What is the slope of a line perpendicular to the line whose equation is 6x+y=-5

The integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi times the sum of the residues of the poles of f (z) inside the circle.

The poles of f (z) inside the circle are z = 0 and z = −1/2.

The residue at z = 0 is f (0) = 0.

The residue at z = −1/2 is f (−1/2) = −7/16.

Therefore, the integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi (−7/16) = −7πi/8.

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The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.

GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.

The given expression is,

16a⁴b + 8ab³

Simplify the expression, by factor method,

8 x 2 x a x a x a x a x b  + 8 x a x b x b x b

The common term is 8ab,

8ab(2a³ + b²)

The required expression is 8ab(2a³ + b²).

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Answer:

one way is that they both have four sides.

another way is that they both have straight lines.

and the other way is that they both have 4 corners.

Step-by-step explanation:

Answer:

According to the web: "A square has four equal sides. In a rectangle, the opposite sides are equal. The diagonals of a square bisect each other at 90°. The diagonals of a rectangle bisect each other at different angles."

Step-by-step explanation:

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The solution of x in the equation is 79/3

From the question, we have the following parameters that can be used in our computation:

y = 69

5x + 15 = y + 2x - 5

Substitute y = 69 in the equation 5x + 15 = y + 2x - 5

So, we have

5x + 15 = 69 + 2x - 5

Collect the like terms

This gives

5x - 2x =69 - 5 + 15

Evaluate the like terms

This gives

3x = 79

Divide both sides by 3

x = 79/3

Hence, the solution is 79/3

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The amount of time it would take for the balloon's diameter to decrease to 8 feet is 56 minutes.

What is an example of diameter?

If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.

In how long would the diameter have decreased to 8 feet?

A circle's diameter is determined by drawing a line across its center, touching both ends of its circumference.

Minutes are calculated as diameter/decline.

56 minutes from 14/0.25

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The slope of a line parallel to the line having equation 10x+12y=-120 is -5/6.

What is the slope of a line parallel to another line?

Parallel lines are coplanar and they never intersect.

Slope is a measure of the angle of a line from the horizontal.

Since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.

According to the given question:

Given equation of line is 10x+12y=-120

Converting this to slope-intercept form we get

y = -5/6 x + 10

Clearly slope of this line is -5/6

Any line parallel to this line will have the same slope

Therefore the slope of a line parallel to the given line is -5/6

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The printed price of the desk on the furniture store is $173. It can be solved by the concept of cost price and selling price.

What is cost price and selling price?

Cost price is the price of the object at which it is purchaged and selling price is the price of the object at which it is sold. If cost price is more than the selling price then the seller will earn a loss. If the cost price is less than then the selling price then the seller will earn a profit.

The cost price of the furniture = $144

Now, 20% of cost price is,

[tex]=\$ 144\times\frac{20}{100}\\=\$28.8[/tex]

Now, price of furniture on the store = Cost price + 20% of cost price

                                                           = $144 + $28.8

                                                           = $172.8$

Round off the price                           = $173

Hence, the printed price of the desk on the furniture store is $173.

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Answer:

D

Step-by-step explanation:

A simpler way to see it, of course, is that the mentioned line segments lie on the same line, so they must have the same slope.

The dimensions of the rectangle should be 150 feet by 400 feet in order to enclose the maximum possible area.

To explain this step by step:

Step 1: We know that the perimeter of a rectangle is equal to 2*length + 2*width.

Step 2: Since we have 600 feet of rope, we can plug this number into the equation: 2*length + 2*width = 600

Step 3: To solve for the length and width, we can divide both sides by 2: length + width = 300

Step 4: We can then separate the equation into two equations: length = 300 - width and width = 300 - length

Step 5: Since we want to find the maximum possible area, we should set width equal to the larger number, 300, and set length equal to the smaller number, 300 - width.

