Equations with rational coefficients
Lisa had $20.50 to spend on eight pens. After buying them she had $2.90. How much did each pen cost? ​

The linear function in this problem is defined as follows:

y = -328.275x + 3142.5.

The number of CD's sold by year decreases by about 328 million per year. About 3143 million of CD's were sold in 2010.

The estimate for the year of 2019 is of: 188 million CD's.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients of the function are defined as follows:

Two points of the linear function in this problem are given as follows:

(2, 2485.6), (6, 1172.5)

The slope is given by the change in y divided by the change in x, hence:

m = (1172.5 - 2485.6)/4 = -328.275.

Then:

y = -328.275x + b.

When x = 2, y = 2485.6, hence the intercept b is obtained as follows:

2485.6 = -328.275(2) + b.

b = 2485.6 + 328.275(2)

b = 3142.5.

Hence the function is:

y = -328.275x + 3142.5.

2019 is nine years after 2010, hence the estimate is obtained as follows:

y = -328.275(9) + 3142.5 = 188 million CD's.

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If the scale factor is equal to one, then there wont be any change in the original shape

The scale factor is defined as the ratio of the original size of the shape to the new size of the shape.

There are three types of scale factors will be there, greater than one, equal to one and between 0 and 1

When the scale factor is greater than 1, then the shape will enlarge

When the scale factor is equal to 1, there wont be any change in original shape

When the scale factor is between 0 and 1, the shape will decrease the size

Therefore, there wont be any change in original shape when scale factor equal to one

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Mrs. Gilmore and Brianna are 17 feet apart.

Pythagoras theorem is one of the mathematical principles that can be applied to determine the value of the unknown side of a right angled triangle. Where a right angled triangle is one with one of its angles to equal [tex]90^{o}[/tex].

In the given question, sketching the distance apart of each person, it would form a right angled triangle.

Let the distance in feet between Mrs. Gilmore and Brianna be represented by d.

Then;

[tex]/Hyp/^{2}[/tex] = [tex]Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]d^{2}[/tex] = [tex]15^{2}[/tex] + [tex]8^{2}[/tex]

   = 225 + 64

   = 289

d = 17

Therefore, Mrs. Gilmore and Brianna are 17 feet apart.

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The zero of the graph is 8 and it represents the time taken for Bart to pass out the flyers i.e 8 minutes

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

The empty graph

Also from the question, we have the following equation

f(x) = 80 - 10x

This means that

The variable f is a function of x i.e. f(x)

To plot the graph, we represent the function f(x) on the y-axis

See attachment for the graph of the function

This is the point where the graph crosses the x-axis

This is represented a f(x) = 0

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

80 - 10x = 0

Add 10x to both sides

10x = 80

Divide both sides by 10

x = 8

Hence, the zero is 8 and it means that Bart passes out the flyers in 8 minutes

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The value of the correlation coefficient between exam 1 score and exam 2 score is -1.

Given:

suppose that every student in this class earns exactly twice as many points on exam 2 as on the exam 1.

what would be the value of the correlation coefficient between exam 1 score and exam 2 score = ?

1. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.

2. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.

3. the coefficient will be exactly one, it doesn't matter which score is higher.

4. the expected value will be 0 since there won't be any correlation between random values.

5. the coefficient will be -1 every high score is matched by a low score on the other test.

Hence we get the required answer.

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A strong negative linear association between two variables is scatter plot 4.

What is standard normal random?
We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.

Very dispersed and lacking in association is scatter plot 1.

Positive correlation may be seen in scatter plots 2 and 3.

Scatter figure #4 clearly illustrates a strong inverse relationship between the variables.

Hence the Correct answer is scatter plot 4.

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Answer:

6t^13-12t^12

Step-by-step explanation:

6t^12(t-2)

6t^12t+6t^12*-2

6t^12+1 +6t^12*-2

6t^13+6t^12*-2

6t^13-12t^12

The Equation for parallel line is: y= 4x - 13

The Equation for perpendicular line is: y= 1/4 x + 2

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

The passing point is (4, 3).

Now, the slope of given line

= Rise / Run

= 4 / 1

= 4

So, the slope for parallel line is 4 and for perpendicular line is -1/4.

