Find an expression which represents the difference when (2x + 4) is subtracted
from (4x + 2) in simplest terms.

Answer:

1 2/3 went in each container

Step-by-step explanation:

10 divided by 6 is 1.666666666677777777777 which equals to 1 2/3 multiply it by 6 and you will get 10.

16 is  Median a sample with data values .

What is the mathematical median?

The middle number, or median, is obtained by sorting all of the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

                                 Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.

Mean = Total of values/ Total number of observations

Total of values = 10+20+12+17+16 = 75

Total number of observations = 5

Mean = 75/5 = 15

Median:

Arrange in ascending order = 10, 12,16,17,20

Median = [n+1] / 2

N = number of observation = 5

Median = [5+1]/2 = 3rd observation

Median = 16

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Answer:

x = 6

Step-by-step explanation:

Vertices of a rectangle are normally listed so that adjacent vertices are connected by edges. Therefore, the edges of rectangle HIJK are HI, IJ, JK and KH.

As the opposite sides of a rectangle are congruent:

Therefore, to find the value of x, set the given expressions for HI and JK equal to each other and solve for x:

[tex]\implies \sf HI=JK[/tex]

[tex]\implies 3x+7=6x-11[/tex]

[tex]\implies 3x+7-7=6x-11-7[/tex]

[tex]\implies 3x=6x-18[/tex]

[tex]\implies 3x-6x=6x-18-6x[/tex]

[tex]\implies -3x=-18[/tex]

[tex]\implies -3x \div -3=-18 \div -3[/tex]

[tex]\implies x=6[/tex]

Reason:

The like terms 2n and -5n combine to -3n. In other words, 2n-5n = -3n

The other pair of like terms 3 and 6 combine to 3+6 = 9

The value of the expression 84.7 divided by 14 will be 6.05.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression 84.7 divided by 14 will be:

= 84.7 / 14

= 6.05

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The Total surface area of a pyramid formula = ½ pl + B, Where 'p' is the perimeter of the base and 'l' is the slant height of the pyramid and B is the area of the base.

A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=13Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.

A triangular pyramid, for instance, has a base area of 20 cm2 and a height of 9 cm. The formula V = (1/3) Bh, where "B" stands for the base area and "h" for the height of the pyramid, is used to calculate the volume of a pyramid.

We can use the formulas for the area of polygons to calculate "B" because we know that the base of a pyramid can be any polygon. A pyramid with a triangle base is referred to as a triangular pyramid. 

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The value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].

A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=1/3Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.

We know that pyramid's volume is

[tex]\mathrm{{\textstyle V={\tfrac {1}{3}}Bh}}[/tex]

B = base area = [tex]25^{1/4} \times25^{1/4}[/tex]

= [tex]\sqrt[4]{25} \times \sqrt[4]{25}[/tex]

= [tex]\sqrt[4]{25}^2[/tex]

= [tex]\sqrt[2]{25}[/tex]

= 5 cm²

and

h = 75 cm

[tex]$\mathrm{{\textstyle V={\dfrac {1}{3}} \times5 \times 75}}[/tex]

V = 125 cm³

Now it is given that  [tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]

So,

[tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]

[tex]\mathrm{5^{\tfrac{x}{6}} = \sqrt[3]{5} }[/tex]

[tex]\mathrm{5^{\tfrac{x}{6}} = 5^{\tfrac{1}{3}} }[/tex]

[tex]\dfrac{x}{6} = \dfrac{1}{3}[/tex]

3x = 6

x = 6/3

x = 2

Thus, the value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].

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The number of slices that Jamal eats will be 10 slices.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Let Amelia's share be x.

Jamal's share will be x + 4.

Therefore, the equation will be Illustrated as:

3/5 = x/(x + 4)

Cross multiply

5x = 3x + 12

5x - 3x = 12

2x = 12

Divide

x = 12 / 2

x = 6

Jamal's share will be

= 6 + 4.

= 10

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Answer:

$195,345.60

Step-by-step explanation:

We can calculate the amount of money remaining in the fund after 6 years by multiplying the initial amount by (1 - 0.2)^6. In this case,

(1 - 0.2)^6 = 0.32768

So the fund will have $597,000 * 0.32768 = $195,345.60 after 6 years.

The win percentage of total 78 boys are 29.49%, 51.28% and 19.23% and of total 53 girls are 33.96%, 18.87% and 47.17% in basket ball, baseball and fencing respectively.

A percentage is a number or ratio in mathematics that represents a fraction of 100. It is one of several methods for representing a dimensionless relationship between two numbers; others include ratios, fractions, and decimal.

The symbol "%" written after a number is commonly used to represent percentages. They can also be indicated by adding "percent" or "pct" to the end of the number. 35%, for example, is represented by the decimal 0.35, as well as the fractions 35/100 and 7/20.

Total boys = 23 + 40 + 15

                  = 78

Win percentage in basket ball = 23/78 × 100

                                                   = 29.49%

Win percentage in baseball = 40/78 × 100

                                                   = 51.28%

Win percentage in fencing = 15/78 × 100

                                                   = 19.23%

Total girls = 18 + 10 + 25

                  = 53

Win percentage in basket ball = 18/53 × 100

                                                   = 33.96%

Win percentage in baseball = 10/53 × 100

                                                   = 18.87%

Win percentage in fencing = 25/53 × 100

                                                   = 47.17%

Thus, The win percentage of total 78 boys are 29.49%, 51.28% and 19.23% and of total 53 girls are 33.96%, 18.87% and 47.17% in basket ball, baseball and fencing respectively.

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Mathematic homework takes longer. It takes 2/3 h longer than language arts homework. Mathematic homework takes longer to complete than language arts homework. We can compare these two fractions by converting them to the same denominator.

Language arts homework: 4/9 h

Mathematic homework: 2/9 h

We can compare these two fractions by converting them to the same denominator.

Language arts homework: 4/9 h = 8/18 h

Mathematic homework: 2/9 h = 4/18 h

Mathematic homework takes 2/3 h longer than language arts homework.

Mathematic homework takes longer than language arts homework, by 2/3 h.

Mathematic homework takes longer to complete than language arts homework. We can compare these two fractions by converting them to the same denominator. Language arts homework takes 4/9 h, or 8/18 h, while mathematic homework takes 2/9 h, or 4/18 h. Mathematic homework takes 2/3 h longer than language arts homework. This means that mathematic homework takes more time to complete than language arts homework, by 2/3 h.

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Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)

What is mean value theorem ?

The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].

The property of derivative  : r'(t) is the rate of change of water flow.

Justification :

r(s) - r(4) = r'(3) (5-4)

        - 5 = r(3)

In (4,5) , r(t) decreasing , so there are value of 3 and r'(3) > 0 , r'(3) = -5.

r(6) - r(5) = r'(3) (6-5)

          4  = r'(3)

In (5,6), r(t) increasing , so there are values of 3 and r'(3) > 0, r'(3) = 4.

∴ Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)

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The complete question is :

Water is flowing into a tank at a rate of r(t) where t is measured in seconds. Is there ever a time where the r'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem.

The angle that needs to be used to draw the sector for L will be 60°. Then the number of people who voted for J will be 5,280.

A circular data visual with slices illustrating numerical proportions is called a pie chart. Each slice's angle in a pie chart corresponds to the material it represents.

In an election there were four candidates, J, K, L, and M. Teri is drawing a pie chart to show the results. The sectors for J and K have been drawn. Twice as many people voted for L as voted for M.

Let 'x' be the number of people who voted for L and M. Then the number of people who voted for J and K will be 2x.

The angle that needs to be used to draw the sector for L will be given as,

⇒ 360° × [x / (2x + 2x + x + x)]

⇒ 360° × [x / 6x]

⇒ 360° × 1/6

⇒ 60°

Altogether, 15,840 people voted. Then the number of people who voted for J will be given as,

⇒ [(2x) / (2x + 2x + x + x)] × 15,840

⇒ (1/3) × 15,840

⇒ 5,280

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Line segment AB is congruent to line segment CD, ∠A ≡ ∠C, BE is congruent to DE and AE is congruent to CE in triangle ABE and triangle CDE. So all the first four options are corresponding parts of the two congruent triangles.

Therefore, the answer is e. None of the above.

Corresponding parts of congruent triangles are any pair of matching or identical elements in two congruent triangles. These can include:

Sides, such as line segment AB being congruent to line segment CD

Angles, such as ∠A being congruent to ∠C

Vertices, such as point E being the intersection of segments BD and AC in both triangles

Any other element that is identical in both triangles, like height, medians, circumcenters, etc.

