Quadrilateral PQRS is located at P (0, 1), Q (3, 2), R (4, −1), and S (1, −2). Russell and Jamie have both classified PQRS differently. Examine their proofs. Who is correct?

A. Russell
B. Jamie
C. Both
D. Neither

5/2 and 3 are the solutions to the equation 2x² - 10x + 15 = x.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

2x² - 10x + 15 = x

2x² - 11x + 15 = 0

2x² -6x -5x + 15 = 0

2x(x-3)-5(x-3)=0

x=5/2, 3

The solutions to the equation 2x² - 10x + 15 = x is 5/2 and 3.

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The equation of the plane  passing through point P with normal vector n A(x-2) + B(y-3) + C(z-4) = 0

(a) Normal Form:

The equation of the plane passing through point P with normal vector n can be written in normal form as:

n • (r - p) = 0

where r is a position vector in three-dimensional space and n is the normal vector of the plane.

Given n = (1,2,3) and p = (2,3,4).

Therefore, n • (r - p) = (1,2,3) • (r - (2,3,4)) = r1 + 2r2 + 3r3 -2 - 3 - 4 = 0

=> r1 + 2r2 + 3r3 - 8 = 0

=> Plane equation in normal form: 1x + 2y + 3z - 8 = 0

(b) General Form:

The equation of the plane passing through point P with normal vector n can also be written in general form as:

A(x-x0) + B(y-y0) + C(z-z0) = 0

where A, B and C are the components of the normal vector n and (x0,y0,z0) are the coordinates of the point p.

Given n = (1,2,3) and p = (2,3,4).

Therefore, A(x-2) + B(y-3) + C(z-4) = 0

=> 1(x-2) + 2(y-3) + 3(z-4) = 0

=> Plane equation in general form: x - 2y + 3z - 8 = 0

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Provide complete question here:Write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.

Systematic random sampling is used when selecting every nth item from a list of items. In this example, every 49th student starting with the 3rd student is selected.

In systematic random sampling, a list of items is created and every nth item is selected for the sample. This technique is useful when selecting a representative sample from a large population of items. In the example given, 496 students were listed and every 49th student starting from the 3rd student was selected. This is a systematic random sampling technique because the items were selected in a systematic and random fashion. The selection of every 49th student starting from the 3rd student ensures that the sample is representative of the population while also randomizing it so that all students have an equal chance of being selected.

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Answer:

Step-by-step explanation:

the fourth one

Answer:

first three answers.

Step-by-step explanation:

each bottle is 1/4d. so all three are 3*1/4d

Answer:

D. I centimeter

Step-by-step explanation:

Since it is only 0.128 nm wide

0.128 nm x 100,000,000 =

1.28 centi meters

Answer:

D)  1 centimeter

Step-by-step explanation:

The SI base unit for length is meters (m).

The radius of a copper atom is 128 pm.

Picometer (pm) is a unit of length equal to 1 × 10⁻¹² meters.

Therefore, the radius of a copper atom in the SI base unit for length is:

[tex]\implies \sf 128 \times 10^{-12} = 1.28 \times 10^{-10}\;m[/tex]

One hundred million = 100,000,000 = 1 × 10⁸

Therefore, the length of a line of one hundred million copper atoms in meters is:

[tex]\implies \sf 1 \times 10^{8} \times 1.28 \times 10^{-10}[/tex]

[tex]\implies \sf 1.28 \times 10^{-10} \times 10^{8}[/tex]

[tex]\implies \sf 1.28 \times 10^{-10+8}[/tex]

[tex]\implies \sf 1.28 \times 10^{-2}\;\;m[/tex]

Centimeter (cm) is a unit of length equal to 1 × 10⁻² meters.

To convert meters to centimeters, divide by 1 × 10⁻²:

[tex]\implies \sf \dfrac{1.28 \times 10^{-2}}{1 \times 10^{-2}}=1.28\;cm[/tex]

Therefore, a reasonable estimate for the length of one hundred million copper atoms arranged in a line is 1 centimeter.

Answer:

4 cm.

Step-by-step explanation:

Area = pi r^2, so:

pi r^2 = 4 / pi

(pi)^2 r^2 = 4

r^2 = 4/ (pi^2)

r = 2/pi

Therefore, the circumference

= 2 pi r

= 2* pi * 2/pi

= 4

To find the percentile, we need to calculate what percentage of the data falls below the $78 thousand dollars wage.

