y is five times X +15

The domain of the rational function  [tex]\frac{x^3 + 5x^2 + 3x - 9}{x^2 -x - 2}[/tex] is:

D: {x ∈ R| x ≠ -1, 2}

The domain will be the set of all real numbers, minus these ones that make the denominator equal to zero.

The denominator will be zero when:

x² - x - 2  =0

Using the quadratic formula we will get:

[tex]x = \frac{1 \pm \sqrt{(-1)^2 - 4*1*-2} }{2*1} \\\\x = \frac{1 \pm 3}{2}[/tex]

The two solutions are:

x = (1 + 3)/2 = 2

x = (1 - 3)/2 = -1

If the numerator is not zero on these values, then we need to remove them from the domain.

When x = 2 the numerator is:

2³ + 5*2² + 3*2 - 9 = 25

When x = -1

(-1)³  + 5*(-1)²  + 3*-1 - 9 = -8

Neither of these is zero, so we need to remove x = -1 and x = 2 from the domain, then the domain is:

D: {x ∈ R| x ≠ -1, 2}

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a. The table represents a function.

b. The domain is given as follows: {1, 2, .., 12 AM, 1, 2, ... , 12 PM).

c. The range is given as follows: {1, 2, 3, ..., 24}.

To obtain whether a relation represents a function, we need to observe if each input is mapped to only one output.

This table gives the conversion of hours in the AM-PM format to hours in the military format. Each hour in the AM-PM format has only one equivalent hour in the military format, that is, each input is mapped to a single output, hence the table in fact represents a function.

The domain of a function is the set that contains all the input values of the function, hence for this problem the domain is the set of hours in the AM-PM format.

The range of a function is the set that contains all the output values of the function, hence for this problem the range is the set of hours in the military format.

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The number of goats sleep in Room 1 is 6, Room 2 is 7 and in Room 3 is 8.

A linear equation can also be generated by equating to zero a linear polynomial over some field and extracting the coefficients.

The values that, when substituted for the unknowns, make the equality true are the solutions to such an equation.

With two variables, each solution can be understood as the Cartesian coordinates of a Euclidean plane point. This is where the name "linear" comes from when describing these types of equations.

Given total goats=21

Let the goats in room 1 be x.

Then, in the second room be x+1

And in the third room be (x+1)+1

x+(x+1)+(x+2)=21

3x+3=21

3x=18

x=6

Therefore, room 1=6

Room 2=7

Room 3=8

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Answer: The number of goats sleeping in Room 1 is 6, Room 2 is 7 and Room 3 is 8.

What is a linear equation?

A linear equation can also be generated by equating to zero a linear polynomial over some field and extracting the coefficients.

When substituted for the unknowns, the values that make the equality true are the solutions to such an equation.

With two variables, each solution can be understood as the Cartesian coordinates of a Euclidean plane point. This is where the name "linear" comes from when describing these types of equations.

Given total goats=21

Let the goats in room 1 be x.

Then, in the second room be x+1

And in the third room be (x+1)+1

x+(x+1)+(x+2)=21

3x+3=21

3x=18

x=6

Therefore, room 1=6

Room 2=7

Room 3=8

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Step-by-step explanation:

the rate at which water is being pumped into the tank in cubic centimeters per minute. is 1508527.582 cm³/min

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 8900 cm³/min,

dV/dt = k - 8900

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 11 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

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By using unitary method, it can be calculated that

For $28, 84 copies can be sold

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here, unitary method is used

For $6, 18 copies can be sold

For $1, [tex]\frac{18}{6}[/tex] copies can be sold

For $1, 3 copies can be sold

For $28, 3 [tex]\times[/tex] 28 copies can be sold

For $28, 84 copies can be sold

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Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

What is the average?

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Henry scored 85, 76, 84, and 69, and let's suppose he scored 'x' marks in the fifth exam.

Average = sum of all marks/total number of exams

  80 =(85 + 76 + 84 + 69 + x)/5

 80 = 314 + x/5

 80 * 5 = 314 + x

 400 = 314 + x

  x = 400 - 314

  x = 86

Hence, Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

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As there are 60 minutes in an hour and 24 hours in a day, there are 6 days as well as 144 days in 8640 minutes.

