Determine the length of HK

Answer:

The correct answer is B.

[tex]f(x) = \frac{1}{(x - 1)(x + 1)} [/tex]

The vertical asymptotes are at x = -1 and at x = 1.

Step-by-step explanation:

Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:

P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.

Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.

Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).

However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.

Answer:

87

Step-by-step explanation:

87

cos(2a + B) is approximately equal to -0.2948.

why it is?

To find cos(2a + B), we can use the double angle formula for cosine:

cos(2a + B) = cos(2a)cos(B) - sin(2a)sin(B)

We already know the values of a and B, so we can substitute them into the formula and simplify using the trigonometric identities:

a = sin²-1(4/5) = 53.13° (rounded to two decimal places)

B = tan²-1(12/5) = 67.38° (rounded to two decimal places)

cos(2a) = cos²2(a) - sin²2(a) = (cos(a))²2 - (1 - (cos(a))²2) = 2(cos(a))²2 - 1

cos(2a) = 2(sin²-1(4/5))²2 - 1 = 2(0.8)²2 - 1 = 0.32

sin(2a) = 2sin(a)cos(a)

sin(2a) = 2(sin(sin²-1(4/5)))cos(sin²-1(4/5)) = 2(4/5)(3/5) = 0.96

cos(B) = 1/sqrt(1 + tan²2(B)) = 1/sqrt(1 + (12/5)²2) = 5/13

sin(B) = tan(B)cos(B) = (12/5)(5/13) = 0.48

Substituting these values into the formula for cos(2a + B) gives:

cos(2a + B) = cos(2a)cos(B) - sin(2a)sin(B)

cos(2a + B) = (0.32)(5/13) - (0.96)(0.48)

cos(2a + B) = 0.166 - 0.4608

cos(2a + B) = -0.2948

Therefore, cos(2a + B) is approximately equal to -0.2948.

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Answer:

Step-by-step explanation:

If they had $11: Fred gets $3, George gets $8.

So the ratio is:  3:8

If λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

[tex]v^T A^T = \lambda v^T[/tex]

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

[tex]\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right][/tex]

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

[tex]v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T[/tex]

Now, for transpose of A:

[tex]A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right][/tex]

The eigen vectors are:

[tex]u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T[/tex]

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.

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Answer:

Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...

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Answer:

80%

Step-by-step explanation:

each side of a square is 30 cm.

decreased by 20%.

find the percentage decrease in the area of the square.

20%x4side= 80%

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{-8}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 +3}{-8 +6} \implies \cfrac{ -1 }{ -2 } \implies \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-6)}) \implies y +3 = \cfrac{ 1 }{ 2 } ( x +6) \\\\\\ y+3=\cfrac{ 1 }{ 2 }x+3\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 2 }x \end{array}}[/tex]

We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm​, here is a guide:

A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.

Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.

Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.

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Therefore, it will cost $350 to carpet Carli's rectangular bedroom with carpet that costs $2.50 per square foot.

Area is a measure of the size of a two-dimensional surface or region. It is usually expressed in square units, such as square meters (m²) or square feet (ft²). To calculate the area of a shape, you need to multiply its length by its width or use an appropriate formula for the specific shape. The concept of area is important in many fields, including mathematics, geometry, physics, engineering, architecture, and more. It is used to quantify the space occupied by objects or regions, to determine the amount of material needed to cover a surface, or to calculate the amount of paint or wallpaper required to decorate a room, among other applications.

Given by the question.

The area of Carli's rectangular bedroom can be calculated by multiplying its length by its width:

Area = Length × Width

Area = 14 ft × 10 ft

Area = 140 sq ft

The cost of carpeting her room can be found by multiplying the area of the room by the cost per square foot of carpet:

Cost = Area × Cost per square foot

Cost = 140 sq ft × $2.50/sq ft

Cost = $350

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Answer:

Step-by-step explanation:

D

Answer:

45,000 is standard form.

4.5 is the coefficient.

4 of 10⁴ is the exponent.

7.6 × 10⁻⁴ is scientific notation.

10 of 10⁻⁴ is the base.

Step-by-step explanation:

Scientific notation is a way of writing very large or very small numbers in a compact and convenient form. It consists of two parts:

The base of scientific notation is always 10, which means that the number is written in terms of powers of 10.

For example, the number 4,000,000 can be written in scientific notation as 4 x 10⁶. In this case, the coefficient is 4, and the exponent is 6.

The standard form of a number is simply the usual way of writing it, without using scientific notation. For example, the standard form of 4 x 10⁶ is just 4,000,000.

Therefore, for the given problem:

Answer: Below.

