18% discount on a list price of $25

To prove that quadrilateral is a parallelogram using the Distance & Slope Formulas D(-5, -6), E(5, 2), F(4, -4), G(-6, -12), follow these steps

:Step 1: Plot the points in a coordinate plane: (D) (-5,-6), (E) (5,2), (F) (4,-4), (G) (-6,-12)

Step 2: Find the distance of all sides using distance formula.

Distance Formula =sqrt((x2 - x1)² + (y2 - y1)²)DE

                              = sqrt((5 - (-5))² + (2 - (-6))²)

                              =sqrt(10²+8²)

                              =sqrt(164)

                              = 2 sqrt(41)EF

                              = sqrt((4 - 5)² + (-4 - 2)²)

                              =sqrt((-1)²+(-6)²)

                              =sqrt(37)FG

                              = sqrt((-6 - 4)² + (-12 - (-4))²)

                              =sqrt((-10)²+(-8)²)

                              = 2sqrt(41)DG

                              = sqrt((-6 - (-5))² + (-12 - (-6))²)

                              =sqrt((-1)²+(-6)²)

                              =sqrt(37)

Since the opposite sides are equal, we can say that DE = FG and DG = EF.

Step 3: Find the slope of all sides using slope formula.

Slope Formula = (y2-y1)/(x2-x1)DE

                         = (2-(-6))/(5-(-5))

                         =8/10=4/5FG

                         = (-12-(-4))/(-6-4)=-8/-10=4/5DG = (-6-(-12))/(-5-(-6))=6/1=6EF = (-4-2)/(4-5)=-6/-1=6

Since opposite sides have the same slope, DE // FG and DG // EF. Therefore, we can conclude that the quadrilateral is a parallelogram.In conclusion, the quadrilateral is a parallelogram because opposite sides are parallel.

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Odd integers are:

1, 3, 5, ...

They are spaced "2" units apart.

So,

if the first odd number is "x",

the next is "x + 2"

the third one is "x + 2 + 2"

the fourth one is " x + 2 + 2 + 2"

Thus, the four consecutive odd numbers are:

We sum the expressions and equal to -8. Then solve for x:

So,

This is the least integer out of the 4:

Answer:

k =5

Step-by-step explanation:

k/6 = 15 / 18

Cross multiply ✖

18k = 15 * 6

18k = 90

k = 90 / 18

k = 5

Hope it helps :)

The perimeter of this figure, to the nearest unit: 38 units

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Given that,

A figure

the perimeter of the given figure  = ?

Arc length, ED = \((\frac{\alpha }{360} ) 2\pi r\)

                        = \(\frac{90}{360}\) x  x \(\frac{22}{7}\) x 5

                        = 7.85 unit

Therefore,

The perimeter of the given figure is,

= AC + CD + ED + EF + FA

= 10 + 5 + 7.85 + 5 + 10

= 37.85 units

rounding off to the nearest unit

≈ 38 units

Thus, the perimeter of the given figure is → 38 units.

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Answer:

(-2,4)

Step-by-step explanation:

B(1,2)

(x-3, y+2)

1-3=-2

x=(-2)

2+2=4

y=4

Hope this helps! :)

Answer:

B'(-2, 4)

Step-by-step explanation:

If it goes 3 units left, that means you're doing x - 3.

If it goes 2 units up that means you're doing y + 2 This would be:

(1 - 3, 2 + 2)

(-2, 4)

Answer:

(Choice A) Only those viewers who called in

Step-by-step explanation:

The statement tell us Ninety percent of the viewers that call in say that they will vote against the tax increase.

This explains it is option A .

Choice B is incorrect as all viewers may not have called in.

Choice C is also incorrect all regular viewers do not call in.

Choice D is incorrect calls are not received at any point at only specific time.

Choice E is incorrect because all voters again may not call in.

The expression that makes v the subject of the formula, W=5+v/v-3 is v= (5 + 3W)/ (W-1).

The concept is the concept of finding the subject of the formula in an expression.

