Question 15 (3 points)

Cameron purchased a house that sold for $317,000. He obtained a mortgage of $299,500. The bank charged 2. 75 points for an origination fee

and 3. 0 discount points. What was the total cost of the origination fee and discount points that Cameron paid? (3 points)

Triangles HIJ and H'I'J have undergone rotation as the exact sort of transformation.

When we translate, we move a figure in any direction. When we reflect, we turn a figure or a line over. The act of rotating a figure around a point is known as rotation. Enlarging or contracting a figure is called dilation. Congruent transformations include rotations, translations, and reflections. A congruence transformation is not resizing. A figure turned over a line of reflection is called a reflection.

Translation, rotation, reflection, and dilation are the four basic forms of transformations. Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You accomplish this by turning one shape so that it is in alignment with the other. A rotation is the name given to such a change.

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Answer:

no

Step-by-step explanation:

Answer:Descartes’s chief contributions to mathematics were his analytical geometry and his theory of vortices, and it is on his researches in connection with the former of these subjects that his mathematical reputation rests. Who is Rene Descartes is he known for? Descartes has been heralded as the first modern philosopher.

Step-by-step explanation:

A state function is a property that depends only on the current state of the system, and not on the path taken to reach that state.

Examples of state functions include temperature, pressure, volume, and internal energy, and they can only be measured if a substance undergoes a phase change.

A state function is a property of a system that depends only on the current state of the system, and not on the path taken to reach that state. In other words, a state function is a property that is path-independent. This means that the value of a state function does not depend on how the system arrived at its current state, only on the current state itself.

One way to think about state functions is to compare them to non-state functions, also known as path functions. A non-state function, such as work or heat, depends on the path taken to reach the current state of the system. For example, the amount of work done on a gas in a piston can be different depending on the path taken to compress the gas. If the gas is compressed slowly, the amount of work done will be less than if it were compressed quickly. However, the internal energy of the gas, which is a state function, will be the same regardless of the path taken to compress it.

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To solve the system of equations we need to add the equations to eliminate y, option A is correct.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given equations

-10x - 6y = -2

-x + 6y = -20

to solve the equations by elimination,

add both the equations

-10x - 6y -x + 6y = -2 - 20

-11x = -22

x = 2

y = -3

Hence option A is correct.

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Answer:

Simple interest is calculated by multiplying the principal amount (the initial deposit) by the interest rate and the number of years.

The formula for simple interest is:

I = P * r * t

Where:

I = Interest

P = Principal (initial deposit)

r = Interest rate (expressed as a decimal)

t = Time (in years)

In this case, the principal amount is $500.00, the interest rate is 4.5% (converted to 0.045), and the time is 15 years.

We can plug in the values into the formula:

I = $500.00 * 0.045 * 15 = $337.50

So, after 15 years with the same interest rate, Arisia’s account would earn $337.50 in interest.

Therefore , the solution is first angle = 63° and second angle = 27° for

complementary angle problem.

A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The slopes of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplemental angle involves two angles joined to create a 180 degree angle.

Here,

Given :

Let us consider first angle be x

and second angle is less than 36°

=>  x - 36°

So , there are complementary angle there sum will be equal to 90°

=> x + x - 36°  = 90°

=>  2x =  90° + 36°

=> x = 126°/2

=> x =63°

First angle = 63°

and second angle = 63° - 36° = 27°

Therefore , the solution is first angle = 63° and second angle = 27° for

complementary angle  problem.

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A linear graph is a graph in which the data points are distributed along a straight line, and the relationship between the variables is represented by a linear equation.

A nonlinear graph is a graph in which the data points are not distributed along a straight line, and the relationship between the variables is represented by a nonlinear equation.

A linear equation is an equation that can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line represents the rate of change of the dependent variable y with respect to the independent variable x. A graph that follows a linear equation will be a straight line.

On the other hand, a nonlinear equation is an equation that cannot be written in the form of y = mx + b. The relationship between the variables in a nonlinear equation is more complex and can be represented by a curve on a graph. The shape of the curve can vary and can be determined by the specific equation being used.

In summary, a linear graph is a graph that shows a straight line relationship between the variables, while a nonlinear graph is a graph that shows a more complex, curved relationship between the variables.

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All the statements for the account balances are true.

Since the balance of Sam's account, y, based on the number of weeks spent saving, x, can be represented by y = 35x+10.

We can also represent his sister's account with equation as follows.

