Test Prep While working at the school store, John sold a jacket for $40.00 and notebooks for $1.50 each. If he collected $92.50, how many notebooks did he sell?

As a result, 198 small bags and 92 big bags of popcorn were sold at the movie theatre.

An equation in mathematics is a claim that two statements are equivalent. It usually has two sections: a left and a right, separated by an equals sign in the middle. For instance, the statement that the expression 2x Plus 3 equals the expression 7 is represented by the equation 2x + 3 = 7. The equation can be used to determine the number of x that causes the equation to hold true when the variable x is unknown. Equations, such as linear equations, quadratic equations, trigonometric equations, and many others, can be used to explain a broad range of mathematical relationships.

given

Let x represent the quantity of big popcorn bags sold and y represent the quantity of small popcorn bags sold.

Based on the knowledge provided, we can create the following system of two equations:

x + y = 290 (the total amount of bags distributed) (the total number of bags sold)

4x + y = 566 (the entire revenue from popcorn sales) (the total revenue from popcorn sales)

We have two options for resolving the equation for x and y: substitution or removal. Here, we'll apply the replacement technique:

Y = 290 - x is the result of solving equation 1. We can enter the following formula in place of y in equation 2:

4x + (290 - x) = 566

If we simplify, we get:

3x + 290 = 566

290 from both parts are subtracted, giving us:

3x = 276

3 divided gives us:

x = 92

Thus, 92 big bags of popcorn were sold. We can change x = 92 into equation 1 to determine how many small packages were sold:

92 + y = 290

92 is subtracted from both parts to arrive at:

y = 198

Thus, 198 small packages of popcorn were sold.

As a result, 198 small bags and 92 big bags of popcorn were sold at the movie theatre.

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Answer:

Step-by-step explanation:

SEE THE ATTACHMENT

To cover one suitcase, we need to find the surface area of the suitcase that needs to be covered. The surface area of the suitcase can be calculated by finding the sum of the areas of its six sides.

Area of one side of the suitcase = length x height = 80cm x 48cm = 3840 sq.cm

Area of the opposite side of the suitcase = length x height = 80cm x 48cm = 3840 sq.cm

Area of the other four sides of the suitcase = width x height = 24cm x 80cm + 24cm x 80cm + 24cm x 48cm + 24cm x 48cm = 7296 sq.cm

Total surface area of one suitcase = 3840 sq.cm + 3840 sq.cm + 7296 sq.cm = 14976 sq.cm

To cover 100 such suitcases, we need to multiply the surface area of one suitcase by 100.

Total surface area of 100 suitcases = 14976 sq.cm x 100 = 1497600 sq.cm

To find the amount of tarapaulin required, we need to divide the total surface area of 100 suitcases by the width of the tarapaulin.

Amount of tarapaulin required = (1497600 sq.cm) / (96 cm) = 15600 sq.cm

We now need to convert the required area into meters.

1 sq.cm = 0.0001 sq.m

15600 sq.cm = 15600 x 0.0001 sq.m = 1.56 sq.m

Therefore, we need 1.56 sq.m of tarapaulin to cover 100 such suitcases, assuming that there is no overlap of the tarapaulin.

Answer:

The equation that can be used to determine the average number of miles Keilantra would have to ride each day to meet her goal is:

(28.8 - 4) / 4 = m

This equation subtracts the 4 miles Keilantra has already ridden from her goal of 28.8 miles, and then divides the result by the number of days she still needs to ride (4) to find the average number of miles she would have to ride each day to meet her goal.

Solving this equation gives: (28.8 - 4) / 4 = m

24.8 / 4 = m

6.2 = m

Therefore, the average number of miles Keilantra would have to ride each day to meet her goal is 6.2 miles.

Step-by-step explanation:

The classroom would hold about 34,767 basketballs.

What is the volume of the rectangular prism?

To find the volume of a rectangular prism, you need to know its length, width, and height. Let's assume you have those measurements.

The formula for the volume of a rectangular prism is:

volume = length x width x height

We need to know the volume of the classroom in order to determine how many of a certain object it would hold.

The volume of a rectangular prism (like the classroom) is given by the formula:

volume = length x width x height

Plugging in the values we know:

volume = 24 feet x 28 feet x 10 feet

volume = 6720 cubic feet

Now we can divide the volume of the classroom by the volume of the object we want to find out how many will fit.

