commonly used to visualize the distribution of a dataset and identify patterns, trends, or outliers.

To create a histogram, you first divide the range of the data into equal intervals or bins, and then count the number of observations that fall within each bin. The bins are usually represented on the x-axis, while the frequency or proportion of observations in each bin is represented on the y-axis.

A line plot, also known as a dot plot, is a simple graphical representation of a dataset that displays the individual data points as dots or small marks along a number line.

To create a line plot, you first choose a number line that covers the range of the data. Then, you plot each data point as a dot or a mark above its corresponding value on the number line. If there are multiple data points with the same value, you can stack the dots vertically to show their frequency.

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Answer:

Line Plot :)

Step-by-step explanation:

Answer:

x = 12

Hope this helps!

Step-by-step explanation:

[tex]x^{2}[/tex] - 5x = 84

[tex]x^{2}[/tex] - 8x = 48

( [tex]x^{2} - x^{2}[/tex],  -5x - ( -8x ), and 84 - 48 )

3x = 36

x = 12

Answer:to be honest i kinda dont know and i just can give you support so try your best or guess b

Step-by-step explanation:

Using the normal distribution, it is found that this type of fishing line have a breaking strength less than the advertised 6 pounds 27.76% of the time.

The z-score of a measure X of a normally distributed variable that has mean represented by  and standard deviation represented by  is given by the following rule:

Z = X - μ /σ

here, we have,

The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.

From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.

The mean and the standard deviation for the breaking strengths are given as follows:

μ = 6.44 and, σ = 0.75

The proportion of times with breaking strength less than 6 inches is given by the p-value of Z when X = 6, hence:

Z = X - μ /σ

Z = (6 - 6.44)/0.75

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

Hence the percentage is of 27.76%.

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What is the missing information?

The question is:

How often will this type of fishing line have a breaking strength less than the advertised 6 pounds.

Roshani thus received 1.14 euros for every £1.

The currency and monetary unit of the European Union is the euro. It was launched as a noncash monetary unit in 1999, and on January 1, 2002, currency notes and coins debuted in member nations3.

The unit of weight and mass is the pound. It is denoted by the abbreviation "lb" and weighs 16 ounces or 453.592 grams.

Roshani converted 300 pounds into 342 euros.

We may divide the entire amount of euros by the total amount of pounds to see how many euros she received for each £1.

342 euros / 300 pounds = 1.14 euros per pound.

Roshani thus received 1.14 euros for every £1.

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the sunglasses will never hit the ground.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The height of the sunglasses at time t is given by the function h(t) = 16t^2 + 5776.

When the sunglasses hit the ground, their height will be 0. So we need to find the value of t that makes h(t) = 0.

16t^2 + 5776 = 0

Dividing both sides by 16, we get:

t^2 + 361 = 0.

This equation has no real solutions since t^2 is always non-negative and can never be equal to a negative number.

Therefore, the sunglasses will never hit the ground.

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The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11

A composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.

The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.

i.e. the function g(x) = 11 always returns the value 11, regardless of the input.

Therefore, we have:

g(-3) = 11

g(5) = 11

g(a) = 11

g(a+h) = 11

So, regardless of the value of a or h, the function g(x) will always return 11.

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Answer:

36 floors

Step-by-step explanation:

We Know

The building is 509 feet tall.

Each floor is about 14 feet tall.

How many floors does the building have?

We Take

509 / 14 = 36 floors

So, the building has about 36 floors.

The required value of x is 2.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. The purpose of an equation is to find the value(s) of the variable(s) that make the statement true. Equations are commonly used in many fields of study, including physics, engineering, and economics, among others.

To solve the equation 2x - 1 = |x| + 1, we can start by noting that |x| is equal to x when x is positive or zero, and equal to -x when x is negative.

Using this property, we can rewrite the equation as follows:

When x is non-negative: 2x - 1 = x + 1

When x is negative: 2x - 1 = -x + 1

We can solve each of these equations separately:

When x is non-negative:

2x - 1 = x + 1

x = 2

When x is negative:

2x - 1 = -x + 1

3x = 2

x = 2/3

So the solutions to the equation 2x - 1 = |x| + 1 are x = 2 and x = 2/3.

To check our solution, we can substitute each value of x back into the original equation:

When x = 2, 2(2) - 1 = |2| + 1, which simplifies to 3 = 3. This is true, so x = 2 is a valid solution.

When x = 2/3, 2(2/3) - 1 = |2/3| + 1, which simplifies to 1/3 = 5/3. This is not true, so x = 2/3 is not a valid solution.

Therefore, the only solution to the equation 2x - 1 = |x| + 1 is x = 2.

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Answer:

   |                              

20 |                              

   |                              

10 |               shading        

   |                  |          

   |                  |          

 0 |_______|__________|__________

   -10     -8        -2       10  

           |         |            

          B-         A            

           |         |            

          -2        6          

Step-by-step explanation:

To graph the linear inequality x - 2y < 2 - 12, we can start by rearranging the inequality into slope-intercept form:

x - 2y < -10

-2y < -x - 10

y > 1/2 x + 5

The inequality y > 1/2 x + 5 represents a half-plane above the line y = 1/2 x + 5. The line has a y-intercept of 5 and a slope of 1/2. To graph this line, we can plot the y-intercept (0,5) and then use the slope to find additional points on the line. For example, we can move one unit to the right and two units up from the y-intercept to get the point (1,6), and then draw a line through both points.

Next, we need to shade the half-plane above the line to represent the inequality y > 1/2 x + 5. To do this, we can pick any point that is not on the line, such as the origin (0,0), and test whether it satisfies the inequality. Plugging in x = 0 and y = 0, we get:

0 > 1/2 (0) + 5

0 > 5

This is false, which means that the origin is not in the shaded region. Therefore, we need to shade the half-plane above the line.

   |                              

20 |                              

   |                              

10 |               shading        

   |                  |          

   |                  |          

 0 |_______|__________|__________

   -10     -8        -2       10  

           |         |            

          B-         A            

           |         |            

          -2        6          

Answer: 1017.36

Step-by-step explanation: The equation set for the volume of a cylinder is V=πr2h (V=pie x radius squared x height). So now all you do is plug in your values! Before that, you have to make sure that your given diameter is converted into radius instead. Radius is just 1/2 of the diameter, so your radius should be 4.5. V=3.14 x 4.5^2 x 16. So the volume should be 1017.36. :)

Answer:

[tex]1017.9cm^3[/tex]

Step-by-step explanation:

[tex]V= volume\\r= 4.5 cm\\h= 16cm \\pi =3.14\\[/tex]

The formula for the volume of a cylinder (can) is [tex]V=\pi r^2h[/tex] first you need to find the radius [tex](r)[/tex] by dividing the diameter by 2 .

[tex]9/2=4.5[/tex]

Now plug your numbers into the formula.

[tex]V=3.14*4.5^2*16\\\\V= 1017.9[/tex]

So the volume of the can of tomatoes (cylinder) is

[tex]=1017.9cm^3[/tex]

The expression 2.8 represents that a new employee is expected to have 2.8 vacation days.

In the given function, f(x) = 2x + 2.8, the constant term 2.8 represents the y-intercept of the linear regression line of the scatter plot.

This means that when x = 0 (which represents the number of years an employee has been working at the company), the corresponding value of y (which represents the number of vacation days reported by the employee) is 2.8.

In other words, according to the linear regression line, a new employee who has just started working at the company (x = 0) is expected to have 2.8 vacation days.

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The associative property of  (p+7) + 9 =  p+(7 + 9) so that both the sides equals p + 16.

The associative property is a property of binary operations, which are operations that involve two elements. It states that the way we group the elements in an operation does not affect the result of the operation.

For any three elements a, b, and c in a set, and a binary operation *, the associative property states that:

(a * b) * c = a * (b * c)

Addition and multiplication are associative operations.

(a + b) + c = a + (b + c) and (a * b) * c = a * (b * c)

The associative property of addition states that when adding three or more numbers, the way we group them does not affect the sum. More formally, for any three numbers a, b, and c, the associative property of addition can be written as:

(a + b) + c = a + (b + c)

In the case of (p+7) + 9, we can apply the associative property of addition as follows:

[(p+7) + 9] = p + (7 + 9)

p + 16 = p + 16

Here, we have grouped the numbers 7 and 9 together and added them first, and then added the result to p. This gives us the same sum as if we had added p and 7 first and then added 9 to the result.

Therefore, the associative property of addition tells us that we can add (p+7) and 9 in any order or group them differently, and still get the same result (p+16).

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tower of height 105 feet and a shadow of length 117 feet. We want to find the angle of elevation of the sun, represented by the angle θ. the angle of elevation of the sun to the nearest degree is  [tex]43[/tex] degrees.

We can use the tangent function to find the angle of elevation of the sun:

tan(angle of elevation) = opposite / adjacent

In this case, the opposite side is the height of the tower (105 feet) and the adjacent side is the length of the shadow (117 feet).

tan(angle of elevation) [tex]= 105 / 117[/tex]

We can solve for the angle of elevation by taking the inverse tangent (tan^-1) of both sides:

angle of elevation [tex]= tan^-1(105 / 117)[/tex]

Using a calculator, we get:

angle of elevation  [tex]\approx 42.9[/tex] degrees

Therefore, the angle of elevation of the sun to the nearest degree is  [tex]43[/tex]degrees.

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The inequality c ≥ 20 represents the minimum number of candles that need to be sold to pay for a visit to Knotts costing $100 when each candle is sold for $5.

To write the inequality that represents c, we need to consider the cost of the visit to Knotts and the price of each candle that is being sold. Let's assume that the cost of the visit to Knotts is $100 and each candle is being sold for $5.

We know that the total amount of money she earns from selling c candles is given by 5c, and this amount must be greater than or equal to the cost of the visit, which is $100. Therefore, we can write:

5c ≥ 100

Dividing both sides of the inequality by 5, we get:

c ≥ 20

Therefore, the inequality that represents c is c ≥ 20. This means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

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26950 is  the total amount he received at the end of seven years.

What is your interest in simple words?

Interest is the price you pay to borrow money or the cost of borrowing money. Interest is usually given as an annual percentage of the loan amount. This percentage is called the interest rate on the loan.  

given,

pv= 14100

r1-4= 8%

n = 7

r5-7= 12%

A) interest  = FV - PV

                 = PV * ( 1 + r )ⁿ - pv

                  = 14100 * ( 1 + 0.08)⁴ * ( 1 + 0.12)³ - 14100

                   = 26,950.59 - 14100

                     = $12850.59

b)   fv= pv * (1 + r)ⁿ

          = 14100 * ( 1 + 0.08)⁴ * ( 1 +0.12 )³

          = 26950

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Required value of 8x is 24.

What is equation?

The mathematical statements that contain two algebraic expressions on either side of an equal sign (=) is called Equations. It shows equality between an expression written on the left side and an expression written on the right side. In any mathematical equation, L.H.S = R.H.S (Left side = Right side). Equations can be solved to obtain the value of the unknown variable that represents the unknown values. If the statement does not have the "=" symbol that means the expression is not an equation. It is treated as an expression.

Here given equation is 5x+4 = 6x

We are Simplifying,

[tex]5x + 4 = 6x \\ 6x - 5x = 4 \\ x = 4[/tex]

Therefore, value of x is 4.

Now,

[tex]8x = 8 \times 3 = 24[/tex]

So, required value of 8x is 24.

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Correct question is "If 5x+4 = 6x, find 8x A) 24 C)0 B)12 D)32"

Therefore, there are 36 possible values of n to satisfy the given equation.

In mathematics, an equation is a statement that asserts the equality of two expressions. Equations are formed using mathematical symbols and operations, such as addition, subtraction, multiplication, division, exponents, and roots. An equation typically consists of two sides, with an equal sign in between. The expression on the left-hand side is equal to the expression on the right-hand side. Equations can be used to model a wide range of real-world situations, from simple algebraic problems to complex scientific and engineering applications.

Here,

We can use the fact that sin(θ) + i cos(θ) = [tex]e^{(iθ)}[/tex], where e is the base of the natural logarithm.

So, the given equation becomes [tex]e^{(iθ)} ^= e^{(inθ)}[/tex]. Taking the natural logarithm of both sides, we get:

iθ = inθ + 2πik (where k is an integer)

Simplifying, we get:

nθ = (k - i)2π

Since b ≤ 2016, we know that n ≤ 2016. We can also see that k - i must be a multiple of n, so we have:

k - i = nm (where m is an integer)

Substituting this back into the equation, we get:

θ = m(2π/n)

So, the number of possible values of n is equal to the number of divisors of 2016. Prime factorizing 2016 as 2⁵ * 3² * 7, we get:

The number of divisors of 2016 = (5 + 1)(2 + 1)(1 + 1)

= 36

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Answer:

2

Step-by-step explanation:

[tex]\sf \frac{6.5}{40.3} =\frac{m}{12.4}[/tex]

Use cross multiplication.

6.5 × 12.4 = 40.3m

80.6 = 40.3m

Divide both sides by 40.3.

2 = m

Answer:

It can be written in interval notation as [-5,5)

Answer:

a) The probability that the T-shirt will be grey is 2/20 or 1/10. This is because Hamid has 2 grey T-shirts out of 20 total T-shirts.

b) The probability that the T-shirt will not be red is 1 - (4/20) or 16/20, which can be simplified to 4/5. This is because Hamid has 4 red T-shirts out of 20 total T-shirts, so the probability of not selecting a red T-shirt is equal to the probability of selecting one of the 16 non-red T-shirts.

c) Hamid has only one light blue T-shirt out of the total 20 T-shirts. So, the probability of selecting a light blue T-shirt is 1/20.

Answer:

Step-by-step explanation:

a) The probability that Hamid pulls out a grey T-shirt is 2/20, or 1/10 in simplified form since there are 2 grey T-shirts out of 20 total.

b) The probability that the T-shirt will not be red is 16/20, or 4/5 in simplified form since there are 4 red T-shirts and 16 T-shirts that are not red.

c) Hamid has only 1 light blue T-shirt out of the 20 total T-shirts. So, the probability that he takes out the light blue T-shirt is 1/20. Note that the numbers of dark blue and white T-shirts are not needed to answer this question.

The minimum sample size required is 95, rounded up to the nearest integer.

We can use the formula to determine the minimum sample size required to construct the confidence interval with the specified characteristics:

[tex]n = (z^2 * s2) / E2,[/tex]

where n denotes the sample size.

z is the z-score that corresponds to the desired level of confidence (in this case, 85% corresponds to a z-score of 1.44) s2 is the population variance

E is the maximum estimate error we want to allow.

Using the given values, we obtain: [tex]n = (1.4412 * 1.96) / 0.062 n = 94.16[/tex]

The minimum sample size required is 95, rounded up to the nearest integer.

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Answer:

The average adult weighing 150 to 180 pounds should have about 1.2 to 1.5 gallons of blood in their body. 160 ounces.

Step-by-step explanation:

The length of the third side in this right - angle triangle can be found to be 30 units.

