Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n

If at 2007 math Olympics, team Canada won 17 out of a possible 100 medals , then the closest fraction for the medals they won is (c) 1/6  .

To find the closest fraction to the number of medals that Canada won, we need to convert 17/100 to a simplified fraction by dividing by 17 .

So , On dividing both the numerator and denominator by 17.

we get , the closest fraction to 17/100 is 1/6 ,

Therefore, the closest fraction to the number of medals won by Canada is 1/6. Option (c) is the closest answer to the question.

The given question is incomplete , the complete question is

At the 2007 math Olympics, team Canada won 17 out of a possible 100 medals. which one of the following is closest to the fraction of medals that they won ?

(a) 1/4

(b) 1/5

(c) 1/6

(d) 1/7

(e) 1/8

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An equation to model the relationship between the number of weeks, x, and the number of site visits, f(x) is 4800 = a(1.5)^x.

He found that before launching the new marketing plan, there were 4,800 visits.

Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.

Over the course of the next 5 weeks, initial visitor at x = 0, 4800

Increasing factor = 1.5

Equation of the model is given as:

f(x) = a(b)^x

From the question b = 1.5

Now the equation of model is:

f(x) = a(1.5)^x

At x = 0, f(x) = 4800

Now the equation of the model is:

4800 = a(1.5)^x

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How you actually measure the variable is called the Operational definition of the variable .

The Operational Definition of a variable is how you actually measure it.

It specifies the methods, techniques, and procedures used to measure a particular variable. It is the concrete, specific, and practical definition of the variable in a way that makes it possible to be observed, measured, and recorded.

The operational definition is also used to ensure that all researchers are measuring the variable in the same way and to reduce the potential for measurement error. It is an important step in the scientific process as it allows for replication of results and makes the variable more concrete and tangible.

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Using Mathematical Expressions, Let's call the number of cherries in the cup "x".  There are 11 cherries in the cup.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

We know that:

Total number of cherries = 780

Number of cherries on the plate = 145

Number of cherries in the bowl = 4 * (Number of cherries in the cup + Number of cherries on the plate)

So we can set up the equation:

x + 145 + 4(x + 145) = 780

Simplifying, we can combine like terms:

x + 145 + 4x + 580 = 780

5x + 725 = 780

Subtracting 725 from both sides:

5x = 55

Finally, we can divide both sides by 5:

x = 11

So there are 11 cherries in the cup.

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The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )

The basic arctan formula can be given by θ = tan-1(Perpendicular / Base). Here, θ is the angle between the hypotenuse and the base of a right-angled triangle.

The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.

= [tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx ; where ([tex]\sqrt{3}[/tex] to 1 )

[tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx = [tex]5\frac{(2\sqrt{3} )ln(2)+2\pi -\sqrt{3} \pi }{4\sqrt{3} }[/tex]

= 5  [tex]\int\limits[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx

= 5 [ x arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )[tex]x_{123}[/tex]

Therefore,

The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )

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If the contractor's truck can haul 17 cubic yards per load, then 21 truckloads are needed.

Earth removed from a building site is 357 cubic yards.

A contractor's truck can haul 17 cubic yards per load.

To find how many truckloads were needed, we needed to divide the earth removed from the building site by the contractor's truck capable of hauling.

That is,  

The number of truckloads = earth removed from the building site/contractors' truck capable of hauling.

The number of truckloads = 357 cubic yards/17 cubic yards per load

The number of truckloads = 21 truckloads.

Therefore, the required truckloads are 21.

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The compound interest on Rs. 24000 compounded semi annually is  

Rs 3783 .

Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit.

Given:

p=24000

r=5%

n=3

As we know,

[tex]A=P (1+\frac{r}{100})^{n}[/tex]

A = 24000 [tex]\\\\(1+\frac{5}{100})^{3}[/tex]

A = 24000 ( 1+ 0.05)³

A = 24000 (1.05)³

A = Rs 27783.

and, we know A = P + I

I=A-P

I=27783-24000

I = Rs 3783

Hence, the interest is Rs 2783.

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using inverse relation, If p= 60, then q= 3x because i find the constant value is 180.

P is approximately equal to 1/Q since P has an inverse relationship to Q. x=k/3 for P=x and Q=3. P = k/x when Q = x.

The correlation between bond prices and interest rates is a prime illustration of an inverse connection. Bond prices normally fall with an increase in interest rates, whereas bond prices often rise with a decrease in interest rates.