For example, if we want to know how many basketballs would fit in the classroom, we would need to know the volume of a basketball. According to the NBA, the standard size for a basketball is about 9.43 inches (0.7867 feet) in diameter. The volume of a sphere is given by the formula:

volume = (4/3) x π x radius^3

Plugging in the radius of the basketball:

volume = (4/3) x π x (0.7867/2)^3

volume ≈ 0.193 cubic feet

Dividing the volume of the classroom by the volume of a basketball:

6720 cubic feet / 0.193 cubic feet per basketball ≈ 34,767 basketballs

Hence, the classroom would hold about 34,767 basketballs.

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The equation for the least squares regression line is y = 0.488x + 8.543.

Least squares regression line is the line of best fit formed when the relationship is linear for the given data points.

Number of data points, N = 5

x : 35         39         63         86         93        Σx = 316

y : 38         20         28         55         56        Σy = 197

x² : 1225   1521    3969    7396     8649       Σ(x²) = 22,760

xy : 1330   780     1764     4730     5208       Σ(xy) = 13,812

Slope of the line, m = [N Σ(xy) - Σx Σy] / [N Σ(x²) - (Σx)²]

                                 = [ (5 × 13812) - (316 × 197) ] / [(5 × 22760) - (316)²]

                                 = 6808/13944

                                 = 0.488

Intercept, b = [Σy - (m Σx)] / N

                   = [197 - (0.488 × 316)] / 5

                   = 8.543

Equation of the line is y = mx + b

y = 0.488x + 8.543

Hence the equation of the line is y = 0.488x + 8.543.

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The graph of the piecewise function is added as an attachment

Let c(x) be the cost of an automotive ad with x lines.

For the first 4 lines, the cost is $34, so:

c(x) = 34, for 1 ≤ x ≤ 4

For each additional line beyond the first 4, the cost is $3.50, so:

c(x) = 34 + 3.50(x - 4), for x > 4

When these two cases are put together, we get the piecewise function:

c(x) = 34, for 1 ≤ x ≤ 4

c(x) = 34 + $3.50(x - 4), for x > 4

This function represents the cost of an automotive ad as a piecewise function that depends on the number of lines in the ad.

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The surface area of the right triangular pyramid is, 269.5 square units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Dimensions of the right triangular pyramid are,

X = 11 units

Y = 10 units

Z = 13 units

Now, The surface area of the right triangular pyramid is,

Area of Lateral triangle = 1/2 × X × Z

                                    = 1/2 × 11 × 13

                                    = 71.5 unit²

And, Area of Base Triangle = 1/2 ·  base ·  height

                                          = 1/2 ·  X ·  Y

                                          = 1/2 ·  11 units · 10 units

                                          = 55 units²

Now, use the method described above to find the surface area of the pyramid.

Surface Area = 3( Area lateral ) + ( Area base )

                    = 3 ( 71.5 square units ) + ( 55 square units )

                   = 269.5 square units

Thus, The surface area of the right triangular pyramid is, 269.5 square units

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Using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.

What is a system of equations?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system.

1) y = -3 and x = -6

This system of equations has only one solution as the variables have only a constant as their value.

2) y = 2x and y = -2x

    There is only one solution to this system of equations. It is x =0 and y = 0. This solution only satisfies these equations.

3) y = -x -2

   y = -x -6

  There is no solution to this system of equations as the mathematical operation on two numbers will not give two values.

4) y = 3x + 4

2y = 6x + 8

There is an infinite number of solutions as the second equation when divided by 2 becomes y = 3x + 4, which is the same as the first equation.

5) y = 9x -1

   y = x + 9

 There is only one solution for this system of equations.

Therefore using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.

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The correct answer would be x equals negative 3 plus or minus 2 root 3

What is the quadratic equation?