In triangle ABE ≡ triangle CDE, congruent sides are

AB ≡ CD

BE ≡ DE

AE ≡ CE

Congruent angles are

∠A and ∠C

∠B and ∠D

∠BEA and ∠DEC

--The question is not readable, answering to the question below--

"Which of the following are not corresponding parts of the congruent triangles, triangle ABE and triangle CDE? Segments BD and AC intersect at point E to form one vertex and two sides of each triangle.

a. line segment AB is congruent to line segment CD

b. ∠A ≡ ∠C

c. BE is congruent to DE

d. AE is congruent to CE

e. None of the above"

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Answer:

Democracy is the best form of government because it promotes equality and representation of all citizens, protects individual rights and freedoms, and encourages participation and accountability in the political process.

71 poles are needed to fence the rectangular field.

What are the dimensions of the rectangle?

A rectangle is a two-dimensional shape with four sides that has opposite sides that are parallel and equal in length. The length and width of a rectangle are its dimensions. The sides that are equal in length are called the "long sides" or "length," and the sides that are shorter are called the "short sides" or "width."

The total length of the fence required to enclose the rectangular field is the sum of the lengths of all four sides. To find this, we multiply the length and width of the field and then add twice:

Total length = 2 * (63.9m + 104.6m) = 2 * 168.5m

Next, we need to determine the number of poles required to fence the rectangular field. To do this, we divide the total length by the maximum distance between poles (2.4m):

Number of poles = Total length / 2.4m

= 168.5m / 2.4m

= 70.21 poles

Since we can't have a fractional number of poles, we round up to the nearest whole number. This means that we need at least 71 poles to fence the rectangular field.

Hence 71 poles are needed to fence the rectangular field.

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a) The average price of a house today is $341,700.

b) The average price of a house next year is $325,865.

What is the average price?

The average price is a measure of the central tendency of a set of data points. It is defined as the sum of all the data points divided by the number of data points.

(a) To find the average price of a house today, we can use the formula:

New price = Original price x (1 + percentage increase)

New price = 260000 x (1 + 0.295) = 3417000

So, the average price of a house today is $341,700

(b) To find the average price of a house next year, we can use the formula:

New price = Original price x (1 - percentage decrease)

New price = 341700 x (1 - 0.05) = $325,865

So, the average price of a house next year is $325,865

Hence,

a) The average price of a house today is $341,700.

b) The average price of a house next year is $325,865.

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Given:

Total Population = 500  millions

Population Under 16 Years of Age or Institutionalized = 120 millions

Not in Labor Force = 150  millions

Unemployed = 23 millions

Now,

A) Labor force

= Total population – Population under 16 years of age – Not in labor force

= 500 – 120 – 150

= 230 millions

B) Unemployment rate [tex]$=\frac{\text { Unemployment }}{\text { Labor force }} \times 100 \%$[/tex]

or

Unemployment rate [tex]$=\frac{23 \text { million }}{230 \text { million }} \times 100 \%$[/tex]

or

Unemployment rate [tex]$=10 \%$[/tex]

The complete question is,

Assume the following data for a country:

Category Number of People (in Millions)

Total Population 500

Population Under 16 Years of Age or Institutionalized 120

Not in Labor Force 150

Unemployed 23

Part-Time Workers Looking for Full-Time Jobs 10

A) What is the size of the labor force (in millions)?

B) What is the official unemployment rate (in percentage)?

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Answer:

wouldnt it just be 1/9

Step-by-step explanation:

The Side-Angle-Side rule is the foundation for this query. The correct response is therefore option A, since ABC=DEF cannot be inferred from the additional statement that AB=EF.

According to this rule, the corresponding two angles of one triangle are congruent with the two angles of the other triangle. The side-angle-side postulate is the only congruence rule that can be applied as a result.

Here,

A=D and C=F in triangle ABC and triangle DEF.

We must choose a statement that prevents you from deducing that triangle ABC = triangle DEF.

The correct response is therefore option A, since ABC=DEF cannot be inferred from the additional statement that AB=EF.

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The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.

What is area of circle ?

area of circle can be defined as the product of pi and square of radius

and here the value of pi is 22/7 or 3.14

Given in the figure,

a circle is within square with diameter 36m .

So, we have to find the

area of a shaded region  = area of square - area of circle .

radius = d/2

radius = 36/2

radius = 18 .

= 36*36 - 3.14 * 18*18

= 1296 - 1017.36

= 278.64

Hence, The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.

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In given word problem the possibility for 3 non repeating digits followed by # sign is 720 ways.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the gate code at your apartment complex is three numerical digits followed by the "#"sign.

