The police department in your city was asked by the mayor’s office to estimate the cost of crime. The police began their study with burglary records, taking a random sample of 500 files. If the average dollar loss in a burglary, for this sample size 500 is $678, with a standard deviation of $560, construct the 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount.

The results of the ANOVA test may not be reliable.

The conditions that must be met for the results of an ANOVA test to be reliable are that the observations must be independent of each other and randomly selected from their populations (A). Additionally, the variances for each population must be approximately equal to each other (B). This can be tested with the F-test, which is calculated by dividing the variance of the sample means by the variance of the individual observations. This test is used to determine if the variability between the groups is greater than the variability within the groups. If the F-test returns a value greater than 1, then the variances are not equal and the results of the ANOVA test may not be reliable. Lastly, the populations from which each group is drawn must be approximately Normal (C). This can be tested with a Shapiro-Wilk test or a visual inspection of a histogram or qqplot. If the populations are not normally distributed, then the results of the ANOVA test may not be reliable. The hypothesized means of the populations from which each group is drawn must be approximately equal (D). This can be tested with a t-test or a confidence interval. If the means are significantly different, then the results of the ANOVA test may not be reliable.

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There are two vertical angles created by the intersection of two lines.

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The distribution of the histogram for the large packages colors is given as follows:

Right skewed.

The distribution depends on whichever of the mean or the median is greater, as follows:

Hence the distribution is defined as follows:

The ordered data-set is given as follows:

21, 21, 24, 30, 32, 86.

The median is the mean of the two-middle values, hence:

Median = (24 + 30)/2

Median = 27.

The mean is the sum of all the observations divided by the number of observations, hence:

Mean = (21 + 21 + 24 + 30 + 32 + 86)/6

Mean = 35.67.

Mean > median, hence the distribution is right skewed.

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The Scale Factor is 0.75, or 3/4

Scale factor is a ratio of two related lengths, areas, volumes, or other quantities. It is used to describe how a figure is enlarged or reduced in size. For example, when a figure is enlarged, the scale factor is greater than one, and when a figure is reduced, the scale factor is less than one. Scale factors can be used to calculate the lengths of sides and areas of figures when one side or area is known.


The Scale Factor is calculated by dividing the coordinates of point A' (9, 3) by the coordinates of point A (12, 4). Therefore, the Scale Factor is 0.75, or 3/4.

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To determine the cost of 6 pencils at 60 cents a dozen, we need to convert the price per dozen to the price per pencil. We know that a dozen is equal to 12, so we can use the following formula:

Price per pencil = (Price per dozen) / (Number of items per dozen)

So, in this case:

Price per pencil = (60 cents) / (12 pencils)

To convert cents to dollars, we divide by 100.

Price per pencil = (60/100) $ = 0.6 $

To find the total cost for 6 pencils we multiply the price per pencil by the number of pencils

Cost of 6 pencils = 6 * 0.6 = 3.6 $

So the cost of 6 pencils at 60 cents a dozen is 3.6 $.

The percentage increase in snakes from last year to this year at the Cincinnati Zoo is 20%.

The percentage increase refers to the ratio of the increase in the number of snakes in the zoo.

The percentage increase can be computed as the quotient of the amount of increase divided by the previous number of snakes, multiplied by 100.

The number of snakes in the zoo last year = 25

The number of snakes in the zoo currently = 30

The increase in the number of snakes = 5 (30 - 25)

The percentage increase = 20% (5/25 x 100)

Thus, we can conclude that the number of snakes in the Cincinnati Zoo has increased by 20 percent since last year.

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The probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.

(a) .1136, .1212 and 0.7955 respectively.

(i) P(X=1) = C(5,1) / C(12,6) = 5/66 = 0.1136

(ii) P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212

(iii) P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955

The probability of one defective compressor among the first 6 examined is P(X = 1) = C(5,1) / C(12,6) = 5/66 = 0.1136. The probability of four or more defective compressors among the first 6 examined is P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212. The probability of 1 to 3 defective compressors among the first 6 examined is P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955.

