The graph shown here is the graph of which of the following rational
functions?

Applying the area of a rectangle, the width of the walkway (x) is: 7 feet.

What is the Area of a Rectangle?

Area of a rectangle = (length)(width)

Total area of the pool and walkway = 621 sq. ft

Length of the pool and walkway = 13 + 2x

Width of the pool and walkway = 9 + 2x

Thus, we will have the equation of the total area as:

(13 + 2x)(9 + 2x) = 300

4x² + 44x + 117 = 621

4x² + 44x + 117 - 621 = 0

4x² + 44x - 504 = 0

Factorize

(x - 7)(x+18) = 0

x = 7

or

x = -18

The width, x, cannot be negative, so, the width of the walkway (x) would be 7 feet.

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An equation is given as y=3x+c, an equivalent equation can be created by by solving for c in terms of y and x as y-3x.

An equation is given as y=3x+c , the concept that can be used to find the expression of c is the subject of the formular.

It should be noted that the  subject of a formula is the variable that is being worked out which is been recognised as the letter on its own on one side of the equals sign.

y=3x+c

c= y-3x

Then solving for c in terms of y and x will give us (y-3x)

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The required mean of the given data is 5.71.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.

The term "average" is frequently used to describe this measure of central tendency.

So, we have the data set:

2, 2, 4, 6, 8, 8, 10

Mean formula: Sum of terms / Number of terms

Now, calculate the mean as follows:

Mean: Sum of terms / Number of terms

Mean: 40 / 7

Mean: 5.71

Therefore, the required mean of the given data is 5.71.

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As our sample size is large and grade point average follows normal curve, we use parametric test.

The normal curve is a statistical measurement which refer that the available data presented in a large number close to the mean value.

The test is used to determine an approximate value of a set of data.

hence, we use parametric test for determining an approximate value.

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Answer:

corrine got 66006 vote

bill got 53450 vote

Answer:

Bill Randall= 53450 votes.

Corrine Brown= 66006 votes.

Step-by-step explanation:

Bill Randall = X

Corrine Brown = 1x

Bill Randall= x+1x+12556=119456

2x+12556=119456

2x=119456-12556

2x=106900

x=106900/2

x=53450

Corrine brown = 53450+12556

                        = 66006

Pascal's law statement states that pressure is equal to the force divided by the area on which it acts.

According to Pascal's law, pressure applied to a fluid inside of a container will be transmitted without a change in magnitude to every point within the fluid as well as the container's walls. Any point in the fluid experiences equal pressure in all directions.

The force multiplied by the surface area on which it acts produces pressure. Pascal's principle states that a pressure increase on one piston in a hydraulic system causes an equal increase in pressure on another piston in the system.

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3 to 1 slope means, there are three horizontal units for every one vertical unit.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

That is to say,

"Ratios like 3:1 are used to represent slopes. This indicates that there is a 1 unit (foot or meter) vertical shift, either up or down, for every 3 units (feet or meters) of horizontal distance."

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The term "infinity" in mathematics refers to something that is bigger than a natural number.

Given that,

We have to find what is infinity means.

We know that,

Something that has no beginning is said to be infinite. It is generally something that has no restrictions. It is a condition in which there are no boundaries in terms of time, space, or any other kind of quantity.

Infinity is denoted by ∞.

If there is a one-to-one relationship between a set of numbers and a suitable subset of itself, that set can be said to be infinite.

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The distance driven is a linear function of the hours traveled, due to the constant addition every time the number of hours is increased by one.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

The points of the function in the table are given as follows:

(1,55), (2,110), (3, 165), (4,220).

(time input, distance output).

The increases to the output when the input time is increased by one are given as follows:

As the increases are constant, the distance driven, in fact, is a linear function of the hours traveled.

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Answer: 2% is equivalent to 1/50

Step-by-step explanation:

We first need to divide the numerator by the denominator.

1 ÷ 50 = 0.02

Once we have the fraction in a decimal format, the answer is then multiplied by 100 to get the correct percentage:

0.02 × 100 = 2%

A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

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Therefore , the given expression of the problem √2 = 2 is a false statement the true statement is √2 ≠ 2.

The number is derived by multiplying the square root of a positive integer by itself.

For instance, the square root of 25 is 5, since 5 x 5 is 25.

As you can see, 5 is also the square root of 25 because (5) (5) = 25.

The square root of a number is always represented by the symbol, which is √.

Here,

The square root symbol, which has the value of 1.414, is used to symbolize the square root of 2, also known as root 2.

Mathematicians frequently utilize this number.

