3 At a restaurant, small tables have a chairs, and large tables have b chairs.
Donna notices that there are 12 small tables and 8 large tables.
How can the expression 12a + 8b help her find the total number of chairs in the dining
room? Explain your reasoning.

The correct answer is B.

N(x) = 40x + 12,500.

This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.

Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.

Based on the given information, the correct answer is B.

N(x) = 40x + 12,500
This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.

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The correct answer is B.N(x) = 40x + 12,500.

This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.

Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.

Based on the given information, the correct answer is B.

N(x) = 40x + 12,500

This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.

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The average rate of change of each function on the interval 2 ≤ x ≤ 6 is given as follows:

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

For the function f(x), we have that:

Hence the rate is given as follows:

r = (2 - 7)/(6 - 2)

r = -5/4

r = -1.25.

For the function g(x), we have that:

Hence the rate is given as follows:

r = (-10.29 - (-7.43))/(6 - 2)

r = -0.715

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From the graph of the parabola, line, and the given values we found out that the parabola will intersect the line at coordinates ([tex]2\sqrt{14}[/tex],7).

As the parabola is originating from the origin and opens at the y-axis, hence:

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Answer:

a = 10

b = 5

Step-by-step explanation:

A 30-60-90 triangle is a right triangle where the interior angles measure 30°, 60° and 90° and the sides are in the ratio 1 : √3 : 2.

The formula for the ratio of the sides is x : x√3 : 2x where:

From inspection of the given triangle, the measure of the side opposite the 30° angle is "b", the side opposite the 60° angle is 5√3, and the hypotenuse is "a". Therefore:

If x√3 = 5√3, then x = 5. Therefore:

An angle formed by a tangent and a chord in a circle is called an "angle between tangent and chord" while an inscribed angle is an angle whose vertex is on the circle and whose sides intersect the circle at two distinct points.

When a tangent line and a chord intersect at a point on the circle, the tangent line is perpendicular to the radius drawn to the point of intersection.

This means that the angle between the tangent and the chord is equal to the angle between the radius and the chord.

Now, consider an inscribed angle that intercepts the same arc as the chord.

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that it intercepts.

Thus, the measure of the inscribed angle is equal to the measure of the arc that the chord intercepts.

Since the angle between the tangent and the chord is equal to the angle between the radius and the chord, and the inscribed angle intercepts the same arc as the chord, it follows that the angle between the tangent and the chord is equal to the inscribed angle that intercepts the same arc.

Therefore, an angle formed by a tangent and a chord has the same measure as an inscribed angle that intercepts the same arc.

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Michelle’s equations that is true for all values of x is 6x + 15 = x + x + x + x + x + x + 15.

Michelle’s equations that is false for all values of x is 6x + 15 = 6(x + 15).

Another equivalent expression for 6x + 15 is 3(2x + 5).

In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).

Michelle’s equations can be written for all values of x as follows;

6x + 15 = x + x + x + x + x + x + 15.

However, Michelle’s equations is false for all values of x when it is written as 6(x + 15).

Another equivalent expression is given by;

6x + 15 = 3(2x + 5).

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Answer:

Part A: The equation 6x + 15 = 6(x + 15) is true for all values of x because it distributes the 6 to both terms inside the parentheses and simplifies to the original expression. However, the equation 6x + 15 = x + x + x + x + x + x + 15 is false for all values of x. While it may be true for specific values of x, such as x = 1 or x = 2, it is not true for all values of x because the number of x terms changes depending on the value of x.

Part B: Another equivalent expression for 6x + 15 could be 3(2x + 5), which also simplifies to the original expression. This is because we can factor out a common factor of 3 from both terms and simplify to 3(2x + 5) = 6x + 15.

Step-by-step explanation:

Answer:

life insurance is the most common type of employee benefit

Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

a.

1. LCM of 2 & 5 is 10

2. [tex]\frac{15x}{10} =\frac{12}{10}[/tex]  -> 15x = 12

3. x = [tex]\frac{12}{15}[/tex] or [tex]\frac{4}{5}[/tex]

b.