Step 6: Plugging this into the equation, we get: width = 300 and length = 300 - width = 300 - 300 = 0.

Step 7: Therefore, the maximum possible area that can be enclosed with 600 feet of rope is 150 feet by 400 feet dimensions.

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The average rate of change of f(x), represented by the table of values, over the interval [-2, 3] is: D. 0.5.

An average rate of change is sometimes referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes with respect to another quantity, over a given interval.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [-2, 3]:

a = -2; f(a) = 2.5

b = 3; f(b) = 5

Substituting the given parameters into the formula, we have the following;

Average rate of change = (5 - 2.5)/(3 - (-2))

Average rate of change = 2.5/5

Average rate of change = 0.5.

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Answer:

b = 20

Step-by-step explanation:

the variables a and b are proportional , so the equation relating them is

a = kb ← k is the constant of proportion

to find k use the condition a = 12 , b = 3

12 = 3k ( divide both sides by 3 )

4 = k

a = 4b ← equation of proportion

when b = 5 , then

a = 4 × 5 = 20

Answer: $83.35

Step-by-step explanation:

Find 15% of 72.48 = 10.87

10.87 + 72.48 = 83.35

The required coupon rate of Samantha's bond is 4%.

The coupon rate is the annual income an investor can expect to receive while holding a particular bond. It is fixed when the bond is issued and is calculated by dividing the sum of the annual coupon payments by the par value. At the time it is purchased, a bond's yield to maturity and its coupon rate are the same.c

We have,

principal amount = $600

Amount after five year = $720

Interest of five year = $(720 - 600) = $120

Then,

Interest of one year = $120/5 = $24

Now,

Coupon rate = ($24/600)×100 = 4%

Thus, required coupon rate is 4%.

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x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like coordinates.

Given,

In response to our inquiry:

Add "-9y²" to each side of the equation.

4x² + 9y² + -9y² + -1z² = 36 + -9y²

9y² + -9y² = 0 when equivalent phrases are combined.

4x² + 0 + -1z² = 36 + -9y²

4x² + -1z² = 36 + -9y²

Add "z²" to both sides of the equation.

4x² + -1z² + z² = 36 + -9y² + z²

Therefore,

x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like dimensions.

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The type of pair of angles that are∠2 and angle∠11 is an alternate interior angles.

When a transversal intersects two coplanar lines, alternate interior angles are formed. They are on the inside of the parallel lines, but on the outside of the transversal.

Angles with the same size that occur on opposite sides of the transversal line are known as alternate angles. The following alternate angles are equal: By drawing a Z shape, we can frequently identify interior alternate angles: Alternate angles are classified into two types: alternate interior angles and alternate exterior angles.

To understand alternate interior angles, imagine a set of parallel lines and then a line intersecting them. The intersecting line is known as a transversal, and all of the angles formed by the parallel lines are known as interior angles.

Both angles are interior angles that lie alternately to each other on the transversal line r. Therefore, they are alternate interior angle.

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Answer:

1.8 inches

Step-by-step explanation:

The amount of sales Terry must make is $1667

How to determine the amount in sales?

From the question, we have the following parameters that can be used in our computation:

Commission = 18% of sales

Commission = $300

These parameters mean that

Commission = 18% of sales

Substitute the known values in the above equation, so, we have the following representation

18% of sales = 300

Divide both sides by 18%

Sales = 1667

Hence, the amount is $1667

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The solution to f(x) = g(x) is

x = 0

x = 1

What do you mean by a solution?

We can substitute a value, or values, for a variable (such as x), making the equation true and thus finding a solution. All values of x in the domain, such that f(x) = g, are the solutions if two functions, f, and g, both map to the same co-domain.

as in: x + 2 = 7.

5 + 2 = 7 is what we get when we substitute 5 for x.

Given that 5 + 2 = 7, x = 5 is a solution.

Solution Explained:

A set of values in the table that tell us what the values of each function f(x) and g(x) are for a given value for the variable "x" is already giving us a hint.

