for each matrix, identify the pivot positions and determine if the corresponding linear system is consistent. explain how the location of the pivots determines whether the system is consistent or inconsistent.

The 95% confidence interval for the mean number of shoes owned by female students is (95.58, 195.14).

Calculate the sample mean:  

Total number of shoes = 45+31+3125+62+15+29+27+28+35+18+55+18+39+28+35+44+18+10+55+50+40+38+22+16 = 3634

Sample mean = 3634/25 = 145.36

Calculate the standard deviation:

Standard deviation = √[(45-145.36)² + (31-145.36)² + (3125-145.36)² + … + (16-145.36)²]/24 = 586.33

Calculate the margin of error:

Margin of error = 1.96∗586.33/√25 = 49.78

Calculate the 95% confidence interval:

Lower bound = 145.36 - 49.78 = 95.58

Upper bound = 145.36 + 49.78 = 195.14

Since the sample mean is not an integer, we must round the lower and upper bounds to the nearest integer, which gives us (29.73, 40.27) as the 95% confidence interval for the mean number of shoes owned by female students.

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The values of x in the triangles are 38.9 and 43.3 degrees

The complete question is added as an attachment

Triangle 1

The value of x can be calculated using the following sine ratio

sin(x) = 15/24

Evaluate the quotient

sin(x) = 0.625

Take the arc sin of both sides

x = 38.9

Triangle 2

The value of x can be calculated using the following cosine ratio

cos(x) = 8/11

Evaluate the quotient

cos(x) = 0.7273

Take the arc cos of both sides

x = 43.3

Hence, the solution is 43.3 degrees

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Considering the other two sides, i.e. 5ft, 25ft, The unknown side length is 24.5 ft.

The unknown side length can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we have one side with a length of 5 ft and another side with a length of 25 ft. To find the length of the third side, we can use the formula: [tex]c^2 = a^2 + b^2[/tex], where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Substituting the given values, we have

[tex]25^2 = 5^2 + b^2[/tex],

[tex]b^2[/tex]= 625 - 25 = 600.

Taking the square root of both sides, we have c = √600 = 24.4949. Rounding to the nearest tenth, the unknown side length is 24.5 ft.

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Complete Question:

Find the unknown side length. Round to the nearest tenth.

a = 5 ft

b = ?

c = 25 ft

Technetium-99m has a half-life of 6 hours. After 21 hours, the remaining radioactive material  in the patient's blood stream is 0.053 mL.

The formula for half life is given by:

P(t) = Po (1/2)^(t/T)

Where:

P(t) = the remaining quantity of the substance at period t

Po = initial quantity

T = half life

Information available in the problem:

Po = 0.6 mL

T = 6 hours

t = 21 hours

Plug these parameters into the formula:

P(21) = 0.6 x (1/2)^(21/6)

P(21) =  0.6 x (1/2)^(3.5)

P(21) = 0.053

Hence, the remaining radioactive material  in the bloodstream is 0.053 mL

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The difference is that in an observational study, the researchers do not control treatment, and in an experiment, they do.

An experiment is a method used to verify or disprove a theory, as well as to determine something's effectiveness or likelihood.

An experiment vs an observational research differs fundamentally in that:

Members of a sample are measured or surveyed during an observational study without any attempt to manipulate them.

In an experiment, decisions are made under controlled conditions, subjects are divided into groups, and one group is given therapy while the other is left untreated. The main distinction between well-executed observational studies and experimental designs is that the replies of participants are unaffected, whereas in experiments, at least some participants are subjected to a treatment condition at random.

As a result, the researchers in an experiment control the therapy, but they do not in an observational study.

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47.) The angle between the plane is 0 degrees.

48.) The angle between the plane is 180 degrees.

What is the angle between the plane?

To find the angle between two planes, we need to find the normal vectors of each plane and then find the cosine of the angle between the normal vectors using the dot product.