1. LCM of 3 & 9 is 9

2. 2x - [tex]\frac{6}{9}[/tex] = [tex]\frac{4}{9}[/tex]  ->  2x = [tex]\frac{10}{9}[/tex]  ->  [tex]\frac{18}{9} x[/tex] = [tex]\frac{10}{9}[/tex]  ->  x = [tex]\frac{10}{9}[/tex] × [tex]\frac{9}{18}[/tex]  ->  x = [tex]\frac{10}{18}[/tex]  ->  x = [tex]\frac{5}{9}[/tex]

3. x = [tex]\frac{5}{9}[/tex]

The sum of the given polynomial  [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]is [tex]9x^{3} - 8x^{2}[/tex].

Polynomials can be added or subtracted when they contain like terms, which are the same alphabets with the same powers.

Whereas there are no such rules for multiplication, any phrase with any power can be multiplied. The powers of the terms are then modified in accordance with exponentiation principles.

The following polynomial equation is [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]

Polynomial addition is accomplished by combining 'like terms'.

As a result, sorting and adding

= [tex](7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).[/tex]

= [tex]7x^{3} + 2x^{3} - 4x^{2} - 4x^{2}[/tex]

= [tex]9x^{3} - 8x^{2}[/tex]

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Complete question:

What is the sum of the polynomials? (7x3 - 4x2) + (2x3 - 4x2)

The equivalent expression for 6r in terms of s is 20s, which we obtain by substituting the value of r from the given equation and simplifying.

The given equation, r = (10/3)s, shows that there is a proportional relationship between the variables r and s. This means that when one variable changes, the other variable changes in direct proportion to it. In other words, if we increase r by a certain factor, s will increase by the same factor, and vice versa.

To find an expression that is equivalent to 6r, we can substitute the value of r from the given equation and simplify.

r = (10/3)s (given equation)

6r = 6(10/3)s (substitute 6r for r in the equation)

6r = 20s (simplify by multiplying 6 and 10/3)

Therefore, the expression that is equivalent to 6r in terms of s is 20s. This means that if we know the value of s, we can use this expression to find the value of 6r in a proportional relationship. For example, if s = 2, then 6r = 20s = 20(2) = 40.

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The a. Perimeter = 22√7 - 2√3 meters. The Area = 4√12 - 3√7 square meters

Area = length * width

Perimeter = 2(length + width)

Given the following:

Length of the rectangle = 5√7 + 2√3 meters

Width of the rectangle = 6√7 - 3√3 meters

a. Perimeter = 2(5√7 + 2√3) + 2(6√7 - 3√3)

10√7 + 4√3 + 12√7 - 6√3

22√7 - 2√3 meters

b. Area = (5√7 + 2√3)(6√7 - 3√3)

= 5√7(6√7 - 3√3) + 2√3(6√7 - 3√3)

= 210 - 15√21 + 12√21 - 18

= 192 - 3√7

= 4√12 - 3√7 square meters

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This sample is likely to be biased because it only includes individuals who use the city's parks, which means it may not represent the entire population of voters who would be affected by a tax increase to improve the parks.

A sample is a subset or a smaller group of individuals or 17 that are selected from a larger population to represent the population.

The park commission's study of 500 park users is likely biassed because it only covers people who use the city's parks. This indicates that the sample does not accurately reflect the full electorate who would be impacted by a tax hike to fund park improvements.

Various people may hold various views regarding whether or not a tax increase is required to develop the parks. For instance, if they don't frequent the parks or have other priorities for their tax money, they might be less likely to approve a tax hike.

If the park commission only conducted surveys of people at specific times of day or in specific locations of the city, the sample may also be skewed. This could omit those who visit the parks at various hours or in various locations around the city.

In order to get accurate and valid results, it's crucial to utilise a representative sample that includes people from different demographic groups. A biased sample can produce results that are erroneous or misleading.

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After answering the presented question, we may conclude that  expressions As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

We need to do the following to figure out how much money Ms. Jimenez puts into her retirement fund each week:

Ms. Jimenez's yearly retirement fund contribution is calculated as follows:

8% of $27,000 = annual retirement fund contribution

= 0.08 x $27,000

= $2,160

To calculate the weekly retirement fund contribution, divide the yearly payment by the number of weeks in the year:

Contribution to a retirement fund on a weekly basis = Annual contribution to a retirement fund divided by the number of weeks in a year

= $2,160 / 52

≈ $41.54

As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.

