the science teacher gives daily homework. for a random sample of days throughout the year, the mean of problem is 5 and the mad is 2. the spanish teacher also gives daily homework. for a random sample of days throughout the year, the mean of the problems is 10 and the mad is 1. if you estimate the mean of science homework, problems to be 5, and the mean number of spanish problems to be 10, which is more likely

Answers

Answer 1

The estimate of the median number of science homework problems is more likely to be accurate, based on the given information about the median and IQR.

The median and IQR (Interquartile Range) provide information about the central tendency and spread of a set of data, respectively. The fact that the median number of science homework problems is 5 and the IQR is 2 with the middle 50% of the data falling between 4 and 6 problems. This indicates that the data is not highly skewed or influenced by outliers.

In contrast, the fact that the median number of Spanish homework problems is 10 and the IQR is 1 with the middle 50% of the data falling between 9 and 11 problems. This indicates that the data is highly skewed and that even small deviations from the median can have a large impact on the IQR.

Therefore, the estimate of the median number of science homework problems is more likely to be accurate than the estimate of the median number of Spanish homework problems, because the science homework data appears to be more consistent and less influenced by outliers or extreme values.

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____The given question is incorrect, the correct question is given below:

The science teacher gives daily homework. For a random sample of days throughout the year, the median number of problems is 5 and the IQR is 2 . The Spanish teacher also gives daily homework. For a random sample of days throughout the year, the median number of problems is 10 and the IQR is 1 . If you estimate the median number of science homework problems to be 5 and the median number of Spanish problems to be 10, which is more likely to be accurate? Explain your reasoning.


Related Questions

A math teacher is trying to analyze her test grades. She surveys the students to find out how many minutes they studied. She then makes a scatterplot of time studying and test grades.


What is the domain?

A) the students' grades on their tests

B) the number of students in the class

C) the different courses the teacher teaches

D) the number of minutes the students studied

Answers

In the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

The domain refers to the set of possible inputs or variables in a given context. In this case, the scatterplot is being created based on the relationship between the time students spent studying and their corresponding test grades. Therefore, the domain in this context would be the number of minutes the students studied (option D).

The domain represents the independent variable, which is the variable that is controlled or manipulated in the analysis. In this scenario, the math teacher wants to analyze the relationship between studying time and test grades, so the number of minutes studied would be the independent variable. The teacher surveys the students to collect data on the time spent studying, and this variable becomes the domain of the scatterplot.

The range, on the other hand, represents the dependent variable, which is the variable that is measured or observed as an outcome or response. In this case, the dependent variable would be the students' test grades. The scatterplot will show how the test grades correspond to the amount of time students studied.

To summarize, in the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

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hey, i forgot how to solve this problem. can you solve it for me?

a/3 + 11 = -5

Answers

ANSWER:
a= -48


Explanation:
I worked it out.

Consider the line y=6/7 x -7. Find the equation of the line that is perpendicular to this line and passes through the point (6,-6). Find the equation of the line that is parallel to this line and passes through the point (6,-6) .

Answers

Answer:

\(y= -\frac76x +1\); \(y= \frac67x -\frac{78}7\)

Step-by-step explanation:

We know from theory that two perpendicular lines have the product of their slope equal to -1. Let's find the second slope:

\(\frac67m = -1 \rightarrow m=-\frac76\)

At this point we can just use the slope-point equation to get our first line:

\(y-y_0 = m(x-x_0)\\y-(-6) = -\frac76(x-6) \\y+6= -\frac76x +7\\y= -\frac76x +1\)

Now, we know that two parallel lines have the same slope. Time to apply the same point-slope formula, with the original m this time.

\(y-(-6) = \frac67(x-6)\\y+6 = \frac67x -\frac{36}7\\y= \frac67x -\frac{36}7 -{\frac{42}7\)

\(y= \frac67x -\frac{78}7\)

how many license plates can be made using either 3 digits followed by 3 letters, or 3 letters followed by 3 digits?

Answers

Answer:

infinite

Step-by-step explanation:

the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite

                            -hope this helps-

                                                   

                 

the percent yield is calculated as the ratio of the

Answers

The percent yield is calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100.

Percent yield is a measure of how efficient a chemical reaction or process is in producing the desired product.

The formula for percent yield is:

Percent Yield = (Actual Yield / Theoretical Yield) * 100

The actual yield is the amount of product obtained from the reaction or process, typically measured in grams or moles. It represents the actual amount of product obtained in the laboratory.

The theoretical yield, on the other hand, is the maximum amount of product that can be obtained based on stoichiometry and other factors. It is calculated using balanced chemical equations and the starting amounts of reactants.

