Eating at the all-you-can-eat buffet at your favorite restaurant currently costs $18.50, and increases in cost by 6% each year.
1. Write a function that correctly depicts this scenario.
2. How much will this buffet cost 10 years from now? Round your answer to the nearest cent.
3. How much did this buffet cost 15 years ago? Round your answer to the nearest cent.

The residue from $0 to $82 is 44 ≡ x(mod83)

17−1≡x(mod83)

17∗17−1≡17x(mod83)      

5∗1≡5∗17=85(mod83)

5≡2x(mod83)

42∗5=210≡2∗42x=84x≡x(mod83)

44 ≡ x(mod83).

A mathematical operations that performs a calculation on two numbers is known as an arithmetic provider. They are used in everyday arithmetic, and most computer languages include a set of such operators that can be used within equations to perform a variety of sequential calculations. The following are examples of basic arithmetic operations are:

(+) Addition

Subtraction (-) (-)

() Multiplication            

() division

In programming, computers use different symbols to represent multiplication (*) and division (/). More complex operators, such as

Let's look at an ice cream multiplication example.              

There are two  groups, each has its own ice cream.

The total number of ice creams is 2x3=6    

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Answer:

the answer is

The answer is

The answer is

The answer is 73

Step-by-step explanation:

The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).

For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.

From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.

To satisfy the second condition the points of a should satisfy the equation given

LHS= 2x+3y

RHS=6

A(0,2)

Substituting the values of x and y in 2x+3y,

2(0)+3(2)=6

Therefore LHS=RHS

Hence, at point A(0,2) the graph of the given equation cuts the Y axis.

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The difference in the volumes of the sphere is 410.29 inches³.

A sphere is a three dimensional circle in which each point on the circumference is equidistant from its center. The volume of a three-dimensional object is the amount of space in the object.

The formula for the volume of the sphere = 4/3πr³

Where:

Difference in the volumes = volume of the larger sphere - volume of the smaller sphere

(4/3 x 5³ x 3.14) - (4/3 x 3³ x 3.14)

523.33 - 113.04 = 410.29 inches³

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Answer:

isosceles triangles have two congruent acute angles

Anytime one makes a traffic manoeuvre, such as changing lanes or passing another vehicle, a person put both himself and other drivers on the road in danger.

What are the methods for passing risky situations?

Avoid driving at intersections with railroads, railroad crossings, and entrances to shopping centres.

Only pass to the left if there are two lanes on the road. It is frequently illegal and dangerous to pass on the right. Only when the car in front of you flashes its left turn signal is there an exemption.

When there is a long line of traffic and an oncoming car is right ahead, it is advisable to wait until the incoming vehicle has passed before making a passing motion.

Therefore, it is best to wait until one can see fully ahead because there might be an approaching car right around the bend.

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The linear regression equation that represents the given set of data is y=0.2x+865.

Linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.

The line of best fit is in the form y=bx+a

The slope is b= [tex]\frac{\sum (x-\bar x)\sum (y-\bar y)}{\sum (x-\bar x)^2}[/tex]

Here, [tex]\bar x[/tex] =(0+1+2+3+4)/5

= 1.8

[tex]\bar y[/tex] = (856+871+924+961+961)/5

= 914.6

∑(x-[tex]\bar x[/tex])=(0-2.5)+(1-2.5)+(2-2.5)+(3-2.5)+(4-2.5)

= -2.5-1.5-0.5+0.5+1.5

= -2.5

∑(y- [tex]\bar y[/tex]) =(865-914.6)+(871-914.6)+(924-914.6)+(961-914.6)+(961-914.6)

= -49.6-43.6+9.4+46.4+46.4

= 9

So, slope b= 1.8×9/9²

b=0.2

Substitute b=0.2 and (0, 865) in y=bx+a, we get

865=0.2×0+a

a=865

Substitute b=0.2 and a=865 in y=bx+a, we get

y=0.2x+865

Therefore, the linear regression equation that represents the given set of data is y=0.2x+865.

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"Your question is incomplete, probably the complete question/missing part is:"

The number of newly reported crime cases in a county in New York State is shown in the accompanying table; where X represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected number of new cases for 2003, rounded to the nearest whole number: Years since 1995 (x) New Cases (y) 856 871 924 961 961

Answer:

b

Step-by-step explanation:

i think b because it makes more sense than a or c

Answer:

Eva spends £35 in a month.

Step-by-step explanation:

We know that Eva gets £42 a month for her allowance and for every £5 she spends, she saves £1.

We are looking to find out how much money does she spend in a month.

To calculate this, we can use the following formula:

Spent money = Allowance - (Allowance / (5 + 1))

Plugging in the known values:

Spent money = 42 - (42 / (5 + 1))

Spent money = 42 - (42 / 6)

Spent money = 42 - 7

Spent money = 35

So, Eva spends £35 in a month.

Answer: 3x+4=34

Step-by-step explanation: let the number be x

A.T.Q

the number is 3 times i.e 3x

4 increase=3x+4.

and it says the equation is equal to 34.