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The equation of the function is f(x) = x² + 3, where x represents the input value and f(x) represents the output value. Graph is in below figure.

The domain of a function is the set of all possible input values (also called the independent variable) for which the function is defined. In other words, it is the set of values that can be plugged into the function to produce a valid output value (also called the dependent variable).

The equation of the function is f(x) = x² + 3, where x represents the input value and f(x) represents the output value.

To graph this function, we can plot points by choosing values of x and computing the corresponding values of f(x). Since the domain of the function is [0, ∞), we will only consider non-negative values of x.

x f(x)

0 3

1 4

2 7

3 12

4 19

We can plot these points on a coordinate plane and connect them with a smooth curve to obtain the graph of the function:

Note that the graph is a parabola that opens upwards and passes through the point (0, 3).

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The experimental probability of drawing a spade is 0.2

When we perform an experiment N times, and we got a given outcome K times, the experimental probability of said outcome is given by the quotient:

P = K/N

Here the experiment is performed:

N = 6 + 4 + 7 + 3 = 20 times

And a spade is drawn 4 times, then the experimental probability is:

P = 4/20 = 1/5 = 0.20

The correct option is the second one.

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If he uses the beach as one side. the minimum length, to 2 decimal places, of rope needed is: 70 meters of rope.

Let's assume that the length of the swimming area is L and the width is W. The perimeter of the swimming area will be the length of the rope that Kyle needs to rope off the area.

From the problem, we know that one side of the swimming area is the beach, so we have:

L + W + L = 70

Simplifying this equation, we get:

2L + W = 70

To find the minimum length of rope needed, we need to minimize the perimeter of the swimming area. We can use the above equation to express W in terms of L:

W = 70 - 2L

Substituting this expression for W into the formula for the perimeter, we get:

P = L + W + L

= 2L + (70 - 2L)

= 70

So the perimeter of the swimming area is fixed at 70 m, regardless of the values of L and W. Therefore, the minimum length of rope needed to rope off the area is simply the perimeter of the swimming area, which is 70 meters.

Therefore, Kyle needs a minimum of 70 meters of rope.

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The surface area of the figure is derived to be equal to 656.4 square meters.

The top of the figure is a triangular prism, the bottom is a triangle, and the sides are 3 same size rectangles, so the surface area is calculated as follows:

area of one top triangle face = 1/2 × 12 m × 5 m = 30 m²

area of top triangular prism = 3 × 30 m² = 90 m².

area of bottom triangle = 1/2 × 12 m × 10.4 m = 62.4 m²

area of one rectangle side = 14 m × 12 m = 168 m²

area of the three rectangle sides = 3 × 168 m² = 504 m²

surface area of the figure = 90 m² + 62.4 m² + 504 m²

surface area of the figure = 656.4 m².

Therefore, the surface area of the figure is derived to be equal to 656.4 square meters.

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Answer:5

Step-by-step explanation:

it would be 5 because

On solving the provided question we can say that As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle.

The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.

The supplied figures reflect the lengths of the three sides of a right triangle, with the hypotenuse (the side opposite the right angle) being 5.47722557505, and the other two sides being 2.2360679775 and 5.

The sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, according to the Pythagorean theorem. In this situation, we can write:

2.2360679775² + 5² = 5.47722557505²

When we simplify and solve for one of the variables, we get:

5² = 5.47722557505² - 2.2360679775²

25 = 24.9999999999971

As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle. We could round the data to approach the sides of a right triangle, but it would not get accurate solutions.

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Answer:

C. 39 ft²

Step-by-step explanation:

Area of the outer rectangle which includes the white triangle

= length x width

= 5 x 9

= 45  ft²

Area of the white triangle

= 1/2 x base x height

= 1/2 x 4 x 3

= 6 ft²

Area of shaded region
= Area of rectangle - Area of triangle

= 45 - 6

= 39 ft²

Answer:

Below

Step-by-step explanation:

To find the break-even point, we need to determine the point at which the total revenue equals the total cost. Let's call the number of shirts sold "x".

