After a 27% decrease the value of a game card was now on sale for $34.00. What was the original price?

The maximum total deduction that can be claimed is OE. $17,100.

What is deduction ?

Deduction refers to the process of subtracting or taking away something. In the context of taxes, a deduction is a specific amount of money that a taxpayer is allowed to subtract from their income before calculating their tax liability. Deductions are one way to reduce the amount of taxes owed and can help to lower a person's overall tax burden.

There are two main types of deductions in the U.S. tax system: standard deductions and itemized deductions. The standard deduction is a fixed amount that varies depending on the taxpayer's filing status, while itemized deductions are specific expenses that a taxpayer can deduct from their taxable income. Some common examples of itemized deductions include mortgage interest, charitable contributions, medical expenses, and state and local taxes.

It's important to note that not all deductions are available to all taxpayers, and there are specific rules and limits that apply to each type of deduction. It's also important to keep accurate records and documentation to support any deductions that are claimed on a tax return.

The maximum total deduction that can be claimed is OE. $17,100, because that is the sum of the deductible expenses and the standard deduction.

The question is asking for the maximum total deduction that can be claimed, given certain deductible expenses and a standard deduction.

The standard deduction for the tax year is $6,100, and the deductible expenses are $6,000 in mortgage interest and $5,000 in charitable contributions.

Since the deductible expenses ($6,000 + $5,000 = $11,000) are less than the standard deduction of $6,100, it makes sense to use the standard deduction instead of itemizing deductions.

Therefore, the maximum total deduction would be the sum of the deductible expenses and the standard deduction:

$11,000 + $6,100 = $17,100

So, the maximum total deduction that can be claimed is OE. $17,100.

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Answer:

9/2

Step-by-step explanation:

Using the given ratio, we can see that there are 48 teachers.

Here we know that the ratio of teachers to male learners to female learners is:

1:7:8

So for each teacher there are 7 female learners and 8 male learners, for a total of 15.

So we can simplify this and say that there are 15 learners for each teacher.

Then if there are 720 learners, the number of teachers is:

720/15 = 48

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The dimension of the square metal sheet is x = 4 ft

Dimensions are the measure of a physical property of an object such as length, width or height.

Since an open box is to be constructed from a square sheet of metal with dimensions x feet by x feet by removing a square of side 1 foot from each corner and turning up the edges.

The volume V of the box is V(x) = (x - 2)².

To find the dimensions of the sheet metal needed to make a box that will hold 4 cubic feet by solving the equation V(x) = 4, we make V(x) = 4 and solve the equation.

So,  V(x) = (x - 2)².

(x - 2)² = 4

Taking square roots of both sides, we have that

√(x - 2)² = ±√4

x - 2 = ±2

x = 2 ± 2

x = 2 - 2 or x = 2 + 2

x = 0 or x = 4

Since the dimension cannot be 0, x = 4

So, the dimension of the sheet is x = 4 ft

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Answer:

A commonly used fraction that helps you understand a different size or amount is called a ratio.

Step-by-step explanation:

A ratio is a comparison of two or more quantities or measurements, expressed as a fraction or a colon. Ratios are commonly used to express the relationship between different amounts or sizes, and they can be used to help solve problems involving proportions, rates, and percentages. For example, if you are making a recipe that calls for two cups of flour and one cup of sugar, the ratio of flour to sugar is 2:1, or 2/1. Ratios can also be expressed in decimal or percentage form!

The sine, cosine and tangent are obtained applying the trigonometric ratios presented in this problem.

The three trigonometric ratios are defined as follows:

The hypotenuse is the slanted segment connecting the horizontal and the vertical segment.

For the desired angle, you must identify the adjacent side(between the angle and the angle of 90º) and the opposite side.

The problem is incomplete, hence the concepts needed to obtain the sine, cosine and tangent were presented.

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The number that completes the square is 12.25

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

x^2 + 7x + 27 = 0

Take the coefficient of x

So, we have

k = 7

Divide by 2

k/2 = 3.5

Take the square of both sides

Square = 12.25

This means that the number to add is 12.25

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Answer:

Step-by-step explanation:

For this kind of problem, all you need to know is one formula:

The Distance Formula

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

in this case,

[tex]x_2=1[/tex], [tex]x_1=0[/tex], [tex]y_2=-3[/tex], [tex]y_1=-10[/tex]

[tex]D = \sqrt{(1-0)^2+(-3--10)^2}[/tex]

[tex]D = \sqrt{1^2+7^2}\\D = \sqrt{1+49}[/tex]