A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

There are 60 minutes in an hour,

=8640/60

=144 hours

There are 24 hours in a day,

=144/24

= 6 days

There is 6 days as well as 144 days in 8640 minutes as there are 60 minutes in an hour and 24 hours in a day.

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The probability of rolling a winning combination will be 7/12 as the winning combination is 21 and Total combination will be 36.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. By dividing the number of positive outcomes by the entire number of potential outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.

Here,

If the first die is red and the second one is green, then the sample space S is the following:

S=

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2, 1), (2,2), (2,3), (2,4), (2,5), (2,6), (3, 1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5, 1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)

Hence n(S)=36.

Let's list the losing combinations:

E={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 1),

(2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6,5)}

n(E)=15

There are 36 total possiblities.

Out of which, winning probability is 21.

=21/36

=7/12

Given that the winning combination is 21 and the total combination is 36, the chance of rolling a winning combination is 7/12.

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Answer:

y=1/2x+5.5

Step-by-step explanation:

When the (∂z/∂x) is 0, the partial derivative (∂z/∂y) will be equal to the total derivative dz/dy.

What is Total Derivative?

The overall change in the dependent variable as a result of changes in all the independent variables is known as the total derivative of a function of multiple variables.

Given that,

A function z(x, y)and its partial derivative (∂z/∂y) is x.

We know that,

total derivative (dz) = (∂z/∂x) dx + (∂z/∂y) dy

here, (∂z/∂y) = x

So, The dz will be equal to (∂z/∂y) dy only if  (∂z/∂x) dx = 0.

hence, (∂z/∂x) should be 0.

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The main difference between qualitative and quantitative data sources is qualitative is the categorial type and quantitative is a type of numerical.

What are the sources of data in mathematics?

In statistics, there are two sources of data. Census data and officially conducted surveys are examples of data that is gathered for some official purposes and are referred to as statistical sources. Non-statistical sources refer to the data that are collected for other administrative purposes or for the private sector.

These are the differences between qualitative vs. quantitative data:

Quantitative data is numbers-based, countable, or measurable. Qualitative data is interpretation-based, descriptive, and related to language.

Quantitative data tells us how many, how much, or how often in calculations.

Qualitative data can help us to understand why, how, or what happened behind certain behaviors.

Quantitative data is fixed and universal. Qualitative data is subjective and unique.

Quantitative research methods are measuring and counting. Qualitative research methods are interviewing and observing.

Quantitative data is analyzed using statistical analysis. Qualitative data is analyzed by grouping the data into categories and themes.

Hence, the main difference between qualitative and quantitative data sources is qualitative is the categorial type and quantitative is a type of numerical.

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The total distance is 13 units he ran during these sessions

The length along a line or line segment between two points on the line or line segment.

From the line plot, we have the following frequency table:

Distance   Frequency

0                    0

1/2                  4

1                     3

[tex]1\frac{1}{2}[/tex]                    1

2                    2

[tex]2\frac{1}{2}[/tex]                   1

3                    0

The total distance from the line plot is then represented as

Total distance = Sum of the product of distance and frequency

Total distance = (0×0) + (1/2 × 4) + (1 × 3) + ([tex]1\frac{1}{2}[/tex]  × 1) + (2 × 2) + ([tex]2\frac{1}{2}[/tex]  × 1) + (3 × 0)

Total distance = 13

Hence, the total distance is 13 units he ran during these sessions

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The measure of angle 'a' is 64.8°.

What is supplementary angles?

Two angles are considered to be supplementary if their sums total 180 degrees.

For instance, angle 130° and angle 50° are supplementary angles since the sum of these two angles is 180°.

The given angle is a = 115.2°.

We have to find the angle 'b' supplementary to the angle 115.2°.

Since, sum of supplementary angles is 180 degrees.

⇒ a + b = 180°

115.2 + b = 180°

Subtract 115.2° from both sides,

b = 180° = 115.2°

b = 64.8°

Hence, the measure of angle 'b' which is supplementary to angle 'a' is 64.8°.

