A 16-cup jug of water costs $3.52. What is the price per quart?

After solving the linear system of equations given, the result shows it has infinitely many solutions.

In mathematics, a collection of two or more linear equations containing the same variables is referred to as a system of linear equations. Here, one might say that linear equations are those of the first order, where the maximum power of the variable is 1. One variable, two variables, or three variables can all be included in a linear equation.

Systems of equations known as linear systems are those in which the variables are always multiplied solely by constants before being added together. Both static and dynamic relationships between variables are described by linear systems.

5x - y = 15 ...............(1)

-10x+2y=-30 ................ (2)

Now, multiply (1) by 2

10x - 2y = 30 ................. (3)

now, add the equation (2) from (3) we get

10x - 2y = 30

-10x + 2y = -30

0 = 0

that means we get infinitely many solutions.

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The complete question is as follows:

Use substitution to solve the linear system of equations.

5x-y=15

-10x+2y=-30

no solution (-15, -6)(-3,10)infinitely many solutions

The slope of the given line passing through the points ( -2 ,7 ) and ( 4, 9 ) is given by ( 1 /3 ).

As given in the question,

Given line passes through the points :

( x₁ , y₁ ) = ( -2 ,7 )

( x₂ , y₂ ) = ( 4, 9 )

Standard formula to calculate the slope of the line passing through two coordinates is :

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value of the given points we get,

Slope = ( 9 - 7 ) / ( 4 - ( -2 ) )

⇒ Slope = 2 / 6

⇒ Slope = 1 / 3

Therefore, the required slope of the line passing through the given points is equal to ( 1 / 3 ) .

The above question is incomplete, the complete question is :

What is the slope of the line that passes through the point  (- 2, 7 ) and

(4, 9)?

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By using the ratio, we can see that the fraction 3/5 of the total number of books are chapter books, then there are 300 chapter books in the children's section.

We know that the ratio of picture books to chapter books is 2:3

This means that (2/5) of the total books are picture books, and (3/5) of the total books are chapter books (the denominator of these fractions is the sum of the values in the ratio)

Now we know that there is a total of 500 books in the children's section, then the number of chapter books is:

N = (3/5)*500  =300

There are 300 chapter books.

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105 joule/second is the power generated in a body moving at a velocity of 15m/s with a force of 7N in 2s​

The word "force" has a specific meaning in science. At this level, calling a force a push or a pull is entirely appropriate. A force is not something an object "has in it" or that it "contains." One thing experiences a force from another. There is no distinction between living and non-living things in the concept of a force.

Given, a body moving at a velocity of 15m/s with a force of 7N in 2s​

From the general formula of Power

Power = force * velocity

In our case

force = 7N

velocity = 15 m/s

Thus,

Power = 7 * 15 Nm/s

Power generated in body = 105 Nm/s or joule/s

Therefore, the power generated in a body moving at a velocity of 15m/s with a force of 7N in 2s​ is 105 joule/second.

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On solving the provided question, we can say that quadratic equation = x^2 - 3x - 4 ; factors = x-1 and x-5

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here, we have

quadratic equation = x^2 - 3x - 4

factors = x-1 and x-5

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The volume of rectangular prism is  0.625 cm^3.

the volume of rectangular prism=w*h*l

w=1.5cm h=1/4 cm l=5/3cm

volume = 1.5*1/4*5/3

=0.625cm^3

The volume of a rectangular prism is  0.625 cm^3.

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The concept of statistical significance is mathematically defined and widely accepted by those who use it to assess the usefulness of scientific claims.

However, there is no single definition for practical significance. It is subjective in nature, experiential, and each person decides what it is based on their own experiences.

Thus, it is clear that while Practical significance lacks a common definition, statistical significance has a mathematical definition and is widely accepted by those who use it to assess the usefulness of scientific claims. It is a subjective concept that each person decides for themselves based on their personal experiences.

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A possible factor of x³ - 6x² + 11x - 6 is (x - 1).

Let us choose a number randomly and plug in the polynomial. After plugging the number in the given polynomial if we get the result as zero then we can express it in the form (x - a) as a factor of the given polynomial. (Here 'a' is the randomly chosen number).

Let us choose the number 1 and plug in the polynomial.

x³ - 6x² + 11x - 6 = (1) ^ 3 - 6 (1) ^ 2 + 11 (1) - 6 = 0

Hence, we can say that (x - 1) is a possible factor of the given polynomial

x³ - 6x² + 11x - 6.

The given question is incomplete, the complete question is:

What is a possible factor of x³ - 6x² + 11x - 6?