To know the subject of the formula, we will need to perform some simplification:

W=5+v/v-3

then this can be expressed as:

W(v-3) = 5+v

Wv - 3W = 5+v

then we can rearrange the expression as:

Wv - v = 5 + 3W

then we can factorize  the expression as :

v(W-1) = (5 + 3W)

v= (5 + 3W)/ (W-1)

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Answer:

okay go to the quickpill app

Step-by-step explanation:

The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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So, the final equation for the sine function is:

\(y = 5 sin(2x - \pi /2) + 2\).

The general form of a trigonometric equation can vary depending on which trigonometric function is being used (sine, cosine, tangent, etc.), but the most general form is:

\(f(x) = A sin(Bx + C) + D\)

where f(x) is the trigonometric function, A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift. The phase shift and vertical shift are optional components and may not always be present in a trigonometric equation.

If using cosine instead of sine, the equation would be:

\(f(x) = A cos(Bx + C) + D\)

If using tangent, the equation would be:

\(f(x) = A tan(Bx + C) + D\)

Other trigonometric functions, such as secant, cosecant, and cotangent, can also be used in trigonometric equations, but the general form would follow the same structure as above.

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All three components of the fire triangle are usually present whenever and wherever surgery is performed. The fire triangle consists of three elements: fuel, heat, and oxygen.

In the context of surgery, nitrous oxide can be considered as a source of the fuel component of the fire triangle. Nitrous oxide is commonly used as an anesthetic in surgery, and it is highly flammable. It can act as a fuel for fire if it comes into contact with a source of ignition, such as sparks or open flames.

Therefore, it is important for healthcare professionals to be aware of the potential fire hazards associated with the use of nitrous oxide in surgical settings and take appropriate safety precautions to prevent fires.

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EXPLANATION

The equation of the function can be represented as shown as follows:

-This function is discrete.

-If we have 20 gallons, we can obtain the number of miles by plugging in the value into the equation, as shown as follows:

Dividing both sides by 12:

Simplifying:

We can make 1.67 miles with 20 gallons.

-The domain of the function are all the Real Numbers and the Range are also the Real numbers.

-Finally, drawing the graph of the function:

The points of the table are the following:

Gallons Miles

2 24

4 48

6 72

8 96

-We can get the number of gallons needed to, make 500 miles by plugging the value 500 into the equation, as shown as follows:

Isolating m:

Simplifying:

The number of gallons to make 500 miles is equal to 41.7 gallons

Finally, labeling the graph:

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

y-4=3(x-2)

Step-by-step explanation:

y-y1=m(x-x1)

Answer: -27

Step-by-step explanation:

-16 + (-11)

= -16 - 11                       *a negative minus a negative equals a negative*

= -27

Answer:

Step-by-step explanation:

The degree of each term in a polynomial is the exponent of the variable. If there are multiple variables in a term, the degree is the sum of their exponents. The degree of the polynomial is the highest of the degrees of the terms.

__

The three terms of the polynomial given here have degrees of 2, 0, and 3. Since the highest degree is 3, the polynomial is 3rd-degree, or "cubic." The "leading term" is the one of highest degree, and its coefficient is the "leading coefficient." The constant term is the one with degree 0 (no variables).

"The expression represents a cubic polynomial with 3 terms. The constant is -2, the leading term is 1/4x³, and the leading coefficient is 1/4."

The length of each side of the square is approximately 4.472 cm. To find the length of each side of the square, we can use the formula for the area of a square.

The area of Square is A = s², where A is the area and s is the length of each side.

Substituting A = 20 into the formula, we get:

20 = s²

Taking the square root of both sides, we get:

s = √(20)

Simplifying the radical, we get:

s = √(4*5)

s = 2√(5)

Therefore, the length of each side of the square is approximately 4.472 cm, rounded to three decimal places.

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======================================================

Explanation:

Of your original given list, let's write down the parallelograms. They are:

So we cross those off the list since we want a quadrilateral with no sides parallel. A parallelogram, by definition, is a quadrilateral with both pairs of opposite sides that are parallel.

We can also rule out the trapezoids because a trapezoid is a four sided figure (quadrilateral) where we have exactly 1 pair of parallel sides, while the other sides are not parallel.

