Which of the following statements about trapezoids must be true?
Question 15 options:

A)

Opposite angles are equal.

B)

Both pairs of opposite sides are parallel.

C)

One pair of opposite sides is parallel.

D)

Opposite sides are equal.

Answer: There is no variable or constant that you can add, subtract, multiply, or divide between the two sides of the sentence to make the sentence false by adding, subtracting, multiplying, or dividing each side of the sentence by the variable x x x and the constant 3.

Answer: No. Adding, subtracting, multiplying, and dividing both sides by the variable x x x and the constant 3 gives a true statement for each operation so there is no variable or constant that you can add, subtract, multiply, or divide to both sides to make the sentence false.

Step-by-step explanation:

[tex]179\times44[/tex]

[tex]=\fbox{7876}[/tex]

__________________________________________________________

The following expressions are equivalent to [tex]179\times44[/tex]:

[tex](179 \times 40) + (179 \times 4) = 179 \times(40 + 4)[/tex]

[tex]4000 + 2800 + 360 + 280 +36[/tex]

[tex](100 \times44) + (70\times44) + (9\times44) = 44 \times (100 + 70 +9) = 44 \times 179[/tex]

The equivalent expression to 2x² + 4 + 3x² + 2x + 7 is 8x² + 2x + 11.

An equivalent equation is an equation that has the same solution set as another equation. It is a mathematical expression that is equal in value to another expression. The two equations can often be solved using the same methods and yield the same result. Equivalent equations are useful in solving complex mathematical problems by breaking them down into simpler equations.

This is obtained by combining the like terms such as 2x² and 3x², which results in 5x², and 4 and 7 resulting in 11. The expression can be written as 5x² + 2x + 11. The final result can be obtained by multiplying 5x² with 2, which results in 8x². Hence, the equivalent expression is 8x² + 2x + 11.

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The cumulative frequency distribution is a type of statistical representation that shows the total number of data points in a sample that are less than or equal to a given value. It is often used to understand the distribution of data within a sample and to identify patterns or trends.

To construct a cumulative frequency distribution for given data, follow these steps:

For example, given the following data:

The cumulative frequency distribution would be:

Data Point | Frequency | Cumulative Frequency

      10         |        1           |                1  

      15         |        1           |                2

     20         |        1           |                3

     25         |        1           |                4

     30         |        1           |                5

     35         |        1           |                6

     40         |        1           |                7

     45         |        1           |                8

This distribution could be represented in a graph by plotting the data points on the x-axis and the cumulative frequencies on the y-axis and connecting the points with a line.

The answer is general since the data is not provided.

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Section 3 have 205 spots, according to the given question.

What do you mean by section?

A section is a part or component that, when combined with the other components, forms the total. like the rhythm section of the band that is reviewed in the arts section of a newspaper.

According to the given question,

We have the given information:

A 900 car parking lot is divided into 3 sections. There are 330 spots in Section 1. Section 2 holds 160 more than the amount of cars in Section 3.

Firstly,

900 - 330 = 570 (spots in section 2 and 3)

Secondly,

There are x spots in section 3 and (x + 160) spots in section 2.

So we have :

x + x + 160 = 570

2x = 410

x = 205

Therefore, the section 3 have 205 spots.

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Answer:

A.

Step-by-step explanation:

Just put the equation 3x+4y≥20 into y=mx+b form. Subtract 3x from both sides so you get 4y ≥ -3x+20

then divide everything by 4 to isolate the y.

You would get y ≥ -3/4+ 5. Then just use the slope and y-intercept to graph.

If ≥ symbol is used, shade above the line.

A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation.

A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation. We can draw the translation in the coordinate plane if we know which way and how far to move the figure.

The triangle can be translated in the following ways:

Step 1: In the first step, determine the coordinates of each vertex of the triangle.

Step 2: To translate each point, add the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. Add a negative number if either the vertical or horizontal translation for these translations is downhill or to the left.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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Answer: 46 chairs

Step-by-step explanation:

First, we have to find the amount of money Darnell spent to rent the chairs by taking

500 - 362 = $138

Then take $138 divided by $3 = 46 chairs

So he rent 1 table and 46 chairs

Answer:

let x - chairs

Darnell rents some tables for $362 and some chairs for $3 each for a party. He spends a total of $500.

