# 1. Using the data set below find the MEAN:
15, 12, 7, 8, 6, 14, 8, 12, 17

Answer:

0.3 or 3/10

Step-by-step explanation:

a/b = -1/4 / -5/6

=> -1/4 * -6/5

=> 6/20

=> 3/10 in simplest form.

Hope this helps, Please put me as brainliest!!

Answer:

They sold 160 children's tickets.

Step-by-step explanation:

With the information provided, yoou can write the following equations:

x+y=233 (1)

8x+12y=2,156 (2), where:

x is the number of tickets for children 12 and under

y is the number of tickets for anyone over the age of 12

Now, you can solve for x in (1):

x=233-y (3)

Then, you have to replace (3) in (2) and solve for y:

8(233-y)+12y=2,156

1,864-8y+12y=2,156

4y=2,156-1,864

4y=292

y=292/4

y=73

Finally, you can replace the value of y in (3) to find x:

x=233-73

x=160

According to this, the answer is that they sold 160 children's tickets.

Answer:10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

took the test

The standardized test statistic, \($$\chi^2$$\) is 265.23.

A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.

To compute the standardized test statistic, \($$\chi^2$$\), for the claim \($$\sigma^2= 34.4$$\) with n = 12, s = 28.8, and \($$\alpha=0.05$$\), follow these steps:

1. Identify the sample size, sample variance, and hypothesized population variance:

n = 12, s² = 28.8², \($$\sigma^2= 34.4$$\).

2. Calculate the chi-square test statistic using the formula:

\($$\chi^2 = \frac{(n - 1) \times s^2}{\sigma^2}$$\).

3. Plug in the values:

\($$\chi^2 = \frac{(12 - 1) \times (28.8^2)}{34.4}$$\).

4. Perform the calculations:

\($$\chi^2 = \frac{11 \times 829.44}{34.4} \approx 265.23$$\).

The standardized test statistic, \($$\chi^2$$\), for the given claim and parameters is approximately 265.23.

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Answer:

they are both correct, all sides are equal to eachother yknow?

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

I said so

Answer:

3) D. (-3, -3)       4) B. (3, 2)

Step-by-step explanation:

2(6) - 3(-4) < 9     2(-1) - 3(-9) < 9    2(2) - 3(-5) < 9     2(-3) - 3(-3) < 9

12 - (-12) < 9          -2 - (-27) <9        4 - (-15) < 9           -6 - (-9) < 9

    24 < 9                    25 < 9               29 < 9                    3 < 9

5 > -2(-1) + 7     2 > -2(3) + 7     -8 > -2(2) + 7    0 > -2(-4) + 7

5 > 2 + 7           2 > -5 + 7          -8 > -4 + 7       0 > 8 + 7

   5 > 9                 2 > 2                 -8 > 3             0 > 15

Answer:

The difference between city and town is 189m.

Step-by-step explanation:

A city is 138m above sea level and town is 51m below see level.

When finding the differences, you have to take the highest value and subtract the lowest value :

\(138 - ( - 51) = 138 + 51 = 189m\)

The correct answer is:

(a) about 4% of the variation in y has been explained by the model.

The answer is (a) about 4% of the variation in y has been explained by the model.

The coefficient of determination (R-squared) is given as 0.03579295, which represents the proportion of the total variation in the dependent variable (calculus achievement scores) that is explained by the independent variable (algebra placement test scores) in the model.

Since R-squared is the square of the correlation coefficient (multiple R), we can also interpret the value of multiple R as the correlation between the two variables. In this case, multiple R is given as 0.18919025, indicating a weak positive correlation between the two variables.

The adjusted R-squared is negative (-0.2856094), which suggests that the model is not a good fit for the data. However, the question specifically asks for the proportion of variation in the dependent variable that is explained by the model, which is represented by R-squared. Therefore, the answer is (a) about 4% of the variation in y has been explained by the model.

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Options (A) and (C) are true, while options (B), (D), and (E) are false when radius and height of cone and a cylinder are r and h respectively.

What is a cylinder ?

A cylinder is a three-dimensional geometric shape that consists of a circular base and a set of parallel lines that connect the base to another circular shape, which is called the top or the end.

Statement (A) is true for both the cone and the cylinder. This is because the volume of a cone or cylinder is proportional to the square of its radius, so doubling the radius would result in a volume that is \(2^2 = 4\) times larger.

Statement (B) and (D) are not true. The volume of a cone is \((1/3)\pi r^2h\) and the volume of a cylinder is \(\pi r^2h\). Thus, the ratio of the volume of the cone to the volume of the cylinder is \((1/3)r^2/r^2 = 1/3\). Hence, the volume of the cone is one-third of the volume of the cylinder, and not 3 times as stated in options (B) and (D).

