Printer A prints 100 pages for $26.99. Printer B prints 275 sheets for $67.99. Which printer has the better rate of cost per page?

Printer A, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Printer B, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Printer A, because the approximate rate of Printer A, $3.71 per page, is less than the approximate rate of Printer B, $4.04 per page
Printer B, because the approximate rate of Printer A, $3.71 per page, is less than the approximate rate of Printer B, $4.04 per page

Answer:

x = 61

Step-by-step explanation:

[tex]x + 119 = 180[/tex]

[tex]x = 180 - 119[/tex]

[tex]x = 61[/tex]

Answer:

x = 61

Step-by-step explanation:

the probability that the man would have done at least as well as 22 out of 30 correct predictions by chance alone is approximately 0.149 or 14.9%, which suggests that his ESP claim may not be supported by the coin flip test results alone.

To determine the probability that the man would have gotten at least 22 correct coin flip predictions if he had no ESP, we can use a statistical tool called a binomial distribution. Assuming the coin is fair, the probability of getting any single coin flip prediction correct is 0.5, since there are only two possible outcomes (heads or tails) and they are equally likely. We can use this probability to calculate the probability of getting exactly 22 correct predictions out of 30 coin flips, which is:

P(X = 22) = (30 choose 22) {multiply} 0.5^22 {multiply} 0.5{power}8 = 0.099

This means that the probability of getting exactly 22 correct predictions by chance is less than 10%. However, the question asks for the probability of getting at least 22 correct predictions, which includes the probabilities of getting 23, 24, 25, 26, 27, 28, 29, or 30 correct predictions as well.              

To calculate this cumulative probability, we can add up the probabilities of getting each of these outcomes separately:

P(X >= 22) = P(X = 22) + P(X = 23) + ... + P(X = 30)

Using a binomial distribution table or calculator, we can find that this cumulative probability is approximately 0.149.

Therefore, the probability that the man would have done at least as well as 22 out of 30 correct predictions by chance alone is approximately 0.149 or 14.9%, which suggests that his ESP claim may not be supported by the coin flip test results alone.

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Similar triangles have different dimensions, but their measurements have the same ratio.

In the image, we can see two triangles. A large triangle and a small triangle. These are similar. How can we tell? They share the same angles.

Now, we can set up a proportion comparing their side lengths:

[tex]\dfrac{82}{28}=\dfrac{(2x+8)+(5x-4)}{2x+8}[/tex]

Theoretically, if we divide corresponding side lengths of two similar shapes, we should get the same value. This is what makes the proportion true.

Now, simplify:

[tex]\dfrac{82}{28}=\dfrac{(2x+8)+(5x-4)}{2x+8}[/tex]

[tex]\dfrac{41}{14}=\dfrac{(2x+8)+(5x-4)}{2x+8}[/tex]

[tex]41(2x+8)=14[(2x+8)+(5x-4)][/tex]

[tex]82x+328=14[2x+8+5x-4]\\82x+328=14(7x+4)\\82x+328=98x+56[/tex]

[tex]328=16x+56\\272=16x\\x=17[/tex]

x = 17

In mathematics, Z means complex number and it is represented as (a+ib) where a is real part and b is the imaginary part.

In mathematics, the number are represented by using some certain notations, like N for all natural number, Z for all complex numbers, R for all real numbers.

Now, here the formula of Z is asked, Z is a combination of two number

Z = a+ib

Where, a is real part, b is the imaginary part and "i" is called the notation Iota that is used with the imaginary part to represent the imaginary part.

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Answer:

To find the central angle of the sector that represents 64% of a circle graph, we can use the proportion:

64% (or 0.64) of the circle is to 360 degrees as x (the central angle of the sector) is to the angle we're trying to find.

Mathematically, we can write:

0.64/1 = x/360

Simplifying this expression, we get:

x = 0.64 x 360/1

x = 230.4

So the central angle of the sector that represents 64% of the circle graph is approximately 230.4 degrees. Rounded to the nearest degree, this is 230 degrees.

