A bag of marbles has 4 Red and 3 Green marbles. You pick from the bag, replace the marble and then pick again. What is the probability of picking red both times?

A. 16/49
B. 12/42
C. 4/7

Answer:

x- intercept = 2, y- intercept = - \(\frac{8}{7}\)

Step-by-step explanation:

To find the x- intercept, let y = 0 in the equation and solve for x

4x - 7(0) = 8 , that is

4x = 8 ( divide both sides by 2 )

x = 2 ← x- intercept

To find the y- intercept , let x = 0 in the equation and solve for y

4(0) - 7y = 8, that is

- 7y = 8 ( divide both sides by - 7 )

y = - \(\frac{8}{7}\) ← y- intercept

Answer:

f(-1) = -1

Step-by-step explanation:

f(x) = -x^2

Let x = -1

f(-1) = - ( -1) ^2

       = -1

Answer:

They complete the hill in 8 hours

Step-by-step explanation:

We will need to solve these equations with a system of equations, so we need to isolate one variable in one of the equations and then replace it with another equation. After this, this means that Beatrice alone would construct the hill in 24 hours and Charlie 40. So, after finding the value A we will need to add A with B and C. This would get us \(0.125h^{-1}\). We will then divide  \(\frac{1}{0.125h^{-1}}\). This will leave with 8h.

A= 7/120h

C=1/40h

B= 1/24h

Answer:

Assume we want to find the solution to this system of equations.

The solution is (2,-2)

Step-by-step explanation:

We can find the solution either mathematically or by graphing.  I'll do both.

Math:

Rearrange:

-2x-6y=8

-6y=8 +2x

y = -(1/3)x -(4/3)

---

Now use this expression of y in the second equation:

-6x-6y=0

-6x-6(-(1/3)x -(4/3)) =0

-6x + 2x +8 =0

-4x = - 8

x = 2

---

Use x = 2 in the first equation to find y:

y = -(1/3)x -(4/3)

y = -(1/3)*(2) -(4/3)

y = -(2/3) -(4/3)

y = -(6/3) or -2

The solution is (2,-2)

===============

Graphing:

See attached graph.

Answer:

Step-by-step explanation:

-2x - 6y = 8

6x + 6y = 0

4x = 8

x = 2

-4 - 6y = 8

-6y = 12

y = -2

(2, -2)

The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).

Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The radius of gyration Rg is defined as follows.

Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.

R(mean) is the mean position vector of all monomers.

Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).

Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).

The ratio R²/Rg² is given by R²/Rg² = L^(D-2).

When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.

This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.

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The correct statement is "the mean of the residuals from least-squares regression is 0".

In order to calculate the mean value we have to adding all numbers in the data set and then dividing by the number of values in the set.

Here we need to find the correct statement from the given statement.

In order to find the correct statement we must know the definition of least-squares regression.

In statistics, the term least-squares regression is defined as  the line that makes the vertical distance from the data points to the regression line as small as possible.

Consider that If the data shows a leaner relationship between two variables, then the line that best fits this linear relationship is known as a least-squares regression line, it mean this minimizes the vertical distance from the data points to the regression line.

Based on the definition, we have identified the option (a) is correct.

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The point slope form finds the equation of a straight line that passes through a given point and is inclined to the x-axis. Each point on a line must satisfy the line's equation. Two-variable linear equations symbolize lines. The point slope formula is utilized when we know the line's slope and a point. The next section explains the point slope form and how to calculate its formula.

The equation of a straight line that is inclined at a particular angle to the x-axis and passes at a given point may be found by using the point slope form. This form is used to get the equation of the line. An equation may be said to be the equation of a line if it can be shown to be fulfilled by every point along the line. This indicates that a line is represented by a linear equation that has two variables. Whereas the Point slope formula is only used in situations in which both the slope of the line and a point on the line are known. In the next part, let's get more in-depth knowledge about the point slope form as well as how to derive the formula that is used to express the point slope form.

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Answer: 13 Hours

Step-by-step explanation:

1. 270/9 = 30 dollars per hour

2. 390/30 = 13 hours

The correlation coefficient that represents the strongest relationship between two variables is -0.75.

In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.

The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.

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We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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a. Choosing the number 9 is a dominated strategy, b. Choosing the number 37 is a dominated strategy, c. The range of numbers for which each number in the range is closer to the winning number than 30 is from 21 to 39, d. The set of best responses for Lisa if she knew that all of her classmates would submit the number 24 is an empty set.

e. The symmetric Nash equilibrium in this game is the number 25.
f. The dominated strategies are choosing the numbers 9 and 37.
g. If Lisa believes that none of her classmates will play the dominated strategies found in part f, the strategies that are never a best response for Lisa are choosing the numbers 9 and 37.
h. The rationalizable strategies in this game are choosing any number between 21 and 39.

Explanation:
a. To show that choosing the number 9 is a dominated strategy, we need to compare the payoffs of choosing 9 with the payoffs of choosing any other number. If we look at the payoff for choosing 9, it is $50 if 9 is closer to the winning number than (1/2X+10), and $0 otherwise. However, if we choose any number greater than 9, our payoff will be $50 if that number is closer to the winning number than (1/2X+10), and $0 otherwise. Therefore, choosing 9 is always dominated by choosing a number greater than 9.
b. Similarly, to show that choosing the number 37 is a dominated strategy, we compare the payoffs of choosing 37 with the payoffs of choosing any other number. The payoff for choosing 37 is $50 if 37 is closer to the winning number than (1/2X+10), and $0 otherwise. However, if we choose any number less than 37, our payoff will be $50 if that number is closer to the winning number than (1/2X+10), and $0 otherwise. Therefore, choosing 37 is always dominated by choosing a number less than 37.
c. If Lisa knows that all of her classmates would submit the number 30, she wants to choose a number that is closer to the winning number than 30. The range of numbers for which each number in the range is closer to the winning number than 30 is from 21 to 39. If Lisa chooses any number between 21 and 39, she will have a higher payoff than if she chooses 30.

d. If Lisa knows that all of her classmates would submit the number 24, there is no best response for her. Choosing any number will not give her a higher payoff than choosing 24.
e. To find a symmetric Nash equilibrium in this game, we need to find a number that is a best response to everyone else submitting that same number. The number 25 is a best response to everyone else submitting 25 because it is the closest number to (1/2X+10). Therefore, the symmetric Nash equilibrium in this game is the number 25.
f. The dominated strategies in this game are choosing the numbers 9 and 37. These strategies are dominated because there are always other numbers that will give a higher payoff.
g. If Lisa believes that none of her classmates will play the dominated strategies found in part f, the strategies that are never a best response for Lisa are choosing the numbers 9 and 37. This is because there will always be other numbers that give a higher payoff.
h. The rationalizable strategies in this game are choosing any number between 21 and 39. These strategies are rationalizable because they are best responses to the belief that all of Lisa's classmates will submit the number 30. By choosing a number in this range, Lisa ensures that she has a higher payoff than if she chooses any other number.

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Using permutation there are 116,280 potential combinations of 4 employees that might go to the 4 conferences.

The number of selections possible for the first problem, where 4 employees are selected to participate in specialized training from a group of 20 employees, can be found using the combination formula:

C(20, 4) = 20! / (4! × (20 - 4)!) = 4845

Therefore, there are 4845 possible selections of 4 employees for the specialized training program.

For the second problem, we need to select 4 employees to attend 4 different conferences.

The order of selection matters, since each employee, will be attending a different conference.

Therefore, we need to use the permutation formula:

P(20, 4) = 20! / (20 - 4)! = 20! / 16! = 20 × 19 × 18 × 17 = 116280

Therefore, there are 116,280 possible selections of 4 employees to attend the 4 different conferences.

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Your answer should be $33.

Explanation:

It isnt $33.50 yet, so you can't round it up to $34.

Answer:

480 calories

Step-by-step explanation:

(240/30)=(400/50)=(x/60)

Therefore

(240/30)=(x/60)

8=(x/60)

8*60=x

480=x

Answer:

rs 1872

Step-by-step explanation:

1% of buying price= 1560÷100= rs 15.60

SP= 15.6x 120%= rs 1872

Answer:

Step-by-step explanation:

Solution,

Here,         CP=Rs.1560

                   P=20%

                   Profit amount= P% *CP

                                            100

           = 20% *Rs.1560

              100

= Rs.312

Now,

SP=CP+P

   =Rs.1560+Rs.312

   = Rs. 1872 is the answer

∴SP of the article is Rs.1872

Given:

Book club A charges $20 for membership and $2 per book rental.

Book club B charges $10 for membership and $3 per book rental.

To find:

The number of books for which the cost be the same at both book clubs.

Solution:

Let x be the number of books.

Book club A charges $20 for membership and $2 per book rental. So, the total cost is

\(C_1=20+2x\)             ...(i)

Book club B charges $10 for membership and $3 per book rental. So, the total cost is

\(C_2=10+3x\)            ...(ii)

Equating (i) and (ii), we get

\(10+3x=20+2x\)

\(3x-2x=20-10\)

\(x=10\)

The total cost is

\(C_1=20+2(10)\)

\(C_1=20+20\)

\(C_1=40\)

Therefore, the total cost at both book clubs are same for 10 rental books and that cost is $40.

Answer:

$368

Step-by-step explanation:

What is 50% of $736?

50% = \(\frac{50}{100}\) = \(\frac{1}{2}\)

We Take

736 x  \(\frac{1}{2}\) = $368

So, 50% of $736 is $368.

For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error decreases as the margin of error increases.

The square root of the variance for the given set of numbers is what the standard deviation examines. It is employed to compute a confidence interval for making judgments (such as accepting or rejecting a hypothesis).

Here, the population standard deviation, and level of significance are the same.

As the margin of error increased.

So, with the increase in the value of the margin of error, there will surely decrease in the value of the sample size

\($$\begin{aligned}&\mathrm{MOE}_\gamma=z_\gamma \times \sqrt{\frac{\sigma^2}{n}}\\&\begin{aligned}\mathrm{MOE} & =\text { margin of error } \\\gamma & =\text { confidence level } \\z_\gamma & =\text { quantile } \\\sigma & =\text { standard deviation } \\n & =\text { sample size }\end{aligned}\end{aligned}$$\)

As the margin of error is in the denominator position in the sample size formula

Hence with an increase in the margin of error sample size decreases.

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Answer:

B

Step-by-step explanation:

Taking a look at the orientation of the image and post-image, you can see that the rotation done was clearly 90 degrees counterclockwise. It was also shifted down by 3 units, and moved to the left by 2 units, mat the correct answer is choice b. Hope this helps!

Answer:

Hope this helps

Step-by-step explanation:

9. 18

10.36

11. 14

12. 6

13. 12

14. 22

15. 8

16. 3

Answer:

9. 6 (3) = 18

10. 12 (3) = 36

11. 3 (3) + 5 = 14

12. 4 (3) -6 = 6

13. 15 - 3 = 12

14. 7+5(3)= 22

15. 24/3= 8

16 27/3 (3) = 3

Answer:

  B.  False

Step-by-step explanation:

In order for segments to form a triangle, the sum of the lengths of the shorter two must be at least as much as the length of the longest one.

The sum of the shorter two is 6 + 5 = 11. This is not as great as 12, the length of the longest one, so no triangle can be formed.

the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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By solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

A mathematical statement known as an equation is made up of two expressions joined by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the number of the variable x is 7.

So, calculate as follows:

Let g represent giraffes and o represent ostriches.

g + o = 70 ...(1)

4*g + 2*o = 200  ...(2)

g = 70 - o, according to equation 1, therefore we may enter that number in place of g in equation 2 to obtain:

4*g + 2*o = 200

4*(70-o) + 2*o = 200

280 - 4o + 2o = 200

-2o = 200 - 280

2o = 80

o = 80/2

o = 40

Ostriches are 40 then giraffes will be:

70 - 40 = 30

Therefore, by solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

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FALSE. The number of degrees of freedom in cross-tabulation data is calculated by subtracting 1 from the product of the number of rows and columns.

Therefore, in this case, the number of degrees of freedom would be (3-1) x (4-1) = 6.

Degrees of freedom refer to the number of independent pieces of information in a data set, which can be used to calculate statistical significance and test hypotheses.

In cross-tabulation, degrees of freedom indicate the number of cells in the contingency table that are not predetermined by the row and column totals.

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Answer:

-6

Step-by-step explanation:

put x=0

(0+3)(-0-2)=y

y=-6

Answer:

35 cm

Step-by-step explanation:

Use the pythagorean theorem, a² + b² = c², where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse:

Plug in the values we know:

a² + b² = c²

12² + b² = 37²

Solve for b (the other leg):

12² + b² = 37²

144 + b² = 1369

b² = 1225

b = 35

So, the length of the other leg of the triangle is 35 cm

Answer:

1. 45

2. 105

3. 95

4. 85

Step-by-step explanation:

For problems 1 and 4:

Consecutive angles are supplementary in a parallelogram, which means they equal 180.

180 - 135 = 45

180 - 95 = 85

For problems 2 and 3:

Opposite angles are congruent or equal each other in a parallelogram,

ANSWER

28.285 units

EXPLANATION

We are given the square EFGH and we need to find the perimeter.

The perimeter of a square is given as:

P = 4 * L

P = 4L

where L = length of the side of the square

To find the length of the side of the square, we have to find the distance between a pair of adjacent vertices of the square.

Let us pick E(0, 5) and F(5, 0).

The distance between the two points is:

where (x1, y1) = (0, 5)

(x2, y2) = (5, 0)

Therefore, the length of the square (distance between the two points) is:

Therefore, the perimeter of the square is:

P = 4 * 7.071

P = 28.284 units