A linear relationship is given in the table.
X-2 -1 0 1 2
y-18 -12 -6 06
What is the slope of the relationship?

Answer:2 + √3

Step-by-step explanation:

The value of tan 5pi/12 in decimal is 3.732050807. . .. Tan 5pi/12 can also be expressed using the equivalent of the given angle (5pi/12) in degrees (75°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)

⇒ 5pi/12 radians = 5pi/12 × (180°/pi) = 75° or 75 degrees

∴ tan 5pi/12 = tan 5π/12 = tan(75°) = 2 + √3 or 3.7320508

36 yards wide is the actual picnic area.

The drawing's length, a colon (":"), and the actual length that corresponds to it are used to illustrate the scale.

Given that this illustration is scaled at "1:10," everything depicted with a size of "1" would have a size of "10" in the real world, a measurement of 150 mm on the image would be 1500 mm on the actual horse.

One unit in the picture equals 100 actual units. In other words, you would draw the table on a piece of paper at a scale of 2 cm if we were to draw it at a scale of 1:50 and it was 100 cm wide by 200 cm long.

width of actual picnic area = 12 × 3 = 36 yards

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p(x) must be equal to (x-a)(x-b) where b is another number.

If p(a) = 0, then this implies that (x-a) is a factor of p(x). Therefore, p(x) can be factored into (x-a)q(x), where q(x) is a polynomial of degree one less than the degree of p. This means that p(x) must be equal to (x-a)(x-b) for some other number b. It does not mean that p(x) must be equal to the zero polynomial or (x-a)².

The product of two factors, (x-a) and (x-b), is a polynomial of degree two, p(x). This can be expressed in expanded form as p(x) = x² - (a + b)x + ab, where a and b are any two numbers

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As per the borrowed amount, the value of IRR is 6.40%

The term IRR is the internal rate of return is a metric used in financial analysis to estimate the profitability of potential investments.

Here we have know that Maggie green just borrowed $5,000. she is planning to pay it back in 5 equal installments of $1,200.

Now, we have to calculate the value of IRR,

The general form of the IRR formula is written as,

=> NPV = [tex]\sum\limits^T_{t=1} {\frac{C_t}{(1+r)^t} }\ -C_0[/tex]

where r is the discount rate / interest rate and T is the number of cash flow periods with t denoting a specific period, C0 is the initial investment while Ct is the return during period t.

Here we apply the values on it, then we get,

=> [tex]NPV = \sum\limits^5_{t=1} {\frac{1200_t}{(1+r)^t} }\ -5000[/tex]

When we simplify this one then we get,

=> Internal Rate of Return = 6.402%

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If the long chord and tangent length of a circular curve of radius R are equal the angle of deflection is 120 °

The term angle of deflection in math is defined as  the angle of which the M particle is deviated

Here we know that the intersection point is the angle between the back tangent and forward tangent.

Here we have also know that the surveyor either computes its value from the preliminary traverse station angles or measures it in the field and it can be denoted by Δ.

Then the Tangent length is calculated as,

=> T = R tan ⁡ Δ/2

Similarly, the long chord is calculated as,

=> L = 2 R sin ⁡ Δ/2

Here we also know that Length of the long chord is defined as,

=> L = T

The it can be calculated as,

=>R tan Δ/2 = 2 R sin ⁡ Δ/2

Here we know tanθ = sinθ/cosθ then it can be written as

=> 1/2 = cos (Δ/2)

=> Δ/2 = 60°

=> Δ = 120 °

Therefore option (d) is correct.

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The rock that has a mass of 35.4 g has a density of: 5.06 g/ cm^3

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

The density formula and the procedure we will use is:

d = m/v

Where:

Information about the problem:

Applying the density formula we get:

d = m /v

d = 35.4 g / 7.0 cm^3

d = 5.06 g/ cm^3

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Correctly written question:

If a rock has a mass of 35.4 g and a volume of 7.0 cm^3. What is the density of the rock in g/cm3

30 hot dogs would contribute $60 to the GDP and 20 hamburgers would also contribute $60 to the GDP.

