3) Find the percentage change. State whether the change is an increase or decrease.
a)
A
Before: 34 shirts
Now: 62 shirts
b)
Original: 36.79
New: 22.88

The first of the three theorems below, known as the Angle-Angle-Side Theorem or AAS Theorem, asserts that two angles and a non-included side of a triangle must be congruent with the corresponding two angles and non-included side of another triangle for the triangles to be considered congruent.

What do you mean by congruent?

Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

Why are triangles congruent?

Two triangles are said to as congruent triangles if their dimensions and shapes match. Two congruent triangles remain congruent even if we flip, rotate, or otherwise alter one of the triangles.

                  Two triangles must have the same angles and, as a result, must be congruent if their sides are equal.

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The symbol "≪" means "much less than," and the symbol "≫" means "much greater than."

These symbols are used to express a strong inequality between two values. For example, if you wanted to say that the value of x is much less than the value of y, you could write "x ≪ y." Similarly, if you wanted to say that the value of x is much greater than the value of y, you could write "x ≫ y."

The symbols "≪" and "≫" are used in mathematics to express a strong inequality between two values. They are similar to the familiar inequality symbols ">" (greater than) and "<" (less than), but they indicate a greater degree of inequality.

For example, if you wanted to say that the value of x is much less than the value of y, you could write "x ≪ y." This means that x is much smaller than y, and the difference between the two values is significant. Similarly, if you wanted to say that the value of x is much greater than the value of y, you could write "x ≫ y." This means that x is much larger than y, and the difference between the two values is significant.

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The question is -

What does ≪ mean in math?

A four-sided geometric object called a trapezoid has one pair of opposing sides that run parallel to one another. Its parallel sides are represented by its two bases, while its non-parallel sides are represented by its two legs. The lateral sides of the trapezoid are another name for the legs.

 We must first locate the location of the trapezoid in order to determine where the grey patch of land will be after the 3 m walkway has been built. The following formula determines the area of trapezoid:

A = (b1 + b2)/2 * h

where h is the height, and b1 and b2 are the bases' lengths.

Inputting the values provided yields:

A is equal to (150m + 100m)/2 * 52m, or 125m * 52m, or 6500m2[tex]m^{2}[/tex].

After the walkway is built, the area of the grey piece of land is equal to the trapezoid's area minus the walkway's area. The walkway is 3 m by 52 m in size, or 156 [tex]m^{2}[/tex].

Therefore, 6500[tex]m^{2}[/tex] - 156[tex]m^{2}[/tex]   = 6344[tex]m^{2}[/tex] is the area of the grey patch of land once the walkway is built.

 So, the area of gray patche of land after construction of the walkway is 6344[tex]m^{2}[/tex].

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The mode for a particular set of observations is 5 since it occurs the majority of the time.

The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.

Here,

given set of observation:

5, 7, 8, 5, 7, 6, 9, 5, 10, 6

Mode is the number which occurs the highest time.

So here 5 occurs the highest times(3 times).

So,5 is the mode.

The mode for given set of observation is 5 as it occurs most time.

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The sum of first five or twelve term in the A.P given the value 60.

The term AP refers a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Here we have given that  A. P. 16,14,12,.

And we need to find the number of term to get the value of 60.

While we looking into the given question we have identified that the  common difference d of the A.P. is − 2

Here we also know that the terms of the A.P. are in descending order.

Now, we have to take n = 5  then then first 5 terms are 16,14,12,10,8.

Here we have identified that the sum is 60.

Similarly, here by taking n = 12 , then the last 7 terms ( 12 − 5 ) (12-5) are 6 , 4 , 2 , 0 , − 2 , − 4 , − 5 6,4,2,0,-2,-4,-5

Here we have identified that the sum of these seven terms is 0.

Therefore, sum of first 12 terms is also 60.

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Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary  when calculated using discriminant.

In mathematics, the number that results in the original number when it is multiplied by itself is called the root.

We can find nature of root using discriminant.

B² - 4AC = 0 ----> Roots are equal ,real & rational

B² - 4AC > 0 , and also a perfect square --> Roots are real , distinct & rational

B² - 4AC >0 ,but not a perfect square -----> Roots are real, distinct & irrational

B² - 4AC <0 , ---> Roots are imaginary

B² - 4AC >= 0 ---> Roots are real

Given 2x² - 4x + 3 = 0

Now, Calculate Discriminant,

Here

B = -4

A = 2

C = 3

==> B² - 4AC

= (-4)² - 4 * 2 * 3

= 16 - 24

= -8 < 0

Discriminant is negative

Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary .

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Interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

Higher Placement The College Board's Advanced Placement Program makes a college-level course and exam in United States Government and Politics available to high school students.

By organizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues, interest groups enable citizen participation in governance.

a group of individuals united by a shared interest or objective and working to sway public policy. group leaders. As adolescents gain knowledge, they frequently form their own groups. government.

Therefore, interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

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An inconsistent system of equations has no solution, whereas a consistent system has at least one solution.

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The point that satisfy linear quadratic  system of equation are (1,0) and (4,-3)

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

we have x + y = 1  ......... (i)

y=4x-3-x²...... (ii)

put y=4x-3-x² in equation (i)

x + y = 1

x + 4x - 3 - x^2 = 1

-x^2 + 5x - 4 = 0

(-x + 1)(x - 4) = 0

-x + 1 = 0      

-x = -1            

x = 1              

To find the value of y put x=1 in equation ii

 y = 4x - 3 - x^2

        y = 4(1) - 3 - 1^2

     y = 4 - 3 - 1 = 0

similarly.

x - 4 = 0        y = 4x - 3 - x^2

x = 4             y = 4(4) - 3 - 4^2

                    y = 16 - 3 - 16

                     y = -3

so the point that satisfy linear quadratic  system of equation are (1,0) and (4,-3)

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we have x + y = 1  ......... (i)

y=4x-3-x²...... (ii)

put y=4x-3-x² in equation (i)

x + y = 1

x + 4x - 3 - x^2 = 1

-x^2 + 5x - 4 = 0

(-x + 1)(x - 4) = 0

-x + 1 = 0      

-x = -1            

x = 1              

To find the value of y put x=1 in equation ii

y = 4x - 3 - x^2

y = 4(1) - 3 - 1^2

y = 4 - 3 - 1 = 0

similarly.

x - 4 = 0        y = 4x - 3 - x^2

x = 4             y = 4(4) - 3 - 4^2

                    y = 16 - 3 - 16

                    y = -3

so the point that satisfy linear quadratic  system of equation are (1,0) and (4,-3)

The expression 2x² + 7x + 3 can be factored as (2x + 3)(x + 1).So, the factored form of 2x² + 7x + 3 is (2x + 3)(x + 1).

To factor this expression, we can use the method of grouping. First, we rewrite the expression as:

2x² + 7x + 3

Then, we group the first and last terms and the middle term:

(2x² + 3) + (7x)

Next, we try to factor in the first group. Since 2x² + 3 can be rewritten as (2x + 1)(x + 3), we can factor the entire expression as:

(2x + 1)(x + 3) + (7x)

Finally, we can rearrange the terms to get the factored form:

(2x + 7x) + (1)(3)

This simplifies to:

(2x + 7x)(1) + (3)

Which is equal to:

(2x + 7x + 3)

And finally:

(2x + 7x + 3) = (2x + 3)(x + 1)

So, the factored form of 2x² + 7x + 3 is (2x + 3)(x + 1).

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Answer:

45n + 60 = 285

Step-by-step explanation:

n=# of weekday classes (this is an unknown value)

45n= each weekday class is 45 mins long, and when you multiply it by "n" which is the number of weekday classes, you will get a total number of minutes.

+60= we add 60 because that is how many mins it takes for the one class on the saturday. there is only one saturday class which means that you dont need a variable attached to it.

=285

this is the total number of mins from last week.

so, the total number of mins from last week has to equal the 60 min class plus however many 45 min classes there are that week.

45n+60=285

and if you really wanted to know how many weekday classes there were that week, n=5

Yes, the expression represented as negative 1 is a number

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

Is negative 1 a number?

As a general rule

Numbers are expressions, words and representations that have an arithmetic value

Using the above as a guide, we have the following:

negative 1

Mathematically, this can be represented as

-1

-1 is an integer

Hence, negative 1 is a number

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Answer:

The 3x+1 problem, also known as the Collatz conjecture, is a problem in mathematics that remains unsolved. It involves taking a positive integer and repeatedly applying a simple rule to it: if the integer is even, divide it by 2, and if it is odd, multiply it by 3 and add 1. The problem is to determine whether this process will always eventually reach the number 1, regardless of which positive integer is chosen as the starting point. Despite much effort by mathematicians, the 3x+1 problem remains unsolved.

Step-by-step explanation:

The 7 types of hazards in the home are Psychosocial  Risks,Physical

Dangers , Chemical Dangers, Biological risks, Constrained Areas,

Changing Equipment and Biohazards

Psychosocial  Risks

Physical dangers include a subgroup called psychosocial hazards. For some workers, these risks might be more severe or restrictive than for others. Poor management or a lack of feedback may be the cause of these risks.

Physical Dangers

Environmental and occupational hazards are two different categories of physical risks. These include unguarded machines, heat, cold, vibration, noise, and temperature extremes. Engineering controls can lessen some physical dangers.

Chemical Dangers

Toxic, flammable, explosive, self-reactive, oxidizing, or corrosive compounds are considered chemical dangers. Chemical risks can have negative health impacts and need special handling techniques and equipment.

Biological risks

Many workplaces have biological risks, which can be harmful to people. They include waste debris, food, fungi, food, hair, skin, and saliva.

Constrained Areas

Flammable gases can accumulate in small places. These gases tend to gravitate toward lower elevations, yet they can rise to the surface if a lid is closed or if they are hanging in the air.

Changing Equipment

For workers, the moving machinery hazard provides a distinct set of mechanical risks. Injuries caused by it include crushing, shearing, tangling, air being ejected, striking, abrading, and trapping.

Biohazards

There are many danger thresholds for biohazards. Agents of biohazard level I pose little risk to people. On the other hand, biohazard class II agents may be extremely contagious and may result in serious sickness if consumed or dispersed through the air.

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The value of the highlighted angle using the alternate angle theorem is 130°.

Alternate angles are angles obtained on the opposite sides of a transversal line that have the same size.

To calculate the value of the highlighted angle, we use the alternate angles theorem.

Note: Alternate angles are equal, From the diagram,the values of the two included angles are equal

Given:

Solve for x

Substitute the value of x into equation 1

Hence, the value of the highlighted angle is 130°.

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If the two triangles have the two congruent side, then the two triangles are congruent.

The term triangle refers the polygon with three side, three vertices, and three edges.

Here we have to prove that the  two triangles are congruent with two congruent sides.

As we know that the term congruent refers if their sides have the same length and angles have same measure.

Based on these theory, and we have to use the another theory called SAS (Side-Angle-Side) tell that any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, if then the two triangles are said to be congruent.

According to this rule, we have clearly identifies that the given two triangles are congruent.

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The total number of books Lori owns is 45.

Let x be the total number of books.

Mark owns 1/4 of x

Kevin own 1/3 of x

Kevin owns 9 more than Mark, so;

1/4x - 1/3x = 9

Multiplying both sides by 12

4x - 3x = 108

x = 108

The total number of books is 108

but;

Mark owns 1/4 of x = 1/4 x 108

Mark = 27

while Kevin owns 1/3 x 108

Kevin = 36

Therefore, Lori would own

108 - 36 - 27 = 45

Lori's number of books will be 45.

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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.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

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.

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Answer:

Step-by-step explanation:

New houses in a neighborhood are selling for $175,000. A down payment of $18,000 is

required and a 25-year mortgage at an annual interest rate of 8% is available. Find the

monthly mortgage payment.

Selling price = 175000

down payment = 18000

interest rate = 8% = 0.08

time = 25 years = 300 months (25 * 12)

First, we will compute the total interest for the loan

I = P * R * T

I = (175000 - 18000)(0.08)(25)

I = (157000)(0.08)(25)

I = 314000

Answer:

x = ± 2√5

Step-by-step explanation:

4x² - 5 = 75

4x² = 75 + 5

x² = 80 ÷ 4

x² = 20

√x² = ± √20

x = ± 2√5

Answer:1696.35

Step-by-step explanation:

if you time 7.89 by 215 you get 1696.35

The final answers are (1) y = 4.133 + 3.0333x, (2) y = 12.55015 and (3) The prediction made in part b) will be underestimated as the residual value will lie below 0 when x = 5.5.

What is linear regression?

Linear regression analysis predicts the value of one variable based on the value of another. The variable you wish to predict is referred to as the dependent variable. The variable you are using to predict the value of the other variable is known as the independent variable.

1) Give the equation of the least-squares regression line. Define any variables you use.

y = 4.133 + 3.0333x

The constant coefficient is what I used as the y-intercept.

2) Use the model from part (a) to predict the area covered by detergent at 5.5 seconds.

y = 4.133 + 3.0333(5.5)

y = 12.55015

3) The prediction made in part b) will be underestimated as the residual value will lie below 0 when x = 5.5.

Hence, the final answers are (1) y = 4.133 + 3.0333x, (2) y = 12.55015 and (3) The prediction made in part b) will be underestimated as the residual value will lie below 0 when x = 5.5.

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The triangles are congruent if there are two pairs of corresponding angles and one pair of corresponding sides.

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The examples of SAS (Statistical Analysis System) are Mathematical Programming

SAS is a statistical software suite developed by the SAS Institute for data management, advanced analytics, multivariate analysis, business intelligence, criminal investigations, and predictive analytics. It is used for

Examples of SAS are :

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The inequalities that match each region are given as follows:

a) x + y ≥ 5. (Option E).

b) y ≤ x + 2. (Option A).

c) y ≥ 4. (Option D).

For item a, we have that values to the right of the line are shaded, meaning that the line is the lower bound of the interval.

The line is decreasing and has an intercept of 5, hence it is given as follows:

y = 5 - x.

As the line is the lower bound of the inequality, the inequality is defined as follows:

y ≥ 5 - x

x + y ≥ 5.

For item b, the line has an intercept of 2, hence it is given as follows:

y = x + 2.

It is an increasing line, and the values to the right of the line are shaded, meaning that the line is the upper bound and the inequality is given as follows:

y ≤ x + 2.

For item c, the lower bound is the horizontal line y = 4, hence the inequality is described as follows:

y ≥ 4.

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The example of a  hypothesis is: a person is innocent until proven guilty. The statement is true

Here the given situation is

A person is innocent until proven guilty.

The hypothesis test is defined as the test in statistics whereby an analyst tests an assumption regarding a population parameter. In hypothesis test using the data from the different types of t sample and the determine the other parameters of the population

The null hypothesis is defined as the a statement of what the statistician expects NOT to find.

Here the given situation is a person is innocent until proven guilty. Therefore, it is a null hypothesis.

In hypothesis test we assume that null hypothesis until it is proven

Therefore, the given statement true

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The another root for the given polynomial is 3 + 2i.

A complex number is defined as a number containing both real and imaginary part which is written as x + iy. The conjugate of a complex number can be obtained by changing the sign of the imaginary part of the number. the product of a complex number and its conjugate is the square of its magnitude.

One of the complex roots of a polynomial is given as 3 - 2i.

Since, all the coefficients of the polynomial P(x) are real.

The another root should be the complex conjugate of the given root.

Thus, the other root is given as below,

3 + 2i

Hence, the additional root is given as 3 + 2i.

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For unbiased sample by data collection, The method to be used is Survey method.

To answer specified research questions, test hypotheses, and assess results, data collection is the act of acquiring and measuring information on variables of interest in a systematic and defined manner. All academic disciplines, including the humanities, social sciences, business, and natural and applied sciences, share the data collection component of research. Although techniques differ depending on the profession, the importance of ensuring accurate and truthful collection does not change.

The popular data collection methods are:

Survey method of data collection is to be used for collection of unbiased sample. It is so because while planning for a on-site gym for the employees, Survey conducted on the employees working would be the best method for data collection which will increase the efficiency for selection of gym hours.

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The probability that the mean of the above sample is $325,000 is 0.0079

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We know that, distribution of prices skewed to the right with mean $290000. Let this be  x.

Random sample of 100 sales so considering 100 as y.

Standard deviation is $145000 let is be w.

SD for $145000 for 100 random sample data is

z = [tex]\frac{w}{\sqrt{y} } }[/tex] = [tex]\frac{145000}{\sqrt{100} }[/tex].

normalcdf(325000,infinity,290000,14500) = 0.0079.

The probability that the mean of the above sample is $325,000 is 0.0079.

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The probability that the fourth marble Amy picks is black: This probability cannot be determined without knowing the total number of marbles and the number of black marbles.

The probability that, if Amy picks a black marble in the fourth attempt, she will pick a red or a black marble in the fifth attempt: This probability cannot be determined without knowing the total number of marbles and the number of red and black marbles.

Probability is a measure of the likelihood of an event occurring. To calculate the probability of an event, you need to know the total number of outcomes and the number of outcomes that are favorable to the event. For example, if there are 10 marbles in total and 4 of them are black, the probability that Amy will pick a black marble on the fourth attempt is:

Probability = Number of black marbles / Total number of marbles = 4/10 = 0.4

Similarly, if Amy picks a black marble in the fourth attempt and there are a total of 10 marbles, with 4 of them being black and 6 of them being red, the probability that she will pick a red or a black marble in the fifth attempt is:

Probability = (Number of red marbles + Number of black marbles) / Total number of marbles = (6 + 4) / 10 = 0.8

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