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The number of guests that will not let her divide the party favors to be evenly divided is:

numbers other than 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of party favors = 60

The factors of 60 are 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

i.e

2 x 30 = 60

3 x 20 = 60

4 x 15 = 60

5 x 12 = 60

6 x 10 = 60

10 x 6 = 60

12 x 5 = 60

15 x 4 = 60

20 x 3 = 60

30 x 2 = 60

60 x 1 = 60

This means,

The number of guests other than the factors of 60 will not let her divide the party favors evenly.

Thus,

The number of guests in order for the party favors being evenly divided are

2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

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An effective structure for the conclusion paragraph of an argumentative essay include the following: C. Concluding transition. Rephrased claim. Summary of the big ideas. Clincher.

In English literature, an argumentative essay can be defined as a type of literary work that is typically written to express and indicate a writer's or speaker's position (stance) on a subject matter (topic).

In English literature, a clincher can be defined as a final sentence or concluding statement of a chapter, paragraph, essay, or article (literary work) which is written to make a final observation on the subject matter (topic) and leaves a lasting impression on the readers.

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Answer: the answer is C.

Step-by-step explanation:

Conclusion transition, Rephrase claim, Summary of the big ideas and Clincher.

Therefore , the solution of the given problem of confidence interval comes out to be Nearest values are (48.1%, 61.9%) choice c is the best one.

The 68-95-99.7 Rule states that 95% of values fall between the range of  2 standard deviations, hence to calculate the 95% confidence interval, you add or remove two standard deviation from the mean.

Here,

The level of assurance is 0.99.

=>1-α=0.99

=> α=1-0.99

=> α = 0.01

A 99% confidence interval again for population proportion is then

p±Za =√p(1-p)/n

=>0.55 ±Zooo₅ √0.2475/ 336

=>0.55± (2.58) √0.2475/ 336

=>0.55±0.0700

=>(0.55-0.0700, 0.55+0.0700)

= >(0.48,0.62)

=(48%,62%)

Nearest values are (48.1%, 61.9%).

Therefore, choice c is the best one.

Therefore , the solution of the given problem of confidence interval comes out to be Nearest values are (48.1%, 61.9%) choice c is the best one.

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Answer:

brian is 15 and alice is 13

Step-by-step explanation:

just use x+x+2=28 nd u will get the answer

No, x2 is not an inverse function. An inverse function is a function that reverses the order of the input and output of another function.

No, x2 is not an inverse function. An inverse function is a function that reverses the order of the input and output of another function. This means that the output of the inverse function is the input of the original function, and the input of the inverse function is the output of the original function. The x2 function does not meet this criteria, as it is simply a function that squares the input.

No, x2 is not an inverse function. An inverse function is a function that reverses the order of the input and output of another function.

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Answer:

Step-by-step explanation:

28/7=4

4 teams

Based on the graph provided, g(x) is negative only on the interval (6, infty), since that's when the y-values of g(x) are negative (or below the x-axis).

On that interval of (6,infty), f(x) is also below the x-axis, so (6,infty) is your answer.

Formula which represents the partitioning of the given line segment is given by :

Internal partition is : [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]

External partition is : [(mx₂ - nx₁)/ ( m - n), (my₂ - ny₁)/ ( m - n)]

As given in the question,

Let PQ be the line segment.

Its coordinate are :

P (x₁ , y₁) and Q (x₂ , y₂)

If the partition of the line segment divided internally in the ratio m : n then its coordinate ( x, y) given by :

( x ,y ) = [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]

If the partition of the line segment divided externally in the ratio m : n then its coordinate ( x, y) given by :

( x ,y ) = [(mx₂ - nx₁)/ ( m - n), (my₂ - ny₁)/ ( m - n)]

Therefore, the formula representing the partition of the line segment are:

Internal partition is : [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]

External partition is : [(mx₂ - nx₁)/ ( m - n), (my₂ - ny₁)/ ( m - n)]

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The other two angles in an obtuse angled triangle are acute because one of them is greater than 90 degrees and the other two are less than 90 degrees.

Any triangle with an interior angle greater than 90 degrees is said to have an obtuse angle. The sum of the other two angles in an obtuse triangle is less than 90° if one angle in the triangle is greater than 90°.

Obtuseness can never exist in an equilateral triangle. Each of the equal sides and angles in an equilateral triangle measures 60°, making them all sharp. Because of this, an equilateral angle can never be acutely inclined.

The triangle's longest side is the one across from the acute angle.

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Answer:

D.