500 = 362 + 3x

500 - 362 = 3x

138 = 3x

x = 46

500 = 362 + 3(46)

500 = 362 + 138

500 = 500

Therefore, Darnell rents 46 chairs.

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Step-by-step explanation:

Answer:

A ∪ B = [3, 9)

Step-by-step explanation:

Set X is 3, and all number greater than 3 up, but not including, 5.

Set Y is all numbers from 4 to 9, but not including 4 or 9.

The union of the sets is all numbers from 3 up to 9, including 3 but not including 9.
A ∪ B = [3, 9)

We say cubic polynomial if the degree of polynomial is odd number, and the graph is said cubic polynomial graph.

The equation which has only positive integer exponent are called   polynomial function. Such as 6x³+4x²+2x+1=0 where the power 3,2, 1 are the degree of polynomial.

The polynomial function whose first degree is odd number is called cubic polynomial.

hence, the graph is cubic polynomial.

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The two triangles are similar under SSS conditions if all three sides of one triangle are in proportion to the three sides of another triangle.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

According to the SSS test for triangle similarity, two triangles are considered similar if their third sides are proportionate to one another.

Therefore, the two triangles are similar under SSS conditions if all three sides of one triangle are in proportion to the three sides of another triangle.

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The number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.

To solve this problem, you can set up a system of equations to represent the given information. The first equation represents the fact that the company uses 138 pounds of peanuts for every 2/3 pound of raisins:

138 pounds peanuts / 2/3 pound raisins = x pounds peanuts

The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:

x pounds peanuts + y pounds raisins = 245 pounds trail mix

To solve for the number of pounds of peanuts used, you can substitute the first equation into the second equation:

(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix

Multiplying both sides of the equation by 2/3 to eliminate the fraction, we get:

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)

Combining like terms, we get:

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)

Simplifying the right side of the equation, we get:

138 pounds peanuts + (2/3)y pounds raisins = 160 pounds

Subtracting 138 pounds from both sides of the equation, we get:

(2/3)y pounds raisins = 160 pounds - 138 pounds

Simplifying the right side of the equation, we get:

(2/3)y pounds raisins = 22 pounds

Dividing both sides of the equation by 2/3, we get:

y pounds raisins = (3/2)(22 pounds)

Simplifying the right side of the equation, we get:

y pounds raisins = 33 pounds

Substituting this value into the first equation, we get:

138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins

Multiplying both sides of the equation by 2/3, we get:

138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins

Simplifying the right side of the equation, we get:

138 pounds peanuts / 22 pounds raisins = 33 pounds raisins

Dividing both sides of the equation by 22 pounds raisins, we get:

138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins

Simplifying the equation, we get:

6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins

This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.

Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.

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138 pounds peanuts / 2/3 pound raisins = x pounds peanuts

The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:

x pounds peanuts + y pounds raisins = 245 pounds trail mix

(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)

138 pounds peanuts + (2/3)y pounds raisins = 160 pounds

(2/3)y pounds raisins = 160 pounds - 138 pounds

(2/3)y pounds raisins = 22 pounds

y pounds raisins = (3/2)(22 pounds)

y pounds raisins = 33 pounds

138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins

138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins

138 pounds peanuts / 22 pounds raisins = 33 pounds raisins

138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins

6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins

This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.

Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.

Answer:

B

Step-by-step explanation:

this just means that the graph has to have x-intercepts (y = 0) at these x-values.

so, which graph intersects the x-axis at x = -7/3 and x = 1/2 ?

only B does that.

the others have other x-intercept points.

Answer:

Step-by-step explanation:

To find the maximum area of one plot, we need to find the greatest common factor of 840 and 396. One way to do this is to use the prime factorization method.

First, we prime factorize 840 and 396:

840 = 2 * 2 * 2 * 3 * 5 * 7

396 = 2 * 2 * 3 * 3 * 11

Then, we find the common factors:

2 * 2 * 3 = 12

So, the greatest common factor of 840 and 396 is 12.

The maximum area of one plot is therefore (840 * 396) / 12 = 140 * 33 = 4620 square meters.

An equation of the form z= a+ib, where a and b are real numbers, is defined to be a complex number. The real part is denoted by Re z = a and the imaginary part is denoted by Im z = ib.

Now, According to the question:

Let's know:

What are Complex Numbers?

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).  Also, ib is called an imaginary number.

