Does the following make a right triangle?
A ceramic tile with sides 20 cm, 21 cm, and 29 cm


A. yes
B. no

Step-by-step explanation:

\( \frac{5.2}{100} \times 156000 \\ = 8112commission\)

Answer:D

Step-by-step explanation:

For products that need to be useful, practical and work, a celebrity endorsed product would not be what I would count on as far as quality and performance.

Answer:

   D

Step-by-step explanation:

Source: Trust me bro

a) The regular expression "+" represents the language of one or more occurrences of the symbol "+". To construct a grammar that represents the same language but is not regular, we can use the following production rule:

S -> "+" S | "+".

This grammar generates strings with one or more "+" symbols.

b) The regular expression "+c" represents the language of one or more occurrences of the symbol "+" followed by the symbol "c". To construct a non-regular grammar for this language, we can use the following production rules:

S -> "+" S | "c".

This grammar generates strings with one or more "+" symbols followed by a "c". Since the language represented by the regular expression is regular, it can be recognized by a finite automaton. However, the grammar we constructed is not regular because it uses a recursive production rule.

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The value of the middle of the three is 25.

Let x be the first odd integer, then the next two consecutive odd integers are x+2 and x+4. The sum of these three consecutive odd integers is given as 75, so we can write the equation:

x + (x+2) + (x+4) = 75

Simplifying the left side of this equation gives:

3x + 6 = 75

Subtracting 6 from both sides gives:

3x = 69

Dividing by 3 gives:

x = 23

So the first odd integer is 23, and the next two consecutive odd integers are 25 and 27. The middle of these three is the second consecutive odd integer, which is 25. Therefore, the value of the middle of the three is 25.

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Respuesta:

A. −3<x<2

B. 0≤x<6

C.7<x<12

Answer:

321/8 ft^2

Step-by-step explanation:

The whole area is 49/4 × 5 = 245/4 ft^2

The area of tiled floor is 13/2 × 13/4 = 169/8

245/4 - 169/8 we need to equalise the bottom of fraction to subtract so

2/2 × 245/4 = 490/8

490/8 - 169/8 = 321/8 ft^2

length = y

width = y- 5

(y-5) * (y) = 750

y^2 - 5y = 750

y^2 -5y - 750 = 0

answer:

(y + 25)(y – 30) = 0

Answer:

y=4/5×-1 is the answer!

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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Answer:

2c + 9

Explanation:

Given the below expression;

To add the above, let's clear the parenthesis, collect like terms and add the like terms together;

Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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The probability that Jack will win is 0.00015. The result is obtained by dividing the number of tickets that Jack has by the total number of events.

Probability of an event is calculated by dividing the number of favorable outcomes by the total number of events in the sample space.

In a certain lottery are 100 balls numbered from 1 - 100 in a large basket. Three numbered balls are randomly drawn without replacement. To win the lottery, a player's ticket must have each of the numbers drawn in no particular order.

If jack buys 21 tickets, find the probability that he will win!

In any the order, the different triples of tickets that a player can have can be found by a combination.

The total number of events would be

\(= \: _{100}C_{3}\)

\(= \frac{100!}{3! \:97!} }\)

\(= \frac{98 \times 99 \times 100}{2 \times 3}\)

= 161700 different triples

Jack has 21 tickets. So, the probability that Jack will win is

P = 21/161700

P = 0.00013

Hence, Jack will win with the probability of 0.00013.

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Answer:

1. She should use Length x Width x Height.

2. The unit of the answer is 30.

3. The volume of the box is 30 units.

Answer:

Step-by-step explanation:

Area = 121 in²

Length = √121 in = 11i in

a. the integral \(I\) becomes \(\[I = a\theta + \sin(\theta) + C\]\) where \(\(C\)\) is the constant of integration. b. the integral \(I\) becomes \(\[I = \frac{1}{2}a\theta^2 + \sin(\theta) + C\]\) where \(\(C\)\) is the constant of integration.

To evaluate the integral \(I = \int (a + \cos(\theta)) \, d\theta\), we can apply the integral rules and properties. Let's consider the two given cases:

(a) If \(a > 1\):

In this case, the integral can be evaluated directly. The integral of \(a\) with respect to \(\theta\) is \(a\theta\), and the integral of \(\cos(\theta)\) is \(\sin(\theta)\). Therefore, the integral \(I\) becomes:

\[I = a\theta + \sin(\theta) + C\]

where \(C\) is the constant of integration.

