Let X and Y be independent x² random X 1. Show that for sufficiently large m, m variables with m, n degrees of freedom. approximately normal (1, 25 m

If two variables x and y are directly proportional, then as x rises, y will rise accordingly, and as x falls, y will fall accordingly. So, y=k x can be written.

The equation for k=y/x is k=b/p.

the proportional relationship between two variables that is always constant.

Constant ratio, constant rate, constant of variation, or even changing rate are examples of proportionality constants.

When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant.

The slope is another name for the constant rate of change.

The rate of change for linear functions will be constant.

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Answer please mark as brainliest:

Allstars typically have the tallest players.

Step-by-step explanation:

To determine which team typically has the tallest players, we can compare the measures of center for each team. The measures of center we can use are the mean and median.

Using a calculator or a spreadsheet, we can calculate the mean and median for each team:

Allstars mean: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 67.1 inches

Allstars median: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.

Champs mean: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 66.4 inches

Champs median: arrange the heights in order from smallest to largest: 58, 60, 60, 62, 65, 67, 67, 68, 69, 69, 70, 70, 70, 75. The median is the middle value, which is 67 inches.

Based on the measures of center, we can see that the Allstars have a higher mean and median height than the Champs. Therefore, we can conclude that the Allstars typically have the tallest players.

Answer:14,641

Step-by-step explanation: 11x11x11x11=14,641 hope this helps :)

Answer:

I just did this question its 14,641

Step-by-step explanation:

Answer:

Step-by-step explanation:

2(8)+4=(8)f equals 16+4=(8)f, which equals 20=8f

Answer:

20

Step-by-step explanation:

Answer:

I prefer A is the option that suits this question

(i) Marginal cost function: C'(x) = 75 - 0.1x.

(ii) Marginal cost at a production level of 500 tanks per week: $25.

(iii) Interpretation:

Producing an additional tank at a production level of 500 tanks per week incurs an additional cost of $25.

(iv) Exact cost of producing the 501st tank:

Substitute x = 501 into the cost function C(x) to calculate the exact cost.

We have,

a) The derivative or differentiation is a fundamental concept in calculus that measures the rate of change of a function with respect to its independent variable.

It allows us to determine the slope or rate of change of a function at any point, providing valuable information about its behavior.

Applications of the derivative are widespread across various fields, including physics, economics, engineering, and more.

b) Given the cost function C(x) = 10000 + 75x - 0.05x², we can find the marginal cost function by taking the derivative of C(x) with respect to x.

(i) Marginal cost function:

C'(x) = 75 - 0.1x

(ii) Marginal cost at a production level of 500 tanks per week:

To find the marginal cost at a production level of 500 tanks per week, we substitute x = 500 into the marginal cost function:

C'(500) = 75 - 0.1(500)

= 75 - 50

= 25

The marginal cost at a production level of 500 tanks per week is $25.

(iii) Interpretation:

The result from part (ii) indicates that producing an additional tank, beyond the current production level of 500 tanks per week, would result in an increase in cost by $25.

It represents the cost incurred by the company to produce one more tank at this particular level of production.

(iv) Exact cost of producing the 501st tank:

To find the exact cost of producing the 501st tank, we substitute x = 501 into the cost function C(x):

C(501) = 10000 + 75(501) - 0.05(501)²

Calculating this expression will give the exact cost in dollars of producing the 501st tank.

Thus,

(i) Marginal cost function: C'(x) = 75 - 0.1x.

(ii) Marginal cost at a production level of 500 tanks per week: $25.

(iii) Interpretation:

Producing an additional tank at a production level of 500 tanks per week incurs an additional cost of $25.

(iv) Exact cost of producing the 501st tank:

Substitute x = 501 into the cost function C(x) to calculate the exact cost.

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3x^2 - x - 2

What are some ways to solve an equation?

Different ways to solve equations. We have 4 ways of solving one-step equations: Adding, Substracting, multiplication, and division. If we add the same number to both sides of an equation, both sides will remain equal.

How do you evaluate an equation?

= (x - 1)(3x + 2)

= 3x^2 + 2x - 3x - 2

= 3x^2 - x - 2

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Answer:

man can u send the pic of the diagram I will solve it

Answer:

2x+5 is the expression

Answer:

The expression is 2x + 5

Answer:

\(LS = 63\)

Step-by-step explanation:

Given

\(LS = 14x - 21\)

\(LH = 15\)

\(HS = 8x\)

Required

Determine the length of LS

Since H is between L and S, then

\(LS = LH + HS\)

Substitute 14x - 21 for LS, 15 for LH and 8x for HS

\(14x - 21 = 15 + 8x\)

Collect Like Terms

\(14x - 8x = 21 + 15\)

\(6x = 36\)

Divide both sides by 6

\(x = 6\)

Substitute 6 for x in \(LS = 14x - 21\)

\(LS = 14(6) - 21\)

\(LS = 84 - 21\)

\(LS = 63\)

Hence, the length of LS is 63 units

The complete question is

"Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each.

Explain what your solution means using complete sentences. How many t-shirts can she buy? Focus your answer on the difference between an equation and an inequality."

The expression that represents the number of t-shirts that Lisa can purchase is 14x + 58 = 150. The number of shirts that can be bought is 6.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each.

Let the number of shirts be x. The expression will be:

= (14 × x) + 58 = 150

14x + 58 = 150

Solving the expression will be:

14x + 58 = 150

14x = 150 - 58

14x = 92

x = 92/14

x = 6.5

The number of shirts that can be bought is 6.

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Answer:

No, Marco is not correct. The number does not actually repeat because after each 9 there is an additional 6 before the next 9. The number is not a rational number.

Step-by-step explanation:

Answer:Marco is not correct 69, and 669, and 6,669 are not the same a repeating decimal must have a digit or a group of digits that repeat this is not a rational number.

Step-by-step explanation:

Answer:

when v increases w tends to increase

Step-by-step explanation:

To start, you would need the relevant data, such as the number of successful attempts and the total number of trials for each group or time interval. Then, you can perform a statistical test, like the chi-square test or a two-proportion z-test, to evaluate if the difference in probability is statistically significant at the 0.05 level. If the resulting p-value is less than 0.05, it would indicate a significant difference in the probability of solving the puzzle within one minute.

To answer your question, we would need to conduct a statistical analysis to compare the probability of solving the puzzle within one minute in two different groups or conditions. We would also need to establish a null hypothesis and an alternative hypothesis and use a statistical test such as a t-test or a chi-square test to determine whether the observed difference in probability between the two groups is statistically significant at the 0.05 level, which means that there is less than a 5% chance that the observed difference is due to chance alone. Without more information about the specific groups or conditions being compared, it is difficult to provide a definitive answer.

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Answer:

x=200

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

200/5-30=10

Answer :

Identity Property.

Step-by-step explanation:

Two matices are given to us , which are ,

Let A = \(\left[\begin{array}{ccc} 6 & -8 & 1 \\ 0 & -2 & -19 \end{array} \right] \) .

Let B = \(\left[\begin{array}{ccc} 0 & 0& 0 \\ 0 & 0 & 0 \end{array} \right] \) .

Here since all the elements of Matrix B are 0 , its a null matrix . Hence adding any matrix to it will give the same matrix which is added . This property is called as Identity Property .

Adding both A and B ,

\(\implies A + B = \left[\begin{array}{ccc} 6 & -8 & 1 \\ 0 & -2 & -19 \end{array} \right] + \left[\begin{array}{ccc} 0 & 0& 0 \\ 0 & 0 & 0 \end{array} \right] \)

\(\implies A + B = \left[ \begin{array}{ccc} ( 6+0) & (-8+0) & (1+0) \\ (0+0) & (-2+0) & (-19 + 0 ) \end{array}\right] \)

\(\red{\implies A + B = \left[\begin{array}{ccc} 6 & -8 & 1 \\ 0 & -2 & -19 \end{array} \right] }\)

Hope it helped !

Answer:

b. identity property

Step-by-step explanation:

EDGE 2021 AQR QUIZ

The Kanizsa triangle illusion helps us understand that our perceptual experiences are not simply the sum of the individual sensory inputs, but rather the result of a complex and variable process of perceptual organization.