Therefore, the probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.

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The method of midpoint rectangles is a numerical integration technique used to approximate the area under a curve.

It is based on the idea of breaking up the area under the curve into a series of rectangles and approximating the area of each rectangle using the midpoint of the interval.

For example,

Let's say we want to approximate the area under the curve f(x) = x^2 from x = 0 to x = 2 using the method of midpoint rectangles.

We divide the interval into n = 4 subintervals of width 0.5.

We can calculate the midpoints of the intervals as follows:

interval 1: (0,0.5)

interval 2: (0.5,1)

interval 3: (1,1.5)

interval 4: (1.5,2)

We find the height of each rectangle as the value of f(x) at the midpoint of the interval.

interval 1: f(0.25) = 0.25^2 = 0.0625

interval 2: f(0.75) = 0.75^2 = 0.5625

interval 3: f(1.25) = 1.25^2 = 1.5625

interval 4: f(1.75) = 1.75^2 = 3.0625

We multiply the width of each rectangle (0.5) by the height of each rectangle to find the area of each rectangle:

interval 1: 0.5 * 0.0625 = 0.03125

interval 2: 0.5 * 0.5625 = 0.28125

interval 3: 0.5 * 1.5625 = 0.78125

interval 4: 0.5 * 3.0625 = 1.53125

Finally, we add the areas of all the rectangles to find the total approximate area under the curve:

0.03125 + 0.28125 + 0.78125 + 1.53125 = 2.64375

Hence, using this method the area under the curve f(x) = x^2 from x = 0 to x = 2 is approximately 2.64375.

Note: The precision of the result will depend on how many rectangles you use, and how small you make the rectangles.

The more rectangles we use and the smaller width of each rectangle, the more accurate our result will be.

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48.28 m/s is the speed .

What is the definition of a velocity simple?

The speed at which a body or object is moving determines its direction of motion. Most of the time, speed is a scalar quantity. Velocity is fundamentally a vector quantity.

                         The rate at which distance changes is what it is. It measures the displacement's rate of change.

Height, y = 52t - 1.86t²

Velocity = ∆y/∆t = 52 - 1.86 * 2t = 52- 3.72t

A. Average velocity = (v1 + v2)/2

(i) At t = 1, 2

Average velocity = (52 - 3.72*1 + 52 -3.72*2)/2 = 46.42 m/s

(ii) At t = 1,1.5

Average velocity = (52 - 3.72*1 + 52 - 3.72*1.5)/2 = 47.35 m/s

(iii) At t = 1,1.1

Average velocity = (52 - 3.72*1 + 52 -3.72*1.1)/2 = 48.09m/s

(iv) At to = 1, 1.01

Average velocity = (52 - 3.72*1 + 52 - 3.72*1.01)/2 = 48.26 m/s

(iv) At t = (1, 1.001)s

Average velocity = (52 - 3.72*1 + 52 - 3.72*1.001)/2 = 48.28 m/s

B. Speed at t = 1s

Velocity = 52 - 3.72 * 1 = 48.28 m/s

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Answer:C. Approx. Normal

Step-by-step explanation:

The simplest choice is a linear transformation, for example, the one given by the

matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]

When you represent a three-dimensional object graphically in the plane con paper, the blackboard, or a computer screen), you have to transform spatial coordinates,

[tex]$\mathrm{x} 1$ & \\[/tex]

[tex]$\mathrm{x} 2$[/tex] & into plane coordinates

[tex]$\mathrm{x} 3$[/tex]& [tex]$\mathrm{y} 1$[/tex]& [tex]$\mid$ \\[/tex]

[tex]$\mathrm{x}$[/tex] &[tex]$\mathrm{y} 2$[/tex] &

The simplest choice is a linear transformation, for example, the one given by the

matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]

The complete question is,

When you represent a three-dimensional object graphically in the plane (on paper, the blackboard, or a computer screen), you have to transform spatial coordinates | x 1 | | x 2 | into plane coordinates | y 1 |. | x 3 | | y 2 | The simplest choice is a linear transformation, for example, the one given by the matrix | -1/2 1 0 0 | 1 |.

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The 4th line plot picture correctly shows the data of the lengths of the sticks that were 3, 3, 4, 3, 3, 5, 4, 6, 5 and 4 inches.

A line plot is a graph that uses symbols to represent data above a frequency number line. It is used to arrange the data simply and is very simple to understand.

A line plot is a graphical representation of data on a number line which uses dots, crosses, or any other symbol. The scale of the graph is represented by each mark, which corresponds to a particular quantity.

The data on a number line can be graphically represented using symbols using a line plot graph. In contrast to a line graph, no cartesian plane or x and y axes are used in this data representation. Simple lines are drawn on a number line to represent a line plot graph.

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Full question:

Andre measured the lengths of 10 sticks to the nearest inch. the lenghts of the sticks were 3,3,4,3,3,5,4,6,5 and 4 inches. Click on the line plot that shows these data. Lengths of Sticks (in inches) Lengths of Sticks (in inches) Lengths of Sticks (in inches) Lengths of Sticks.

Data aggregation involves creating a unified collection of data that originally came from multiple sources.

It is the process of combining data from multiple sources into one file, report or summary. Data aggregation can be done using a variety of methods, such as mathematical formulas, grouping, filtering and sorting. For example, a mathematical formula can be used to calculate the average of a set of numbers. Grouping data can be used to divide data into categories and subcategories, such as by country or by product. Filtering data involves removing unnecessary or unwanted data, such as outliers or irrelevant information. Finally, sorting data can be used to organize data in a specific order, such as alphabetically or numerically. Data aggregation is a useful tool for making sense of large datasets and providing greater insight into the data.

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Answers:

90 ounces of solution A.

60 ounces of solution B.

====================================================

Explanation:

x = amount of solution A

150-x = amount of solution B

Each amount is in ounces and they add to 150 ounces.

Solution A is 35% salt, so we get 0.35x ounces of pure salt from solution A.

Solution B is 60% salt, so we get 0.60*(150-x) = 90-0.60x ounces of pure salt from solution B.

We want 150 ounces of 45% salt solution, which means we want 150*0.45 =  67.5 ounces of pure salt when everything is mixed.

Here's a table showing this info

[tex]\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 0.60(150-\text{x}) = 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 150*0.45 = 67.5 \\\cline{1-3}\end{array}[/tex]

Cleaning up the table a bit shows

[tex]\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 67.5 \\\cline{1-3}\end{array}[/tex]

Focus on the "pure salt" column.

We want the 0.35x and 90-0.60x to add to 67.5

So,

0.35x+(90-0.60x) = 67.5

90-0.25x = 67.5

-0.25x = 67.5-90

-0.25x = -22.5

x = -22.5/(-0.25)

x = 90

She must use 90 ounces of solution A.

150-x = 150-90 = 60 ounces of solution B must be used as well.

-------------------

Check:

35% of 90 = 0.35*90 = 31.5 ounces of pure salt comes from solution A.

60% of 60 = 0.60*60 = 36 ounces of pure salt comes from solution B.

31.5+36 = 67.5 ounces of pure salt in total, which matches with the value mentioned earlier. The answers are confirmed.

Answer:

  10 yards

Step-by-step explanation:

You want the height of a cylinder of radius 3 yards that has a volume of 282.6 cubic yards, using pi = 3.14.

The volume of a cylinder is given by ...

  V = πr²h

Using the given values, this is ...

  282.6 yd³ = 3.14(3 yd)²·h = 28.26h yd²

Dividing by the coefficient of h, we find it to be ...

  h = (282.6 yd³)/(28.26 yd²) = 10 yd

The height of the cylinder is 10 yards.

The holding pulse is nonzero only for[tex]0 \leq t \leq T[/tex], the autocorrelation of X(t) is given by\begin{align}

[tex]R_{xx}(t,t+\tau) =[/tex]

[tex]\begin{cases}\sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT) & 0 \leq \tau \leq T \\0 & \text{otherwise}.\end{cases}\end{align}[/tex]

The autocorrelation of X(t) is defined as[tex]R_{xx}(t,t+\tau) = E[X(t)X(t+\tau)][/tex]where E[.] is the expectation operator. Since V(nT) has zero mean and is statistically independent, we can write

[tex]R_{xx}(t,t+\tau) &= E[X(t)X(t+\tau)]\\ &= E\left[\sum_{n=-\infty}^{\infty}V(nT)h(t-nT)\sum_{m=-\infty}^{\infty}V(mT)h(t+\tau-mT)\right]\\&= \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}E[V(nT)V(mT)]h(t-nT)h(t+\tau-mT)\\&= \sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT)\end{align}[/tex]

Since the holding pulse is nonzero only for[tex]0 \leq t \leq T[/tex], the autocorrelation of X(t) is given by\begin{align}

[tex]R_{xx}(t,t+\tau) =[/tex]

[tex]\begin{cases}\sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT) & 0 \leq \tau \leq T \\0 & \text{otherwise}.\end{cases}\end{align}[/tex]

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If the magnitude of two vectors is 10 and 6 and their dot product is 30, then the angle between the vectors is 60°.

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

There are two ways to define a dot product: algebraically and geometrically. The sum of the products of the matching entries of the two number sequences is the definition of the dot product in algebra. Geometrically, it is the sum of the cosine of the angle formed by the two vectors and their Euclidean magnitudes.

The magnitude of the vector 1 is, |a| = 10

The magnitude of the vector 2 is, |b| = 6

The dot product of the two vectors is, a·b = 30.

The formula for dot product of vectors is -

a·b = |a| |b| cos θ

Solve the equation to get the angle -

30 = (10 × 6) cos θ

30 = 60 cos θ

cos θ = 30/60

cos θ = 1/2

θ = cos^-1 (1/2)

θ = 60°

Therefore, the angle is obtained as 60°.

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Answer:

50

Step-by-step explanation:

140/x = 168/60

x = 60*140/168 = 50

Answer:

50

Step-by-step explanation:

168/60=2.8

140/2.8=50

Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

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Answer:

It is not possible for the sum of consecutive integers to be -11. The sum of n consecutive integers is n times the average of the first and last integers. The average of any two integers is a fraction, which when multiplied by n, will always yield a fraction, which cannot equal -11. Therefore it is not possible to have n consecutive integers that sum to -11.

Note that these points are not different from each other and are on the same line y = 5/3x - 2.

Any point on this line will have the coordinates (x, y) such that y = 5/3x - 2.

Generally, A point on a line is any place along that line that is represented by a set of coordinates in either two- or three-dimensional space, denoted by the letters x, y, or x, y, z, respectively.

An equation, such as y = mx + b, may be used to define a line in a mathematical context. In this equation, m refers to the slope, while b refers to the y-intercept.

Any point that can be made to fit into this equation is up for grabs.

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The tall of the building is 175m and the baseball strikes the ground in 4.53 seconds, 195 ft/s.

Assume that the acceleration due to gravity is 10m/s2.  

The equation for the ball’s velocity in the downward direction is

v(t) = at + v₀.

Here

v₀=10m/s a=10m/s² v(t)=60m/s

Solving this for  t we get the:  

[tex]t =\frac{60m/s-10m/s}{10m/s^2}\\ \\t=\frac{50m/s}{10m/s^2}\\[/tex]

t=5s

The total distance traveled will be  

[tex]x(t)=\frac{1}{2} at^2+v_{0} +x_{0}[/tex]

Here x₀ = 0 and we get:

[tex]x(t)=\frac{1}{2} (10m/s^2)(5s)^2+(10m/s)(5s)[/tex]

x=125m+50m

x=175m

The given values are:

u = 50 ft/s

h = 555 ft

g = 32 ft/s²

Let the time taken by the ball to reach the ground be t and the velocity of the ball as it hits the ground be v.