Lastly, we can rule out the kite because any kite has perpendicular diagonals.

The only thing left is quadrilateral. In my opinion this answer should be more specific and say "quadrilateral that isn't a parallelogram, a trapezoid, or a kite", but I think I see what your teacher was going for here.

The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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The probability a state highway inspector could select a sample of 50 trucks is option 1 which is 0.1251

Population mean = 15.8

Population standard deviation = 9.2 ,

n = 50

To find : P( xbar < 14.3 )

We know, xbar ~ N( μ , σ / √(n) )

P( Z < ( 14.3 - 15.8 ) / 9.2/ ( √50 ) ) = P( Z < -1.5/ 1.3010 ) = P( Z < -1.15)  

= 1 - P( Z < 1.15)  

= 1 - 0.87493  (Standard normal probability table)

= 0.12507 = 0.1251

Hence the correct option is option (1) which is 0.1251

A standard deviation (or σ) is a proportion of how distributed the information is corresponding to the mean. A low standard deviation implies information is bunched around the mean, and an exclusive requirement deviation demonstrates information is more fanned out.

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The answer is FALSE. The alternative hypothesis is a statement that there is a difference or an effect in the population being studied, and it contradicts the null hypothesis, which is a statement that there is no difference or no effect in the population being studied.

The alternative hypothesis is a statement that contradicts the null hypothesis and is generally the hypothesis that the researcher wants to support. It is a statement that there is a difference or an effect in the population being studied.

In hypothesis testing, the null hypothesis is a statement that there is no difference or no effect in the population being studied. The null hypothesis is typically the default hypothesis, which is assumed to be true unless evidence suggests otherwise. The alternative hypothesis, on the other hand, is a statement that there is a difference or an effect in the population being studied, and it is typically the hypothesis that the researcher wants to support.

For example, if a researcher wants to test the effectiveness of a new drug, the null hypothesis might be that the drug has no effect on the condition being treated, while the alternative hypothesis might be that the drug has a positive effect on the condition being treated.

In summary, the alternative hypothesis is a statement that there is a difference or an effect in the population being studied, and it contradicts the null hypothesis, which is a statement that there is no difference or no effect in the population being studied.

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She should:

LaToya should address the pay discrepancy by looking into the company's pay practices and ensuring they are in compliance with sex and gender discrimination laws. She should calculate the total compensation her drivers receive, including benefits and perks. She should also educate all of her drivers on how Home Health's pay practices work to avoid any misunderstandings.

It is not appropriate to assume that female drivers are performing at a lower level or to consider factors such as the frequency of asking for pay raises as a basis for pay disparities. Addressing pay disparities and promoting equality is a crucial part of LaToya's role as Vice President of HR.

Complete question:

Sex and gender discrimination laws LaToya is the Vice President of Human Resources at Home Health, a company that delivers oxygen and other supplies to patients in their homes. Recently, LaToya discovered that her male delivery drivers were earning 25% more than her female delivery drivers. What can she do to handle this problem? Check all that apply.

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Among the probability distributions listed, the normal distribution is the only one that is always symmetric.

The normal distribution is a continuous probability distribution that is symmetric around its mean. Its probability density function (PDF) has a bell-shaped curve with the peak at the mean, and the distribution is symmetric on both sides. This means that the probability of observing a value to the left of the mean is the same as the probability of observing a value to the right of the mean, resulting in a symmetric distribution. Regardless of the specific parameters of the normal distribution, such as the mean and standard deviation, its shape remains symmetric.

On the other hand, the other distributions listed—Student's t distribution, chi-square distribution, and F distribution—are not always symmetric.

The Student's t distribution is also symmetric, but its symmetry depends on the degrees of freedom (df) parameter. When the degrees of freedom are equal to or greater than 2, the distribution is symmetric. However, when the degrees of freedom are less than 2, the distribution is not symmetric. Therefore, while the Student's t distribution can be symmetric under certain conditions, it is not always symmetric.

The chi-square distribution is not symmetric. It is a positively skewed distribution with a longer right tail. The shape of the chi-square distribution depends on the degrees of freedom parameter. As the degrees of freedom increase, the distribution approaches a normal distribution in shape, but it remains positively skewed for smaller degrees of freedom.