P×1/q

( formula now)  P= K/Q here K is a constant

                                 30= k/6

                                 k=30×6

                                 k= 180

when P is equal to 60 then q=

because constant k=60

60= 180/q

q=180/60

q=3 unit .

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The term "domain" refers to a group of potential input values, and the domain of a graph is made up of all the input values visible on the x-axis.

All the y values from the ordered pairings are listed to determine the range. Values that are repeated inside the domain or range don't need to be listed more than once. Each x must have a unique y value in order for a relation to be a function.

Simply solving for y = f(x) yields the values of the independent variable x and the domain, which we can use to determine the domain and range. Simply write x as x=g(y) to determine the function's range, and then identify g's domain.

Utilizing graphs is another method for determining the domain and range of functions. The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.

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Salut/Hello!

Answer: 20 ft

Step-by-step explanation:
We can imagine the ladder, wall and ground as a triangle.
(And because we don't know if our triangle has a 90 degrees angle it means it's an ordinary triangle.)

We know that a triangle that has an angle with 60 degrees means all of its angles have 60 degrees because 180 : 3 angles = 60 degrees which means the triangle is equilateral.

Definition of the equilateral triangle: The triangle that has the 3 side with the exact same length.


From the equilateral triangle we know all sides are equal. If the ladder is 20 ft that means the distance between the building and the base of the ladder (which is actually the base of our triangle) is 20 ft.

I hope it was useful! :]

A quantum computer is a type of computer that uses quantum mechanics.

Quantum computers use quantum mechanics, a branch of physics that deals with the behavior of matter and energy at the subatomic and quantum scale, to perform operations and solve problems.

Unlike classical computers, which use binary digits (bits) to represent and process information, quantum computers use quantum bits, or qubits, which can exist in multiple states at the same time, allowing for exponentially faster processing of complex computations and simulations. Quantum computers have the potential to revolutionize fields such as cryptography, drug discovery, and artificial intelligence.

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The graph of the inequality is added as an attachment

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

x≤ 8

The above expression is an inequality that implies that

The value of x does not exceed 8

Next, we plot the graph

See attachment for the graph of the inequality

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The length of the crust around the larger pizza is equal to: B. 51.81 inches.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

For Restaurant 1: One large 16-inch pizza is sold for $14.99.

1 inch = 2.54 centimeters

16 inches = 16 × 2.54 = 40.64 centimeters

Therefore, restaurant 1 sells one large 40.64 cm pizza for $14.99.

For Restaurant 2: One large 41.91-centimeter pizza is sold for $14.99

Since we know that 41.91 centimeters is greater than 40.64 centimeters, restaurant 2 offers the larger pizza.

Now, we can calculate the length of the crust around the pizza, which is the same as the circumference of the pizza (circle)

C = π × d

C = 3.14 × 41.91

C= 131.5974 centimeters

In inches, we have:

C = 131.5974/2.54 = 51.81 inches.

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We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x

A new function called the reciprocal function is produced when the reciprocal function is found. These functions have intriguing characteristics and distinctive graphs. We also represent these patterns using reciprocal functions when two expressions are inversely proportional. A constant on the numerator and an algebraic expression in the denominator makes up reciprocal functions.

How to find the reciprocal of a function?

By dividing 1 by the provided number, we can find the reciprocal of a given number. Similar reasoning is used to get a function's reciprocal: we divide 1 by the function's expression.

We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x

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Answer:

29%

Step-by-step explanation:

23 + 11 + 23 + 8 = 65 people

So, 65 people are taking the survey.

11 + 8 = 19 people shopping online

19 divided by 65, times 100 = 29%

So, there are 29% of the people surveyed shop online.

After solving the equation the triangle given in question the 63.8°.

A triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry and is very versatile as it can be used to create many other shapes and structures. Triangles are generally classified by the length of their sides, which can be equal (an equilateral triangle), longer in one side than the other two sides (an isosceles triangle) or different in length on all three sides (a scalene triangle). They can also be classified by their angles, which can be acute (the angles are all less than 90 degrees), right (one angle is exactly 90 degrees) or obtuse (one angle is greater than 90 degrees).

x = 63.8°
Using the Law of Cosines, we can calculate the value of x:
x² = 17² + 9² - 2(17)(9)cos(90°)
x² = 289 + 81 - 306
x² = 64
x = √64
x = 8
Therefore, x = 63.8° (rounded to the nearest tenth).

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Answer:

see below

Step-by-step explanation:

z+66+z+69+43z=180

so 45z=180-66-69 = 45

so z=1

so angle U= 43 its opposite side length ST is the smallest

same logic for the other 2.

66+1=67

69+1=70

so ST<US <TU

The values of t and s that satisfy the equality are t = sqrt(3 * 74.67 / 49) and s = sqrt(3 * 74.67 / 49).

The equality ⟨−(7t^2), 3s-2t⟩ = ⟨3s-t,24t⟩ means that the two vectors are equal, so the components must be equal:

-7t^2 = 3s-t

3s-2t = 24t

Solving for t, we can subtract 24t from both sides:

3s-26t = 0

Dividing both sides by 3, we get:

s - 8.67t = 0

So, t = s / 8.67.

Substituting t = s / 8.67 back into the first equation, we get:

-7(s / 8.67)^2 = 3s - s / 8.67

Expanding and simplifying, we get:

-49s^2 / 74.67 + 3s = s^2 / 74.67

Dividing both sides by s^2 / 74.67, we get:

-49 + 3 * 74.67 / s = 1

Multiplying both sides by s^2 / 74.67, we get:

-49s^2 + 3 * 74.67 = s^2

Expanding and rearranging, we get:

s^2 - 49s^2 + 3 * 74.67 = 0

Combining like terms, we get: -49s^2 + 3 * 74.67 = 0

Dividing both sides by -49, we get: s^2 = 3 * 74.67 / 49

Taking the square root of both sides, we get: s = sqrt(3 * 74.67 / 49)

Thus, the values of t and s that satisfy the equality are t = sqrt(3 * 74.67 / 49) and s = sqrt(3 * 74.67 / 49).

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The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1 is No as well as x and y are not independent

What is variables?

Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.

The joint p.d.f of X and Y is f(x, y)

f(x,y) = cxy/ 1+[tex]x^{2}[/tex]+[tex]y^{2}[/tex] for 0 < x < 1 and 0 < y < 1

marginal p.d.f of x = f(x):

f(x) = {1y_of(x,y)dy

= {1y=0 /cxy/ 1+x+[tex]y^{2}[/tex] dy

Cx/2 ( {1y=0 /2y/1+ [tex]x^{2}[/tex] + [tex]y^{2}[/tex] dy)

Take substitute 1+[tex]x^{2}[/tex]+ [tex]y^{2}[/tex] = t⇒2y dy=dt

Lower limit: y = 0⇒t=1+[tex]x^{2}[/tex]

Upper limit: y=1➡t=1+[tex]x^{2}[/tex]+1

F(x) =  cx/2

f 1y= 0 2y

=0 1+2+[tex]y^{2}[/tex]dy)

=Cx/2({1+[tex]x^{2}[/tex]+1dt/t

=1+[tex]x^{2}[/tex]t)

=cx/2(In(t) - ln(1+[tex]x^{2}[/tex])/1[tex]x^{2}[/tex])

=cx/2 (In (1+[tex]x^{2}[/tex]+1))-In(1+[tex]x^{2}[/tex]))

=cx/2 (In (1+[tex]x^{2}[/tex]+1/1+[tex]x^{2}[/tex]))

=Cx (In(1+1/1+[tex]x^{2}[/tex]))

marginal p.d.f of y = f(y):

f(y) = {1x

=0(x,y)dx

= F1x

=0/cxy/ 1+[tex]x^{1}[/tex][tex]y^{2}[/tex]=dx

= cy/2({1x)

=0/2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]dx}

Take substitute 1 + [tex]y^{2}[/tex] + [tex]x^{2}[/tex] = t 2x dx = dt

Lower limit: x = 0

t = 1 + [tex]y^{2}[/tex]

Upper limit: x =1

=t + [tex]y^{2}[/tex] + 1

F(y)=cy/2({1x=0 2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]/dx)

=cy({1+[tex]y^{2}[/tex]+1dt/t

=1[tex]y^{2}[/tex]t/)

=Cy/2((In(t))1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex])

=cy(In(1+[tex]y^{2}[/tex]+1) – In( 1+[tex]y^{2}[/tex]))

=cy(In(1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex]))

=cy/2(In(1+1/1+y2))

Now we have to check for independence.