Gestalt is a German word meaning "shape" or "form," and in psychology, it refers to a set of principles that describe how people perceive and organize sensory information into meaningful wholes. These principles propose that the whole is greater than the sum of its parts, and that we tend to organize our perceptual experiences into coherent, holistic forms rather than isolated, unrelated sensations.

Experimental examples such as the Necker cube, visual cliff, and others help demonstrate principles of perceptual organization by highlighting how our minds naturally try to impose structure and order on sensory input. For example, the Necker cube is a two-dimensional drawing that can be perceived as a cube that can be viewed from different angles. However, as one stares at the image, it appears to flip back and forth between different possible interpretations. This phenomenon illustrates the Gestalt principle of figure-ground, which describes how we tend to perceive objects as being distinct from their surrounding context.

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A zero is a value that represents nothingness or the absence of a value, but it is still considered a constant because it does not change in value. The constants in the expression 12x - 3.7 - 8y + one-third are -3.7 and one-third, so the answer is option C.

The constants are terms that have fixed values and do not have variables. In this expression, -3.7 and one-third are the only terms that are constants.

A constant is a numerical or alphabetic value that does not vary in a given equation. A variable is a quantity that can change in magnitude or value. The following are some examples of constants:π, the ratio of the circumference of a circle to its diameter, is an irrational number with a value of roughly 3.14159.e is an irrational number that represents the base of the natural logarithm.

Its value is roughly 2.71828.

A zero is a value that represents nothingness or the absence of a value, but it is still considered a constant because it does not change in value.

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Answer:

y = |x| is a parent function

y = |x| - 7 is a translation of the parent function vertically by 7 points down

The shape is same, just the entire graph has shifted down.

It's translated edition of parent function y=|x|

If we translate it 7units down then the function is

So

Everything is same

Just the graph shifted 7units downwards

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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The a = 0.Substituting the values of a, b, and c in the general equation, we get:y = 0x² + 2x + 3The quadratic function is:y = 2x + 3Answer: The quadratic function is y = 2x + 3.

The given table illustrates the values of a quadratic function. Here is how you can find the quadratic function:Step 1: Write the general form of a quadratic function y = ax² + bx + c, where y is the dependent variable and x is the independent variable. a, b, and c are constants that affect the shape and position of the parabola.Step 2: Substitute the values from the table for x and y to form a system of equations.Step 3: Solve the system of equations to find the values of a, b, and c. Once you have found these values, substitute them into the quadratic equation to get the quadratic function.

The given table is as follows:x   |  0   |  2   |  4  |   6y   |  3   |  1   |  -1  |   -3Step 2:Form a system of equations using the values in the table. Here are the equations:y = a(0)² + b(0) + cy = a(2)² + b(2) + cy = a(4)² + b(4) + cy = a(6)² + b(6) + cStep 3:Solve the system of equations.Using the first equation, y = c. Hence, we have:y = 0²a + 0b + c3 = cThe value of c is 3.Using the second equation, we have:y = 2²a + 2b + 3y = 4a + 2b + 3Subtracting the two equations, we get:- 2a - b = - 2a + b = 2b = 4Therefore, b = 2.Substituting the values of b and c into the first equation, we get:3 = a(0)² + 2(0) + 3

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The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

What is rectangle short answer?

the points (-1 , 2) and (3 , 2 ) form one the of the rectangle w =     \(\sqrt{( 3 + 1 )^{2} + ( 2 - 2 )^{2} }\)

= \(\sqrt{4^{2} + 0 }\)

= √ 16

= 4

The length can be obtained by finding distance between the points (-1,2) and ( -1, - 5)  = \(\sqrt{( -1 -2 )^{2} + ( -5 + 1)^{2} }\)

                 = \(\sqrt{(-3)^{2} + ( -6)^{2} }\)

                 = √9 + 36

                  = √45 = 3√5

The perimeter of the rectangle is: P = 2( w + L) = 2( 4 + 3√5) ⇒ 8 + 6√5 unit

The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

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The probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053.