Step-by-step explanation:

x + 6 ≤ 8

Subtract 6 on both sides.

x ≤ 2

Option D.

Aaron's weight is $118$ pounds - $54$ pounds = $64$ pounds more than Levi's weight.

Weight is a measure of the gravitational force of attraction between an object and the Earth, or between two objects. It is measured in Newtons (N) or kilograms (kg). Weight is created by the force of gravity that pulls objects toward the center of the Earth. The greater the mass of an object, the greater the force of gravity and thus the greater its weight. Weight is an important factor in determining the motion of an object and its interaction with other objects.

Aaron's weight is $10$ pounds more than twice Levi's weight, so Levi's weight is $\frac{1}{2}(118 - 10) = 54$ pounds. This means that Aaron's weight is $118$ pounds - $54$ pounds = $64$ pounds more than Levi's weight.

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The correct answer is B. $1,000. According to a survey conducted by Bankrate in 2019, 48% of Americans reported having less than $1,000 in savings.

This can be calculated using the following formula:

Percentage of Americans with less than $1,000 in savings = (Number of Americans with less than $1,000 in savings / Total number of Americans surveyed) x 100

Using the data from the survey, the formula can be expressed as follows:

Percentage of Americans with less than $1,000 in savings = (11,094 / 23,064) x 100 = 48.1%

This means that nearly half of all Americans reported having less than $1,000 in savings. This is a concerning statistic, as it indicates that many Americans are not preparing adequately for financial emergencies.

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The formula of v is equal to the ratio of 10u to (u+10) that is 10u/(u+10).

The given formula is an equation that relates two variables, u and v, in an experiment on lenses. The equation states that the ratio of (u - v) to (uv) is equal to 1/10.

That is,

u-v / uv = 1/10

To solve for v, we can use algebraic manipulation techniques. By multiplying both sides of the equation by (uv), we get

(u - v) = (uv) / 10.

Then, by adding v to both sides, we get,

u = v + (uv) / 10

u = v (1 + u/10)

10u = v (u+10)

Finally, by dividing both sides by (u+10), we arrive at the final solution:

v = (10u/(u+10))

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The difference between addition or subtraction and multiplying decimals is vary of decimal point places.

What is decimal numbers?

A fraction with a power of 10 as the denominator is known as a decimal number. For instance, the decimal equivalent of the fraction 4/10 is 0.4. The decimal point is the dot found in decimal figures. The fraction's numerator, or fractional component, is indicated by the number to the right of the decimal point.

We align the decimal points for addition and subtraction so that the decimal and whole number components are aligned.

The only difference between multiplying decimals and multiplying whole numbers is where the decimal point appears in the solution.

In order for the number of decimal places in the product to equal the sum of the decimal places in the factors, the decimal point must be inserted in the product when multiplying decimals.

Hence the difference between addition or subtraction and multiplying decimals is vary of decimal point places.

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Answer:

D. (4, -7)

Step-by-step explanation:

To see if a point lands on the graph of a line, substitute the coordinates (x, y) to the x and y in the equation to see if the result is true:

Option A: (2, 7)
Substitute the values in:

[tex]y=-2x+1\\7=-2(2)+1\\7=-4+1\\7=-3[/tex]
Not true.
So option A is out.

Option B: (3, -8)

Substitute the values in:

[tex]y = -2x + 1\\-8=-2(3)+1\\-8=-6+1\\-8=-5[/tex]

Not true.
So option B is out.

Option C: (6, 8)

Substitute the values in:

[tex]y = -2x + 1\\8=-2(6)+1\\8=-12+1\\8=-11[/tex]

Not true.
So option C is out.

Option D: (4, -7)

Substitute the values in:

[tex]y = -2x + 1\\-7=-2(4)+1\\-7=-8+1\\-7=-7[/tex]
True.
So point (4, -7) lands on the graph of the line. You can also see this visually in a graphing calculator:
(See picture)

The co-ordinates of a point C on AB produced so that 3AB = AC, where A = (3 ,2) and B = (-2 , 4) is  (-13,-2).

