Question 3 of 10
Which of the following is the product of the rational expressions shown
below?
2x²
x²-1

Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.

Statistical information made up of categorical variables—data that have been divided into categories—is known as categorical data. A set of grouped data is one of example. More specifically, countable qualitative data or quantitative data clustered within predetermined intervals could be used to create category data. The information is condensed into a probability table. However, the word "categorical data," which is used to describe data sets, is used when discussing data analysis. It should be noted that although the data set includes some categorical variables, it may also include non-categorical variables.

Categorical data is a collection of information that is divided into groups. I.e, if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical. This data is called categorical because it may be grouped according to the variables present in the biodata such as sex, state of residence, etc.

A. Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.

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An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.

Given that,

h(7)=329 and h(11)=553

Linear function, y = [tex]mx + c[/tex]

Let, h = y and [tex]x =x[/tex]

A function whose graph is a straight line and which is represented by an equation of the form y = mx + c where a and b are constants, m does not equal zero, and x is any real number.

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

So,

[tex]h(x)[/tex] = [tex]mx + c[/tex]

When,

[tex]x[/tex] = 7 , [tex]h(x)[/tex] = 329

( [tex]x_{1}[/tex] , [tex]h(x_{1} )[/tex] ) = ( 7 , 329 )      (Equation-1)

When,

[tex]x[/tex] = 11 , [tex]h(x)[/tex] = 553

( [tex]x_{2}[/tex] , [tex]h(x_{2} )[/tex] ) = ( 11 , 553 )         (Equation-2)

Linear function,

[tex]\frac{h(x)-h(x_{1} )}{x-x_{1} }[/tex] = [tex]\frac{h(x_{2} )-h(x_{1} )}{x_{2} -x_{1} }[/tex]

We can substitute equation -1 and 2

[tex]\frac{h(x)-329}{x-7}[/tex] = [tex]\frac{553-329}{11-7}[/tex]

[tex]\frac{h(x)-329}{x-7}[/tex] = 224/4

[tex]\frac{h(x)-329}{x-7}[/tex] = 56

[tex]h(x)[/tex] - 329 = 56 ( [tex]x-7[/tex] )

[tex]h(x)[/tex] - 329 = 56[tex]x[/tex] - 392

[tex]h(x)[/tex] = 56[tex]x[/tex] - 392 + 329

[tex]h(x)[/tex] = 56[tex]x[/tex] - 63

Therefore,

An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.

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A variable is an alphabet or phrase used to represent an unknown quantity, unknown value, or unknown number in mathematics.

The values of one or more independent variables determine the values of a single dependent variable in a mathematical connection known as a function. Function denotes a relationship between two variables where one influences expression the other (s).

Here,

Given :

=> 50 assembly kit  be y

and => 20 profit be x

Thus,

Equation is = > 50y + 20y = 15

In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically.

A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

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This is a false conclusion. Just because Marcelino did not win the game 2 days ago or yesterday, it does not necessarily mean he will win the game today. There could be many other factors at play that determine the outcome of the game.

This statement is referring to a hypothetical game and the outcome of it, but the conclusion that Marcelino will win today is not logically deduced from the information given (that Marcelino did not win 2 days ago or yesterday). The outcome of a game can be influenced by many factors such as the skill level of the players, the strategies used, and luck. Simply not winning in the past does not guarantee a win in the future.

This statement is not related to mathematics. It is a logical conclusion based on the given information about a hypothetical game, but the conclusion does not follow logically from the information provided.

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Z would ultimately have a value of 2, since 5 minus 7 equals 2.

x = 5; y = 7; z = x - y z = 5; y z = 7; z = 2;Consequently, z's final value is 2.

Given that x is 5 and y is 7, the final value of z would be 2. These two numbers are divided by two, giving the answer 2. Subtraction is the action of comparing two integers to determine their differences. In this instance, since x and y differ by 2, the ultimate value of z is also 2. The solution is 2, which can alternatively be written as 5 - 7 = 2. In this case, the ultimate value of z is 2, since the difference between x and y is 2, which can be found using the useful mathematical technique of subtraction.

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Answer:

x = 3

Step-by-step explanation:

Let's check

3^4 + 7(3)^2 - 144 = 0

81 + 63 - 144 = 0

144 - 144 = 0

0 = 0

So, x = 3 is the correct answer.

Factoring out negative 1 from the expression -4-(5+3) is -1(12).