The calculation for the number of hamburgers that would contribute the same to the GDP as 30 hot dogs is as follows:

GDP (Hot Dogs) = 2 x 30 = 60

GDP (Hamburgers) = 3 x x = 60  

Therefore, the number of hamburgers needed to equal the GDP of 30 hot dogs is equal to 20:

GDP (Hamburgers) = 3 x 20 = 60

Therefore, the answer is C) 20.

To explain this in more detail, Gross Domestic Product (GDP) is a measure of the total value of all goods and services produced in a country during a specific period of time. It is calculated by multiplying the price of a good or service by the amount produced. In this case, the price of a hot dog is $2 and the price of a hamburger is $3. Therefore, 30 hot dogs would contribute $60 to the GDP and 20 hamburgers would also contribute $60 to the GDP.

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Answer:

Step-by-step explanation:

The volume of a cube is the edge length cubed (S^3)

To find the edge length when the volume is known find the cubic root of the volume.

Edge = ∛1/27

Edge = 1/3 ft.

Answer:

h(13) = 3

h(25) = 7

h(34) = 10

Step-by-step explanation:

In this situation, you plug in the number inside h, replacing t because the original function is h(t).

So,

h(13) = (13-4)/3

9/3 = 3

h(25) = (25-4)/3

21/3 = 7

h(34) = (34-4)/3

30/3 = 10

Hope this helps!

You were on the right track, I totally understand why you'd get stuck where you are currently in the process. To start with, you technically found the wrong ratio between the two triangles. Your ratio is just 2x, while it should be 2x/5.

To start, let's find the ratio between triangle FEG and ABC by dividing angle F by and A:

[tex]R=\frac{2x}{5}[/tex]

Now, multiply angle B by this ratio:

[tex](x+4)(\frac{2x}{5} )=\frac{2x^2}{5}+\frac{8x}{5}=\frac{2x^2+8x}{5}[/tex]

We can now set this expression equal to angle E, as we have multiplied by the common ratio:

[tex]\frac{2x^2+8x}{5} =18[/tex]

This looks rather daunting, but let's keep calm... you can do this!!

Start by subtracting 18 from both sides:

[tex]\frac{2x^2+8x}{5}-18=0[/tex]

Now, let's get the whole expression under the denominator 5:

[tex]\frac{2x^2+8x-90}{5}=0[/tex]

Notice that the denominator can now be removed:

[tex]2x^2+8x-90=0[/tex]

Now, factor the equation (you could also use the quadratic eq if you want)

[tex]2(x-5)(x+9)=0[/tex]

Notice that we have two potential values for x (5 and -9).

Think about this logically... If we use -9 and plug it in for x, we will end up with values of -5 degrees for an angle, which is impossible! Therefore 5 is the only valid answer!

I encourage you to also approach the problem from a different angle and use the common factor (5/2x) and multiply it by 18 :)

1. The variable in the solution is the population every year

2. The model can be presented as

y= 1175-20x

3. The value of slope is -20 which says that the population decreases by 20 members for every one year increase from 2010

Let y be the population after x years from 2010

So, the model can be presented as

y= 1175-20x

Now for example, in year 2011

x= 2011-2010= 1

The population is y = 1175-20(1) = 1155

The population in year 2012 is

x= 2012-2010= 2

Population is y= 1175-20(2) = 1135

The result obtained is satisfactory and hence ok

The population follows a linear trend with slope of -20 and intercept of 1175.

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The par coupon rate of four-year, default-free security with annual coupon payments is 112%.

The par coupon rate of a four-year, default-free security with annual coupon payments can be calculated by taking the present value of all future coupon payments, plus the face value of the security, and dividing that amount by the face value of the security.

Par Coupon Rate = (Present Value of Coupon Payments + Face Value) / Face Value

Annual interest payment = [tex]\frac{12}{100} *1000[/tex]

Annual interest payment = $120

A face value of $1,000 and the present value of all future coupon payments is $120, the par coupon rate for this security would be 112%.

Par Coupon Rate = ($120 + $1,000) / $1,000

Par Coupon Rate = 1120 / 1000

Par Coupon Rate = $1.12

Par Coupon Rate = 112/100

Par Coupon Rate = 112 %.

Therefore,

The par coupon rate of four-year, default-free security with annual coupon payments is 112%.