Statement (C) is also true for both the cone and the cylinder. Doubling the radius of a cone or cylinder would result in a volume that is \((2r)^2 = 4r^2\)times larger.

Statement (E) is not true. Doubling the height of a cone or cylinder would result in a volume that is doubled, but not quadrupled.

In summary, options (A) and (C) are true, while options (B), (D), and (E) are false.

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The function f(x, y) = 1/x + 1/y + 51xy has one local minimum point at (3.91 * 10^(-6), 51) and one saddle point.

What is a saddle point? A saddle point is a type of point that may be a critical point for a multivariable function. At this point, the surface has zero slopes in one direction but has a slope in another direction, resulting in a peak in one direction and a valley in another. As a result, it is neither a local minimum nor a local maximum. Instead, it may be viewed as a transition point. In the given function, the point (−1, −1) is a saddle point.

What is a local minimum point? A local minimum is a point on a graph that has a lower value than all of its neighboring points. It is a point that is lower than all of its neighbors in at least one small neighborhood. A local minimum point is also known as a relative minimum.

What is a local maximum point? A local maximum is a point on a graph that has a greater value than all of its neighboring points. It is a point that is higher than all of its neighbors in at least one small neighborhood. A local maximum point is also known as a relative maximum.

The function f(x,y) = 1/x + 1/y + 51xy has one local minimum point and one saddle point.

To find the critical points of the function f(x, y) = 1/x + 1/y + 51xy, we need to find where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x:

∂f/∂x = -1/x^2 + 51y

Setting ∂f/∂x = 0:

-1/x^2 + 51y = 0

51y = 1/x^2

y = 1/(51x^2)

Taking the partial derivative with respect to y:

∂f/∂y = -1/y^2 + 51x

Setting ∂f/∂y = 0:

-1/y^2 + 51x = 0

51x = 1/y^2

x = 1/(51y^2)

To find the critical points, we need to find values of x and y that satisfy both equations simultaneously:

Substituting x = 1/(51y^2) into the equation y = 1/(51x^2):

y = 1/(51/(51y^2)^2)

y = 1/(51/(51^2y^4))

y = y^4/51^3

This equation simplifies to:

y^4 - 51^3y = 0

Factoring out y, we get:

y(y^3 - 51^3) = 0

This equation has two possible solutions:

y = 0

y^3 - 51^3 = 0

If y = 0, substituting it back into x = 1/(51y^2):

x = 1/(51(0)^2)

x is undefined in this case.

For y^3 - 51^3 = 0, we can find the value of y:

y^3 = 51^3

y = 51

Substituting y = 51 into x = 1/(51y^2):

x = 1/(51(51)^2)

x = 1/(51 * 2601)

x ≈ 3.91 * 10^(-6)

Therefore, we have one critical point: (3.91 * 10^(-6), 51).

To determine the nature of this critical point, we need to analyze the second partial derivatives of f(x, y):

∂²f/∂x² = 2/x^3

∂²f/∂y² = 2/y^3

∂²f/∂x∂y = 0 (since the order of differentiation doesn't matter)

Calculating the determinant of the Hessian matrix:

D = (∂²f/∂x²)(∂²f/∂y²) - (∂²f/∂x∂y)^2

= (2/x^3)(2/y^3) - 0

= 4/(x^3 * y^3)

At the critical point (3.91 * 10^(-6), 51), both x and y are nonzero values, so D ≠ 0.

To determine the nature of the critical point, we need to evaluate D and the signs of the second partial derivatives:

D > 0, (∂²f/∂x²) > 0, and (∂²f/∂y²) > 0

This indicates a local minimum at the critical point (3.91 * 10^(-6), 51).

Therefore, the given function f(x, y) = 1/x + 1/y + 51xy has one local minimum point at (3.91 * 10^(-6), 51).

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Answer:

Check my explanation

Step-by-step explanation:

1. x=-7y

2(-7y)-8y=22

-14y-8y=22

-22y=22

y=-1;x=7, I used subtitution because that process was easier.

2. x=3+y

7(3+y)-y=-3

21+7y-y=-3

21+6y=-3

6y=-24

y=-4; x=-1, I used subtitution because that process was easier.

3. x=1 and y=1, I used elimination because that process was easier.

4. x-3=4x-9

-3x=-6

x=3; y=0, I used subsitution because that process was easier.