We can infer from the table that f(x) decreases when x>0 and moves in the opposite way when x0.

G(x) follows a distinct path; it grows as x increases and shrinks as x lowers.

As a result, there is not much room for equality between the two functions.

You can thus utilize the points shown in the table to begin your test.

f(0)= 0,25 ^ 0=1 since a number raised to 0 is always 0.

g(0)=-0.75 * 0 + 1 = 1

f(1)=0.25^1=0.25 since a number raised to 1 is always equals to itself

g(1)=-0.75*1+1=0.25

So f(x)=g(x), when x=1 and when x=0

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Answer: Slade should use 1/3 cup of milk

Step-by-step explanation:

2/3 divided by 1/2 = 1/3

In other words, if you have 2 of something and you give someone half, you would give them 1.

Using the conversion factor, we can say that each sheet of paper is 0.0012mm thick.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

So, 500 sheets of A4 paper make up a conventional ream. Each paper measures 297mm in length by 210mm broad, and one ream contains 3742.2cm of paper.

to change cm to mm

3742.2cm = 37422 mm

Sheet 1's surface

(297mm) X 210mm) = 62370mm²

1st volume sheet:

37422mm : 500 = 74.844mm

One sheet's thickness is:

74.844mm : 62370mm = 0.0012mm

Therefore, each sheet of paper is 0.0012mm thick.

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Correct question:
A ream of A4 paper contains 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm find the thickness of each sheet of paper answer in millimeters​

Examining the function  -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0

Where a parabolic curve opens up or down in this case depends on the sign on the coefficient of the x².

The coefficient of  x² is a and in this function is -9

A negative coefficient leads to opening downwards while a positive coefficient will result to opening upwards

The y intercept

-9x² + 7x = 0

x(-9x + 7) = 0

x = 0

-9x + 7 = 0

-9x = -7

x = 7/9

the y intercept is 0 ad 7/9

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The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

What is integration?

It is defined as the mathematical approach to calculating the smaller parts or components.

It is given that:

A barn is 100 feet long and 40 feet wide.

Find the first derivative of the given function:

After solving the above integration:

= 20(e - 1/e)

The roofing = 100(20(e - 1/e))

= 4701 square feet

Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

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Answer: 25 days

Step-by-step explanation:

We know that it takes 55 days with 15 workers, so we need to find how many days it takes with 1 worker by taking 55 timed 15 = 825 days for 1 worker.

Then we take 825 divided by 33 and get 25 days for 33 workers.

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The population variance of the capacities is 30.76

the capacities (in ampere-hours) of 10 batteries are 140, 136, 150, 144, 148, 152, 138, 141, 143, 151.

The number of observations n = 10

mean = (x₁ + x₂ + x₃.....x₁₀)/10

mean = (140 + 136 + 150 + 144 + 148 + 152 + 138+ 141 + 143 + 151)/10

mean = 1443/10 = 144.3

variance = ∑(x - mean)²/(n - 1)

variance = ((140 - 144.3)² + (136 - 144.3)² + (150 - 144.3)² + (144- 144.3)² + (148 - 144.3)² + (152 - 144.3)² + (138 - 144.3)² + (141-144.3)² + (143 - 144.3)² + (151 - 144.3)²)/(10 - 1)

variance = 276.9/9 = 30.76

Therefore, the population variance of the capacities is 30.76

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The cost of the book after the discount and coupon is $7.32

From the question, we have the following parameters that can be used in our computation:

Amount  = $15.40

Coupon = $5 offer

Discount = 20% off

This means that

Total amount = Amount  * (1 - Discount) - Coupon

So, we have

Total amount = 15.40 * (1 - 20%) - 5

Evaluate

Total amount = 7.32

Hence, the total amount = 7.32

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The value of g is g = w² - 14w + 49, according to the question.

What do you mean by formula?