Because Root 2 has an unlimited number of decimals and cannot be stated as a fraction, it is an irrational number.

and 2 has a value of 2.

Thus,

=> √2 ≠ 2

as

=> 1.414 ≠ 2.00

Therefore , the given expression of the problem √2 = 2 is a false statement the true statement is √2 ≠ 2.

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On solving the provided question, we can say that - there are 67 numbers less than 100 are divisible by 3

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

= n(A ∪ B)

= n(A) + n(B) - n(A ∩ B)

= 33 + 50 - 16

= 67

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The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. The two roots can be calculated using the quadratic formula.

The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. This can be seen by calculating b² - 4ac, which in this case gives (6² - 4*1*9) = 36 - 36 = 0. A discriminant of zero or higher means that the equation has two real roots. The two roots can be calculated using the quadratic formula, which is x = [-b ± Â√(b² - 4ac)] / 2a. In this case, a = 1, b = 6, and c = 9, so the formula becomes x = [-6 ± Â√(6² - 4*1*9)] / 2, which simplifies to x = [-6 ± Â√0] / 2, or x = [-6 ± 0] / 2. So the two roots are x = -3 and x = -3, which means that the equation has two equal real roots.

x² + 6x + 9

b² - 4ac = (6² - 4*1*9) = 36 - 36 = 0

x = [-6 ± Â√(6² - 4*1*9)] / 2

x = [-6 ± Â√0] / 2

x = [-6 ± 0] / 2

x = -3 and x = -3

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Answer: 216 small balls

Step-by-step explanation:

The volume of a ball:

                                [tex]\displaystyle\\V=\frac{4}{3} \pi R^3[/tex]

Let us calculate the volume of a big metallic ball:

[tex]\displaystyle\\V_{big}=\frac{4}{3} (3)(3^3)\\\\ V_{big}=4(27)\\\\V_{big}=108 \ cm^3[/tex]

Now let us calculate the volume of a big small ball:

[tex]\displaystyle\\V_{small}=\frac{4}{3} (3)(0.5^3)\\\\ V_{small}=4(0.125)\\\\V_{small}=0.5 \ cm^3[/tex]

Thus, the number of identical small balls should work:

[tex]\displaystyle\frac{V_{big}}{V_{small}} =\frac{108}{0.5} \\\\\frac{V_{big}}{V_{small}} =216\ units[/tex]

Minimum Increment operations to make Array unique

The UNIQUE function will return an array, which will spill if it's the final result of a formula. This means that Excel will dynamically create the appropriate sized array range when you press ENTER .

ArrayList is like an array behind the scenes as it’s backed by an array of type java.lang.Object in java.

Normally arrays are fixed in size which means the number of elements that can be added are fixed and cannot be increased once created. ArrayList can dynamically increase in size once the array that backs is full so, these way we won’t encounter runtime exceptions.

When we say list.get(0), it’s equivalent to array[0]. It can be said the ArrayList is a kind of more convenient way to use dynamic arrays.

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The total cost for the meal with tax and tip is $22.26.

This can be calculated using the following formula:

Total Cost with Tax and Tip = Meal Cost + (Meal Cost * Sales Tax Rate) + (Meal Cost * Tip Rate)

In this case, the formula would be:

Total Cost with Tax and Tip = 17.00 + (17.00 * 0.07) + (17.00 * 0.18)

This simplifies to:

Total Cost with Tax and Tip = 17.00 + 1.19 + 3.06

Which yields a final total cost of 22.26.

To explain in more detail, the meal cost is the original cost of the meal, which in this case is 17.00. Then, the sales tax rate is applied to the meal cost, which is 7% or 0.07. This gives us an additional cost of 1.19 (17.00 * 0.07). Lastly, the tip rate is applied to the meal cost, which is 18% or 0.18. This gives us an additional cost of 3.06 (17.00 * 0.18). Adding the meal cost of 17.00, the tax cost of 1.19, and the tip cost of 3.06 together gives us a total cost of 22.26.

Therefore, the total cost for the meal with tax and tip is $22.26.

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Answer:

its a commutative property becaus its just changing the order

The age of the son is 10 years old.

Lets simplify the above problem ,

Let assume man's age = a

Let assume son's age = b

If  a man is 4 times as old as his son, then

=> a= 4b

In 5 years, he will only be 3 times as old as his son, then

= a+5

= 3(b+5)

Apply substitution method :

4b+5

=3b+15

b=10

a =40

Hence the son age is 10 years old.

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The 12 types of sets are empty set, singleton set, finite set, infinite set, subset, equal set, universal set, power set, proper subset, superset, equivalent set and proper superset.

An empty set does not contain any element, while a singleton set contain only one element.

