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In a chi-square test, the expected values should be greater than or equal to 5 for each cell in the contingency table. If any expected value is less than 5, then the validity of the chi-square test is in question and a different test or a modification of the chi-square test may be necessary. Therefore, the correct answer to your question is "greater than or equal to 5".

The chi-square test is a statistical test used to determine if there is a significant association between two categorical variables. The test involves comparing the observed frequencies of the categories with the expected frequencies that would be observed if there were no association between the variables.

The expected frequencies are calculated based on the assumption that there is no association between the variables, and are obtained by multiplying the marginal totals for each row and column, and dividing by the total sample size.

In order for the chi-square test to be valid, the expected frequencies for each cell should be greater than or equal to 5. This is because the chi-square test relies on the assumption that the expected frequencies follow a normal distribution, and if the expected frequencies are too small, the distribution may not be normal and the test may not be accurate.

If any of the expected frequencies are less than 5, there is a risk of a type I error (rejecting the null hypothesis when it is actually true), and a different test or a modification of the chi-square test may be necessary.

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Answer:

\( \sqrt[3]{2y} = 6 - 4\)

2y=2³

2y=8

y=4

Answer:

15 × 5

Step-by-step explanation:

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The value of variable x in the coordinate plane is 3.

A coordinate plane is a two-dimensional plane that is created when two number lines cross. The x-axis, one of these number lines, is a horizontal number line, and the y-axis, another number line, is vertical. The coordinate plane is formed by the perpendicular intersection of these two number lines.

The reason the plane is referred to as two-dimensional is because any point on it to which you can put your finger will require two measurements to determine its location: its distance from the x-axis and its distance from the y-axis.

For negative integers, the left and bottom portions of the plane have negative x- and y-axes. The origin is the place where the number lines come together.

Given that ΑF =  FE

So if triangle DFE Transforms with F as centre and rotate E to become A

Then we will have an rectangle ACDF and E became A

In rectangle ACDF,

AC = FD

AC = 5x + 9

FD = 2(2x +6)

5x + 9 = 4x + 12

5x - 4x = 12 - 9

x = 3

Thus, the value of variable x in the coordinate plane is 3.

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Answer:

Step-by-step explanation:

The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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The probability that battery lasts more than 3 years is \(e^{-0.6 }\).

Parameter of Exponential Distribution

It is given that the average lifespan of the car battery = 5 years

⇒ μ = 5

And, we have to find the probability that the car battery lasts more than 3 years.

Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,

1/ λ = μ

⇒ λ = 1/5

Calculating the Probability

The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.

P(N>3) = 1 - P(N≤3)

P(N>3) = 1-F(4)

Here, F is the exponential distribution  for the lifespan of the car battery.

P(N>3) = 1-(1-e^(-λn))

P(N>3) = \(e^{-3/5}\)

Thus, the required probability is,

P(N>3) = \(e^{-0.6 }\)

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Answer:

60%

Step-by-step explanation:

54 /90  x 100% = 60%

Answer:

60 percent

Step-by-step explanation:

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Answer:

option 4

Step-by-step explanation:

-3.4x + 4.7 - (3 + 2.9x) = -3.4x + 4.7 - 3  - 2.9x  (combine like terms)

                                   = -3.4x - 2.9x + 4.7 - 3

                                  = - 6.3x + 1.7

If two number have same sign, add and put the common sign for the answer.

If two numbers have different sign, subtract and the answer will have the sign of the bigger number

Given:

The arrow diagram of a relation.

To find:

Whether the given relation is a function or not.

Solution:

A relation is a called a function it there exist a unique y-value or unique output value for each x-value or input value.

From the given arrow diagram it is clear that y=2 and y=-1 for x=-1.

Since we have more than one value of y at x=-1, therefore, the given relation is not a function.

Hence, the correct option is B.

To simulate drawing a tile from the Scrabble bag, you can use the random digits you created in part a, using the concepts of permutation and combination.

Here is a method you can use:

1. Assign the digits 0-41 to represent the vowels in the bag.
2. Assign the digits 42-97 to represent the consonants in the bag.
3. Assign the digits 98-99 to represent the blank tiles in the bag.

To simulate drawing a tile:
1. Generate a random number between 0 and 99.
2. If the number falls between 0 and 41 (inclusive), consider it a vowel.
3. If the number falls between 42 and 97 (inclusive), consider it a consonant.
4. If the number falls between 98 and 99 (inclusive), consider it a blank tile.

Repeat this process each time you need to simulate drawing a tile from the Scrabble bag.

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2x + 3x = 100

5x=100

x=100/5

x= 20

Therefore, 2x=2×20=40

3x=3×20=60

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Answer:

\(y=-\frac{2}{5} x+5\)

Step-by-step explanation:

\(y-3=-\frac{2}{5} (x-5)\)

Distribute \(-\frac{2}{5}\) into \((x-5):\)

\(y-3=-\frac{2}{5} x+2\)

Add \(3\) to both sides of the equation:

\(y=-\frac{2}{5} x+5\)

Answer:

0.73

Step-by-step explanation:

There are 100 total squares, and 73 are highlighted

73/100 = 0.73

If my answer is incorrect, pls correct me!

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Answer:



To find the indirect utility function, we need to solve the utility maximization problem subject to the budget constraint and express the maximum utility achieved as a function of the prices and income.

Given the utility function U = max(X, Y) and the budget constraint P₁X + P₂Y = M, we can solve for X and Y in terms of prices (P₁, P₂) and income (M).