Step-by-step explanation:

Substituting x = 2 in each function, we get:

A. f(x) = 8x – 2 --> f(2) = 8(2) - 2 = 14 (not a match)

B. f(x) = 4x + 4 --> f(2) = 4(2) + 4 = 12 (a match)

C. f(x) = 6x – 4 --> f(2) = 6(2) - 4 = 8 (not a match)

D. f(x) = –4x – 4 --> f(2) = -4(2) - 4 = -12 (not a match)

Therefore, the equation of the function could be f(x) = 4x + 4 (option B).

Explanation:

1 balloon needs 12 ft of string.

48 balloons need 48*12 = 576 ft of string.

Divide by 3 to convert from feet to yards. This is because 1 yard = 3 ft.

576 ft = 576/3 = 192 yards

Answer:120

Step-by-step explanation:

Answer:

The length of the other two equal sides is 11.75 yards.

Step-by-step explanation:

Let's call the length of the two equal sides of the rectangular enclosure "x". We know that the total amount of fencing used is 65 yards and that two sides already use 41.50 yards of fencing.

So, we can set up the equation:

2x + 41.50 = 65

To solve for x, we first need to isolate x on one side of the equation. We can start by subtracting 41.50 from both sides:

2x = 23.50

Then, we can divide both sides by 2 to solve for x:

x = 11.75

Therefore, the length of the other two equal sides is 11.75 yards.

Answer:

3.16666667

Step-by-step explanation:

convert in a calculator online

inches to feet

Answer:

67.872

Step-by-step explanation:

The vertex form of a parabola is  y = a(x - h)² + k , where: a — Same as the a coefficient in the standard form; h — x-coordinate of the parabola vertex; and. k — y-coordinate of the parabola vertex.

The extremal value of a quadratic curve is represented by the vertex of a parabola, which is a point. The quadratic portion is still valid because two is our variable's most important power (x). For a parabola to open up, the vertex can either be a minimum or a maximum (for a parabola opening down).

As an alternative, we might state that the parabola's vertex is where its symmetry axis meets it.

The vertex is typically represented by the point P(h,k), where h stands for the x-coordinate and k for the y-coordinate.

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Answer:

Using 3.14 for π, we have:

[tex]32(26) + \frac{1}{2} (3.14)( {13}^{2} ) = 1097.33[/tex]

about 1,097.33 square feet

The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

What is the equilateral triangle?

In an equilateral triangle, all sides are equal in length.

That means that all the angles of the triangle will be congruent.

Since a triangle has 3 angles that always add up to 180 degrees, each angle is 60 degrees.

Therefore, the hypotenuse of the equilateral triangle is 1.

So,

[tex]x = 1 * sin60[/tex]°

[tex]x = 1 * \sqrt{3} /2\\x = \sqrt{3} /2[/tex]

Hence, The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

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The quadrilateral FGHI is a parallelogram

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

F = (0, -6), G = (7, -4), H = (8, 4), I = (1, 2)

The lengths can be calculated as

Lengths = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the above as a guide, we have the following:

FG = √[(0 - 7)² + (-6 + 4)²] = √53

GH = √[(8 - 7)² + (4 + 4)²] = √65

HI = √[(8 - 1)² + (4 - 2)²] = √53

IF = √[(1 - 0)² + (2 + 6)²] = √65

For the slopes, we have

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

FG = (-6 + 4)/(0 - 7) = 2/7

GH = (4 + 4)/(8 - 7) = 8

HI = (4 - 2)/(8 - 1) = 2/7

IF = (2 + 6)/(1 - 0) = 8

Based on the above computations, we have

Hence, the shape is a parallelogram

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The height of Amber's scale model of the Washington Monument should be 2.775 feet.

To find the height of Amber's scale model, we need to multiply the actual height of the Washington Monument by the scale factor:

Scale factor = 1/200

Height of Amber's model = (1/200) * 555 feet

Height of Amber's model = 2.775 feet

Therefore, the height of Amber's scale model of the Washington Monument should be 2.775 feet.