To find the percentile, we sort the data in ascending order and find the percentage of the data that falls below $78 thousand dollars. Here's one way to do this:

69 58 43 43 43 51 57 57 62 68 69 75 76 78 78 80 91 97 102 124 130 135 144 157 185 217

Out of 28 observations, 22 of them are below $78 thousand dollars. So, the percentile for someone who earns $78 thousand dollars is 22/28 * 100 = 78.5714.

In this context, the value of the percentile represents the percentage of the population of full-time employed people who hold at least a Bachelor's degree and earn less than $78 thousand dollars. So, someone who earns $78 thousand dollars is in the 78.5714th percentile of this population.

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The function represented in Cartesian plane have the following features: Domain of function: - 4 ≤ x ≤ 2, Range of function: - 4 ≤ y ≤ 4. (Right choice: B)

In this question we find the representation of a function on Cartesian plane. There are two important hints to answer this question:

Then, by direct inspection we find the following results: Domain: - 4 ≤ x ≤ 2, Range: - 4 ≤ y ≤ 4.

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The value of y is 11/3 when the value of x = 3

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

If y varies inversely as x^2, and y=11/9 when x=9

when x =3,

y = 11/9 *x²

y = 11/3

Hence, the value of y is 11/3 when the value of x = 3

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The ordered pair that represents (c•d)(4) on the graph of the combined function is (4, -12)

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

The graph

The function of the graph is a combined function (c . d)(x)

To calculate (c . d)(4), we trace the point x = 4 to the curve

So, we have

(c . d)(4) = -12

See attachment for the graph

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174 number of students must be in the 8th grade class.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that The eight grade class is planning a trip to Washington, D.C. this spring.

They need a minimum of 75 people to attend in order to reserve busses.

1/3 of the 8th grade class plus 17 parent chaperones have signed up and this is enough to satisfy the requirement,

We need to find the number of students must be in the 8th grade class

1/3x+17≤75

Subtract 17 on both sides

1/3x≤58

x≤174

Hence, 174 number of students must be in the 8th grade class.

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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.

Part A:

Answer: The probability of a drought within the next 4 years if the probability of a drought in any one year is 12% is approximately 48%.

Part B:

Answer: Pairs of digits starting at 00 and ending at 11 represent a drought happening. Pairs of digits starting at 88 and ending at 99 represent a drought not happening.

Part C:

Answer: Using the random numbers, the estimated probability that a drought happens at least once over the next 4 years is 68%.

Part D:

Answer: The probability that was calculated is greater than the probability predicted. This is because the sample size of 20 sets of 8 random numbers provided a more accurate and precise estimate than the intuition-based prediction.

Part E:

Answer: Yes, the estimated probability changes when the pairs of digits that represent a drought happening are changed so that they start at 10 instead of 00. Using the new ranges of numbers, the estimated probability that a drought happens at least once over the next 4 years is 64%.

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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.

Predictions based on historical data, patterns, and trends are known as estimated probability. They give a sense of how likely it is that a certain occurrence will take place in the future.

Estimated probabilities calculation Part A:

If the likelihood of a drought in any given year is 12%, the likelihood that one will occur within the next four years is roughly 48%.

Part B:

Answer: The drought is represented by pairs of numerals beginning at 00 and ending at 11. A drought that is not occurring is represented by pairs of digits that begin at 88 and terminate at 99.

Part C:

According to the random numbers, there is a 68% chance that a drought will occur at least once over the next four years.

Part D:

Answer: The calculated probability is higher than the expected probability. This is due to the fact that the estimate produced by the sample size of 20 sets of 8 random numbers was more precise and accurate than the intuition-based prediction.

Part E:

Answer: When the pairs of digits that represent the occurrence of a drought are modified so that they begin at 10 instead of 00, the predicted likelihood does indeed change. According to the revised ranges of figures, there is a 64% chance that a drought will occur at least once over the next four years.

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The student is trying to construct a bisector of a given Angle i.e. A.

what is a bisector?

