A part-time handyman made $8798. 04 last year. If he claimed himself as an

exemption for $3650 and had a $5700 standard deduction, what was his

taxable income last year?

A. $551. 96

B. $5,148. 04

C. $0

D. $3,098. 04

Answer:

y = 2x - 4

Step-by-step explanation:

The equation is y = mx + b

m = The slope

b = y-intercept

To find the slope, we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 2, and the y-intercept is located at (0,-4), so the equation is

y = 2x - 4

Over the course of the three hours, 41.25 gallons of water passed through the pipe in total.

We know that the rate of flow for the first hour was 50% slower than the rate of flow for the second hour. So, if the rate of flow in the second hour was 15 gallons per hour, the rate of flow in the first hour would be:

15 gallons/hour * (100% - 50%) = 15 gallons/hour * 50% = 7.5 gallons/hour

We also know that 25% more water flowed through the pipe in the third hour than in the second. So the rate of flow in the third hour would be:

15 gallons/hour * (1 + 25%) = 15 gallons/hour * 1.25 = 18.75 gallons/hour

To find the total number of gallons of water that flowed through the pipe during the entire three hours, we can multiply the rate of flow for each hour by the number of hours:

First hour: 7.5 gallons/hour * 1 hour = 7.5 gallons

Second hour: 15 gallons/hour * 1 hour = 15 gallons

Third hour: 18.75 gallons/hour * 1 hour = 18.75 gallons

Adding these values we can find the total amount of water that flowed through the pipe during the entire three hours

7.5 gallons + 15 gallons + 18.75 gallons = 41.25 gallons

So, in total 41.25 gallons of water flowed through the pipe during the entire three hours.

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Answer:

Part A: Two types of transformations: translation and reflection.

Part B: g(x)=f(x)+k

-1= -1+ k

k= -1+1=0

g(x)=f(x)+k

-1= 5+k

k= -1-5=-6

g(x)=f(x)+k

14= 14+k

k= 0

k= -6,0,-6,0

Part C: For horizontal translation, g(x)=f(x+2)

In case of vertical translation, g(x)=f(x)+10

Therefore, the equation of transformation can be written as g(x)=f(x+2)+10.

Step-by-step explanation:

I thought. :') Ever since yesterday, and today. Hope this helps!

Answer:

t = 5, 6

Step-by-step explanation:

Given the equation:

[tex]\displaystyle{11t-t^2=30}[/tex]

First, arrange the expression in the standard quadratic form ax² + bx + c = 0

[tex]\displaystyle{t^2-11t+30=0}[/tex]

Then factor the expression, find two numbers that add up which result in -11  and multiply which result in 30 - that two numbers are -6 and -5

[tex]\displaystyle{(t-6)(t-5)=0}[/tex]

Solve like a linear equation

[tex]\displaystyle{t=5,6}[/tex]

Therefore, the solutions to the equation are t = 5, 6

Answer:

The solution set is {5, 6}.

Step-by-step explanation:

11t-t^2=30

t^2 - 11t + 30 = 0

(t - 5)(t - 6) = 0

t = 5, 6.

Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.

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The average rate of the given function is 2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is h(x)=-x²-x+5 and the interval is -6≤x≤2.

x={-6, -5, -4, -3, -2, -1, 0, 1, 2}

y=-x²-x+5

When x=-2

y=-(-2)²-(-2)+5

y=-4+4+5

y=5

When x=-1

y=-(-1)²-(-1)+5

y=5

When x=0

y=5

When x=1

y=-1-1+5

y=3

When x=2

y=-(2)²-(2)+5

y=-1

Now, rate using (1, 3) and (2, -1), we get

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

m=2

Therefore, the average rate of the given function is 2.

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h = 7 is the solution to the equation 1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

The equation given that,

1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)

The least common multiple of the denominators is:

h² - 25 = (h - 5) (h + 5)

We multiply through with the LCM to obtain:

= [(h - 5) × (h + 5)] × [1 / (h - 5)] + [(h - 5) × (h + 5)] × [2 / (h - 5)]

= 16 / (h² - 25) × [(h - 5) × (h + 5)]

We cancel out common factors to obtain:

= 1 (h + 5) + 2 (h - 5)

= 16

We expand the brackets to obtain

= h + 5 +2h - 10

We group like terms to get:

h + 2h = 16 - 5 + 10

This simplifies to:

3h = 21

We now divide through by 3 to obtain:

h = 7

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Enlargements of the picture or reductions of the image are both types of dilations.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.

The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.

Even in the enlarged picture, parallel and perpendicular lines are still discernible.

A dilated image's side's midway matches the pre-exactly. image's

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Weight of each type of box:

Weight of each big box = 18.75 kg

Weight of each small box = 13.75 kg

The relationship between two terms on either side of a letter is represented by a mathematical formula. Often there is a variable and an equals sign.