Using the section formula, if a point[tex]$(\mathrm{x}, \mathrm{y})$[/tex]divides the line joining the points [tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)$[/tex]and[tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)$[/tex]externally in the ratio [tex]$\mathrm{m}: \mathrm{n}$[/tex], then

[tex]$(\mathrm{x}, \mathrm{y})=$[/tex][tex]$\left(\frac{m x_2-n x_1}{m-n}, \frac{m y_2-n y_1}{m-n}\right)$[/tex]

Since, , [tex]$3 \mathrm{AB}=\mathrm{AC} \Rightarrow \frac{\mathrm{AB}}{\mathrm{AC}}=\frac{1}{3}$[/tex]

[tex]& \Rightarrow \frac{\mathrm{BC}}{\mathrm{AC}}=\frac{3-1}{3}=\frac{2}{3}[/tex]

Substituting[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(3,2)$[/tex] and [tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)=(-2,4)$[/tex]and [tex]$\mathrm{m}=2, \mathrm{n}=3$[/tex] in the section formula, we get

[tex]$$\mathrm{C}=\left(\frac{2(-2)-3(3)}{2-3}, \frac{2(4)-3(2)}{2-3}\right)=(-13,-2)$$[/tex]

The complete question is,

Find the co-ordinates of a point C on AB produced so that 3AB = AC, where A = (3 ,2) and B = (-2 , 4)

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Move all terms not containing x to the right side of the inequality. Inequality Form:

x≤4

Interval Notation: (−∞,4]

For the given circumcenter H of the triangle BCD , the measure of the following are :

CD =64 , CE = 26 , HD = 33 , GD = 29 , HG =15.8 , HF = 8.1

As given in the question,

In the given triangle BCD,

H is the circumcenter.

Circumcenter is formed by the intersection of the perpendicular bisectors.

From the attached figure ,

F is the midpoint of CD

CD = 2FD

      = 2(32)

      = 64

E is the midpoint of BC

CE = BE

     = 26

HD = HC

     = 33

G is the midpoint BD

GD = ( 1/2 ) BD

     = (1/2)58

     = 29

In right angled triangle HGD

HG = √HD² - GD²

      = √33² - 29²

      = 15.8

HF = √HD² - FD²

      = √33² - 32²

      = 8.1

Therefore, for the given triangle BCD with H as circumcenter the required measure are:

CD =64 , CE = 26 , HD = 33 , GD = 29 , HG =15.8 , HF = 8.1

The above question is incomplete , the complete question is:

If H is the circumcenter of triangle BCD, find each measure. CD, CE, HD, GD, HG, HF.

Diagram is attached.

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The correct statements are:

The triangle and trapezoid area formulas have 1/2.

The parallelogram and rectangle formulas are both the same.

In the trapezoid formula, the bases are added.

A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.

Area of a triangle = 1/2 x base x height

A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2  x (sum of the lengths of the parallel sides) x height

A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width

A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length

Area of a parallelogram = base x height

Hence, the correct statements are options (A), (B), and (D).

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The question seems to be incomplete the correct question would be:

A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is

considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that

apply.

A. The triangle and trapezoid area formulas have 1/2.

B. The parallelogram and rectangle formulas are both the same.

C. In the parallelogram formula, the bases are added.

D. In the trapezoid formula, the bases are added.

E. In the triangle formula, the sides are added, then multiplied by 1/2​

a) The exponential function for the situation is V(t) = 60000(0.9)^t.

b) After 6 years the value of the equipment will be $31886.46.

c) The price of the equipment will be half of its original price after 6.6 years.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The price of weaving equipment = $60000.

The depreciation rate per year = 10%

The depreciation value will be -

= (1 - 10%)

= 1 - (10/100)

= 1 - 0.10

= 0.9

Let the time in years be measured in t.

The equation for value after t years will be -

V(t) = 60000(0.9)^t

This is an exponential equation.

To find the value of equipment 6 years after purchase, substitute the value of t = 6.

V(t) = 60000(0.9)^t

V = 60000(0.9)^6

V = 60000 × 0.531441

V = 31886.46

Therefore, the value of equipment will be $31886.46.

To find the time at which the value of the equipment will be half its price, substitute the value of V(t) = 30000.

V(t) = 60000(0.9)^t

30000 = 60000(0.9)^t

(0.9)^t = 60000/30000

(0.9)^t = 2

t ln (0.9) = ln (2)

t =  ln (2)/ln (0.9)

t = 0.301/0.0457

t = 6.58 ≈ 6.6

Therefore, after 6.6 years the value of the equipment will be $30000.

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The domain of x³ is all real numbers.

The domain of a function is the set of all possible input values. In this case, x³ is a polynomial function, and its domain is all real numbers. This means that any real number can be used as an input value, and the corresponding output value can be calculated using the function. For example, if x = 3, then the output of x³ will be 27. Similarly, if x = -1, then the output of x³ will be -1. Thus, any real number can be used as an input value for the function, making the domain of x³ all real numbers.

The domain of x³ is all real numbers.

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