The total cost includes the initial costs of $1,500 and the cost per shirt of $3x, so the total cost is:

y = 1500 + 3x

The total revenue is the price per shirt of $10 multiplied by the number of shirts sold, so the total revenue is:

y = 10x

To find the break-even point, we need to set the total cost equal to the total revenue and solve for x:

1500 + 3x = 10x

Simplifying this equation, we get:

1500 = 7x

Dividing both sides by 7, we get:

x = 214.29

Therefore, Steve needs to sell 215 shirts to break even.So the correct system to find the break-even point is:

y = 1500 + 3x (total cost)

y = 10x (total revenue)

On solving the provided question we can say that - 12.99(y - 9) + 2.75y = 100 , by solving, the expression  x = 11.2, y = 19

What is  linear equation?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

let x be the base ball cards.

and y be page card.

x + y = 9 -------------------1

12.99x + 2.75y = 100-------------------2

12.99(y - 9) + 2.75y = 100

by solving

x = 11.2

y = 19

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A possible solution to the equation cos(x+2)=sin(3x) is x = 22 degrees

The correct answer is an option (C)

Consider a trigonometric equation,

cos(x+2) = sin(3x)

For value x = 0.5 degrees,

cos(x + 2) = cos(2.5)

                = 0.999

and sin(3x) = sin(1.5)

                 = 0.026

For x = 1 degree,

cos(x + 2) = cos(3)

                =0.9986

sin(3x) = sin(3)

           = 0.052

For x = 22 degrees

cos(x + 2) = cos(24)

                = 0.913

sin(3x) = sin(66)

           = 0.913

for x = 44 degrees,

cos(x + 2) = cos(46)

                = 0.69

sin(3x) = sin(132)

           = 0.743

Therefore, the solution to an equation cos(x+2) = sin(3x) is x = 22 degrees

The correct answer is an option (C)

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The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

The value of x in the right triangle below by using Pythagorean Theorem (H² = P² + B²) is 19.53

According to question; Perpendicular (P) = 16, Base (B) = 11.2 and Hypoteneus (H) = X

According to Pythagorean Theorem

H² = P² + B²

X² = 16² + 11.2²

X² = 256 + 125.44

X² = 381.44

X = 19.53

The Pythagorean Theorem, or, in standard algebraic notation, a² + b² = c², states that the total of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).

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Answer:

Step-by-step explanation:

Recall that the formula for the circumference of a circle is:

[tex]2\pi r[/tex]

Also recall that the formula for the area of a circle is:

[tex]\pi r^2[/tex]

Both formulas use the radius; one squares it, while the other doubles it.

Let's start by turning the formula for the circumference of a circle into the formula for the area of a circle. We start off with:

[tex]2\pi r[/tex]

We want to square the radius, but we can't do that without squaring everything else, too, so let's get rid of the other terms.

Divide the circumference by [tex]2\pi[/tex]:

[tex]2\pi r\\\frac{2\pi r}{2\pi } =\\r[/tex]

Now, we can square r:

[tex]r\\r^2[/tex]

Now, all we have to do is multiply by pi:

[tex]r^2\\\pi r^2[/tex]

We now have the area.

Let's look back at out steps.

First, we divided the circumference by [tex]2\pi[/tex].

Next, we squared the number we had left (the radius).

Finally, we multiplied by [tex]\pi[/tex].

answer

as we all know volume is equal to length times width times height therefore to get you answer you have to multiply all the three giving measurements the answer that you get you are supposed to round it to the nearest to decimal places when you say around it off to the nearest two decimal places it means that they need to be too this two numbers after the coma

The proportion of scores in a standard Normal Distribution that are greater than 1.25 is closest to a. a is 0.1056.

The proportion of scores in a standard Normal Distribution that are greater than 1.25 is:

[tex]P(Z > 1.25) = 1 - P(Z < 1.25)[/tex]

Using a standard normal distribution table or a calculator.

The area to the left of 1.25 is 0.8944, so:

[tex]P(Z > 1.25) = 1 - P(Z < 1.25) = 1 - 0.8944 = 0.1056[/tex]

The closest answer choice is (a) 0.1056.

The percentage of scores in a normal distribution with a standard deviation larger than 1.25 is:

either a calculator or a normal distribution standard table.

0.8944 is the region to the left of 1.25, so:

The nearest possible response is (a) 0.1056.

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