Suppose that you are conducting a survey on how many pets each employee has in his or her household. The mean number of pets is 4 per household, and the standard deviation is 2. Rob only owns cats, and he has 10 of them. Which of the following statements is true? A. Rob's number of pets is 3 standard deviations to the left of the mean. B. Rob's number of pets is 3 standard deviations to the right of the mean. C. Rob's number of pets is 6 standard deviations to the left of the mean. D. Rob's number of pets is 6 standard deviations to the right of the mean.

(a) To find the inverse Laplace transform of the function 45/(s² - 4), we first factor the denominator as (s - 2)(s + 2).

Using partial fraction decomposition, we can express the function as A/(s - 2) + B/(s + 2), where A and B are constants. By equating the numerators, we get 45 = A(s + 2) + B(s - 2). Simplifying this equation, we find A = 9 and B = 9. Therefore, the inverse Laplace transform of 45/(s² - 4) is 9e^(2t) + 9e^(-2t).

(b) Using the Laplace transformation technique to solve the given initial value problem y'' - 4y = e^(3t), y(0) = 0, y'(0) = 0, we start by taking the Laplace transform of the differential equation. Applying the Laplace transform to each term, we get s²Y(s) - sy(0) - y'(0) - 4Y(s) = 1/(s - 3). Since y(0) = 0 and y'(0) = 0, we can simplify the equation to (s² - 4)Y(s) = 1/(s - 3). Next, we solve for Y(s) by dividing both sides by (s² - 4), which gives Y(s) = 1/((s - 3)(s + 2)). To find the inverse Laplace transform, we need to decompose the expression into partial fractions. After performing partial fraction decomposition, we obtain Y(s) = 1/(5(s - 3)) - 1/(5(s + 2)). Taking the inverse Laplace transform of each term, we get y(t) = (1/5)e^(3t) - (1/5)e^(-2t).

Therefore, the solution to the initial value problem y'' - 4y = e^(3t), y(0) = 0, y'(0) = 0 is y(t) = (1/5)e^(3t) - (1/5)e^(-2t).

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Answer

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

Answer

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

The correct answer is option O: 5 V.

To determine the average voltage (Vavg) given a peak-to-peak voltage (Vpp) of 10 V, we need to consider the relationship between Vavg and Vpp in an alternating current (AC) waveform.

The average voltage of an AC waveform is related to its peak-to-peak voltage by the formula: Vavg = 0.5 * Vpp.

Applying this formula to the given Vpp of 10 V, we can calculate the Vavg as follows: Vavg = 0.5 * 10 V = 5 V.

The average voltage is equal to half of the peak-to-peak voltage, resulting in an average voltage of 5 V for a Vpp of 10 V.

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The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.

Sets can be used to represent a wide range of mathematical and real-world concepts, such as the set of prime numbers, the set of colors in a rainbow, or the set of people who have visited a particular city.

Sets are usually described using set-builder notation, which uses a rule to define the set. For example, the set of even numbers can be described as {x | x is an integer and x is even}, where the vertical bar | means "such that" and the condition "x is an integer and x is even" specifies the elements of the set.

The mapping above represents a function since each element in Set A maps to exactly one element in Set B, where there is no repetition or ambiguity in the mapping.

To fill in the blanks:

The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.

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Answer:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Step-by-step explanation:

So we have the rational function:

\(f(x)=\frac{x}{x-7}\)

The domain restrictions of rational functions are the zeros of the denominator.  In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.

So, solve for the denominator by setting it to 0:

\(x-7=0\)

Add 7 to both sides:

\(x=7\)

So, our domain is all real numbers except for 7.

(When x=7, we have 7/0, which is undefined.)

Therefore:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Answer:

the picture has it all!

whatever equals zero is not the domain and whatever doesnt equal zero is the domain!

hope i helped :)

Answer:

Formula for percent change is C = {x_2 - x_1}/{x_1}  

C = relative change

x_1 = initial value

x_2 = final value

Step-by-step explanation:

Answer:

<_> daddy

Step-by-step explanation:

In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

The load from the structural element is transferred to the foundation at a bearing point, which is often a concentrated load point.