[tex]D = \sqrt{50}\\D = \sqrt{25*2} D = 5\sqrt{2}[/tex]

Answer: To simplify the expression, we can start by rewriting it as the product of the first fraction and the reciprocal of the second fraction. Then, we can factor the denominators of each fraction and simplify as much as possible.

x + 1 / (x^2 + x - 6) ÷ (x^2 + 5x + 4) / (x - 2)

= (x + 1 / (x + 3)(x - 2)) ÷ ((x + 4)(x + 1) / (x + 4)(x - 1))

= (x + 1 / (x + 3)(x - 2)) * ((x + 4)(x - 1) / (x + 4)(x + 1)) (reciprocal of second fraction)

= (x + 1 / (x + 3)(x - 2)) * (x - 1 / (x + 1)) (cancel out (x + 4) and simplify)

= (x + 1) * (x - 1) / (x + 3)(x - 2)(x + 1) (multiply the numerators and simplify)

= (x - 1) / (x + 3)(x - 2) (cancel out (x + 1) in the numerator and denominator)

Therefore, the simplified form of the expression is 1 / ((x + 3)(x - 2) / (x - 1)). This can be further simplified to:

1 / ((x + 3)(x - 2) / (x - 1)) = (x - 1) / ((x + 3)(x - 2)) * (x - 1) / 1 = (x - 1)^2 / ((x + 3)(x - 2))

So the answer is: 1 over the quantity (x + 3) times the quantity (x - 2), all multiplied by the quantity (x - 1) squared.

Step-by-step explanation:

The simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

The given expression is:

[tex]\frac{x+1}{x^2+x-6} / \frac{x^2+5x+4}{x-2}[/tex]

When a fraction is in the denominator, we take the reciprocal of the fraction and multiply it with the numerator.

So the expression becomes,

[tex]\frac{x+1}{x^2+x-6} * \frac{x-2}{x^2+5x+4}[/tex]

We can factorize the expression x² + x - 6

x² + 3x - 2x - 6

= x(x+3) -2 ( x+3)

= (x-2) (x+3)

We can also factorize the expression x² +5 x +4

x² + 4x + x +4

= x(x+4) +1 ( x+4)

= (x+1) (x+4)

Substituting these values, the expression becomes as follows:

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

Therefore the simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

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If x represents the number of apples purchased and y represents the number of mangos we can set up the following:

Kayden has $20, so can spend up to this amount:

He must buy a minimum of 16 apples and mangos altogether:

Also, he must buy no less than 16 apples:

We also need to consider y can't be negative, hence add one more inequality:

Plot all four inequalities and see what is the zone of intersection.

The solution is the set of whole coordinates for x and y within the triangle with vertices at (16, 0), (16, 4) and (26.67, 0).

One possible solution is (20, 2) another one (24, 1).

See attached.

Answer:

33

Step-by-step explanation:

Please brainliest, and Hope this helped you, I also answered first! :D

Answer: 33

Step-by-step explanation:

The rate at which Mandy used up her bags of dog food is 2/3 bags per day

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Slope = change in y /change in x

Here,   Slope = change in bags of food/ /change in days

form the graph = 4/6  = 4  bags per 6 days

4/6 simplifies to 2/3

=>  2/3 bags per day

The rate at which Mandy used up her bags of dog food is 2/3 bags per day

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The coordinates of point l are (8,9).

Numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.


To find this point, we must first calculate the midpoint between j and k. The midpoint can be found by taking the average of the x-coordinates and y-coordinates. The midpoint between j and k is (8,10). Since the ratio of jl:kl is 5:1, we can determine that l is 5 units away from j and 1 unit away from k. This means that l must be 5 units up and 1 unit to the right from the midpoint. Thus, the coordinates of l are (8,9).

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Answer:

x=11.34

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because u can tell

At the closing of her home purchase, Michelle should expect to pay prepaid interest of $6,934.50. This amount represents the interest accrued from April 8th to the end of the month.

The monthly payment for Michelle's mortgage is calculated as follows:

Principal and interest payment = (95,000 - 15,000) x 0.0495 / 12

This equals a monthly payment of $420.63.

Michelle's total interest over the life of the loan is $119,750. This amount is the sum of her prepaid interest and the total interest she pays over the life of the loan.

The value of x in the triangle, given the angle measures of the other angles, is D. 100 degrees

To find the value of x, you first need to find the value of the last interior angle in the triangle.