First, let's find the normal vectors for the two planes:

Plane 1: x + y = 1

The normal vector for this plane can be found by taking the coefficients of x, y, and z and forming a vector:

n1 = ⟨1, 1, 0⟩

Plane 2: 2x + y - 2z = 2

The normal vector for this plane can be found in the same way:

n2 = ⟨2, 1, -2⟩

Next, we will find the cosine of the angle between the normal vectors using the dot product:

cosθ = (n1 • n2) / (|n1| * |n2|)

where |n1| and |n2| are the magnitudes of the normal vectors.

Calculating the dot product and magnitudes:

n1 • n2 = 1 * 2 + 1 * 1 + 0 * -2 = 3

|n1| = sqrt(1^2 + 1^2 + 0^2) = sqrt(2)

|n2| = sqrt(2^2 + 1^2 + (-2)^2) = sqrt(9)

Substituting into the formula:

cosθ = 3 / (sqrt(2) * sqrt(9)) = 3 / (3) = 1

Since cosθ = 1, θ = 0, so the angle between the two planes is 0 degrees or a coincident plane.

Next, let's find the normal vectors for the two planes:

Plane 1: 5x + y - z = 10

The normal vector for this plane can be found by taking the coefficients of x, y, and z and forming a vector:

n1 = ⟨5, 1, -1⟩

Plane 2: x - 2y + 3z = -1

The normal vector for this plane can be found in the same way:

n2 = ⟨1, -2, 3⟩

Next, we will find the cosine of the angle between the normal vectors using the dot product:

cosθ = (n1 • n2) / (|n1| * |n2|)

Calculating the dot product and magnitudes:

n1 • n2 = 5 * 1 + 1 * (-2) + -1 * 3 = -3

|n1| = sqrt(5^2 + 1^2 + (-1)^2) = sqrt(27)

|n2| = sqrt(1^2 + (-2)^2 + 3^2) = sqrt(14)

Substituting into the formula:

cosθ = -3 / (sqrt(27) * sqrt(14)) = -3 / (3 * sqrt(2)) = -sqrt(2) / sqrt(2) = -1

Since cosθ = -1, θ = 180 degrees, so the angle between the two planes is 180 degrees, or perpendicular.

Hence,

47.) The angle between the plane is 0 degrees.

48.) The angle between the plane is 180 degrees.

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The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' will be Dilation and Reflection.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

Then the scale factor about the origin is given as,

Scale factor = 2 / 4

Scale factor = 1/2

The reflection does not change the shape and size of the geometry. But flipped the image.

Reflection of the image over the y-axis.

The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' will be Dilation and Reflection.

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a) The slope is 1

b) The equation of the tangent line is x-y=20.

What is slope?

Slope is calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.

a) To find the slope of the curve, the derivative of a function f(x) at the given point is a slope of the curve

Slope of the given curve y = x at the point P(25, 5) is the derivative f'(x) at P(25,5)

=>m = f'(x) = dy/dx

=>1

Since the derivative of x is 1

f'(x) at P(25, 5) is 1

= > Slope = 1

b) To find an equation of the tangent line at P (25,5) for the curve y = x.

The equation of tangent line in for the function f(x) at P ([tex]x_1,y_1[/tex]) is (y - [tex]y_1[/tex]) = m (x - [tex]x_1[/tex])

Given:

[tex]x_1[/tex] = 25 and  [tex]y_1[/tex] = 5, f(x) =x and slope of tangent m = 1

The equation of the tangent line is (y - 19) = - 24(x - 2)

⇒ y - 5 = 1(x -25)

=> y=x-25+5

=> y=x-20

=> x-y=20

The equation of tangent is x-y=20.