3x+4=34

Answer: 26

Step-by-step explanation:

In the picture, we are given a right triangle. Based on that, we can use the Pythagorean Theorem, which helps us find the missing side length with the formula [tex]a^2+b^2=c^2[/tex].

a and b represent the legs, and c is the hypotenuse. The hypotenuse is the longest side of the right triangle. It is also the side that is diagonal from the right angle.

In the picture, we are presented with the legs. So, we can plug in the legs into a and b to solve for c.

[tex]a^2+b^2=c^2[/tex]               [plug in a and b]

[tex]10^2+24^2=c^2[/tex]            [exponent]

[tex]100+576=c^2[/tex]            [add]

[tex]676=c^2[/tex]                      [square root both sides]

[tex]c=26[/tex]

This tells us that the length of the third side is 26.

Answer for the given problem,

a.  Percentage of 160 in number 40 is, 400%

b. The number for which 40 is 160% of that number is,  25

c.  The number which is 40% of 160 is, 64

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

a.   present quantity = 160

     whole quantity  = 40

    Percentage = 400 %

b.  present quantity = 40

    Percentage = 160

    Whole quantity  = 25

c.   whole quantity  = 160

     Percentage = 40%

     Present quantity = 64

Hence, Answers are respectively,  400%,  25,  64

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The solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

What is an equation?

An equation is a statement that two expressions are equal to each other. It is a mathematical sentence that asserts the equality of two expressions. An equation can be written in the form of:

expression_1 = expression_2

The given equation is √2x – 1- x = −8.

[tex]2x=x^2-14x+49[/tex]

[tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex]

Hence, the solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

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The equation that relates x and y for the given data is y = (3/4)x.

The relationship between the number of shutters (x) and the number of hours (y) is an inverse variation because as the number of shutters increases, the number of hours required to paint them decreases and vice versa.

An inverse variation is a relationship between two variables in which their product is always equal to a constant value. Mathematically, it can be represented by the equation: y = k/x where k is a constant and x and y are the variables in question.

Hence, the equation that relates x and y can be found using the information given:

y = (9 hours) / (12 shutters) * x shutters

y = (3/4)x is the required equation.

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The usage of first and third quadrant is explained below.

The term quadrant in math is known as a region defined by the two axes (x-axis and y-axis) of the coordinate system.

Here we need to list down the usage of first and third quadrant is as follows:

As we all know that the Third Angle Projection schema imagines the object in the third quadrant.

And in one can place an object on the bottom of the horizontal plane and behind the vertical planes.

Where as the first angle projection is utilized mostly in the United States and it places the object between the observer and the object.

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Option (D) that is (3.5, 8.75) is the ordered pair of point S.

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions. Two variables are frequently represented by ordered pairs. We mean x = 7 and y = -2 when we write (x, y) = (7, -2). The x-coordinate is the number that corresponds to the value of x, and the y-coordinate is the number that corresponds to the value of y.

Here,

The ordered pair of point S is option (D), which is (3.5, 8.75).

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Complete question: Pentagon OPQRS is shown on the coordinate plane below:

Pentagon OPQRS on a coordinate plane with ordered pairs at O negative 1, 2, at P negative 5, 3, at Q negative 3, negative 2, and R 2, 1, at S 2, 5.

If pentagon OPQRS is dilated by a scale factor of seven over four from the origin, to create O’P’Q’R’S’, what is the ordered pair of point S’?

Answer:

7/12

Step-by-step explanation:

y = 12

x = 7

y = Kx

K = y/x

K = 7/12

A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.

The area occupied within an object's three-dimensional bounds is referred to as its volume. The basic formula for volume is length, width, and height, as opposed to the basic formula for the area of a rectangular shape, which is length, breadth, and height. No matter how you refer to the various dimensions, the calculation remains the same. It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.

given

Calculate the box's volume and provide your answer in units.

Due to the fact that x = 4.28, the remaining sides are 2x + 5 = 2(4.28) + 5 = 13.56

and x - 2 = 4.28 -2 = 2.28.

We are aware that volume is calculated as follows: 13.56 (4.28) ( 2.28 )

=[tex]135.25cm^{3}[/tex]

A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.

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Answer:

The population by 2020 is 191,900

Step-by-step explanation:

Given that;

population 2010 (population in 2010): 191000

the population grew from 2010 to 2015: by 3.9%

so, population by 2015 = [tex]191000(1 + \frac{3.9}{100})[/tex]

                                      = [tex]191000(1 + 0.039)[/tex]

                                      = [tex]191000(1.039)[/tex]

                                      = [tex]198449[/tex]

the population drop from 2015 to 2020: 3.3%

so, population by 2015 = [tex]198449(1 - \frac{3.3}{100})[/tex]

                                      = [tex]198449(1 - 0.033)[/tex]

                                      = [tex]198449(0.967)[/tex]

                                      = [tex]191,900.183[/tex]

Fourteen types of angles are Acute Angles, Obtuse Angles, Right Angles, Straight Angles, Reflex Angles, Positive Angles, Negative Angles, Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles,  Alternate interior angles and Alternate exterior angles.

