All of the points in the graph are on the same line.

Find the slope of the line.

Answer:

$72,920

Step-by-step explanation:

36,460 x 2 = 72,920

We are given that the average SAT verbal score is 490, with a standard deviation of 96. Therefore, percent of the scores that lie between 298 and 586 is 81.5% .

Here, we have,

given that,

The average SAT verbal score is 490, with a standard deviation of 96.

we know that,

for normal distribution

z score =(X-μ)/σx

we have,  

here

mean is: μ = 490

std deviation is: σ= 96

now, we have,

we have to Use the Empirical Rule to determine what percent of the scores lie between 298 and 586.

so, we get,

probability =P(298<X<586)

=P((298-490)/96)<Z<(586-490)/96)

=P(-2<Z<1)

=0.84-0.025

=0.815

~ 81.5 %

81.5%  of the scores lie between 298 and 586.

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1. Variable manufacturing overhead rate variance

The formula Actual Hours × (Actual Rate - Standard Rate) is used to calculate the variable manufacturing overhead rate variance. This variance measures the difference between the actual variable manufacturing overhead cost incurred and the standard variable manufacturing overhead cost that should have been incurred, based on the standard rate per hour.

Variable manufacturing overhead rate variance = Actual Hours × (Actual Rate - Standard Rate)

The variable manufacturing overhead rate variance provides insight into how efficiently a company is utilizing its variable manufacturing overhead resources in terms of the rate per hour. A positive variance indicates that the actual rate paid per hour for variable manufacturing overhead was higher than the standard rate, resulting in higher costs. On the other hand, a negative variance suggests that the actual rate paid per hour was lower than the standard rate, leading to cost savings.

By analyzing this variance, management can identify areas where the company may be overspending or underspending on variable manufacturing overhead and take corrective actions accordingly, such as renegotiating supplier contracts or optimizing resource allocation.

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

5 = y

7.1 = x

Step-by-step explanation:

(There are so many ways we can solve this, let's solve this the easiest way):

Let's solve for y first =

We can say;

Tan(45) = y/5

Tan(45) * 5 = y

1 * 5 = y

5 = y

Now let's solve for x;

5² + y² = x²

5² + 5² = x²

25 + 25 = x²

50 = x²

\(\sqrt{50\\}\) = x

7.1 = x

Hope this helps!

Answer:

Y=5 x=50

Step-by-step explanation:

Okay, I'm gonna name this triangle XYZ.

An isosceles triangle is when two sides are equal. We know that an area of a triangle is always 180 degrees. A right triangle always has one degree of 90 degrees. We know that y∠45, x∠90, so z has to be 45 as well.  We know this is a right isosceles triangle due to the angles it has given us.

Now, we know y and z are the same sizes. y=z

using the Pythagorean theorem

take a square root of sums of squares \(x=y^2+z^2\)

\(5^2=25\)

25+25=50

The reason why Lagrange interpolation is preferred over Hermite interpolation when approximating the derivative of a function using difference schemes is that Hermite interpolation involves calculating both the function value and its derivative at each data point.

This can be computationally expensive and may not always be possible if the function's derivative is not known or difficult to calculate.

On the other hand, Lagrange interpolation only requires knowledge of the function's values at the data points, making it a simpler and more practical choice for many applications.

Additionally, Lagrange interpolation produces a polynomial function that is continuous and differentiable, which is ideal for approximating derivatives.

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A knitter with 14 skeins of yarn can make 7 scarves.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The table shows a proportional relationship between the number of skeins of yarn and the number of scarves made from the yarn.

Skeins of Yarn; 4  8  14

Scarves;           2  4   x

Now,

Since, The table shows a proportional relationship between the number of skeins of yarn and the number of scarves made from the yarn.

So, By definition of proportional, we get;

⇒ 4 / 2 = 14 / x

Solve for x as;

⇒ 4 / 2 = 14 / x

⇒  2x = 14

⇒ x = 7

Thus, A knitter with 14 skeins of yarn can make 7 scarves.

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The first two numbers between 100 and 150 that have a HCF of 22 are 110 and 132

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

According to the question, we are to find two numbers between 100 and

150 that have a HCF of 22.

