Find the range of the data set: 7, 12, 15, 4, 23, 15, 25, 9

The statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

Given data:

7, 11, 12, 18, 20, 22, 43.

To find out whether the last observation is an outlier or not, let's use the three standard deviation criterion.

That is, if a data value is more than three standard deviations from the mean, then it is considered an outlier.

The formula to find standard deviation is:

S.D = \sqrt{\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N-1}}

Where, N = sample size,

             x = each value of the data set,

    \bar{x} = mean of the data set

To find the mean of the given data set, add all the numbers and divide the sum by the number of terms:

Mean = $\frac{7+11+12+18+20+22+43}{7}$

          = $\frac{133}{7}$

          = 19

Now, calculate the standard deviation:

$(7-19)^2 + (11-19)^2 + (12-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (43-19)^2$= 1442S.D

                                                                                                                               = $\sqrt{\frac{1442}{7-1}}$

                                                                                                                                ≈ 10.31

To determine whether the value of x = 43 is an outlier, we need to compare it with the mean and the standard deviation.

Therefore, compute the z-score for the last observation (x=43).Z-score = $\frac{x-\bar{x}}{S.D}$

                                                                                                                      = $\frac{43-19}{10.31}$

                                                                                                                      = 2.32

Since the absolute value of z-score > 3, the value of x = 43 is considered an outlier.

Therefore, the statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

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Answer:

19

Step-by-step explanation:

Product of 5 and a number is 5a

5a - 26 = 69

Add 26 to both sides

5a = 69+26

5a = 95

Divide both sides by 5

A = 19

Check

(5× 19) - 26 = 65

The dimensions of each column of this rectangular prism are 1/12, 24, and 12 foot respectively. Also, 11,289.6 lbs of iron was used to make one column.

Given the following data:

First of all, we would determine the width of this rectangular prism by using this expression:

Depth = ½ × width;

Therefore, width = 2 × depth = 2 × 12 = 24 feet.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

V = Length × Width × Depth

24 = Length × 24 × 12

Length = 1/12 feet.

The total weight of this steel is given by:

Total weight = 24 × 490

Total weight = 11,760 lbs.

Since carbon represents 4% of the mass of steel, the mass of iron is given by:

Mass of iron = 100 - 4 = 96%

Quantity of iron = 96/100 × 11,760

Quantity of iron = 11,289.6 lbs.

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The equation of a straight line can be written if its slope and any one point lying on it is given. The  equation of the line for given slope and point is  (y - 3) = -1 / 7 × (x - 3). The correct answer is option B.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given that,

The slope of the line = -1 / 7

The coordinate of the point on the line = (3,3)

The equation of a line having slope m and passing through a point (x₁, y₁) is given as,

(y - y₁) / (x - x₁) = m

Thus, the equation of the line for given slope and point is given as,

(y - 3) / (x - 3) = -1 / 7

=> (y - 3) = -1 / 7 × (x - 3)

Hence, the equation of the line for given slope and point is  (y - 3) = -1 / 7 × (x - 3).

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Answer:

\(\frac{4}{5}\)

Step-by-step explanation:

\(M=\frac{x2-x1}{y2-y1}\)

\(M=\frac{5-1}{-5-(-10)}\)

\(M=\frac{4}{5}\)

No, the simple digraph with 3 vertices and in-degrees 0, 1, 2, and out-degrees 0, 1, 2 respectively does not exist, while the simple digraph with 3 vertices and in-degrees 1, 1, 1, and out-degrees 1, 1, 1 does exist.

What is digraph?

A digraph is a directed graph where each edge has a direction associated with it. In-degrees refer to the number of edges pointing into a vertex, while out-degrees refer to the number of edges pointing out of a vertex.

For the first case, having in-degrees of 0, 1, 2, and out-degrees of 0, 1, 2 for the three vertices is not possible. The sum of in-degrees must equal the sum of out-degrees in a digraph. However, in this case, the sum of in-degrees is 3 while the sum of out-degrees is 3, which does not match. Therefore, such a digraph does not exist.