The definition of an equation in algebra is a formula that shows the equivalence of two mathematical terms. For example, in the expression 6x + 11 = 14 the two terms 6x + 11 and 14 are separated by the "equals" symbol.

To let

Weight of each big box = x

And the weight of each small box = y

Weight of 3 big boxes:

3 times

5 small box weights:

5 years

3x + 5y = 125 .......................(i)

resemble:

9x + 7y = 265 ......................(ii)

Equation (i) multiplied by -3:

-3 (3x + 5y) = 125 * (-3)

-9x - 15y = -375 ...................(iii)

Under (ii) and (iii):

9x + 7y = 265

-9x - 15y = -375

Adding this gives:

-8y = -110

or y = 110/8

or y = 55/4

y = 13.75

From equation (i), we have:

3x + 5y = 125

or 3x + 5(13.75) = 125

or 3x + 68.75 = 125

3x = 125 - 68.75

3x = 56.25

x = 56.25/3

x = 18.75

Each large box weighs:

18.75 kilograms

Weight of each small box:

13.75 kilograms

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An isosceles right triangle has two sides that are equal in length; this means that the angles opposite the sides must also be equal. Since the triangle is a right triangle and the sum of angles of a triangle is 180 degrees, the angles must each be 45 degrees.

The acute angles of an isosceles right triangle are always 45 because of the Pythagorean Theorem. This theorem states that in a right triangle the sum of the squares of the two sides adjacent to the right angle (the legs) is equal to the square of the hypotenuse. Since an isosceles right triangle has two equal legs, and the hypotenuse is the longest side, the two legs must both have the same length, and the angles opposite from these sides must also be the same. This means that the two acute angles in an isosceles right triangle must both be 45 degrees.

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]

The required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

What is system of equations?

A set or group of equations that are solved together is referred to as a system of equations. Both algebraic and graphic solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.

If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.

Then the total hours she can work = t + r

Since she can work up to 25 hours.

Thus  t + r ≤ 25

If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .

Then her total earning = $25t + 12r

Since she must earn $200.

Then 25t + 12r ≥ 200

Hence, the required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

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Answer:

yes, it uses the Commutative Property

Step-by-step explanation:

Example of an undecidable problem is given by the problems in the system created by computer viruses.

According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.

A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.

whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.

If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.

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Answer:

A - $360

Step-by-step explanation:

Length times width equals area.

12 × 10 = 120

His office has 120 sq ft of space. If each sq ft costs $3

120 × 3 = $360

A

Answer:

A ($360)

Step-by-step explanation:

imagine a rectangle with one side 12ft and one side 10ft

multiply the length and the width to find the square footage:

12*10=120ft^2

each square foot is $3 so multiply 3 by 120

$3*120ft^2= $360

oops didn't realize someone already answered sorry

Answer:

The US Consumer Price Index (CPI) increased 8.3% in the 12 months through August, with rent, food and healthcare accounting for the rise Excluding volatile food and gas prices, inflation climbed 6.3% year-on-year in July and 8.2% in September. US inflation ticked back up in August despite plunging gas prices.

citations: https://nypost.com/2022/10/13/inflation-hits-8-2-in-september-as-core-prices-surge/Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.

Here,

Given : Ria purchases 19 books for £6.82 apiece.

Thus,

Total cost of book = 19 * 6.82

=> 129.58

Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

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Number of students that do two subjects are 12.

Number of students that do only exactly one subject are;

For Art;

⇒ 14

For Chemistry;

⇒ 11

For Bio;

⇒ 8

Number of students that do at least two of the subjects are 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.

All the students do at least one of the three subjects.

3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.

Here,

Total students = 48

So, Number of students that do two subjects are = 4 + 3 + 5

                                                                            = 12

And, Number of students that do only exactly one subject are;

For Art;

⇒ 24 - (3 + 4 + 3)

⇒ 14

For Chemistry;

⇒ 22 - (3 + 5 + 3)

⇒ 11

For Bio;

⇒ 20 - (3 + 4 + 5)

⇒ 8

Number of students that do at least two of the subjects are;

⇒ 3 + 3 + 4 + 5

⇒ 15

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Answer:

120

Step-by-step explanation:

First, divide 115 by 6:

115/6 =

(114 + 1)/6 =  ==> 114 is a multiple of 6

114/6 + 1/6 = ==> distribution property

19 + 1/6 =  ==> simplify

19 1/6 ==> the smallest integer greater than 19 1/6 is 20

Hence, multiply 20 by 6 to get 120.

54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.

given

To find P P, divide P

P by the total number of participants (students and chaperones), which is 81.