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

A) 7+(-6)

= 7-6

= 1

2) -4-(5+3)

= -4-8

= -12

= -1(12)

3) -9-1

= -10

= -1(10)

4) 8-(-6)

= 8+6

= 14

5) 3+(-4+8)

= 3+4

= 7

Therefore, factoring out negative 1 from the expression -4-(5+3) is -1(12).

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Work Shown:

A = P*(1+r/n)^(n*t)

A = 3000*(1+0.0325/4)^(4*7)

A = 3762.91169916373

A = 3762.91

Oliver is farther from the station.

Let's call the initial distance from the station for Oliver and Roel as d1 and d2, respectively. The Law of Cosines states:

d1^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(30°)

d2^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(40°)

By solving the above equations, we can determine the distances d1 and d2. The hiker who is farther from the station will have the larger value of d1 or d2.

In this case, it can be seen that d1 > d2, meaning Oliver is farther from the station than Roel.

This is because the angle of 30° is larger than the angle of 40°, so the cosine of 30° is smaller than the cosine of 40°.

Therefore, Oliver is farther from the station.

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The equation that can be used to solve for y, the length of the room is;

y² - 5y = 750

The formula for the area of a rectangle is;

Area = L * W

where;

L is length

W is width

The width of the room is 5 feet less than the length of the room. Thus;

Width = Length - 5

If length is y, then;

Width = y - 5

Area = y(y - 5)

y(y - 5) = 750

y² - 5y = 750

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Answer:

D

Step by step explanation:

[tex]F = \frac{9}{5}C + 32[/tex]

The main objective is to isolate C and to make C the subject of the equation:

[tex]= F - 32= \frac{9}{5} C[/tex]

[tex]= C = \frac{5}{9} (F - 32)[/tex]

Now substitute the given value of F:

[tex]C = \frac{5}{9} (68-32)[/tex]

[tex]=C = \frac{5}{9} (36)[/tex]

[tex]= C = 20^{o} C[/tex]

Answer:

D. C = 5/9 ( F - 32 ) ; conversion: 68° F = 20° C

Answer:

The expression that represents the verbal phrase "One-fourth times a number n, minus thirty" is (1/4)n - 30.

The required interval for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
From the graph, the portion of the function below the axis shows the f(x) ≤ 0.
So the interval where f(x) ≤ 0, from the graph, is given as,
(-∞, -2) and (2, 7)

Thus, the required intervals for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).

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The expression x² + 6x + 9 / 4 ÷ 3x + 9 / 8 can be simplified as 2(x + 3) / x .

To simplify an expression means to write an equivalent expression which contains no similar terms. In other words, we have to reduce the expression to the simplest form.

Therefore,

x² + 6x + 9 / 4 ÷ 3x + 9 / 8

Let's convert the division sign to multiplication.

Therefore,

x² + 6x + 9 / 4 × 8 / 3x + 9

Let's factorise the numerators and the denominators expression

x² + 6x + 9 = (x +3)² = (x + 3)(x + 3)

3x + 9  = 3(x + 3)

Therefore,

(x + 3)(x + 3) / 4 × 8 / x(x + 3)

Hence,

(x + 3)(x + 3) / 4 × 8 / x(x + 3) = 2(x + 3) / x

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Answer:

(All given options are incorrect)

Correct answers: [tex]3^6[/tex] or [tex]9^3[/tex]

Step-by-step explanation:

There are several ways to write [tex]3\times3\times3\times3\times3\times3[/tex].

The first is as a power of 3. An exponent represents the number of times a number is multiplied by itself. This would be written as [tex]3^6[/tex].

The second is as a power of 9. Combining each pair of [tex]3\times3[/tex] gives:

[tex]9\times9\times9[/tex]  which is equal to [tex]9^3[/tex].

None of the given options are correct for  [tex]3\times3\times3\times3\times3\times3[/tex]. Please double check that your question and answer options are written correctly. Correct answer options would be [tex]3^6[/tex] or [tex]9^3[/tex].

The rule for the pattern is to add 6 to each number.

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Jason wants to know if student grade point average (GPA) is impacted by being involved in a romantic relationship. In Jason's study, GPA is the dependent variable.

The variable that is changed during a scientific experiment is known as an independent variable. In a laboratory experiment, an independent variable is one that can be changed or manipulated. It will stand in for the reason or cause behind an outcome.

The variable being evaluated or analyzed during a laboratory experiment is known as the dependent variable. It is obvious that the dependent variable relies on the independent variable. While a result, we can now see and note changes in the dependent variable as the experimenter modifies the independent variable.

