A tabletop in the shape of a trapezoid has an area of 7,722 square centimeters. Its longer base measures 131 centimeters, and the shorter base is 85 centimeters. What is the height?

The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:

[tex]P(X=x)[/tex] = (e^-μ * μ^x) / x!

Where, x is the number of successes

e = 2.71828 is the Euler number, μ is the mean in the given interval.

Given that, total of 515 bombs hit the combined area of 573 regions.

The mean hits per region is;

μ = 515/573 = 0.898

We want to find the probability that a randomly selected region had exactly three hits, that is P(X = 3)

[tex]P(X=x)[/tex] = (e^(-μ) * μ^x) / x!

[tex]P(X=3)[/tex] = (e^(-0.898) * (0.898)^3) / 3!

[tex]P(X=3)[/tex] = 0.04915

Therefore, 4.915% probability that randomly selected region had exactly three hits.

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The values are, e = 2.71828 is the Euler number, μ = 0.898, x = 3, probability = 4.915%

A subfield of statistics known as probability studies random events and their odds of happening. It is used to predict the future and determine the likelihood of events by dividing the number of favorable outcomes by the total number of possible outcomes.

The following formula gives the probability that X indicates the number of successes of a random variable in a Poisson distribution:

[tex]p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}[/tex]

Where, x is the number of successes

e = 2.71828 is the Euler number, μ is the mean in the given interval.

As a result, 573 regions were struck by a total of 515 bombs.

The mean hits per region is;

[tex]\mu=\frac{515}{573}[/tex]

[tex]\mu= 0.898[/tex]

P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.

[tex]p(X=x)=\frac{(e^{-\mu} \times\ \mu^x)}{x!}[/tex]

[tex]P(X=3)=\frac{e^{-0.898}\times\ \(0.898^3 }{3!}[/tex]

p(X=3)= 0.04915

P(X = 3) stands for the probability that a randomly chosen region contained precisely three hits.

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As per the proportion, we need to replace 3.6 liters of the mixture with pure wine to get a concoction containing wine and spirit in equal proportion.

Let's start by understanding the given information. We have a concoction of 12 liters that contains wine and spirit in the ratio of 2:3. This means that out of every 5 liters of the concoction, 2 liters are wine and 3 liters are spirit.

We are asked to find 'x', the quantity of the mixture that needs to be replaced, such that the resultant mixture has wine and spirit in equal proportion. In other words, we need to find 'x' such that:

(2x + 2)/(12 + 'x') = 3(12 - 'x')/5(12 + 'x')

Let's simplify this equation using cross-multiplication:

5(2x + 2)(12 - 'x') = 3(12 + 'x')(12 - 'x')

Simplifying further:

10x² - 36x + 36 = 0

Dividing both sides by 2:

5x² - 18x + 18 = 0

We can solve this quadratic equation using the quadratic formula:

x = [18 ± √(18² - 4(5)(18))]/(2(5))

Simplifying:

x = [18 ± 6]/10

x = 1.8 or 3.6

Since we cannot replace a fraction of a liter, the only possible value of 'x' is 3.6 liters.

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The expression [tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex] when simplified to the simplest form is [tex]\frac{x^{x+y}}{y^{x+y}}}[/tex]

From the question, we have the following expression to be used in our computation:

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex]

Simplifying the numerator, we get

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x}/y^{x+y}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex]

Simplifying the denominator, we get

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x}/y^{x+y}}{\left(x^2y^2 - 1}\right)^y\cdot \left(xy\:+\:1\right)^{x-y}/x^{y+x}}}[/tex]

Applying the following fraction rule:

(a/b)/(c/d) = (a * d)/(b * c)

So, we have

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x} \cdot x^{x+y}}{\left(x^2y^2 - 1}\right)^y\cdot \left(xy\:+\:1\right)^{x-y} \cdot y^{x+y}}}[/tex]

Cancel the common factors

So, we have

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{x^{x+y}}{y^{x+y}}}[/tex]

Hence, the expression when simplified is [tex]\frac{x^{x+y}}{y^{x+y}}}[/tex]

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The area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

A field of length l and width w has a perimeter of 320 yards.

As we know, the perimeter of the rectangle = 2(l + w)

2(l + w) = 320

l + w = 320/2

l + w = 160

The area of the rectangle = lxw

Let a is the area of the rectangle.

a = lw

Plug w = 160 - l in the above equation:

a = l(160 - l)

a = 160l - l²

The above expression represents the area of the rectangle in terms of l.

Thus, the area of the rectangle can be represented by the expression a = 160l - l² if the field of length l and width w has a perimeter of 320 yards.

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Factor of equation 4x²-x-3 is (x-1)(4x+3)

Factorization, also known as factoring, is the process of breaking down a mathematical object (such as a number, polynomial, or matrix) into simpler pieces called factors. In number theory, factorization involves expressing a positive integer as a product of smaller integers (factors). For example, the number 12 can be factored as 2 × 2 × 3, where 2 and 3 are prime factors and the quadratic expression x² + 7x + 10 can be factored as (x + 2)(x + 5), which can be verified by expanding the product.

4x²-x-3

Simplifying the terms;

4x²-4x+3x-3

Taking x-1 common from the equation

4x(x-1)+3(x-1)

(x-1)(4x+3)

Hence, factor of 4x²-x-3 is (x-1)(4x+3)

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The complete question is;

Factorise 4x²– x – 3​

The y-coordinate of the solution of the system is -10.

What is the linear equation?

A linear equation is an equation that describes a straight line in a two-dimensional space. It is a mathematical expression that relates two variables, usually x and y, such that one variable is a function of the other. The general form of a linear equation is:

y = mx + b

To find the y-coordinate of the solution of the system:

3x - y = 22 ...(1)

y = x - 14 ...(2)

We can substitute the expression for y from equation (2) into equation (1) to eliminate y:

3x - (x - 14) = 22

Simplifying this equation:

3x - x + 14 = 22

2x + 14 = 22

Subtracting 14 from both sides:

2x = 8

Dividing both sides by 2:

x = 4

Now we can substitute x = 4 into equation (2) to find the corresponding value of y:

y = x - 14

y = 4 - 14

y = -10

Therefore, the y-coordinate of the solution of the system is -10.

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Answer:

0.0234189518

Step-by-step explanation:

Answer:

Step-by-step explanation:

im sorry im not sure

17 a 15 c to b

Answer:

6.28

Step-by-step explanation:

to find circumference of a circle you have to do 2×π×r

Answer: 260:455

260 / 455 = .57

4 / 7 = .57

455 - 260 = 195

The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668 (rounded to four decimal places).

The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668(rounded to four decimal places).Here's how to calculate it:Given data mean μ = 9,000 and standard deviation σ = 1,000.To calculate the probability that a random light bulb lasts more than 10,500 hours, convert the problem to a standard normal distribution.

z = (10,500 - μ)/σ = (10,500 - 9,000)/1000 = 1.50

Here's the standard normal distribution curve with the shaded area representing the probability required: Standard normal distribution curve with the shaded area

Now, the area under the curve to the right of z = 1.5 is the probability that a randomly chosen light bulb will last more than 10,500 hours.

Using the Z table, we can look up the value corresponding to a z-score of 1.5. The table gives us a value of 0.9332.Now, the area to the left of z = 1.5 is 1 - 0.9332 = 0.0668, which is the probability that a randomly chosen light bulb lasts more than 10,500 hours, rounded to four decimal places.

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Answer:37.8541 or 37.9

Step-by-step explanation: round up from five

Answer:

About 37.8541, or 37.9

Answer:

(24.5, 6.5)

Step-by-step explanation:

We can set up two equations:

x+y=31

x-y=18

Now, when we add the two equations, we get

2x=49

When we divide we get

24.5 for x.

Now we can plug this in the first equation:

24.5+y=31

minus 24.5 on both sides to get

y=6.5

Hope this helped!

~Cain

Answer:

The sum of two numbers is 31 and their difference is 18

what are the two numbers? Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 31. In other words, x plus y equals 31 and can be written as equation A:

x + y = 31

The difference between x and y is 17. In other words, x minus y equals 17 and can be written as equation B:

x - y = 18

Now solve equation B for x to get the revised equation B:

x - y = 18

x = 17 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 31

17 + y + y = 31

17 + 2y = 31

2y = 13

y = 6

Now we know y is 6.5 .Which means that we can substitute y for 6.5 in equation A and solve for x:

x + y = 31

x + 6.5 = 31

X = 25.5

Summary: The sum of two numbers is 31 and their difference is 18. What are the two numbers? Answer: 25.5 and 6.5 as proven here:

Sum: 25.5 + 6.5 = 31

Difference: 25.5 - 6.5 = 19

The missing length a of the shaded region is calculated to be 12.8 miles using the area and the height of the triangle.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

Given the area as 117.76 mi², we have the base of the triangle to be "a" and the height as 18.4 miles, so we solve for the length "a" as follows:

117.76 mi² = 1/2 × a × 18.4 miles

by cross multiplication;

a = (117.76 mi² × 2)/18.4 mi

a = 235.52 mi²/18.4 mi

a = 12.8 miles

Therefore, the missing length "a" of the shaded region is calculated to be 12.8 miles using the area and the height of the triangle.