There are mainly 5 types of angles based on their magnitude. They are Acute Angles, Obtuse Angles, Right Angles, Straight Angles and Reflex Angles.

Positive Angles and Negative Angles are the angles based on the direction of measurement or the direction of rotation.

When two angles are paired, then there exist different angles, such as Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles,  Alternate interior angles and Alternate exterior angles.

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The equation can be solved by adding 3 to both sides of the equation.

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if the y-intercept is (0,5), you have:

y = (3/4)x + 5

To graph a line with a slope of 3/4, you can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Since the slope is 3/4, the equation of the line is y = (3/4)x + b.

To find the y-intercept, you can plug in the coordinates (0,b) into the equation. So if the y-intercept is (0,5), you have:

y = (3/4)x + 5

You can then plot the point (0,5) on the graph, and use the slope of 3/4 to find the next point by going up 3 and right 4.

Another way is to pick two points on the line and plot them, you can use the slope formula (rise over run) to find the next point on the line.

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i thinj the answer is 2-1

The y-intercept represents the loan amount initially. And the rate of change of the function will be negative The equation of Mr. Allen's plan will be y = - 80x + 560 and Mr. Jessup's plan will be y = - 40x + 400.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the y-intercept of the line represents the value of the loan initially.

From the graph, the slope of both lines is negative, then the rate of change of the function will be negative.

Let 'x' be the number of months and 'y' be the amount owed.

The two points are (0, 560) and (1, 480). Then the equation of the line is given as,

(y - 560) = [(560 - 480) / (0 - 1)](x - 0)

y - 560 = - 80x

y = - 80x + 560

And the equation of the line for Mr. Jessup's plan will be given as,

y = - 40x + 400

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Answer:

y= 12

Step-by-step explanation:

3(-12)-24

-36-24

-12

The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:

side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))

The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:

side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))

This formula is derived from the Law of Cosines, which states that the sum of the squares of any two sides of a triangle is equal to the square of the third side, minus twice the product of those two sides multiplied by the cosine of the angle between them.

In other words, the formula states that:

side_3^2 = side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle)

which is then solved for side_3 by taking the square root of both sides. Thus, the formula for the third side can be written as:

side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))

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f(x)=1/2x^2+1/2x-10 in intercept form is (1/2)(x+4)(x-3)

The x-intercepts are x=-5 and x=4.

The vertex of symmetry is (-1/2, -81/8).

The axis of symmetry is:  x = -1/2

A vertical intercept is a point where the graph of a function or relation meets the y-axis of the coordinate system in analytical geometry,

f(x) = 1/2x^2+1/2x-10

=  (1/2)(x² + x - 20)

= (1/2) (x² + 5x - 4x - 20)

= (1/2) { x(x+5) -4(x+5)

= (1/2) (x+5)(x-4)

Hence, Intercept form: f(x) =(1/2) (x+5)(x-4)

The x-intercepts will be where the factors = 0

x + 5 = 0 ⇒x = -5

x - 4 = 0  ⇒ x = 4

Therefore, the x-intercepts are x=-5 and x=4

To find the axis of symmetry, take the average of intercepts (to find the center of parabola)

(-5 + 4)/2 = -1/2

Axis of symmetry ⇒ x = -1/2

To find the vertex, put the axis of symmetry into the equation

f(x) = (1/2)(x + 5)(x - 4) = (1/2)(-1/2 + 5)(-1/2 - 4) = (1/2)(9/2)(-9/2) = -81/8

vertex is  (-1/2, -81/8)

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The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

f(x) = (1/2)x² + (1/2)x - 10

2f(x) = x² + x - 20

2f(x) = x² + x + 1/4 - 1/4 - 20

2f(x) = (x + 1/2)² - 81/4

f(x) = 1/2 (x + 0.50)² - 10.125

The x-intercepts are given as,

f(x) = 0

1/2 (x + 0.50)² - 10.125 = 0

(x + 0.50)² = 20.25

x + 0.50 = ± 4.50

x = - 0.50 ± 4.50

x = - 0.50 - 4.50, - 0.50 + 4.50

x = - 5, 4

The equation of the axis of symmetry is given as,

x + 1/2 = 0

x = - 1/2

The graph is attached below.

The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.

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The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P

Let

F = k/ d²

Where k = constant of proportionality

If F = 0.045 Newtons and d = 2.4 metres

F = k/ d²

0.045 = k / 2.4²

cross product

k = 0.045 × 2.4²

k = 0.2592

Find d when F = 0.7 Newton's

F = k/ d²

0.7 = 0.2592 / d²

cross product

0.7 × d² = 0.2592

0.7d² = 0.2592

divide both sides by 0.7

d² = 0.2592 / 0.7

d² = 0.370285714285714

find the square root of both sides

d = √0.370285714285714

d = 0.6085110634045

d = 0.61 to 2 decimal place.

Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.

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