given a and b in exercises 11 and 12, write the augmented matrix for the linear system that corresponds to the matrix equation a x=b. then solve the system and write the solution as a vector.

Answer:

Step-by-step explanation:

Since the numerator is missing, you want to multiply the denominator onto the other side.

5 x 7 =35

x=35

Answer:

x=35

Step-by-step explanation:

Easy way to solve is making x/5 an improper fraction (fraction whose numerator is equal to or greater than its denominator.)

How I solved it was by multiplying 7×5=35, then I plugged the value into x making it (35/5)=7.

Now just make it a proper fraction, 35÷5=7, now we have 7=7.

The value for (1.0x10³) / 2.0x[tex]10^5[/tex] is 0.005.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

(1.0x10^3) and 2.0x10^5

We don't have any sign so we proceed with operation division

(1.0x10³) ÷ 2.0x[tex]10^5[/tex]

= (1.0x10³) / 2.0x[tex]10^5[/tex]

Suing exponents

[tex]a^m/ a^n= a^{m-n[/tex]

= 1/2 x [tex]10^{3-5[/tex]

= 0.5 x [tex]10^{-2[/tex]

= 0.5 / 10²

= 0.5 /100

= 0.005

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In algebra, a number exists even equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

2. AD = BC due to the congruence of a rectangle's opposite sides.

3. Due to the reflexive property of congruence, DC=DC, each segment is identical to itself.

4. ADC and BCD are right angles since any rectangle's internal angles are right angles (Definition of rectangle).

5. Since they form right angles and all right angles are congruent, ADC=BCD.

6. ADC and BCD are congruent because they have two congruent sides (AD with BC and DC with DC) and a congruent angle between them: Side Angle Postulate Side Congruence Postulate (SAS Congruence Postulate).

7. AC must match BD because Congruent Parts in Congruent Triangles must match (CPCTC).

Statement                                    Reason

1. Rectangle ABCD                         Given

2. AD=BC                                        Opposite sides of a rectangle are congruent

3. DC=DC                                        Reflexive Property of Congruence

4. <ADC and <BCD are                  Definition of rectangle

  right angles

5.  <ADC=<BCD                              All right angles are congruent

6. ∆ADC=∆BCD                              SAS Congruence Postulate

7. AC=BD                                        CPCTC  

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The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

(a) Length of time to complete an exam - Ratio: This is measured on a scale of time, and can be expressed as a ratio (i.e. the amount of time spent on the exam divided by the total time allotted for the exam).

(b) Time of first class - Interval: The time of the first class is measured on a scale of minutes, hours, and days, and can be expressed as an interval (i.e. the amount of time between two classes).

(c) Major field of study - Nominal: This is a categorical measurement and can be expressed as a nominal variable (i.e. the student's major field of study is either engineering, business, etc).

(d) Course evaluation scale: poor, acceptable, good - Ordinal: This is a scale of quality and can be expressed as an ordinal variable (i.e. the quality of the course can be rated as poor, acceptable, or good).

(e) Score on last exam (based on 100 possible points) - Ratio: This is measured on a scale of points, and can be expressed as a ratio (i.e. the student's score on the exam divided by the total number of points possible).

(f) Age of student - Ratio: This is measured on a scale of years, and can be expressed as a ratio (i.e. the student's age divided by the total number of years they have been alive).

The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

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Last week, Toby bought 11 book and 8 movie for a total of $207. Today, Toby bought 16 book and 9 movie for a total of $280 the cost of book is 13$.

Toby bought 11 book and 8 movie for a total of $207 so,

11B + 8M = 207

Today, Toby bought 16 book and 9 movie for a total of $280 so,

16B + 9M = 280

Solving equations simultaneously we get,

11B + 8M = 207

16B + 9M = 280

99B = 1863

B = $13

So, the cost of a book in dollar is $13.

Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.

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Answer:

[tex]\frac{51}{8} \:or \: 6\frac{3}{8}[/tex]

Step-by-step explanation:

solution given:

[tex]\frac{3}{4} *8\frac{1}{2}[/tex]

let make mixed fraction to normal fraction

[tex]8\frac{1}{2} =\frac{8*2+1}{2} =\frac{17}{2}[/tex]

replace [tex]\frac{17}{2}[/tex]

we have

[tex]\frac{3}{4} *\frac{17}{2}[/tex]

in multplication fraction, we multiply numerator to numerator and denominator to denominator.