(b) If \(a = a_0 + i e\), where \(a_0\) and \(e\) are real and positive:

In this case, the integral can also be evaluated using the same rules. The integral of a constant multiplied by a variable is \(\frac{1}{2}a\theta^2\), and the integral of \(\cos(\theta)\) is \(\sin(\theta)\). Therefore, the integral \(I\) becomes:

\[I = \frac{1}{2}a\theta^2 + \sin(\theta) + C\]

where \(C\) is the constant of integration.

It's important to note that the integral is evaluated based on the assumption that \(d\theta\) is the differential of \(\theta\) and not a different variable. Also, \(C\) represents the constant of integration, which can take any value.

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Answer:

Let's start by assigning a variable to the original side length of the square photograph. We'll use g to represent this length.

According to the problem, each side of the new photograph will be 1 inch more than twice the original side length g. This means that the new side length will be:

2g + 1

Since this is a square photograph, all four sides are equal in length. Therefore, the area of the new photograph can be represented by the square of the new side length:

(2g + 1)^2

To simplify this expression, we can use FOIL (First, Outer, Inner, Last) to expand the squared binomial:

(2g + 1)^2 = (2g + 1)(2g + 1)

= 4g^2 + 2g + 2g + 1

= 4g^2 + 4g + 1

So the trinomial that represents the area of the enlarged photograph is:

4g^2 + 4g + 1

To check our work, we can plug in a value for g and compare the areas of the original and enlarged photographs. For example, if g = 2 (meaning the original side length is 2 inches), then the area of the original photograph is:

2^2 = 4 square inches

And the area of the enlarged photograph is:

4(2)^2 + 4(2) + 1 = 25 square inches

This makes sense, since the new photograph has sides of length 2(2) + 1 = 5 inches, and therefore an area of 5^2 = 25 square inches, which is indeed 1 inch more than twice the original area of 4 square inches.

Answer:

magnitude of a shown vector is

\(4 \sqrt{5} \)

If it has a 15% yearly interest rate and the interest is compounded monthly and the card has $0 minimum payments for the first four years it is active. Therefore, Emma will owe approximately $529.27 in four years.

To calculate how much Emma will owe in four years, we need to use the compound interest formula: A = P (1 + r/n)^(n*t)

where:

A = the amount of money at the end of the investment period

P = the principal amount (the initial amount of money borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period in years

In this case, the principal amount is $300, the annual interest rate is 15%, and the interest is compounded monthly (so n = 12). The time period is four years.

Plugging in the values, we get:

A = 300(1 + 0.15/12)^(12*4)

A ≈ $529.27

Therefore, Emma will owe approximately $529.27 in four years if she doesn't pay off her credit card until after college.

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In this question, we are given a consumer with a utility function and a budget set defined by prices and income. We are asked to analyze various aspects related to the consumer's optimization problem, including drawing indifference curves.

Aproving the compactness of the budget set, analyzing changes in the budget set, solving the consumer's optimization problem using the KKT formulation, and discussing the differentiability of optimal demand with respect to income.

(a) The indifference curve that achieves a utility level of -1 can be obtained by setting the utility function equal to -1 and solving for x and y. Plotting the resulting equation will give us the shape of the indifference curve. The concavity of the utility function determines whether it is quasi-concave or not. If the utility function is concave, then the indifference curves will be convex, indicating that it is quasi-concave.

(b) To prove that the budget set B is compact, we need to show that it is closed and bounded. Closedness can be demonstrated by showing that the complement of B is open. Boundedness can be shown by demonstrating that there exists a finite number M such that the Euclidean distance between any point in B and the origin is less than or equal to M.

(c) When p = 0, the budget set reduces to the entire two-dimensional space, as there are no price constraints. In this case, the budget set is not compact since it is unbounded.

(d) To obtain a solution to the consumer's optimization problem using a diagram, we can plot the budget set and indifference curves. The optimal consumption bundle will be the point where the budget line is tangent to the highest possible indifference curve within the budget set. This tangency point represents the maximum utility the consumer can achieve given the budget constraints.

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The surface area of the portion of the plane 2x + 8y + z = 16 inside the first octant is 8 units squared.