In Geometry, a “Bisector” is a line that divides the line into two different or equal parts. It is applied to the line segments and angles. A line that passes through the midpoint of the line segment is known as the line segment bisector, whereas the line that passes through the apex of an angle is known as the angle bisector. The bisector of a segment always contains the midpoint of the segment. There are two types of bisectors based on what geometrical shape it bisects.

Line Segment Bisector (Perpendicular Bisector Theorem)

Angle Bisector (Triangle Bisector Theorem)

Now,

As we can see from the figure given that the bisector is dividing the angle in two equal segments.

Hence,

          The student is trying to construct a bisector of a given Angle.

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The fraction of a pound of granola that Marty bought is 3/4 pounds.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 3/4.

The unit of conversion of ounces to pounds is :

1 pound = 16

12 ounces of granola =  12/16 pounds = 3 /4 pounds

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The probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.

What is the central limit theorem?

The central limit theorem, which states that the sample means of large samples (n > 30) from a population with any distribution approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

We can solve this problem by using the central limit theorem,

In this case, the sample size is n = 56, which is larger than 30, so we can assume that the sample means are normally distributed. The mean of the sample means is equal to the population mean, which is 55.5 inches, and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size:

standard deviation = 6 / √(56) = 0.801

To find the probability that the mean height of the sample will be greater than 53 inches, we can standardize the sample mean using the standard deviation calculated above:

z = (sample mean - population mean) / (standard deviation)

= (53 - 55.5) / 0.801

= -3.12

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -3.12:

P(Z > -3.12) = 0.9991 (rounded to four decimal places)

Therefore, the probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.

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Answer:

-0.50, -0.10, 0.60, 0.68, 0.98

An expression using the distributive property to find the earnings Jessica made on Friday and Saturday is 10(4 + 7).

The distributive property postulates that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend by the number and then adding the products together.

The distributive property helps to solve mathematical expressions written in the form of a(b + c).

The amount Jessica makes per hour babysitting = $10

The number of hours of babysitting on Friday = 4 hours

The number of hours of babysitting on Saturday = 7 hours

According to the distributive property, the results from 'a' and 'b' below are the same.

a) 10(4 + 7) = 40 + 70 = 110

b) 10(4 + 7) = 10 x 11 = 110

Thus, using the distributive property, Jessica will make $110 for babysitting on Friday and Saturday, notwithstanding whether process A or B was followed.

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The maximum error in the volume of the cone is approximately 20π cubic centimeters.

In this problem we must estimate the maximum error in the volume of the cone, based on uncertainties in radius and height of a circular cone. The volume formula for a circular cone is:

V = (π / 3) · R² · h

Where:

And the maximum error formula (ΔV), in cubic centimeters, is found by total differentials:

ΔV = (dV / dR) · ΔR + (dV / dh) · Δh

Where:

All first derivatives are shown below:

dV / dR = (2π / 3) · R · h

dV / dh = (π / 3) · R²

If we know that R = 10 cm, h = 25 cm, ΔR = 0.1 cm and Δh = 0.1 cm, then the maximum error in volume of circular cylinder is:

dV / dR = (2π / 3) · (10 cm) · (25 cm)

dV / dR = 500π / 3 cm²

dV / dh = (π / 3) · (10 cm)²

dV / dh = 100π / 3 cm²

ΔV = (500π / 3 cm²) · (0.1 cm) + (100π / 3 cm²) · (0.1 cm)

ΔV = 20π cm³

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The unit square that covers the figure is attached

The quantity of unit squares necessary to completely cover a shape is its area.

Consequently, area is represented and measured in square units.

The attached figure shows the 9 squares that makes up the figure

Each side has 3 squares and hence

= 3 squares * 3 squares

= 9 squares

The image is attached

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A solution to the given system of equations include the following:

x = -2.

y = -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

y = 2x + 3      .......equation 1.

y = 3x + 5      .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

2x + 3 = 3x + 5

By re-arranging and collecting like terms, we have the following:

3x - 2x = 3 - 5

x = -2.

For the value of y, we have the following:

y = 2x + 3

y = 2(-2) + 3

y = -4 + 3

y = -1.

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In the below we have compared deaths in A and B in terms of ratio, percentage and in terms of proportion.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The first comparison is in terms of rato.

The ratio of deaths due to a deadly disease in the United States at A and B is A : B = 17821 : 52093.

The second comparison in terms of percentage,

The percentage of people died in A is (52093/17821)×100 = 292.31% more than people died in B.

The third comparison is in terms of fractions.

The fraction of people died in A is (52093/17821) = 2.92 times more than people died in B.

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The given circumstance is represented by the linear equation 2y = x, and the graph is included below.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, A student traveled a distance of 68 miles in 136 minutes.

From the general formula of a linear equation:

y = mx + c

where,

m = slope

c = y-intercept

Since At 0 minutes, he started traveling so at 0 minutes total distance he traveled is 0. So the graph will pass through origin.

Thus, the y-intercept will be zero

And Slope of the graph that passes through the origin is always the ratio of the y and x values at any point of the line.

Thu, m = 68/136

m = 1/2

Therefore, a linear equation that represents the given situation is 2y = x, and the graph is attached below.

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Complete question:

The absolute values of inequality equations totally depend on the symbols.

An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in unequal absolute values. By comparing the absolute valuesof two numbers on the number line, inequality is most frequently utilized. Different types of inequality are represented by a variety of different notations, including:

The symbol a b indicates that an is less than b.

A bigger value for a than a lesser value for b is indicated by the notation a > b.

a is not equal to b in either situation. These relationships are referred to be stringent inequalities since an is either strictly less than or strictly greater than b. Equivalence is not included.

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When calculating the finance charges, the monthly interest rate (MPR) is multiplied by the D. average daily balance.

The finance charge refers to the interest and other fees a borrower pays on a credit card.

To compute the finance charge, the annual percentage rate (APR) or the monthly percentage rate (MPR) is multiplied by the balance owed.

The balance commonly used for this calculation is the average daily balance.

Thus, Option D is multiplied by the MPR to compute the finance charges.

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Using the arithmetic operation, the number of worker in San Diego is obtained as 260, and the number line which represents the same is option 1.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of offices are = 3

The number of workers in the company is = 480

The number of workers in New York city = 90

The number of workers in Denver city = 130

The number of workers in San Diego city = x

To find the number of workers in San Diego use the formula -

Number of workers in San Diego = Total Number of Workers - (Number of workers in New York + Number of workers in Denver)

The arithmetic operation of addition and subtraction is used.

Substitute the values into the equation -

Number of workers in San Diego = 480 - (90 + 130)

Number of workers in San Diego = 480 - 220

Number of workers in San Diego = 260

The number line which represents the number of workers in San Diego is  option 1.

Therefore, the number of workers in 260.

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A company has offices in 3 different cities and a total of 480 workers. There are 90 workers in New York and 130 workers are in Denver. Which number line represents the number line represents the number of workers in San Diego?

The value of the z-test statistic = 1.16667

When told the question that a random number of samples is tested

z test statistic formula = x - x bar(x with bar above it) /Standard error

From the question

x = raw score = 46 pounds

x bar (x with bar above it)= sample mean = 45.5 pounds

Standard Error = σ/√n

Standard deviation = σ = 3

n = random number of samples = 49

z = 46 - 45.5/3/√49

z = 0.5/ 3/7

z =0.5/ 0.4285714286

z = 1.16667

Therefore, the value of the z-test statistic = 1.16667

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The probability hat 1st winner lives in Guston and the 2nd living in Pikes = 3/25

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

1. P(E) = [Number of favorable outcomes of E]/[Total number of potential outcomes of E] is the formula for calculating an event's probability.

2. The likelihood of a given occurrence or a sure thing happening is 1.

3. There is no chance that an impossible occurrence will occur.

4. A number P(E) that has the formula 0 P(E) 1) represents the probability of an occurrence E. The probability scale is always positive.

5. If events A and B are two occurrences that can never occur together, then P(AB) = P(A) + P (B).

6. An basic event is one that has just one result. The total likelihood of such outcomes in an experiment is 1, or 1.

7. The probability of an event plus the probability of its complementary occurrence equals one. P(A) + P(A').

Total number of Customers = 10

Customers lives in Guston = 6

Customers living in Pikes = 2

Customers living in Wells = 2

Probability that 1st winner lives in Guston and the 2nd living in Pikes = 6/10 * 2/10 = 3/25

The probability hat 1st winner lives in Guston and the 2nd living in Pikes = 3/25

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