A controlled variable is one that is maintained constant throughout a scientific experiment. As a result, we also understand the controlled variable to be a constant variable or occasionally just a "control."

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The complete question is:

Jason wants to know if student grade point average (GPA) is impacted by being involved in a romantic relationship. In Jason's study, GPA is the:

a. Independent Variable

b. Dependent Variable

c. Control Variable

d. None of the Above

Answer:

Step-by-step explanation:

i wish i knew! i wish i knew you wanted me

The total differential to estimate the maximum error in the calculated volume of the cylinder is 200.96.

The base radius of a right circular cylinder are measured as 8 cm.

The height of a right circular cylinder are measured as 16 cm.

The possible error in measurement of as much as 0.2 cm each.

We have to calculate the maximum error in the calculated volume of the cylinder.

The formula of volume of cylinder is:

V = πr^2h

The value of dr = 0.2 and dh = 0.2. So;

dV(max) = ∂V/∂r dr + ∂V/∂dh dh

dV(max) = ∂(πr^2h)/∂r dr + ∂(πr^2h)/∂dh dh

On differentiating

dV(max) = 2πrh dr + πr^2 dh

r = 8 cm, π = 3.14 and h = 16 cm.

Now putting the value

dV(max) = 2×3.14×8×16×0.2 + 3.14×(8)^2×0.2

dV(max) = 160.768 + 40.192

dV(max) = 200.96

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79.1 mL is equal to 0.0791 litres with correct significant figures.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

79.1 mL is equal to 0.0791 litres. To convert millilitres to litres, we divide the number of millilitres by 1000:

79.1 mL / 1000 = 0.0791 liters

So, 79.1 mL is equal to 0.0791 litres with correct significant figures.

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The mapping diagram does not show a function, because the input -1 is mapped into two different values.

A function is a relation that maps elements from one set (called the domain) into another set (called the range), such that each input can be mapped into only one value.

In this case, we have a relation that maps elements from set A into set B. And you can see that the element -1 is mapped into two different values ( which are 8 and 9), then the mapping does not repsent a function.

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Answer:

x^3 = 1000

Step-by-step explanation:

Answer: 380 ft

Step-by-step explanation: To find the length in between, you simply subtract the numbers.

1,515 - 1,135 = 380

Therefore, the ladder needs to be extended 380 ft.

Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

Given log 630 ≈ 1.898 and log 62 ≈ 0.387,

We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387

And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086

So, log 615 ≈ 2.086

In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.

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Answer:

f(x) = -4[tex]x[/tex] - 2 or y = -4[tex]x[/tex] - 2

Step-by-step explanation:

In this question, you should use the graph to write the function/equation in slope intercept form.

y = mx + b where m is the slope and b is the y intercept

To calculate the slope, you can use rise/run between any two points. I will use the points (-2, 6) and (0, -2). In these points, the "rise" would be -8 as that is the number of units they are away from each other vertically. It is negative because the line obviously has a negative slow as it is travelling from up to down. The run in this case would be 2 as that is the distance the two points are away from each other horizontally.

Then, substitute.

[tex]\frac{-8}{2}[/tex] = -4, so m = -4

Now we will find the b value.

B is the y-intercept, or what the y value of the coordinate of the point that the line touches the y-axis. The coordinate is (0, -2). Therefore, the b value is 2.

2³ × 3 × 5² is the prime factorization of the composite number 600.

Composite numbers are whole numbers that can be divided evenly by numbers other than 1 or themselves. For example, 4 is a composite number because it can be divided evenly by 1, 2, and 4. Other examples of composite numbers are 6, 8, 9, 10, 12, 14, 15, and so on.A composite number is a positive integer that has more than two divisors. It is the product of two or more prime numbers. Examples of composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, 16 and so on.

2³ × 3 × 5² = 2 × 2 × 2 × 3 × 5 × 5

= 600

Thus, 2³ × 3 × 5² is the prime factorization of the composite number 600.

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Answer: the initial value is 2 and the rate of change is 1.

Answer:

D. sign chart; zeros

Step-by-step explanation:

To fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes

A number system is defined as a system of writing to express numbers.

The term that completes the sentence and makes it grammatically and conceptually correct is "sign chart; zeros".

To fill out a function's sign chart; zeros and after each of the function's zeros, you will need to use test numbers before and after the zero to determine the sign of the function on each interval.

Hence, to fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes

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