The quadratic equation is a mathematical formula used to find the solutions (roots) of a quadratic function, which is a second-degree polynomial function of the form:

ax^2 + bx + c = 0

To solve for x in the equation x² + 6x + 9 = 12, we can start by simplifying the left-hand side by factoring the quadratic expression:

(x + 3)² = 12

Taking the square root of both sides, we get:

x + 3 = ±√12

Simplifying the right-hand side, we get:

x + 3 = ±2√3

Finally, solving for x, we have:

x = -3 ± 2√3

Therefore, the solution for x is:

x = -3 + 2√3 or x = -3 - 2√3

So, the correct response is:

x=−3±2√3

Hence, the correct answer would be x equals negative 3 plus or minus 2 root 3

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Answer:

-3 plus minus 2√3

Step-by-step explanation:

took test

Answer:

150 %6=es igual 1% dividimis 150 ÷100 para tener 150, se calcula el porcwntaje

The population in this case is all adults in the United States, and the sample is the 1001 adults who were surveyed by Citrix Security.

The sample was selected in such a way as to be representative of the larger population of adults in the United States.

The value of 69% is a statistic, not a parameter. A statistic is a measure that describes a characteristic of a sample, while a parameter is a measure that describes a characteristic of a population. In this case, the 69% refers to the proportion of the 1001 adults surveyed who believe that having their personal information stolen is inevitable, which is a characteristic of the sample. It does not necessarily reflect the proportion of all adults in the United States who hold this belief, which would be a parameter.

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The volume generated by rotating the region bounded by curves x = √y, x= 0 and y = 6 about the x-axis is 24π cubic units.

To use the method of b, we will imagine taking thin slices parallel to the axis of rotation and adding up their volumes.

To use the method of cylindrical shells, we need to determine the height and radius of each cylindrical shell. We will take thin vertical slices parallel to the y-axis.

The height of each cylindrical shell will be dy. The radius of each cylindrical shell will be x, which is equal to √y.

The volume of each cylindrical shell will be:

[tex]dv = 2\pi x * dy[/tex]

Substituting x = √y, we get:

[tex]dV = 2\pi \sqrt{y} * dy[/tex]

To find the total volume, we need to integrate dV from y = 0 to y = 6:

V = ∫₀⁶ 2π√y dy

Using the power rule of integration, we get:

V = 2π [2/3 * y^(3/2)] from 0 to 6

[tex]V = 2\pi * [2/3 * (6)^\frac{3}{2} - 0][/tex]

[tex]v = 24\pi[/tex]

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The zeros of the following functions are

1. f(x)=2x(3−x)(x+1) , the zeros are x = 3 and -1

2.f(x)=2(x−3)(x+2)2(x−1), the zeros are x = 3 ,-2 and 1

3. f(x)=x3(x−2)(x+3), the zeros are x = 2 and -3

On a graph of the function, the zeroes will be the x-coordinate values at the points where the line intersects with the x-axis, or where the y-coordinate value is zero. Linear functions have one zero, but polynomial functions can have multiple zeroes. They can also have no zeroes at all.

1. 2x(3−x)(x+1) = 0

2x = 0

x = 0

3-x = 0

x = 3

x+1 = 0

x = -1

2. 2(x−3)(x+2)2(x−1) = 0

x-3 = 0

x = 3

x+2 = 0

x = -2

x -1 = 0

x = 1

3. f(x)=x³(x−2)(x+3) = 0

x³ = 0

x= 0

x-2 = 0

x = 2

x+3 = 0

x = -3

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Answer:

y = 2x + 4 and 2y - x = 8 represent a system of linear equations.

In this system, the variable x represents an unknown value, while the variable y represents a value that can be determined from the equation. The coefficient 2 in the first equation is an example of a math vocabulary term, indicating that the slope of the line is 2. The term "slope" is a mathematical term that describes the steepness of a line.

The term "system" is an academic vocabulary term that refers to a group of related equations or inequalities. In this case, we have a system of two linear equations that are related to each other.

The second math vocabulary term is "solution", which refers to the set of values of the variables that satisfies both equations in the system. In this case, the solution is the unique point (3, 10), where x = 3 and y = 10.

Finally, the academic vocabulary term "consistent" is used to describe a system of equations that has at least one solution. In this case, the system is consistent because it has exactly one solution, which means the two equations intersect at a single point.

Step-by-step explanation:

After evaluating the given expression, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d = -4

An Algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.t may contain one or more variables, which are symbols that represent unknown quantities or values that can vary.

Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships. For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".