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The solution of the given equation is y = y = e^(6x -∞) ,y = e^(6x)

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

[tex]I = e^(int (6 dy/6y)) = e^(ln y)[/tex]

Multiplying both sides of the equation by I:

[tex]Iy' = 6y5/6 ⇒ dy/y = 6/6 dy ⇒ ln y = 6x + c[/tex]

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

[tex]0 = e^(6(0) + c) ⇒ c = -∞[/tex]

Therefore, the solution of the given equation is:

y = e^(6x -∞)

Solution 2:

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

[tex]I = e^(int (6 dy/6y)) = e^(ln y)[/tex]

Multiplying both sides of the equation by I:

Iy' = 6y5/6

⇒ dy/y = 6/6 dy

⇒ ln y = 6x + c

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

0 = e^(6(0) + c)

⇒ c = 0

Therefore, the solution of the given equation is:

y = e^(6x)

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The probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male is 0.0000907 or 0.00907%.

To determine the probability P, we can use the formula for combinations:

P = (number of ways to select A's and B's from the females) * (number of ways to select C's and D's from the males) / (number of ways to assign grades to all students)

Let's first find the number of ways to select A's and B's from the females:

There are 2 ways to select 2 A's from 7 females.

There are 7 choose 5 ways to select 5 B's from 7 females, which is 21.

So, there are 2 * 21 = 42 ways to select A's and B's from the females.

Next, let's find the number of ways to select C's and D's from the males:

There are 8 ways to select 8 C's from 11 males.

There are 11 choose 3 ways to select 3 D's from 11 males, which is 165.

So, there are 8 * 165 = 1320 ways to select C's and D's from the males.

Finally, let's find the number of ways to assign grades to all students:

There are 18 choose 2 ways to select 2 A's from 18 students, which is 153.

There are 18 choose 5 ways to select 5 B's from 18 students, which is 18564.

So, there are 153 * 18564 = 2827672 ways to assign grades to all students.

Putting it all together, the probability P is:

P = (42) * (1320) / (2827672) = 0.0000907

Therefore, the probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male is 0.0000907 or 0.00907%.

Complete Question:

An EEOC investigation into course grading encountered the following situation. In a course with eighteen students, 7 females and 11 males, grades were assigned as follows: 2 A’s, 5 B’s, 8 C’s, and 3 D’s. Determine the probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male.

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The total number of bars which were sold Online = 14816

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.

The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers.

Multiplication is used to make repetitive adding of the same number easier.

The number of cases of Essence soap sold is one-third as many as the number of Zing soap,

So:

Essence soap = 72 cases / 3 = 24 cases

The total number of cases sold will be:

72 cases + 24 cases = 96 cases.

And the total number of bars sold is:

96 cases * 156 bars/case = 14816 bars.

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Maximum or the upper limit of the amount of water leaked in 2 hours will be r(2) since t = 2 hrs.

The lower bound or limit will be zero if the leaked is fixed or the amount of water is zero.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The set of integers x for which a function has a valid definition is known as its domain. A closed interval is referred to as a function's domain if it is specified across the interval a≤ x ≤b.

A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is precisely one y in Y such that f connects x to y for every x in X.

The tank is leaking in the function of time givenas

r(t), where t is measured in hours

Maximum or the upper limit of the amount of water leaked in 2 hours will be r(2) since t = 2 hrs.

The lower bound or limit will be zero if the leaked is fixed or the amount of water is zero.

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Answer:

The linear function for the first store is y = 2.5x + 10.75, where x is the number of comic books and y is the cost of the package. The linear function for the second store is y = 2.5x + 5.75. The second store has the better deal, as the cost of the package is lower for any given number of comic books.

100 kilograms (kg) converts to 220.463 pounds (lb).

Conversion. 100 kilograms (kg) converted to pounds (lb). 100 kilograms (kg) equals 220.463 pounds (lb). A kilogram weighs approximately 2.2046226218 pounds. The method for converting kilos to pounds is pretty straightforward. All you have to do is multiply the kilogram amount by 2.2046226218.

The term “pound” derives from the ancient Roman libra pondo, which means “a pound by weight.” According to the BBC, the English term “pound” is derived from the pondo component of the sentence. However, the abbreviation “lb” is taken from the word libra.

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Answer: q = 16

Step-by-step explanation:

When given the equation 3(q - 7) = 27,  you would solve for the variable.

The variable in this equation is q, so we need to isolate the variable.

Solving process:

3(q - 7) = 27

lets distribute, due to the orders of PEMDAS.

PEMDAS stands for: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

3(q - 7) = 27

distributing is multiplying the number correlated outside of the parenthesis with the inside components.

3q - 21 = 27

lets add 21 to both sides

3q = 48

now lets divide by 3 (we are trying to get q by itself)

q = 16

----

To check if your solution is correct, you replace the value (16) of the variable (q) within the original equation:

3 (16 − 7) = 27

Following PEMDAS you get:

3(9) = 27

27 = 27 (meaning that the solution is correct)

Thank you.

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The critical values of the given function are 0, +2, and -2.

According to the question

Given function f(x) = y^2(4-y^2)

Setting the partial derivatives of the function y2(4-y2) to zero and solving for y will reveal where the function's crucial points are.

The partial derivatives of y^2(4-y^2) with respect to y are:

⇒ d/dy (y^2) = 2y

⇒ d/dy (4-y^2) = -2y

⇒ d/dy (y^2(4-y^2)) = 2y(-2y) + 2(y^2)

⇒ -4y^2 + 4y^2 = 0

Setting the partial derivative equal to zero:

-4y^2 + 4y^2 = 0

Solving for y:

y = 0 or y = ±2

The critical values are therefore y = 0 and y = 2. Using the second derivative test or by examining the behavior of the function close to these locations, these key points can be categorized as local minima, local maxima, or inflection points.

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78.740 inches in 2 meters. 2 meters equals 6.56168 ft. One meter is equivalent to 3.28084 ft.

2 meters into inches

1 inch = 39.370

2 meters = 2 × 39.370

Then we get ,

= 78.740 inches

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No, the angles are not Complementary because the sum is not 90 degree.

Two angles are called complementary when their measures add to 90 degrees.

For example, 30 degrees and 60 degrees are complementary angles.

Given:

The pair of angles measure 38 degrees and 67 degrees.

Now, we know that if the sum of angles are 90 then they are said to be pair of Complementary Angle.

so, 67 + 38

= 105 > 90

Thus, the given pair is not pair of Complementary Angle.

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The function g(x) = (3x + 5) + 8 is a translation of 8 units upwards of f(x).

For a general function f(x), we define a vertical translation of N units as:

g(x) = f(x) + N

if N > 0, then the translation is upwards.

if N < 0, then the translation is downwards.

For a general function f(x), we define a horizontal translation of N units as:

g(x) = f(x) + N

if N > 0, then the translation is to the left.

if N < 0, then the translation is to the right.

Here we start at:

f(x) = 3x + 5

Function g(x) is:

g(x) = (3x + 5) + 8

g(x) = f(x) + 8

So this is a translation of 8 units up.

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The light post's height is 21 metres higher than the structure,

A lamp post is 45 feet away from where you are. You are standing at a 36" angle and are 5 feet tall as you stare up at the top of the light post.

tan 60 degrees is equal to 36/x sqrt(3),

36/x, and 36/(sqrt(3))*m. sqrt (3)

36/3 = 36 - h

h = 36 - 12

h = 24m

The distance between AB and CD is thus

60/(sqrt(3)) * 1.

The light post is 24 metres tall.

The light post's height is 45 -24 =21 metres higher than the structure, which is 21 metres higher.

The light post's height is 21 metres higher than the structure,

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On solving the linear equations 14x + 5y = 975 and 10x + 4y = 750, the price for small ad and full page ad is obtained as $25 and $125 respectively.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The two linear equations given are -

14x + 5y = 975 .... (1)

10x + 4y = 750 .... (2)

Here, x represents the price of small ad and y represents the price of a full-page ad.

To get the value of x and y solve the system of linear equations -

Multiply equation (1) by 4 and (2) by 5 -

4 (14x + 5y) = 4 × 975

56x + 20y = 3900 .... (3)

5 (10x + 4y) = 5 × 750

50x + 20y = 3750 .... (4)

Subtract equation (4) from (3) -

56x + 20y - (50x + 20y) = 3900 - 3750

56x + 20y - 50x - 20y = 3900 - 3750

6x = 150

x = 150/6

x = 25

Substitute the value of x in equation (1) -

14(25) + 5y = 975

350 + 5y = 975

5y = 975 - 350

5y = 625

y = 625/5

y = 125

So , the prices of small ad is $25 and prices of full-page ad is $125.

Therefore, the values for x and y are $25 and $125 respectively.

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Answer:

obtuse

Step-by-step explanation:

or acute triangle

is the answer

randomly choosing a male first and randomly choosing a male second are independent events.

Sample Space:

M1, M2, M3, M4, F1, F2, F3, F4, F5

Independent Events:

M1, M2, M3, M4, M1, M2, M3, M4

The sample space includes all of the possible outcomes of picking two contestants from the audience of 5 females and 4 males. Since the order of choosing does not affect the outcome, the sample space does not change regardless of which gender is chosen first. Therefore, randomly choosing a male first and randomly choosing a male second are independent events.

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The correct response is D, all real numbers x can either be greater than or equal to 2 or less than 2.

solving a problem by either a method or action; communicating the answer. a range of values for something like a statistic that fulfill an equation, specifically The solution of just an equation is any variable of a variable that makes the Left Hand Side (Dataframe) and the Dominant Hand Side (RHS) of the equation equal. To solution an equation is to identify its solution or solutions. One manner to express the concentration of a solvent is as a percentages of the solute in the solvent. The ratio of something like the mass of the solute to the mass of something like the solution, and the fraction of the mass of the solute toward the mass of the solution, is one of two supplementary techniques for computing the percentage.

given

(x Ix<2}u [xlx ≥2]

x<2 or x>=2

The correct response is D, all real numbers x can either be greater than or equal to 2 or less than 2.

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Lines AB and CD are parallel to each other because the lines make the same angle as the transversal line.

When the distance between the lines is constant then the lines are called parallel lines. The lines do not intersect when they are separated from each other. And the slope of the lines is equal.

Let the transversal line be EF to line AB and CD.

Line AB and line CD make the same angle as the transversal line. Then we can say that the lines AB and CD are parallel to each other.

The diagram is given below.

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Hz (Hertz) is a unit of frequency, which measures the number of events or occurrences of a certain phenomenon per second. In this case, the tape timer creates 28 dots per second, which means that the frequency of dot creation is 28 Hz.

To find the time interval between 3 successive dots, we need to calculate the time it takes for the tape timer to create 3 dots. This can be done by dividing the total time by the number of dots created.

Since the tape timer creates 28 dots per second, the time interval between 3 dots can be calculated as follows:

Time interval = 1 second / 28 dots = 1/28 seconds

So, the time interval between 3 successive dots created by the tape timer is 1/28 seconds, which is the amount of time that elapses between the creation of each dot.

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Linear relationships can be represented mathematically by equations of the form y = mx + b or visually by graphs.

A linear relation, also known as a simple relation, is a linear equation in linear algebra that contains the elements of a vector space or a module as its solution.

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.

If the slope is upward, there is a positive linear relationship, meaning that when one rises, the other rises as well. A negative slope indicates a negative linear relationship, whereby as one variable rises, the other falls. If the slope is 0, the two variables do not change as one rises.

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Answer:

x>-3

Step-by-step explanation:

Divide both sides by 5

x > -3

-15/5 = -3

Answer:

x = 15

Step-by-step explanation:

We take x as the variable that replicates the number

When we put it into a equation we get

x + 15 = 2x

x = 15

When we check

15 + 15 = 2(15)

30 = 30