Of the last 18 trains to arrive at Kensington Station, 12 were on time. What is the experimental probability that the next train to arrive will be on time?

the square root of 598 is 24.4540385

The " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

The equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.    

" Eight  further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've =  " 3" is the value to which the expression on the left side is equal, so we've 3  Putting it all together the  judgment " Eight  further than the quotient of a number and 7 is equal to 3" can be  restated into the equation ( x/ 7) =  3  

In this equation, x represents the number we're trying to find. To  break for x, we can manipulate the equation using algebraic operations to  insulate x on one side of the equation.  By abating 8 from both sides of the equation, we get ( x/ 7)- 8 =  3- 8  Simplifying, we have  x/ 7 = -5

To  insulate x, we can multiply both sides of the equation by 7  *( x/ 7) = -5 * 7  This gives us  x = -35  thus, the equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

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The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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Answer:

10 centimeters

Step-by-step explanation:

For the height:

40 ft / 20 cm = 2 ft / cm

With this ratio, we find the length as follows:

2 ft / cm = 20 ft / x cm

\(2 = \frac{20}{x} \)

\(2x = 20\)

\(x = 10\)

Answer:

10 cm

Step-by-step explanation:

Look at the answer

Answer:

24

Step-by-step explanation:

if you look at them they are each multiplied by 3

a. Eliminating the parameter yields the equation \(x2+y2=100\), which is a circle centered at the origin with a radius of 10.

b. The curve is a circle with a positive orientation, going counterclockwise from the origin.

a. To eliminate the parameter, we first square both sides of the equations to obtain: \(x2=(−10cos2t)2 and y2=(−10sin2t)2.\)Then, since cos2t and sin2t are both between -1 and 1, the terms on the right hand side of each equation can be simplified to 100. Thus, the equation \(x2+y2=100\)is obtained.

b. This equation describes a circle centered at the origin with a radius of 10. The positive orientation of the curve is counterclockwise from the origin, i.e. it starts at the origin and moves up, then to the right, then down, and then to the left.

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The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

Step-by-step explanation:

It’s A

The length of the altitude of the right triangle given is 6.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

The given triangle is an equilateral triangle.

All the sides are equal.

Each of the side = 4√3

Altitude divides one of the side in to two equal halves.

Using Pythagoras theorem,

Altitude = √(4√3)² - (2√3)²

             = √(16×3) - (4 × 3)

             = √48 - 12

             = √36

             = 6

Hence the altitude of the triangle is 6.

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Answer:

ok

Step-by-step explanation:

Answer:

A = 20 percent

B = 41 percent

Step-by-step explanation:

simply use 300 as your denominator

60/300 = 20

123 / 300 = 41

Answer:

Ten miles

Step-by-step explanation:

Use this inequality

20 + 3m = 5m

We will have the following:

We are given that m < 3 = 66°.

Using corresponfing angles we have that m<3 = m<7 = 66°.

Using supplementary angles we have that:

So, we solve for angle 8:

So, the measure of angle 8 is 114°.

Answer:

Step-by-step explanation:

So the final answer is $2274.

Answer:

The answer is "\(\bold{\frac{(m-1)(m-2)}{(m-n)}}\)"

Step-by-step explanation:

Given:

\(\bold{\frac{(m-n)}{m^2-n^2} + \frac{?}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0}\\\\\)

let,  ? = x then,

\(\Rightarrow \frac{(m-n)}{m^2-n^2} + \frac{x}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0\\\\\Rightarrow \frac{(m-n)}{m^2-n^2} - \frac{2m}{m^2-n^2}=- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{(m-n)-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{m-n-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-n-m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-(m+n)}{(m+n)(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-1}{(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\)

\(\Rightarrow -((m-1)(m-2))=-x(m-n) \\\\\Rightarrow x= \frac{- (m-1)(m-2)}{- (m-n)} \\\\\Rightarrow \boxed{x= \frac{(m-1)(m-2)}{(m-n)}} \\\)

Answer:

1/2

Step-by-step explanation:

pues el ejercicio te da la respuesta

te dice que el aula usa la MITAD = 1/2 para trabajos artisticos.

respuesta 1/2

kaaaaaaaaaaaaaaaaabbbichaStep-by-step explanation:

The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Part 1: You can simplify \(a_n\) to

\(\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}\)

Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

\(|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}\)

(b) And because both fractions in \(a_n\) converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,

\(|a_n| \ge \boxed{0}\)

(c) Finally, \(a_n\) is bounded above and below, so it is a bounded sequence.