The general form of  the equation of a line is given by y = mx+b,

where m is the slope (rate) and b is the y-intercept (starting point)

From the graph:

Sam's sister starts with $60 i.e. b = 60

The amount she saved per week can be found by calculating the slope.

Slope = (y₂-y₁) /(x₂-x₁)

Using x₁= 0, y₁ = 60 and x₂ = 2, y₂ = 120

Slope = (120-60) /(2-0)  = 60/2 = 30

y = mx+b

y = 30x + 60

After 5 weeks:

For Sam:

y=35x+10

y=35(5) +10 = $185

For his sister:

y = 30x + 60

y = 30(5) + 60 = $210

Difference = $210 -  $185 =  $25

Statement           T/F

Statement 1          T  

True because Sam's equation has m = 35 and his sister's has m = 30.

Statement 2         T

True because Sam's equation has b = 10 and his sister's has b = 60.

Statement 3          T

True because the difference is $25

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The scale factor that is used to dilate JA is 3.

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Length of the segment JA = 7 in

Length of the segment JA' = 21 in

Now,

The scale factor.

= New segment / Old segment

= 21/7

= 3

Thus,

The scale factor is 3 in.

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Hi there!  For this one, just set up an equation of what you know and don't know.

20 x __% = 15, I think you're asking.

20 x (n) = 15

Divide both sides by 20 to isolate n.  Go on from there!  If you need more help, just let me know.

The value of the given expression log 3 base 3 is equal to 1.

As given in the question,

Given expression is written as :

x =  log 3 base 3

In the logarithmic function ,

When the base value and number for which log needs to be calculated is same then it is equal to one.

In standard form logarithmic function is written as :

logₐ a = ( log a ) / ( log a )

⇒ logₐ a = 1

Substitute the value of a = 3 we get,

log₃ 3 = ( log 3 ) / ( log 3 )

⇒ log₃ 3 = 1

Therefore, the value of the given logarithmic expression log 3 base 3 is equal to 1.

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Part A: The volume of the small fish tank is 576 cubic inches.

Part B: The length of the large fish tank is 24 inches.

Part A:

The volume of the small fish tank can be found by multiplying its length, width, and height.

Length x Width x Height
= 12 inches x 8 inches x 6 inches
= 576 cubic inches

Part B:

We know that the large fish tank's volume is two times that of the small fish tank. So:

The volume of the large fish tank

= 576 cubic inches x 2 = 1152 cubic inches

We also know that the width and height of the large fish tank are the same as the small fish tank (8 inches and 6 inches respectively). So we can use the formula for volume (length x width x height) to find the length(L) of the large fish tank:

1152 cubic inches = L x 8 inches x 6 inches

                             = L x 48 inches²

To solve for L, we divide both sides by 48 :

L = 24 inches

So the large fish tank is 24 inches long.

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The complete question is -

A store sells two fish tanks. The small fish tank is 12 inches long, 8 inches wide, and 6 inches high The large fish tank is 8 inches wide and 6 inches high. The volume of the large fish tank is two times the volume of the small fish tank.

Part A: What is the volume of the small fish tank (in cubic inches)?

Part B: How long is the large fish tank (in inches)?

The required function for the given values of x and y is  y = 16/x.

If two quantities are inversely related, one will increase while the other will decrease. Building a wall would be an example of an inverse proportion in action. The time it takes to construct a wall decreases as more people work on it.

We have,

x = 2 and y = 8

Then

y ∝ 1/x

y = k/x

K is constant

So, Putting the values

8 = k/2

k = 16

Function is y = 16/x

Thus, required function is y = 16/x.

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Answer: 27x^{2} y^{12}

Step-by-step explanation:

RemoveRemoveRemove parentheses and brackets by multiplying factors. ...

Use the exponent rule to remove grouping if the terms contain exponents. ...

Combine like terms by adding or subtracting coefficients. ...Combine

Combine the constants.

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

Answer:m

Step-by-step explanation:

The value of the angle ∠PRQ using sine rule is;  36.9°

The sine rule is a rule in trigonometry that states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

Thus;

a/sin A = b/sin B = c/sin C

Now, applying the sine rule to the given problem, we can say that;

130/sin ∠PRQ = 187.5/sin 60

sin ∠PRQ = (130/187.5) * sin 60

sin ∠PRQ = 0.6

∠PRQ =  sin⁻¹0.6

∠PRQ = 36.9°

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The lower bound for a 95% confidence interval for the average length of the entire population of fish is 65.492.

