a professor pays 25 cents for each blackboard error made in lecture to the student who points out the error. in a career of n years filled with blackboard errors, the total amount in dollars paid can be approximated by a gaussian random variable yn with expected value 40n and variance 100n. what is the probability that y20 exceeds 1000? how many years n must the professor teach in order that p[yn > 1000] > 0.99?

A positively skewed distribution is due to an extremely large number.

A positively skewed distribution is a type of distribution in which the majority of the data values are clustered towards the left side of the distribution, with a tail extending to the right. This means that there are relatively more smaller values in the dataset than larger values. In a positively skewed distribution, the mean of the dataset is typically larger than the median, and the mode may not be a good representation of the central tendency of the data. This is because the presence of a long tail on the right-hand side of the distribution pulls the mean towards the higher values, while the median remains closer to the center of the dataset. Some common examples of positively skewed distributions include income distributions, where there are a few extremely high earners that skew the data towards the right, and test scores, where there may be a few students who perform extremely well and pull the average higher than the median.

Here,

A positively skewed distribution occurs when the tail of the distribution extends to the right, and the majority of the data is clustered towards the left side of the graph. This means that there are relatively more smaller values in the dataset than larger values. One common cause of positive skewness is the presence of extremely large values, also called outliers, in the dataset. These large values pull the mean of the dataset towards the right, resulting in the tail of the distribution stretching in that direction.

Therefore, out of the options provided, the correct answer is "an extremely large number."

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By examining a scatterplot, you can gain valuable insights into the relationship between the two quantitative variables x and y, such as direction, strength, form, and outliers.

From examining a scatterplot of two quantitative variables x and y, you can observe the following features about the relationship between the variables:

1. Direction: You can determine whether the relationship between the variables is positive (both variables tend to increase or decrease together) or negative (one variable tends to increase while the other tends to decrease).

2. Strength: You can assess the strength of the relationship by observing how closely the data points are clustered around an imaginary line (e.g., a straight or curved line). A strong relationship has points closely clustered, while a weak relationship has points more scattered.

3. Form: You can identify the form of the relationship, such as linear (points form a straight line) or nonlinear (points form a curve).

4. Outliers: You can detect any outliers, which are data points that do not follow the general pattern of the relationship between the variables.

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The score that falls exactly in the middle of the distribution of scores after they have been ranked from highest to lowest is known as the median.

The median is a measure of central tendency that is calculated by arranging the data points in order from smallest to largest and then identifying the middle value.Therefore, it is the value that separates the highest from the lowest 50% of the data, making it an ideal measurement for skewed data.

The median is the value that is halfway between the upper and lower quartiles of a dataset when it is divided into four equal parts. This measurement is less sensitive to outliers and extreme values in comparison to the mean.

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Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

Answer:

110.5 cubic inches

Step-by-step explanation:

Base is parallelogram, so area is

A = 4.7×5 = 23.5

Height(h) is 4.7, so volume is,

V = A×h

= 23.5×4.7

= 110.45 ≈ 110.5

Answered by GAUTHMATH

Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

An illustration of data or mathematical functions is a graph. It is a method for presenting numerical data in a way that is simple to comprehend and interpret. A set of axes, one for each variable being represented, and one or more plots or lines that reflect the data or function being graphed are the main components of a graph. There are many distinct graph kinds, each of which is appropriate for displaying various sorts of data, including line graphs, bar graphs, scatter plots, and pie charts.

given

The axes cannot be identified because they are not specified in the query.

The blue ABC bar graph is as follows:

Using the equation (x, y) (y, -x), rotate AABC 90 degrees clockwise by applying the following transformation to each point:

A(-3, 0) → A' (0, 3) (0, 3)

B(-2, 4) → B' (-4, -2) (-4, -2)

C(1, -1) → C' (1, -1) (1, -1)

The red A'B'C' coordinates are as follows: A' (0, 3), B' (-4, -2), and C' (1, -1).