First, let's consider the different cases:

If P₁ ≤ P₂:

In this case, the individual would choose to consume only good X. Therefore, X = M / P₁ and Y = 0.

If P₂ < P₁:

In this case, the individual would choose to consume only good Y. Therefore, X = 0 and Y = M / P₂.

Now, we can express the indirect utility function in terms of the prices (P₁, P₂) and income (M) for each case:

a) If P₁ ≤ P₂:

In this case, the individual maximizes utility by consuming only good X.

Therefore, the indirect utility function is V(P₁, P₂, M) = U(X, Y) = U(M / P₁, 0) = M / P₁.

b) If P₂ < P₁:

In this case, the individual maximizes utility by consuming only good Y.

Therefore, the indirect utility function is V(P₁, P₂, M) = U(X, Y) = U(0, M / P₂) = M / P₂.

c) and d) do not match any of the cases above.

Therefore, among the given options, the correct answer is:

a) M / max(P₁, P₂).

Answer:

Step-by-step explanation:

Given the expression

√x = √2 + 1

To get x, we will have to square both sides

(√x)² = (√2 + 1)²

x = (√2 + 1)(√2 + 1)

x = √4+√2+√2+1

x = 2+2√2+1

x = 3+2√2

Hence the value of x is 3+2√2

Using the SSA method, the maximum number of triangles that can be generate is 1.

In the given question,

In SSA case for an obtuse angle, we have to find the maximum number of triangles that can be generate with the given information.

As we know that,

There cannot be a second obtuse angle if the specified first angle is already obtuse since the triangle's angle total would be greater than 180°. As a result, there is only one way to construct the triangle, making SSA a valid congruence theorem when the supplied angle is acute.

So the maximum number of triangles that can be generate is 1.

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a) To solve the upper nonlinear problem using the Kuhn-Tucker conditions, we apply the necessary conditions for optimality, which involve Lagrange multipliers and inequality constraints. b)To solve the problem using GAMS, code needs to be written that represents the objective function and constraints.

To solve the upper nonlinear problem using the Kuhn-Tucker conditions, we apply the necessary conditions for optimality, which involve Lagrange multipliers and inequality constraints. The Kuhn-Tucker conditions are a set of necessary conditions that must be satisfied for a point to be a local optimum of a constrained optimization problem. These conditions involve the gradient of the objective function, the gradients of the inequality constraints, and the values of the Lagrange multipliers associated with the constraints.

In this case, the objective function is given as minz = (y-x)^2 + xy + 2x + 3y, and we have several constraints: x + y = 103, x + y ≥ 16, -x - 3y ≤ -20, x ≥ 0, and y ≥ 0. By using the Kuhn-Tucker conditions, we can set up a system of equations involving the gradients and the Lagrange multipliers, and then solve it to find the optimal values of x and y that minimize the objective function while satisfying the constraints. This method allows us to incorporate both equality and inequality constraints into the optimization problem.

Regarding the second part of the question, to solve the problem using GAMS (General Algebraic Modeling System), GAMS code needs to be written that represents the objective function and constraints. GAMS is a high-level modeling language and optimization solver that allows for efficient modeling and solution of mathematical optimization problems. By inputting the objective function and the constraints into GAMS, the software will solve the problem and provide the optimal values of x and y that minimize the objective function while satisfying the given constraints. GAMS provides a convenient and efficient way to solve complex optimization problems using a variety of optimization algorithms and techniques.

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Answer & Step-by-step explanation:

a. 4x + 3 {sum means add the numbers together}

b. \(\frac{5}{9 + y}\)  {quotient means divided by}

c. \(\frac{7}{y}\)

The maximal value of the sample covariance is \(sx*sy\), which represents the highest correlation possible between X and Y.

The formula for the sample covariance between X and Y is given by \(cov(X,Y) = (1/(n-1)) Σ (xi - xmean)(yi - ymean)\). The maximal value for the sample covariance is equal to the product of the standard deviations of X and Y, which can be calculated using the formula \(sx*sy = (1/(n-1)) Σ (xi - xmean)^2 * (1/(n-1)) Σ (yi - ymean)^2\). Using the Cauchy-Schwarz Inequality, we can know that \(cov(X,Y) < = sx*sy\). Therefore, the maximal value of the sample covariance is sx*sy, which represents the highest correlation possible between X and Y.

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The radian measure of the angle at the center of the circle is approximately 1.6623 radians.

We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.

To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.

The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)

Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.

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Answer:

146304 marbles

Step-by-step explanation:

We do not need to worry about the color part, at least right now

One box contains 576 marbles

To find how many are in 2 boxes we would do 576 * 2

To find 254, we would do 576 * 254

Now, I would suggest using lattice multiplication here. If you do not know how to do that, long multiplication works fine.

I can't show that here, but I can show the answer:

576 * 254 = 146304

So, there are 146304 marbles is 254 boxes

Step-by-step explanation:

The slope of the line is - 5, the equation will be y=-5x-1.

y+5x=-1

Answer:

the second choice

Step-by-step explanation:

The last two choices could not be correct, because it would need a dashed line.  The line under the greater than or less than symbol mean  that the line is included in the answer and it will be a solid line like you see in the picture.  For both of the top two answers the slope that they y intercept is correct.  You just have to decide is the symbol will be greater than or equal to or less than and equal to.  

If we put 0 in x for in the form y = mx + b, what would y be?

y = 1/3 x - 1

y = 1/3(0) - 1

y = -1

The ordered pair is (0,1).  That is the part that is shaded so that shows us that the second answer is correct.

The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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