The sum of the interior angles of a triangle would add up to 180 degrees which means that the angle inside would be :

= 180 - 65 - 35

= 180 - 100

= 80 degrees

Angles on a straight line add up to 180 degrees so the value of x, which is on a straight line with 80 degrees, is :

= 180 - 80

= 100 degrees

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We require x = 170 televisions to minimize total cost

The minimum of a function is the lowest value of that function.

Given that a television manufacturer produces x sets per week so the total cost of production is given by relation C(x) = x² - 195x² + 66000x + 15000.

To find the minimum value, we differentiate C(x) with respect to x and equate to zero.

So,  C(x) = x² - 195x² + 66000x + 15000

dC(x)/dx = d(x² - 195x² + 66000x + 15000)/dx

= dx²/dx - d195x²/dx + d66000x/dx + d15000/dx

= 2x - 195(2)x + 66000 + 0

= 2x - 390x + 66000

= -388x + 66000

Equating to zero, we have

dC(x)/dx = 0

-388x + 66000 = 0

-388x = -66000

x = -66000/-388

x = 170.1

x ≅ 170

So, we require x = 170 televisions to minimize total cost

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If u and v be linearly independent unit vectors then  the set of all possible values of u⋅v is zero.

Vectors are used in science to describe anything that has both a direction and a magnitude.

Since u and v are unit vectors, their magnitudes are both 1.

|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v

= 1 + 2u⋅v + 1

= 2 + 2u⋅v.

On the other hand, we also have:

|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v = 2,

since u and v are linearly independent and hence orthogonal.

Equating the two expressions for |u + v|² we get:

2 + 2u⋅v = 2,

u⋅v = 0.

Therefore, the only possible value for u⋅v is 0.

Hence,  u and v be linearly independent unit vectors then  the set of all possible values of u⋅v is zero.

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The width of the arch at floor level is 10 feet.

In mathematics, a function is a relationship between two sets of objects, where each object in the first set (called the domain) is paired with exactly one object in the second set (called the range). In other words, a function is a rule that assigns a unique output value to each input value.

Functions can be described in several ways, including algebraic expressions, tables of values, graphs, and verbal descriptions. They can be used to model real-world phenomena, solve equations, and make predictions based on data.

The input values of a function are typically denoted by the variable x, while the output values are denoted by the variable y. The notation f(x) is often used to represent a function, where f is the name of the function and x is the input value.

Functions can be classified into different types based on their properties, such as linear, quadratic, exponential, trigonometric, and logarithmic functions. They can also be combined and manipulated using operations such as addition, subtraction, multiplication, division, composition, and inversion.

One of the key concepts in calculus is the derivative, which is the rate at which the output of a function changes with respect to its input. The derivative is used to calculate slopes, rates of change, and optimization problems in a wide range of applications.

Overall, functions are a fundamental concept in mathematics and have many important applications in science, engineering, economics, and other fields.

To find the width of the arch at floor level, we need to find the x-intercepts of the function y = -1/3(x-5)(x+5). At the x-intercepts, y is equal to zero, so we can set the equation equal to zero and solve for x:

0 = -1/3(x-5)(x+5)

There are two solutions to this equation: x = -5 and x = 5. These are the x-coordinates of the points where the arch intersects the x-axis.

The distance between these two points is the width of the arch at floor level. We can calculate this distance by subtracting the smaller x-value from the larger x-value:

Width = 5 - (-5) = 10 feet

Therefore, the width of the arch at floor level is 10 feet.

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The terminal point of p(x,y) on the unit circle is (-2, -1).

The unit circle is a circle with a radius of 1, centered at the origin (0, 0) on a Cartesian coordinate system. It is used to illustrate relationships between angles and their corresponding trigonometric functions. The unit circle is also used to explain concepts in trigonometry such as the sine and cosine functions, the Pythagorean theorem, and the definitions of the six trigonometric functions. It is especially useful in solving problems involving angles, such as finding the values of trigonometric functions given the angle in radians.

Step 1: Find the angle t in its standard form.

t = -4π/3 + 2π = -2π/3

Step 2: Calculate the coordinates using the unit circle formula.

x = cos(-2π/3)

x = -1/2

y = sin(-2π/3)

y = -√3/2

Step 3: The terminal point of p(x,y) on the unit circle is (-2, -1).