The F distribution is also not symmetric. It is a right-skewed distribution with a longer right tail. The shape of the F distribution depends on the degrees of freedom parameters for the numerator and denominator. As the degrees of freedom increase, the distribution becomes less skewed, but it remains right-skewed.

To summarize, among the probability distributions listed, only the normal distribution is always symmetric. The Student's t distribution, chi-square distribution, and F distribution are not always symmetric and their symmetry depends on the specific parameters involved.

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Answer:

theyre correct

Step-by-step explanation:

While both Lincoln and Davis faced significant challenges as wartime presidents, Lincoln's leadership and strategic abilities set him apart as the better leader. His legacy as a wartime president, combined with his commitment to ending slavery, has cemented his place in American history.

Abraham Lincoln and Jefferson Davis were both wartime presidents during the American Civil War. While they had similar roles, they had different approaches to leadership and faced different challenges. Lincoln was the President of the Union, while Davis was the President of the Confederacy.
Lincoln was faced with the challenge of keeping the Union together and ending slavery, while Davis was faced with the challenge of defending the Confederacy against the Union's military might. Lincoln was able to overcome these challenges by using his strategic mind and political skills to rally the Union's troops and support from the North. He also utilized his famous Emancipation Proclamation to show his commitment to ending slavery. Davis, on the other hand, struggled with a lack of resources, including money and troops. He also faced internal conflicts within the Confederacy, including states wanting to secede from the Confederacy.
In terms of leadership, Lincoln is widely considered the better leader due to his success in keeping the Union together and ultimately winning the war. He was able to inspire and motivate his troops, as well as effectively communicate with the North and Congress. Davis, on the other hand, was criticized for his leadership style and his inability to unite the Confederacy.
Overall, while both Lincoln and Davis faced significant challenges as wartime presidents, Lincoln's leadership and strategic abilities set him apart as the better leader. His legacy as a wartime president, combined with his commitment to ending slavery, has cemented his place in American history.

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The value of 2 ½ is 2.5. As 2 ½ is the same as mixed fraction 2 ½ = 5/2.

2 ½ is a mixed number, it is a whole number combined with a fraction. In this case, 2 is the whole number and ½ is the fraction. The value of 2 ½ is calculated by adding the value of the whole number to the value of the fraction.

The value of the whole number 2 is 2, and the value of the fraction ½ is 0.5. To find the value of 2 ½, we add 2 to 0.5:

2 + 0.5 = 2.5

So, the value of 2 ½ is 2.5.

It's important to note that mixed numbers are used to represent numbers that are between two whole numbers, they consist of a whole number and a proper fraction. This mixed number representation is commonly used in everyday life, and it's easy to understand.

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2 If we were to deposit money for nine years, the answer may change as compounding frequency would have a greater effect over a longer time period.

3 The future value of a loan of $1000 would be $1,238.36, while at Trusty Bank it would be $1,169.81.

3 it takes approximately 11.55 years for the money to triple at Trusty Bank with monthly compounding.

When comparing the two banks, it is important to note that Happy Bank is offering semiannual compounding while Trusty Bank is offering monthly compounding. To compare the two rates on an equal basis, we need to convert them into their equivalent annual rates with continuous compounding, which takes into account compounding frequency.

The formula for the continuous compounding rate is e^(r/n)-1, where r is the nominal rate and n is the compounding frequency. For Happy Bank, the continuous compounding rate would be e^(0.06/2)-1 = 0.0294, or 2.94%. For Trusty Bank, the continuous compounding rate would be e^(0.06/12)-1 = 0.0049, or 0.49%.

Using these rates, we can calculate the future value of $1000 over three years. At Happy Bank, the future value would be $1,238.36, while at Trusty Bank it would be $1,169.81. Therefore, Happy Bank is the better deal for a three-year deposit.

If we were to deposit money for nine years, the answer may change as compounding frequency would have a greater effect over a longer time period. However, without additional information about compounding frequency and rates, we cannot determine which bank would be the better deal.