The surface area of the portion of the plane 2x + 8y + z = 16 inside the first octant will be determined.

To find the surface area, we first need to determine the intercepts of the plane with the coordinate axes. Setting x=0, we get y=2 and z=16, setting y=0, we get x=8 and z=16, and setting z=0, we get x=8 and y=2. Therefore, the plane intersects the x-axis at (8,0,0), the y-axis at (0,2,0), and the z-axis at (0,0,16).

Next, we find the area of the triangle formed by the three intercepts, which is given by the formula for the area of a triangle: A = 1/2 × base × height. The base of the triangle is the distance between (8,0,0) and (0,2,0), which is √(8² + 2²) = 2√34. The height of the triangle is the distance from (0,0,16) to the plane, which is given by the equation 2x + 8y + z = 16 with z=0, so 2x + 8y = 16, which simplifies to x + 4y = 8. Setting y=0, we get x=8, so the point (8,0,0) lies on the plane. Therefore, the height of the triangle is the distance from (0,0,16) to (8,0,0), which is √(8² + 16²) = 8√5. Hence, the area of the triangle is A = 1/2 × (2√34) × (8√5) = 32√17.

Finally, we need to find the area of the portion of the plane inside the first octant. This can be done by projecting the triangle onto the xy-plane and then finding the area of the projected triangle. The projected triangle has vertices (0,0), (8,0), and (0,2), and its area is A = 1/2 × base × height = 1/2 × 8 × 2 = 8.

Therefore, the surface area of the portion of the plane 2x + 8y + z = 16 inside the first octant is 8 units squared.

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Answer:

tan(θ) is undefined.

Step-by-step explanation:

Recall that tan(θ) = sin(θ) / cos(θ). We are given that sin(θ) = -1. Hence:

\(\displaystyle \tan\theta=\frac{\sin\theta}{\cos\theta}=-\frac{1}{\cos\theta}\)

Since 1 / cos(θ) = sec(θ):

\(\tan\theta=-\sec\theta\)

We can square both sides:

\(\tan^2\theta=\sec^2\theta\)

From the Pythagorean Identity:

\(\tan^2\theta+1=\sec^2\theta\)

Substitute:

\(\tan^2\theta+1=\tan^2\theta\)

So:

\(1\neq0\)

Since we acquire an untrue statement, no solutions exist.

If needed, refer to the unit circle. Recall that sin(θ) only equals -1 when θ = 3π/2 (on the interval [0, 2π)). At 3π/2, cos(θ) = 0. Since tan(θ) = sin(θ) / cos(θ), tan(θ) is undefined whenever sin(θ) = -1 (or 1).

Answer:

41.18

Step-by-step explanation:

CD=22-6=16

42=1/2×6×AC

AC=14

tanθ=O/A

tanθ=(14/16)

x=tan-1(14/16)

x=41.18

The measure of the angle x in the right triangle ABD is 41.2 degrees.

A right angle triangle has one of its angles as 90 degrees. Therefore, the sides of the triangle can be found using trigonometric ratios.

area of a triangle = 1 / 2 bh

where

Hence,

area of a triangle =  1 / 2 × 6 × h

42 = 3h

h = 42 / 3

h = 14 cm

DC =  22 - 6 = 16 cm

AC = 14 cm

tan x = opposite / adjacent

tan x = 14 / 16

x = tan ⁻¹ 0.875

x = 41.1859251657

x = 41.2 degrees.

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The break-even point for the business with sales of $4,000,000 and a margin of safety of 25% is $3,000,000 (option a).

In this scenario, we are given that the business had sales of $4,000,000 and a margin of safety of 25%. To find the break-even point, we first need to calculate the margin of safety amount.

Margin of Safety Amount:

Margin of Safety = Sales - Break-even Sales

Since the margin of safety is 25%, it can also be expressed as a decimal: 0.25. Therefore, we can write the equation as follows:

0.25 * Sales = Sales - Break-even Sales

Simplifying the equation, we get:

0.25 * Sales = Sales - Break-even Sales

0.25 * Sales - Sales = -Break-even Sales

0.75 * Sales = Break-even Sales

Now we can substitute the given sales value of $4,000,000 into the equation:

0.75 * $4,000,000 = Break-even Sales

$3,000,000 = Break-even Sales

The break-even sales amount is $3,000,000. This means that the business needs to generate $3,000,000 in sales to cover all expenses and reach the break-even point.