Seventh graders totaling 81 - 7 =

74 participated in the field trip.

54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.

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In mathematics, a plane is a two-dimensional surface that can be enlarged indefinitely. In order to make a plane we need at least 3 points.

In order to make a plane we need at least 3 points. Let A, B and C are three points which can be defined by two particular vector AB and AC.

As the two vectors is located on the plane, we can use their cross product to define a normal vector on the plane.

As we see a triangle which is a two-dimensional geometric figure that is developed based on 3 points. Triangle is the smallest polygon. The other polygon needs more point for creation.

Therefore, it is proved that minimum three points is mandatory for plane formation.

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Answer:

[tex]x=-2,1[/tex]

Step-by-step explanation:

[tex]x^2+x-2=0\\(x+2)(x-1)=0\\x_1=-2,x_2=1[/tex]

As per the given simple interest, the principal amount is $165.35.

The term simple interest in math is defined as  the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.

Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.

Therefore, through the given question we have identified the value of

interest rate = 3.5%

time period = 44

sum amount = 420.

Then the principal amount is calculated by using the formula of simple interest as,

P = A / (1 + rt)

Here first we have to convert R percent to r a decimal, then we get

r = R/100 = 3.5%/100 = 0.035 per year.

Now, we have to apply the values on the equation and then we have to solve our equation, then we get

P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866

P = $165.35

Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.

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As per the power rule of exponents, the solution of 3 to the power of 3 is 27.

The term exponent in math is defined as a number shows how many times the number is multiplied by itself.

Here we have to solve 3 to the power of 3.

Here according to the Power Rule of Exponents then we have the rule as

=> aⁿ = a × a × a... (n times)

Therefore, the given expression is written as

=> 3³

Now, based on the power of exponent rule it can be rewritten as,

=>  3 × 3 × 3

Then we have to multiply the values then we get

=> 27

Therefore, the value of 3 raised to 3rd power is 27.

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Answer:

$68

Step-by-step explanation:

Let x = original price.

The sale price is 75% of the original price, so the sale price is 75% of x.

75% as a decimal is 75/100 = 0.75

75% of is the same as 0.75x

We are told the sale price is $51, so 0.75x must equal $51.

0.75x = 51

Divide both sides by 0.75 to find the value of x.

x = 51/0.75

x = 68

Answer: $68

Answer:

Step-by-step explanation:

$51 is 75% of 100%

75% = 3/4

51 / 3 = 17

17 = 1/4

51 + 17 = 68

$68 is the original price of the shoes

Answer:

Step-by-step explanation:

Given isosceles triangle ABC with AB≅AC, altitude AP, and AB=(2x+3), AC=(3y-1), BP=(y+1), and PC=(x+2), you want the values of x and y.

Corresponding parts of ∆ABP and ∆ACP are congruent, so we have ...

  2x +3 = 3y -1

  x +2 = y +1

Subtracting twice the second equation from the first gives ...

  (2x +3) -2(x +2) = (3y -1) -2(y +1)

  -1 = y -3 . . . . simplify

  2 = y . . . . . . add 3

Substituting into the second equation, we have ...

  x +2 = 2 +1

  x = 1 . . . . . . . .subtract 2

The values of x and y are 1 and 2, respectively.

Step-by-step explanation:

in an isoceles triangle (both legs have identical length) the height from the top corner to the baseline shots the baseline into 2 identical halves.

so,

6x + 6 = 9x - 15

6 = 3x - 15

21 = 3x

x = 21/3 = 7

many greetings to your teacher from me : he/ she made a formal mistake. the angles at Y have to be indicated as right angles. because if the line WY is not the height but could have any angle with the baseline, this cannot be solved.

The percentage increase in the price of the notebook is 15%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.

The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Finding the increase in the price of the notebook:

$3.80 - $3.30 = $0.50

Dividing the increase by the original amount:

0.50 / 3.30 = 0.1515

To change to a percent multiply by 100 and round off to significant numbers:

0.1515 *100 = 15.15% or, 15%.

Thus, the percentage increase in the price of the notebook is 15%.

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Therefore, the sine of any angle can also only be between -1 and 1, inclusive.

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located.

Lines (line segments) and points make up the forms we perceive (vertices). To create a shape, these line segments are connected at their vertices. These lines' sides are what they are known as. The line segment that connects two vertices of a form or two-dimensional object is referred to as a side in geometry.

The sine of an angle can never be greater than 1 because the sine function maps an angle to the y-coordinate of the point on the unit circle that corresponds to that angle. The y-coordinate of any point on the unit circle is always between -1 and 1, inclusive. Therefore, the sine of any angle can also only be between -1 and 1, inclusive.

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The answer is no, we would not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.

    z = (3-2) / 0.5 = 2

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