In order to do that we will multiply 22 by the values 5 and 6

First number = 22 * 5 = 10

Second number = 22 * 6 = 132

Hence the first two numbers between 100 and 150 that have a HCF of 22 are 110 and 132

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While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no relationship between variables.

What is alternative hypothesis?

The alternative to your research topic is represented by the alternative hypothesis (Ha). It asserts that there is a population-wide impact.  

                                     Frequently, your study hypothesis and alternate hypothesis are the same. Alternatively said, it's the assertion that you anticipate or hope will be accurate.

What is meant by a null hypothesis?

A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.

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Answer:

She can sell 20 general admission tickets for 800 dollars. Now, we have 5 tickets left, so we can sell 5 VIP tickets to family and friends.

Step-by-step explanation:

We have 20 general admission tickets and each of them costs 40 dollars, so 20 times 40 is $800. Now, we have 5 extra tickets, and we can have over $800 dollars, so we have 5 VIP tickets for friends. She will have 25 tickets and at least

$800 dollars.

Answer:

3 is the x

2 is the y

Step-by-step explanation:

The percentage of respondents who play only hockey is 27.24%.

According to the given question.

Total number of respondents = 2302

And, the number of reposdents who play only hockey = 627

Therefore,

The percentage of respondents said that they play only hockey

= (number of respondents who play only hockey/ total number of respondents)  × 100

\(= \frac{627}{2302} \times 100\)

= 27.237 %

≈ 27.24%

Hence, the percentage of respondents who play only hockey is 27.24%.

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Answer:

23 days

Step-by-step explanation:

We are told that the stadium holds 7500 individuals.

Now, if 600 seats have already been made, It means the number of seats left to be made to complete the stadium = 7500 - 600 = 6900 seats

We are told that 300 seats can be made in a day. Thus, number of days to be used to finish the remaining seats = 6900/300 = 23 days

Thus, it will take 23 days to complete all the 7500 seats.

Given the graph in the attached image.

The red line represents f(x) and the blue line represents g(x);

From the graph;

The intercept, b, of f(x) is

and the slope, m, of f(x) is;

So, f(x) is;

For g(x)

The y-intercept, b, of g(x) is;

and the slope, m, of g(x) is;

So, g(x) is;

To derive the solution, let us equate the two equations;

Answer:

1/5

Step-by-step explanation:

width of picture 7 3/5 cm. to fit in the frame the picture cannot be more than 7 3/10 cm. how much should the picture be trimmed

Given that :

Original Width of picture = 7 3/5 cm

Width required for picture to fit into frame=7 3/10

For picture to fit into frame:

(7 3/5 - 7 3/10) must be trimmed off from the frame.

(7 3/5 - 7 3/10)

(7 - 7) = 0

(3/5 - 3/10)

Taking the L. C. M

(6 - 3) / 10

= 2 / 10

= 1/5

THEREFORE, 1 / 5 of the width should be trimmed in other to ensure the picture fits into the frame.

The probability that the sample mean height will be less than 69 inches is 0.966 or 96.6%.

The normal distribution, like any other probability distribution, defines how well the values of a statistic are distributed. Because it accurately captures the range of values for many natural occurrences, it is the most significant probability distribution in statistics.

The formula for normal distribution is;

\(Z=\frac{\bar{X}-\mu}{\left(\frac{\sigma}{\sqrt{n}}\right)}\)

Where, X is the sample average( = 69).

μ is the mean (= 70).

σ is the standard distribution ( = 4)

n is the sample size (= 54).

Substituting above values in the formula;

\(z=\frac{69-70}{\left(\frac{4}{\sqrt{54}}\right)}\)

z = -1.83

So the likelihood that it sample mean is less than 69 would be the probability of Z will be greater than -1.83 This is determined using the Z-table:

P( < 69) = P(Z < -1.83) = 0.966

Therefore, the probability for getting the sample mean height will be less than 69 inches is 0.966 or 96%.

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\(\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m\)

Answer:

16c+7d

Step-by-step explanation:

The best measure of center for this data is the median, and its value is 3.

Option B is the correct answer.

We have,

From the line plot,

The median is the best measure of center for this type of data, as it is not affected by outliers.

To find the median, we need to arrange the data in order from least to greatest:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 10

Since there are 15 data points,

The median is the middle value, which is 3.

Therefore,

The best measure of center for this data is the median, and its value is 3.