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2) The equation of tangent line is,

⇒ y = 324x log 3  + 84 - 648 log 3

3) And, The value of x is,

⇒ x = nπ ± π/6

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

2) The equation of curve is,

y = 3ˣ² + 3

At x = 2

y = 3⁴ + 3

y = 84

Hence, The value of point = (3, 84)

Now, Find dy/dx as;

y = 3ˣ² + 3

dy/dx = 3ˣ² log 3 × 2x

dy/dx = 2x × 3ˣ² log 3

At x = 2

dy/dx = 2 × 2 × 81 × log 3

m = dy/dx = 324 log 3

We know that;

The slope intercept form of equation of line is,

y = mx + c

y = 324x log 3  + c

At point (x, y) = (2, 84)

84 = 324 × 2 log 3 + c

⇒ c = 84 - 648 log 3

Hence, The equation of tangent line is,

⇒ y = 324x log 3  + 84 - 648 log 3

3) We know that;

Horizontal tangent will have a slope of 0.

Hence, The derivative represent the rate of change of a function.

The equation of graph is,

y = 4x - 3 tan x

y' = 4 - 3 sec²x = 0

sec²x = 4/3

sec²x = (2/√3)²

x = nπ ± π/6

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Trains make up approximately 49.04% of the total journeys across all modes of transportation.

We must divide the total number of train trips by the total number of trips made using all modes of transportation, then multiply the result by 100 to get the percentage that trains make up of the total.

There have been 2320 train trips overall, and there have been 4730 trips overall using all forms of transportation.

Trains therefore account for the following proportion of the total:

(2320 / 4730) x 100% = 49.04%

Train travel thus accounts for roughly 49.04 percent of all travels made using all modes of transportation.

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The width of the rectangle whose perimeter is 37 cm is 6.25 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The length of a rectangle is 6 cm more than its width, w cm.

So, the length = w + 6

The perimeter of the rectangle is 37 cm.

Then, Perimeter of the rectangle = 37

2(l+ w) = 37

2( w+ 6 +w )= 37

2(2w + 6)= 37

4w + 12 = 37

4w = 25

w = 6.25 cm

and, length = w+ 6 = 6 + 6.25 = 12.25 cm

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The coterminal angle is 304°, which lies in the fourth quadrant with a reference angle of 44°.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To find the coterminal angle of 664°, we can add or subtract any multiple of 360° to it.

664° - 360° = 304°

The coterminal angle of 664° is 304°.

To determine the quadrant that 664° lies in, we can divide it by 90° and take the quotient:

664° ÷ 90° = 7 with remainder 34

As remainder is 34 and it is less than 90, the angle lies in the fourth quadrant.

To find the reference angle of 664°

we can subtract the nearest multiple of 90°:

664° - 6(90°) = 44°

The reference angle of 664° is 44°.

Therefore, the coterminal angle is 304°, which lies in the fourth quadrant with a reference angle of 44°.

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The distance between the man and the monument is 1060.16 feet.

Here we have the angle of elevation to be 18°

and the angle of depression to be 3°

Let the distance between the man and the monument be x feet

Now for any angle a, tana = opposite angle / adjacent angle

Hence we can sum up the building's height to be

x tan18 + x tan3 = 400

or, x(tan18 + tan3) = 400

or, x(0.3249 + 0.0524) = 400

or, 0.3773x = 400

or, x = 400/0.3773

or, x = 1060.16

Hence the distance between the man and the monument is 1060.16 feet.

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The image of the polygon after the rotation is added as an attachment

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

(1, 0), (2, 0), (0, 2) and (2, 2)

The location of point G is

G = (3, -1)

To rotate about point G, we start by subtracting the points from G

So, we have

[(1, 0), (2, 0), (0, 2) and (2, 2)] - (3, -1)

This gives

(-2, 1), (-1, 1), (-3, 3) and (-1, 3)

The rule is 90 degrees clockwise rotation

This is represented as

(x, y) ⇒ (y, -x)

So, we have

(-2, 1), (-1, 1), (-3, 3) and (-1, 3) ⇒ (1, 2), (1, 1), (3, 3) and (3, 1)

Next, we plot (1, 2), (1, 1), (3, 3) and (3, 1)

See attachment for the image of the transformation

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Answer:Il y a 2 configurations de Thalès La première donne BC/CE = AC/CD = 1/2

la seconde donne BC/CE = CF/CA => CF = CA/2 = 3/2

Step-by-step explanation:

The number of positive results for all persons with TB will be D. 423

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true

Rate of incidence of TB is 450 per 100,000

Column Totals of "Has TB" = (450 / 100,000) * Grand Total = (450 / 100,000) * 100,000 = 450

If a person does have TB, then the DNA test will be positive 94% of the time.

Therefore, P = Number of positive results for all persons with TB:

= 0.94 * 450

= 423

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