You are studying the lengths of time people spend reading books
each day. You randomly select 50 people and observe that, in average, they spend 25 minutes
reading books each day. Find the probability that the mean time they spend reading each day is
between 24.7 and 25.5 minutes? Assume that  = 1.5 minutes and also you can use the Central
Limit Theorem.

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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Answer:

3/7

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

Let’s assume that we have 7 units of paint in total. Then, we have 3 units of green paint and 4 units of red paint. When we mix them together, we get 7 units of brown paint.

Because 3 out of the 7 units of paint are green, the fraction of the brown paint that is green paint is [tex]\frac{3}{7}[/tex].

Therefore, [tex]\frac{3}{7}[/tex] of the brown paint is green.

The value of x is 8

The theorems of triangle are the rules that governs solving mathematical problems. Part of this theorem is a theorem that states that: The line joining the midpoint of the two sides of a triangle is parallel to the base.

Therefore ;

If we represent a side by y, using similar triangle,

y/2y = x+8/(3x+8)

1/2 = x+8/(3x+8)

3x +8 = 2(x+8)

3x +8 = 2x +16

collect like terms

3x-2x = 16-8

x = 8

therefore the value of x is 8

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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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Answer:

0.0234189518

Step-by-step explanation:

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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If at least 3 of 4 balls must be blue then the number of possible selections = 462

Let us assume that m represents the number of red balls in a bowl.

So, m = 7

And n  represents the number of blue balls in a bowl.

So, n = 8

A woman selects 4 balls at random from the bowl.

We need to find the number of possible selections if at least 3 balls must be blue.

The first combination would be 4 blue balls + 0 red balls

And the second combination would be 3 blue balls + 1 red ball

so, using combination formula the number of possible selecctions:

(⁸C₄ × ⁷C₀) + (⁸C₃ ×  ⁷C₁)

= (70 × 1) +(56 × 7)

= 462

Therefore, the number of possible selections: 462

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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%.

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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The length of the segment SR for the given pentagons is 9 units.

A polygon having 5 sides and 5 angles is called a pentagon. The words "pentagon" (which implies five angles) are formed up of two other terms, namely Penta and Gonia. End to end, the sides of a pentagon come together to form a shape. Hence, there are 5 sides in a pentagon.

The pentagon is a polygon with five sides and five angles, just like other polygons including triangles, quadrilaterals, squares, and rectangles. There are several sorts of pentagon forms, including regular and irregular pentagons as well as convex and concave pentagons, depending on the sides, angles, and vertices.

We know that, for similar figures the length of the ratios of their corresponding segments are equal.

Thus,

NM/TS = ML/SR

4/7.2 = 5/x

Using cross multiplication we have:

4x = 5(7.2)

4x = 36

x = 9

Hence, the value of the segment SR for the given pentagons is 9 units.

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According to the information, each of the cases of equations has a different solution depending on the value that is given to the unknown or x.

Let p = √(x - 3), then the equation becomes p^2 - 2p - 3 = 0. This is a quadratic equation that can be factored as (p - 3)(p + 1) = 0. Therefore, p = 3 or p = -1. Since p = √(x - 3) and we want real solutions, we have two cases:

Case 1: p = √(x - 3) = 3. Squaring both sides, we get x - 3 = 9, so x = 12.

Case 2: p = √(x - 3) = -1. This case gives no real solution, since the square root of a real number cannot be negative. Therefore, the only real solution is x = 12.

Let p = √(x - 5), then the equation becomes p^2 - 4p - 12 = 0. This is a quadratic equation that can be factored as (p - 6)(p + 2) = 0. Therefore, p = 6 or p = -2. Since p = √(x - 5) and we want a real solution, we have only one case:

Case 1: p = √(x - 5) = 6. Squaring both sides, we get x - 5 = 36, so x = 41. However, we need to check that this solution is valid. Since p = √(x - 5) = 6 > 0, we have x - 5 > 0, so x > 5. Therefore, the only real solution is x = 41.

Let p = 3^x, then the equation becomes p^2 + 11p - 12 = 0. This is a quadratic equation that can be factored as (p + 12)(p - 1) = 0. Therefore, p = -12 or p = 1. Since p = 3^x and we want a real solution, we have only one case:

Case 1: p = 3^x = 1. This gives x = 0. However, we need to check that this solution is valid. Since 3^x > 0 for all x, we have x > -∞. Therefore, the only real solution is x = 0.

There is only one real solution because the function 9^x + (11x3^x) - 12 is continuous and strictly increasing for all x, which means that it can cross the x-axis at most once. Since we have found one real solution, there cannot be any others.

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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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April has six pieces of paper, each measuring 8 inches in length which can be calculated using fractions.

April starts with a sheet of paper that is 4 feet long, which is equivalent to 48 inches since there are 12 inches in a foot. She then cuts the length of paper into halves, which gives her two pieces, each of them 24 inches long.

Next, she cuts the length of each of these 24-inch pieces into thirds, which gives her six pieces in total. Each of these pieces is 8 inches long, since 24 divided by 3 equals 8. Therefore, April has six pieces of paper, and each piece is 8 inches long.

It's worth noting that April's process of cutting the paper into halves and then into thirds is an example of how fractions can be used to divide a whole into equal parts. In this case, cutting the paper into halves means dividing it into two equal parts, and cutting each of these halves into thirds means dividing each half into three equal parts.

Overall, April has six pieces of paper, each measuring 8 inches in length. These pieces could be useful for various purposes, such as for creating small origami figures, for making decorations, or for use in a crafting project.

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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 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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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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Answer:

i believe its D

im sorry if i am incorrect

Answer:

D is the answer

Step-by-step explanation:

Answer:26

Step-by-step explanation:

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:

144

Step-by-step explanation:

The angles on the line next to the big c must add up to 180, and 180-58=122, so the space next to the 58 must be 122

The interior angles of a polygon can be calculated with 180(n-2) where n is the sides, so a pentagon has 540 degrees of interior angles

540 - 96 - 88 - 90 - 122 = 144

Answer:

Step-by-step explanation:

90+96+88+180-58=540-k

k=540-396

k = 144

Answer:

7.81 units

Step-by-step explanation:

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the coordinates given in the problem, we can plug in the values into the formula:

d = √((4 - (-2))^2 + (1 - (-4))^2)

Simplifying this expression, we get:

d = √((6)^2 + (5)^2)

d = √(36 + 25)

d = √61

Therefore, the distance between the two points (-2,-4) and (4,1) is √61 (square root of 61), which is approximately 7.81 units.

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

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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Answer: the answer is x < 2.80

Step-by-step explanation: can i get brainliest pls

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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The coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).

In mathematics and geometry, a scale factor is a numerical factor that describes how much a figure or object has been enlarged or reduced in size. It is the ratio of any two corresponding lengths in the original figure and the scaled figure.

In geometry, a vertex (plural vertices) is a point where two or more line segments, lines, or rays meet to form an angle. In other words, a vertex is a point where two or more edges of a polygon, polyhedron, or any other geometrical shape meet.

In the given question,

To enlarge the shape A by a scale factor of 2 with a centre of enlargement of (-3, -5), we need to:

Translate the centre of enlargement to the origin (0, 0) by adding 3 to the x-coordinates and 5 to the y-coordinates of all points.

Apply the enlargement by multiplying the coordinates of each point by 2.

Translate the centre of enlargement back to its original position by subtracting 3 from the x-coordinates and 5 from the y-coordinates of all points.

So, the coordinates of the vertices of the enlarged shape A are:

Vertex 1:

Original coordinates: (0, -4)

Translate to origin: (3, 1)

Enlarge: (6, 2)

Translate back: (3, -3)

Final coordinates: (3, -3)

Vertex 2:

Original coordinates: (2, -4)

Translate to origin: (5, 1)

Enlarge: (10, 2)

Translate back: (7, -3)

Final coordinates: (7, -3)

Vertex 3:

Original coordinates: (1, -6)

Translate to origin: (4, -1)

Enlarge: (8, -2)

Translate back: (1, -6)

Final coordinates: (1, -6)

Vertex 4:

Original coordinates: (0, -6)

Translate to origin: (3, -1)

Enlarge: (6, -2)

Translate back: (0, -6)

Final coordinates: (0, -6)

Therefore, the coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).

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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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