For the second case, a simple digraph with in-degrees of 1, 1, 1, and out-degrees of 1, 1, 1 is possible. Each vertex has exactly one incoming edge and one outgoing edge, forming a cycle among the three vertices. This configuration satisfies the condition of a simple digraph, where each vertex has the same in-degree and out-degree.

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A minimum of three data points is required to find a single quadratic model for a data set.

A quadratic model is represented by an equation of the form y = ax² + bx + c, where a, b, and c are coefficients. This model has three parameters that need to be determined in order to fit the data accurately.

To uniquely determine the values of a, b, and c, we need three independent equations. Each data point provides one equation, with the x and y values substituted into the quadratic equation. These equations form a system of three equations that can be solved simultaneously to find the coefficients.

Having fewer than three data points would result in an underdetermined system, meaning there would be more than one possible solution for the coefficients. Therefore, at least three data points are needed to find a single quadratic model that best fits the data.

A minimum of three data points is required to find a single quadratic model for a data set.

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True, the standard deviation is a resistant measure of spread.

The standard deviation is calculated as the square root of the variance of the data set. Variance is calculated as the average of the squared differences between each data point and the mean of the data set. The standard deviation is the square root of this average.

In mathematical terms, the standard deviation can be calculated using the following formula:

σ = √(1/n ∑(x - μ)²)

Where σ is the standard deviation, n is the number of data points in the data set, x is the value of the i-th data point, and μ is the mean of the data set.

The standard deviation is an important measure because it gives an idea of how much the individual values in a data set differ from the mean.

In summary, the standard deviation is a resistant measure of spread because it gives a robust measure of the spread of the data in a set and is not easily influenced by outliers or extreme values.

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Answer:

24 square miles

Step-by-step explanation:

6 miles × 4 miles= 24 square miles

The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

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Answer: 392 meters

Step-by-step explanation:

We will set up a proportion to help us solve.

         \(\displaystyle \frac{112 \;\;meters}{x \;\;meters\;\; shadow} = \frac{1 \;meter}{3.5 \;\;meters \;\;shadow}\)

Next, we will cross-multiply:

         1 * x = 112 * 3.5

         x = 392 meters

The shadow will be 392 meters long.

The shape of the distribution of the number of siblings can vary depending on the specific data set.

However, if we are considering the general case, the most common shape of the distribution is likely to be unimodal and skewed to the right.

This means that the majority of individuals are likely to have fewer siblings,

and as the number of siblings increases,

the frequency of individuals with that number decreases.

The distribution may also have a long tail on the right side,

indicating a few individuals with a significantly larger number of siblings.

However, it is important to note that this is just a general observation, and in specific cases,

the distribution may be different.

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Answer:umm so with my super jimmy neutron powers the answer is 14 because since P = 6 the equation turns into 6 + 8=14

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

i think d then b ...........

As per the given values, the area of the hemisphere is 45065.41 m³

Volume = 450000 m³

Calculating the volume of the hemisphere -

Volume = 2/3 πr³

Substituting the values -

450,000 =2/3 x 3.14 x r³

Solving for r³

r³ = 450000 x 3/(2 x 3.14)

r³ = 214968.1

r = √214968.1

r = 59.9

Calculating the area of the hemisphere -

Area = 4πr²

Substituting the values -

Area = 4 x 3.14 x (59.9)²

= 12.56 x (59.9)²

= 45065.41

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Answer:

199000 i think

Step-by-step explanation:

1800 x 5 = 9000

9000 + 190000 = 199000

5/x = x/ 9

Cross-multiply

x² =45

Take the square root of both-side

x = 3√5 or 6.7082039325

Answer:

Step-by-step explanation:perp. 3/2

y + 8 = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14

The numerator of the rational expression a/b + 2/b = ?/b is

(2 + a)

The numerator is solved by adding the fractions together

since the denominator is same, and in this case we have b, then the addition is easier.

The given expression is added below

= a/b + 2/b

= (a + 2) / b

hence ? = (a + 2)

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The boundaries of the class 1.87-3.43 are D) 1.865-3.435. The lower boundary is 1.865 and the upper boundary is 3.435.