Step-by-step explanation:

To find each we must use the left side to put the first letter. The top for the right letter.

First row - AA

Second row - CB

Third row - CD

Fourth row - BD

As a result, there is a 90° angle separating each couple of animal residences.

A geometric shape known as an angle is created by two rays that meet at a spot in the middle known as the vertex. The rays are typically depicted as a line section with an arrow pointing in the direction of the ray's extension on one end. When a complete circle is divided into 360 equal parts, each component being one degree, an angle is created that is measured in terms of degrees. The angle created when the radius of a circular equals the length of its arc is measured in radians.

given

A circle that includes the tree, pond, spider web, and bird's nest has been drawn by the photographer, with the camera in its middle. This is due to the fact that each time she rotates the camera anticlockwise, she is actually rotating it around the middle of this circle.

Call the angle between each set of animal residences "x" for simplicity. We can infer the following because the shooter always rotates the camera through the same angle:

Angle from pond to spider's web turned equals x Angle from tree to pond turned equals x

Angle from bird's nest to branch turned equals x

Since the photographer has made a full rotation, the total of these angles must be 360 degrees. Therefore:

x + x + x + x = 360

4x = 360

x = 90

As a result, there is a 90° angle separating each couple of animal residences.

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√5 /x²y is equivalent  expression to the given question . Then the correct option is C.

What is Expression?

A mathematical expression is a phrase with at least two variables or integers and one arithmetic operation.

a)Constant It has a set numerical value and is a constant.

For instance: 7,45,413,18,5.

b) Variables don't accept any predetermined values. Value is depend on Equation

Like a, p, and z

Constants, variables, or constants multiplied by variables are all acceptable terms (s). The "+" or "" symbol or both separates each term in an expression.

Instance: 5a+12b.

d) Operators: Addition (+), subtraction (-), multiplication (-), and division (-) are the four operations that are used to combine the terms in an expression.

Therfore, √5 /x²y is equivalent  expression to the given question . Then the correct option is C.

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Answer:

19

Step-by-step explanation:

We are given the following two functions of s

[tex]p(s) = s^3 + 10s\\f(s) = 6s - 3\\\\\text{To find p(2) substitute 2 for s in p(s)}\\p(2) = (2)^3 + 10(2) = 8 + 20 = 28\\\\[/tex]

[tex]\text{To find f(2) substitute 2 for s in f(s)}\\f(2) = 6(2) - 3= 12 - 3= 9\\[/tex]

[tex]p(2) - f(2) = 28 - 9 = 19[/tex]

Perimeter, area, and circumference are important mathematical concepts that have numerous real-world applications.

How to apply?

For example, in construction and architecture, these concepts are used to measure and design buildings, rooms, and other structures. Knowledge of perimeter is important when determining how much material is needed for a fence or wall, while understanding area is crucial for calculating how much paint or flooring material is needed for a room.

Circumference is important for designing circular objects such as wheels, pipes, and round tables. In addition to construction and design, these concepts are also used in various fields such as engineering, science, and finance.

For instance, understanding area and circumference is important in calculating the surface area and volume of 3D objects in science, while in finance, perimeter and area can be used to calculate the cost of goods or real estate. Overall, the applications of perimeter, area, and circumference are numerous and essential in many aspects of our daily lives.

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Step-by-step explanation:

So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered

Answer:

Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.

Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.

Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.

Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.

Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.

Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.

Step-by-step explanation:

The balance of the account after the seventh deposit can be calculated using the formula below:

A = P (1 + r/n)ⁿ

where:

A = the balance of the account

P = The initial deposit of $800

r = the interest rate of 5%

n = the number of times the interest is compounded annually

n = 1

Therefore, the balance of the account after the seventh deposit is:

A = 800 (1 + 0.05/1)⁷

A = 800 (1.05)⁷

A = 800 (1.4176875)

A = 1128.54

Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.

The value of the probability is 0.3125 and this is proved by the calulations below

The probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.

The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.

There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.

For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.

Therefore, the probability of getting exactly 3 heads is:

Probability = 10 * (1/32)

Probability = 10/32

Probability = 0.3125.

Hence, the value of the probability is 0.3125.

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Answer:

C = 5n + 4f + 15b

With four decimal places added, we have P(2.04 Z 3.04) 0.0189.

To round a decimal value to two decimal places, use the hundredths place, which is the second place to the right of the decimal point.

Subtracting the area to the left of 1.25 from the area to the left of 2.15 will give us the standard normal area between 1.25 and 2.15.

The area to the left of 1.25 is 0.8944, and the area to the left of 2.15 is 0.9842, according to a conventional normal distribution table or calculator.

