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The probability of a z-score larger than 2 is approximately 0.0228, or 2.28%.

Therefore, the answer is (b) .0228.

To find the probability that the mean of a sample of 49 observations will be larger than 82, we need to calculate the standard error of the mean first. The standard error of the mean is equal to the standard deviation of the population divided by the square root of the sample size. Therefore, in this case, the standard error of the mean is 7 / sqrt(49) = 1.

Next, we need to convert the sample mean of 82 to a z-score. The formula for a z-score is:

\(z = (x - μ) / SE\)

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean. Plugging in the values, we get:

\(z = (82 - 80) / 1 = 2\)

To find the probability of a z-score larger than 2, we can use a standard normal distribution table or calculator. The probability of a z-score larger than 2 is approximately 0.0228, or 2.28%.

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The possible values of n are all the factors of 28, which are:

1, 2, 4, 7, 14, 28.

A natural number is a positive integer that is greater than or equal to 1. In other words, it is a whole number that can be used to count objects or elements in a set. Examples of natural numbers include 1, 2, 3, 4, 5, and so on.

It includes all the natural numbers (positive integers) as well as their additive inverses (negative integers). Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on. Integers are used in a variety of mathematical operations, including addition, subtraction, multiplication, and division.

When we divide 33 by n and get a remainder of 5, we can write this as:

   33 ≡ 5 (mod n)

This means that 33 is congruent to 5 modulo n. In other words, 33 and 5 have the same remainder when divided by n.

We can use modular arithmetic to solve this problem.

When we divide 33 by n and get a remainder of 5, we can write this as:

33 ≡ 5 (mod n)

This means that 33 is congruent to 5 modulo n. In other words, 33 and 5 have the same remainder when divided by n.

We can simplify this expression by subtracting 5 from both sides:

   28 ≡ 0 (mod n)

This means that 28 is congruent to 0 modulo n. In other words, n divides evenly into 28.

Therefore, the possible values of n are all the factors of 28, which are:

1, 2, 4, 7, 14, 28

So these are all the possible values of n that satisfy the condition that when you divide 33 by n, the remainder is 5.

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Answer:

y = -7x + 11

Explanation:

Just get y by itself. Subtract 7x from both sides. Substitute in each x value individually to get the next answers, which will be 25, 11, and -10.

Based on Fairs' assumption of an average speed of 50 mph, his estimated arrival time in London would be 7:24 pm.

Based on Fairs' assumption that the coach will travel at an average speed of 50 mph, we can calculate an estimated arrival time in London. The driving distance between Manchester and London is 195 miles, and if we divide this by the average speed of 50 mph, we can determine the estimated travel time.

The estimated travel time can be calculated as follows:

Travel time = Distance / Speed = 195 miles / 50 mph = 3.9 hours

Since Fairs intends to leave Manchester at 3:30 pm, we can add the travel time of 3.9 hours to this departure time to find the estimated arrival time in London.

3:30 pm + 3.9 hours = 7:24 pm.

Therefore, based on Fairs' assumption of an average speed of 50 mph, his estimated arrival time in London would be 7:24 pm.

However, it's important to note that this calculation assumes a constant average speed throughout the journey, which may not always be the case due to factors such as traffic conditions or rest stops.

It's always a good idea to account for potential delays or variations in travel time when planning a journey.

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If T: R³ -> R³ is a one-to-one linear operator and B = {v1, v2, v3} is a linearly independent set of vectors in R³, then [T]B may or may not be an invertible matrix. The invertibility of [T]B depends on whether the vectors T(v1), T(v2), T(v3) form a linearly independent set in R³.

The matrix [T]B represents the transformation T with respect to the basis B. To determine if [T]B is invertible, we need to consider the linear independence of the images T(v1), T(v2), and T(v3) under T.

If T(v1), T(v2), and T(v3) form a linearly independent set in R³, then the matrix [T]B will be invertible. This is because the columns of an invertible matrix are linearly independent, and the columns of [T]B correspond to T(v1), T(v2), and T(v3).

However, if T(v1), T(v2), and T(v3) are linearly dependent, then [T]B will not be invertible. In this case, the columns of [T]B will be linearly dependent, leading to a singular matrix.

Therefore, whether [T]B is invertible or not depends on the linear independence of the images of the vectors v1, v2, and v3 under T. If T(v1), T(v2), and T(v3) are linearly independent, [T]B will be invertible; otherwise, it will not be invertible.

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Answer:

2nd

1st

3rd

is the answers

The general solution of the given recurrence equation is Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n.

The given recurrence equation is

Qn-1 + 5Qn-2 + 3Qn-3 = 3

Let's find the characteristic equation of the given recurrence equation:

By assuming Qn = rn,

the characteristic equation can be derived as:

r3 - r2 - 5r - 3 = 0

So, the characteristic polynomial is

(r + 1)(r - 3)2

Let α = -1 and β = 3 (repeated roots)

Now, the solution of the given recurrence equation is:

Qn = Arn + Bnαn + Cnβn

As α = -1 and β = 3 are the roots of the characteristic equation, substitute these values in the above equation.

We have

A(-1)n + Bn(-1)n + Cn(3)n ... (1)

As we are going to find the general solution of Qn, the constants A, B, and C need to be determined.

Let's solve for A, B, and C by considering the first few terms of the given recurrence equation.

Suppose n = 3 in the recurrence equation Qn-1 + 5Qn-2 + 3Qn-3 = 3, we have

Q2 + 5Q1 + 3Q0 = 3 ... (2)

Now, substitute n = 2 in the general solution (1), we have

Q2 = A(-1)2 + B2(-1)2 + C23 ... (3)

Now, substitute n = 1 in the general solution (1), we have

Q1 = A(-1)1 + B1(-1)1 + C31 ... (4)

Now, substitute n = 0 in the general solution (1), we have

Q0 = A(-1)0 + B0(-1)0 + C30 ... (5)

Now, let's solve for A, B, and C using equations (2), (3), (4), and (5).

Q2 + 5Q1 + 3Q0 = 3:

2A + 5B + 3C = 3A(-1)2 + B2(-1)2 + C23:

A - B + 9C = 3A(-1)1 + B1(-1)1 + C31:

-A - B + 3C = 1A(-1)0 + B0(-1)0 + C30:

A + B + C = 1

On solving the above equations,

we get A = -1/4, B = 1/4, and C = 1/2

So, the general solution of the given recurrence equation is  

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

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a)There are 200 students who attended the survey.

b)There are 18 students who prefer the gym in the morning.

c)There are 38 grade 10 students who participated in the survey.

d)There are 110 student students who prefer to have a gym in the afternoon.

A data table is a piece of writing made up of rows, columns, and cells that each contain a particular value. They keep data that people can access later and update as required.

The given data is shown in table,

The data table's title, column headers, and row headers can all aid a user in better comprehending the data in the table. Data tables present information in a format resembling a grid with rows and columns.

To enable users to find patterns and draw conclusions from data, they arrange information in ways that are simple to scan.

Thus, there were 200 students who participated in the poll, 18 of whom preferred the gym in the morning, 38 grade 10 students, and 110 of them preferred to have a gym in the afternoon.

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The probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night can be calculated using the Normal Distribution.

To calculate the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night, we can use the Normal Distribution. First, we need to calculate the difference between their means, which is 18. Then, we need to calculate the standard deviation of the difference between their scores, which is the square root of the sum of the squares of their standard deviations (√(31²+40²) = 51.96). To calculate the probability, we use the z-score formula, which is (x - mean) / standard deviation. In this case, the z-score is (18 - 0) / 51.96 which is 0.35. Plugging this z-score into a z-table, we get a probability of 0.6379. Therefore, the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night is 0.6379.

The complete question: Mr. Voss and Mr. Cull bowl every Tuesday night. Over the past few years, Mr. Voss’s scores have been approximately Normally distributed with a mean of 212 and a standard deviation of 31. During the same period, Mr. Cull’s scores have also been approximately Normally distributed with a mean of 230 and a standard deviation of 40. Assuming their scores are independent, what is the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night?

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Answer:

x = 9

Step-by-step explanation:

The 2 angles are equal because of Corresponding Angles.

Step 1: Set up equation

(13x + 12) = 129

Step 2: Solve for x

Quadrilateral ABCD is a square.

A quadrilateral is a four-sided polygon with four angles. It is a two-dimensional shape that can be either convex or concave. Quadrilaterals are classified according to their sides and angles.

Examples of quadrilaterals include squares, rectangles, rhombi, trapezoids, and parallelograms.

Quadrilaterals can be further divided into special types such as squares, rectangles, parallelograms, trapezoids, and kites.

It can be proved that a Quadrilateral ABCD is a square by showing that the diagonals of the quadrilateral are perpendicular and congruent.

Distance between A and C:

\($d = \sqrt{(3 - (-3))^2 + (-2 - 2)^2} = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52}$\)

Distance between B and D:

\($d = \sqrt{(5 - 3)^2 + (-2 - (-2))^2} = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20}$\)

Since the distances are equal, the diagonals of the quadrilateral are congruent.

Slope of AC:

\($m = \frac{(-2 - 2)}{(3 - (-3))} = \frac{-4}{6}$\)

Slope of BD:

\($m = \frac{(-2 - (-2))}{(5 - 3)} = \frac{-4}{2}$\)

Since the slopes are negative reciprocals, the diagonals of the quadrilateral are perpendicular.

Since the diagonals of the quadrilateral are congruent and perpendicular, the quadrilateral is a square.

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I like Math debating but it takes too long sometimes. This is so because mathematics, despite being an exact science, provides several alternatives to reach the same final result.

Thus, for example, a probability percentage can be obtained by means of a binomial formula or by means of a cross multiplication calculation, where both results will be correct.

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Answer:

oh my god

Step-by-step explanation:

A Tim fraction of answered 1730 questions correctly.

To determine the number of questions Tim answered correctly, to find the total number of incorrect answers and subtract it from the total number of questions.

Given:

Number of incorrect answers = 101010

Points for each correct answer = 444

Total score = 767676

calculate the number of questions Tim answered correctly:

Total score = Points for each correct answer ×Number of correct answers

767676 = 444 × Number of correct answers

Number of correct answers = 767676 / 444

Number of correct answers = 1730.43

Since Tim cannot have a fraction of an answer, round down to the nearest whole number:

Number of correct answers =1730

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There are 25,053,600 different tests of 5 questions each that can be made from Ms. Wood's collection of 25 questions.

To find the number of different tests of 5 questions each that can be made from a set of 25 questions, you can use the combination formula. The combination formula is:

n! / (r! * (n-r)!)

Where n is the total number of items and r is the number of items being chosen at a time.

In this case, n is 25 (the total number of questions) and r is 5 (the number of questions per test). Plugging these values into the formula gives:

25! / (5! * (25-5)!) = 25! / (5! * 20!) = 25 * 24 * 23 * 22 * 21 / (5 * 4 * 3 * 2 * 1) = 25,!053,!600

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Answer:

Seasonal allergies

Step-by-step explanation:

She migtht have seaonal allergies

The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart. The histogram for the given data is attached with the answer below.

The histogram is a diagram with rectangles whose width is similar to the specified range and whose area is equal to the regularity of variables.

The histogram is a chart for comparing the data by plotting it in a rectangular form in the chart.

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Answer:

"C" has to be the answer...

there is a vertical asymptote at -5

thus you need a denominator that is zero at -5

plug in -5 into the equations only "C" ends up with a zero in the denominator at that point

Step-by-step explanation:

The range of the function g(x) is [300, ∞)

In this question, we have been given that we have deposited $300 into a savings account that earns interest annually.

The function g(x) = 300(1.04)^x used to find the amount of money in the savings account, g(x), after x years.

We need to find the range of the function.

Since a savings account earns interest annually, x can have take values from 0 to infinity.

For x = 0 year,

g(0) = 300(1.04)^0

g = 300 * 1

g = 300

For x tends to ∞, the value of function would be ∞

Therefore, the range of the function g(x) is [300, ∞)

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The answer is 40 Grams

120 divided by 3 = 40

Answer:

all values less than 5.5

Step-by-step explanation:

Given the inequality expression – 6 + 2y < 5

We are to find all the possible values of x

-6 + 2 y < 5

Add 6 to both sides

-6 + 2y + 6 < 5 + 6

2y < 11

Divide both sides by 2

2y/2 < 11/2

y < 11/2

y < 5.5

hence the possible values of y are all values less than 5.5

The asked net for the cube of side length 2 cm has been shown.

The surface area is defined as a region of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,
The cube of side length 2 cm is given we have to draw the net for the given cube.

So first we calculate the surface area,

surface area of the cube  = 6 [a]²
surface area = 6 (2)² = 24 cm²

Here, as the cube has 6 faces, unbind the cube on the coordinate plate.

Thus. the required net for the cube has been shown.

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Accupunture is best these days for medication and health therapy.

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Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

A reasonable amount to pay for the things will be equal to $27. Hence, option D is correct.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given information in the question,

Price of gasoline = $2.29 per gallon

Then, the price of 10-gallon gasoline = 10 × 2.29 = $22.9

Price of quart = $1.89 per quart for oil.

Then, the price of 2 quarts of oil = 2 × $1.89 = $3.78.

Then, the total price will be,

$22.9 + $3.78 = 26.68 ≈ $27

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Answer: 10

Step-by-step explanation:

We know the slope is Δy/Δx, so plug the numbers in, and you 10.

The area of the composite figures are

First figure = 120 square ft

second figure = 22 square in

The area is calculated by dividing the figure into simpler shapes.

First figure

The simple shapes used here include

rectangle and

triangle

The area of the composite figure = Area of rectangle + Area of triangle

The area of the composite figure = (12 * 7) + (0.5 * 12 * 6)

The area of the composite figure = 84 + 36

The area of the composite figure = 120 square ft

Second figure

The simple shapes used here include

parallelogram and

rectangular void

The area of the composite figure = Area of parallelogram - Area of rectangle

The area of the composite figure = (5 * 5) - (3 * 1)

The area of the composite figure = 25 - 3

The area of the composite figure =  22 square ft

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Answer:

55 inches = 4 feet 7 inches

Step-by-step explanation:

As we know 12 inches = 1 feet

so, 55 inches = 55÷12

4 feet 7 inches

Answer:

55 inches=4 feet 7 inches

Hope it helps

confidence interval is (53.0, 60.8), where 53.0 is the lower limit and 60.8 is the upper limit. This means we are 95% confident that the population means lies within this interval.

a) The length of a confidence interval is twice the margin of error. In this case, the margin of error is 3.9, so the length of the confidence interval would be 2 * 3.9 = 7.8.

b) To obtain the confidence interval, we need the sample mean and the margin of error. Given that the sample mean is 56.9, we can construct the confidence interval as follows:

Lower limit = Sample mean - Margin of error = 56.9 - 3.9 = 53.0

Upper limit = Sample mean + Margin of error = 56.9 + 3.9 = 60.8

Therefore, the confidence interval is (53.0, 60.8), where 53.0 is the lower limit and 60.8 is the upper limit. This means we are 95% confident that the population means lies within this interval.

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