In mathematics, scale refers to the ratio between measurements of the real world and measurements of a model or a drawing. It is a way of representing an object or a phenomenon that is too large or too small to observe directly, by creating a scaled-down or scaled-up representation of it.

For example, in maps, the scale represents the ratio between distances on the map and distances in the real world. A scale of 1:50,000 means that 1 unit on the map represents 50,000 units in the real world. Similarly, in architectural drawings, the scale represents the ratio between the size of the drawing and the size of the actual building.

Scales are used in many fields, including engineering, architecture, cartography, and model making. They allow us to represent objects and phenomena in a way that is more manageable and easier to visualize, while preserving the important proportions and relationships between the different elements of the object or phenomenon.

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The amount of money that will be used to drive only one mile by the different vehicles given above such as Deswagon and DesMobile would be =$57.35 and $56.78 respectively.

The total mileage that can be covered by Deswagon = 490miles.

The total cost of gas for the Deswagon = $28,100

Therefore the amount that will be paid for only one mile = X.

That is , 490 miles = $28,100

1 mile = ×

make X the subject of formula;

X = 28,100/490

= $57.35.

The total mileage that can be covered by DesMobile = 575miles.

The total cost of gas for the DesMobile = $32,650.

Therefore the amount that will be paid for only one mile = X.

That, 575 miles = $32,650

1 mile = X

Make X the subject of formula;

X = 32,650/575

X = $56.78.

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If int j = 3, then the value of J++ is 3.

The post-increment operator ++ increments the value of the variable by 1, but returns the original value of the variable. So when j++ is executed, j is incremented to 4, but the expression evaluates to the original value of j, which is 3.

To see the effect of the increment operator, you could print the value of j before and after the j++ operation:

int j = 3;

System.out.println(j);  // output: 3

j++;

System.out.println(j);  // output: 4

Note - that the pre-increment operator, ++j, would increment the value of j and return the new value, so ++j would evaluate to 4.

j++ is a shorthand notation in many programming languages, including Java and C++, which increments the value of the variable j by 1.

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The correct answer is option (c): They are both solid lines.

In mathematics, an inequality is a statement that two values are not equal. Instead, one value is either greater than or less than the other value. Inequalities are represented by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, the inequality 5 < 8 means that 5 is less than 8, while the inequality x + 3 > 7 means that the sum of x and 3 is greater than 7.

Inequalities can be graphed on a number line, which is a horizontal line that represents the set of real numbers. To graph an inequality on a number line, you can draw a closed or open circle at the value of the variable that satisfies the inequality, and shade the region to the left or right of the circle, depending on the direction of the inequality.

For example, to graph the inequality x < 3, you would draw an open circle at 3 on the number line, and shade the region to the left of the circle, because x is less than 3. Similarly, to graph the inequality y ≥ -2, you would draw a closed circle at -2 on the number line, and shade the region to the right of the circle, because y is greater than or equal to -2.

Graphing inequalities on a number line is a useful tool for solving problems and visualizing the solutions to inequalities in one variable.

The inequality y ≤ 3x + 5 can be written as y = 3x + 5 or y > 3x + 5. Similarly, the inequality y ≤ (2/3)x + 5 can be written as y = (2/3)x + 5 or y > (2/3)x + 5. Since the inequality symbols are less than or equal to, the lines representing these inequalities will be solid lines.

Also, since the coefficients of x and y are positive in both the inequalities, the lines will have a positive slope and will slant upwards from left to right. The y-intercept of both lines is 5.

Hence, the correct answer is option (c): They are both solid lines.

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The lines will have a positive slope and slant upward from left to right since the coefficients of x and y in both inequalities are positive. Both lines have a y-intercept of 5.

Hence, option (c) is the appropriate response: Both of them are solid lines.

In mathematics, an inequality is a statement that two values are not equal. Instead, one value is either greater than or less than the other value. Inequalities are represented by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, the inequality 5 < 8 means that 5 is less than 8, while the inequality x + 3 > 7 means that the sum of x and 3 is greater than 7.

Inequalities can be graphed on a number line, which is a horizontal line that represents the set of real numbers. To graph an inequality on a number line, you can draw a closed or open circle at the value of the variable that satisfies the inequality, and shade the region to the left or right of the circle, depending on the direction of the inequality.

For example, to graph the inequality x < 3, you would draw an open circle at 3 on the number line, and shade the region to the left of the circle, because x is less than 3. Similarly, to graph the inequality y ≥ -2, you would draw a closed circle at -2 on the number line, and shade the region to the right of the circle, because y is greater than or equal to -2.

Graphing inequalities on a number line is a useful tool for solving problems and visualizing the solutions to inequalities in one variable.

The inequality y ≤ 3x + 5 can be written as y = 3x + 5 or y > 3x + 5. Similarly, the inequality y ≤ (2/3)x + 5 can be written as y = (2/3)x + 5 or y > (2/3)x + 5. Since the inequality symbols are less than or equal to, the lines representing these inequalities will be solid lines.

Also, since the coefficients of x and y are positive in both inequalities, the lines will have a positive slope and will slant upwards from left to right. The y-intercept of both lines is 5.

Hence, the correct answer is an option (c): They are both solid lines.

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According to the concept of unit conversion, 57 feet is equal to 1737.36 centimeters.

Unit conversion is an essential skill to have in science, engineering, and everyday life. It allows us to convert between different units of measurement and compare them easily.

To convert 57 feet to centimeters, we need to know the conversion factor between these two units. One foot is equal to 30.48 centimeters. So, we can multiply the given number of feet by this conversion factor to get the equivalent number of centimeters.

57 feet x 30.48 cm/ft = 1737.36 cm

In unit conversion, it is important to keep track of the units and make sure they cancel out correctly. In this case, the feet unit cancels out with the feet unit in the conversion factor, leaving us with only the centimeter unit.

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The probability that a continuous random variable will be equal to any specific value is zero. This is because the probability of an individual value for a continuous random variable is represented by the area under the probability density function (PDF) at that particular value, and the area of a single point is zero.

The algebra math can be calculated in online by using online calculators, educational websites and mobile apps etc.

There are many online resources available that can help you calculate algebra math problems. Here are a few options:

Online calculators: You can use various online calculators to calculate algebra problems.

Educational websites: There are many educational websites that provide lessons and tutorials on algebra.

Mobile apps: There are many mobile apps available that can help you solve algebra problems on-the-go.

Online courses: There are many online courses available that can teach you algebra from the basics to the advanced level.

Whichever option you choose, it's important to make sure that you understand the steps involved in solving algebra problems so that you can apply the principles to new problems in the future.

Therefore, the different different methods to calculate algebra online has been explained

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Online calculator system of equation is an open-source online calculator that shows the value of the variable for the specified set of equations.

The collection or set of equations is referred to as a system of equations in mathematics. The variables in the equations can have their answers found by solving the corresponding equations. We are aware that variables, constants, coefficients, and exponents make up an algebraic equation. There are three different kinds of systems of equations that can be seen when working with a system of linear equations. As follows:

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Two ways an individual can improve his or her credit score is,

Pay bills on time and Ask for higher credit limits

Three-digit credit scores are used to determine how risky it would be for a lender to give credit to a certain individual.

Ask to be added as an authorized user if a family member or acquaintance has a credit card account with a large credit limit and a solid track record of on-time payments.

The credit limit on the account can help your utilization because it is added to your credit reports.

If you make late payments, no credit improvement plan will work.

Even worse, missed payments may appear on your credit records for up to 7 1/2 years.

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The six trigonometric functions are mathematical functions used in geometry and trigonometry to describe the relationships between angles and sides of triangles.

The six trigonometric functions are:

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle.

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side of a right triangle.

Cotangent (cot): The cotangent of an angle is the ratio of the length of the adjacent side to the length of the side opposite the angle of a right triangle.

Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle, or the ratio of the hypotenuse to the adjacent side of a right triangle.

Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle, or the ratio of the hypotenuse to the opposite side of a right triangle.

The six trigonometric functions can be used to solve various problems in mathematics, physics, and engineering, among other fields.

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The solution to the system of equation y = 5x + 4 and y = 6x + 1 is (3,19).

Given the system of equation in the question;

y = 5x + 4

y = 6x + 1

To solve the system of equation, first plug equation one into equation two and solve for x.

y = 6x + 1

Plug in y = 5x + 4

5x + 4 = 6x + 1

Solve for x

6x - 5x = 4 - 1

x = 3

Now, plug x = 3 into equation one and solve for y.

y = 5x + 4

Plug in x = 3

y = 5( 3 ) + 4

y = 15 + 4

y = 19

Therefore, the value of x is 3 and y is 19.

Option A) (3,19) is the correct answer.

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Using Poisson distribution, the probability mass function is approximately 4.2%

To solve the problem, we can use the Poisson distribution since we are interested in the probability of a certain number of events (in this case, cars with 4 occupants) occurring in a given time period (morning commute).

The Poisson probability mass function is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable (number of cars with 4 occupants), λ is the mean (average) number of occurrences in the given time period (morning commute), and k is the number of occurrences we are interested in (k = 4 in this case).

Since the average number of non-driver passengers per car is 0.52, we can assume that the average number of total occupants (including the driver) is 1.52. Therefore, the mean (average) number of cars with 4 occupants in a given time period can be calculated as:

λ = (1.52)^4 * e^(-1.52) / 4!

Using a calculator, we get λ ≈ 0.0331.

Now we can plug in the values of λ and k into the Poisson probability mass function:

P(X = 4) = (e^(-0.0331) * (0.0331)^4) / 4!

Using a calculator, we get P(X = 4) ≈ 0.042

Therefore, the probability that a randomly selected car passing through the toll booth during the morning commute has 4 occupants (the driver and 3 passengers) is approximately 0.042 or 4.2%.

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George has put rice on the 10th square, he has placed a total of 1,023 grains of rice on the chessboard.

What is geometric progression ?
A geometric progression, also known as a geometric sequence, is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number called the common ratio.

The general form of a geometric progression is:

[tex]a, ar, ar^2, ar^3, ...[/tex]

where:

a is the first term of the sequence

r is the common ratio between successive terms

Given by the question:
To find the total number of grains on the first 10 squares, we can use the formula for the sum of a geometric series, which is:

[tex]sum = a(1 - r^n) / (1 - r)[/tex]

where:

a is the first term (in this case, 1)

r is the common ratio (in this case, 2)

n is the number of terms (in this case, 10)

Using this formula, we can calculate the sum of the grains of rice on the first 10 squares as:

[tex]sum = 1(1 - 2^10) / (1 - 2)[/tex]

[tex]sum = 1(1 - 1024) / (-1)[/tex]

[tex]sum = 1023[/tex]

Therefore, once George has put rice on the 10th square, he has placed a total of 1,023 grains of rice on the chessboard.

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The expansion of the series sum from n equals 1 to 4 of 3 to the n plus 1 power is 9 27 81 243.

An arithmetic sequence is one in which each term is produced by either increasing or decreasing the preceding number by a specific amount.

Geometric progressions: A geometric sequence is one where each phrase is produced by multiplying or dividing a certain integer by the one before it.

Harmonic patterns: If the reciprocals of every number in a sequence form an arithmetic sequence, the numbers are said to be in harmonic sequence.

To expand the series, we substitute the value of n in the given expression to get the final value.

The given series is:

[tex]\sum_{n=1}^{4} (3)^{n+1}[/tex]

Substitute the value of n from 1 to 4 in the given expression.

[tex]\sum3^{1+1} = 9\\\\\sum3^{2+1} = 27 \\\\\sum3^{3+1} = 81 \\\\\sum3^{4+1} = 243[/tex]

Hence, the expansion of the series sum from n equals 1 to 4 of 3 to the n plus 1 power is 9 27 81 243.

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