Now, the line passes through (4, 3)

For parallel line

y= 4x+ b

3 = 4(4)+ b

3- 16 = b

b= -13

So, Equation for parallel line is: y= 4x - 13

For Perpendicular line

y= 1/4 x+ b

3 = 1/4(4)+ b

3- 1 = b

b= 2

So, Equation for Perpendicular line is: y= 1/4 x + 2

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The rules for an infinitive is:

(1) Noun forms include infinitives.

(2) Use of an infinitive is not appropriate if a preposition follows the verb.

(3) An infinitive may follow a common statement that ends with a preposition.

In the given question we have to wrote the rules for an infinitive.

There are certain fundamental guidelines for using infinitives.

(1) Noun forms include infinitives. They are the verb's subject if they are used before the main verb; if they are used after the main verb, they are the verb's object.

(2) Use of an infinitive is not appropriate if a preposition follows the verb.

(3) An infinitive may follow a common statement that ends with a preposition.

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Answer:

it is equal to 8.07

Step-by-step explanation:

Answer:

Step-by-step explanation:

To put in slope intercept form, isolate y.

4y = -2x +4

Further divide by 4 to isolate y.  What you do on one side of an equation, you also do on the other side.

4y/4 = -2x/4 +4/4

y = -1/2x +1

Equation of line having passing point (-2,5) and (2,-3) is  y − 5 = −2(x + 2).

Hence, option B is correct.

What do you mean by equation of line?

A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. A number of points that together form a line of axes, represented as a set of variables x,y, form an algebraic equation called the line equation.

Given passing points of line (-2,5) and (2,-3)

Equation of line having two passing points (a,b) and (c,d) is

y - b = [tex]\frac{d-b}{c-a}[/tex] (x - a)

So, equation of line having passing point (-2,5) and (2,-3) is

y - 5 = [tex]\frac{-3-5}{2+2}[/tex] (x + 2)

y - 5 = -2(x + 2)

y - 5 = -2x - 4

2x + y - 5 + 4 = 0

2x + y - 1 = 0

Therefore, equation of line having passing point (-2,5) and (2,-3) is  y − 5 = −2(x + 2).

Hence, option B is correct.

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The degree of the product of the two polynomial is 6.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² − 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Given that there are two polynomial.

The sum of two polynomials has degree 4.

Thus the degree of a polynomial is 4.

The degree of the another polynomial is less than or equal to 4.

Also the difference of their degree is 2.

Thus the degree of the another polynomial is (4 - 2) =2.

The degree of the polynomials whose degree are a and b is a+b.

The degree of the product of the given polynomial is (4 + 2) = 6.

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The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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Answer:

The cost for the video game system is $96.90.

Step-by-step explanation:

With the help of time -distance formula we can calculate travel time in km for any given problem or situation.

We know the formula we relate to distance and  time that which  is called time -distance formula is :

t= d/s, where d is the distance and s is the speed of the object.To calculate travel time in km, first, we need to divide the total distance in km by the average speed of travel in terms of km/hour, later multiplying the result by 60 to get the travel time in minutes.

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Answer:

 . .

Step-by-step explanation:;

Answer:

y = -1/6x + 5

Step-by-step explanation:

y = mx + c

Gradient (m) = -1/6

Y-intercept (c) = 5

so

y = -1/6x + 5

Answer:

Its C. y = x - 1

Step-by-step explanation:

For Example:

-4 = -3 - 1

1 = 2 -1

4 = 5 - 1

The Balance chemical equation using given coefficients: 2, 3, 4, and 5 is

2[tex]C_{2} H_{2}[/tex]+ 5[tex]O_{2}[/tex] -> 4[tex]CO_{2}[/tex] + 2 [tex]H_{2}O[/tex]

The given chemical Equation:

[tex]C_{2} H_{2}[/tex] + [tex]O_{2}[/tex] -> [tex]CO_{2}[/tex]+ [tex]H_{2}O[/tex]

Balance chemical equation using given coefficients: 2, 3, 4, 5

2[tex]C_{2} H_{2}[/tex]+ 5[tex]O_{2}[/tex] -> 4[tex]CO_{2}[/tex] + 2 [tex]H_{2}O[/tex]

A chemical equation is the symbolic illustration of a chemical response in the shape of symbols and chemical formulas. The reactant entities are given at the left-hand side and the product entities at the proper-hand facet with a plus sign between the entities in both the reactants and the products, and an arrow that points towards the goods to expose the route of the response. The chemical formulation can be symbolic, structural (pictorial diagrams), or intermixed. The equal holds for the whole electric-powered rate, as stated by way of the rate conservation regulation. An equation adhering to these necessities is said to be balanced.

