In a large class of introductory Statistics students, the professor has each person toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. a. What shape would you expect this histogram to be?

Step-by-step explanation:

It doesn't have neither the greater than or equal to or less than or equal to signs so

To find \(\(g'(1.5)\)\), we need to calculate the derivative of the function \(\(g(x)=|2-x|+|(x-1)(x-2)|\)\) and evaluate it at \(\(x=1.5\)\).

The given function \(\(g(x)\)\) is a combination of two absolute value functions. We can find the derivative of \(\(g(x)\)\) by considering the cases where the argument of the absolute value function changes sign. Let's break down the function \(\(g(x)\)\) into its constituent parts:

For \(\(x < 2\), \(g(x) = (2-x) + (x-1)(x-2) = -x^2 + 4x - 1\)\). Taking the derivative of this expression yields \(\(g'(x) = -2x + 4\)\).

For \(\(x > 2\), \(g(x) = (2-x) + (x-1)(2-x) = -x^2 + 4x - 3\)\). The derivative of this expression is \(\(g'(x) = -2x + 4\).\)

At \(\(x=2\)\), both expressions meet, resulting in a kink. However, since we are interested in \(\(g'(1.5)\)\), we only need to consider the left side of \(\(x=2\)\). Hence, \(\(g'(1.5) = -2(1.5) + 4 = 1\)\).

Therefore, \(\(g'(1.5) = 1\),\) indicating that the slope of the function \(\(g(x)\)\) at \(\(x=1.5\)\) is positive.

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On solving the expression 90 + x, the duration of game with 4 minutes stoppage is obtained as 94 minutes.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression is given as -

90 + x

Here 90 is the duration of the soccer game.

x represents the duration of stoppage.

The stoppage time is given as 4 minutes.

Substitute the value of x with 4 in the expression.

The total time of game is -

90 + x

90 + 4

94 minutes

Therefore, the total duration of game is 94 minutes.

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The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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Answer: The Malay world or Malay realm, is a concept or an expression that has been utilised by different authors and groups over time to denote several different notions, derived from varied interpretations of Malayness, either as a racial category, as a linguistic group or as a political-cultural group. The use of the term 'Malay' in much of the conceptualisation is largely based on the prevalent Malay cultural influence, manifested in particular through the spread of the Malay language in Southeast Asia as observed by different colonial powers during the Age of Discovery.

-Your friend, Bill Cipher

Step-by-step explanation: Have a great Valentines day <3

The inverse of a biconditional statement is not equivalent to the original statement. The inverse statement may have a different meaning or convey a different condition.

The inverse of a biconditional statement involves negating both the "if" and the "only if" parts of the statement. In this case, the inverse of the biconditional statement would be:Inverse of Statement 1: A figure is not a polygon if and only if not all of its sides are line segments.

Now, let's analyze the relationship between Statement 2 and its inverse.

Statement 2: A figure is not a polygon if and only if not all of its sides are line segments.

Inverse of Statement 2: A figure is not a polygon if and only if all of its sides are line segments.

The inverse of Statement 2 is not equivalent to Statement 1. In fact, the inverse of Statement 2 is a different statement altogether. It states that a figure is not a polygon if and only if all of its sides are line segments. This means that if all of the sides of a figure are line segments, then it is not considered a polygon.

In contrast, Statement 1 states that a figure is a polygon if and only if all of its sides are line segments. It affirms the condition for a figure to be considered a polygon, stating that if all of its sides are line segments, then it is indeed a polygon.

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The double integral of the function 1L 4x² dA over the region D can be found by following these steps: determine the limits of integration, set up the double integral, integrate with respect to y, integrate with respect to x, and calculate the result.

To evaluate the double integral of the function 1L 4x² dA over the region D, where D is the region in the first quadrant bounded by y = 7x and y = -x³, follow these steps:

1. Determine the limits of integration: To find the limits of integration, first find the points of intersection between y = 7x and y = -x³. Set the two functions equal to each other and solve for x:

7x = -x³
x³ + 7x = 0
x(x² + 7) = 0

The points of intersection are x = 0 and x² + 7 = 0 (which has no real solutions). So, the limits of integration for x are [0, x₁], where x₁ is the positive root of x² + 7 = 0.

2. Set up the double integral: The double integral can be set up as follows:

∬ₐᵦ 4x² dy dx

Here, a and b represent the limits of integration for x (0 and x₁), and α(y) and β(y) represent the limits of integration for y.

3. Integrate with respect to y: Since there is no y in the function 4x², the integral with respect to y becomes:

∫ₐᵦ (4x²) * (β(y) - α(y)) dx

The functions y = 7x and y = -x³ can be rewritten as x = y/7 and x = \(-y^{\frac{1}{3} }\) respectively. So, β(y) = y/7 and α(y) = \(-y^{\frac{1}{3} }\). Thus, the integral becomes:

∫₀ˣ₁ (4x²) * (y/7 - (\(-y^{\frac{1}{3} }\))

4. Integrate with respect to x: Now, we need to integrate the function with respect to x:

∫₀ˣ₁ (4x²) * (y/7 - (\(-y^{\frac{1}{3} }\)) dy = (4/3)x³(y/7 - \((-y^{\frac{1}{3} })\) evaluated from x=0 to x=x₁.

5. Calculate the result: After evaluating the expression, the result is the value of the double integral over the region D.

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The evaluated probabilities for the given question are 0.20 for the men who asked for promotion, 0.59 for the men who received the promotion when asked, and  0.118 for men who asked for promotion and received.under the condition that from the men interviewed  20% had asked for a promotion and 59% of the men who had asked for a promotion and  received.
Then,
P(man asked for a promotion)
= 20/100
= 0.20

P(man received promotion, given he asked for one)
= 59/100
= 0.59

P(man asked for promotion and received )
= P(man asked for a promotion) x P(man received promotion, given he asked for one)
= 0.20 x 0.59
= 0.118
Probability is considered as  the percentage of an event taking place in a specific time frame, in a given place. It is said to be a great aid in the horizons of science and mathematics.


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Answer:

Step-by-step explanation:

By geometric mean theorem,

In a triangle ABC,

\(\frac{BC}{AC}=\frac{CD}{BC}\)

\(\frac{y}{(4+6)}=\frac{6}{y}\)

y² = 60

y = √60

y = 7.75

Similarly, \(\frac{AB}{AC}=\frac{AD}{AB}\)

\(\frac{x}{(4+6)}=\frac{4}{x}\)

x² = 40

x = √40

x = 6.32

Answer:

(14, 42)

Step-by-step explanation:

(-4, 2, 14, 34, 42) are all elements of b, and (-7. 14, 21, 42) are all elements of c. (14, 42) are the only elements that are in both sets

Answer:

13x+4y+27

Step-by-step explanation:

Answer:

13x + 4y + 27

Step-by-step explanation:

6x +12+4y+7x+15

- Rearrange the like terms together.

6x + 7x + 4y + 12 + 15

13x + 4y + 27

The largest even number that cannot be expressed as the sum of two composite numbers is 38.

A composite number is a number that has more than two factors, including 1 and itself. A prime number is a number that has exactly two factors, 1 and itself.

If we consider all even numbers greater than 2, we can see that any even number greater than 38 can be expressed as the sum of two composite numbers. For example, 40 = 9 + 31, 42 = 15 + 27, and so on.

However, 38 cannot be expressed as the sum of two composite numbers. This is because the smallest composite number greater than 19 is 25, and 38 - 25 = 13, which is prime.

Therefore, 38 is the largest even number that cannot be expressed as the sum of two composite numbers.

Here is a more detailed explanation of why 38 cannot be expressed as the sum of two composite numbers.

The smallest composite number greater than 19 is 25. If we try to express 38 as the sum of two composite numbers, one of the numbers must be 25. However, if we subtract 25 from 38, we get 13, which is prime. This means that 38 cannot be expressed as the sum of two composite numbers.

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Answer:

x = 6 , y = 1.5

Step-by-step explanation:

1

\(\frac{3}{4}\) = \(\frac{x}{8}\) ( cross- multiply )

4x = 3 × 8 = 24 ( divide both sides by 4 )

x = 6

2

\(\frac{5}{y}\) = \(\frac{10}{3}\) ( cross- multiply )

10y = 5 × 3 = 15 ( divide both sides by 10 )

y = 1.5

Answer:

$3 because if they are having a product at 4 dollars and lose a Dollar for ever one sold then $4-$1 = $3

Answer:

y o = 2 sin ( π/6 ) = 2 * 1/2 = 1

x o = π / 6

y ` = 2 cos x = 2 cos (π/6) = 2 * √3 / 2 = √ 3;

m = √3

An equation of the tangent line is:

y - y o = m ( x - x o )

Answer:

y - 1 = √3 ( x - π/6 )

Step-by-step explanation

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The set of points at which the function \(f(x, y) = (1 - x^2)(1 - y^2) / (6 - x^2 - y^2)\) is continuous is the entire domain of the function except for the points on the circle defined by \(x^2 + y^2 = 6\).

To determine the set of points at which the function is continuous, we need to identify any potential discontinuities. In this case, the function f(x, y) can be expressed as:

\(f(x, y) = (1 - x^2)(1 - y^2) / (6 - x^2 - y^2)\)

The function will be continuous everywhere except for the points where the denominator becomes zero, as division by zero is undefined. Therefore, we need to find the values of x and y that satisfy the equation:

\(6 - x^2 - y^2 = 0\)

This equation represents a circle centered at the origin with a radius of √6. The set of points at which the function is continuous is the entire domain of the function except for the points on this circle. In other words, it is the set of all points (x, y) such that \(x^2 + y^2 ≠ 6\).

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Answer:

A. y = 3x.

Step-by-step explanation:Relation 2 is a straight line that does not pass through the origin, so it is a partial variation.

The equation of an ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0) is \($\frac{x^2}{16}+\frac{y^2}{81}=1$$\).

As per the given data the ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

If the ellipse has its x-intercepts at points (4, 0) and (-4, 0) and y-intercepts at points (0, 9) and (0, -9), then it's symmetric across the y- axis and the x-axis.

The equation of an ellipse where the major axis 2a is greater than the minor 2b.

When 2b > 2a , then the equation becomes \($\frac{(y-h)^{2} }{b^{2} } + \frac{ (x-k)^{2} }{a^{2} } =1\)

Moreover h = 0 and k = 0 because the center is on the origin, so the equation becomes:

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Moreover,

a = 4

b = 9

The equation of the such ellipse is

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Hence, the equation of the ellipse is

\($\frac{x^2}{4^2}+\frac{y^2}{9^2}=1\)

\($\frac{x^2}{16}+\frac{y^2}{81}=1$$\)

Therefore the equation of an ellipse is  \($\frac{x^2}{16}+\frac{y^2}{81}=1$$\).

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Find the equation of the ellipse with the following properties. The ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

To determine whether the vectors (-2,1,-1) and (0,3,1) are parallel, we need to compare their direction. If they have different directions, they are not parallel. the correct answer is option c) Not parallel.

To check if two vectors are parallel, we can compare their direction vectors. The direction vector of a vector can be obtained by dividing each component of the vector by its magnitude. In this case, let's calculate the direction vectors of the given vectors.

The direction vector of (-2,1,-1) is obtained by dividing each component by the magnitude:

Direction vector of (-2,1,-1) = (-2/√6, 1/√6, -1/√6)

The direction vector of (0,3,1) is obtained by dividing each component by the magnitude:

Direction vector of (0,3,1) = (0, 3/√10, 1/√10)

Comparing the direction vectors, we can see that they are not equal. Therefore, the vectors (-2,1,-1) and (0,3,1) are not parallel. Hence, the correct answer is option c) Not parallel.

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The minimum score that assures a student an A in the midterm is 87.7.

Given that the average score of a midterm exam in a large class is 69.7 and the standard deviation is 18.0. Suppose that in order to get an A in the midterm, the student's score in the test has to be at least one standard deviation above the mean.

To find the minimum score that assures a student an A in the midterm, we use the following formula: Minimum score = Mean + 1(Standard Deviation). Substituting the given values in the above formula, Minimum score = 69.7 + 1(18.0)Minimum score = 87.7. Therefore, the minimum score that assures a student an A in the midterm is 87.7.

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The statement, "A statistic is a formula calculable with data," is True. A statistic is a mathematical calculation that uses data to summarize, organize, analyze, and interpret data.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In summary, a statistic is a numerical value that represents a piece of information about a particular data set. It is calculated using mathematical formulas, statistical models, or algorithms.

The purpose of using statistics is to provide objective and accurate descriptions of the data, measure the degree of variability, identify patterns and trends, make inferences, and test hypotheses. In conclusion, statistics are used in different fields such as social sciences, business, finance, medicine, engineering, and environmental studies, to name a few, to make informed decisions based on data analysis.

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The exponential distribution may be used to predict the failure rate of certain items over time. An LED light bulb has an expected lifetime of 25000 hours. Assuming that the lifetime of the LED light bulb follows the exponential distribution, the probability that it will last more than 3 years is closest to (C) 53%. Correct answer is option C

This is because the lifetime of an LED light bulb can be estimated using the following equation : P(x > 3 years) = 1 - P(x ≤ 3 years)where x is the lifetime of the LED light bulb.If we convert 3 years to hours, we get 3 * 365 * 24 = 26280 hours. As a result, P(x ≤ 3 years) = P(x ≤ 26280 hours)

Using the formula for exponential distribution, the probability of the LED light bulb failing after 26280 hours is : Probability = 1 - e^{-λx} Where λ is the failure rate per hour and x is the length of time in hours.We can now calculate the value of λ by dividing the expected lifetime of the bulb by the total number of hours.

 λ = 1/25000 hours  This implies that the probability of the LED light bulb failing after 26280 hours is : P (x ≤ 26280 hours)

Therefore, the probability that the LED light bulb will last more than 3 years is approximately 53 percent. The Correct answer is option C

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True, x-1 is a factor of P(x) = 17x¹² + 8x⁵ – 25.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.

Given function

P(x) = 17x¹² + 8x⁵ – 25

P(1) = 0

By the Remainder Theorem,

Dividend = Divisor * Quotient + Remainder

P(x) = (x – 1). Q(x) + P(1)

P(1) = 0

P(x) = (x – 1). Q(x)

Hence, x-1 is a factor of P(x).

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The ore contains approximately 11.0% copper. Out of the 540 castings, approximately 81 castings were scrapped. In a ton of Monel metal, there are approximately 1380 lbs of nickel and 560 lbs of copper. The discounted amounts for the bills are: (a) $382.20, (b) $1,004.30. The amount due on the $144.00 bill, subject to discounts of 40% and 2% if paid within 15 days, is $86.40.

26.To calculate the percentage of copper in the ore, we divide the weight of copper (0.357 lbs) by the weight of the ore (3.249 lbs) and multiply by 100. The ore contains approximately 11.0% copper.

27. Out of the 540 castings, 15% were found defective and scrapped. To find the number of scrapped castings, we multiply 540 by 15% to get approximately 81 castings that were scrapped.

28. In a ton of Monel metal, 69% of the weight is nickel and 28% is copper. Assuming a ton is 2000 lbs, we calculate the weight of nickel as 69% of 2000 lbs, which is approximately 1380 lbs. The weight of copper is 28% of 2000 lbs, approximately 560 lbs.

29. The given bills of $390.00 and $1,024.80 are subject to a 2% discount if paid within 30 days. To find the discounted amounts, we subtract 2% of each bill from the original amounts. The discounted amount for (a) $390.00 is approximately $382.20, and for (b) $1,024.80 is approximately $1,004.30.

30. A bill for $144.00 is subject to discounts of 40% and 2% if paid within 15 days. First, we apply the 40% discount to get $86.40. Then, we apply the additional 2% discount to the discounted amount, which remains $86.40. Therefore, the amount due on the bill is $86.40.

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The second is a Uniform distribution with a minimum value of 50 and a maximum value of 100, where all values have equal frequencies.

Frequency distribution is a statistical representation of the number of occurrences of each value in a set of data. Let's consider the given set of values and describe two types of distributions for it.

Distribution Type 1: Normal Distribution with mean = 75 and standard deviation = 25.

This distribution follows a bell-shaped curve that is symmetric around the mean value of 75. The standard deviation of 25 indicates that the data is spread out with a moderate amount of variability. The highest frequency occurs at the mean value of 75, and as we move away from the mean in either direction, the frequency gradually decreases. The distribution provides information about how the values are distributed around the mean.

Distribution Type 2: Uniform Distribution U[50, 100].

This distribution is characterized by a rectangular shape, where all values have the same frequency. In this case, the minimum value is 50, and the maximum value is 100, resulting in a range of 50. The frequencies are uniform throughout the distribution, meaning that each value has the same frequency. In this case, since there are seven values in the set, each value has a frequency of 1/7.

To summarize, the given set of values can be represented by two different distributions. The first is a Normal distribution with a mean of 75 and a standard deviation of 25, which shows the overall pattern and spread of the data.

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a) Events A (even number) and B (4 or smaller) are not independent.

b) Events B (4 or smaller) and C (3 or larger) are not independent.

To determine the independence between events, we need to check if the probability of their intersection is equal to the product of their individual probabilities. Let's analyze each case:

a) Are events A (even number) and B (4 or smaller) independent?

The event A consists of the outcomes {2, 4, 6}, and the event B consists of the outcomes {1, 2, 3, 4}. To check independence, we compare the probabilities.

P(A) = 3/6 = 1/2 (since there are 3 favorable outcomes out of 6 possibilities)

P(B) = 4/6 = 2/3 (since there are 4 favorable outcomes out of 6 possibilities)

P(A ∩ B) = 2/6 = 1/3 (since there are 2 outcomes common to both A and B, which are 2 and 4)

To determine independence, we check if P(A ∩ B) = P(A) × P(B).

1/3 ≠ (1/2) × (2/3)

Since the equation does not hold, events A and B are not independent.

b) Are events B (4 or smaller) and C (3 or larger) independent?

The event B consists of the outcomes {1, 2, 3, 4}, and the event C consists of the outcomes {3, 4, 5, 6}.

P(B) = 4/6 = 2/3 (since there are 4 favorable outcomes out of 6 possibilities)

P(C) = 4/6 = 2/3 (since there are 4 favorable outcomes out of 6 possibilities)

P(B ∩ C) = 2/6 = 1/3 (since there are 2 outcomes common to both B and C, which are 3 and 4)

To determine independence, we check if P(B ∩ C) = P(B) × P(C).

1/3 ≠ (2/3) × (2/3)

Since the equation does not hold, events B and C are not independent.

In conclusion:

a) Events A (even number) and B (4 or smaller) are not independent.

b) Events B (4 or smaller) and C (3 or larger) are not independent.

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