We take the y-coordinate of each point and subtract 3 to translate AA'B'C' three units down:

A' (0, 3) → A" (0, 0) (0, 0)

B' (-4, -2) → B" (-4, -5) (-4, -5)

C' (1, -1) → C" (1, -4) (1, -4)

Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

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The complete question is:-  

1. Label the axes.

2. Graph: A(-3, 0) B(-2, 4) C(1,-1) Draw ABC in blue.

3. Rotate AABC 90° clockwise to

create ▲A'B'C' in red. List the coordinates below:

Formula: (x, y) → (y, -x)

A(-3, 0) A' ()

B(-2, 4)→ B' ()

C(1, -1) C' ()

4. Translate AA'B'C' three units down to create ▲A"B"C" in green. What are the coordinates of AA"B"C"?

Answer:

\(x = -1\)

Step-by-step explanation:

-Solve for \(x\) :

\(8x + 1 = -8 - x\)

-Add both side by \(x\) :

\(8x + 1 + x = -8 - x + x\)

\(9x + 1 = -8\)

-Subtract both sides by \(1\) :

\(9x + 1 - 1 = -8 - 1\)

\(9x = -9\)

-Divide both sides by \(9\) :

\(\frac{9x}{9} = \frac{-9}{9}\)

\(x = -1\)

So, the value of \(x\) is \(-1\).

Answer:

\( \boxed{\sf x = - 1} \)

Step-by-step explanation:

\( \sf Solve \: for \: x: \\ \sf \implies 8x + 1 = - 8 - x \\ \\ \sf Add \: x \: to \: both \: sides: \\ \sf \implies 8x + x + 1 = - 8 + (x - x ) \\ \\ \sf x - x = 0 : \\ \sf \implies 8x +x + 1 = - 8 \\ \\ \sf 8x + x = 9x : \\ \sf \implies 9x + 1 = - 8 \\ \\ \sf Subtract \: 1 \: from \: both \: sides: \\ \sf \implies 9x + (1 - 1 )= - 8 - 1 \\ \\ \sf 1 - 1 = 0 : \\ \sf \implies 9x = - 8 - 1 \\ \\ \sf - 8 - 1 : \\ \sf \implies 9x = - 9 \\ \\ \sf Divide \: both \: sides \: of \: 9 x = 9 \: by \: 9: \\ \sf \implies \frac{9x}{9} = - \frac{9}{9} \\ \\ \sf \frac{9}{9} = 1 : \\ \sf \implies x = - 1\)

The correct answer is option B) £.6159/Can$, is the £/Can$ cross-rate.

The given spot rate for the British pound and the Canadian dollar is used to calculate the £/Can$ cross-rate.

The steps are outlined below:

Step 1: Find the dollar value of the pound and the dollar value of the Canadian dollar:

£.7277 = $1Can$1.1815 = $1

Step 2: Divide the dollar value of the pound by the dollar value of the Canadian dollar to obtain the £/Can$ cross-rate:

£.7277/$1 ÷ Can$1.1815/$1= £.6159/Can$

Thus, the correct answer is option B) £.6159/Can$.

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The optimal rank-2 approximation of the symmetric matrix is:

1.5  0.0  -1.0

0.0  0.5   0.0

-1.0 0.0   1.5

Let's denote the symmetric matrix as A, and the columns of A as v1, v2, and v3. Also, let's denote the eigenvectors given as q1 and q2, and their corresponding eigenvalues as λ1 and λ2.

We know that the optimal rank-k approximation of A can be found by performing a truncated Singular Value Decomposition (SVD) of A, which consists of finding the matrices U, Σ, and V such that A ≈ UΣV^T, where U and V are orthogonal matrices, and Σ is a diagonal matrix with non-negative entries on the diagonal, called the singular values of A.

In this case, since A is symmetric, we have that A = QΛQ^T, where Q is the matrix whose columns are the eigenvectors q1, q2, and q3, and Λ is the diagonal matrix whose entries are the eigenvalues λ1, λ2, and λ3.