The boundaries of the class 1.87-3.43 can be determined by subtracting and adding half of the smallest possible unit of measurement to the given class limits. In this case, since the given class limits are 1.87 and 3.43, we need to find the boundaries by subtracting and adding half of the smallest possible unit of measurement.

Let's assume the smallest possible unit of measurement is 0.01.

To find the lower boundary:

Lower Boundary = Lower Limit - (0.01/2)

Lower Boundary = 1.87 - 0.005

Lower Boundary = 1.865

To find the upper boundary:

Upper Boundary = Upper Limit + (0.01/2)

Upper Boundary = 3.43 + 0.005

Upper Boundary = 3.435

Therefore, the boundaries of the class 1.87-3.43 are:

D) 1.865-3.435

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Answer:

(3x3) /9

Step-by-step explanation:

first you triple the three (3x3) then divide by 9

Answer:

1

Step-by-step explanation:

its:

3×3/9

=9/9

= 1⠀⠀⠀⠀⠀⠀

Answer:

8

Step-by-step explanation:

Answer:

its 8 i think but i need more info

Step-by-step explanation:

If the coordinates of the point a is (2,1) and midpoint is (0.-3), then the coordinates of b is (-2,-7).

Midpoint:

Midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The formula for midpoint is,

\((x_{m},y_{m})= (\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )\)

Where

(x₁,y₁) is the coordinates of the first point and

(x₂,y₂) is the coordinates of the second point

and

\((x_m,y_m)\) is the mid point of the first and second points.

Given,

Mid point = (0,-3)

Point a = (2,1)

Here we need to find the point b.

Let (x,y) be the point of b.

Now,

Apply the values on the formula,

Then we get,

\((0,-3)=(\frac{2+x}{2},\frac{1+y}{2})\)

Compare the values in order to solve it,

=> 0 = (2 +x)/ 2

=> 0 = 2 + x

=> x = -2

Similarly,

=> -3 = (1 + y)/2

=> -3 x 2 = 1 + y

=> -6 = 1 + y

=> y = -6 - 1

=> y = -7

Therefore, the coordinates of b is (-2,-7).

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Answer:The boat is traveling at a rate of 3 ft/s.

Step-by-step explanation:

To determine the effect of the interaction of the number of pages and cover type on cost, a statistical analysis would need to be performed using data on the number of pages, cover type, and cost. The analysis would likely involve running a regression model that includes both the number of pages and cover type as predictor variables, as well as an interaction term between the two.

 To answer your question, the effect of the interaction between the number of pages and cover type on the cost can be determined through a step-by-step process:

1. Identify the base cost of each cover type (e.g., hardcover, paperback, etc.).
2. Determine the cost per additional page for each cover type.
3. Calculate the cost for a specific number of pages and cover type by adding the base cost and the cost of additional pages.

For example:
- Base cost for hardcover: $5.00
- Base cost for paperback: $3.00
- Cost per additional page for hardcover: $0.10
- Cost per additional page for paperback: $0.05

Now, let's say you want to find the cost of a 100-page hardcover book:

1. Start with the base cost of a hardcover: $5.00
2. Multiply the number of pages (100) by the cost per additional page for hardcover ($0.10): 100 * $0.10 = $10.00
3. Add the base cost and the cost of additional pages: $5.00 + $10.00 = $15.00

So, the cost of a 100-page hardcover book is $15.00.

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Answer:

\((fog)(x)=-36x^2-2\)

Step-by-step explanation:

In order to solve this problem, you plug in the function of g(x) into f(x)

\((fog)(x)=-4(-3x)^2-2\\=-4(9x^2)-2\\=-36x^2-2\)

The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.

For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.

The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.

Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.

The cumulative probability for z = 3 is approximately 0.9987.

For the area to the right of z = 3, we subtract the cumulative probability from 1.

Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.

In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.

This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.

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Answer: 5, 1 and -1

Step-by-step explanation:

f(2)  

= 2(2) + 1

= 4 + 1

= 5

f(0)

= 2(0) + 1

= 0 + 1

= 1

f(-1)

= 2(-1) + 1

= -2 + 1

= -1