So, the standard normal area between 1.25 and 2.15 is:

P(1.25 < Z < 2.15) = 0.9842 - 0.8944 = 0.0898

Rounding to four decimal places, we get:

P(1.25 < Z < 2.15) ≈ 0.0898

We follow the same procedure as before to determine the standard normal region between 2.04 and 3.04:

P(2.04 < Z < 3.04) = P(Z < 3.04) - P(Z < 2.04)\

The area to the left of 2.04 is 0.9798, and the area to the left of 3.04 is 0.9987, according to a conventional normal distribution table or calculator.

So, the standard normal area between 2.04 and 3.04 is:

P(2.04 < Z < 3.04) = 0.9987 - 0.9798 = 0.0189

Rounding to four decimal places, we get:

P(2.04 < Z < 3.04) ≈ 0.0189

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Check the picture below.

btw, we could have used the f(4) for both subfunctions just the same.

A)  The mean distance walked by the group of office workers on Monday was approximately 6.89 km.

b) The interquartile range was approximately 2.2 km.

c)   The value of r would be: r ≈ 4.1 km

d)  (i) Total distance walked = 1.7 km * 20 = 34 km

(ii),  the combined mean distance walked by all thirty workers was approximately 3.28 km.

(iii) the standard deviation is not given directly, we can use the fact that the standard deviation is equal to the square

(a) The mean distance walked by the group of ten office workers on Monday can be found by adding up all of their distances and dividing by the number of workers:

Mean = (5 + 2 + 3 + 6 + 5 + 8 + 5 + 7 + 6 + 4) / 10

= 51 / 10

= 5.1 km

(b) (i) The value of p is the median of the data set. Since there are 10 data points, the median is the average of the 5th and 6th smallest values:

p = (5 + 5) / 2

= 5 km

(c) The value of r represents the maximum distance that is not considered an outlier. From the box-and-whisker plot, we can see that the maximum value is 8 km, which is not an outlier. Therefore,

r = 8 km

(d) (i) The total distance walked by the group of 20 freelancers can be found by multiplying their mean distance by the number of freelancers:

Total distance = Mean distance * Number of freelancers

= 1.7 km * 20

= 34 km

(d)

(i) The total distance walked by the group of 20 freelancers can be found by multiplying their mean distance by the number of freelancers:

Total distance = Mean distance * Number of freelancers

= 1.7 km * 20

= 34 km

(ii) The combined mean distance that all 30 workers walked on Monday can be found by adding up the total distance walked by all workers and dividing by the total number of workers:

Combined mean distance = (Total distance by office workers + Total distance by freelancers) / Total number of workers

= (51 km + 34 km) / 30

= 85 / 30

= 2.83 km

(iii) On Tuesday, all 20 freelancers walked double the distance they walked on Monday. The variance in the distance walked by the freelancers on Tuesday can be found using the formula for the variance of a constant times a random variable:

Var(aX) = a^2 Var(X)

Since the freelancers walked double the distance, the variance of the distance they walked on Tuesday is:

Var(Tuesday distance) = 4 * Var(Monday distance) = 4 * (1 km)^2 = 4 km^2

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Answer: There is a 5.32544378% Chance of a face card being pulled twice

Step-by-step explanation: If there is 52 cards in a deck, and 12 of them are face cards, there is roughly a 23% (23.0769%) chance of pulling one in the first draw. Multiply .230769 x .230769 and you get .0532544378 which equals 5.32544378%

The value of x in the equation that is given as 2/3x + 4/5x = 6 will be 4.

Based on the information given, one should note that an equation has to do with the statement in a question which depicts the variables given. In this case, one should note in an equation, one will need to consider two or more components are to be able to illustrate the scenario.

In this case, it is important to note that an equation simply depicts the mathematical statement which can be made up of two expressions which are simply connected by an equal sign.

The equation is explained thus:

2/3x + 4/5x = 6

10/15x + 12/15x = 6

22/15x = 6

1.467x = 6

x = 6 / 1.467

x = 4

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Solve the equation

2/3x + 4/5x = 6

Answer: 90$

Step-by-step explanation:  50% of 60 is 30 so 60+30=90

A catapult, seatbelt, parachute, safety net, or unbalanced force can be used to stop moving objects.

When a seatbelt is fastened during sudden braking or a crash, it exerts pressure on the passenger's body and prevents them from moving forward.

Similar to this, when a parachute is opened, a significant amount of air resistance force is generated, slowing the wearer's descent.

A safety net exerts force on an object that is falling on it as well, absorbing the kinetic energy and stopping it.

A catapult can apply a significant unbalanced force that can halt an object in motion by quickly transferring energy from its springs or elastic materials to the target.

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