Use the information given about the angle theta, 0 le theta le 2pi, to find the exact value of the indicated trigonometric function. sin theta = 1/4, tan theta > o find cos theta/2. squareroot 10/4 squareroot 6/4 squareroot 8 + 2 squareroot 15/4 squareroot 8 1 2 squareroot 15/4 Find the exact value of the expression.

The area of the triangle is 15.5 square units.

To find the area of the triangle with the given vertices, we can use the formula:

A = 1/2 * |(x1y2 + x2y3 + x3y1) - (x2y1 + x3y2 + x1y3)|

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.

Substituting the given values, we get:

A = 1/2 * |(03 + 58 + 30) - (50 + 33 + 08)|

A = 1/2 * |(0 + 40 + 0) - (0 + 9 + 0)|

A = 1/2 * |31|

A = 15.5

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The solution to the given system of differential equations with initial conditions x(0) = 0 and y(0) = 1 is:
x(t) = (2/3) - (1/3) * e^t
y(t) = (2/3) - (2/3) * e^t

To solve the given system of differential equations:

dx/dt = 3x - 3y
dy/dt = 2x - 2y

We can use the method of solving systems of linear differential equations. Let's proceed step by step:

Step 1: Write the system in matrix form:
The system can be written in matrix form as:
d/dt [x y] = [3 -3; 2 -2] [x y]

Step 2: Find the eigenvalues and eigenvectors of the coefficient matrix:
The coefficient matrix [3 -3; 2 -2] has the eigenvalues λ1 = 0 and λ2 = 1. To find the corresponding eigenvectors, we solve the equations:

[3 -3; 2 -2] * [v1 v2] = 0 (for λ1 = 0)
[3 -3; 2 -2] * [v3 v4] = 1 (for λ2 = 1)

Solving these equations, we obtain the eigenvectors corresponding to λ1 = 0 as v1 = [1 1] and the eigenvectors corresponding to λ2 = 1 as v2 = [1 -2].

Step 3: Write the general solution:
The general solution of the system can be written as:
[x(t) y(t)] = c1 * e^(λ1t) * v1 + c2 * e^(λ2t) * v2

Substituting the values of λ1, λ2, v1, and v2 into the general solution, we get:
[x(t) y(t)] = c1 * [1 1] + c2 * e^t * [1 -2]

Step 4: Apply initial conditions to find the particular solution:
Using the initial conditions x(0) = 0 and y(0) = 1, we can solve for c1 and c2:

At t = 0:
x(0) = c1 * 1 + c2 * 1 = 0
y(0) = c1 * 1 - c2 * 2 = 1

Solving these equations simultaneously, we find c1 = 2/3 and c2 = -1/3.

Step 5: Substitute the values of c1 and c2 into the general solution:
[x(t) y(t)] = (2/3) * [1 1] - (1/3) * e^t * [1 -2]

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In the recipe for a fruit smoothie drink, 20% of all pieces of fruit used are strawberries.

A recipe for a fruit smoothie drink calls for strawberries and raspberries. The ratio of strawberries to raspberries in the drink is 5:20.

The ratio of strawberries to raspberries in the drink is 5:20, i.e., the total parts are 5 + 20 = 25.

The fraction representing strawberries is: 5/25 = 1/5.

Now we have to convert this fraction to percent form.

This can be done using the following formula:

Percent = (Fraction × 100)%

Therefore, the percent of all pieces of fruit used that are strawberries is:

1/5 × 100% = 20%

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Solutions with y(0) > 2 diverge to infinity

To draw a direction field for the differential equation y' = y(y - 2)^2, we will choose a set of points in the (t, y)-plane and plot small line segments with slopes equal to y'(t, y) = y(y - 2)^2 at each of these points.

Here is the direction field:

               |     /

               |   /

               | /

               |/

               /|

             /  |

           /    |

         /      |

       /        |

     /          |

   /            |

 /              |

/________________|

The direction field shows that there are two equilibrium solutions: y = 0 and y = 2. Between these two equilibrium solutions, the direction field shows that the solutions y(t) are increasing for y < 0 and y > 2 and decreasing for 0 < y < 2.

To see how the solutions behave as t → ∞, we can examine the behavior of y'(t, y) as y → 0 and y → 2. Near y = 0, we have y'(t, y) ≈ y^3, which means that solutions with y(0) < 0 will approach 0 as t → ∞, while solutions with y(0) > 0 will diverge to infinity as t → ∞. Near y = 2, we have y'(t, y) ≈ -(y - 2)^2, which means that solutions with y(0) < 2 will converge to 2 as t → ∞, while solutions with y(0) > 2 will diverge to infinity as t → ∞.

Therefore, the behavior of y as t → ∞ depends on the initial value of y at t = 0. Specifically, solutions with y(0) < 0 approach 0, solutions with 0 < y(0) < 2 decrease to 0, solutions with y(0) = 2 converge to 2, and solutions with y(0) > 2 diverge to infinity.

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Given that, In ΔFGH, the measure of ∠H = 90°, the measure of ∠F = 52°, and FG = 4.3 feet.To find: The length of HF to the nearest tenth of a foot.

Let's construct an altitude from vertex F to the hypotenuse GH such that it meets the hypotenuse GH at point J. Then, we have: By Pythagoras Theorem, [tex]FH² + HJ² = FJ²Or, FH² = FJ² - HJ²[/tex]By using the trigonometric ratio (tan) for angle F, we get, [tex]HJ / FG = tan F°HJ / 4.3 = tan 52°HJ = 4.3 x tan 52°[/tex]Now, we can find FJ.[tex]FJ / FG = cos F°FJ / 4.3 = cos 52°FJ = 4.3 x cos 52°[/tex]Substituting these values in equation (1), we have,FH² = (4.3 x cos 52°)² - (4.3 x tan 52°)²FH = √[(4.3 x cos 52°)² - (4.3 x tan 52°)²]Hence, the length of HF is approximately equal to 3.6 feet (nearest tenth of a foot).Therefore, the length of HF to the nearest tenth of a foot is 3.6 feet.

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The researcher needs at least 67 participants in the sample size to adequately conduct a study to estimate the population mean to within 5 points at a 90% level of confidence. The sample size is an essential part of any research study. The sample size is the number of participants or observations in the study.

To estimate the sample size, we should use the following formula:

N = (Z² * s²) / E²

Where: N = Sample Size, Z = Z-score (z-score for a 90% confidence level is 1.645), s = Standard deviation, E = Margin of error (We have 5 points or 0.05 in decimal form)

Now, we will calculate the Standard deviation which is the square root of the variance. The variance is obtained by dividing the population range by 4. It's 80/4 = 20s = √20 = 4.47

Plugging in these values to the above formula: N = (1.645² * 4.47²) / 0.05²

N = 66.7 ≈ 67

Therefore, the researcher needs at least 67 participants in the sample size to adequately conduct a study to estimate the population mean to within 5 points at a 90% level of confidence. The sample size is an essential part of any research study. The sample size is the number of participants or observations in the study. A sample is taken from the population because it's usually impossible to collect data from the entire population. The sample size must be adequately determined to produce accurate results and avoid errors that may affect the study's validity. A larger sample size is more representative of the population, and it minimizes the effect of random errors. However, a sample that is too large can lead to waste of resources, time, and money. Therefore, researchers determine the sample size required based on various factors, including the population's size, variability of the data, the level of confidence desired, and the margin of error. The formula for calculating the sample size is N = (Z² * s²) / E², where N is the sample size, Z is the Z-score, s is the standard deviation, and E is the margin of error.

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Matthew can make a total of 7 bowls with the 3.5 pounds of clay he has.

To find the number of bowls Matthew can make, we need to divide the total amount of clay he has by the amount of clay needed to make one bowl. Matthew has 3.5 pounds of clay, and he needs 1/2 of a pound to make one bowl. To divide these two values, we can write the division equation as:

3.5 pounds ÷ 1/2 pound per bowl

To simplify this division, we can multiply the numerator and denominator by the reciprocal of 1/2, which is 2/1. This gives us:

3.5 pounds ÷ 1/2 pound per bowl × 2/1

Multiplying across, we get:

3.5 pounds × 2 ÷ 1 ÷ 1/2 pound per bowl

Simplifying further, we have:

7 pounds ÷ 1/2 pound per bowl

Now, to divide by a fraction, we multiply by its reciprocal. So we can rewrite the division equation as:

7 pounds × 2/1 bowl per 1/2 pound

Multiplying across, we get:

7 pounds × 2 ÷ 1 ÷ 1/2 pound

Simplifying gives us:

14 bowls ÷ 1/2 pound

Dividing by 1/2 is the same as multiplying by its reciprocal, which is 2/1. So we have:

14 bowls × 2/1

Multiplying across, we find:

28 bowls

Therefore, Matthew can make a total of 28 bowls with the 3.5 pounds of clay he has.

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A number that has a digit in the tenths place that is 100 times smaller than the 8 in the hundreds place is 184.36.

Let's break down the given number, 184.36. The digit in the hundreds place is 8, which is 100 times larger than the digit in the tenths place.

In the decimal system, each place value to the right is 10 times smaller than the place value to its immediate left. Therefore, the digit in the tenths place is 100 times smaller than the digit in the hundreds place. In this case, the tenths place has the digit 3, which is indeed 100 times smaller than 8.

So, by considering the value of each digit in the number, we find that 184.36 satisfies the condition of having a digit in the tenths place that is 100 times smaller than the 8 in the hundreds place.

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Answer: b

Step-by-step explanation: if I’m smart enough then this answer is right

Answer:

Inferences

Step-by-step explanation:

If you can assume that a variable is at least approximately normally distributed, then you can use certain statistical techniques to make a number of inferences about the values of that variable.

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You must select 1,096 teenagers to ensure that 4 of them were born on the exact same date.