If the number of elements in  a set is finite, the set is a finite set. If the number of elements in  a set is not finite, that is not countable it is an infinite set.

A set, say A contain only elements of another set, say B but not necessarily all elements, than set A is a subset of set B.

Whenever a set A is a subset of set B, we say the B is a superset of A. If A and B are two sets, then A is called the proper subset of B if A is a subset of B but B is not a subset of A i.e., A ≠ B.

If a set contains all and only elements of another set, then both set are said to be equal sets.

A universal set contains all elements of related sets.

Power set is the collection of all subsets of a particular set.

The set B is the proper superset of set A, then all the elements of set A are in B, but set B must contain at least one element which is not present in set A.

Equivalent sets are sets that have same number of elements.

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Answer:

Step-by-step explanation:

value of y is 87*

because linear pair always sum up to give 180*

we know 93+y=180

so y=180-93=87

y= 87°

180-93 = 87

The fraction of the instructions that used the word off is [tex]\frac{9}{25}[/tex]

The statistical mode of a set of numbers is the number that occurs most frequently in the set. In the set {9, 10, 6, 5, 6}, the number 6 occurs twice, which is more than any other number. Therefore, the mode of this set is 6.

The field of statistics, which is applied mathematics, encompasses the gathering, describing, analyzing, and drawing of conclusions from quantitative data. The fundamental mathematical ideas in statistics include calculus of differential and integrals, linear algebra, and probability theory.

When attempting to estimate the population of a town, it is vital to determine the percentage of its residents who watch TV. This context makes reference to the sample, which is a condensed selection from the population.

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Based on the given task content; the percent chance is 1 out of 20 is 5%.

Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.

The percent chance is 1 out of 20

= 1/20 × 100

= 0.05 × 100

= 5%

Un conclusion, 5% is the percent chance is 1 out of 20

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Answer:

Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. ...

Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

At the y-axis intercept, the value of x = 0      <==== put '0' in for 'x' and calculate the y-axis intercept

The nature of the roots of a quadratic equation is known by a value known as the discriminant,  which is calculated by seeing the equation and comparing it with the standard equation which is given by -

ax^2 + bx +c , where a , b , c are constants .

The root of the equation is given by -

x= [(-b )± (b^2 - 4ac)] / 2a

Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .

This discriminant is the defining factor of the nature of the roots.

Now, here arise three cases-

(i) If (b^2 - 4ac) > 0, the roots are real and distinct .

(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.

(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.

For example , we have an equation x^2 + 2x + 1.

Here, a =1, b=2 and c=1.

Putting these values in the discriminant , we get -

b^2 - 4ac = 4-4(1)(1) = 0.

So, the roots of the equation are real and equal i.e. x=2,2.

Hence, it is the discriminant which determines the nature of roots.

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Answer:

m=-2

Step-by-step explanation:

Recall slope (m) can be found using the following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For this problem, let:

[tex](x_1,y_1)=(-9,-4)\\(x_2,y_2)=(-3,-16)[/tex]

So,

[tex]m=\frac{(-16)-(-4)}{(-3)-(-9)}\\m=\frac{(-16)+4}{(-3)+9}\\m=\frac{-12}{6}\\m=-2[/tex]

Let x= 3^4. So the value of given expression after applying power rule is x=81.

What is meant by power?

How many times you should multiply a number depends on its power. Exponents and indices are other names for powers. For instance, 82 may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."

What is meant by n^5 where n can be any number?

By n^5 means n^5=n*n*n*n*n that is multiplying n five times.

3^4=(3^2)^2

=(9)^2

=81

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Generally it is not possible. But if someone applying for early retirement after being forced to leave their jobs due to an illness or injury. In order to help them pay their costs until their SSDI claim is approved and the waiting period for those benefits has passed, they can start collecting early retirement payments.

Generally speaking, it is not possible to receive both Social Security retirement benefits and Social Security Disability Insurance (SSDI) at the same time. However, if you fulfill the severe financial requirements while receiving SSDI or retirement payments from Social Security, you can be eligible for Supplemental Security Income (SSI).

To fill the gap between when someone must leave the working due to a disability and when they can receive retirement benefits, the Social Security Administration (SSA) established the SSDI program. Because of this, there is only one option to get SSDI and retirement benefits at the same time.

This happens when a person chooses to retire early between the ages of 62 and their full retirement age but is later granted SSDI payments. Some people do this on purpose by applying for early retirement after being forced to leave their jobs due to an illness or injury. In order to help them pay their costs until their SSDI claim is approved and the waiting period for those benefits has passed, they can start collecting early retirement payments.

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