[tex]\frac{3}{4} *\frac{17}{2}=\frac{3*17}{4*2} =\frac{51}{8}[/tex]

again

in mixed fraction =[tex]6\frac{3}{8}[/tex]

The one which not the benefit of being a member of a professional organization is providing certificate examinations at discounted rate. The correct option is D.

Professional associations provide the better networking opportunities with people who are specifically in our industry. Whether we are looking to pursue employment opportunities, link with other industry professionals, or even looking for a mentor in our profession, the networking opportunities are invaluable.

Another benefits of joining in a professional organization is that it helps build the career portfolio of a professional. Organizations which can provide opportunities for speaking engagements, career specialization, publication and even scholarship and training programs abroad.

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Although part of your question is missing, you might be referring to this full question: All of the following are benefits of being a member of a professional organization, except:

A. providing a wide range of continuing education units.

B. publishing newsletters and magazines dealing with current issues and trends in healthcare.

C. providing tuition reimbursement.

D. providing certificate examinations at discounted rate.

They need to dilate the box by a scale factor of  ∛8.

This refers to the number/amount by which a figure is bigger or smaller than the original figure.

Solving for scale factor  they need to dilate the box:

The volume of a cube with sides of length "s" is given by the formula:

V = s³.

If the basic box has a volume of 1 cubic foot (V = 1), then a box with a volume of 8 cubic feet (V = 8) can be found by scaling the basic box by a factor of ∛8.

Hence, the scale factor is  ∛8.

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The relation between the number of ide, edge, and vertice in each shape Euler’s Formula for Polyhedron.

Polyhedron Euler's Formula

One of the most significant mathematical theorems, the Euler theorem is named Leonhard Euler and is widely recognized as such.

The link between a polyhedron's face, vertex, and edge counts is stated in the theorem.

F + V = E + 2 is the formula for Euler's equation, where F is the number of faces, V is the number of vertices, and E is the number of edges.

According to Euler's formula, many solid shapes have a number of faces plus vertices plus vertices minus vertices equal to two.

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If a 4x7 coefficient matrix has four pivot columns, the system is consistent and has exactly one solution.

A coefficient matrix is a matrix that represents a system of linear equations. In the case of a 4x7 coefficient matrix, the matrix has 4 rows and 7 columns.

When it comes to determining the consistency of a system of linear equations, the presence of pivot columns is a key factor.

A pivot column is a column that contains a leading 1 in the row reduced echelon form of the matrix. If a system has four pivot columns, this means that the system has 4 linearly independent equations, meaning that there is exactly one solution to the system.

Therefore, the system is considered consistent.

However, if the number of pivot columns is less than the number of unknowns, then the system is considered inconsistent, meaning that there is either no solution or an infinite number of solutions.

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A function equation in slope-intercept form to model the situation are as follows;

Slope: 3.

Y-intercept: 48.

Equation: y = 3x + 48.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the liquid started at a temperature of 48 degrees and drops 3 degrees per minute, an equation that model the situation is given by:

y = mx + c

y = 3x + 48

Next, we would fill in the table as follows. At x = 0, the temperature of liquid (y) is given by:

y = 3(0) + 48

y = 48.

At x = 1, the temperature of liquid (y) is given by:

y = 3(1) + 48

y = 51.

At x = 2, the temperature of liquid (y) is given by:

y = 3(2) + 48

y = 54.

At x = 3, the temperature of liquid (y) is given by:

y = 3(3) + 48

y = 57.

At x = 4, the temperature of liquid (y) is given by:

y = 3(4) + 48

y = 60.

At x = 5, the temperature of liquid (y) is given by:

y = 3(5) + 48

y = 63.

At x = 6, the temperature of liquid (y) is given by:

y = 3(6) + 48

y = 66.

At x = 7, the temperature of liquid (y) is given by:

y = 3(7) + 48

y = 69.

At x = 8, the temperature of liquid (y) is given by:

y = 3(8) + 48

y = 72.

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After 6 hours, Anderson and Addison will be 126 miles apart.

Let's call the time they have been traveling "t" (in hours).

Anderson will have traveled 15t miles and Addison will have traveled 6t miles. The total distance between them is 15t + 6t = 21t miles.

We know that they need to be 126 miles apart, so we can set up the equation:

21t = 126

Now we can solve for t:

t = 126 / 21

t = 6

So after 6 hours, they both will be 126 miles apart.