A chemical equation is balanced by assigning appropriate values to the stoichiometric coefficients. simple equations can be balanced by using inspection, that is, by using trial and blunder. another method entails solving a gadget of linear equations.

Balanced equations are generally written with the smallest natural-wide variety coefficients. but on occasion, it can be high quality to just accept a fractional coefficient if it simplifies the opposite coefficients.

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Complete question: -

Drag each tile to the correct location in the equation. each tile can be used more than once, but not all tiles will be used. balance the chemical equation with the correct coefficients. 2 3 4 5 in the chemical equation  

[tex]C_{2} H_{2}[/tex] + [tex]O_{2}[/tex] -> [tex]CO_{2}[/tex] + [tex]H_{2}O[/tex]

Answer:

Yes, 11/81 is an irrational number.

Step-by-step explanation:

Because it is a fraction with a non-terminating, non-repeating decimal expansion.

Solution of the inequality representing charges of company A is less than the company B for the mileage of 75miles or more.

As given in the question,

Let 'x' miles be the number of miles driven by company A.

For the given conditions:

Equation of company A is:

110 + 0m

Equation of company B is

65 + 0.60x

Inequality between company A and company B is:

110 + 0m < 65 + 0.60x

⇒0.60x > 110 - 65

⇒x > 45 / 0.60

⇒ x > 75 miles or more

Therefore, from the inequality 75 miles or more company A charges less than the company B.

The complete question is:

Laura is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices. company A charges $110 and allows unlimited mileage. company B has an initial fee of $65 and charges an additional $0.60 for every mile driven. For what mileages will company A charge less than company B? use for the number of miles driven, and solve your inequality for .

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The Volume of the Cylindrical Silo is 88000 cubic feet

What is Volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.

Solution:

Given:

Height of the Container = 70 feet

Circumference of the Base = 125.7 feet

To Find: Volume of the Container

Volume = πr²h

Circumference = 2πr

125.7 = 2 * 3.14 * r

r = 20.01

Volume = 3.14 * 20.01 * 20.01 * 70

Volume = 88007.94 cubic feet

Volume = 88000 cubic feet (approx)

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The range of the given piecewise function is [-1, 27].

A function with many parts of curves in its graph is said to be a piecewise function. It is a function with various definitions at various intervals of x.

The given function is a piecewise function,

[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]

From the given function,

The set of values for all the output values can be referred to as a function's range. To find a range,

Then, the range can be written as [-1, 27]. Therefore, the first option is correct.

The complete question is -

Find the range of the following piecewise function.

[tex]f(x)=\begin{cases}{{x^2+2\;&\text{if}\;-5\le x < 3 \\{x-4\;&\text{if}\;3\le x < 7}}\end{cases}[/tex]

a)  [-1,27] b) [18,-2] c) [1,27] d) [-4,0].

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As per the question, Total Annual Cash Inflows = 5000, Discount Factor = 3.72 and New Machine's internal rate of return = 16%

Note: The query is not complete and does not contain the necessary information for part 4. It is impossible to fully answer this question without the exhibits stated in the questions. Up until part 3, we will be solving it.

1) The entire annual cash inflows must be calculated for this, and the formula is given below:

Total annual cash inflows are equal to the annual savings from part-time labor plus the additional contribution margin from anticipated sales.

Annual Cash Inflows Total = 3800 + ( 1000 x 1.20)

= 3800 + 1200

= 5000

2. Formula for figuring up the discount percentage:

Discount Factor = New Machine Price/Annual Cash Flow

New machine cost is 18600 USD.