If we were to borrow money for three years, the calculations would be similar but the direction would be reversed. At Happy Bank, the future value of a loan of $1000 would be $1,238.36, while at Trusty Bank it would be $1,169.81. Therefore, Trusty Bank would be the better option for a three-year loan.

To determine how long it takes for the money to triple at Trusty Bank, we can use the formula FV = PV * e^(rt). If we start with $1000 and want to find when it will triple, we can set FV = $3000 and solve for t. This gives t = ln(3)/0.06 = 11.55 years. Therefore, it takes approximately 11.55 years for the money to triple at Trusty Bank with monthly compounding.

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Juliette's tax situation will depend on the specifics of her income and expenses for the year.

Based on the information provided in Chapter 9 TRP 9-1, we can determine that Juliette White is a head of household taxpayer with a dependent daughter named Sabrina. She works at a law firm and attends school at Reno Community College in the evenings. Juliette's mother watches Sabrina after school and in the evenings at no charge.

It is assumed that Juliette does not wish to contribute to the Presidential Election Fund and that she did not acquire any financial interest in any virtual currency during the year.

To file her taxes, Juliette will need to gather her income information from her job at the law firm and any financial aid or scholarships she received for attending RCC. She will also need to provide information on any other income sources she may have, such as interest earned on savings accounts or investment income.

As a head of household taxpayer, Juliette may be eligible for certain tax credits and deductions, such as the Child Tax Credit or the Earned Income Tax Credit. She will also need to provide information on any deductions she is eligible for, such as student loan interest or tuition and fees paid for attending RCC.

Overall, It is important that she accurately reports all of her income and deductions to ensure that she pays the correct amount of taxes and avoids any penalties or fines.

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a) To find the value of k that makes f(y) a probability density function, we need to ensure that the integral of f(y) over the entire range of y is equal to 1. That is:

∫[0,1] k y(1 − y) dy = 1.

Solving this integral, we get:

k ∫[0,1] y(1 − y) dy = 1

k [(1/2)y^2 - (1/3)y^3] [0,1] = 1

k (1/6) = 1

k = 6.

Therefore, f(y) is a probability density function with k = 6.

b) To find P(0.4 ≤ Y ≤ 1), we need to integrate f(y) over the range [0.4,1]:

P(0.4 ≤ Y ≤ 1) = ∫[0.4,1] f(y) dy

= ∫[0.4,1] 6y(1 − y) dy

= 0.54.

Therefore, P(0.4 ≤ Y ≤ 1) = 0.54.

c) To find P(Y ≤ 0.4|Y ≤ 0.8), we use the formula for conditional probability:

P(Y ≤ 0.4|Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8)/P(Y ≤ 0.8)

= P(Y ≤ 0.4)/P(Y ≤ 0.8)

= [∫[0,0.4] 6y(1 − y) dy]/[∫[0,0.8] 6y(1 − y) dy]

= 0.0225/0.36

= 0.0625.

Therefore, P(Y ≤ 0.4|Y ≤ 0.8) = 0.0625.

a) To find the value of c that makes f(y) a probability density function, we need to ensure that the integral of f(y) over the entire range of y is equal to 1. That is:

∫[0,2] c y dy = 1.

Solving this integral, we get:

c ∫[0,2] y dy = 1

c (1/2) y^2 [0,2] = 1

c = 1/2.

Therefore, f(y) is a probability density function with c = 1/2.

b) To find F(y), we integrate f(y) from 0 to y:

F(y) = ∫[0,y] (1/2) y dy

= (1/4) y^2.

For y < 0 or y > 2, F(y) = 0.

Therefore, the cumulative distribution function F(y) is given by:

F(y) = { 0, y < 0

    (1/4) y^2, 0 ≤ y ≤ 2

    1, y > 2 }

c) To find P(1 ≤ Y ≤ 2), we use the cumulative distribution function:

P(1 ≤ Y ≤ 2) = F(2) - F(1)

= (1/4) (2)^2 - (1/4) (1)^2

= 3/4.

Therefore, P(1 ≤ Y ≤ 2) = 3/4.

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