To avoid structural failure, settling, or excessive deflection of the part, it is crucial to make sure the bearing point is properly designed and supported.

Since the bearing of C from A is 050°, we can find the bearing of A from C by adding 180° to 50°, which gives us:

Bearing of A from C = 50° + 180° = 230°

Therefore, In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

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Complete question -

Answer: [-4.5  -3.5]

                 [-4     -3]

Step-by-step explanation:

Music and a matrix calculator online, mwah

Answer:

24 cups is the answer!

Step-by-step explanation:

Hope this helps :)

Answer:

24 cups

Step-by-step explanation:

1/3

2=6/3

4*6= 24

Answer:

factor the polynomial

6 (7x-3)

Step-by-step explanation:

\( - 18 + 42x \\ divide \: both \: sides \: by \: 6 \\ 2(7x -3)\)

The boat has traveled approximately:

The boat has traveled 101 miles on a course of bearing S 64° 50' E. To determine how many miles the boat has traveled south and east, we need to break down the bearing into its respective components. The bearing S 64° 50' E can be broken down into two angles: 64° for the direction south of due east and 50' for the further rotation within that direction.

To calculate the distance traveled south, we need to find the southward component of the 101-mile distance. Since the angle is south of due east, we can use trigonometry to find the southward distance. We can use the sine of the angle to calculate the opposite side, which represents the distance traveled south. Applying this formula, we find:

Southward distance = sin(64°) * 101 miles = 0.8988 * 101 miles ≈ 90 miles.

Rounding this value to the nearest ten, the boat has traveled approximately 90 miles south.

To calculate the distance traveled east, we need to find the eastward component of the 101-mile distance. Since the angle is south of due east, the eastward component will be less than the total distance traveled. Using trigonometry again, we can calculate the adjacent side, which represents the distance traveled east. Applying this formula, we find:

Eastward distance = cos(64°) * 101 miles = 0.4384 * 101 miles ≈ 44 miles.

Rounding this value to the nearest ten, the boat has traveled approximately 40 miles east.

Therefore, the boat has traveled approximately 30 miles south and 90 miles east.

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An airplane is flying from New York City to Los Angeles. The distance a travels in miles D is related to the time in second T by the equation D equals 0. 15t. The plane is flying at a speed of 792 feet per second.

The distance a travels in miles D is related to the time in second T by the equation D equals 0. 15t. An airplane is flying from New York City to Los Angeles.

The formula relating distance (D), time (T), and speed (S) is given by

D = ST

This means that the speed of the plane is given by:

S = \frac{D}{T}

From the given formula, we have D = 0.15T.

We need to determine the speed S of the plane.

Substituting D, we have:

S = \frac{D}{T}

  = \frac{0.15T}{T}

  = 0.15

Therefore, the plane is flying at a speed of 0.15 miles per second. (Remember that the distance is in miles and time is in seconds)

We know that 1 mile is equivalent to 5280 feet. Therefore, to convert miles per second to feet per second, we multiply by 5280.

Thus, the plane is flying at a speed of 792 feet per second.

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Answer:

FG = 18

Step-by-step explanation:

FD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

\(\frac{24}{54}\) = \(\frac{x}{x+10}\) ( cross- multiply )

54x = 24(x + 10)

54x = 24x + 240 ( subtract 24x from both sides )

30x = 240 ( divide both sides by 30 )

x = 8

Then

FG = x + 10 = 8 + 10 = 18

Answer:

50

Step-by-step explanation:

90-54=36

then u do 36-10 which will give u 26

that will be f then u do 90-50 which is 40 and 40 is the x so now that u got x u can add that to ten which will give u fifty if that's not the way u want it or if this is wrong then i tried cause that what i got

Answer:

6.25 * 10^-2

Step-by-step explanation:

hmmmmmmmmm

Answer:

20/19

Step-by-step explanation:

y2-y1/x2-x1

= 8-3/5-1/4

=20/19

Answer:

15 inches

Step-by-step explanation:

you use Pythagorean Theorem

Yes, the triangles are congruent.