Since we are interested in finding the rank-2 approximation of A, we can truncate the SVD by keeping only the first two columns of U and V, and the first two entries of Σ. This gives us the following approximation:

A ≈ UΣV^T = (v1 v2) Σ (v1 v2)^T

Finally, substituting the given values for v1 and v2, we get:

A ≈ 1.5  0.0  -1.0

   0.0  0.5   0.0

  -1.0  0.0   1.5

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No, it is not possible for 5 vectors in R4 to be linearly independent.

In order to understand why 5 vectors in R4 cannot be linearly independent, let's first define what it means for vectors to be linearly independent.

A set of vectors is said to be linearly independent if no vector in the set can be written as a linear combination of the others. In other words, the only way to obtain the zero vector by combining the vectors in the set is by assigning all the coefficients to zero.

Now, let's consider R4, which is a vector space with dimension 4. This means that any basis for R4 will contain exactly 4 vectors. A basis is a set of linearly independent vectors that span the entire vector space.

Since the maximum number of linearly independent vectors in R4 is equal to its dimension, which is 4, it is not possible to have a set of 5 linearly independent vectors in R4. Adding a fifth vector to the set would introduce linear dependence, as it could be expressed as a linear combination of the other four vectors.

Therefore, 5 vectors in R4 cannot be linearly independent.

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The percentage of the females in grade 11 and 12 is 60%. Option C

A number can be expressed as a fraction of 100 using a percentage. The letter "%" stands for it. To find a percentage, divide the value under consideration by all possible values, then multiply the result by 100.

Females in grade 11 can be obtained from;

Number of students in grade 11 = 27 + 50

Percentage of female students = 50/27 + 50 * 100/1

= 65%

Females in grade 12;

Number of students in grade 12= 37 + 61

Percentage of female students in grade 12 = 61/37 + 61 * 100

= 62%

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The efficiency of the algorithm is O(n), as the run-time is directly proportional to the input size.

To determine the efficiency of an algorithm, we analyze how the run-time of the algorithm scales with the input size. In this case, we have two data points: for n = 4096, the run-time is 512 milliseconds, and for n = 16,384, the run-time is 2048 milliseconds.

By comparing these data points, we can observe that as the input size (n) doubles from 4096 to 16,384, the run-time also doubles from 512 to 2048 milliseconds. This indicates a linear relationship between the input size and the run-time. In other words, the run-time increases proportionally with the input size.

Based on this analysis, we can conclude that the efficiency of the algorithm is O(n), where n represents the input size. This means that the algorithm's run-time grows linearly with the size of the input.

It's important to note that big-O notation provides an upper bound on the algorithm's run-time, indicating the worst-case scenario. In this case, as the input size increases, the run-time of the algorithm scales linearly, resulting in an O(n) efficiency.

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There are the temperature of 98.68°F in Celsius temperature of 36.6°c.

To elaborate, the formula for converting Celsius to Fahrenheit is based on the freezing and boiling points of water, where 0°C is the freezing point and 100°C is the boiling point. In Fahrenheit, these points are 32°F and 212°F, respectively.

To convert 36.6°C to degrees Fahrenheit, we can use the formula:

F = (C × 9/5) + 32

where F is the temperature in degrees Fahrenheit, and C is the temperature in degrees Celsius. The formula relates the two scales by multiplying the Celsius temperature by 9/5 and adding 32.

Substituting 36.6°C into this formula, we get:

F = (36.6 × 9/5) + 32

F = 98.68°F

Therefore, 36.6°C is equivalent to 98.68°F.

The given Celsius temperature of 36.6°C is equivalent Fahrenheit temperature of 98.68°F.

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The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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If the scale drawing of a rectangular park has a scale of 1cm = 120 m, then the actual perimeter of the park is 3960 meters

To find the actual perimeter of the park in meters, we need to first find the perimeter of the park in centimeters using the scale drawing, and then convert it to meters.

The length of the park in the scale drawing is 11.1cm, which corresponds to an actual length of:

11.1 cm x 120 m/cm = 1,332 m

The width of the park in the scale drawing is 5.4cm, which corresponds to an actual width of:

5.4 cm x 120 m/cm = 648 m

So, the actual perimeter of the park is:

2(length + width) = 2(1,332 m + 648 m) = 3,960 m

Therefore, the actual perimeter of the park is 3,960 meters.

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The given question is incomplete, the complete question is:

A scale drawing of a rectangular park has a scale of 1cm = 120 m. What is the actual perimeter of the park in meters?

Answer:

\({ \bf{x = \sqrt{ {12}^{2} - { \sqrt{122} }^{2} } }} \\ x = \sqrt{22} \: in\)

The total amount earned this week is 12x - 15

From the question, we have the following parameters that can be used in our computation:

Number of hours = x

Rate per hour = $12

Late delivery charge = $15

The total amount of earning is the difference between the total actual earnings number and late delivery charges

This is represented as

Total = Number of hours x Rate per hour - Late delivery charge

Substitute the known values in the above equation

So, we have the following equation

Total = x * 12 - 15

Evaluate

Total = 12x - 15

The above equation cannot be further simplified

Hence, the expression is 12x - 15

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Answer:

-8

Step-by-step explanation:

-31 and +31 cancel each other out leaving you with -8

The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

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Answer:

slope of st is -0.25

slope of tu is 1

slope of us is -0.25

slope of sv is 1 so it is a parallelogram. the slope of the parallel lines needs to be the same to be a parallelogram. to find the slope, you need to find the change from the points of the referenced line, for example, slope of st you would label each point as x1, y1 and x2,y2. it does not matter which one you label and you can change them for each different line. you would then find the difference by subtracting (y2-y1) divided by (x2-x1) so 4-3=1 and 1-5 is -4. you then divide 1/-4 is -0.25. you the follow the steps for each line. is the parallel lines have the same slope, it is a parallelogram

Answer:

a

Step-by-step explanation:

Answer:

Four and One thousand five hundred thirty-eight ten thousandths

Step-by-step explanation:

This is in standard form

Answer:

32

Step-by-step explanation:

it says he already had 32 and earns 10 per week so initial is 32 and increment is 10/week

Given the provided coordinates of the points, The shape that is formed is a parallelogram because the slopes of the opposite sides are same.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

slope between (1,1) and (4,4),

m1 = 4-1/4-1 =3/3 =1

slope between (4,-2) and (7,1),

m2= 1+2/7-4 = 3/3 =1

m1=m2

similarly, slope between (1,1) and (4,-2),

m3= -2-1/4-1 = -3/3 =-1

slope between (7,1) and (4,4)

m4= 1-4/7-4 = -3/3 =-1

m3=m4

So, slopes of opposite sides are same that means they are parallel, The shape is parallelogram.

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Answer:

28.61

Step-by-step explanation:

\(tan^{-1} (6/11)\)

Answer:

The answer is

t = 41/4

Alternate form: t = 10 1/4

Decimal form: t = 10.25

Answer:

Step-by-step explanation:

an isosceles triangle, 2 angles equal to 45, one is 90 degrees

in this case a=b

c^2=a^2+b^2, lets solve for a, as it doesn't matter which leg we find first due to the fact that they are equal

c^2=2a^2

10^2=2*a^2

100/2=a^2

50=a^2

a=5\(\sqrt{2}\)

Answer:

$1720 total liabilities

Step-by-step explanation:

The total liabilites are $1,720.

Liability usually means that you are responsible for something, and it can also mean that you owe someone money or services.

Now given that,

Car worth = $3,200

Loan amount = $1,400

Owe on credit card = $320

Now since liability is the money owe by someone so in the present condition.

Total liabilities = Loan amount + Owe on credit card

⇒ Total liabilities = $1,400 + $320

⇒ Total liabilities = $1,720

which is the required total liabilities.

Thus, the total liabilites are $1,720.

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