Hence the correct option is (a).

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Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

1000 mililiters are equivalent to 1 liter, then Tina has to multiply 4.5 by 1,000 to convert liters to mililiters

Note that the absolute maximum and minimum values of f on the set d are:

The set d isthe set of all points (x, y)   such that x² + y² <= 1.

To find the absolute maximum   and minimum values of fon the set d, we can use the following steps.

The   critical points off ar -

(0, 0)

(1,   0)

(0,1)

The values of-f at the critical points are -

f(0, 0) = 0

f(1,   0)  =-16

f(0,   1) =-16

The values of f at the boundary points of d are

f(0,   1) =-16

f(1,1)    = -16

f(-1,0)   = -16

f(0,   -1)= -16

The largest value   off is 0, and   the smallest value of f is -16.

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Let's solve the problem step by step.According to the given data;Farmer Jones has x sheepFarmer Smith has 100 more sheep than Farmer Jones. Thus, Farmer Smith has x + 100 sheep.Farmer White has twice as many sheep as Farmer Jones. Thus, Farmer White has 2x sheep.The total number of sheep is 2500. So; x + x + 100 + 2x

= 25004x + 100

= 25004x

= 2500 - 1004x

= 2400x

= 2400/4x

= 600

Therefore, Farmer Jones has 600 sheep. Farmer Smith has 600 + 100 = 700 sheep.

Farmer White has 2(600) = 1200 sheep.

Therefore, there are 600 + 700 + 1200 = 2500 sheep.

The content describes the number of sheep owned by three farmers: Farmer Jones, Farmer Smith, and Farmer White. It provides the following information:

1. Farmer Jones has "x" number of sheep. The exact number of sheep owned by Farmer Jones is not specified.

2. Farmer Smith has 100 more sheep than Farmer Jones. This means Farmer Smith's sheep count is "x + 100."

3. Farmer White has twice as many sheep as Farmer Jones. Therefore, Farmer White's sheep count is "2x."

4. The total number of sheep owned by all three farmers combined is 2500.

So, to summarize:

- Farmer Jones: x sheep

- Farmer Smith: x + 100 sheep

- Farmer White: 2x sheep

- Total sheep count: x + (x + 100) + 2x = 2500

From this information, we can solve for the value of "x" and calculate the number of sheep each farmer owns.

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Considering the given information the number of sheep with the farmers will be:

Farmer Jones has 600 sheep.

Farmer Smith has 700 sheep.

Farmer White has 1200 sheep.

Let's suppose that the number of sheep Farmer Jones has is x

.Therefore, Farmer Smith has 100 more sheep than Farmer Jones has.

The number of sheep Farmer Smith has can be given by the equation:

              x + 100

Farmer White has twice as many sheep as Farmer J has.

Hence, the number of sheep Farmer White has is:

                               2 x

Now, the sum of the sheep Farmer Jones, Farmer Smith and Farmer White have is 2500.

Sheep Farmer Jones has = x

Sheep Farmer Smith has = x + 100

Sheep Farmer White has = 2x

Therefore,

x + x + 100 + 2x = 2500

4x + 100 = 2500

4x = 2500 - 100

4x = 2400

x = 2400/4

x = 600

Therefore, Farmer Jones has 600 sheep. Farmer Smith has 600 + 100 = 700 sheep. Farmer White has 2 * 600 = 1200 sheep.

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Answer:

x=9

Step-by-step explanation:

In each statement, the decision of whether Lucy should survey a population or a sample are:

A) Sample

B) Population

C) Sample

How to identify a population or sample?

Lucy wants to test the statements A, B and C. She doesn't want to use a sample unless she has to. For each statement, decide whether Lucy should survey a population or a sample.

Let us access each of the given options:

A. Students in her class prefer to watch movies at the cinema:

To determine whether students in her class prefer to watch movies at the cinema, Lucy can survey a sample of students in her class rather than surveying the entire population of all students.

B. People living in the UK prefer to holiday in Europe:

This statement pertains to a larger group, the population of people living in the UK, and it would be more appropriate to gather data from the entire population rather than just a sample.

C. Players in the school rugby team also play another sport:

Lucy can survey a sample of players from the rugby team. It is not necessary to survey the entire population of all players in the school.

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