Given that a figure, where VY ≅ WY and ZY ≅ XY, we need to see whether the triangles ZYV and XYW are congruent,

So, in triangles ZYV and XYW,

VY ≅ WY [given]

ZY ≅ XY [given]

∠ZYV ≅ ∠XYW [vertical angles]

Therefore, the triangles ZYV and XYW are congruent, by SAS rule.

Hence the triangles are congruent.

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Answer: D

Step-by-step explanation:

The most appropriate hypothesis test to determine whether there is support for the claim that the average of the predicted charges is more than $500 greater than the average actual charges would be: c. Two-sample T-test assuming unequal variances (upper-tailed).

In this case, we have two independent samples: one for the predicted charges and another for the actual charges. We want to compare the means of these two samples to determine if there is a significant difference.

Unequal variance refers to the situation where the variances of two groups or populations being compared are not assumed to be equal. In statistical hypothesis testing, it is important to consider the assumption of equal variances, as violating this assumption can affect the accuracy of the results.

Since we are specifically interested in whether the average of the predicted charges is more than $500 greater, we would perform an upper-tailed test.

Assuming unequal variances is appropriate when the variances of the two samples are not assumed to be equal. This test allows for a more accurate assessment of the difference between the means when the variances differ between the groups.

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Answer:  

30 + 18x = 6(5+3x)

Step-by-step explanation:

for this all you have to do is distribute the 6 by doing 6 x  5 = 30 and  

6 x 3 = 13 and then you just have to add them together to get

30 + 18x = 30 +18x

Explanation:

Looking at the scatter plot, we can see that for the most part, as temperature increases, the sales of hot cocoa decrease. The data points on day 17 and 18 do not follow this pattern.

Out of 18 data points, 12 of them are from 0-10 degrees. 7 of the data points are from 0-10 cups

Answer:

The true statements are:

- Statement 2

- Statement 3

-Statement 4

Answer:

29 ounces

Step-by-step explanation:

1 pound equals to 16 ounces

Answer:

29 ounces

Step-by-step explanation:

1 pound is 16 ounces so 29 ounces is equal to 1.8 pounds.

The length of each piece of wood is 0.725 feet.

We are given that the Length= 3.5feet

Now,

This is a word problem that can be solved by using algebra and arithmetic.

Part A: Let x be the length of each of the four pieces of wood he cut. Then, according to the problem, we have:

4x + 0.6 = 3.5

This is the equation that could be used to determine the length of each piece of wood.

Part B: We know the equation from part A is correct because it represents the total length of the wood before and after cutting. The left side of the equation is the sum of the lengths of the four pieces of wood and the leftover piece of wood. The right side of the equation is the original length of the wood. Since cutting does not change the total length of the wood, these two sides must be equal.

Part C: To solve the equation from part A, we need to isolate x by using inverse operations. We get:

4x + 0.6 = 3.5 4x = 3.5 - 0.6 (subtract 0.6 from both sides) 4x = 2.9 x = 2.9/4 (divide both sides by 4) x = 0.725

Therefore, by the algebra the answer will be 0.725 feet.

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Using translation concepts, the series of transformations that shows that pentagon A is congruent to pentagon B is:

B. Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, we have that the Pentagons have different orientations, meaning that it was rotated, eliminating options A and D.

For the vertices to reach the position they reached in Pentagon B, there had to be a shift left, and before the shift left, the Pentagon must have been entirely at the fourth quadrant, meaning that it was reflected about the point (1,1), and option B is correct.

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Answer:

8 box

Step-by-step explanation:

Chocolate Bliss : 3.5x + 4

Expressions : 3.5x

where x is the number of chocolates  the relationship would be:

3x + 4 < 3.5x

4 < 0.5x

8 < x

it will be cheaper to buy from CB when you purchase less than 8 candies

Answer: