Ruby and her children went into a movie theater and she bought $42 worth of bags of popcorn and drinks. Each bag of popcorn costs $6 and each drink costs $4. She bought a total of 8 bags of popcorn and drinks altogether. Determine the number of bags of popcorn and the number of drinks that Ruby bought.​

Answer: 10: 6 is

ration add them 16

Step-by-step explanation:

Using the elimination method, the solution to the system of equations is as follows:

x = 19 / 13  and y = - 74 / 13

System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.

Let's use the elimination method to solve the system of equations as follows:

The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Therefore,

4x - 7y = 10

3x + 2y = -7

multiply equation(ii) by 3.5

4x - 7y = 10

10.5x - 7y = 24.5

subtract equation(i) from equation(ii)

6.5x = 14.5

x = 14.5 / 6.5

x =  145 / 65

x = 19 / 13

Let's find y

3(19 / 13) + 2y = -7

57 / 13 + 2y = -7

2y = - 7 - 57 / 13

2y = -91 - 57  / 13

2y = - 148 / 13

cross multiply

26y = - 148

y = - 148 / 26

y = -  74 / 13

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Answer: x=7

Step-by-step explanation:

2/5=x+1/3x-1

find the LCD

15x-5

multiply 2/5 by 3x-1

multiply x+1/3x-1 by 5

6x-2=5x+5

x=7

There is a 7°F difference in temperature between the morning and the afternoon.

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One of the six countries sent 41 representatives to the congress.

What, in the simplest words, is the Congress?

The Congress is our country's legislative body, which drafts our laws. The United States Senate and the United States House of Representatives are the two branches of Congress.

                    Each state has two U.S. Senators and a minimum of one U.S. Representative; the number of U.S. Representatives that can be elected depends on the number of citizens in the state.

(1) One of the six countries sent 41 representatives to the congress

(2) Country A sent fewer than 12 representatives to the congress

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Answer:

300

Step-by-step explanation:

the way to find perimeter is to add the numbers that are on the outside of the shape.

Answer: 300m

Step-by-step explanation: To find the Perimeter of the triangle or any shape, you need to add the length of the outside!

In this case, it is 104, 58, 138. Add all of them together you get 300m

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The value of the shortest of the three sides of the triangle is 13 cm.

A triangle is a polygon with threes sides. The perimeter of a triangle is the sum of the whole three sides.

The lengths of the three sides of a triangle (in centimetres) are consecutive odd integers. The perimeter is 45 cm.

The shortest side of the three sides can be calculated as follows:

let

the first side = x

second side = x + 2

third side = x + 4

Hence,

perimeter = x + x + 2 + x + 4

45 = 3x + 6

45 - 6 = 3x

3x = 39

divide both sides by 3

x = 39 / 3

x = 13

Therefore,

shortest side = 13 cm

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The required competition mark is given as 60, as of the given condition.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60

Thus, the competition mark is  60.

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The median would lie in the mean of the 15th and the 16th position.

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

The mean (average), mode, and standard deviation are some other descriptive statistics that are frequently contrasted with the median.

Given, the total number of basketball players present (n) = 30

Total number of attempts made = 6

Since there are even number of players present, 30, the location of the median would be n/2 and n/2 + 1 positions.

For 30, the positions would be

= 30/2 and 30/2 + 1

= 15 and 16th position

Hence, the median would lie in the mean of the 15th and the 16th position.

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Answer: (1/4)CD

Step-by-step explanation:

CD is 100% when the line segment is 25% of it or 1/4 of it! Then the line segment is (1/4)CD.

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Answer:

1 minute, Because per minute is $2, 12 cents

Answer:SLOPE

Step-by-step explanation:M in a equation is slope

Answer:

68 feet tall

Step-by-step explanation:

Imagine the shadows for both the tree and the person are set up like right triangles. The length of their shadows are the bases of the triangles, while the actual heights of the tree and person are the heights of the triangle. We can set up proportions since  "height of the person" divided by " their shadow's length" should equal "height of tree" divided by "tree shadow length".

Set up a proportion of the person's high height relative to their shadow's length (which is 6/4.5). Set this equation equal to the tree's proportion (which is x/51).

Solve for x.