A truth or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more values. When you are aware of the value of one quantity, you can use the formula to determine the value of the other. It facilitates speedy question resolution. Formulas are used in algebra, geometry, and other subjects to speed up and simplify the process of arriving at the result.

According to the given question,

We have :

w = 7 - √g

Firstly isolate the g,

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides,,

w (-7) = -√g + 7 (-7)

w - 7 = -√g

Now, multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g

-1w + 7 = √g

To get rid of the square root, you must square both sides,

Note: -1w is the same as -w.

Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²

g = (-w + 7)²

g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or                                            g = (-w + 7)²    )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²

(-w)(7) = -7w

(7)(-w) = -7w

(7)(7) = 49

g = w² - 7w - 7w + 49

Then, simplify (combine all like terms):

g =w² - 7w - 7w + 49

g = w² - 14w + 49

Therefore, the value of g = w² - 14w + 49 .

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You are writing an article for your school newspaper about the Oakland Athletics.  Season tickets go on sale next week and you have been assigned to write an article to help fans determine whether they should buy season tickets or single-game tickets based on their expected attendance at the games this season.

Buying a season ticket allows you to attend all 81 home games for a single price.  Without a season ticket you have to pay for every single game that you attend.

Image result for Oakland Athletics Tickets Box Office

The table shows different ticket price options.

In this task you will answer six questions about the ticket price options and recommend which is best for fans. Be sure to show all your work for each item.

1. A season has 81 home games. If you purchase a season ticket in the bleacher section , what is the cost per game, in dollars for this ticket?

.2. Complete the table based on the single game ticket for seats in the Left field reserve section.

Step-by-step explanation:

The key role for CPS is to minimize stigma and be an ambassador for recovery. Describe a situation where you had to confront stigma

The probability that the mean blood pressure will be less than 125 is 0.9938

The mean of the pressure readings = 123

The standard deviation = 9.6

Total population = 144

The value is less than 125

The equation of the z-score is

z-score = (Observed value - Mean ) / (Standard deviation /[tex]\sqrt{N}[/tex])

Substitute the values in the equation

z-score = (125 - 123) / (9.6/[tex]\sqrt{144}[/tex])

= 2 / (9.6/12)

= 2 / 0.8

= 2.5

Using the statistical table

The probability of that their mean blood pressure less than 125

P(z < 2.5) = 0.9938

Therefore, the probability is 0.9938

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The probability, which is calculated using the hypergeometric distribution, is 0.845, or 84.5%.

Given,

The answer to this question involves using the hypergeometric distribution because the patients are randomly selected from the sample without replenishment.

Hypergeometric distribution:

The probability of x successes is given by:

P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]

The parameters are:

x is the number of successes.

N is the size of the population = 56074

n is the size of the sample = 40

k is the total number of desired outcomes = 235

The number of unique combinations of x objects from a set of n elements is provided by the following formula:

Cₙ,ₓ = n! / x! (n - x)!

The probability that none left against medical advice is P(X = 0), so:

P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]

P(X = 0) = h(0, 56074, 40, 235) = (C₂₃₅, ₀ × C₅₆₀₇₄₋₄₀, ₄₀₋₀) / C₅₆₀₇₄, ₄₀

= (C₂₃₅, ₀ × C₅₅₈₃₉, ₄₀) /  C₅₆₀₇₄, ₄₀

= 0.845

The probability is 0.845 = 84.5%.

Therefore,

The probability that none of them left the treatment center against medical advice is 0.845 = 84.5%

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The expression in terms of x that represents the total amount that Zoe paid is 1.2x

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A tax of 5% is applied to the bill.

Zoe decides to leave a tip of 15% on the entire bill (including the tax).

let the bill cost $x.

So, the price after tax and tip

= x+ 5% of x+ 15% of x

= x + 0.05x + 0.15x

= x + 0.20x

= 1.2x

Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x

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