To find the length of the hypotenuse (C) in a right-angled triangle with sides A and B given as 24 units and 18 units, respectively, you can use the Pythagorean theorem:

A² + B² = C²

In this case, A = 24 and B = 18. Plug the values into the formula:

(24)² + (18)² = C²

576 + 324 = C²

900 = C²

Now, take the square root of both sides to solve for C:

C = √900

C = 30

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Answer:

Sarah's gross bi-weekly income is:

$18.33/hour x 40 hours/week x 2 weeks = $1,466.40

Her net bi-weekly income is $1,100, so her net monthly income would be:

$1,100/2 weeks x 2.17 weeks/month = $2,383

Therefore, the answer is B. $2,383.

To subtract two numbers in base 5, you perform the subtraction column by column, just like in base 10, but carrying and borrowing are done in base 5. Let's subtract 431 (base 5) - 144 (base 5):

431

- 144

42(1+5)

- 1 4

-------

2

42

- 1

-------

1

4

-

-------

4

431

- 144

-----

412

The values of the given trigonometric functions are 240° and 60° respectively.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The three primary trigonometric functions are sine, cosine, and tangent.

The sine function (sin) relates the length of the opposite side of an angle to the length of the hypotenuse of a right triangle. It is defined as sin(θ) = opposite/hypotenuse.

The cosine function (cos) relates the length of the adjacent side of an angle to the length of the hypotenuse of a right triangle. It is defined as cos(θ) = adjacent/hypotenuse.

The tangent function (tan) relates the length of the opposite side of an angle to the length of the adjacent side of a right triangle.

Now To find

(a.)  sin⁻¹(-√3/2)

(b.)  cos⁻¹ (1/2)

For a

sin⁻¹(-√3/2)=sin⁻¹(-0.8660)=-⁻60° or 240°

and

For b

cos⁻¹ (1/2)=cos⁻¹ (0.5)=60°

Hence,

             the values of the given trigonometric functions are 240° and 60° respectively.

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23 child tickets were sold that day.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given: At the movie theatre, child admission is 5.40, and adult admission is 9.40. On Saturday, twice as many adult tickets as child tickets were sold, for a total sales of 556.60.

We have to find out how many tickets were sold that day.

let x = number of adult tickets

let y = number of child tickets

x = 2y  (twice as many adult tickets as child tickets)

9.40x + 5.40y = 556.60.....(1)

We put the value of x in equation(1) and we get

9.40(2y) + 5.40y = 556.60

18.8y + 5.40 = 556.60

24.2y = 556.60

y = 556.60/24.2

y = 23

Now we put the value of y in x = 2y and we get

x = 2×23

x = 46

Hence, 23 child tickets were sold that day.

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Therefore, the equation of the line parallel to y - 4x = 0 and passing through (-6, 3) is y = 4x + 27.

An equation is a mathematical statement that asserts that two expressions are equal. It typically involves one or more variables and is written using mathematical symbols such as addition, subtraction, multiplication, division, and exponents. For example, the equation "2x + 5 = 13" asserts that the expression 2x + 5 is equal to 13, and the variable x can be solved for by rearranging the equation. Equations are fundamental tools in mathematics and are used in a wide range of applications, including physics, engineering, economics, and more.

The given line is y - 4x = 0 (I assumed that the 4x is in the denominator).

To find the equation of the line that is perpendicular to this line and passes through the point (-6, 3), we first need to find the slope of the given line. The slope of the given line is 4 (because the coefficient of x is 4). The slope of the line perpendicular to this line will be the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is -1/4.

Now, we can use the point-slope form of a line to find the equation of the perpendicular line:

[tex]y - 3 = (-1/4)(x + 6)[/tex]

Simplifying this equation, we get:

[tex]y = (-1/4)x - 9/4[/tex]

Therefore, the equation of the line perpendicular to [tex]y - 4x = 0[/tex] and passing through.[tex](-6, 3) is y = (-1/4)x - 9/4[/tex].

To find the equation of the line parallel to the given line and passing through the point (-6, 3), we just need to use the same slope as the given line, which is 4. Then, we can use the point-slope form of a line to find the equation of the parallel line:

[tex]y - 3 = 4(x + 6)[/tex]

Simplifying this equation, we get:

[tex]y = 4x + 27[/tex]

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