[tex]\frac{6}{4.5} = \frac{x}{51}\\Isolate x by multiply 51 to both sides\\\\(306/4.5)=x\\68=x[/tex]

The proportion is solved and the height of the tree is A = 68 feet

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

Now , we can set up the following proportion:

Height of tree / length of tree's shadow = height of person / length of person's shadow

On simplifying , we get

A / 51 = 6 / 4.5

Now we can solve for A by cross-multiplying and simplifying:

A = 51 x 6 / 4.5

A = 68 feet

Therefore, the tree is 68 feet tall

Hence , the proportion is solved

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The range of the function will be;

⇒ Range = (91, 16, - 5)

The set of all inputs of the function is called Domain of set.

Given that;

The function is,

⇒ f (x) = x² - 6x

And, The domain = (- 7, - 2, 1)

Now,

Since, The function is,

⇒ f (x) = x² - 6x

We know that;

The range of the function gives the value of y.

Here, The domain (x) = (- 7, - 2, 1)

Put x = - 7;

⇒ f (-7 ) = (-7)² - 6 × - 7

            = 49 + 42

            = 91

Put x = - 2;

⇒ f (- 2) = (-2)² - 6 × - 2

            = 4 + 12

            = 16

Put x = 1;

⇒ f (1) = (1)² - 6 × 1

         = 1 - 6

         = - 5

Thus, The range = (91, 16, - 5)

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Step-by-step explanation:

Area of parallelogram = base • height

Where,

Base = 4.5 cm

Height = 5 cm.

Area = 4.5 cm • 3 cm

Area = 13.5 cm²

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Answer: 30 meters

Step-by-step explanation:

A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second.

In 1 day, there are 24 hours.

In 1 hour, there are 60 minutes.

To convert 1.3 days into hours, multiply by 24:

[tex]1.3*24=31.2[/tex]

Therefore, 1.3 days is equivalent to 31.2 hours.

To convert 31.2 hours into minutes, multiply by 60:

[tex]31.2*60=1872[/tex]

Therefore, 31.2 hours is equivalent to 1872 minutes.

1.3 days

31.2 hours

1872 minutes

Answer:

A = 4

Step-by-step explanation:

4x2-20x=-3 and A(x2-5x)=-3

Hence:

4x2-20x = A(x2-5x)

4x^2 - 20x = A(x^2 - 5x)

Divide both sides by (x^2 - 5x) to isolate A:

(4x^2 - 20x)/(x^2 - 5x) = (x^2 - 5x) * A/(x^2 - 5x)  

A = (4x^2 - 20x)/(x^2 - 5x)

A = (4x(x - 5)) / (x(x - 5))  ==> factor each polynomial

A = (4x) / (x)   *   (x - 5)/(x - 5)

A = (4x) / (x)   *   1   ==> (x-5)/(x-5) = 1

A = (4x) / (x)

A = 4x/x  ==> simplify

A = 4

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The value of a is -4 from the given system of linear equations.

The system of given equations are ax+12y=-6 and 2x-6y=4.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here, ax+12y=-6 -------(I) and 2x-6y=4 -------(II)

Given, no solution for the system

So, (a1/a2) = (b1/b2) ≠ (c1/c2)

Now, a/2 = 12/(-6)

a=-4

Hence, the value of a is -4 from the given system of linear equations.

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Answer:

Step-by-step explanation:

A 10% slope is one that rises by 1 unit for every 10 units travelled horizontally (10 %). For example, a roof with a 10% slope that is 20 m across will be 2 m high. This is the same as a gradient of 1/10, and an angle of 5.71° is formed between the line and the x-axis.

Answer: About 15 feet.

Step-by-step explanation: To solve this problem, we can use the Pythagorean theorem. The ladder forms the hypotenuse of a right triangle with the building and the ground, with the angle at the building forming the right angle. If the ladder is 8 feet away from the building, then the length of the ladder is the same as the length of the other leg of the triangle.

We can use trigonometry to find the length of this leg. In a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the adjacent side is the length of the ladder and the opposite side is 8 feet, so we can write the following equation:

tan(25 degrees) = opposite side / adjacent side

tan(25 degrees) = 8 feet / adjacent side

To find the length of the adjacent side (the ladder), we can divide both sides of the equation by the tangent of 25 degrees:

adjacent side = 8 feet / tan(25 degrees)

According to my calculations, the length of the ladder is about 15 feet, so the correct answer is A: About 15 ft.

Proof that the bisector of an isosceles triangle also bisects the angle.

A line segment's midpoint is the point on the segment where it divides into two congruent parts. a right-angled segment bisector that crosses the segment. A line (or portion of a line) that cuts through the middle is known as a segment bisector.