By dividing the actual yield by the theoretical yield and multiplying by 100, we get the percent yield, which is expressed as a percentage.

This value provides insight into the efficiency of the reaction or process, with a higher percent yield indicating a more efficient conversion of reactants into products.

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What is the greatest common factor of 60,70, and 80

Answers

Answer:

10

Step-by-step explanation:

Answer: The GCF of 60, 70, and 80 is 10.

Step-by-step explanation: If you think about it, the GCF is definitaly going to be 10. That is because you can multiply 10 to get 60, 70, and 80. There is no other number higher than 10 that can be multiplied by something to get all of these values.  

Need help ASAP!!! It’s DUE TOMORROW!!!!!

Need help ASAP!!! Its DUE TOMORROW!!!!!

Answers

Answer:

1. 7%

2. 55%

3. 15%

Step-by-step explanation:

That's the answer

Why would a railway be important to either side in the civil war?

Answers

Answer:

Either side would have been improved by a railway so they could get more ammo in and get food in and also get the sick and wonded out to get medical attention

Step-by-step explanation:

to transport food the wounded ammo and healthy tripp’s

5. For an LTI system described by the difference equation: \[ \sum_{k=0}^{N} a_{k} y[n-k]=\sum_{k=0}^{M} b_{k} x[n-k] \] The frequency response is given by: \[ H\left(e^{j \omega}\right)=\frac{\sum_{k

Answers

The frequency response of an LTI system described by the given difference equation can be expressed as:

\[ H(e^{j\omega}) = \frac{\sum_{k=0}^{M} b_k e^{-j\omega k}}{\sum_{k=0}^{N} a_k e^{-j\omega k}} \]

This expression represents the ratio of the output spectrum to the input spectrum when the input is a complex exponential signal \(x[n] = e^{j\omega n}\).

The frequency response \(H(e^{j\omega})\) is a complex-valued function that characterizes the system's behavior at different frequencies. It indicates how the system modifies the amplitude and phase of each frequency component in the input signal.

By substituting the coefficients \(a_k\) and \(b_k\) into the equation and simplifying, we can obtain the specific expression for the frequency response. However, without the specific values of \(a_k\) and \(b_k\), we cannot determine the exact form of \(H(e^{j\omega})\) or its properties.

To analyze the frequency response further, we would need to know the specific values of the coefficients \(a_k\) and \(b_k\) in the difference equation. These coefficients determine the system's behavior and its frequency response characteristics, such as magnitude response, phase response, and stability.

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Declan said, "I know 3/4 is greater than 1/2, so that means 3/4 is greater than 6/12. " Does Declan’s reasoning make sense?

Answers

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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The fair spinner shown is spun 2 times. The set of possible outcomes are: S = {RR, BB, YY, GG, RB, BR, RY, YR, RG, GR, BY, YB, BG, GB, YG, GY} The number of yellows in the outcome is summarized in the table on the right. A 2-column table has 3 rows. The first column is labeled Yellow with entries 0, 1, 2. The second column is labeled Frequency with entries 9, 6, 1. Using the data from the theoretical probability table, what is the probability of the spinner landing only once on yellow in two spins?
0.0625
0.5625
0.375
1

Answers

Answer:

Answer is 0.375 :)

Step-by-step explanation:

The probability of the spinner landing only once on yellow in two spins is 0.375.

What is Probability?

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

As per the given data:

We are given the sample space of possible outcomes for a fair spinner.

Also, we are given a table which denotes the frequency of the color yellow appearing on the spinner.

For finding out the probability of the spinner landing only once on yellow in two spins.

= Favorable outcomes / Total number of outcomes

From the given table:

Favorable outcomes = 6

= Favorable outcomes / Total number of outcomes = 6 / 16

= 0.375

The probability of the spinner landing only once on yellow in two spins is 0.375.

Hence, The probability of the spinner landing only once on yellow in two spins is 0.375.

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2D and ZE are complementary. If m2D = 5x + 3and mZE = 3x - 1, what is x?

Answers

hello

the question presented before me seem incomplete due to lack of diagram to give a detailed expression

if 2D and ZE are complimentary, then the sum of both angles must be equal to 90 degrees

\(\begin{gathered} <2D\text{ = 5x }+\text{ 3} \\ solve the expression by finding x\(\begin{gathered} 3x\text{ }-\text{ 1 }+\text{ 5x }+\text{ 3 }=90^0 \\ 8x\text{ }+\text{ 2 }=\text{ 90} \\ 8x\text{ = 90 }-\text{ 2} \\ 8x\text{ }=\text{ 88} \\ \end{gathered}\)

divide both sides of the equation by 8

\(\begin{gathered} \frac{8x}{8}\text{ }=\text{ }\frac{88}{8} \\ x\text{ }=11^0 \end{gathered}\)

x = 11

Three objective functions for linear programming problems are 7A+10B,6A+4B, and −4A+7B. Show the graph of each for objective function values equal to 420 .