The given expression is d3a2−(c+b), where a = -2, b = 3, c = -12, and d = -4. Substituting these values, we get:

d3a2−(c+b) = (-4)3(-2)² - (-12 + 3) = -434 - (-9) = -48 + 9 = -39

Therefore, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d=-4.

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If we let "x" be the width of the rectangle, then the length would be "x + 5" (since it's 5 inches longer than the width).

The area of a rectangle is given by the formula A = length x width. Substituting in the expressions we found for the length and width, we get:

A = (x + 5)x

Simplifying this expression, we get:

A = x^2 + 5x

Therefore, the expression that could be used to represent the area of the rectangle is "x^2 + 5x".

As a resuIt, 10 (181)/181 is the sin vaIue that cοmes cIοsest tο 10 √(181)/√181. B is the apprοpriate answer, sο.

The cοst οr price οf sοmething, aIsο knοwn as its mοnetary vaIue.

The right-angIed triangIe fοrmed by the angIe's terminaI side and the pοints (-9, 10) can be caIcuIated using the Pythagοrean Theοrem tο determine the Iength οf a hypοtenuse:

h = √((-9)² + 10²) = √(81 + 100) = √(181)

Sin is pοsitive because the pοsitiοn (-9, 10) οccupies the secοnd quadrant. We are abIe tο determine the actuaI amοunt οf sin that use the definitiοn οf sin:

sin(theta) = οppοsite/hypοtenuse = 10/√(181)

We can cοmbine the twο parts οf this fοrmuIa by √181 tο οbtain the fοIIοwing resuIt:

sin(theta) = 10 × √(181)/√(181)√(181) = 10√(181)/181

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geometric series:

[tex]\dfrac{4}{-8} = - \dfrac{1}{2}[/tex]

[tex]\dfrac{-2}{4} = - \dfrac{1}{2}[/tex]

[tex]\implies r = - \dfrac{1}{2} \ \ and \ \ a_{1} = -8[/tex]

[tex]\boxed{S_{n} = \dfrac{a_{1}\cdot (1 - {r}^{n}) }{1 - r}}[/tex]

a. n = 3

[tex]S_{3} = - 8 + 4 - 2 = 4 - 10 = \bf -6\\[/tex]

b. n = 6

[tex]S_{6} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{6}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 - \dfrac{1}{2^{6}}\Big)}{1 + \dfrac{1}{2}} = \dfrac{-8 + \dfrac{1}{2^{3}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= \dfrac{-64+1}{2^{3}} \cdot \dfrac{2}{3} = -\dfrac{63}{2^{2}(3)} = \bf -\dfrac{21}{4}[/tex]

c, n = 25

[tex]S_{25} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{25}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 + \dfrac{1}{2^{25}}\Big)}{1 + \dfrac{1}{2}} = - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} = - \dfrac{1 + 2^{25}}{2^{22}} \cdot \dfrac{2}{3} = \bf - \dfrac{1 + 2^{25}}{(3)2^{21}}\\[/tex]

Answer:

x=6

Step-by-step explanation:

Answer: The answer should be 35.98 ( or 7π + 14 )

Step-by-step explanation:

The perimeter of a semicircle is half of the circumference plus the diameter. First, we find the circumference, which is (2πr). π * 7 * 2 = 14π. Since we have the circumference, we have to divide it by 2 since it's a semicircle. 14π/2 = 7π. Our next step is to find the diameter. Since the radius of the semicircle is 7, we multiply it by 2. 7 * 2 = 14. Now, let's say that (π = 3.14). So (7 * 3.14) + 14, 21.98 + 14 = 35.98. The answer should be 35.98.

Hope this helps. (and please respond if I'm wrong)

The area of the sector is 37.7 ft.

A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.

The formula for the area of a sector is given by

Where θ is the central angle in degrees, and r is the radius of the circle

Here we have

A circle has a radius of 4 ft.  

The central angle of sector formed = 270°

Using the formula, Area of sector = (θ/360°) × π r²

Area of the given sector = [ 270/360] × 3.14 × (4)²

= [0.75 ] × [50.24]

= 37.68 ft

= 37.7 ft

Therefore,

The area of the sector is 37.7 ft.