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As t increases the curve is changing according to the plot points given by the parametric equations.

Define parametric equations?

The coordinates of the points that make up a geometric object, such as a curve or surface, are frequently expressed using parametric equations; in this case, the equations are collectively referred to as a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. It describes a collection of numbers that represent functions with one or more independent variables. The parameters used here are the independent variables. For the representation of the coordinates that make up geometric objects like curves and surfaces, parametric equations are used. Additionally, a curve that is not a function can be drawn using parametric equations.

The equations are

x=1-t²

y=2t-t²,-1≤t≤2

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Answer: 9/4

Step-by-step explanation:

1 1/8 divided by 1/2 can be rewrite as

=9/8 divided 1/2

=9/8 timed 2/1

=18/8

= 9/4

If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!

Answer:

y=-1x+3

Step-by-step explanation:

Find the equation of a line given the slope m = -1 and the point P = (-12 , 15)

Now, the y-intercept is b=y1−m⋅x1

b = 15 - (-1) ⋅ (-12) = 3

Finally, the equation of the line can be written in the form y=mx+b.

y = -1x + 3

Slope-intercept form is:

y = -1x + 3

Point-slope form is:

y - (15) = -1 ⋅ ( x - (-12))

If you want to check if right then:

Input the point given it should give you the y output if the equation of the line is correct.

-1x-(12)=12 and then add 3 and you get 15. It is therefore correct (-12,15).

I hope this helps!^^

Variable location is an example of a lurking variable in a study of medicine to remove the redness in eyes when tested in a group of 100 students. The statement is true.

Hidden variable is a variable that has a connection (e.g., may be correlated) with the answer and the explanatory variable but is neither the explanatory variable nor the response variable. Although it is not taken into account in the study, it might affect how the variables are related.

A hiding variable may misidentify a significant correlation between variables or may conceal the real correlation. A research scientist might, for instance, look at how nutrition and exercise affect someone's blood pressure. Smoking status and stress levels are additional factors that also influence blood pressure.

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The expression equivalent to the given expression will be x+y+3(1+y).

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,( x + 3) +4y

We have to write the equivalent expression for the given expression,

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered.

=( x + 3) +4y

=x+3+4y

=x+3+y+3y

=x+y+3+3y

=x+y+3(1+y)

Thus, the expression equivalent to the given expression will be x+y+3(1+y).

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Answer:

D

Step-by-step explanation:

24cd-36c²d = (4×6)c×d-(4×9)c×c×d

Then we take the common numbers and variables

4cd(6-9c) and to check our answer we can distribute 4cd to get:

4cd×6-(4cd×9c)

24cd-36c²d

After printing the long pdf Document of 47 pages , the remained balance in Fathi's printing account is -$4.90 ..

In mathematics, a basic algebraic operation is any of the common arithmetic operations, including addition, subtraction, multiplication, division, raising integers to powers, and taking square roots.

We have given that,

Total or initial balance of fathi's printing account

= $1.10

Each sheet of paper reduce his balance by $0.25..

Total number of pages in pdf document

= 47

He wants to print this pdf document.

When he print both sides of paper then it reduce the counts of paper used for printing the pdf.

That's if he print only one side then he will print 47 pages but now, he print on both sides .

so, total pages used to print pdf Document= 47/2

= 23 both sided printed + 1 one side printed = 24 pages

Using all provided details, we get

After Fathi print, the balance in his printing account = Initial balance - 24 × balance reduce by each page print

= $1.10 - 24 × $0.25 = $1.10 - $ 6

= - $4.90

Hence, - $4.90 balance in his printing account.

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18 months of All-Star Library membership cost $76 in total.

For the given equation.

The sign-up fee for the library-all-star-members club = $40.

Let 'x' be the total number of months.

Let 'y' be the total cost.

Monthly fee = $2.

Then, the linear equation models is-

y = 2x + 40

Given that a particular club member has been a part of it for 19 months, we replace x with the number 19 as follows:

y = 2x + 40

y = 2 * 18 + 40

y = = 36 + 40

y = 76.

Thus, 18 months of All-Star Library membership cost $76 in total.