There are 10 digits (0 to 9)

Compute the number of possible gate codes if each code contains non repeating digits as follows,

The first 3 place in the code must be filled by three non-repeating digits.

So, there are 10 possibility for first  digit and 9 possibility for second digit and 8 possibility for third digit.

Hence the 3 non repeating digits can occur un 10×9×8 ways.

The three non repeating digit followed by #. Then sign # can occur in only way, then,

Total possibility = 10×9×8×1 = 720 ways.

Hence the possibility for 3 non repeating digits followed by # sign is 720 ways.

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The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles

The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.

Always true. The opposite angles of an isosceles trapezoid are supplementary because the diagonals of an isosceles trapezoid bisect each other. Therefore, the angles formed by the intersection of the diagonals are supplementary, since the sum of two supplementary angles is 180 degrees.

The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.

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Answer:

c. Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

Step-by-step explanation:

if wrong pls tell

Answer: C - 5 cups

Step-by-step explanation:

Hello! The art teacher mixes 3 cups of blue paint with 2 cups of red paint.  Since the art teacher combines the two, you have to add the two.  3 + 2 = 5, which should be your answer.  Hope this helps!

Using mathematical operations, the distance that differentiates Terry and Damon is 7 kilometers.

Mathematical operations are the computation of values using mathematical operands (÷, ×, +, -, etc), and mathematical operators like addition, subtraction, division, and multiplication.

In this situation, we use the subtraction operation to determine the difference or the distance between Terry and Damon.

The total distance between Toronto and Sudbury = 418 km

The distance covered by Terry from Sudbury to Toronto = 310 km

The length yet to be covered by Terry = 108 km (418 - 310)

The distance covered by Damon from Toronto to Sudbury = 303 km

The length remaining for Damon = 115 km (418 - 303)

The distance apart between Damon and Terry = 7 km (115 - 108)

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The table of values for the equation xy =5 are

x       y  

5       1

10     1/2

15     1/3

20   1/4

25    1/5

The relationship between the various data points is displayed using tables of values. In scientific lesson, a table of values could be used. Tables of values are used by scientists and researchers to record their data, which is subsequently examined for patterns. Then, they can use this pattern to forecast things.

In the problem, the equation to derive the table of value is xy = 5, this is re written to be y = 5/x

The values of y are solved as follows

For x = 5, y = 5/5 = 1

For x = 10, y = 5/10 = 1/2

For x = 15, y = 5/15 = 1/3

For x = 20, y = 5/20 = 1/4

For x = 25, y = 5/25 = 1/5

Table of values

x       y  

5       1

10     1/2

15     1/3

20   1/4

25    1/5

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R13 fiberglass batt insulation, typically used in walls and floors, is 3 5/8 inches thick, according to Energy.gov.

To determine the number of insulation batts required, first determine the area to be insulated in square meters (m2). Calculating the square metre (m2) area of your walls is actually fairly simple; simply multiply the length by the breadth.

To assess the cost of cellulose insulation for your project, first decide how much insulation you would require. To do so, divide the square footage of the space by the depth or the desired R-value. R-25 EcoTouch insulation is designed to fit snugly between outside wall wood studs. After installing cover material on one side of the cavity, friction-fit unfaced insulation between studs.

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the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.

Lx + My = N ---------(1)

Ax + By = C ---------(2)

System 2 :

(L - A)x + (M - B)y = N - C -------(3)

Lx + My = N ---------(4)

If we subtract equation (2) from equation (1),

(Lx + My) - (Ax + By) = N - C

Lx - Ax + My - By = N - C

(L - A)x + (M - B)y = N - C

Which is similar to equation (3) of the system 2.

And equation (1) of the system (1) is similar to the equation (4) of the system (2)

Therefore, equation (3) of the system 2 is the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.

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Answer:

Step-by-step explanation:

Given that 79 balcony and 27 general admission tickets sell for $5550, and 79 balcony and 36 general admission tickets sell for $5820, you want the cost of each kind of ticket.

The equations representing the sales are ...

  79b +27g = 5550

  79b +36g = 5820

Subtracting the first equation from the second, we have ...

  (79b +36g) -(79b +27g) = (5820) -(5550)

  9g = 270 . . . . . . . . . simplify

  g = 30 . . . . . . . divide by 9

  79b +27(30) = 5550 . . . . . . substitute into the first equation

  79b = 4740 . . . . . . . . . . subtract 810 & simplify

  b = 60 . . . . . . . divide by 79

A balcony seat ticket costs $60; a general admission floor ticket costs $30.