Why are rectangles relatable to factors

The area of a horizontal cross-section of the cylinder whose diameter is 2.75 inches and height is 6 inches is 5.9 inch².

Diameter of the base of the container = 2.75 inch

Height of the cylinder = 6 inch

Area of a horizontal cross-section of the cylinder = πr²

Here, r = radius of the container

Radius = Diameter/2

Radius = 2.75/2

Radius = 1.375

Area of the horizontal cross-section of the cylinder = 3.14 × 1.375 × 1.375

Area = 5.9365625

Area of the horizontal cross- section of the cylinder to the nearest tenth is 5.9

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A triangle with side lengths 6 cm, 7 cm, and √13 cm is right triangle and the side lengths form a Pythagorean triple.

To determine if the triangle with side lengths 6 cm, 7 cm, and √13 cm is a right triangle and if these side lengths form a Pythagorean triple, we'll use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Identify the longest side. In this case, it's the side with length 7 cm.

Check if the Pythagorean theorem holds true for these side lengths:
(6 cm)² + (√13 cm)² = (7 cm)²

Calculate the squares of the side lengths:
(6 cm)² = 36 cm²
(√13 cm)² = 13 cm²
(7 cm)² = 49 cm²

Check if the sum of the squares of the two shorter sides equals the square of the longest side:
36 cm² + 13 cm² = 49 cm²

Compare the results:
49 cm² = 49 cm²

Since the equation holds true, the triangle is indeed a right triangle, and the side lengths 6 cm, 7 cm, and √13 cm form a Pythagorean triple.

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Manuel can type 68 words in two minutes at a rate of 34 words per minute.

Given that; Manuel types at a rate of 34 words per minute.

To determine how many words Manuel can type in two minutes, we simply need to multiply his typing rate by the number of minutes he is typing.

Since Manuel is typing for two minutes

Hence;

Number of words = Typing rate × Time

Plugging in the values we have from the problem.

Number of words = 34 words/minute × 2 minutes

Simplifying

Number of words = 34 words × 2

Number of words = 68 words

Therefore, he can type 68 words in two minutes.

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The distance from P to the airplane is y = x + 100 ≈ 628.38 m.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

From a certain point Q on a straight road, which forms an angle of 22° with the horizontal, the angle of elevation of an airplane at point A is 57°. At the same instant from another point Q, 100 meters ahead of the first point, the angle of elevation of the airplane is 63°. The points P, Q, and A are in the same vertical plane. Find the distance from P to the airplane.

To solve the problem, we can use the concept of similar triangles. Let's call H the height of the airplane and x the distance from Q to the airplane. Then, the distance from P to the airplane is given by y = x + 100.

From triangle QA1H, we have:

tan(57°) = H / x

From triangle QA2H, we have:

tan(63°) = H / (x + 100)

Dividing these two equations, we get:

tan(57°) / tan(63°) = x / (x + 100)

Solving for x, we get:

x = 100 * tan(63°) / (tan(63°) - tan(57°)) ≈ 528.38 m

Therefore, the distance from P to the airplane is:

y = x + 100 ≈ 628.38 m.

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By using the method of undetermined coefficients, The general solution is y = ae^(4x)cos(3x) + be^(4x)sin(3x) + (7/2cos(3t) + 5/2sin(3t))e^(4t). The solution to the initial value problem is y = 3e^(2x) + 14e^(4x) - 3e^(3x).

By using the method of undetermined coefficients, the associated homogeneous equation is y''-8y'+297=0, which has the characteristic equation r^2-8r+297=0. The roots of this equation are r=4+3i and r=4-3i, so the homogeneous solution is yh=a*e^(4x)cos(3x)+be^(4x)*sin(3x).

To find the particular solution, we make the ansatz yp = (Acos(3t) + Bsin(3t))e^(4t), where A and B are constants to be determined. Substituting this into the differential equation, we get

y" - 8y' + 297 = (16A - 18B)e^(4t)cos(3t) + (16B + 18A)e^(4t)sin(3t)

On the right-hand side, we have 48e^4tcos(3t) + 80e^4tsin(3t), which suggests setting

16A - 18B = 48, and

16B + 18A = 80

Solving these equations simultaneously, we get A = 7/2 and B = 5/2. Therefore, the particular solution is

yp = (7/2cos(3t) + 5/2sin(3t))e^(4t)

And the general solution is

y = yh + yp = ae^(4x)cos(3x) + be^(4x)sin(3x) + (7/2cos(3t) + 5/2sin(3t))e^(4t)

For the second problem, the associated homogeneous equation is y''-6y'+8y=0, which has the characteristic equation r^2-6r+8=0. The roots of this equation are r=2 and r=4, so the homogeneous solution is yh=ae^(2x)+be^(4x).

To find the particular solution, we make the ansatz yp = Ce^3x, where C is a constant to be determined. Substituting this into the differential equation, we get

y" - 6y' + 8y = 9Ce^3x - 18Ce^3x + 8Ce^3x = (8C - 9C)e^3x = -C*e^3x

On the right-hand side, we have 3e^x, which suggests setting -C = 3. Therefore, the particular solution is

yp = -3e^(3x)

And the general solution is

y = yh + yp = ae^(2x) + be^(4x) - 3e^(3x)

To find the values of a and b, we use the initial conditions

y(0) = a + b - 3 = 14

y'(0) = 2a + 4b - 9 = 29

y''(0) = 2a + 8b = 25

Solving these equations simultaneously, we get a = 3 and b = 14. Therefore, the solution to the initial value problem is

y = 3e^(2x) + 14e^(4x) - 3e^(3x)

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--The given question is incomplete, the complete question is given

"  (1 point) Use the method of undetermined coefficients to find a solution of a y" – 8y' + 297 = 48e4t cos(3t) + 80e4t sin(3t) + 3 - Use a and b for the constants of integration associated with the homogeneous solution. Use a as the constant in front of the cosine term. y = yh + yp = - = (1 point) Find y as a function of x if ' y" – 6y" + 8y' = 3e", - - = y(0) = 14, y'(0) = 29, y"(0) = 25."--

The inequalities in the given table are "t > 0" and "3 < a."

To identify the inequalities from the provided options, we need to understand the meaning of the symbols and check if they represent a comparison between two values.

-3 = y: This is not an inequality symbol but rather an equality symbol. It represents that -3 is equal to y, not greater or less than.

t > 0: This is an inequality symbol. The symbol ">" represents "greater than." Therefore, t is greater than 0.

-4. 3 < a: This is another inequality symbol. The symbol "<" represents "less than." Hence, 3 is less than a.

g = 5 and one-half: This is an equality symbol. The symbol "=" denotes equality, indicating that g is equal to 5 and one-half, not greater or less than.

k less-than Negative Start Fraction 5 Over 7 End Fraction: This is also an inequality symbol. The phrase "less than" indicates a comparison. The fraction "Negative Start Fraction 5 Over 7 End Fraction" represents -5/7. Therefore, k is less than -5/7.

x = 1: This is an equality symbol. The symbol "=" indicates that x is equal to 1, not greater or less than.

In summary, the inequalities in the table are "t > 0" and "3 < a."

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The measure of the angle is 50.7° and the measure of its complementary angle is 39.3°.

Let x be the measure of the angle and y be the measure of its complementary angle.

Then we have:

x = y + 11.4 (since the angle measures 11.4° more than its complementary angle)

x + y = 90 (since the two angles are complementary)

Substituting the first equation into the second equation, we get:

(y + 11.4) + y = 90

2y + 11.4 = 90

2y = 78.6

y = 39.3

Substituting y = 39.3 into the first equation, we get:

x = y + 11.4 = 50.7

So, we have

x = 50.7

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Answer:

38/93

Step-by-step explanation:

11/31 x 38/33

11 x 38 = 418

31 x 33 = 1023

= 418/1023

Simplifying

The simplified form of 418/1023 is 38/93.

38/93 is your final answer.

Answer:

that is really hard but im pretty sure one of the answers to the first one is -16? for the second x

Step-by-step explanation:

Answer:

252

Step-by-step explanation:

So their are 38 more numbers to get to 41 and the numbers are adding by 6, so mulitply 6 by 38 and you get 228 and add 228 to the biggest number of 24 and your final answer becomes 252.

Answer:

A

Step-by-step explanation:

2.17 > 2.017

because

2.017 = 2 + 17/1000

while

2.17 = 2 + 17/100 = 2 + 170/1000

170/1000 is larger than 17/1000.

for that reason D is wrong, of course.

2.17 is NOT equal to 2.017. 17/1000 is NOT equal to 170/1000.

2.018 = 2 + 18/1000

2.17 = 2 + 17/100 = 2 + 170/1000

also 18/1000 is NOT larger than 170/1000.

2.16 = 2 + 16/100 = 2 + 160/1000

2.017 = 2 + 17/1000

17/1000 are NOT larger than 160/1000.