F(x,y)= cxy/1+[tex]x^{2}[/tex]+[tex]x^{2}[/tex] for0<x<1 and 0<y<1

F(x) = cx/2( In(1+1/1+[tex]x^{2}[/tex])) for 0<x<1

F(y)=cy/2(In(1+1/1+[tex]y^{2}[/tex])) for < y <1

=f(x)*f(y)

=c2xy/4 ( In ( 1+1/1+[tex]x^{2}[/tex] ) *In( 1+1/1+[tex]y^{2}[/tex])) #f(x,y)

F(x,y) #f(x)* f(y) for all x and y

=x and y are not independent.

no is correct answer.

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Answer:

the value of x that makes ACDE~AFGH is 27

The equation to show the number of hours that Steven worked will be S = O - G - 15

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, Dr Steve has worked more night shift than Dr. Greg who has worked five night shifts. Dr. Okon has worked fifteen night shifts more than Dr Steve an Dr Greg combined. Dr Uche has worked eight night shifts less than Dr Steve.

The expression can be illustrated as:

G = 5

O = G + S + 15

The equation for Steven will be:

S = O - G - 15

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The length of the other diagonal is 22.36 cm.

Diagonal is defined as a sloping line or the slant line, that connects to the vertices of a shape.

Let's call the length of the other diagonal "d".

Since a rhombus has perpendicular diagonals that bisect each other

we can use the Pythagorean theorem to find the length of the other diagonal:

d^2 = 10^2 + 10^2 = 100

d = sqrt(100) = 10 * sqrt(10) = 10 * 2.236 = 22.36 cm

Therefore, the length of the other diagonal is 22.36 cm.

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The fountain should be located at the coordinates (4,2). This is the midpoint of the line segment that connects the vertices a(-1,-1) and c(7,-1). It is also the same distance from b(4,4).

To find the location of the fountain, we first need to find the midpoint of the line segment connecting the vertices a(-1,-1) and c(7,-1). This midpoint is located at the coordinates (4,2). To verify that this is the correct location, we can calculate the distance between the midpoint and each vertex. To do this, we use the distance formula, which is d=√((x2-x1)2+(y2-y1)2). Using the coordinates for the midpoint (4,2) and the coordinates for vertex a(-1,-1), we get d=√((42-(-12))2+((22-(-12))2). This simplifies to d=√((52+52))=√(50)=7.07. We can repeat the same process for the midpoint and vertex b(4,4) and for the midpoint and vertex c(7,-1). In both cases, we find that the distance is 7.07, so the fountain should be built at the coordinates (4,2).

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1.05 quarts of blue colors paint they mixed to make seafoam green paint.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

From the given figure, total quantity of paint is 1.5 quarts.

70% of blue paint and 30% of yellow paint.

Let the quantity of blue paint be x.

Now, x =70% of 1.5

x =70/100 ×1.5

x =0.7×1.5

x =1.05 quarts

Therefore, 1.05 quarts of blue colors paint they mixed to make seafoam green paint.

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The student's lifetime value for a four-year degree at this college is $80,000.

The student's lifetime value for a four-year degree can be calculated as follows:

Determine the cost per semester: $10,000 per semester

Determine the number of semesters for a four-year degree: 4 years * 2 semesters/year = 8 semesters

Multiply the cost per semester by the number of semesters to get the total cost of tuition: $10,000 * 8 = $80,000

Therefore, the student's lifetime value for a four-year degree at this college is $80,000.

It is important to note that this calculation only considers the cost of tuition and does not take into account other costs such as room, board, books, and supplies, which can add significantly to the total cost of obtaining a degree.

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Answer:

8 bags of chips.

Step-by-step explanation:

First, find the cost per individual unit. It is given that 2 bags of chips cost $6. Find the cost of one bag by dividing 6 with 2:

$6/2 bags = $3/bag

Next, you are solving for the amount of chips you can buy with $24. Divide 24 with the individual cost of $3:

$24/$3 per bag = 8

You can buy 8 bags of chips assuming all things are the same.

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Answer:

C' (-2, -2)

D' (-2, 2)

E' (2, 0)

F' (0, -2)

Step-by-step explanation:

A dilation of factor k about the origin is a transformation that enlarges a figure by a factor of k, while keeping the origin fixed.

It means that each point (x, y) on the pre-image is transformed to a new point (kx, ky) in the dilated figure.

Therefore, the rule for a dilation of 2 about the origin is:

From inspection of the given diagram, the vertices of the pre-image are:

Applying the dilation rule (x, y) → (2x, 2y):