We can use the concept of combinations.

The total number of ways to choose 4 elk out of 24 is given by the combination formula:

C(24, 4) = 24! / (4!(24-4)!) = 10,626

Now, we need to consider the number of ways to choose 3 tagged elk out of the 8 tagged elk and 1 untagged elk. The number of ways to do this is given by:

C(8, 3) * C(1, 1) = 8! / (3!(8-3)!) * 1! / (1!(1-1)!) = 56

Therefore, the probability that 3 out of the 4 captured elk have been tagged is:

P = (Number of ways to choose 3 tagged elk out of 8 tagged elk and 1 untagged elk) / (Total number of ways to choose 4 elk out of 24)

P = 56 / 10,626

Calculating this division gives us the probability:

P ≈ 0.0053

So, the probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053 .

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The confidence level in constructing a confidence interval determines the probability that the interval contains the true population parameter. It represents the level of certainty or confidence we have in the accuracy of our estimate.

When constructing a confidence interval, the confidence level is typically chosen in advance and expressed as a percentage, such as 95% or 99%. This level corresponds to the proportion of intervals, calculated from repeated sampling, that would contain the true population parameter. For example, a 95% confidence level means that if we were to construct 100 different intervals using the same method, approximately 95 of them would contain the true parameter. The remaining 5 intervals would not.

A higher confidence level leads to a wider interval, as we need to be more certain about capturing the true parameter. Conversely, a lower confidence level results in a narrower interval, but with a lower level of certainty. It is important to choose an appropriate confidence level based on the desired trade-off between precision and reliability of the estimate.

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Answer:

Step-by-step explanation:

plug in the points minus the constant for 7=3*4 + x and you will get -5 for your constant  

y=3x - 5

Answer:

y = 3x - 5

Step-by-step explanation:

7 = 3(4) + b

---> b = -5

y = 3x - 5

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

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Using Normal distribution formula,

The chance that the review will take longer than 30 minutes is 6.6%..

We have given that,

The time taken by a search committee review the application for certain job .

Mean (μ) = 15 minutes

standard deviations (σ) = 10 minutes

The time review is Normally distributed,

Using Normal distribution formula,

Z =( x - μ)/σ

where, Z ---> Z-value

x---> individual value

μ--> population mean

σ---> standard deviations

we have , x = 30

plugging all the known values in above formula we get,

Z = (30 - 15) / 10 = 15/10

=> Z = 1.5

For Z-score of 1.5 , the p-value is 0.9332

This is Probability that review wI'll take exactly or less than 30 minutes and its area under the curve shades left side .

but we have to calculate probability that the review will take longer than 30 minutes i.e ,

P( x > 30 ) = 1 - P(x= 30)

=> P( x > 30 ) = 1 - 0.9332 = 0.668

Hence, required probability or chance is 6.6%..

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Probability when a student is selected at random to be the captain. Probability the captain has a blue shirt is unlikely. Probability the captain has a red shirt is impossible. Probability the captain has a blue or white shirt is likely certain.

The total number of students is 15.

4 students are wearing blue shirt.

11 students are wearing white shirt.

10 students are wearing yellow shirt.

Only any one student can be captain.

The total outcomes are 25.

Probability that the student has blue shirt B is,

Total favorable outcomes = 4

P(B) = 1/25.

Probability that the student has red shirt R is,

Total favorable outcomes = 0

P(B) = 0/25.

P(B) = 0

Probability that the student has blue or white shirt B and W is,

Total favorable outcomes = 15

P(B&W) = 15/25.

P(B&W) = 3/5.

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Answer:

Two real world situations are shown below.

Step-by-step explanation:

Initial population of a certain bacteria is 1 thousand and the population doubles in each hour. So, population of bacteria (in thousands) after x hours is

\(f(x)=1(2)^x\)

\(f(x)=(2)^x\)

A person invests 1 lakh rupees in shares and the amount is twice at the end of each year. So, total amount (in lakhs) after x years is

\(f(x)=1(2)^x\)

\(f(x)=(2)^x\)