Answer:

Subtract the smaller amount of [tex]x[/tex] → [tex]2x+6 > 15[/tex]

Then subtract 6 from 15 as it is a plus you do the opposite → [tex]2x > 9[/tex]

Now divide 9 by 2 to isolate [tex]x[/tex] → [tex]x > 4.5[/tex]

Answer:

a_48000cm^3

b_48000000mm^3

Step-by-step explanation:

first of all, let's find the base area:

Ab=((b+B)h)/2=((10cm+30cm)20cm)/2=400cm^2

then, to find the volume, we need to multiplicate the base area to the height of the prism:

V=Ab*H=400cm^2*120cm=48000cm^3=48000000mm^3

The library is approximately 19.2 kilometers from the community pool. The distance between the library and the community pool can be calculated using the Pythagorean theorem since the problem describes a right-angled triangle (due south and due west directions).

It is given that the distance between library and courthouse is 12 kilometers (south) and the distance between courthouse and community pool is 15 kilometers (west). Let's call the distance between the library and the community pool "x" kilometers.

According to the Pythagorean theorem:
a² + b² = c²

12² + 15² = x²

Now, calculate the square of the distances: 144 + 225 = x²
Add the numbers: 369 = x²

Finally, find the square root of the sum to find "x":
x = √369
x ≈ 19.2
The library is approximately 19.2 kilometers from the community pool.

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Answer:

mail

Step-by-step explanation:

skating Dinero broke 1p revision yahoo d10

Answer:

91%

Step-by-step explanation:

As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.

As a quarter of 100, a number can be expressed as a percentage. It is frequently used to describe distinctions or express changes in numbers. The symbol for percentages is %, and they are frequently utilized to describe ratios, rates, and certain other numerical connections. An 80 percent score on a test, for instance, indicates that the student correctly answered 80 of the 100 questions. Similar to this, if a retailer were offering a 20% discount on a $100 item, the sale price would be $80.

given

With P = 10000, r = 0.08 (8% stated as a decimal), n = 12 (compound monthly), and t to be found when A = 20000, the situation is as follows.

When these values are added to the formula, we obtain:

[tex]20000 = 10000(1 + 0.08/12)^(12t) (12t)[/tex]

By multiplying both sides by 1000, we obtain:

[tex]2 = (1 + 0.08/12)^(12t) (12t)[/tex]

When we take the natural logarithm of both sides, we obtain:

ln(2) = 12t ln(1 + 0.08/12)

When we multiply both sides by 12 ln(1 + 0.08/12), we obtain:

t = ln(2) / (12 ln(1 + 0.08/12))

Calculating the answer, we discover:

10.24 years is t.

As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.

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This tells him that his salary is significantly below the average salary of quality management professionals surveyed by the ASQ, and that he is in the bottom percentile of salaries in this group.

The z-score is a statistical measure that indicates the number of standard deviations that a data point is from the mean of a distribution. A negative z-score indicates that the data point is below the mean.

In this case, the quality control specialist's z-score of -2.50 indicates that his salary is 2.50 standard deviations below the mean salary of the quality management professionals surveyed by the ASQ.

Without knowing the specific mean and standard deviation provided by the survey, it is difficult to determine the exact value of the specialist's salary. However, we can use the z-score to estimate the percentile rank of his salary compared to the rest of the survey respondents.

Using a standard normal distribution table, we can see that a z-score of -2.50 corresponds to a percentile rank of approximately 0.0062 or 0.62%. This means that only about 0.62% of quality management professionals surveyed by the ASQ earn a salary lower than that of the quality control specialist.

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The velocity with which a ball reaches the ground when it is dropped

from a height of 64 m is 35.44m/sec

From the information given, we have that the equation representing the velocity of the ball is expressed as;

V = 4.43√h

Given that the parameters of the formula are;

Since the height of the ball from the ground is 64m, we have to substitute the value, we have;

V = 4.43√64

Find the square root of the value

V= 4.43(8)

Now, multiply both the values to determine the velocity, we get;

V = 35.44m/sec

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The sum of the series Σ (2k² - 4) from k = 1 to n can be found using the following formula:

Σ (2k² - 4) = [2(1²) - 4] + [2(2²) - 4] + [2(3²) - 4] + ... + [2(n²) - 4]

= 2(1² + 2² + 3² + ... + n²) - 4n

The sum of squares of the first n natural numbers can be calculated using the formula:

1² + 2² + 3² + ... + n² = [n(n + 1)(2n + 1)] / 6

Substituting this value in the above equation, we get:

Σ (2k² - 4) = 2[(n(n + 1)(2n + 1)) / 6] - 4n

= (n(n + 1)(2n + 1)) / 3 - 4n

Therefore, the sum of the series Σ (2k² - 4) from k = 1 to n is (n(n + 1)(2n + 1)) / 3 - 4n.

The surface area of the triangular prism is 4800 square yard.

The surface area of a triangular prism is sum of the areas of the faces that make the prism.

The surface area of a triangular prism is given by:

SA = (a + b + c)L + bc

Where a and b are the bases of the rectangular faces, c is the height of the triangle and h is the total length of the prism

In this case:

L = 40, a = 34, b = 32 and c = 30

SA = (34 + 32 + 30)40 + (32 * 30)

SA = 3840 + 960

SA = 4800 square yard

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Answer:

Step-by-step explanation:

The probability of drawing 2 red cards from a standard 52-card deck can be calculated as follows:

There are 26 red cards in the deck, so the probability of drawing a red card on the first draw is 26/52.

After the first card is drawn, there are 25 red cards remaining in the deck out of 51 total cards, so the probability of drawing a red card on the second draw is 25/51.

To find the probability of both events happening together (drawing 2 red cards), we multiply the probabilities of each event:

(26/52) * (25/51) = 0.245 or approximately 24.5%

Therefore, the probability of drawing 2 red cards in a standard 52 card deck is approximately 24.5%.

Therefore, we need 3/4 of a quart of grape juice to mix with 3 3/4 quarts of sparkling water.

In mathematics, a fraction represents a part of a whole or a ratio between two numbers. It consists of a numerator and a denominator, separated by a horizontal or diagonal line. The numerator is the number above the line and the denominator is the number below the line. The numerator and denominator can be any real numbers, including integers, decimals, or even other fractions.

Here,

The punch recipe requires a ratio of 1 1/2 quarts of sparkling water to 3/4 of a quart of grape juice. To determine how much grape juice is needed to mix with 3 3/4 quarts of sparkling water, we can set up a proportion:

1 1/2 quarts of sparkling water : 3/4 quart of grape juice = 3 3/4 quarts of sparkling water : x

To solve for x, we can cross-multiply and simplify:

(1 1/2) / (3/4) = (15/4) / (3/4)

= 15/3

= 5

3 3/4 * 1 / 5 = 15/20

= 3/4

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The correct statement regarding the solution to the system of equations is given as follows:

4) (2, 1) is the solution to both lines A and B.

The system of equations in the context of this problem is defined as follows:

Replacing the second equation into the first, the value of x is obtained as follows:

-3x + 7 = x - 1

4x = 8

x = 2.

Hence the value of y is given as follows:

y = 2 - 1

y = 1.

Meaning that point (2,1) is a solution to both lines.

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When rt is a diameter of circle p, it divides the circle into two equal halves. Since the sum of angles in a circle is 360 degrees, each half of circle p measures 180 degrees.

Thus, each arc of circle p that is intersected by diameter rt measures half of the circle or 90 degrees.

Therefore, each arc of circle p measures 90 degrees when rt is a diameter.

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The probability of the next elk caught in the park being unmarked can be calculated as follows:

The probability of capturing an unmarked elk in a nature reserve park can be calculated by dividing the number of unmarked elks by the total number of elks.

In this case, the number of unmarked elks is 5,400 out of a total of 5,625 elks. This gives a probability of 96% or 0.96 in decimal form. Marking and tracking animals is a common method used by scientists to study animal populations in nature reserves.

This data is crucial for designing conservation strategies that promote the survival of endangered species. Nature reserves play a crucial role in preserving and protecting wildlife and their habitats, given the significant threats they face from habitat loss, poaching, and climate change.

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The area of garage is 36,504 square inches.

The width of Scott's garage is 156 inches (since it is 1.5 times shorter than the length of 234 inches).

so width = 234/1.5

=> 156

To find the area, we multiply the length by the width:

=> 234 inches x 156 inches

=> 36,504 square inches.

To explain, the formula for finding the area of a rectangle is length x width. In this problem, we are given the length of the garage as 234 inches and are told that the width is 1.5 times shorter than the length.

To find the width, we can multiply the length by 1.5 to get 351 inches (which is longer than the length, so we know it must be incorrect). Instead, we need to divide the length by 1.5 to find the width, which gives us 156 inches. Then, we can multiply the length by the width to find the area of the garage, which is 36,504 square inches.

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The value of x such that fg(x) = 20 is 6.5.

To find the composite function fg(x), we need to substitute the expression for g(x) into f(x), as follows:

fg(x) = f(g(x)) = f(x + 4) = 2(x + 4) - 1 = 2x + 7

So, fg(x) = 2x + 7

ii) To find the value of x such that fg(x) = 20, we can substitute fg(x) into the equation and solve for x, as follows:

fg(x) = 2x + 7 = 20

2x = 13

x = 6.5

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