an odd number of people (at least 3) are standing in a flat plane such that the distances between them are different. they each have water pistols and shoot the person who is closest to them. does everyone get wet? (canadian mathematical olympiad 1987)

The 90% confidence interval for the mean is (6.63, 15.55). Lower limit = X - Margin of error = 11.091 - 4.459 ≈ 6.63 and Upper limit = X + Margin of error = 11.091 + 4.459 ≈ 15.55

To find the 90% confidence interval for the mean, we can use the formula:

CI = X ± Zα/2 * (σ/√n)

Where X is the sample mean (11.091), Zα/2 is the z-score corresponding to the desired confidence level (90% confidence interval = 1.645), σ is the sample standard deviation (14.404), and n is the sample size (30).

Plugging in the values, we get:

CI = 11.091 ± 1.645 * (14.404/√30)

CI = (3.20, 18.98)

Therefore, the 90% confidence interval for the mean is (3.20, 18.98).

The 90% confidence interval for the mean. Given the sample size (n = 30), the sample mean (X = 11.091), and the sample standard deviation (s = 14.404), we can calculate the confidence interval using the formula:

X ± t * (s / √n)

First, we need to find the t-value for a 90% confidence interval with 29 degrees of freedom (n - 1). You can use a t-table or a calculator to find this value. For a 90% confidence interval, the t-value is approximately 1.699.

Next, we calculate the margin of error:
Margin of error = t * (s / √n) = 1.699 * (14.404 / √30) = 4.459

Now, we can find the confidence interval:
Lower limit = X - Margin of error = 11.091 - 4.459 ≈ 6.63
Upper limit = X + Margin of error = 11.091 + 4.459 ≈ 15.55

Thus, the 90% confidence interval for the mean is (6.63, 15.55).

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Based on your question, you have a dataset with five observations for two variables and an Excel file named "data14-25.xlsx". You'd like to estimate the regression equation.

In this context, "observations" refer to the data points collected for each of the two variables, and "variables" represent the attributes being measured or analyzed. The estimated regression equation is a mathematical model that describes the relationship between these two variables.

Unfortunately, I cannot access the Excel file you mentioned. However, I can guide you on how to estimate the regression equation using Excel:

1. Open the "data14-25.xlsx" file in Excel.
2. Organize your data with one variable in column A and the other variable in column B.
3. Click on the "Data" tab, then click "Data Analysis."
4. Select "Regression" from the list and click "OK."
5. In the "Input Y Range" box, select the range for the dependent variable (typically the one you want to predict). In the "Input X Range" box, select the range for the independent variable (the predictor).
6. Choose an output range or create a new worksheet for the results.
7. Click "OK."

The output will display the estimated regression equation, represented by the formula ŷ = b0 + b1x, where ŷ is the predicted value of the dependent variable, b0 is the intercept, and b1 is the slope of the regression line.

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The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49). The probability of X being greater than 10 is very small, less than 0.001%.

In this communication system, the signal Θ is a Gaussian distributed random variable with a mean of 0 and standard deviation of 1. The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49).

The receiver observes X, which is the sum of 2Θ and W. Since Θ and W are independent, we can calculate the mean and variance of X as follows:

E[X] = E[2Θ + W] = 2E[Θ] + E[W] = 0 + 0 = 0

Var[X] = Var[2Θ + W] = 4Var[Θ] + Var[W] = 4(1) + 49 = 53

Therefore, X is also a Gaussian distributed random variable with a mean of 0 and standard deviation of √53 = 7.2801.

To find the probability of X taking a certain value, we can use the formula for the Gaussian probability density function:

f(x) = (1/√(2πσ^2)) * e^(-(x-μ)^2/(2σ^2))

where μ is the mean and σ is the standard deviation. For example, the probability that X is equal to 0 can be calculated as:

f(0) = (1/√(2π*53)) * e^(-(0-0)^2/(2*53)) = 0.0494

To find the probability of X being greater than a certain value, we can use the cumulative distribution function (CDF) of the Gaussian distribution. For example, the probability that X is greater than 10 can be calculated as:

P(X > 10) = 1 - Φ((10 - μ)/σ)

where Φ is the standard normal CDF. Substituting the values for μ and σ, we get:

P(X > 10) = 1 - Φ((10 - 0)/7.2801) = 0.00002

So the probability of X being greater than 10 is very small, less than 0.001%.
In the given communication system with Gaussian noise, the signal Θ is a Gaussian distributed random variable Θ∼N(0,1), and the noise W is also a Gaussian distributed random variable W∼N(0,49), independent of the signal. The receiver observes X = 2Θ + W. To provide accurate information, answers should be given to at least 4 decimal places.

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Answer:

120, The answer is 120

Step-by-step explanation:

Determine the measure of the interior angle at vertex C.

A. 120

B. 180

C. 90

D. 200

The volume of the pentagonal prism is 645 cubic millimeters.

We have,

The formula for the volume of a pentagonal prism is:

V = A x h

where A is the area of the pentagonal base and h is the height of the prism.

In this case, we are given the area of the base as 43 square millimeters and the height as 15 millimeters.

Therefore, we can calculate the volume as:

V = 43 x 15

V = 645 cubic millimeters

Therefore,

The volume of the pentagonal prism is 645 cubic millimeters.

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The volume of the composite figure is solved to be

The volume of the composite figure is calculated by dividing the figure into simpler figure and solve each volume. The volumes calculated is the added to give the volume of the composite figure

formula for volume = length x width x depth

First simpler part

volume = 10.5 ft x 3 ft x 6 ft

volume = 189 cubic ft

second simpler figure

volume = (9 - 3) ft x 4 1/2 ft x 6 ft

volume = 162 cubic ft

volume of the composite figure

= 189 + 162

= 351 cubic ft

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The lengths of the sides of the square is 8 cm.

The area of this parallelogram is 24 cm².

In Mathematics and Geometry, the area of a square can be calculated by using the following mathematical equation (formula);

A = x²

Where:

For the lengths of the sides or side lengths of the square, we have:

64 = x²

x = √64

x = 8 cm.

Next, we would determine the area of this parallelogram;

Area of parallelogram = Area of square - 2(Area of triangle)

Area of parallelogram = 64 - 2(1/2 × (8 - 3) × 8)

Area of parallelogram = 64 - 40

Area of parallelogram = 24 cm².

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Answer:748cm^2

Step-by-step explanation:

The total area to be painted as given in the figure is 467.4 sq ft

Area refers to the expanse of 2-Dimensional shapes. It has a different formula for different shapes. Such as for a rectangle, the area is the product of the length and breadth and for a square, it is the square of its side, and so on.

In the figure, the side is a combination of a rectangle and a triangle.

Therefore, the area of the side = area of the rectangle + area of the triangle

area of rectangle = l * b

where l is the length

b is the breadth

l = 22.8 ft

b = 14.5 ft

Area = 22.8 * 14.5

= 330.6 sq ft

area of triangle = [tex]\frac{1}{2}[/tex]bh

where b is the base

h is the height

b = 22.8 ft

h = 26.5 - 14.5 = 12 ft

Area = [tex]\frac{1}{2}[/tex] * 22.8 * 12

= 136.8 sq ft

Area of side = 330.6 + 136.8

= 467.4 sq ft

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The complete question might be:

The diagram shows one side of a storage barn. This side needs to be painted. Find the total area to be painted.

Based on the given p-value of 0.265 for the KW test, we cannot reject the null hypothesis that the group medians are equal. The correct answer is: d. No more test to do.

Therefore, we do not need to do any post-hoc tests such as Dunn.test or Tukey test. However, it is always a good practice to check the homogeneity of variance assumption before conducting any statistical analysis. Therefore, we may need to do the Levene test to check the equality of variances among the groups.

Based on the information provided, the correct answer is:

d. No more test to do.

Explanation: The p-value of the Kruskal-Wallis (KW) test is 0.265. Since it is greater than the given alpha level of 0.10, we fail to reject the null hypothesis. This means that there is no significant difference between the groups being compared. Therefore, no further tests, such as Dunn.test, Tukey test, or Levene test, are needed.

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Answer:

To solve for x in the equation −12(x + 5) = -10, we will use the following steps:

Distribute the -12 to the terms inside the parentheses:

-12x - 60 = -10

Add 60 to both sides of the equation to isolate the variable term:

-12x = 50

Finally, divide both sides of the equation by -12 to solve for x:

x = -50/12

Simplifying the answer, we get:

x = -25/6 or -4.1667 (rounded to four decimal places)

Step-by-step explanation:

Answer:

960 grams

Step-by-step explanation:

We know from the problem that grams is proportional to fluid ounces.  Therefore, if we allow g to represent the number of grams of ground coffee Paula used, we can find it using a proportion:

[tex]\frac{64}{32}=\frac{g}{480}\\\\ 32g=30720\\\\ g=960[/tex]

Answer:

Step-by-step explanation:

menu 7,1 Open table labe A , B as x y

type the numbers provided and then 4 1 and whatever problem click it\

and you will see a table again type x y and there you will get youre asnwers

The rate of change of weight of the rabbit in pounds per week is 0.5 pounds per week.

To calculate the rate of change of weight of Samuel's rabbit in pounds per week, we need to look at how much the weight of the rabbit changes as the number of weeks since birth increases by one. This is also known as the slope of the linear relationship between the number of weeks and the weight of the rabbit.

Looking at the table below, we can see that when the rabbit is born (week 0), it weighs 0.5 pounds. As the number of weeks since birth increases by one, the weight of the rabbit increases by 0.5 pounds. This pattern continues for each subsequent week, with the weight of the rabbit increasing by 0.5 pounds each time.

| Number of Weeks Since Birth | Weight of Rabbit (in pounds) |
|-----------------------------|------------------------------|
|              0              |             0.5              |
|              1              |             1.0              |
|              2              |             1.5              |
|              3              |             2.0              |
|              4              |             2.5              |
|              5              |             3.0              |

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The explanatory variable in this scenario would be the length of the lesson. The instructor wants to see if a longer lesson would have an impact on student test scores, so the length of the lesson is the variable being tested.

This is also known as the independent variable, as it is being manipulated by the instructor to see how it affects the dependent variable, which in this case is student test scores. The instructor would need to design an experiment where some students receive a longer lesson and others receive the regular lesson length, then compare the scores of both groups to see if there is a significant difference. By doing so, the instructor can determine whether or not a longer lesson is truly a factor in improving student test scores.

The explanatory variable, or independent variable, is the factor that is manipulated or controlled to observe its effect on the dependent variable, which, in this case, is the students' test scores.

The instructor would likely conduct an experiment by varying the length of lessons and comparing the resulting test scores. By analyzing the relationship between the explanatory variable (lesson length) and the dependent variable (test scores), the instructor can determine whether or not increasing the lesson duration contributes to improved student performance.

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Based on the provided data, the p-value for determining whether or not there is a significant difference between the hourly wages of Company A and Company B is 0.0042. This analysis is only applicable to the specific sample sizes and population standard deviations provided, and may not be generalizable to other populations or data sets.

To determine if there is a significant difference between the hourly wages of Company A and Company B, we can conduct a two-sample t-test. Here's the step-by-step process:

1. Identify the given information:

Company A:
Sample size (n1) = 50
Sample mean (X1) = $16.75
Population standard deviation (σ1) = $1.00

Company B:
Sample size (n2) = 60
Sample mean (X2) = $16.25
Population standard deviation (σ2) = $0.95

2. Calculate the t-value:
t = (X1 - X2) / √((σ1²/n1) + (σ2²/n2))

t = ($16.75 - $16.25) / √(($1.00²/50) + ($0.95²/60))

3. Calculate the degrees of freedom (df):
df = min(n1-1, n2-1)

df = min(50-1, 60-1) = min(49, 59) = 49

4. Using a t-table or a calculator, find the p-value for the calculated t-value and degrees of freedom. In this case, the p-value is 0.0042.

So, the p-value is 0.0042.

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Answer:

The equation has no real solutions. It has 2 imaginary, or complex solutions.

Step-by-step explanation:

Good boy

Answer: 0

Step-by-step explanation:

none you can't take the square root of a negative number

Or if you square any number you can never get -49

7*7 = +49

(-7)(-7)=+49

It' only has 2 imaginary solution 7i

101.9 cm is the length of the paper.

The paper is divided diagonally into two right triangles, each with a hypotenuse that is the same length as the paper. Let's call the paper's length "x" for short.

Using the Pythagorean theorem, we know that:

[tex]x^2 = 72^2 + 72^2[/tex]

Simplifying this equation, we get:

[tex]x^2 = 2(72^2)\\x = \sqrt{2(72^2)} = 101.9 cm[/tex]

(rounded to one decimal place)

Therefore, the paper's length is approximately 101.9 centimeters.

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Therefore, the probability of having at least 50 smokers in a sample of 300 adults is: 0.7467 or about 74.67%.

This problem can be solved using the binomial distribution, where X represents the number of smokers in a sample of size n = 300. We are interested in finding the probability that at least 50 are smokers, which can be written as:

P(X >= 50)

To calculate this probability, we need to use the binomial probability formula:

[tex]P(X = k) = C(n, k) * p^k * (1-p)^{(n-k)}[/tex]

where C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success (being a smoker), and 1-p is the probability of failure (not being a smoker).

Since we are interested in at least 50 smokers, we need to calculate the probabilities for X = 50, 51, 52, ..., 300 and add them up. However, this would be very time-consuming and cumbersome. Fortunately, we can use the complement rule and calculate the probability of the complement event (i.e., fewer than 50 smokers), which is easier to compute:

P(X < 50) = P(X <= 49)

To calculate this probability, we can use a binomial probability calculator or a statistical software package. Using a binomial calculator, we find:

P(X <= 49) = 0.2533

Therefore, the probability of having at least 50 smokers in a sample of 300 adults is:

P(X >= 50) = 1 - P(X < 50) = 1 - 0.2533 = 0.7467

So the probability that at least 50 are smokers is 0.7467 or about 74.67%.

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If you wanted to measure satisfaction with this course on a scale from 1, not very satisfied, to 7, very satisfied, you would use an ordinal scale.

An ordinal scale is a type of scale used to measure variables that have an inherent order or ranking, such as the level of satisfaction in this case. However, the differences between the categories are not necessarily equal or measurable, which rules out the use of an interval or ratio scale. A nominal scale is used for variables that are categorical and cannot be ranked or ordered, which is not appropriate for this scenario.

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Answer: $640

Step-by-step explanation:

4 x 10 (months)

= 40

$600 + $40

= $640

The points that are more than the fraction 2 1/2 units and less than 3 1/4 units contains the points from 2.5 to 3.25.

Given measurements are 2 1/2 and 3 1/4.

We have to shade the region in between these two points.

Both are written in mixed fractional form.

This can be written in decimal as,

2 1/2 = 2 + 1/2 = 2 +6 0.5 = 2.5

3 1/4 = 3 + 1/4 = 3 + 0.25 = 3.25

Hence the shaded region will contain the points from 2.5 to 3.25.

2.5 is at the exact middle of 2 and 3.

3.25 is at 1/4th distance of 3 and 4. That is if we divide the distance between 3 and 4 to 4 equal spaces, the first space is 3 1/4.

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The measure of arc angle DC is 60.

The measure angle A is  45⁰.

The measure angle B  is 50⁰.

The measure angle C is  45⁰.

The measure angle D  is 50⁰.

The measure of arc angle DC is calculated as follows;

arc DC = 360 - (100 + 110 + 90) (sum of angles in a circle)

arc DC = 60

The measure angle A is calculated as follows;

m∠A = ¹/₂( arc BC ) (intersecting chord theorem)

m∠A = ¹/₂ x 90

m∠A = = 45⁰

The measure angle B  is calculated as follows;

m∠B = ¹/₂( arc AD ) (intersecting chord theorem)

m∠B = ¹/₂ x 100

m∠B  = 50⁰

The measure angle C is calculated as follows;

m∠C = m∠A (vertical opposite angles)

m∠C = = 45⁰

The measure angle D is calculated as follows;

m∠D = m∠B  (vertical opposite angles)

m∠C = = 50⁰

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The general solution for the second differential equation is y = [tex]e^[(1/2)x^2 + C2] - 4[/tex]

1. [tex]dy/dx = 2x/y[/tex]

Step 1: Separate variables. To do this, multiply both sides by y and divide both sides by dx:
[tex]y dy = 2x dx[/tex]

Step 2: Integrate both sides:
[tex]∫y dy = ∫2x dx[/tex]

Step 3: Evaluate the integrals:
[tex](1/2)y^2 = x^2 + C1[/tex], where C1 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
[tex]y^2 = 2x^2 + 2C1\\y = ±√(2x^2 + 2C1)[/tex]

So, the general solution for the first differential equation is [tex]y = ±√(2x^2 + 2C1[/tex]).

2. [tex]dy/dx = x(y+4)[/tex]

Step 1: Separate variables. To do this, divide both sides by (y+4) and multiply both sides by dx:
[tex]dy / (y+4) = x dx[/tex]

Step 2: Integrate both sides:
[tex]∫[1 / (y+4)] dy = ∫x dx[/tex]

Step 3: Evaluate the integrals:
[tex]ln|y+4| = (1/2)x^2 + C2[/tex], where C2 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
[tex]y+4 = e^[(1/2)x^2 + C2]\\y = e^[(1/2)x^2 + C2] - 4[/tex]

So, the general solution for the second differential equation is y = [tex]e^[(1/2)x^2 + C2] - 4[/tex]

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Answer:

99.5in^2

Step-by-step explanation:

10×12/2=60

5×5×3.14/2=39.25

60+39.5=99.5

Answer: 99.2699

Step-by-step explanation:

Area of a Triangle- HeightxWidthx0.5

Area of a Circle- Pi times the radius squared. Since it is a half circle, divide the answer in half.

a) The sampling distribution of the sample mean has mean μ=300 and standard deviation  is 4.

b)Normal distribution.

c)No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.The correct answer is B.

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with a mean (μ) of 300 and a standard deviation (σ) of 28/√49 (which is 28/7 or 4).

b. For part (a) to be true, the assumption made about the distribution of the variable under consideration is C. Normal distribution.

c. The statement in part (a) is still true if the sample size is 16 instead of 49 because of the Central Limit Theorem. However, the standard deviation will change.

The correct answer is B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.

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To determine the appropriate prefix multiplier for reporting a measurement of 5.57 × 10^(-5) m, we need to find a suitable metric prefix that would make the number easier to read and understand.

1. Convert the original measurement (5.57 × 10^(-5) m) to a more suitable metric unit.
2. Compare the metric prefixes and their corresponding multipliers to find the best fit.

In this case, the closest metric prefix for 10^(-5) is "micro" (symbol: µ), which has a multiplier of 10^(-6). To use this prefix, we need to convert the measurement to micrometers (µm).

3. Divide the original measurement by the multiplier of the chosen prefix: (5.57 × 10^(-5) m) / (10^(-6) µm/m) = 55.7 µm.

So, the appropriate prefix multiplier for reporting the measurement of 5.57 × 10^(-5) m is "micro," and the measurement can be reported as 55.7 µm.

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The size of the tire that he needed to buy is the one with a circumference of 75.4 inches.

Given that,

while working as a reace driver, Jalen needed to replace the tire on his car.

Tire is in the shape of a circle.

Diameter of the circle = 24 inches

Radius of the circle = 24/2 = 12 inches

We have to find the circumference of the tire.

Circumference = 2πr, where r is the radius.

Substituting,

Circumference = 2πr = 2π × 12 = 24π = 75.4 inches

Hence the size of the tire is 75.4 inches.

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The cost of each strand of Christmas lights is $4, and the cost of each decoration is $3.5 which is calculated using equations 3x + 6y = 33 and 2x + 8y = 36.

Let x= price in dollars of each strand of Christmas lights, and let y =price in dollars of each ornament. Then, we can set up the following system of equations:

3x + 6y = 33

2x + 8y = 36

The first equation represents the amount spent by the first customer, who bought 3 strands of Christmas lights and 6 ornaments for $33. The second equation represents the amount spent by the second customer, who paid $3 more than the first customer for 2 strands of Christmas lights and 8 ornaments.

To solve for x and y, we can use either substitution or elimination. Here, we will use elimination:

Multiplying the first equation by 2, we get:

6x + 12y = 66

Multiplying the second equation by 3, we get:

6x + 24y = 108

Subtracting the first equation from the second equation,

12y = 42

Dividing both sides by 12, we get:

y = 3.5

Substituting y = 3.5 into the first equation, we get:

3x + 6(3.5) = 33

Simplifying, we get:

3x + 21 = 33

Subtracting 21 from both sides, we get:

3x = 12

Dividing both sides by 3, we get:

x = 4

therefore, the cost of each strand of Christmas lights is $4, and the cost of each decoration is $3.5.

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The value of the side x = 114. 34

We have that the six different trigonometric identities in mathematics are listed thus;

We also have that their ratios are given as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram, we have;

Adjacent side = 98

Hypotenuse = x

Angle = 31

cos 31 = 98/x

cross multiply

x = 114. 34

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