Let the sample mean be ( x ) = 66.7

Standard deviation for the given sample be = s = 8.5

random sample of 190 fish is collected from the ocean so ( n )= 190

Confidence level be 95% so the Z-score be 1.959 ≈ 1.96.

By using the formula ,

x ± [tex]Z \frac{s}{\sqrt{n} }[/tex]

= 66.7 ± 1.96 (8.5/√190)

= 66.7 ± 1.208

where 1.208 indicates margin error (E).

So upper bound be 66.7 + 1.208 = 67.908

and lower bound be 66.7 - 1.208 = 65.492.

95% of samples contain the population mean (μ) within the confidence interval x ± E.

"A confidence interval is the range of values, obtained from sample statistics, that is likely to include the value of an unknown population parameter," according to the definition.

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Yes -17 is an integer

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z.

Example of integers are: 0 , 1 ,-2, - 67 ,50 e.t.c. Other examples of integers are : -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .

Since it is stated that an integer is a number that is zero, a positive number and a negative number . It can be the therefore said that -17 is an integer

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The number -17 is an integer number, as it has a decimal part of zero.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For the number -17, we have that:

As the decimal part of the number -17 is of zero, the number can in fact be classified as an integer number.

The problem asks if the number -17 can be classified as an integer number.

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The point which is at  equal distance from y-axis to the given points           A(- 5,-2 )and B(3, 2 ) is given by ( 0,-2).

As given in the question,

Let us consider a point C(0 ,y) be the point on the y -axis.

Point C (0, y) is at the equal distance from point A(- 5,-2 )and B(3, 2 ).

AC = BC

⇒ √( y + 2 )² + ( 0 + 5)² = √( y - 2)² + ( 0 -3)²

Squaring both the sides we get,

⇒ y² + 4y + 4 + 25 = y² - 4y + 4 + 9

⇒ 8y = 9 - 25

⇒ y = -16 /8

⇒ y = -2

Therefore, the required point of y-axis which is at equal distance from the given points A and B is equal to ( 0, -2 ).

The above question is incomplete , the complete question is:

What point on the Y-axis is at equal distances from A(- 5,-2 )and B(3, 2 )?

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The value of HI in the figure is solved using similar triangle to get 34

The figure the triangle HJI and triangle JKL are similar triangles. This means that the angles are congruent and corresponding sides are proportional

The corresponding proportional sides that will be used for the calculation are

JK and JH, KL and HI

equating the proportional sides

since k is the id point of JK then JK / JH = 1/2

JK / JH = KL / HI

substituting the values

1 / 2 = (-25 + 7x) / (8x - 14)

cross multiplying

8x - 14 = 2(-25 + 7x)

8x - 14 = -50 + 14x

collecting like terms

8x - 14x = -50 + 14

-6x = -36

x = 6

since HI = 8x - 14

substituting the value of x

= 8 * 6 - 14

= 48 - 14

= 34

Hence HI = 34

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Inferential data uses strategies that take an end result from a pattern, increase it to a populace, and degree the reliability of the result. Variables are the traits of the individuals within the populace.

Inferential records use measurements from the pattern of topics within the experiment to examine the remedy agencies and make generalizations about the larger populace of subjects. there are numerous varieties of inferential facts and every one is suitable for a particular research design and sample characteristics.

Inferential statistics is a department of statistics that makes the usage of diverse analytical equipment to attract inferences approximately the population information from pattern facts. aside from inferential information, descriptive records form another branch of information.

Statistical inference is the procedure of the usage of facts evaluation to deduce houses of an underlying distribution of opportunity. Inferential statistical evaluation infers homes of a populace, for instance through testing hypotheses and deriving estimates.

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Complete Question:

_______ statistics uses methods that take a result from a sample, extend it to a population, and measure the reliability of the result.

Log 4 to the base 10 has a value of 0.6020. The logarithmic function allows us to calculate the value of log 4 in terms of both natural and common logarithms.

Logarithmic functions, also referred to as log functions, are the opposite of exponentiation. According to its definition, a logarithm is a measurement that depicts the degree to which a base (fixed number) is raised to generate a specific number.

"[tex]log_{10} 4[/tex]" stands for the logarithm of 4 to the base 10.

Base's explanation of the logarithmic function is that a = 10 and [tex]10_x[/tex] = b.

The value of log 4 to the base 10 is obtained by 0.6020 using a logarithm table.

[tex]log_{10} 4[/tex] = 0.6020

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b. is the right answer which has all points to the right.

A rectangular plane with a grid network created by the junction of horizontal and vertical lines is referred to as a coordinate grid. The location where the horizontal and vertical lines intersect at a perpendicular angle.

A reflection is referred to as flipping in geometry. Reflection is the term for a shape's mirror image. A line along which an image reflects is known as the line of reflection. A figure constructed around a single point is referred to as a reflection of point on graph paper.

A coordinate grid from negative 3 to positive 3 on both axes is drawn in increments of  2.

Point A is plotted 2 grid lines to the right of the y-axis and 4 grid lines above the x-axis.

Point B is plotted at 6 grid lines to the right of the y-axis and 2 grid line below the x-axis.

Point C is plotted at 6 grid lines to the left of the y-axis and 4 grid line below the x-axis.

Each unit is represented by 2 grid lines.

This means the coordinates of B (3, 2) will be 2×(3, 2) = (6, 4) grid lines.

The reflection of B across the y-axis to get C will change the sign of the x-coordinate, so C is (-6, -4) in terms of grid lines.

(Positive is above or right; negative is below or left.)

The above description is the only one that has the points in the right places.

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There is a probability of 0.64 that Hugo buys more than 2 packs to get the card of his favorite player.

Therefore P( X > 2) is 0.64.

The random variable X in this situation represents the number of packs of baseball cards that Hugo buys before he gets the card of his favorite player. Since Hugo can buy at most 4 packs and the probability of getting the desired card in each pack is 0.2, we can use this information to create the probability distribution for X.

Here is the probability distribution for X using binomial distribution:

X > 4: The probability that Hugo does not get the card in any pack is

= (1 - 0.2)⁴

= 0.4096

X = 1: The probability that Hugo gets the card in the first pack is

= 0.2

X = 2: The probability that Hugo gets the card in the second pack is

= (1 - 0.2)(0.2)

= 0.16

X = 3: The probability that Hugo gets the card in the third pack is

= (1-0.2)²(0.2)

= 0.128

X = 4: The probability that Hugo gets the card in the fourth pack is

= (1-0.2)³(0.2)

= 0.1024

Probability that Hugo has to but more than 2 pack is

P( X>2) = P(3) + P(4) + P(X > 4)

= 0.128 + 0.1024 + 0.4096

= 0.64

--The question is incomplete, answering to the question below--

"Hugo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most 4 packs. Suppose that each pack has probability 0.2 of containing the card Hugo is hoping for. Let the random variable X be the number of packs of cards Hugo buys. Here is the probability distribution for X. Find P(X > 2)."

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Answer:

Step-by-step explanation:

A quadratic equation has the general form ax2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.

To convert the above equation "x+9+18=0" to quadratic equation form, we must transfer all of the terms to one side of the equation and set it equal to 0.

The following equation may be rewritten: x+9+18 = 0.

Combining like terms yields: x+27 = 0.

x = -27 after subtracting 27 from both sides.

As a result, the answer to the equation is x = -27. It's not a quadratic formula.

To prove whether two lines are parallel, check the alternating angles and interior angles. Also, check their perpendicular and parallel property with the third line.  

If two lines never cross one other, they are said to be parallel. The theorems that follow show that lines are parallel:

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According to the given information in the question the value of x is 85. Hence answer will be x = 85.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: Angle FGH is a straight angle.

The measure of angle FGJ is 95°.

The measure of angle JGH is x°

Angles that form a straight line add up to equal 180°

Thus, x + 95 = 180

180 - 95 = 85

x = 85

Hence, the value of x is 85.

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No, this is not a quadratic equation. A quadratic equation is an equation of degree two, and this equation is of degree five.

A quadratic equation is an equation of degree two, meaning it is an equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are constants, and x is a variable. This equation, X² x³ 2 0, is of degree five, and therefore is not a quadratic equation. Quadratic equations are commonly used to solve problems involving a parabola or a maximum or minimum point. They are also important in calculus, where they are used to calculate the area under a curve. The solutions to a quadratic equation can be found using the quadratic formula, which states that the solutions are given by x = (-b ± √(b² - 4ac))/2a. In this equation, a, b, and c are the constants from the quadratic equation, and x is the variable.

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