Part 2: Yes, \(a_n\) is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since \(a_n\) is decreasing and bounded below by 0, its limit as n goes to infinity is 0.

Part 4:

(a) We have

\(\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10\)

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

\(\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty\)

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

Answer: 25.52

Step-by-step explanation: correct on khanacademy

The amount Siya will spend on tiles is given by the expression (1.1 x T / 6) x R234, where T represents the required number of tiles. To calculate the amount Siya will spend on tiles, we need to determine the number of boxes of tiles he needs to purchase and then multiply it by the price per box.

First, we need to determine the number of tiles required. Let's assume the required number of tiles is represented by the variable "T."

Since the builder recommends buying 10% more tiles in case of breakages, Siya needs to purchase 110 percentage of the required number of tiles. This can be calculated as:

110% of T = 1.1 x T

Next, we need to convert the number of tiles into the number of boxes required. We know that one box contains 6 tiles, so the number of boxes Siya needs to purchase is:

Number of boxes = (1.1 x T) / 6

Finally, we can calculate the total cost by multiplying the number of boxes by the price per box:

Total cost = (1.1 x T / 6) x R234

Please note that without knowing the specific number of tiles required (T), we cannot provide an exact amount Siya will spend.

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The transformation that occurred to get from the figure ABCD to EFGH, including the necessary terminologies is as follows:

Step 1: Reflection

The reflection using the y axis as the line of reflection at point C After the reflection the points changed A = E,  D = H, C = G, and B = F

Step 2: Rotation

The rotation occurred with point A now E as the center of rotation.  The angle of rotation is 90 degrees anticlockwise direction.

Step 3 Translation

The quadrilateral is now moved 4 units to the left to arrive at the new position.

Transformation is a term used in mathematics to describe some technical movements that objects makes. This objects are usually plotted to ensure that every movement can be calculated.

Some terms in transformation are reflection, rotation, translation and so on. Reflection produces mirror image of the object, Rotation is achieved using a specified angle and the direction is specified with either clockwise or anticlockwise then Translation is more of a straight forward movement.

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To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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The shape that we obtained will be a triangle. Then the correct option is E.

In terms of geometry, a pyramid is a polygon that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex. It has a polygonal basis and is a conic solid. There are n + 1 points, n + 1 sides, and 2n edges in a pyramid with an n-sided base. Every pyramid is dual in itself.

If the base of the pyramid is a rectangle then the pyramid is known as a rectangular pyramid.

If the pyramid is separated by slicing a rectangular pyramid perpendicular to its base. Then the shape that we obtained will be a triangle.

Then the correct option is E.

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The options provided are incorrect, and the correct solution of the equation is  is x = 6 or x = -2.

To solve the quadratic equation -4x = -x^2 + 12, we can rearrange it into standard quadratic form, which is ax^2 + bx + c = 0.

In this case, we have -x^2 - 4x + 12 = 0.

To solve this equation numerically using tables of x- and y-values, we can substitute different values of x into the equation and calculate the corresponding y-values. We then look for the values of x where the equation equals zero.

By substituting x = 6, we get:

-6^2 - 4(6) + 12 = -36 - 24 + 12 = -48 + 12 = -36.

By substituting x = -2, we get:

-(-2)^2 - 4(-2) + 12 = -4 + 8 + 12 = 16.

Since the equation equals zero at x = 6 and x = -2, the correct answer is:

x = 6 or x = -2.

Therefore, the options provided are incorrect, and the correct solution is x = 6 or x = -2.
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Answer: B x = 6 or x = -2

Step-by-step explanation:

right on edge 2023

Answer:

x=67

Step-by-step explanation:

Two ways to solve it:

1st way: Just looking at it, x is definitely not 180° because it’s to big of an angle, it is definitely not 113° because it’s still to big of an angle, and it’s also not 90° because it doesn’t form a right angle. So it must be 67°.

2nd way: Since two angles in a straight line add up to 180°, you can subtract 113° from 180° to find what x is. You can tell that 180° - 113° is equal to 67°

So either way, the answer is: x=67

Hope this helped! :)

Answer:

4 ft

Step-by-step explanation:

288=16 * 18

12+4=16

14+4=18

The dimensions increased by 4 feet.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given;

Dimensions of rectangle = 12 + x and 14 + x

The area of the rectangle= (12 + x) (14 + x) = 288

x² + 26x + 168 = 288

x² + 26x - 120 = 0

(x + 30) (x - 4) = 0

x=-30, x =4

Hence, The dimensions increased by 4 feet.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

Thanks

Step-by-step explanation:

Thanks