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The value of the collector's edition comic when t=8 is approximately $32.77.

The growth factor for the value of the collector's edition comic is 1.10 per year (10% increase). Therefore, after t years, the value V of the comic can be calculated using the formula:

V = 15 × 1.10^t

To find the value when t=8, we can substitute t=8 into the formula:

V = 15 × 1.10^8

V ≈ $32.77

Therefore, the value of the collector's edition comic when t=8 is approximately $32.77.

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Answer:

a = 12

Step-by-step explanation:

Pythagorean theorem states that the the square value of hypotenuse is equal to the sum of the squares of two legs.

Now, according to this statement:

15² = 9² + a²

225 = 81 + a²

144 = a²

12 = a

As the angle ∠c in a triangle increases, the length of the middle section on line p decreases.

Conversely, as the angle ∠c decreases, the length of the middle section on line p increases. This is because the middle section on line p is a portion of the altitude of the triangle, which is the perpendicular segment from the vertex of the angle to the opposite side. As the angle ∠c increases, the altitude of the triangle gets shorter, resulting in a shorter middle section on line p. Similarly, as the angle ∠c decreases, the altitude of the triangle gets longer, resulting in a longer middle section on line p. Examples of triangles can include equilateral, isosceles, scalene, acute, right, and obtuse triangles, among others.

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[tex]\cfrac{1}{2}(1-x)-\cfrac{1}{3}(2+x)+\cfrac{1}{4}(3-x)=1 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{2}(1-x)-\cfrac{1}{3}(2+x)+\cfrac{1}{4}(3-x) \right)~~ = ~~12(1)} \\\\\\ 6(1-x)-4(2+x)+3(3-x)=12\implies 6-6x-8-4x+9-3x=12 \\\\\\ 7-13x=12\implies 7=13x+12\implies -5=13x\implies \cfrac{-5}{13}=x[/tex]

The solution to the system of inequalities is:

x > 10/3 and x > 0

What is inequality?

In mathematics, an inequality is a statement that shows the relationship between two values, expressions or quantities using inequality symbols such as <, >, ≤, or ≥. Inequalities convey that one value is not the same as the other, but rather is either greater than or less than the other value.

The system of inequalities is:

3x-10 > 0

2x > 0

To solve this system, we need to find the values of x that satisfy both inequalities at the same time.

From the first inequality, we can isolate x by adding 10 to both sides:

3x - 10 + 10 > 0 + 10

3x > 10

Then, we can divide both sides by 3:

x > 10/3

So we know that x is greater than 10/3.

From the second inequality, we know that x must be greater than 0.

Therefore, the solution to the system of inequalities is:

x > 10/3 and x > 0

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We can use trigonometry to solve this problem. Let h be the height of the radio tower. Then we have:

tan(69°) = h/60

Multiplying both sides by 60, we get:

h = 60 tan(69°)

Using a calculator, we find that:

h ≈ 178.37 feet

Therefore, the height of the radio tower is approximately 178.37 feet.

The student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

Tο find the z-scοre οf the student whο scοred 428, we can use the fοrmula:

z = (x - μ) / σ

where x is the student's scοre, μ is the mean οf the distributiοn (400 in this case), and σ is the standard deviatiοn οf the distributiοn (60 in this case).

Plugging in the values, we get:

z = (428 - 400) / 60 = 0.467

Since the z-scοre οf the student is less than 0.524, which is the z-scοre cοrrespοnding tο the tοp 30% οf the distributiοn, we can cοnclude that the student did nοt scοre in the tοp 30%.

Therefοre, the student will nοt be admitted tο the schοοl based οn the admissiοn criteria οf scοring in the tοp 30%.

Hence, the student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

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Answer:

84%

Step-by-step explanation:

This is a pretty normal grading weight system. Think of a perfect score being 100. The grade earned may be a percent but think of it as 100/100.

So we can set up an equation to represent the missing grade earned in the "Final Exam" row.

0.4(x) + 0.3(80) + 0.2(90) + 0.1(100) = 85

The x represents the percent grade earned for the final exam, in order to achieve an 85% total.

Evalulate and solve the above equation for x to find its value.

0.4x + 24 + 18 + 10 = 85

0.4x = 33

x = 33/0.4

x = 82.5

The question asks for the minimum grade to achieve 85% total. This means that whatever choice we choice must be the least choice that is also greater than 82.5%. That answer is B, 84%.

The value of the angle x using trigonometric ratio is: x = 53.13°

Some of the trigonometric ratios in mathematics based on a right angle triangle are:

Sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Similarly:

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

We are given that:

sin x = 12/15

Thus:

x = sin⁻¹(12/15)

x = 53.13°

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Comparing the percentage reductions, option 2 would result in a higher reduction in fuel consumption compared to option 1.

It should be noted that to determine which option is better in terms of decreasing total litres used, we need to calculate the total amount of fuel consumed in each case and compare them.

Option 1: For every 100 km traveled, the first vehicle consumes 23.5 litres of fuel.

For the same distance, the second vehicle consumes 11.7 litres of fuel.

Thus, the second vehicle would save 23.5 - 11.7 = 11.8 litres of fuel per 100 km traveled compared to the first vehicle.

So, the percentage reduction in fuel consumption would be:

(11.8 / 23.5) x 100 = 50.21%.

Option 2: For every 100 km traveled, the first vehicle consumes 11.7 litres of fuel.

For the same distance, the second vehicle consumes 4.7 litres of fuel.

Thus, the second vehicle would save 11.7 - 4.7 = 7 litres of fuel per 100 km traveled compared to the first vehicle.

So, the percentage reduction in fuel consumption would be:

(7 / 11.7) x 100 = 59.83%.

Comparing the percentage reductions, option 2 would result in a higher reduction in fuel consumption compared to option 1. Therefore, replacing an 11.7 L/100 km vehicle with a 4.7 L/100 km vehicle is better in terms of decreasing the total litres used.

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The percent of change is approximately -15.5% (rounded to the nearest tenth).

To find the percent change between last year's enrollment and this year's enrollment, we can use the following formula

percent change = [(new value - old value) / old value] x 100%

where "new value" is the enrollment for this year, and "old value" is the enrollment for last year

Plugging in the numbers, we get:

percent change = [(87 - 103) / 103] x 100%

percent change = (-16 / 103) x 100%

percent change = -15.53%

Therefore, the percent of change is approximately -15.5% . This means that there was a decrease of about 15.5% in the enrollment for the drama club from last year to this year.

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A sample size of 541 is required to be 98% confident that the estimate is within 0.1 of the true population mean.

To calculate the required sample size for a given population mean, standard deviation, and confidence level, you can use the following equation:
n = (z * σ / E)^2

where:

n = sample size

z = z-score for the desired level of confidence (98% = 2.33)

σ = population standard deviation  (we assume σ = 1)

E = desired margin of error (0.1)

Therefore,
Sample size  = (23.3 * 1)^2

Sample size = 540.89

Rounding up to the nearest whole number, we get a sample size of n = 541

Therefore, a sample size of 541 is required to be 98% confident that the estimate is within 0.1 of the true population mean.

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The coordinates of B, considering the proportions in the context of the problem, are given as follows:

(4.33, 8).

The coordinates of B are obtained applying the proportions in the context of the problem.

BC is 50% longer than AB, hence point B is at one-third of the way from A to C, and thus the equation is given as follows:

B - A = 1/3(C - A).

The x-coordinate of B is then given as follows:

x - 1 = 1/3(11 - 1)

x - 1 = 3.33

x = 4.33.

The y-coordinate of B is then given as follows:

y - 3 = 1/3(18 - 3)

x - 3 = 5

y = 8.

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The probability of observing that the difference between the average height of the 6 waves in California and the average height of the 6 waves in Florida (California minus Florida) is greater than 0.5 feet is 0.55.

A beach in California has an almost normal distribution of wave heights, averaging 7.2 feet. The wave height distribution on a Florida beach is about normal, average 6.6 feet. Six waves are randomly selected from each beach and the heights are recorded.

Probability distributions generate the possible outcomes of any random event. It also defines the set of possible outcomes for any random experiment based on the underlying sample space. These parameters can be a set of real numbers or a set of vectors or a set of any entity. This is part of probability statistics.

A randomized experiment is defined as the result of an experiment whose outcome cannot be predicted.

Suppose if we toss a coin, we cannot predict whether the outcome will be heads or tails. The possible outcomes of a random experiment are called outcomes. The resulting set is called a sample point. With these experiments or events, we can always create tables of probability models based on variables and probabilities.

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