Use the third equation of motion

v²=u²+2as

v²=50²+2*32*555

v = 195 ft /s

Thus, the ball strikes the ground with a velocity of 195 ft/s.

Use the first equation of motion

v = u + at

195 = 50 + 32 t

32 t = 145

t = 4.53 second

Thus, the ball reaches the ground in 4.53 seconds.

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The ordered pair that is included in the solution to this system of inequalities is: B. (−6, −3)

In order to determine the ordered pair is included in the solution to this system of linear inequalities, we would first of all translate the word problem into an algebraic equation as follows;

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ 2x/3 + 1.

y is less than negative one-fourth times x plus 2 ⇒ y < -x/4 + 2.

Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Therefore, the required solution for the given system of linear inequalities is the shaded area below the solid line, which is given by the ordered pair (−6, −3).

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To find the x-intercept of the graph of the equation 2x - 4y = 9, we need to find the value of x when y = 0.

We can solve for x as follows:

2x - 4y = 9

2x - 4(0) = 9 (substitute y = 0)

2x = 9

x = 9/2

Therefore, the x-intercept of the graph of the equation 2x - 4y = 9 is (9/2, 0).

Answer: D. The distance from A to C

Step-by-step explanation:

This formula can be used to find the distance between two points on a three-dimensional coordinate system:

D(x, y, z) = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2} }[/tex]

If you apply the formula for all options, you will find the distance from A to C is equal to [tex]\sqrt{5}[/tex]. The other distances are:

A. [tex]\sqrt{17}[/tex]

B. [tex]\sqrt{45}[/tex]

C. [tex]\sqrt{44}[/tex]

So, the answer is D.

Patient needs to 500,000 unit of penicillin, then according to capsule availability we shall provide the 2 capsules of 200,000 unit and 1 capsule of 100,000 unit.

The doctor orders 500,000 unit of penicillin for the patient. the capsule available are 200,000 unit and 100,000 units.

we have to find out the number of capsules required for 500,000 unit,

let's see,

we have 200,000 unit of penicillin and 100,000 units of penicillin available,

patient need of 500,000 unit of penicillin,

so we shall provide the 2 capsule of 200,000 units of penicillin and 1 capsule of penicillin 100,000 unit to the patient,

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The price of the share of stock in fossil oil refineries after the three-for-one split is $50.

A stock split is an event in the stock market when the company declares split of stock into multiple parts to decrease the cost per share and make it easier to purchase.

Given,

          The selling price of a stock in fossil fuel before split = $150

          After one year the stock split into three parts

         ∴ Probable prices per share = Price before split/3

                                                         = $150/3

                                                         = $50

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Answer:

$963.00

Step-by-step explanation:

.9(3x150) + .95(2x200) + 250

.9(450) + .95(400) + 250

405 + 308 + 250 = 963

If we are taking 10% off, that is like leaving 90% (.9) on.

If we are taking 5% off, that is like leaving 95% ( .95) on.

No discount for the watch because she only bought one.

The probability of getting exactly 1 three, to the nearest thousandth is 0.347.

Binomial distribution is the distribution of a random variable X for which there are only two possibilities. The probability p for the success and the probability of 1-p for the failure, which consist of n trials.

The binomial distribution has the formula,

P(x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

where x : number of times for a specific outcome within n trials

p : probability of success in each trial

n : number of trials

Given that a fair die is rolled 3 times.

Here, n = 3, x = 1

p = probability of getting three for 1 trial = 1/6

1 - p = 1 - 1/6 = 5/6

P(1) = ³C₁ (1/6)¹ (5/6)³⁻¹

     = 0.347

Hence the probability of getting exactly 1 three is 0.347.

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