Representation of the Complex Numbers:

z = a + ib

'a' represent the Real part

'ib' represent imaginary number and imaginary part.

Some of the examples of complex numbers are :

2 + 3i , -3 - 4i , 1/2 + 1/3i etc.

Power of i

The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers. We have the value of [tex]i^2[/tex] = -1, and this is used to find the value of √-4 = √[tex]i^2[/tex]4 = ±2i  The value of [tex]i^2[/tex] = -1 is the fundamental aspect of a complex number. Let us try and understand more about the increasing powers of i.

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The triangle has the following characteristics: A triangle (of any kind) has a total angle of 180 degrees. In a triangle, the lengths of the first two sides are bigger than the length of the third side. The difference between the two sides of a triangle are also smaller than the third side's length.

The 3-sided polygon known as a triangle is also known as the trigon, however this term is not particularly common. There are three sides to every triangle as well as three angles, some of which may be the same.

It is one of the fundamental shapes in geometry. Triangle ABC refers to a triangle with vertices A, B, and C.

The triangle has the following characteristics: A triangle (of any kind) has a total angle of 180 degrees. In a triangle, the lengths of the first two sides are bigger than the length of the third side. The difference between the two sides of a triangle are also smaller than the third side's length.

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The exact surface area of the cylinder in terms of π is = 10 π

What is the answer for surface area?

As a refresher, the surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units.

Where can I find the surface area?

A three-dimensional shape's surface area is the total area on its surface. Add the areas of each of the six rectangular sides of a cuboid to determine its surface area. The cuboid's length, width, and height can also be labeled, and the surface area (SA) can be calculated using the formula SA=2lw+2lh+2hw.

Given that :

Radius = 1 1/4 cm

Height = 2 3/4 cm

Surface area is 2π r h + 2π r² = 2π ( 1 1/4 cm*2 3/4 cm) + 2π (1 1/4)²

= 2π (55/16) + 2π (25/16)

= 160/16 π

= 10 π

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A regression table mainly shows us that what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0) .

A regression table is a statistical technique that describes how strongly a dependent variable and one or more independent variables are correlated (s). A field or variable you are attempting to predict or comprehend could be a dependent variable.

Regression allows researchers to predict or explain the variation in one variable based on another variable. The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.

What is interpretation of regression statistics table?

In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable. When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression.

A regression table primarily reveals the values of the coefficients as well as the significance of each coefficient (how likely it is that it will depart from 0).

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The mean of grade-point averages of 20 college seniors selected at random from a graduating class is 2.50.

Mean is the average of all numbers in the data set. The average can be found by dividing the sum of all numbers in the observed data by the number of data observations. This helps researchers, statisticians, etc. to find mean values in datasets. The formula for calculating the

average is:

mean = sum of values / number of values

It is denoted by X-bar.

We have the grade-point averages of 20 college seniors. The the random sample of graduating class as :

2.2, 1.6 ,2.7, 2.2, 2.4, 2.6, 3.8, 3.0, 2.5, 3.3, 1.8, 2.3, 3.3, 2.8, 2.0, 3.2, 2.1, 2.0, 2.9, 1.3

The Sum of grade point averages of 20 college seniors is calculated as follows,

∑ x = 2.2 + 1.6 + 2.7 + 2.2 + 2.4 + 2.6+ 3.8 + 3.0 + 2.5 + 3.3 + 1.8 + 2.3 + 3.3 + 2.8 + 2.0 + 3.2 + 2.1 + 2.0 + 2.9 + 1.3

∑x = 50

Total number of colleges , n = 20

Mean of distribution is calculated as follows,

X- bar = ∑x / n

where n is number of observations

X- bar = 50/20

=> X-bar = 2.5

Hence, required mean is 2.5 ..

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Complete question:

The grade-point averages of 20 college seniors selected at random from a graduating class are as follows:

2.2, 1.6 ,2.7, 2.2, 2.4, 2.6, 3.8, 3.0, 2.5, 3.3, 1.8, 2.3, 3.3, 2.8, 2.0, 3.2, 2.1, 2.0, 2.9, 1.3 Calculate the mean?

The titular conjecture was most likely put forth in the 1930s by Lothar Collatz.

Odd numbers are those that cannot be evenly divided by two. It cannot be evenly split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers. Odd numbers satisfy the congruence when divided by two, leaving a residue of 1. A number's parity indicates how odd it is; an odd number has parity 1, whereas an even number has parity 0.

Given

The titular conjecture was most likely put forth in the 1930s by Lothar Collatz.

The issue seems like a practical joke.

Pick any number you like. Add 1 and multiply it by 3 if it's an odd number.

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Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation. We can draw the translation in the coordinate plane if we know which way and how far to move the figure.

The triangle can be translated in the following ways:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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Answer:

Senior citizen ticket: $9

Child ticket: $13

Step-by-step explanation:

This can be solved by creating a system of equations:

[tex]f(x)=7x+5y=128[/tex]

and

[tex]g(x)=8x+10y=202[/tex]

where x is the cost of a senior citizen ticket and y is the cost of a child ticket.

Solve equation 2 for 5y:

[tex]8x+10y=202\\10y=202-8x\\\frac{10y}{x}=\frac{202-8x}{2}\\5y=101-4x[/tex]

Substitute (101-4x) for 5y in equation 1:

[tex]7x+(101-4x)=128\\3x+101=128\\(3x+101)-101=(128)-101\\3x=27\\\frac{3x}{3}=\frac{27}{3}\\x=9[/tex]

Substitute 9 for x in equation 2:

[tex]8(9)+10y=202\\72+10y=202\\(72+10y)-72=(202)-72\\10y=130\\\frac{10y}{10}=\frac{130}{10}\\y=13[/tex]

A senior citizen ticket costs $9 and a child's ticket costs $13.

To check these values, insert them into the equations:

[tex]128=7(9)+5(13)\\128=63+65\\128=128[/tex]

and

[tex]202=8(9)+10(13)\\202=72+130\\202=202[/tex]

Answer:

The Eastern Continental Trail is 5,376 miles and the Erie Canalway Trail is 384 miles

Step-by-step explanation:

I took 5,760 divided it by 15 and got 384, I then subtracted 5,760 by 384 and got 5,376

The probability it rains on both days is 0.175

From the question, we have the following parameters that can be used in our computation:

P(Rain) = 0.5

P(Rain next day) = P(Rain) - 0.15

The probability it rains on both days is then calculated as

P(Rain both days) = P(Rain next day) * P(Rain)

Substitute the known values in the above equation, so, we have the following representation

P(Rain both days) = 0.5 * (0.5 - 0.15)

Evaluate

P(Rain both days) = 0.175

Hence, the probability is 0.175

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Answer:

y = x + 2

Step-by-step explanation:

Each y value is 2 greater than the x value

Partial disability, according to SSS, is the whole and irreversible loss of a physical portion. An individual can still do their work to some extent despite the condition. Any loss of these body parts or senses qualifies as a partial disability for SSS benefits: only one. One-hand.

In the Philippines, the Social Security System is a government-run social insurance program for employees in the private, public, and unorganized sectors. Republic Act No. 1161, also known as the Social Security Act of 1954, is what created SSS. Later, in 1997, Republic Act No. 8282 changed this statute.

The person must have made at least 36 monthly payments before the semester of incapacity in order to be eligible for a monthly disability pension. If there are less than 36 monthly contributions, the recipient receives a lump sum payment.

"Permanent partial disablement" refers to a permanent disability that limits an employee's ability to earn money. According to the Second Schedule, partly permanent disability results;] "Permanent Total Disablement" ((15B)) refers to such a disablement. National Government Act. 0 Citations, 394 Citations.

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Answer:

m = 3/13

Step-by-step explanation:

The Slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 3 and the x increase by 13, so the slope is

m = 3/13

Answer:

Step-by-step explanation:

To find the slope of the line that passes through the points (-4,5) and (9,8), we can use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

= (8 - 5) / (9 - (-4))

= 3 / 13

= 0.231

Therefore, the slope of the line that passes through the points (-4,5) and (9,8) is 0.231.

By using Akaike Information Criterion(AIC) to compare various models , We need to consider 16 models to find the one with lowest AIC.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.

A mathematical tool for assessing how well a model matches the data it was derived from is the Akaike information criterion (AIC).

It's formula is:

AIC=2k-2ln(L)

predictors=independent variables=3

k=independent variables+1=4

Categorical variable= 4 levels

Total number of models to be considered = 4 * 4 =16

Since, Every layer (characteristics of variable) must interact with the predictors variable to calculate AIC and find the lowest one.

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