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The integral function is equal to, Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy = [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).

In calculus, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive.

Given that,

Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy

=  [tex]\int\limits^[/tex] y d([tex]e^{6y}[/tex])

= [ y ([tex]\frac{e^{6y} }{6}[/tex]) - [tex]\int\limits^[/tex] (1)  ([tex]\frac{e^{6y} }{6}[/tex]) ]

= [tex]\frac{ye^{-6y} }{6}[/tex] + [tex]\frac{e^{-6y} }{36}[/tex]  where, 0 and 1

= [ [tex]\frac{1}{6e^{2} }[/tex] + [tex]\frac{1}{36e^{2} }[/tex] ] - [1/36]

= [ 7/36[tex]e^{2}[/tex] ] - [1/36]

= [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

Therefore,

The integral function is equal to, Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy = [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

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The tire will need to rotate 38.2 times to travel the whole length of the street.

We will first compute the tire's circumference in order to determine how many times it will need to revolve while traveling the distance of the roadway.

The formula for determining a circle's circumference may be used to get the tire's circumference because it is circular.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 3.5ft and π = 3.14

∴ C = 3.14 × 3.5

C = 10.99ft

Therefore, the circumference of the tire is 10.99ft

The tire will need to turn 38.2 times to travel the whole length of the street. We will now divide the street's length by the tire's circumference to determine how many times it tire will need to turn to go its whole length.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 420 ft ÷ 10.99 ft

Number of times the tire will have to turn = 38.2165 times

Number of times the tire will have to turn ≅ 38.2 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 38.2 times

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His speed for the remaining 26 km of the course is given as follows:

24.3 km/h.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which the parameters are given as follows:

The time is obtained as the distance divided by the velocity, hence:

t = d/v.

Then the time taken for the first 29 km is given as follows:

t = 29/15

t = 1.93 hours.

180 minutes = 3 hours, hence he took 1.07 hours for the remaining 26 km, hence the velocity is of:

v = 26/1.07

v = 24.3 km/h.

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John has 6 quarters, 12 nickels, and 6 dimes, for a total of 24 coins. This is because he has twice as many nickels as quarters (12 nickels, 6 quarters), and two more dimes than nickels (12 nickels, 6 dimes). With this combination, the total value of all the coins would be $3.50.

To calculate the number of coins John has, we can use the following steps:

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Answer:

Step-by-step explanation:

There are 16 ounces in 1 pound. Take 3/4 and multiply it by 16.

3/4 x 16 ounces = 12 ounces

There are 12 ounces in 3/4 lb.

The chef uses 1/8 of the 12 ounces (or 3/4 lb) of cheese for the top of the lasagna.

1/8 of 12 ounces

1/8 x 12 ounces = 1.5 ounces

The chef uses 1.5 ounces for the top of the lasagna.

To convert the ounces to pounds, use 1 lb/16 ounces. The ounces cancel and you are left with pounds.

1.5 ounces x (1 lb/16 ounces) = 0.09375 lb

The required equation is 2x + 2 = 6x and the value of 'x' is 1/2.

The total length covered by the outline or boundary of a rectangle is known as the perimeter of the rectangle. And the formula is given by

Where l = length and b = breadth  

Here we have

Rectangle-A and rectangle-B  

Dimensions of Rectangle-A are (x + 2) × x  

=> Perimeter of Recatngle-A = 2(x + 2 + x)

= 2(2x + 2)

Dimensions of Rectangle-B are 4x × 2x  

=> Perimeter of Rectangle-B = 2(4x + 2x)

= 2(6x)    

Given that both rectangles have the same perimeter

=> 2(2x + 2) = 2(6x)

=> 2x + 2 = 6x  [ Divide by 2 ]    

∴ The required equation is 2x + 2 = 6x

We can solve the above equation as follows

=> 2x + 2 = 6x

=> [ 2x + 2 - 2x] = 6x - 2x         [ Subtract -2x from both sides  ]

=> 4x = 2

=> x = 2/4

=> x = 1/2

Therefore,

The required equation is 2x + 2 = 6x and the value of 'x' is 1/2.