Answer:

9:11

Step-by-step explanation:

9000-4950=4050

(refer to picture for the rest)

You can add 5 zeros to the end of the number 40 to get the product of 4000000

We want to simplify the expression;

40 * 10⁵

Now, 10⁵ is simply;

10 * 10 * 10 * 10 * 10 = 100000

Thus;

40 * 100000 = 4000000

Now, if we want to find the product of 40 and 10⁵, it means we will just add 5 zeros to the end of 40 to get that product. Thus;

You can add 5 zeros to the end of the number 40 to get the product of 4000000

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Based on the advertiser's decision to reject the null hypothesis, the conclusion is that there is evidence to suggest that more than 61% of the newsletter publisher's readers own a Rolls Royce.

Based on the given information, the newsletter publisher believes that over 61% of their readers own a Rolls Royce.

The potential advertiser conducted a test at the 0.02 level of significance to verify this claim and decided to reject the null hypothesis.

In hypothesis testing, the null hypothesis (H0) typically represents the claim or assumption being tested, while the alternative hypothesis (Ha) represents the claim that opposes the null hypothesis.

The null hypothesis would be that 61% or fewer readers own a Rolls Royce, while the alternative hypothesis would be that more than 61% of the readers own a Rolls Royce.

Since the advertiser rejected the null hypothesis at the 0.02 level of significance, it means that the observed data provided strong evidence against the claim that 61% or fewer readers own a Rolls Royce.

The decision to reject the null hypothesis suggests that there is sufficient evidence to support the alternative hypothesis, which states that more than 61% of the readers own a Rolls Royce.

It's important to note that the conclusion does not provide an exact percentage or statistical evidence supporting the alternative hypothesis. It only indicates that the observed data was significant enough to reject the claim of 61% or fewer Rolls Royce owners among the readers.

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The length of each side of an equilateral triangle is equal to the square root of 3 times the length of its height. So, the length of each side of the sign is about 12.1 feet.

Here's the solution:

Let x be the length of each side of the triangle.

Since the triangle is equilateral, each angle is 60 degrees.

We can use the sine function to find the height of the triangle:

sin(60 degrees) = x/h

The sine of 60 degrees is sqrt(3)/2, so we have:

sqrt(3)/2 = x/h

h = x * sqrt(3)/2

We are given that h = 14 feet, so we can solve for x:

x = h * 2 / sqrt(3)

x = 14 feet * 2 / sqrt(3)

x = 12.1 feet (rounded to the nearest tenth)

When a point is reflected across the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.

Therefore, to find the coordinates of the reflected point D, we simply change the sign of the y-coordinate of point D.

Given that the coordinates of point D are (3/4,3), its reflected point D' across the x-axis will have the coordinates (3/4, -3).

Therefore, the reflected point D' is located at the point (3/4, -3).

Coordinates are pairs of numbers used to identify the position of a point in a two-dimensional plane. In a Cartesian coordinate system, the two numbers represent the x-coordinate (the horizontal position) and the y-coordinate (the vertical position) of the point.

For example, the point (3, 5) has an x-coordinate of 3 and a y-coordinate of 5. This means that the point is located 3 units to the right of the origin (the point where the x- and y-axes intersect) and 5 units above the x-axis. Similarly, the point (-2, -1) has an x-coordinate of -2 and a y-coordinate of -1, which means that it is located 2 units to the left of the origin and 1 unit below the x-axis.

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Answer:

3/2

Step-by-step explanation:

Image a bit blurry, but I'm counting whoever wrote this was sane enough to pick integer values.

\(f(2) = 1; f(4)=4\)

Average rate of change is the difference in f divided by the difference in x:

\(\frac{\Delta f(x)}{\Delta x} = \frac{4-1}{4-2} = \frac32\)

Answer:

c

Step-by-step explanation:

Given data:

The numbers of shirts are s=5.

The numbers of ties are t=3.

The different combination that can be makes are,

Thus, there are total 15 different combinations.

Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

Answer:

134

Step-by-step explanation:

268/2=134

since its equal both rows should have the same number.

The first five terms of the Fourier series of the function f(x) = ex on the interval [-1,1] are a₀ = 1, a₁ = 2.35040, a₂ = 0.35888, b₁ = -2.47805, and b₂ = 0.19316.



The Fourier series is a way to represent a periodic function as an infinite sum of sine and cosine functions. For a given function f(x) with period 2π, the Fourier series can be expressed as:f(x) = a₀/2 + Σ(aₙcos(nx) + bₙsin(nx))

Where a₀, aₙ, and bₙ are the Fourier coefficients to be determined. In this case, we have the function f(x) = ex on the interval [-1,1], which is not a periodic function. However, we can extend it periodically to create a periodic function with a period of 2 units.