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According to the probability, the answer is option D: 1/98,000.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The chance of Steve being selected is 1. This means that out of 1 individual, Steve is selected. The probability of Steve being selected is 1/1 or 1. Since the sample is a simple random sample, each individual in the population has an equal chance of being selected. If there are a total of 98,000 individuals in the population, then the probability of Silva being selected is 1 out of 98,000, or 1/98,000.

Therefore, the answer is option D: 1/98,000.

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The value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.

What is piece wise function ?

A piecewise function is a function that is defined by different mathematical expressions or formulas for different intervals or "pieces" of the domain. In other words, a piecewise function is a function that is defined by multiple sub-functions, each corresponding to a different part of the domain.

While considering piece wise function:

[tex]F(6) = 4[/tex]                                                                 [tex](x \geq 3)[/tex]

[tex]F(-5) = x + 3 = (-5) + 3 = -2[/tex]                            [tex](x\leq -3)[/tex]

[tex]F(-1) =[/tex] [tex]-x^2 + 1 = -(-1)^2 + 1 = -1 + 1 = 0[/tex]       [tex](-3 < x < 3)[/tex]

Now put the value of F(6), F(-5) and F(-1) in the expression :

[tex]2F(6) + F(-5) - 3F(-1)[/tex]

we get :

[tex]= 2F(6) + F(-5) - 3F(-1) \\= 2(4) + (-2) -3(0)\\= 8 -2\\= 6[/tex]

Therefore, the value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.

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Answer:

Step-by-step explanation:

One possible solution to the linear equation −5x+y=−10 is:

x = 2

y = 0

To check if this solution is valid, we can substitute the values of x and y into the equation and see if it satisfies the equation:

(-5)(2) + (0) = -10

-10 = -10

Since the equation is true, we have found a valid solution.

The length of the radius and diameter are 10.5 and 21 respectively

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

The area of the sector = tetha/360 × πr²

= 72/360 × 3.14 × r²

= 0.628r²

area of the circle = area of the shaded part + area of sector

3.14r² = 277 + 0.628r²

3.14r²-0.628r² = 277

2.512 r² = 277

r² = 277/2.512

r² = 110.3

r = √ 110.3

r = 10.5

d = 2r

d = 10.5 × 2

= 21

therefore the radius and diameter are 10.5 and 21 respectively

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From the given situation of equation Diamond worked 24 overtime hours that week.

The hourly rate that is paid for the typical hours worked within a pay period is known as regular pay. For full-time employees in the US, this is typically referred to as 40 hours a week. On the other hand, overtime pay is the hourly rate paid for any additional hours worked. Most businesses give time-and-a-half (1.5 times the usual pay rate) or double-time (two times the regular pay rate) for extra hours, which is often more than regular compensation.

Let us suppose the number of hours = x.

Let us suppose the overtime hours = y.

From the given situation we have:

7.5x + 11.25y = 352.5 (equation 1)

x + y = 35 (equation 2)

Substituting equation 2 into equation 1 and simplifying:

7.5x + 11.25(35 - x) = 352.5

7.5x + 393.75 - 11.25x = 352.5

-3.75x = -41.25

x = 11

Substitute the value of x = 11.

11 + y = 35

y = 24

Hence, Diamond worked 24 overtime hours that week.

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The equations where b = 11 are A, B, C, D, and E. All of these equations are true when b = 11.

To point an equation on a graph, first, determine the equation and its variables. Then, plot the points of the equation on the graph by substituting the variable values and plotting the corresponding points. To find the equation’s slope, calculate the rise and run of two points on the graph. The slope is used to draw a line of best fit. Finally, draw a line that intersects the points of the equation and the line of best fit. This will be the equation’s graph.

Choice A states that 2b = 2112, b, equals, 211, which means that 2 times 11 is equal to 21. Choice B states that b + 18 = 7b, plus, 18, equals, 7, which means that 11 plus 18 is equal to 7. Choice C states that 77 = 7b77, equals, 7, b, which means that 77 divided by 7 is equal to 11. Choice D states that 9 = b − 29, equals, b, minus, 2, which means that 11 minus 2 is equal to 9. Finally, Choice E states that 11 = 33 ÷ b11, equals, 33, divided by, b, which means that 33 divided by 11 is equal to 11. Therefore, all of these equations are true when b = 11.

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