When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized halves is known as a bisector. A line segment's perpendicular bisector implies that it intersects the segment at a 90-degree angle and splits it into two equal halves.

Let ABC be the isosceles triangle with AB=AC, B=C, and BAD=CAD as the vertical angle bisectors.

As a result, the triangles satisfy the ASA criterion.

⟹BD=DC

Thus, the base is divided by the vertical angel's bisector.

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7) The minimum temperature is 31⁰F. So, the answer is option B.

The frequency of various types of values can be easily observed using a stem and leaf plot, also known as a stem and leaf diagram. This graph displays numerical data that is arranged in chronological order. There is a stem and a leaf for each piece of data.

Each first or second digit of the data value is divided into a stem, and the last digit is represented by a leaf, in a stem and leaf plot, which is represented by a particular table. The stem and leaf plot key is the "|" symbol that is used to indicate the values of the stem and the leaf. In the case of 46, the stem is 4 and the leaf is 6.

7) The minimum value in the stem is 3

And the minimum value in the leaf is 1

So, according to the given key 4|3=43°F

Here | denotes the key symbol.

So, in this solution the minimum value of stem is 3 and the minimum value of leaf is 1

Therefore, it must be 3|1

Hence, from the given key

This can be written as 31⁰F

Therefore, the answer is option B.

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The intersection region of every solution in the system of inequalities is the system's solution. Inequality y≤x2 should be graphed first. y=x2 serves as the related equation.

Example

Graph the inequalities and solve the system:

y≤x−2y>−3x+5

Inequality yx2 should be graphed first. y=x2 serves as the related equation.

The border line is solid due to the inequality's, which is not a rigid one.

The inequality yx2 should be substituted in for a point that is not on the line, such as (0,0).

0≤0−20≤−2

It's untrue. The point (0,0) is therefore not part of the solution. Subtract from the line's lower half.

To do the same for the second inequality's related equation, y>3x+5, which has a rigorous inequality, draw a dashed line. The half that does not contain the point (0,0) should be shaded because it does not satisfy the inequality at that location.

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The statistic said to be Unbiased Estimator If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States. On the other hand, a sample statistic is the average income for a sample taken from the United States. Although both figures correspond to the mean income, only one is a statistic.

Here,

The reported statistic is Independent Estimator If the mean of the sampling distribution for a statistic used to estimate a parameter matches the actual value of the parameter being estimated.

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The mass of the ball is 278.1 g, the material used to make the ball must be brass which having density of 8.6 g/cm³.

To determine the material used to make the ball, we need to first calculate the volume of the ball.

The volume of a sphere with radius r is given by:

V = (4/3) * π * r^3

Plugging in the given values, we get:

V = (4/3) * π * (2 cm)^3

= (4/3) * π * 8 cm^3

= (4/3) * 8π cm^3

= 32π cm^3

We can then use the density of each material (given in g/cm³) to calculate the mass of the ball if it were made of that material:

Copper: 8.3 g/cm³ * 32π cm³ = 266.4 g

Brass: 8.6 g/cm³ * 32π cm³ = 275.2 g

Iron: 7.8 g/cm³ * 32π cm³ = 250.4 g

Since the mass of the ball is 278.1 g, the material used to make the ball must be brass.

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Simplifying the algebraic expression [tex]( x + 4 ) ( 2 x + 9 )[/tex] will give an answer [tex]2x^{2}+17x+36[/tex].

The technique of writing an algebraic expression in the most effective and compact form without altering the original expression's value is known as simplification.

The procedure involves gathering related phrases, which calls for adding or removing terms from an expression.

According to the distributive property of algebraic expressions, each term in an expression's sum or difference must be multiplied by a number outside of the parenthesis. A number is used as the value outside of the parenthesis with the total or difference.

Here the algebraic expression is:

[tex]( x + 4 ) ( 2 x + 9 )[/tex]

Use the distributive property to simplify the expression,

⇒ [tex]( x + 4 ) ( 2 x + 9 )[/tex]

⇒ [tex](x)(2x)+(x)(9)+(4)(2x)+(4)(9)[/tex]

⇒ [tex]2x^{2} +9x+8x+36[/tex]

⇒ [tex]2x^{2} +17x+36[/tex]

Therefore, the solution will be [tex]2x^{2} +17x+36[/tex] when the algebraic expression is simplified.

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