Mia buys a house for $95,500, restores it, and then sells it for $126,060. Find the percent of change.

If you rent a car, you should choose Option 3 and accept the fixed price of $50 for gasoline if you expect to drive 150 miles.

1. Total gasoline consumed (gallons):

To calculate the total gasoline consumed, divide the expected distance by the car's fuel efficiency:

Total gasoline consumed = Distance / Fuel efficiency

Total gasoline consumed = 150 miles / 28 miles per gallon

Total gasoline consumed ≈ 5.36 gallons

2. Option 1 cost:

In Option 1, you need to return the car with a full gas tank. Since the car has a 16-gallon tank and you've consumed approximately 5.36 gallons, you need to fill up the remaining 16 - 5.36 = 10.64 gallons.

Option 1 cost = 10.64 gallons * $3.95 per gallon = $42.01

3. Option 2 cost:

In Option 2, you return the car without filling it up and pay $5.45 per gallon. As calculated before, you've consumed approximately 5.36 gallons.

Option 2 cost = 5.36 gallons * $5.45 per gallon = $29.20

4. Option 3 cost:

In Option 3, you accept the fixed price of $50 for gasoline. This fixed price is the most cost-effective option compared to the other two choices.

Therefore, the best choice is Option 3, accepting the fixed price of $50 for gasoline, as it offers a better value for the expected distance of 150 miles.

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When a right triangular prism is cut perpendicular to its base, the resulting cross-section will be a rectangle.

What is the right triangular prism?

A right triangular prism is a three-dimensional geometric shape that consists of two parallel triangular bases and three rectangular faces joining them. The perpendicular line segment joining the bases is called the altitude of the prism. If the perpendicular line segment is perpendicular to the base and passes through the center of the base, it is called a right prism.

This is because the cross-section will intersect the triangular base of the prism along a line perpendicular to the base, forming a triangle.

When this triangular section is removed, the cross section of the prism will be a rectangle that is parallel to the base of the prism.

This is because the edges of the prism that are perpendicular to the base will be cut by the plane of the cross section, and these edges will form the two parallel sides of the rectangle.

The other two sides of the rectangle will be formed by the sides of the triangular base of the prism.

hence, when a right triangular prism is cut perpendicular to its base, the resulting cross-section will be a rectangle.

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Answer:

The objects of a set are called its elements. If a set has no elements, it is called the empty set and is denoted by ∅.

Step-by-step explanation:

Could I have branliest and heart please

Have a good day.

(x + a)^2 + b form can be achieved by a method known as completing the square.

Step 1: Divide the b term by 2 and square it

8 / 2 = 4

4^2 = 16

Step 2: Add and subtract 16 from the expression

---Adding 16 creates a perfect square trinomial between x^2 + 8x + 16. But, if we add 16, we also need to subtract it. So, we will subtract 16 from our c term, 14.

x^2 + 8x + 16 + 14 - 16

x^2 + 8x + 16 - 2

Step 3: Factor the perfect square trinomial

(x^2 + 8x + 16) - 2

(x + 4)(x + 4) - 2

(x + 4)^2 - 2

Answer: (x + 4)^2 - 2

Hope this helps! :)

Answer:

Step-by-step explanation:

Since both equations equals y, then both equations equal each other.

3x - 1 = 2x + 2

Subtract 2x from both sides

x - 1 = 2

Add 1 to both sides

x = 3

Plug x = 3 into one equation(doesn't matter which)

y = 3x - 1

y = 3(3) - 1

y = 9 - 1

y = 8

Answer:

\(x=3\)

\(y=8\)

Step-by-step explanation:

From these two equations, we can substitute the first equation into the second equation (or the other way round). This gives us:

\(3x-1=2x+2\)

\(3x-2x=2+1\) (minus \(2x\) and add \(1\) on both sides)

\(x=3\)

To solve for \(y\), we can use substitution again:

\(y = 3(3)-1\) (using the first equation given)

\(y=8\)

Hope this helps :)

Given

The point,

To find the value of csc theta.

Explanation:

It is given that,

Then,

Therefore,

Hence,

The total length of road they built is 5 15/21 kilometers.

Here, we have,

given that,

A construction crew has just finished building a road. The crew worked for 2 2/3 days. If they built 2 1/7 kilometers of road each day.

so, we get,

The total number of days that it took the construction crew to finish the road 2 2/3.

Converting 2 2/3 days to improper fraction, it becomes 8/3 days.

If they built 2 1/7 kilometers of road each day,

converting 2 1/7 kilometers to improper fraction, it becomes 15/7 kilometers.

so, we have,

The total number of days that it took the construction crew to finish the road is 8/3 days.

they built 15/7 kilometers of road each day

Therefore, the total length of road that they built is

15/7 × 8/3

= 120/21 kilometers

Converting to mixed fraction, it becomes

5 15/21 kilometers.

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A Decision Support System (DSS) is a computer-based information system that assists decision-makers in making informed and effective decisions. It provides analytical tools, models, and data to support decision-making processes. The key components of a DSS include a database, model base, user interface, and decision-making tools.

A suitable diagram illustrating the purpose and key components of a Decision Support System (DSS) would typically show the interrelationship between these components. The diagram would highlight the flow of information from the database to the user interface, where decision-makers interact with the system using decision-making tools. The model base represents various analytical models and algorithms used to analyze data and generate insights for decision-making.

Individual DSS and Group DSS differ in terms of the support they provide. Individual DSS focuses on assisting individual decision-makers in their decision-making processes. It provides personalized support tailored to the specific needs and preferences of the individual user. On the other hand, Group DSS facilitates collaborative decision-making among a group of individuals. It supports communication, information sharing, and consensus-building among group members.

The evolutionary approach to Management Information System (MIS) development involves incremental and iterative development of the system. It starts with a basic version of the system and gradually adds new features and functionalities based on feedback and evolving requirements. This approach is most suitable for the development of an Individual DSS when the user's decision-making needs are not fully understood or when the requirements are likely to change over time.

By adopting an evolutionary approach, the system can be refined and enhanced iteratively, ensuring it remains aligned with the user's evolving needs and provides effective decision support.

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Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

Answer:

1.4 people out of 10

Step-by-step explanation:

Just divide it by 10

Answer:

only 4 people

Answer:

Their are many other answers to this question this is one of the ones that are correct.

Answer:

\(y = \frac{1}{3}x + 3\)

Step-by-step explanation:

Parallel lines have same slope

y = 1/3x - 4

m =\(\frac{1}{3}\\\)    and the line passes through (-3, 2)

Equation: y - y₁ = m(x - x₁)

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

Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624 the amount paid as tax is $ 3,765.

Given details in the question are as follows:

Jim Bouche is married but is filing a separate tax return. His taxable income is $23,624,

By using the given tax table on the screenshot we are calculating the tax paid by Jim.

if your taxable income is greater than the $23,600 but lesser than the $23,624 and you fill separate tax return, the amount will be paid as tax is

$ 3,765.

Married filing separately is a tax status for married couples who choose to record their respective incomes, exemptions, and deductions on separate tax returns.

The alternative to married filing separately is married filing jointly. Usually, it makes sense financially for married couples to file jointly. However, when one spouse has significant medical expenses or miscellaneous itemized deductions, or when both spouses have about the same amount of income, it might be wiser to file separately.

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To determine the angle of rotation from point P to point Q on the unit circle, we can use trigonometric principles and the concept of arc length.

By connecting the two points with a line segment, we form an arc on the unit circle. The length of this arc represents the angle of rotation in radians.To find the angle of rotation, we can consider the unit circle as a reference. Point P is located at an angle of -π/3 radians (or -60 degrees) from the positive x-axis, while point Q is situated at an angle of π/3 radians (or 60 degrees) from the positive x-axis.

The angle of rotation can be calculated by finding the difference between the angles of P and Q. In this case, it is 2π/3 radians (or 120 degrees). This means that the object has rotated counterclockwise by an angle of 2π/3 radians or 120 degrees from point P to point Q.

It's important to note that when rotating counterclockwise on the unit circle, the positive direction is used for measuring angles. The angle of rotation represents the change in position as the object moves from one point to another on the unit circle.

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Answer:

  (c)  (x +7)/3

Step-by-step explanation:

Factor each expression and cancel common factors.

 \(\dfrac{x^2+12x+35}{3x+15}=\dfrac{(x+7)(x+5)}{3(x+5)}=\boxed{\dfrac{x+7}{3}}\)

Answer:

C

Step-by-step explanation:

passed the quiz

After 5.4 years, the value of the car will be half the initial value.

We know that the value decreases by 12% each year.

Then the value of the car can be modeled with an exponential decay, written as:

\(V(t) = A*(1 - 12 \% /100 \%)^t = A*(1 - 0.12)^t = A*(0.88)^t\)

Where A is the initial value, and t is the number of years.

The value will be halved when:

\((0.88)^t = 0.5\)

We need to solve that, to do it, we can apply the natural logarithm to both sides, so we get:

\(Ln(0.88^t) = Ln(0.5)\\\\t*Ln(0.88) = Ln(0.5)\\\\t = Ln(0.5)/Ln(0.88) = 5.4\)

This means that after 5.4 years, the value of the car will be half the initial value.

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An equilateral triangle is a triangle where all the sides are congruent to each other.It's an isosceles triangle since two of its sides are congruent to each other. As a result, all of the angles of the triangle are equivalent. If a triangle is equilateral, then it is equiangular.

Given that ΔABC is an equilateral triangle.Prove: ΔABC is equiangular. Solution:An equilateral triangle is a triangle where all the sides are congruent to each other. It's an isosceles triangle since two of its sides are congruent to each other. As a result, all of the angles of the triangle are equivalent. Let's look at the proof.Theorem: If a triangle is equilateral, then it is equiangular.

Proof:Given: ΔABC is an equilateral triangle.Show: ΔABC is an equiangular triangle.ABC is equilateral, so AB = BC = AC. As a result, AB ≅ BC ≅ AC.1. Draw the perpendicular bisectors of each side of the triangle.2. The perpendicular bisectors of the sides of an equilateral triangle are concurrent. Let G be their intersection point.3. Since AB ≅ BC ≅ AC, ΔABC is isosceles. As a result, AG, BG, and CG are all equivalent.4. Since G is the centroid of ΔABC, AG is two-thirds the length of a median.5. Since the three medians of ΔABC are concurrent at G, ΔABC is equiangular.Therefore, ΔABC is equiangular.

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Answer:

y = -1x + 3 or y = -x + 3 (**That is the last option which is D**)

Step-by-step explanation:

You need to do slope-intercept formula and the slope formula.

The Slope-Intercept Formula: y=mx+b

The Slope Formula: y2 - y1 / x2-x1

Your coordinates:

(-1,4) and (1,2)

2 - 4/1- (-1)

-2/2

Simplified is -1

Your "m" in the slope-intercept formula is -1

Formula: y=-1x + b

Now, you need to find the Y-Intercept which is the "b"

Using our slope-intercept formula, you need to plug in "x1" and "y1"

4 = -1(-1) + b

4 = 1 +b

4-1 = b

3 = b

So your equation is:

y = -1x + 3 or y = -x + 3

The limit of `f(x)` as `x → 2+` is equal to `1`.

The function `f(x)` is given as `|x + 3| / x + 3`. Find the limit of the function `f(x)` as `x → 2+`.

To find the limit of `f(x)` as `x → 2+` means we need to find the limit as `x` approaches `2` from the right side (that is, `x > 2`). To calculate the limit, we need to analyze both the numerator and denominator of the fraction. Let's begin by analyzing the numerator:

As `x` approaches `2` from the right, `|x + 3|` approaches `|5|` or `5`.

Now let's analyze the denominator:

As `x` approaches `2` from the right, the expression `x + 3` approaches `5`.

Now, let's put the numerator and denominator together to find the limit of the function as `x → 2+`. We can do this by replacing `x` with `2` in the expression:

`f(2) = |2 + 3| / 2 + 3``f(2) = 5 / 5``f(2) = 1`Therefore, the limit of `f(x)` as `x → 2+` is equal to `1`.

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Answer:

1

Step-by-step explanation:

Substitute 3 for x and 2 for y:

3^2 - 2(3)(2) + 2^2

= 9 - 12 + 4

= 1

3^2−(2)(3)(2)+2^2

3^2−(2)(3)(2)+2^2

= 1

Answer:

\(k=-\frac{2}{5}\)

Step-by-step explanation:

\(k=-\frac{8}{20}=-\frac{4(2)}{4(5)}=-\frac{2}{5}\)

Answer: y = -32 and -(2/5)

Step-by-step explanation:

Let z equal to the difference,

x - z = -4

20 - z = -4

20 + 4 = z

z = 24

y - z

= -8 - 24

= -32

Therefore y = -32

For the second part of the question

-8 = k(20)

-8 = k * 20

-8/20 = k <-- Divide both sides by 20

Therefore k = -(8/20) = -(2/5)

Answer: a6=70

Step-by-step explanation:

we know that

In the Arithmetic Sequence the formula is:

an= a1 + d(n−1)

where

a1 is the first term

d is the common difference

n is the number of terms

in this problem

a1=5

a2=18

a3=31

a4=44

a5=57

so

d=a2-a1 or a3-a2 or a4-a3 or a5-a4

d=57-44----> 13

find a6

a6= a1 + d(n−1)

n=6

d=13

a1=5

a6=5+13*(6-1)----> a6=5+13*5----> a6=70

Answer:

Answer:

1 slice will be left because there are 16 slices and 15 guests

Step-by-step explanation:

Step-by-step explanation:

Rotation would be the best answer

In completing the square method, considering the equation X^2 + 82x +  the number to be added should be 1681 to make it a perfect square

The quadratic equation is an equation of the form

ax^2 + bx + c

The completing the square method is on of the methods of solving equations of the form above

The factor to be added on the both sides of the equation while using the completing the square method is

(b / 2a)^2

compared to the equation in the problem X^2 +82x

= (b / 2a)^2

= (82 / 2)^2

= (41)^2

= 1681

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The length of the side of the triangle BC is 0. 97 cm

It is important to note that their are different trigonometric identities. These identities are;

From the information given, we have that;

cos θ = adjacent/hypotenuse

sin θ = opposite/hypotenuse

tan θ = opposite/adjacent

Then, we have;

sin 17 = BC/√11

cross multiply the values, we have;

BC = sin 17 (√11)

BC = 0. 97 cm

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So, the probability of winning is 1/5 or 1:5 expressed as a fraction.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It involves the measurement and analysis of the likelihood of various events occurring. The probability of an event is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In other words, probability is the measure of the likelihood of an event occurring. It is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability plays an important role in various fields such as science, engineering, finance, and statistics, and is used to model and predict outcomes of uncertain events.

If the odds on a bet are 4:1 against, it means that the probability of winning is 1 out of 4+1 = 5 (i.e., there are 5 possible outcomes, of which only 1 is a win).

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