Name an appropriate method to solve each system of equations. Then solve the system.

-5 x+2 y=13

2x+3 y=-9

The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:

$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$

We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:

$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$

Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.

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The above function is a Discontinuity function. A Discontinuity function is one which is removable as x tends towards an integer 'a'.

Thus in the circled region, as shown in the image below, as the function tends to -4 in either direction (left or right), the limit of the function is 2.

Answer:

41.616

Step-by-step explanation:

The scale of the drawing is given as follows:

1 : 4.5.

The scale of the drawing is obtained applying the proportions in the context of this problem.

The scale is defined as the division of the drawn length by the actual length.

The lengths are given as follows:

90/20 = 4.5, hence the scale of the drawing is given as follows:

1 : 4.5.

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Answer:

9

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

Step-by-step explanation:

11x - 47 = 6x - 2                  Corresponding angle. Add 47 to both sides

11x = 6x + 47 - 2                 Combine

11x = 6x + 45                      Subtract 6x from both sides

11x - 6x = 45                       Combine

5x = 45                              Divide by 5

5x/5 = 45/5

x = 9

The set of survey results that is most likely to show biased results for people who buy food at the mall is Lewie's survey.

Lewie's survey samples only every fifth person leaving the mall's main entrance, which means that it only captures a small percentage of the total number of mall visitors. Additionally, by only surveying people leaving the main entrance, Lewie's survey may not capture people who enter and exit the mall through other entrances or exits and may also miss those who don't leave the mall after buying food. As a result, Lewie's survey may not accurately represent the total number of people who buy food at the mall and may lead to biased results.

On the other hand, Kelvin's survey samples every other person leaving the food area. This method captures a larger percentage of the total number of people who buy food at the mall and is more likely to provide a more accurate representation of the total number of people who buy food at the mall.

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Answer:

A. Kelvin’s because he surveyed people leaving an area where food is sold

Step-by-step explanation:

Two integer variables x and y, prompts the user to enter values for them using the Scanner class, and performs addition, subtraction, multiplication, and division operations on those variables:

import java.util.Scanner;

public class VariableOperations {

   public static void main(String[] args) {

       Scanner scanner = new Scanner(System.in);

       System.out.print("Enter the value for x: ");

       int x = scanner.nextInt();

      System.out.print("Enter the value for y: ");

       int y = scanner.nextInt();

       // Addition

       int addition = x + y;

       System.out.println("Addition: " + addition);

       // Subtraction

       int subtraction = x - y;

       System.out.println("Subtraction: " + subtraction);

       // Multiplication

       int multiplication = x * y;

       System.out.println("Multiplication: " + multiplication);

       // Division

       if (y != 0) {

           double division = (double) x / y;

           System.out.println("Division: " + division);

       } else {

           System.out.println("Cannot divide by zero.");

       }

   }

}

This code prompts the user to enter values for x and y, performs the four basic arithmetic operations, and displays the results on the screen.

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The sum of roots in the given equation is (2 - √3). The correct answer would be an option (A) (2 - √3).

A sum of a quadratic equation is a number that can be evaluated for the variable to provide a true number statement.

For an equation of the form ax² + bx + c = 0, the sum of root for x is given by:

α + β = -b/a

The given equation is:

(2 - √3)x² - (7 - 4√3)x + (2 + √3) = 0

We can solve for x by using the sum of root formula, which states that

α + β = -b/a

Here, a = 2 - √3, b = -(7 - 4√3), and c = 2 + √3. Substituting these values into the formula, we get:

(7 - 4√3)/(2 - √3)

(7 - 4√3)/(2 - √3) × (2 + √3)/(2 + √3)

(7 - 4√3)(2 + √3) = 14 +7√3 - 8√3 -12

(2 - √3)

Thus, the sum of roots in the given equation is (2 - √3).

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The complete question would be as:

What is the sum of roots in this equation (2 - √3)x²- (7 - 4√3)x + (2 + √3) = 0?

A. (2 - √3)

B. (2 +√3)

C. 2

D.√3

The sampling distribution is illustrated below.

Based on the information given, the population is illustrated as 1, 4, 7. The sample without replacement will be:

Sample Mean

1 and 4. 2.5

1 and 7. 4

4 and 7. 5.5

The population mean will be:

= (1 + 4 + 7)/3

= 4

The sample mean is an unbiased estimator of the population mean.

The sampling with replacement illustrates that the mean will be:

= 36/9 = 4

Also, when n = 3, the number of samples will be:

= 3³ = 27

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The expression is factorized to give x(x+ 12) + 8( y + 12)

From the information given, we have that the expression as;

(x+y)²+8(x+y)+12

Now, expand the bracket, we get;

(x + 2) (x+2) + 8x + 8y + 12

expand the squared bracket, we get;

x² + 2x + 2x + 4 + 8x + 8y + 12

Now, collect like terms

x² 2x + 2x + 8x + 8y + 4 + 12

Add the collected like terms, we get;

x² + 12x + 8y + 16

Now, let's factorize in airs by grouping, we get;

(x² + 12x) + (8y + 16)

Factor the common terms

x(x+ 12) + 8( y + 12)

Hence, the expression is x(x+ 12) + 8( y + 12)

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Answer:

y = 10x-37

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 10x+b

Substitute the point into the equation

3 = 10*4+b

3 = 40+b

Subtract 40

3-40 = 40+b-40

-37 = b

y = 10x-37

Answer: y = 10x - 37

Step-by-step explanation:

Hope it helps <3

To find the amount of oatmeal in ounces for 1 ounce of milk, we use the following proportion

Now, we solve for x.

So, for 1 ounce of milk, the amount of oatmeal is 4/5 ounces.

Now, let's find the amount of milk for 5 1/10 ounces of oatmeal.

Now, we solve for x

Hence, there are needed 6 3/8 ounces of milk to get 5 1/10 ounces of oatmilk.

Answer:

The answer is "More accurately is the left hand".

Step-by-step explanation:

In the given-question when we look at the given equation and see its given graph. This graph offers a much more reliable right hand because it has a smaller distance than that of the left. That being said, the left hand never surpassed the target, again and again, that's why the above given choice is correct.

Answer:

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Step-by-step explanation:

75% more revenue in theaters than it did via streaming video.

The sum of the revenues is 100%.

So the theaters were responsible for the following percentage:

\(P = 50 + \frac{75}{2} = 50 + 37.5 = 87.5\)

How much money did Gray Widow make in theaters on opening weekend?

87.5% of the total revenue, that is, 0.875 out of $127,265,468.

0.875*127,265,468 = $111,357,284.5

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Answer: Adding and subtracting polynomials are both arithmetic operations used in algebra. The main difference between the two operations is the sign of the terms being combined.

Adding polynomials involves combining like terms by adding their coefficients. When adding polynomials, the terms being added have the same sign. For example, when adding the polynomials x^2 + 2x + 1 and 3x^2 + 4x + 2, we combine the like terms (x^2 terms, x terms, and constant terms) by adding their coefficients:

(x^2 + 2x + 1) + (3x^2 + 4x + 2) = 4x^2 + 6x + 3

Subtracting polynomials involves subtracting one polynomial from another by changing the sign of each term in the polynomial being subtracted and then adding the resulting polynomials. When subtracting polynomials, the terms being subtracted have opposite signs. For example, when subtracting the polynomial 3x^2 + 4x + 2 from the polynomial x^2 + 2x + 1, we first change the sign of each term in the polynomial being subtracted:

(x^2 + 2x + 1) - (3x^2 + 4x + 2) = x^2 + 2x + 1 - 3x^2 - 4x - 2

Then, we combine the like terms by adding their coefficients:

x^2 -  x - 1

In summary, the main difference between adding and subtracting polynomials is that adding involves combining like terms with the same sign, while subtracting involves changing the sign of one polynomial and then adding the resulting polynomials.

Step-by-step explanation:

Answer:

wowo

Step-by-step explanation:

Answer:

t = 8; u = 14.

Step-by-step explanation:

If the two triangles are to be congruent, their side lengths and angles must be equal.

In this case, segment RQ corresponds with segment HI, and segment QS corresponds to segment IJ.

Since they are equal, we know that...

3u = u + 28

and

16t - 32 = 12t

Solve for both!

3u = u + 28

2u = 28

u = 14

16t - 32 = 12t

4t = 32

t = 8

So, t = 8 and u = 14.

Hope this helps!

Answer他媽的你你一個愚蠢的屁股妓女，你需要做你贏了他媽的作業傻瓜屁股

Step-by-step explanation:

Answer:x − x^{2} − 1.

Step-by-step explanation:

.

There are no perfect cubes between 4^3 = 64 and 5^3 = 125. Therefore, no full m-ary tree with 84 leaves and height 3 exists.

We can show that no full m-ary tree with 84 leaves and height 3 exists as follows:

A full m-ary tree with height 3 has 1 + m + m^2 nodes (including the root). If we let the number of leaves be L, then we have:

L = m^3

Since we want L = 84, we need to find a positive integer m such that m^3 = 84. However, this equation has no integer solutions. To see this, we can note that 84 is not a perfect cube, and we can check that there are no perfect cubes between 4^3 = 64 and 5^3 = 125. Therefore, no full m-ary tree with 84 leaves and height 3 exists.

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Answer:

I'm gonna say false

GDP or Gross Domestic Profit is the money that is being spent/made inside the country. So it stands to reason that if people are spending more, the GDP would go up.

Hope this helps!

The function f(z) is an analytic function of z. To determine if the function u(x, y) = e^x cos y + 2x + y is harmonic, we need to check if it satisfies Laplace's equation:

∇²u = 0

where ∇² is the Laplacian operator.

i. To show that u(x, y) is harmonic, we need to calculate the Laplacian of u and verify if it equals zero.

∇²u = ∂²u/∂x² + ∂²u/∂y²

Taking the partial derivatives:

∂u/∂x = e^x cos y + 2

∂u/∂y = -e^x sin y + 1

∂²u/∂x² = ∂/∂x(e^x cos y + 2) = e^x cos y

∂²u/∂y² = ∂/∂y(-e^x sin y + 1) = -e^x sin y

Substituting these values into Laplace's equation:

∇²u = e^x cos y - e^x sin y

Since e^x is a common factor, we have:

∇²u = e^x (cos y - sin y)

For ∇²u to be zero, we need the expression in parentheses to be zero:

cos y - sin y = 0

By using the identity cos y - sin y = √2 sin(y + π/4), we can see that this condition is satisfied when y + π/4 = nπ, where n is an integer. Therefore, u(x, y) is harmonic.

ii. To find the harmonic conjugate v(x, y) of u(x, y), we need to find a function v such that the complex function f(z) = u + iv is analytic.

From the given function u(x, y) = e^x cos y + 2x + y, we can identify the real and imaginary parts:

Re(f) = u(x, y) = e^x cos y + 2x + y

Im(f) = v(x, y)

Since the Cauchy-Riemann equations relate the partial derivatives of u and v, we can equate them:

∂u/∂x = ∂v/∂y

∂u/∂y = -∂v/∂x

Taking the partial derivatives:

∂u/∂x = e^x cos y + 2

∂u/∂y = -e^x sin y + 1

Equating the partial derivatives:

∂v/∂y = e^x cos y + 2

∂v/∂x = e^x sin y - 1

Integrating with respect to y:

v(x, y) = e^x sin y + 2y + h(x)

Here, h(x) represents an arbitrary function of x.

iii. To write the function f(z) = u + iv as an analytic function of z, we combine the real and imaginary parts:

f(z) = e^x cos y + 2x + y + i(e^x sin y + 2y + h(x))

By using the relation z = x + iy, we can rewrite the function in terms of z:

f(z) = e^Re(z) cos Im(z) + 2Re(z) + Im(z) + i(e^Re(z) sin Im(z) + 2Im(z) + h(Re(z)))

Therefore, the function f(z) is an analytic function of z.

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If Aliyah's position is less than 1.79 kilometers, then Diego is in front of Aliyah.

If Aliyah's position is greater than 1.79 kilometers, then Diego is behind Aliyah.

To determine if Diego is behind or in front of Aliyah at 3:00 PM, we need to simply the function

Then, we have that g(t) at t = 0 represents 3:00 PM and compare it with Aliyah's position.

For Diego, when t = 0

Substitute the values, we have;

g(0) = 1.59 + 0.2 + 0.01(0²)

expand the bracket, we have;

g(0) = 1.59 + 0.2 + 0

g(0) = 1.79 kilometers

Note that no information was given about Aliyah's position.

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The shortest length of fence that the rancher can use is 6000 ft.

What is meant by length?

The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.

Main Body:

x = width of rectangle

y = length of rectangle

A = area of rectangle = xy = 1500000 ft^2

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

Sketch and see that there will be a minimum in Quadrant I.

dL/dx = 3 - 3(10^6)x^(-2)

Extrema occur when dL/dx = 0:

3 - 3(10^6)x^(-2) = 0

(10^6)x^(-2) = 1

x^2 = 10^6

x > 0, so x = 1000 feet for shortest length.

Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.

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Answer:

A number line with a closed circle on 6 and shaded to the right.

Step-by-step explanation:

Answer:a number line with a closed circle on 6 and shading to the right

Step-by-step explanation:I think I’m right! Good luck

Answer:

B

Step-by-step explanation:

f(x) = 2x+5

f^(-1) (x) = (x-5)/2

f^(-1) (8) = 3/2

Answer:

5n-8

Step-by-step explanation:

Because this is an arithmetic progression, there is simply an addend that is being added to every number. Because that is 5, the expression, for now, would be 5n. However, the progression does not start at 0, so we will have to subtract 3, and then it would be 5n - 3. We're still not at the answer; this is because the first term starts at 1, not 0. We will have to account for that, so subtract the coefficient, or 5, from the whole expression. That would be 5n - 8, and that would be the answer.

The following parts can be answered by the concept of Confidence interval.

a. The lower confidence bound at the 95% confidence level is approximately 0.031.

b. The true proportion of all ceramic hip recipients who experience squeaking is greater than 0.031 (3.1%).

(a) To calculate the lower confidence bound at the 95% confidence level for the true proportion of ceramic hips that develop squeaking, we will use the formula for a one-sample proportion confidence interval:

CI = p-hat ± Z × √(p-hat × (1 - p-hat) / n)

Where:
- p-hat is the sample proportion (9/156)
- Z is the critical value for a 95% confidence level (1.96)
- n is the sample size (156)

p-hat = 9/156 ≈ 0.0577

Standard error (SE) = √(0.0577 × (1 - 0.0577) / 156) ≈ 0.0138

Margin of error (ME) = Z × SE = 1.96 × 0.0138 ≈ 0.0271

Now, since we want the lower confidence bound, we will subtract the margin of error from the sample proportion:

Lower confidence bound = p-hat - ME = 0.0577 - 0.0271 ≈ 0.0306

So, the lower confidence bound at the 95% confidence level is approximately 0.031.

(b) The 95% confidence level used in (a) can be interpreted as: We are 95% confident that the true proportion of all ceramic hip recipients who experience squeaking is greater than 0.031 (3.1%).

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The sampling error is usually smaller with larger samples and decreases as the sample size increases.

When we talk about sampling error, we refer to the discrepancy or difference between the sample statistic (e.g., mean, proportion) and the population parameter it is intended to estimate. The sampling error arises due to the inherent variability in the data and the fact that we are working with a sample rather than the entire population.

By increasing the sample size, we are capturing a more extensive representation of the population, reducing the impact of random variation. As a result, the estimate tends to be more accurate and closer to the true population parameter.

Therefore, larger samples tend to have smaller sampling errors.

It's important to note that although increasing the sample size generally reduces sampling error, there may be other factors to consider, such as the sampling design, representativeness of the sample, and the quality of data collection, which can also influence the accuracy of the estimate.

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