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The complete question is-

3. In order to become a member of the library-all-star-members club, there is a $40 sign-up fee and a $2 monthly fee. Write an equation in slope-intercept form that models this situation. Use equation you wrote in problem 3 to find the total cost of being an all-star library member for 18 months.

Answer:

Step-by-step explanation:

its x= 1

13-12=1

7-6=1

and i multiplied 13(1)-12 which equals one and 7(1)-6 which also equals one, the answers just have to match with each other

The value of [x] is equivalent to 9.5.

Given are two triangles ABC and DEF as shown.

Since AB is congruent to DE, then -

AB = DE

2x - 1 = 18

2x = 19

x = 9.5

Therefore, the value of [x] is equivalent to 9.5.

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The value of the expression, 13(a • b + a²) + 4, when a = 5 and b = -3 is: B. 134.

To find the value of an expression, we have to plug in the respective values for each of the variables given in the expression, then simplify.

Given the expression, 13(a • b + a²) + 4, where:

a = 5

b = -3

To find the value, substitute a = 5 and b = -3 into the expression:

13(5 • -3 + 5²) + 4

13(-15 + 25) + 4

13(10) + 4

= 130 + 4

= 134

The value is: B. 134.

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Answer:

Length=153 yards

Width=54 yards

Hope this helps! :)

Step-by-step explanation: (153*=306, 54*2=108, 306+108=414)

P=2l+2w                                              

P=414

L=3w-9

W=w

414=2(3w-9)+2w

414=6w-18+2w

414=8w-18

+18      +18

432=8w

/8

54=w

L=3(54)-9

L=162-9

L=153

Answer:

top

Step-by-step explanation:

In the bottom, y=5x for all of the columns. In the top, y=2x for all except third column, so it is not proportional.

Answer:

There are 48 pages in the whole book.

Step-by-step explanation:

We know that 36 is 3/4 of the book. To find the total number of pages, we have to divide 36 by 3. We know that is 12. Then, we have to multiply 12 by 4 to get the answer, 48.

Answer: There are not any roots for that equation.

Prediction interval is more relevant than confidence interval.

What is Prediction Interval?

A prediction interval is an estimate of the range within which a future observation will fall, with a particular probability, given what has already been observed, in statistical inference, more especially predictive inference.

Short term measures:

Undoubtedly, short-term decisions and actions serve as important starting points for both real accomplishments and symbolic commitments. Taking into account the challenges, assets, and weaknesses that have been identified, a number of immediate activities seem to have the highest chance of fostering intelligent growth in the long run.

Long term measures:

The phrase "Long-Term Performance Measures" refers to the performance metrics developed and employed by the Committee to evaluate the Company's performance and ascertain the quantity of Common Stock to be paid to the Participant at the end of a Restriction Period.

Here,

Prediction intervals must take into consideration both the random variation of the individual values and the uncertainty in predicting the population mean. Consequently, a prediction interval is always larger than a confidence interval. Additionally, as the sample size grows, the prediction interval won't condense to a single value.

Hence, Prediction interval is more relevant than confidence interval.

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There is insufficient evidence to support that bolts are too long or too short.

What is Mean and Standard Deviation?

Mean: Dividing the sum of all values in a data set by the number of values.

Standard Deviation: The standard deviation is a measure that summarizes how far away from the mean each observation is.

Given:

mean: 0.94cm

standard deviation = 0.31cm

Alright, so a manufacturer must test that these bolts are long as they come off the manufacturing line and he must readjust the machines if they're too long or too short. Consequently, sample 121V and sample mean are 0.94 cm. So we want to test whether or not these are actually equal to two, so are no hypothesis is that the mean is too and our alternative hypothesis, because it says that we have to recalibrate if they're too short or too long, is that the mean is not too we could probably go with the left tail test here because the sample mean is under but we'll be safer with a two tail test um just because the standard deviation may sway things.

So what we want to do next is compute the test statistic and that's gonna be a Z score and that's just supplied by X bar minus population mean over standard deviation over squared event. And we're using Z here because we have a high sample size and since we know the population standard deviation.

Hence, There is insufficient evidence to support that bolts are too long or too short.

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