Answers

Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

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Three objective functions for linear programming problems are 7A+10B,6A+4B, and 4A+7B. Show the graph

The ratio of fabric bandage to platic bandage i 3 to 9. A mall kit ha 16 fabric bandage. How many platic bandage hould a mall kit have?

Answers

48 plastic bandages should a small kit have

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that the ratio of fabric bandages to plastic bandages in each kit is 3 to 9

A small kit has 16 fabric bandages then we have to find the number of plastic bags.

Let x be the number of plastic bags for 16 fabric bandages.

3/9=16/x

Apply cross multiplication

3x=16×9

3x=144

Divide both sides by 3

x=48.

Hence, 48 plastic bandages should a small kit have

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.When a partition is formatted with a file system and assigned a drive letter it is called a volume.
True or False

Answers

The statement given "When a partition is formatted with a file system and assigned a drive letter it is called a volume." is true because when a partition is formatted with a file system and assigned a drive letter, it is called a volume.

A volume refers to a partition on a storage device, such as a hard drive or SSD, that has been formatted with a file system and assigned a drive letter. The file system determines how data is organized and stored on the volume, while the drive letter provides a unique identifier for accessing the volume. This allows the operating system to interact with the partition as a separate entity and enables users to store and retrieve data from that specific volume. Therefore, the statement is true.

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if 1/2=-3/7q, then q= -1 1/6 true or false

Answers

Answer:

false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

\(\frac{1}{2}=\frac{-3}{7}q\)

1/2*7/-3= -7/6

q = -7/6 NOT -11/6 so the statement is false

write an anonymous function to compute the euclidean distance given two points (x1, y1) and (x2, y2). use the following equation to calculate the distance.

Answers

The anonymous function to compute the euclidean distance given two points (x1, y1) and (x2, y2) is ``python
euclidean_distance = lambda x1, y1, x2, y2: ((x2 - x1)**2 + (y2 - y1)**2)**0.5.

To compute the Euclidean distance given two points (x1, y1) and (x2, y2). Here's the step-by-step explanation using the Euclidean distance equation:

1. Recall the Euclidean distance equation: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
2. Use an anonymous function, which is a function without a name, typically represented using the "lambda" keyword in programming languages like Python.
3. Define the function parameters as the coordinates of the two points: (x1, y1) and (x2, y2).
4. Implement the Euclidean distance equation inside the anonymous function.

Here's an example using Python:

```python
euclidean_distance = lambda x1, y1, x2, y2: ((x2 - x1)**2 + (y2 - y1)**2)**0.5
```

Now you can use this anonymous function to compute the Euclidean distance between any two points (x1, y1) and (x2, y2) by calling it with the appropriate arguments:

```python
distance = euclidean_distance(1, 2, 4, 6)
print(distance)  # Output: 5.0
```

This example demonstrates how to write an anonymous function to compute the Euclidean distance given two points (x1, y1) and (x2, y2).

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Choose the correct correspondence. 5
a, 6
b, 7
c, 8

Answers

Answer:

c

Step-by-step explanation:

Answer is B

Trust why would I lie to you

A room in the shape of a cube has a floor area of 20.25 square metre what is its height ? what is its volume ? ​

Answers

Answer:

Height= 4.5 Volume= 91.125

Step-by-step explanation:

Height. Is the square root of the floor area = 4.5 volume is this length cubed = 91.125

Zoe invested $5,500 in an account paying an interest rate of 8 1/2% compounded continuously. Aubrey invested $5,500 in an account paying an interest rate of 8 1/4% compounded annually. To the nearest dollar, how much money would Aubrey have in her account when Zoe's money has doubled in value?

Answers

Answer:

Audrey will have $10,498.10 when Zoe's money has doubled in value.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra II

Natural Logs and Exponentials

Compounded Continuously Interest Rate Formula: \(\displaystyle A = Pe^{rt}\)

P is the principle amountr is the interest ratet is time

Compounded Annually Interest Rate Formula: \(\displaystyle A = P(1 + r)^t\)

P is the principle amountr is the interest ratet is time

Step-by-step explanation:

Step 1: Define

Identify.

Zoe:

P = $5,500

r = 0.085

A = 2P

Aubrey:

P = $5,500

r = 0.0825

Step 2: Find Time

Find time elapsed by using Zoe.

Substitute in variables [Compounded Continuously Interest Rate]:        \(\displaystyle 2P = 5500e^\big{0.085t}\)Substitute in P:                                                                                             \(\displaystyle 2(5500) = 5500e^\big{0.085t}\)Simplify:                                                                                                        \(\displaystyle 2 = e^\big{0.085t}\)Isolate t term:                                                                                               \(\displaystyle \ln 2 = 0.085t\)Isolate t:                                                                                                        \(\displaystyle t = \frac{\ln 2}{0.085}\)

So the time it takes for Zoe to get double her money is approximately 8.15467 years.

Step 3: Find Audrey's Money

Substitute in variables [Compounded Annually Interest Rate]:                \(\displaystyle A = 5500(1 + 0.0825)^\big{\frac{\ln 2}{0.085}}\)Evaluate:                                                                                                       \(\displaystyle A = 10498.10\)

∴ after the elapsed time of approximately 8.15467 years, Zoe would have made double her money valued at $11,000 and Audrey would have made $10,498.10.

---

Topic: Algebra II

Unit: Logarithmic Functions

Write a quadratic function in standard form whose graph passes through (−6,0) (−4,0) and (−3,−18)

Answers

The quadratic function in standard form that passes through the points (-6,0), (-4,0), and (-3,-18) is f(x) = -2x^2 + 4x + 4.

To write the quadratic function in standard form, we can use the fact that a quadratic function can be expressed as

f(x) = a(x - h)² + k,

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.

Since the graph passes through (-6, 0), (-4, 0), and (-3, -18), we can set up three equations based on these points and solve for the unknowns a, h, and k.

First, using the point (-6, 0), we get

0 = a(-6 - h)² + k

Expanding the square and simplifying, we get

36a + ah² + k = 0 ----(1)

Similarly, using the point (-4, 0), we get

0 = a(-4 - h)² + k

Expanding and simplifying, we get

16a + ah² + k = 0 ----(2)

Using the point (-3, -18), we get

-18 = a(-3 - h)² + k

Expanding and simplifying, we get

9a + 6ah + ah² + k = -18 ----(3)

We now have three equations with three unknowns (a, h, k). We can solve them simultaneously to get the values of a, h, and k.

Subtracting equation (1) from (2), we get

20a = -4ah²

Dividing by -4a, we get

-5 = h²

Taking the square root of both sides, we get

h = ±√5 i

Since "h" is a real number, we must have h = 0.

Substituting h = 0 in equations (1) and (2), we get

36a + k = 0 ----(4)

16a + k = 0 ----(5)

Subtracting equation (4) from (5), we get

20a = 0

Therefore, a = 0.

Substituting a = 0 in equation (4), we get

k = 0.

Thus, the quadratic function is

f(x) = 0(x - 0)² + 0

Simplifying, we get

f(x) = 0

Therefore, the graph is a horizontal line passing through the x-axis at x = -6, -4, and -3.

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Given the following code sample, what value is stored in values[1, 2)? intl. I values - 17, 2, 3, 4). 2 (5, 6, 9, 81); a. 2 b.6 c. 9 d. 3

Answers

The value stored in values[1, 2] is 9.

How to determine the value stored in values[1, 2)?

Based on the given code sample, the value stored in values[1, 2] is 9.

In the code snippet, the variable values appears to be a two-dimensional array or matrix. The first dimension represents rows, and the second dimension represents columns. So values[1, 2] corresponds to the element at the second row and the third column of the matrix.

According to the provided array values - [17, 2, 3, 4], the third element in the array has the value 3. Therefore, values[1, 2] holds the value 3

Therefore, the correct answer is option d. 3.

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If it took 8 people 10 hours to build a barn, how long would it take 14 people to build the same barn?

Answers

Answer:

17.5

Step-by-step explanation:

Please help, and please give step by step answer. Thank you!

Please help, and please give step by step answer. Thank you!

Answers

a) As per the given percentage, the number of registered voters in the town who cast the votes are 155,952.

b) Reese claim is incorrect. The number he mentioned as registered voters is greater than the actual number of registered voters..

Percentage:

A percentage is a number or ratio which can be expressed as a fraction of 100.

For example, 57% can be written as 57/100.

Given,

The register voters and other in the town cast their vote on the election day.

a. In that particular town, 273,600 votes were cast in an election. And there are 57% of those who were registered voted.

Here we need to find how many registered voters are there in the town.

b. Reese claims that there are 60% of the registered voters cast 273,600 votes, there would be fewer registered voters than above.

Now we have also need to find whether his statement is correct or not with the reason.

Let x be the total number of registered voter who cast the vote.

From the given details, we know that, there are 273,600 voters are cast.

And 57% of them are registered voters.

So, it can be calculated as follows,

=> x  = 273600 of 57%

=> x = 273600 x 57%

=> x = 273600 x 57/100

=> x = 2736 x 57

=> x = 155, 952

Therefore, there are 155,952 registered voter in the town who cast the vote.

Based on these calculation we know that, Reese claims is incorrect because there the number of registered voters is 155, 952 which is not equal to the number he mentioned.

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The question is in the image above ^

The question is in the image above ^

Answers

Answer:

the answer is 8 and you are welcome

8 dollars are no longer in his account

write an equation in slope-intercept form of the line shown (1,-9) , (-3,-9)

Answers

Answer:

y = -9

Step-by-step explanation:

y2 - y1 / x2 - x1

-9 - (-9) / -3 - 1

0 / -4

y = 0 + b

-9 = b

Answer:

\(\boxed{\sf{y=-9}}\)

Step-by-step explanation:

The slope-intercept form is the only way to solve this problem.

Slope-intercept form:

\(\rightarrow \sf{y=mx+b}\)

The m represents the slope.The b represents the y-intercept.

Using the slope is another way to solve.

(1,-9) and (-3,-9)

Use a slope formula.

Slope:

\(\sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{rise}{run} }\)

y2= (-9)

y1= (-9)

x2= (-3)

x1= (1)

Rewrite the problem.

\(\sf{\dfrac{(-9)-(-9)}{(-3)-1}=\dfrac{0}{-4}=\boxed{\sf{0} }\)

Therefore, the slope is 0.

We're not done yet.

y-intercept= (-9).

The m represents is 0.

The b represents is (-9).

So, the correct answer is y=-9.

I hope this helps you! Let me know if my answer is wrong or not.

Ravi has an ant problem at his house, so he asked pest control to come spray to get rid of the ants. The pesticide that the pest control company uses kills ants at a rate of 35.6% per hour. Before spraying, the pest control company determines that Ravi has about 25,000 ants. Write an equation to model the number of ants, A, Ravi will still have after h hours. ________=________*(________)^________ QUESTION 11 How many ants does Ravi still have after 3 hours? Round to the nearest ant. ________ants QUESTION 12 How long will it take until all of Ravi's ants are gone? ________hours

Answers

The equation to model the number of ants, A, Ravi will still have after h hours is: A = 25,000 * (1 - 0.356)^h. This equation represents the initial number of ants, 25,000, multiplied by the decay factor, (1 - 0.356), raised to the power of h, the number of hours that have passed.



To find out how many ants Ravi still has after 3 hours, we can plug in h = 3 into the equation: A = 25,000 * (1 - 0.356)^3 = 25,000 * 0.644^3 = 10,563.91. Round to the nearest ant, Ravi still has 10,564 ants after 3 hours.

To find out how long it will take until all of Ravi's ants are gone, we can set A = 0 and solve for h: 0 = 25,000 * (1 - 0.356)^h. Taking the natural log of both sides and rearranging gives us: ln(0/25,000) = h * ln(1 - 0.356), or h = ln(0/25,000)/ln(1 - 0.356). However, since the natural log of 0 is undefined, we cannot find an exact value for h. This means that it will take an infinitely long time for all of Ravi's ants to be gone.

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pls help and thank you ​

pls help and thank you

Answers

Answer:

cost price of the bat: $3130.43

Step-by-step explanation:

3600/1.15 = 3130.43

Hope this helps

consider an infinitely long three-sided triangular enclosure with side lengths 2 cm, 3 cm, and 4 cm. the view factor from the 2 cm side to the 4 cm side is

Answers

The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

The view factor (F) from Surface A to Surface B can be calculated using the formula:

F = A / (A + B)

where A and B are the areas of Surface A and Surface B, respectively.

The area of a triangle can be calculated using Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.

For Surface A:

a = 2 cm

b = 3 cm

c = 4 cm

s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm

Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))

= √(4.5 * 2.5 * 1.5 * 0.5)

=√(5.625) ≈ 2.37 cm²

For Surface B:

a = 2 cm

b = 4 cm

c = 3 cm

s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm

Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))

= √(4.5 * 2.5 * 0.5 * 1.5)

=√(5.625) ≈ 2.37 cm²

Now we can calculate the view factor (F):

F = Area_A / (Area_A + Area_B)

= 2.37 / (2.37 + 2.37)

≈ 0.5

Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

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Consider the function f(x,y) = 8x3 + y3 - 6xy + 2 a.) Find the critical points of the function. b.) Use the Second Derivative Test to classify each critical point as a local maximum, local minimum, or a saddle point.

Answers

The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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