Annual inflow of cash = 5000

Discount Factor is equal to 18600/5000.

Discount Ratio is 3.72.

3.  The examples, which are absent from this question, show that the discount factor for six years is roughly closest to 16%, hence the internal rate of return for the new machine is equal to 16%.

Note, without the exhibits indicated in the questions, the question is insufficient and cannot be utilized in Part 4. It cannot be solved any further.

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Sampling bias, also known as sample selection bias, refers to flaws in research studies that arise when researchers do not appropriately select their subjects.

When a sample is collected in such a way that some members of the intended population have a significantly lower or higher sampling risk than others, sampling bias is reduced.

It yields a skewed sample of a population (or non-human variables) in which not all individuals, but rather cases, were picked in the same way. If this is not considered, the outcomes may be incorrectly attributed to the study problem rather than the sample method.

Sampling bias is often classified as a subset of selection bias, also known as sample selection bias, but some believe it to be a separate type of bias.

The difference between sampling bias and selection bias, though not frequently recognized, is that sampling bias reduces a test's external validity, whereas selection bias only addresses the internal validity of differences or similarities detected in the sample at hand.

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The factors of the polynomial  t¹² – r³s¹⁵ is (t⁴ + rs⁵)(t⁸ - rs⁵t⁴+ r²s¹⁰). The correct answer is B.

The definition of a factor is a number that completely divides another number. If adding two whole numbers results in an item, the numbers we are adding are variables of the item since the item can be used to separate them.

By using formula

(a³ - b³) = ( a+ b)( a² -ab + b²)

Then,

t¹² – r³s¹⁵ = (r⁴)³ - (rs⁵)³

=(r⁴ + rs⁵)((t⁴)² - rs⁵t⁴ + (r⁵)²)

=(r⁴ + rs⁵)(t⁸ - (rs⁵t⁴) + r²s¹⁰)

Thus, required answer is (r⁴ + rs⁵)(t⁸ - (rs⁵t⁴) + r²s¹⁰), So option (B) is correct.

Your question is incomplete but most probably your full question was

Factor t¹² – r³s¹⁵ is

a.(t⁸ – rs⁵t⁴ – r²s¹⁰)

b. (t⁴ – rs⁵)(t⁸- rs⁵t⁴+ r²s¹⁰)

c. (t⁹ – rs¹²)(t¹⁸+rs¹²t⁹ +r²s²⁴) (t⁴ rs⁵)

d. (t⁸ – rs⁵t⁴)( r²s¹⁰)

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Answer:

Step-by-step explanation:

So hi this is saveon and this is how you do the question so first you divide 44.52 by 21 you will get 2.12 feet and that is your answer

It is 2.12 feet wide.

What is rectangle ?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

An equiangular quadrilateral is another name for a rectangle. The reason for this is that a rectangle is a quadrilateral form (4-sided shape) with parallel sides that are equal to one another and four corners with 90o angles. A rectangle can also be referred to as an equiangular quadrilateral because all of the angles are 90 degrees.

Rectangle area = width * height

44.52 / 21

= 2.12 feet

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Answer: 0.25 inches per hour.

Step-by-step explanation:

The mile-a-minute weed can grow up to 0.5 ft per day. To convert this to inches per hour, we need to convert the distance from feet to inches and the time from days to hours.

There are 12 inches in 1 foot, so the mile-a-minute weed can grow up to 0.5 x 12 = <<0.5*12=6>>6 inches per day.

There are 24 hours in 1 day, so the mile-a-minute weed can grow up to 6 / 24 = <<6/24=0.25>>0.25 inches per hour.

Therefore, the mile-a-minute weed can grow up to 0.25 inches per hour.

Here's the complete solution using the correct conversion factors:

1 ft = 12 inches

1 day = 24 hours

0.5 ft/day * (12 inches/1 ft) / (24 hours/1 day) = 0.25 inches/hour

The point that the line also pass would be; C. (8,4)

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that line has a slope of - 1/4 and passes through the point (4,2).

Now Write the equation as;

y - 2 = -1/4(x - 4)

y = -1/4x + 6

Hence, The answer is; C. (8,4)

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