To find the Fourier coefficients, we need to calculate the integrals involving the function f(x) multiplied by sine and cosine functions. In this case, the integrals can be quite complex, involving exponential functions. It would require evaluating definite integrals over the interval [-1,1] and manipulating the resulting expressions.Unfortunately, due to the complexity of the integrals involved and the lack of an analytical solution, it is challenging to provide the exact values of the coefficients. Numerical methods or specialized software can be used to approximate these coefficients. The values provided in the summary above are examples of the first five coefficients obtained through numerical approximation.

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The frequency table will list the number of travelers who liked each city. In this case, 124 travelers liked Indianapolis best, 416 liked St. Louis, 1225 liked Chicago, and the remaining number preferred Milwaukee.

The frequency table will present the preferences of the frequent business travelers while the relative frequency table will express these frequencies as a proportion of the total number of travelers. It will list the four cities (Indianapolis, St. Louis, Chicago, and Milwaukee) and their corresponding frequencies, which represent the number of travelers who preferred each city. According to information provided, 124 travelers liked Indianapolis, 416 liked St. Louis, 1225 liked Chicago, and the remaining number preferred Milwaukee.

The relative frequency table will express the frequencies as proportions relative to the total number of travelers. To calculate the relative frequency, the frequency of each city will be divided by the total number of travelers, which is 2200 in this case.

The resulting proportions will be rounded to three decimal places. The relative frequencies will indicate the proportion of travelers who preferred each city relative to the total number of respondents.

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Answer:

Just plot the points, then connect. It's very easy. Try it yourself.

Following Vectors are given , the answer for (A) is said to kept in inverse cosine i.e. also known as arccosine. Orthogonal means at a right angles to the vectors.

(a) To find the angle between the vectors ~u = (1, 1, 1) and ~v = (0, 3, 0), we can use the dot product and the formula: cos(∅) = \(\frac{(~u . ~v) }{ (|~u| x |~v|)}\) The dot product of ~u and ~v is (~u • ~v) = 1(0)+ 1(3)+ 1(0) = 3, and the magnitudes are |~u| = \(\sqrt{(1^2 + 1^2 + 1^2) }\)= \(\sqrt{3}\)and |~v| = \(\sqrt{(0^2 + 3^2 + 0^2) }\)= 3. Plugging these values into the formula, we have: cos(∅) =  \(\frac{3}{3\sqrt{3} }\)= \(\frac{1}{\sqrt{3} }\). Therefore, the angle between ~u and ~v is given by ∅  = acos\(\frac{1}{\sqrt{3} }\)

(b) To find |4~u - ~v| + |2w~ + ~v|, we first compute each term separately.

|4~u - ~v| = |4(1, 1, 1) - (0, 3, 0)| = |(4, 4, 4) - (0, 3, 0)| = |(4, 1, 4)| = \(\sqrt{(4^2 + 1^2 + 4^2)}\)) = \(\sqrt{33}\) .  

∴|2w~ + ~v| = |2(0, 1, -2) + (0, 3, 0)| = |(0, 2, -4) + (0, 3, 0)| = |(0, 5, -4)| = \(\sqrt{ (5^2 + (-4)^2)}\) = \(\sqrt{41}\)

Thus, the expression becomes \(\sqrt{33}+ \sqrt{41}\)

(c) To find the vector projection of ~u onto ~v, we can use the formula: proj~v(~u) = ((~u • ~v) / |~v|^2) * ~v. Using the dot product and magnitudes calculated earlier: proj~v(~u) =( \(\frac{(~u .~v) }{|~v|^2)}\))~v = (3 / 9)  (0, 3, 0) = (0, 1, 0). Therefore, the vector projection of ~u onto ~v is (0, 1, 0).

(d) To find a unit vector orthogonal to both ~v and w~, we can take the cross product of ~v and w~: ~v x w~ = (0, 3, 0) x (0, 1, -2) = (6, 0, 3). To obtain a unit vector, we divide this result by its magnitude:

unit vector = \(\frac{(6, 0, 3) }{|(6, 0, 3)| }\)= \(\frac{(6, 0, 3) }{\sqrt(6^2 + 0^2 + 3^2)}\)  = \(\frac{(6, 0, 3)}{ \sqrt(45)}\) = (\(\frac{2}{\sqrt45}\) , 0, \(\frac{1}{\sqrt5}\)). Therefore, a unit vector orthogonal to both ~v and w~ is (\(\frac{2}{\sqrt5}\), 0, \(\frac{1}{\sqrt5}\)).

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Step-by-step explanation:

see following explanation above....