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Because it permits one to assume that the sampling distribution of the mean would typically be normally distributed, the central limit theorem is helpful when examining big data sets. This makes statistical analysis and inference simpler.

Hypothesis :

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

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The general syntax for regression modeling in R is as follows:

lab5.reg4 = lm(formula, data = dataset)

summary(lab5.reg4)

In the first line, "formula" should be replaced with the regression formula that defines the relationship between the dependent variable and the independent variables. The formula should be written using the appropriate variables and operators, such as "+" for addition, "-" for subtraction, "*" for multiplication, and "/" for division. For example, a simple linear regression formula could be written as "y ~ x" to represent the dependent variable y and the independent variable x.

In the second line, "dataset" should be replaced with the name of the dataset being used for the regression analysis. The dataset should be properly imported or defined in R before running the regression model.

After running the regression model, the "summary" function is used to obtain a summary of the regression results, including the coefficients, standard errors, p-values, and other relevant statistics.

It is important to note that the specific variables and dataset used in the regression model will determine the actual syntax used. The syntax provided above serves as a general template, and you should fill in the blanks with the appropriate variables and dataset to generate the regression model and summary statistics for your specific analysis.

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Answer:

a. x² + 6x + 9 = -22 + 9

Step-by-step explanation:

they moved the 22 to the right by subtracting it. this leaves a binomial on the left side, which if what you want to solve it.

then they completed the square by dividing b (6) by 2 = 3. then squaring 3 to get 9.

if you added 9 to the left, then you have to add 9 to the right, therefore resulting in -22 + 9.

Answer:

In TTM/Imagine Math it is top left or a.

Step-by-step explanation:

A M function file 'tconvert.m', which can convert coordinates (x, y) into Polar from Cartesian coordinates. is:
"```matlab
function [theta, r] = tconvert(x, y)
```"

To create the M function file 'tconvert.m' that converts Cartesian coordinates (x, y) into Polar coordinates, follow these steps:

1. Open the MATLAB Editor or any text editor and create a new file named 'tconvert.m'.

2. In the file, start with the function declaration line: `function [theta, r] = tconvert(x, y)`.

3. Inside the function, write the conversion code using MATLAB's built-in functions:

  - Calculate the angle theta using `atan2(y, x)`, which returns the angle in radians.

  - Calculate the radius r using `sqrt(x^2 + y^2)`, which gives the distance from the origin.

4. End the function with the `end` keyword.

5. Save the file in a directory accessible by MATLAB.

The function 'tconvert' takes the Cartesian coordinates (x, y) as input and returns the corresponding Polar coordinates (theta, r). The angle theta represents the direction in radians, and the radius r represents the distance from the origin.

The function can be called from the MATLAB command window or from another script or function file.

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Complete question:

Write a M function file 'tconvert.m', which can convert from Cartesian coordinates (x,y) into Polar coordinates.

A. Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

B. The recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

(a) If Manager B always truthfully reports the state of the economy (s = 0.7), Manager A would send a recommendation that minimizes their disutility Ua. In this case, Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

(b) In a Nash equilibrium, both managers strategically make their recommendations based on their own utility. Manager A wants to minimize their disutility Ua, which increases as the decision deviates from 0.4. Manager B wants to minimize their disutility UB, which increases as the decision deviates from 0.7.

To find the Nash equilibrium, we need to consider the recommendations made by both managers simultaneously. Let's denote the recommendations as rA (from Manager A) and rB (from Manager B). The principal's decision, d, would be the average of the recommendations, so d = (rA + rB) / 2.

Given that both managers strategically choose their recommendations, they will aim to minimize their disutility. In this case, Manager A would recommend a decision of 0.4 (as it minimizes Ua), and Manager B would recommend a decision of 0.7 (as it minimizes UB). Therefore, the recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

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Answer:

They are all true

Step-by-step explanation:

1. 3² +4² = 5²

3x3 + 4x4 = 5x5

  9   +  16  =  25

25 = 25

-----------------------

2. 6² + 8² = 10²

36 + 64 = 100

100 = 100

------------------

3. 9² + 12² = 15²

81 + 144 = 225

225 = 225

-------------------

4. 5² +12² =13²

25 + 144 = 169

169 =169

-------------------

The function my squares[v, m, µ, σ] constructs m samples of v sums-of-squares of the deviation from the mean with the X drawn from the normal distribution N(µ,σ). The function histxsq [v, m, µ, σ] plots a PDF histogram of the samples, with the appropriate x² PDF plotted over the top of it.

First, let's define the mysquares[v, m, µ, σ] function. The function takes in four inputs:
- v: an integer representing the number of deviations from the mean to be squared and summed
- m: an integer representing the number of samples to be generated
- µ: a float representing the mean of the normal distribution
- σ: a float representing the standard deviation of the normal distribution



Here is the code for both functions:

```
import nu m p y as np
import matplotlib. py plot as plt
from scipy.stats import chi2

def mysquares(v, m, µ, σ):
   x = np.random.normal(µ, σ, (v, m))
   x_bar = np.mean(x, axis=0)
   return np.sum((x - x_bar)**2, axis=0)

def histxsq(v, m, µ, σ):
   x_sq = mysquares(v, m, µ, σ)
   chi_sq = chi2.pdf(np.linspace(0, np.max(x_sq), 100), v)
   plt.hist(x_sq, bins='auto', density=True, alpha=0.7)
   plt.plot(np.linspace(0, np.max(x_sq), 100), chi_sq, linewidth=2)
   plt.show()
```

Let's test the functions with the provided inputs. We will plot histograms for the following cases:
- v = 2, µ = 1, σ = 2
- v = 6, µ = 3, σ = 10
- v = 16, µ = 0, σ = 1

```
histxsq(2, 10000, 1, 2)
histxsq(6, 10000, 3, 10)
histxsq(16, 10000, 0, 1)
```

The resulting histograms show that the x² distribution fits the samples quite well.

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The width of the brick walkway which is a rectangular garden should be approximately 2.36 feet.

The length of the garden: 27 + 2w.

Similarly, the width of the garden: 19 + 2w.

The total area of the garden: (27 + 2w) * (19 + 2w)

We know that the area of the walkway itself is 301 square feet, so we can set up the following equation:

(27 + 2w) * (19 + 2w) - 27 * 19 = 301

(27 + 2w)(19 + 2w) - 513 = 301

(513 + 73w + 38w + 4w²) - 513 = 301

Combining like terms:

4w² + 111w - 301 = 0

w = (-111 ± √(111^2 - 4 * 4 * -301)) / (2 * 4)

Calculating the discriminant:

√(111² - 4 * 4 * -301) ≈ √(12321 + 4816) ≈ √17137 ≈ 130.89

Using the quadratic formula:

w ≈ (-111 ± 130.89) / 8

Therefore, the possible solutions are:

w ≈ (-111 + 130.89) / 8 ≈ 2.36

w ≈ (-111 - 130.89) / 8 ≈ -3.36

Since the width cannot be negative in this context, we discard the negative solution.

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The final volume of CO2 gas is approximately 2.2 liters.

Dry ice, or solid carbon dioxide (CO2), sublimates from a solid to a gas at standard temperature and pressure. The density of solid CO2 is 1.56 g/cm^3, and the density of gaseous CO2 at STP is 1.96 g/L.

First, we need to convert the mass of dry ice to moles of CO2:

4.4 g / 44.01 g/mol = 0.1 mol CO2

Since the volume of the bag is 5 liters, we can use the ideal gas law to calculate the final volume of CO2 gas:

PV = nRT

Where

At STP, the pressure is 1 atm and the temperature is 273 K. We can solve for V:

V = nRT/P = (0.1 mol)(0.08206 L·atm/mol·K)(273 K)/(1 atm) = 2.24 L

So the final volume of CO2 gas is approximately 2.2 liters, to the nearest tenth of a liter.

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The probability of getting a single tails =

p = 1/2

The probability of not getting a single one =

q = 1 -p = 1/2

Now, using binomial theorem of probability:

The probability of getting exactly r = 4 tails in total n = 10 tosses =

(10 x 9 x 8 x 7)/4! * (1/2^4) * (1/2^6) = 105/2^9 = 20.51%

Answer:

y=1/2x-3/2

Step-by-step explanation:

m1=-2

m1m2=-1

-2m2=-1

m2=1/2

-1=1/2(1)+b

b=-3/2

y=1/2x-3/2