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Answer:

Given;

Total number of pencil=55

number of pencil lost=11

Then,

percentage of pencil lost=((Number of pencil lost/Total number of pencil)*100)

% of pencil lost= ((11/55)*100)

% of pencil lost=0.2*100

% of pencil lost=20%

Therefore,

The percentage of pencil lost is 20%

The equation of line J that is perpendicular to line K is: 3. y = 1/2x + 6.

Perpendicular lines have slopes that are negative reciprocals to each other, that is, if the slope of one is 3, the other will be -1/3.

Given that the slope of line K is -2, the slope of line J that is perpendicular to line K would be 1/2.

Substitute m = 1/2 and (x, y) = (6, 9) into y = mx + b to find b:

9 = 1/2(6) + b

9 = 3 + b

9 - 3 = b

6 = b

b = 6

Substitute b = 6 and m = 1/2 into y = mx + b:

y = 1/2x + 6.

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If we change the symbols, the system will have one solution.

x ≥ 2

x ≤ 2

Where the solution is x = 2.

Here we have the system of inequalities:

x > 2

x < 2

So, x can be smaller than 2 or larger than 2. Is easy to see that there are no values of x that are solutions of both inequalities, but if we replace both symbols by ≤ and ≥, then x = 2 will be a solution of both inequalities, and thus, a solution of the system.

x ≥ 2

x ≤ 2

That system has one solution.

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A rashguard costs $25 at full price, which is calculated as 3x - 15 = 60.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given Blue Tide Swim Shop is having its annual summer sale,

rashguards sell for $5 less than the full price,

let the actual price of rashguards be x

price to be payed = x - 5

Miguel purchases 3 rashguards,

at cost  = $60

cost of 3 rashguards is 3(x - 5) = 3x - 15

3x - 15 = $60

3x = 60 + 15

3x = 75

x = 75/3

x = 25

cost of rashguards is $25.

Hence the actual cost is $25, and the equation is 3x - 15 = 60.

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The only correct option from the given graph is Graph X.

A function's derivative can be used to detect whether a function is rising or decreasing on any interval in its domain. If f′(x) > 0 at every point in an interval I, the function is said to increase on I. If f′(x) 0 at every point in an interval I, the function is said to be declining on I.

When we draw tangents to the curve, we can see that if the gradient of the tangent is positive, the function is rising, and if the gradient is negative, the function is dropping.

The given figure  Y is the graphs only increase when x = 0.

Let's look at each graph individually.

When x0, graph W really decreases, therefore it is erroneous.

Because graph X grows when x0 but not when x0, it is a plausible explanation.

Because graph Y drops at x0, it is erroneous.

Graph Z grows when x0, but it also increases when x0, indicating that Graph Z is erroneous.

The only right answer is Graph X.

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The statement which is strictly true for algorithms is :

Option d. Each step of algorithms should be very clear and unambiguous.

Therefore, the option d. each step of algorithms represents steps clearly and unambiguous is the true statement of algorithms.

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Kapitan Tiago borrowed 560,000 × 60 % = 336,000 from the bank.

To find the amount borrowed, we multiply the balance Kapitan Tiago paid in cash by the loan percentage he obtained. The loan percentage is expressed as a decimal, so we multiply 560,000 by 0.6 to get 336,000.

This means Kapitan Tiago borrowed 336,000 from the bank and paid

560,000 - 336,000 = 224,000     in cash.

The total amount he spent on the car is

336,000 + 224,000 = 560,000.

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Alan would have to sell less than 540 boxes to earn less than $2050.

A transaction known as "selling" occurs when a product or service is traded for cash. The act of convincing a person or group to purchase something is sometimes referred to as persuasion. Your selling efforts should be concentrated on explaining the benefits to the customer if you're trying to sell a good or service. Selling's goal is to persuade customers to acquire something so they can use it. The course becomes further in-depth to explain the distinctions between traditional and consultant sales, two major schools in the field of sales. Transactional selling is one of the four forms of selling.

Selling solutions.

selling with consultation.

provocative sales tactics.

So, from the graph given it state that: Alan would have to sell less than 540 boxes to earn less than $2050.

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Answer: there’s no attachment so I’m not sure what you need help with

Step-by-step explanation: