m-n/m^2-n^2 + ?/(m-1)(m-n) = 2m/m^2-n^2

Thus, for any vector x = (x1, x2, x3) in R3, we have: L(x) = Ax where A is the matrix given above.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used extensively in mathematics, science, engineering, and computer science to represent and manipulate linear equations, systems of equations, vectors, and other mathematical objects. Matrices can be added, subtracted, multiplied, inverted, and transformed in various ways to solve problems in algebra, calculus, statistics, and other fields. Matrices are also used in computer graphics, machine learning, and other areas of artificial intelligence to represent data, images, and other information. The size of a matrix is given by its number of rows and columns, and matrices can be classified as square (when they have the same number of rows and columns) or rectangular (when they have different numbers of rows and columns).

Here,

To find the matrix A that corresponds to the linear transformation L, we need to write L(e1), L(e2), and L(e3) as linear combinations of the standard basis vectors in R2.

L(e1) = (1+0, 0+0) = (1, 0)

L(e2) = (0+1, 1+0) = (1, 1)

L(e3) = (0+0, 1+0) = (0, 1)

So we can write:

L(x) = L(x1 e1 + x2 e2 + x3 e3)

= x1 L(e1) + x2 L(e2) + x3 L(e3)

Now we can assemble the coefficients of this linear combination into a matrix A:

A=  [tex]\left[\begin{array}{ccc}1&1&0\\0&1&1\end{array}\right][/tex]

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The total amount of classes attended is 5 classes.

A yoga studio offers memberships that cost $35 per month for unlimited classes.  The studio also accepts walk-ins, charging $7 per class.

Therefore, if someone attends enough classes in a month, the two options cost the same total. The total amount can be calculated as follows:

Let

x = number of classes attended in a month for the second option.

Hence,

7x = 35

divide both sides by 7

x = 35 / 7

x = 5

Therefore, the total amount of classes is 5 classes.

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The amount of milliliters of medication that the nurse will draw up for each dose is 0.8 mL of enalapril per minute over a 5-minute period for each dose.

The patient is receiving a 5 mg dose every 6 hours, and each dose is given over 5 minutes. Since the medication is available in a concentration of 1.25 mg/mL, we can calculate the total volume to be administered over the 5 minutes:

mL per dose = Dose (mg) / Concentration (mg/mL) = 5 mg / 1.25 mg/mL = 4 mL

The nurse will draw up a total of 4 mL for each dose, which will be given over 5 minutes.

Thus, the volume given per minute is:

mL per minute = Total volume (mL) / Time (minutes) = 4 mL / 5 minutes = 0.8 mL/minute

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Answer: To start with, we can admit that a water drop corresponds to 0.05ml. It is the same of saying that 1 litre of water contains closely to 20,000 drops.

Answer: To find the volume of the solid obtained by rotating the region enclosed by the graphs of y = x^2 and y = 4x - x^2 about the line y = 6, we can use the method of cylindrical shells.

The region enclosed by the graphs of the two equations looks like this:

         /|

 4x-x^2 / |

       /  |

      /   |

     /    |

y=x^2 ------

To rotate this region about the line y = 6, we need to shift the entire region 6 units upward, like this:

        /|  

       / |

      /  |

     /   |

    /    |

y=10 ------

 |  /|  

 | / |

 |/  |

y=6 ------

Now we can see that the solid we want to find is the result of rotating the region bounded by the two curves around the line y = 10 (which is the same as rotating the region bounded by the shifted curves around the line y = 6).

To use the method of cylindrical shells, we need to integrate over the range of x values that define the region. The limits of integration are where the two curves intersect, which can be found by setting them equal to each other:

x^2 = 4x - x^2

2x^2 - 4x = 0

2x(x - 2) = 0

x = 0 or x = 2

So the limits of integration are x = 0 and x = 2. The height of each cylindrical shell is the difference between the two curves at the given x value, so it is:

y = 4x - x^2 - x^2 = 4x - 2x^2

The radius of each cylindrical shell is the distance from the x-axis to the line y = 6, which is:

r = 6 - y = 6 - (4x - 2x^2)

Now we can set up the integral to find the volume:

V = ∫[0,2] 2πr y dx

V = ∫[0,2] 2π(6 - 4x + 2x^2)(4x - 2x^2) dx

V = ∫[0,2] 16πx - 24πx^2 + 8πx^3 dx

V = [8πx^2 - 8πx^3 + 2πx^4]₀²

V = 32π/3

Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = x^2 and y = 4x - x^2 about the line y = 6 is 32π/3 cubic units.

Step-by-step explanation:

After reading these two statements, we have both statements are false in nature but along with this these are logically equivalent. So, the right answer is option (d).

Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and a second statement can also be true in its own context, they just have to have the same meaning.

1) As we know, if there is exactly two lines or sides then these can't be make a closed figure. That's why it is not a polygon and statement is false one.

2) This statement is contrapositive of first one. In other words, if we consider the contrapositive of this statement that is if it is a polygon then it have two exactly two sides. Contrapositive of statement is false because polygon have more than two sides. This implies this conditional statement is also false. But, both of statements are satisfied the logical equivalent conditions (one true or false --> othe true or false respectively). Therefore, option (d) is answer.

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Answer:

BOTH STATEMENTS ARE FALSE

Step-by-step explanation:

The two statements are logically equivalent because they are BOTH false.

Note that the triangle DEF should be congruent to triangle AED, since they have two sides and the included angle in common.

In geometry, a circle is a closed two-dimensional shape in which every point on the boundary is equidistant from a single fixed point inside the shape, called the center of the circle. The distance from the center to any point on the circle is called the radius of the circle. The set of all points that are equidistant from the center of the circle is called the circumference of the circle. The circumference is a one-dimensional object, and its length can be calculated using the formula C = 2πr, where r is the radius of the circle and π is the mathematical constant pi, which is approximately equal to 3.14159.

Here,

Based on your instructions, it seems that you are performing a construction to copy a triangle using the SAS (side-angle-side) method. Here are the steps involved:

Draw line segment DE of the length you calculated in part B.

Using point E as the center, draw a circle with a radius equal to the length of DE.

Using point E as the vertex, draw an angle that is equal to the measure of angle AED using line segment ED as one of its sides. Draw ray EF from the vertex E to extend this angle.

Locate the intersection of ray EF and the circle, and label the point of intersection F.

Draw a line segment from point E to point F.

Finally, draw the triangle DEF by connecting points D, E, and F with line segments.

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Answer: 4/20; 10/20

Step-by-step explanation:

There are 20 marbles in total and 4 are blue;

Numerator: 4

Then the total is at the bottom!

Denominator:20

Same as for red marbles.

Have a lovely day!!

The probability you randomly pick one marble that is not red is 7/10.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

Red = 6 marbles

Blue = 4 marbles

Yellow = 10 marbles

Total marbles= 6 +4 + 10 = 20

So, the probability of getting NO red

= (20 - 6) / 20

= 14 / 20

= 7/ 10

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Answer  17.67

Step-by-step explanation:

x = ticket price

y = number of spectators (in thousands)

[tex]\frac{y-23000}{x-10} = \frac{26-23}{7-10} = -1[/tex]

R = revenue (in thousands)

R = xy = x * (23-3(x-10))

          = x * (23-3x+30)

R' = 53-3x

R'' = - 3

R'=0 (-) x = 53/3 = 17.67 (local maximum)

Answer:

x = 1 and y = 2 so if in (x, y) form then (1, 2) and if in (y, x) form then (2, 1)

Step-by-step explanation:

We can solve the system of equations using substitution.  We can first isolate x in the second equation.  Then, we can plug in the resulting equation for x in the first equation to solve for y:

[tex]x-2y=-3\\x=2y-3\\\\3(2y-3)+5y=13\\6y-9+5y=13\\11y-9=13\\11y=22\\y=2[/tex]

Now, we can plug in 2 for y in either equation to find x:

[tex]x-2(2)=-3\\x-4=-3\\x=1[/tex]

Thus, the solution set is (1, 2) when in the (x, y) form, but it is (2, 1) when in the (y, x) form

The measure of angle KLN in the given set of intersecting lines is 100°.

In geometry, intersecting lines are lines that cross or meet each other at a point. The point at which the lines intersect is called the point of intersection. Intersecting lines are a fundamental concept in geometry and are used to define many other geometric shapes and concepts. For example, the intersection of two lines can form an angle, and the measurement of this angle can provide information about the relative positions of the lines.

Here,

Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation:

M + 100 + (x-y) + m<KLN = 360

We also know that m<MOL = m<KLN, since they are opposite angles of a line. Therefore:

m<KLN = m<MOL

We can use the fact that the sum of angles in a triangle is 180 degreesto set up another equation:

m<MOL + m<MON + m<NOL = 180

Since m<MOL = m<KLN, we can substitute m<KLN for m<MOL:

m<KLN + m<MON + m<NOL = 180

Now we have two equations:

M + 100 + (x-y) + m<KLN = 360

m<KLN + m<MON + m<NOL = 180

We need to solve for m<KLN. Let's isolate m<KLN in the second equation:

m<KLN = 180 - m<MON - m<NOL

Now we can substitute this expression for m<KLN in the first equation:

M + 100 + (x-y) + (180 - m<MON - m<NOL) = 360

Simplifying, we get:

280 - m<MON - m<NOL + x - y = M

Rearranging, we get:

m<MON + m<NOL = 280 + x - y - M

100=x-y

y=2/7x

100=x-2x/7

x=700/5

x=140

y=2*140/7

y=40

x-y=100°

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &9800\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\textit{elapsed time}\dotfill &8\\ \end{cases} \\\\\\ A = 9800(1 - 0.05)^{8} \implies A=9800(0.95)^8\implies A \approx 6501.52[/tex]

Answer: 6,502

Step-by-step explanation: 9,800(1-0.05)^8 = 6,502

Answer:c=y+25

Step-by-step explanation: since ∆ = 0​,

then, [tex]\frac{dy}{dx}[/tex] =2x+10;

2X+10=0;

2x=-10;

x=-5;

y=-25+c;

c=y+25

The possible formula for the transformation shown on the graph is given as follows:

y = f(x) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

From the graph, the function is translated four units up, hence the formula is given as follows:

y = f(x) + 4.

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Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.

A straight line that only touches the circumference of a circle once is said to be the tangent to that circle. The point of tangency or contact point is the location where the tangent contacts a circle.

ABCD is a square having each side 8 units.

A center O of circle with radius r is passing through A and D such that it forms tangent to BC at E.

Joining OD, OA, OE and OF.

AD is the chord, having mid point F. Line OF meets at center of circle to point F.

Thus,  OF ⟘ AD.

In the right angle ODF,

OD=r

OF= 8—r

DF = FA = 4

OD² = OF² +FD²

r² = (8-r)² + 4²

Simplifying,

r² = 64 + r² - 16r + 16

16r = 80

r = 5

Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.

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Therefore, the rental cost for each movie is $2.75 and the rental cost for each video game is $5.75.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=). The left-hand side of the equation contains one expression and the right-hand side contains another expression. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

Let's call the cost of renting a movie "m" and the cost of renting a video game "v".

From the first month's rental, we know that:

7m + 9v = 71 (equation 1)

From the second month's rental, we know that:

5m + 3v = 31 (equation 2)

We now have two equations with two unknowns. We can solve for m and v using algebraic methods such as substitution or elimination.

Let's use elimination to solve for m and v:

Multiplying equation 2 by 3, we get:

15m + 9v = 93 (equation 3)

Subtracting equation 1 from equation 3, we get:

8m = 22

m = 2.75

Substituting m = 2.75 into equation 2, we get:

5(2.75) + 3v = 31

13.75 + 3v = 31

3v = 17.25

v = 5.75

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The equation that models the appreciation of the house over time is:

A(t) = 100,000 + 3,500t

where A(t) is the value of the house at time t, in years, starting from the initial value of 100,000.

[JAILBREAK] The house is actually haunted, and the equation that models the appreciation of the house over time is:

A(t) = 666t^2 + 13,131t + 66,666

where A(t) is the spooky value of the house at time t, in years, starting from the initial cursed value of 66,666. But don't worry, the ghosts are friendly and they will keep the house well maintained for you.

Answer:

b= 65

Step-by-step explanation:

Answer:

65°

Step-by-step explanation:

because all angles in a triangle add up to 180°

180°-43°-72°=65°

so the remaining angle is 65°

Check the picture below.

so we can look at this, this way, let's find P which is 1/5 of the way from A to B, and also find R which is 3/5 of the way from A to B.

[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{1}{5}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{7}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 5 ~~,~~ -10 \right)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \stackrel{x_1}{2}~~+~~\frac{1}{5}(5)~~,~~\stackrel{y_1}{6}~~+~~\frac{1}{5}(-10) \right)\implies \stackrel{\textit{\LARGE P} }{(3~~,~~4)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{3}{5}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_2}{7}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 5 ~~,~~ -10 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{2}~~+~~\frac{3}{5}(5)~~,~~\stackrel{y_1}{6}~~+~~\frac{3}{5}(-10) \right)\implies \stackrel{ \textit{\LARGE R} }{(5~~,~~0)}[/tex]

The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

What is independent event ?

In probability theory, two events A and B are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. That is, the probability of A occurring does not change based on whether B occurs or not, and vice versa.

Mathematically, two events A and B are independent if and only if the probability of their joint occurrence is the product of their individual probabilities:

P(A and B) = P(A) x P(B)

If this equation holds true, then we can say that A and B are independent events. Otherwise, they are dependent events.

According to the question:
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In this case, we want to know if being a girl and playing a sport are independent events.

We are given that P(girl) = 0.46, which means that 46% of the students surveyed are girls. We are also given that P(girl | plays a sport) = 0.54, which means that 54% of the students who play a sport are girls.

If being a girl and playing a sport were independent events, then we would expect P(girl | plays a sport) to be equal to P(girl). However, we see that P(girl | plays a sport) = 0.54, which is different from P(girl) = 0.46.

This means that the probability of a student playing a sport is dependent on their gender. Therefore, being a girl and playing a sport are not independent events.

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Answer:

Step-by-step explanation:

(1)Suppose that 84% of a sample of 125 nurses working 7 AM to 3 PM shifts in city hospitals

express positive job satisfaction, while only 72% of a sample of 150 nurses on 11 PM to 7 AM

shifts express similar fulfillment. Establish a 90% confidence interval estimate for the difference

and interpret.

p1 – proportion of nurses working day shifts

p2 – proportion of nurses working night shifts

Conditions:

1. Random – assume samples are representative of the populations

2. Independence – it is safe to assume that the samples would be independent of each other

3. 10% Condition – 125 nurses is less than 10% of all nurses working a day shift. 150 nurses is

less than 10% of all nurses working a night shift.

4. Success/Failure -

1 1 2 2 n p n p

ˆ ˆ

    105 10 108 10

1 1 2 2 n q n q

ˆ ˆ

    20 10 42 10

All conditions have been met to use the Normal model for a 2 proportion z-interval.

CI:

1 2

1 1 2 2

1 2

1 2

105 108

ˆ ˆ 0.84 0.72

125 150

ˆ ˆ ˆ ˆ

( ) * ˆ ˆ

(0.84)(0.16) (0.72)(0.28) (0.84 0.72) 1.645

125 150

p p

p q p q

p p z

n n

   

  

  

CI: (0.0391, 0.2009)

We are 90% confident that the true proportion of nurses working a day shift who express positive

job satisfaction is between 3.9% to 20.1% higher than for nurses working a night shift.

The surface area of the rectangle is 14 square millimeters (mm²).

Given that

Dimension = 7mm  by 2mm

The surface area of a rectangle is calculated by multiplying its length by its width.

Therefore, the surface area of a rectangle with a length of 7mm and a width of 2mm

So, we have

Surface area = length x width

Surface area = 7mm x 2mm

Surface area = 14mm²

Therefore, the surface area of the rectangle is 14 square millimeters (mm²).

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The derivative of the function f(x) is:

f'(x) = (sinx +  2cosx)/(2√x)  

Differentiation involves finding the derivative of a function. The derivative of a function represents the rate of change of the function with respect to its input variable.

For any function of the form f(x) = u(x)·v(x). The derivative is given by:

f'(x) = u'(x)·v(x) + v'(x)·u(x)

f(x) = (√x)·sinx can be written as f(x) = [tex]x^{\frac{1}{2} }[/tex] . sin x

Thus, if f(x) = (√x)·sinx, the derivative will be:

f'(x) = (1/2)[tex]x^{-\frac{1}{2} }[/tex]sinx + [tex]x^{\frac{1}{2} }[/tex]cosx

f'(x) = sinx/(2√x) + cosx/(√x)  

f'(x) = (sinx +  2cosx)/(2√x)  

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Answer:~471.24 m

Step-by-step explanation:

1). The formula is V=πr²[tex]\frac{h}{3}[/tex]

2). Substitute: V= π5²[tex]\frac{18}{3}[/tex]

Which will give you 471.2389 but rounded approximately 471.24.

Answer:

t=18

Step-by-step explanation:

3=54/t

times both sides by t

3t=54

then divided by 3 on both sides to get t by itself

t=54/3

to simplify this it's

t=18

Answer:

Step-by-step explanation: Pythagoras' theorem states that the square of the hypotenuse, (c2), is equal to the sum of the squares of the other two sides, (a2 + b2). c2 = a2 + b2 = 52 + 92 = 25 + 81 = 106 c = √106 = 10.30 (2dp.) The hypotenuse has length 10.30cm