If another teacher with an age of 45 is added to the data, how would the mean be impacted?

The mean would decrease in value to about 41.
The value of the mean would remain the same at about 44.
The value of the mean would remain the same at about 46.
The mean would increase in value to about 47.

Answer:

24/7

Step-by-step explanation:

Answer:

Length = 18 ft

Width = 4 ft

Step-by-step explanation:

Let the width of the rectangle be x ft

Therefore, length = (x + 14) ft

Area of rectangle = 72 sq ft

\( \therefore \: x(x + 14) = 72 \\ \therefore \: {x}^{2} + 14x - 72 = 0 \\\therefore \: {x}^{2} + 18x - 4x - 72 = 0 \\\therefore \: x(x + 18) - 4(x + 18) = 0 \\ \therefore \:(x + 18)(x - 4) = 0 \\ \therefore \:x + 18 = 0 \: \: or \: \: x - 4 = 0 \\ \therefore \:x = - 18 \: or \: \: x = 4 \\ \because \: dimensions \: of \: a \: rectangle \: \\ cn \: not \: be \: negative \\ \therefore \: x \neq \: - 18 \\ \implies \: x = 4 \\ \therefore \: x + 14 = 4 + 18 = 18 \\ length \: of \:the \: rectangle \: = 18 \: ft \\ width \: of \: the \: rectangle = 4 \: ft\)

There are seven lines of symmetry in a heptagon. In a heptagon, the sides and angles are equal. Each vertex and the center of a regular heptagon are where the line of symmetry crosses.

What is Reflectional Symmetry ?

Any symmetry with regard to a reflection is referred to as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry. In other words, a figure with reflectional symmetry does not alter when it is reflected. There is a line/axis of symmetry in 2D and a plane of symmetry in 3D. When a form or pattern is mirrored in a line of symmetry or a mirror line, this is known as reflective symmetry. The reflected form will have the same size, distance from the mirror line, and other characteristics as the original shape. When a figure can be split into two equal halves that match, it has line symmetry or reflection symmetry.

If a figure can be reflected over a line and retain its original appearance, it possesses reflection symmetry. If a figure can be altered while maintaining its appearance, it possesses symmetry.

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Complete question

Which statements are true about the reflectional symmetry of a regular heptagon? Check all that apply. It has only 1 line of reflectional symmetry. A line of symmetry will connect 2 vertices. A line of symmetry will connect a vertex and a midpoint of an opposite side. It has 7-fold symmetry. A line of symmetry will connect the midpoints of 2 opposite sides.

Answer:

Step-by-step explanation:

1. Since we know that Lila wants to use 1 cup of pretzels, we can multiply 1/2 x 1/2, which is 1.

2. Now that we multiplied 1/2 by 1/2, we have to multiply 1 1/4 by 1/2.

So 5/4 x 1/2 is 5/8.

3. Lila will need 5/8 cups of raisins.

Answer:

124m/s

Step-by-step explanation:

There is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less.

To find the probability of a sample proportion of 0.48 or less if the true population proportion is 0.60, we can use the sampling distribution of the sample proportion and the z-score.

Given:

Sample size (n) = 100

Observed sample proportion ) = 0.48

True population proportion (p) = 0.60

To find the probability, we need to standardize the observed sample proportion using the z-score formula:

z = ( - p) / √(p * (1 - p) / n)

Substituting the values:

z = (0.48 - 0.60) / √(0.60 * (1 - 0.60) / 100)

= -0.12 / √(0.24 / 100)

= -0.12 / √0.0024

= -0.12 / 0.049

Using a standard normal distribution table or a statistical calculator, we can find the probability associated with the z-score.

The probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is the probability to the left of the z-score obtained.

P ≤ 0.48) = P(z ≤ -0.12)

Using a standard normal distribution table, we find that the probability of z ≤ -0.12 is approximately 0.4522.

Therefore, the probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is approximately 0.4522 or 45.22%.

This means that there is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less, if the true population proportion is 0.60.

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Answer: 4% of ___days is 56 days Answer If 0.04x = 56 days 0.01x = 14 days x = 14*100 = 1400 days To see more answers head over to College Study Guides

Step-by-step explanation:

Answer:

They are equal to one another

Step-by-step explanation:

1/2 is equal to .5, so id you have 6.5 on one side and 6.5 on the other, they are equal.

Answer: =

6 \(\frac{1}{2}\) = 50/100

=6.5

so 6.5 = 6 \(\frac{1}{2}\)

Answer: No

Step-by-step explanation:

The domain consists of the numbers 6, 5, 6, 2

6 is repeated twice

The criteria for a function is that there are no repeating numbers in the domain

This does not follow the criteria, therefore this is not a function

Answer-No

The coordinates of the third vertex of the equilateral triangle will be (x1, y1) and (x2, y2).

To find the coordinates of the third vertex of an equilateral triangle, given two of its vertices, we can use the concept of equidistant points.

In an equilateral triangle, all three sides have the same length, and the distance between any two vertices is equal.

Let's consider the given vertices as A(-2, 0) and B(0, 2). To find the third vertex, let's denote it as C(x, y).

Using the distance formula, we can set up two equations to equate the distances between the vertices:

1. Distance between A and B:

AB = AC

2. Distance between B and C:

BC = AC

Using the distance formula, the equations become:

1. \(\sqrt{(x+2)^2 + (y-0)^2} = \sqrt{(-2-0)^2 + (0-2)^2}\)

2. \(\sqrt{(x-0)^2 + (y-2)^2} = \sqrt{(0+2)^2 + (2-0)^2}\)

Simplifying these equations, we have:

1. \((x+2)^2 + y^2 = 4 + 4\)

2. \(x^2 + (y-2)^2 = 4 + 4\)

Simplifying further:

1. \(x^2 + 4x + y^2 = 8\)

2. \(x^2 + y^2 - 4y + 4 = 8\)

Rearranging the equations, we get:

1. \(x^2 + 4x + y^2 = 8\)

2. \(x^2 + y^2 - 4y = 4\)

Now, we can solve these two equations simultaneously to find the coordinates (x, y) of the third vertex.

By subtracting equation 2 from equation 1, we eliminate the squared terms:

\(4x + 4y = 4\)

Dividing by 4, we get:

\(x + y = 1\)

Now, we substitute this value in either equation 1 or 2:

\(x^2 + y^2 - 4y = 4\)

Substituting \(x = 1 - y\), we have:

\((1 - y)^2 + y^2 - 4y = 4\)

Expanding and simplifying:

\(1 - 2y + y^2 + y^2 - 4y = 4\)

Combining like terms:

\(2y^2 - 10y + 1 = 4\)

Rearranging the equation:

\(2y^2 - 10y - 3 = 0\)

Now, we can solve this quadratic equation to find the values of y. Once we have the value(s) of y, we can substitute it back into \(x = 1 - y\) to find the corresponding x-coordinate.

Solving the quadratic equation, we get two values of y, let's denote them as y1 and y2. Substituting these values back into \(x = 1 - y\), we get two corresponding x-values, x1 and x2.

Therefore, the coordinates of the third vertex of the equilateral triangle will be (x1, y1) and (x2, y2).

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The major reason that exponential smoothing has become well accepted as a forecasting technique is its accuracy and ease of use.

Exponential smoothing is a popular method for forecasting time series data because it is simple to implement, requires minimal computational resources, and can produce accurate forecasts for a wide range of time series data.

Additionally, exponential smoothing models can be easily updated with new data, making them well suited for real-time forecasting applications.

This makes exponential smoothing an appealing option for many businesses and organizations looking to make accurate forecasts without the need for complex or expensive analysis tools.

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Answer:

f(3) = 12

Step-by-step explanation:

F(x) = 2x2. What is f(3)

f(3) = 2(3) 2

= 6x2

= 12

f(3) = 12

The integral ∫(4x - 2)dx from [-2, 2] is equal to the area between the x-axis and the function 4x - 2 over the interval [-2, 2], which is 32.

The integrand is 4x - 2.

To evaluate the integral geometrically in terms of area, we can interpret the integral as the area between the x-axis and the function 4x - 2 over the interval [-2, 2]. We can break this area into two parts: the area under the line y = 4x and the area under the line y = 4x - 2.

The area under the line y = 4x is given by the integral ∫4x dx from -2 to 2, which is equal to [2x^2] from -2 to 2, or 2(2^2) - 2(-2^2) = 16.

The area under the line y = 4x - 2 is given by the integral ∫(4x - 2) dx from -2 to 2, which is equal to [2x^2 - 2x] from -2 to 2, or 2(2^2) - 2(2) - [2(-2^2) - 2(-2)] = 8 - (-8) = 16.

Therefore, the total area between the x-axis and the function 4x - 2 over the interval [-2, 2] is 16 + 16 = 32.

So, the integral ∫(4x - 2)dx from [-2, 2] is equal to the area between the x-axis and the function 4x - 2 over the interval [-2, 2], which is 32.

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Answer: 44

Step-by-step explanation:

since the inscribed angle is half of true arc measure, (3x+10)= 2(2x-17).

when you work this out, you get 44 as x.

The value of x from the given figure is 44°. Therefore, option B is the correct answer.

The angle subtended by an arc at the center is twice the angle subtended at the circumference . More simply, the angle at the center is double the angle at the circumference.

From the given figure,

Angle at circumference is (2x-17)° and angle at center is (3x+10)°.

Now, (3x+10)°=2(2x-17)°

3x+10=4x-34

4x-3x=10+34

x=44°

Therefore, option B is the correct answer.

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Answer:

A grade of 7% = 7 / 100 ;

This means that the elevation or vertical heighy of the interstate highway changes 7 feets for every 100 feets of horizontal distance moved

Step-by-step explanation:

Given that :

A road has a grade of 7%. This means that the slope of the of the highway is 7%. The slope is the proportion of rise and run. Hence the change in vertical distance with horizontal distance moved.

A grade of 7% = 7 / 100 ;

This means that the elevation or vertical heighy of the interstate highway changes 7 feets for every 100 feets of horizontal distance moved

Answer:

E

G

A

I

Step-by-step explanation:

Option B "There is a positive nonlinear association" describes the pattern of association between the variables.

A scatter plot is a kind of graph that uses a coordinate system to show the values of two variables as points. Each point addresses a perception in the informational index, with the upsides of one variable deciding the situation on the level hub and the upsides of the other variable deciding the situation on the upward pivot.

Based on the scatter plot, it appears that there is a positive nonlinear association between age and the number of hours slept. The points on the graph follow a general upward trend, but the rate of increase slows down as age increases.

Therefore, option B "There is a positive nonlinear association" describes the pattern of association between the variables.

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(a) To demonstrate graphically that the feasible region is unbounded, we can plot the given constraints on a graph. The first constraint, -2x1 + 3x2 ≤ 12, can be represented by a line. The second constraint, -3x1 + 2x2 ≤ 12, can also be represented by a line. Additionally, we have the constraints x1 ≤ 0 and x2 ≤ 0, which define the non-positive regions of the x1 and x2 axes, respectively. By combining these constraints, we can see that there are no upper bounds on the feasible region in the positive direction for either x1 or x2. This indicates that the feasible region is unbounded.

(b) When the objective is to maximize Z = 4x1 + x2, the model does not have an optimal solution. Since the feasible region is unbounded, we can continuously increase the values of x1 and/or x2, resulting in an infinitely increasing objective function value. Therefore, there is no maximum value for Z in this case.

(c) When the objective is to maximize Z = x1 - x2, the model also does not have an optimal solution. Similar to part (b), the feasible region being unbounded allows us to continuously increase the values of x1 and/or decrease the values of x2, resulting in an infinitely increasing objective function value. Thus, there is no maximum value for Z.

(d) The fact that the model does not have an optimal solution does not mean that there are no good solutions according to the model. It simply implies that the objective function cannot be maximized or minimized within the given constraints. There could still be feasible solutions that satisfy the constraints, but they do not result in an optimal value for the objective function.

(e) To select an objective function for which the model has no optimal solution, we can consider an objective such as Z = x1 + x2. Using the simplex method step by step, we would observe that the algorithm does not terminate and continues to iterate indefinitely. This indicates that Z is unbounded, as the objective function value can increase without bound.

(f) Using a software package based on the simplex method, we can confirm that Z is unbounded for the selected objective function. The software would iterate through the simplex algorithm and indicate that the solution is unbounded, meaning there is no maximum or minimum value for the objective function within the given constraints.

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

The integral of e^(-cos(8)) can't be evaluated using elementary functions. However, it can be expressed in terms of the special function called the exponential integral function, denoted as Ei(x). The integral is equal to Ei(cos(8)) + C, where C is the constant of integration.

Unfortunately, there is no straightforward way to integrate e^(-cos(8)) using elementary functions. The function e^(-cos(x)) is known as the Fourier transform of the Bessel function of the first kind of order zero. This function does not have an elementary antiderivative, which means that we need to use alternative methods to evaluate the integral.

One possible way to express the solution is by using the special function Ei(x), known as the exponential integral function. This function is defined as:

Ei(x) = -∫(-x, ∞) e^(-t)/t dt

Using this function, we can write the integral of e^(-cos(8)) as:

∫ e^(-cos(8)) dx = Ei(cos(8)) + C

where C is the constant of integration. This result holds true for any value of x, not just x=8.

To understand this result better, note that Ei(x) is a well-studied function in mathematics and has many important applications in physics, engineering, and statistics. It is closely related to other special functions such as the logarithmic integral and the gamma function. The function Ei(x) can be expressed in terms of other elementary functions, but these expressions are usually more complicated than the original definition. In conclusion, the integral of e^(-cos(8)) can't be evaluated using elementary functions. However, we can express the solution in terms of the special function Ei(x). The result is Ei(cos(8)) + C, where C is the constant of integration. The function Ei(x) is an important special function in mathematics, with many applications in various fields of science.

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We can use the fact that angle ACB is 30° to find v. We can use the tangent function:DB = CD - 50

DB = 2950 / v

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

To solve this problem, we will use trigonometry and geometry.

First, let's draw a diagram to better understand the situation:

              /|

             / |

            /  | h

        b /   |

          ----

           d

    a         c

    |\        |

    | \       |

 H  |  \ h'   |

    |   \     |

    |    \    |

    |     \   |

    |      \  |

    |       \ |

    |        \|

   ------------

          D

In this diagram, we have the lighthouse at point A with height H, the boat at point C, and after traveling for 1 minute at a constant speed, it reaches point B. We are given that angle ACB is 30°, angle AHB is 90°, and angle ABH is 60°.

We need to find the height of the lighthouse and the speed of the boat from C to B.Let's start by finding the height of the lighthouse. We can use the tangent function:

tan(ABH) = H / d

tan(60) = H / d

sqrt(3) = H / d

H = sqrt(3) * d

Now, let's find the distance d. We can use the law of cosines:scss

d² = h² + (AB)² - 2 * h * AB * cos(ABH)

We know that AB = 50 meters, ABH = 60°, and h = CD - h', where CD is the distance the boat traveled from C to D and h' is the height of the boat at point D. We can also use the tangent function to find h':

tan(ACH) = h' / CD

tan(30) = h' / (CD + DB)

1/sqrt(3) = h' / (CD + 50)

h' = (CD + 50) / sqrt(3)

Substituting h' in the previous equation:

d² = (CD - (CD + 50) / sqrt(3))² + 50² - 2 * (CD - (CD + 50) / sqrt(3)) * 50 * cos(60)

d² = (CD² + 2 * CD * 50 / sqrt(3) + 2500 / 3) + 2500 - (CD² - CD * 50 / sqrt(3) + 2500 / 3)

d² = 10000 / 3 + CD * 100 / sqrt(3)

Finally, we can use the fact that angle ACB is 30° to find v. We can use the tangent function:

tan(ACB) = h' / (CD + DB)

tan(30) = (CD + 50) / sqrt(3) / (CD + DB)

1 / sqrt(3) = (CD + 50) / sqrt(3) / (CD + DB)

DB = CD - 50

DB = 2950 / v

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No.

The 3 angles of a triangle need to equal 180 degrees.

The sum of the 3 given angles is greater than 180 ( 160 + 20 + 20 = 200) so it cannot form a triangle.

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

True , In any random sample drawn from a population, the sample mean is an unbiased estimator of the population mean.

What is the central limit theorem formula?

The central limit theorem gives a formula for the sample mean and the sample standard deviation when the population mean and standard deviation are known. This is given as follows: Sample mean = Population mean = μ μ Sample standard deviation = (Population standard deviation) / √n = σ / √n.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

The expression that represent the area of the cabin for rectangular floor plan is 2w² + 5w.

What is the area of rectangular shape?

In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.

Given that the length of a cabin is equal to 5 feet more than twice the width.

Assume that the width of the cabin be w.

Then the mathematical expression of twice the width is 2w.

Then the mathematical expression of 5 feet more than twice the width is 2w + 5.The length of the cabin is 2w + 5 feet.

The area of rectangular shape is product of length and width.

The area of the cabin is (2w + 5)w

Apply distributive property:

= 2w × w + 5 × w

= 2w² + 5w

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Answer:

Step-by-step explanation:

The  area of the triangle when the vertices of the triangle are given can be calculated by the following formula:

Area of triangle = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|  where the vertices are A(Ax, Ay), B(Bx, By), C(Cx, Cy)

Now, we have been given the values of vertices as A(4, -3) B(9,-3) , and C(10, −11)

Therefore,

By applying the formula and substituting the given values, we get

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Area = 0.5 * |44|

Area = 22

Hence, the area of triangle ABC with the given vertices is 22 square units

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