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Answer:

Step-by-step explanation:

The answer will be the third one because 2/3 * (3/10 X 1) is the same as 2/3 already being multiplied to 3/10.

If you use a calculator and put 2/3 * (3/10 X 1), you will get 0.2 and if you put (2/3 * 3/10) x 1 you will also 0.2.

So (2/3 * 3/10) x 1 is equal to 2/3 * (3/10 X 1)

When the slope of the line is 3 the equation of the line using point slope formula is

D. у - 8 = 3 (x - 6)

Point slope formula is giving by (y - y₁) = m (x - x₁)

where

m = slope

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

For slope of 3, equation passing through point (5, 8)

(y - y₁) = m (x - x₁)

y - 8 = 3 (x - 6)

y - 8 = 3x - 18

y = 3x - 18 + 8

y = 3x - 10

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The volume of this prism = 2 × 3 × 9 units³.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given figure we get,

A rectangular prism made up of unit cubes.

There are 3 layers, and each layer is 9 units long and 2 units wide.

i.e. l = 9

w = 2

h = 3

so, the volume = V

we know, V= l.w.h

so, V = 9.2.3

Hence, The volume of this prism = 2 × 3 × 9 units³.

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Answer:

No solution, because the slopes are the same and the y-intercepts are different.

Step-by-step explanation:

The two equations are:

y = 1/4x + 1 and y= 1/4x - 1

Since the left sides are equal we can equate the right sides:
1/4x + 1 = /4x - 1

1/4x cancels out of the equation and we get the absurdity:

1 = -1

This indicates no solution to the system of equations

Answer:
No solution, because the slopes are the same and the y-intercepts are different.

We can see that the slopes are the same (1/4) and the y-intercepts are different (1 and -1)

The angle has a measure of 0° and is in standard position with its vertex at the origin. On the terminal side of lies the point (-2, 3).

The vertex of an angle in standard position on a coordinate plane is at the plane's origin. The angle's terminal side is rotated anticlockwise from the starting side while the angle's initial side is on the positive x-axis. The number of degrees the terminal side has travelled away from the initial side anticlockwise is how an angle is measured in standard position. This signifies that the terminal side is exactly on the same line as the initial side because the angle has the smallest positive measure of 0°. Since the line segment from the origin to the point (-2,3) is on the terminal side of, the point (-2,3) is on that side as well.

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The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.

Caffeine is a natural chemical with stimulant effects.

Let's call the new half-life time for an individual with extended half-life as t. The function for the amount of caffeine (C) in the bloodstream after time t can be expressed as:

C(t) = 80 * (1/2)^(t/8)

Using this formula, we can determine the amount of caffeine in the bloodstream after different times:

1 hour:

C(1) = 80 * (1/2)^(1/8) = 80 * (1/2)^0.125 ≈ 79.28 mg

5 hours:

C(5) = 80 * (1/2)^(5/8) ≈ 64.51 mg

10 hours:

C(10) = 80 * (1/2)^(10/8) ≈ 51.37 mg

20 hours:

C(20) = 80 * (1/2)^(20/8) ≈ 25.68 mg

Therefore, The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.

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The evaluation of obtuse angle ∠AOC is 124°.

Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.

3x + 94 + x + 30 + 2x - 4 = 180

Sum of angle in a triangle

6x + 120° = 180°

6x = 180° - 120°

6x = 60°

x = 10°

Now, ∠AOC = 3x + 94

3 × 10 + 94

30 + 94

124°

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An argument that supports Argument A is given below:

Geometric figures play a crucial role in many areas of mathematics and science, including engineering, architecture, physics, and computer graphics.

Being able to construct these figures accurately and efficiently is therefore an important skill for students to have. By using only a compass and straightedge, students can explore and understand the properties of different shapes and their relationships with one another.

This helps them develop their spatial reasoning abilities and improves their understanding of mathematical concepts such as congruence, similarity, and symmetry.

Furthermore, this skill can be applied to solving real-world problems, such as determining the dimensions of a building or designing a circuit board.

In conclusion, the ability to construct geometric figures using a compass and straightedge is essential for students' mathematical and scientific development and should be taught as part of their education.

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There are 5 inches between the two picnic areas on the map. Therefore, option A is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, a map of a national forest has a scale in which 1 inch represents 3 miles.

If two picnic areas in the national forest are actually located 15 miles apart, then on map it is 15/3 =5 inches

Therefore, option A is the correct answer.

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The dot product of a.b is 20.

What is the dot product?

The dot product (also called scalar product or inner product) of two vectors a and b in a Euclidean space is a scalar value that represents the projection of one vector onto the other and the cosine of the angle between them. The dot product of two vectors a and b is defined as:

a · b = ||a||||b||cos(θ) = a1b1 + a2b2 + ... + anbn

where a = (a1, a2, ..., an) and b = (b1, b2, ..., bn) are the components of the vectors and θ is the angle between the vectors.

Finding a · b:

Given a = (4, 1, 1) and b = (8, -3, -9), we can calculate the dot product as:

a · b = 4 * 8 + 1 * -3 + 1 * -9 = 32 - 3 - 9 = 20

Hence, the dot product of a.b is 20.

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The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.

The probability of both events happening is the product of the individual probabilities:

P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196

So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

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The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.

The probability of both events happening is the product of the individual probabilities:

P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196

So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

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Each decimal number has a unique bit structure that starts at 1 bit, that's why it is impossible to convert a decimal number to binary digit-by-digit as is achievable with hexadecimal.

It impossible to convert a decimal number to binary on a digit-by-digit basis as can be done for hexadecimal because each decimal number has a separate bit structure that starts at 1 bit and goes quickly, it is difficult to convert a decimal number to binary string of 4 bits digit by digit.

However, since each hexadecimal number has a width of 4 bits, this is achievable. It is relatively easy to go back and forth between binary and hexadecimal. The comparable 4-bit binary string is used to replace each hexadecimal digit in the original number.

Hexadecimal Number FD13.

1111 1101 00010011 each hexadecimal digit with its corresponding 4-bit binary value.

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Every molecule has a unique molecular formula.

A molecular formula is a chemical formula that represents a molecule and gives information about the number and type of atoms present in the molecule. This formula is unique to each molecule and distinguishes one molecule from another, even if they have the same number and type of atoms arranged in a different way.

For example, the molecular formula for glucose (C6H12O6) is different from that of fructose (C6H12O6), even though they have the same number and type of atoms. The molecular formula represents the actual number of atoms present in the molecule and their chemical makeup, which in turn determines the chemical properties and behavior of the molecule.

Thus, for a given number of domains, the characteristic that is common to every molecule is their unique molecular formula.

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Marginal Revenue is negative, the firm should consider reducing its output to increase its total revenue.

Therefore, correct answer will be a. increase.

Marginal Revenue (MR) is a crucial concept in economics that measures the change in a firm's total revenue as a result of selling one additional unit of output. MR is used by firms to make decisions about how much output to produce and what price to charge.

In a linear (inverse) demand function, MR is negative when the elasticity of demand is less than one, meaning that the demand for a product is relatively inelastic. In other words, as the firm increases output, the price will decrease, causing total revenue to decline.

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The length of AG which is the diagonal of the cuboid is; 8.5 cm

A cuboid is defined as a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.

A diagonal in geometry is defined as a line segment that connects two polygonal vertices when they are not on the same edge.

The parameters are;

A, B, C, D, E, F, G & H form a cuboid. AB= 3.2 cm, BC = 1.6 cm & CG = 7.7 cm. That is l=3.2 cm, b=1.6 cm, h=7.7 cm.

A body diagonal is referred to as the diagonal of cuboid. The diagonal of cuboid formula is;

Diagonal length = √(l² + b² + h²) units.

Thus lugging in the relevant values;

Diagonal length = √(3.2² + 1.6² + 7.7²)

Diagonal Length = 8.49 cm

≈ 8.5 cm

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No, it's not possible for Trevor to use 1/2 of the poster for his pictures, 3/8 for his hypothesis, and 1/4 for the experiment process.

This is discovered by addition of fraction

= 1/2 + 3/8 + 7/8

= 7/8

The fractions 1/2, 3/8, and 1/4 add up to 7/8, which is greater than 1.

Since the fractions represent parts of a whole poster, the total must be less than or equal to 1.

Therefore, Trevor needs to adjust the fractions so that their sum is less than or equal to 1.

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The probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16

Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1

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.

A statistical function known as a probability distribution explains all the potential values and probabilities for a random variable within a certain range.

The uniform probability distribution is a distribution composed by two bounds, given by a and b, in which each possible outcome within these two bounds is equally as likely.

The probability that a call is made in the first quarter is 15/60

Now the probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16

Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1

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