To ensure that 4 teenagers were born on the exact same date (mm/dd/yyyy), you must consider the total possible birthdates in a non-leap year, which is 365 days.

By using the Pigeonhole Principle, you would need to select 3+1=4 teenagers for each day, plus 1 additional teenager to guarantee that at least one group of 4 shares the same birthdate.

Therefore, you must select 3×365 + 1 = 1,096 teenagers to ensure that 4 of them were born on the exact same date.

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The MAD is approximately 15.4. The MAD tells us that on average, the forecast errors are about 15.4 units away from the mean forecast error.

The Mean Absolute Deviation (MAD) is a measure of the variability of a set of data. It represents the average distance of the data points from the mean of the data set.

To calculate the MAD, we need to first find the mean of the forecast errors. The mean is the sum of the forecast errors divided by the number of errors:

Mean = (-22 - 10 + 15)/3 = -4/3

Next, we find the absolute deviation of each error by subtracting the mean from each error and taking the absolute value:

|-22 - (-4/3)| = 64/3

|-10 - (-4/3)| = 26/3

|15 - (-4/3)| = 49/3

Then, we find the average of these absolute deviations to get the MAD:

MAD = (64/3 + 26/3 + 49/3)/3 = 139/9

Therefore, the MAD is approximately 15.4. The MAD tells us that on average, the forecast errors are about 15.4 units away from the mean forecast error.

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The two numbers are -4 and 15.Let's assume that x is the first integer and y is the second integer.Using the given information, the sum of two integers is 11:

Therefore, we can write the following equation:

x + y = 11

We are also given that the difference between two numbers is 19. Mathematically, we can represent the difference between two numbers as the absolute value of their subtraction.

Therefore, the second equation is:

y - x = 19

We can now solve for x and y using the above system of equations. Rearranging the first equation to get y in terms of x:y = 11 - x

Substituting the value of y in the second equation:

y - x = 19(11 - x) - x = 19

Simplifying this equation:

11 - 2x = 19-2x = 19 - 11-2x = 8x = -4

Now we can use the value of x to find the value of y:

y = 11 - x = 11 - (-4) = 15

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The determinant of matrix C is 0.

(a) To compute the determinant of the matrix PAPT, we can use the property that the determinant of a product of matrices is equal to the product of the determinants of the individual matrices. Therefore:

det(PAPT) = det(P) * det(A) * det(P)

Substituting the given determinant values:

det(PAPT) = det(P) * det(A) * det(P) = 2 * 5 * 2 = 20

So, the determinant of the matrix PAPT is 20.

(b) To find the determinant of matrix C, we can expand along the first row or the first column. Let's expand along the first row :

C = | a 006 |

| 0 0 1 |

| 0 1 0 |

Using the expansion along the first row:

det(C) = a * det(0 1) - 0 * det(0 1) + 0 * det(0 0)

| 1 0 |

We can simplify this:

det(C) = a * (1 * 0 - 0 * 1) = a * 0 = 0

Therefore, the determinant of matrix C is 0.

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the probability of not being the victim of the theft involving the bicycle, if the victim of the theft is randomly selected, is 0.961.

According to the given data, it is given that there was a 3.9% probability of theft involving a bicycle in 2002. Thus, the probability of not being the victim of the theft involving the bicycle can be calculated by the complement of the probability of being the victim of the theft involving the bicycle.

The formula for calculating the probability of the complement is:

P(A') = 1 - P(A)

Where P(A) represents the probability of the event A, and P(A') represents the probability of the complement of event A.

Thus, the probability of not being the victim of the theft involving the bicycle can be calculated as:

P(not being the victim of the theft involving the bicycle) = 1 - P(the victim of the theft involving the bicycle)

Now, substituting the value of P(the victim of the theft involving the bicycle) = 3.9% = 0.039 in the above formula, we get:

P(not being the victim of the theft involving the bicycle) = 1 - 0.039P(not being the victim of the theft involving the bicycle) = 0.961

Therefore, the probability that the randomly selected victim was not the victim of bicycle theft is 0.961 Thus, the probability of not being the victim of the theft involving the bicycle, if the victim of the theft is randomly selected, is 0.961.

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The statement is false because Samuel Houston did not receive official permission from Mexico to settle a large number of Americans in Texas.

The permission and land grant to bring American settlers to Texas were obtained by Stephen F. Austin, not Samuel Houston. Austin is widely recognized as the "Father of Texas" and played a crucial role in the early colonization and development of the region.

Furthermore, the capital of Texas, Austin, is named after Stephen F. Austin, not Samuel Houston. Houston, although a significant figure in Texas history, served as the president of the Republic of Texas and later as a U.S. senator.

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If you were writing a newspaper article that ended with recommendations to fans about buying tickets and the research showed that the average local baseball fan plans to attend 67 games during the season,

You would recommend the average fan to purchase season tickets since they plan to attend 67 games during the season. Season tickets guarantee the fan a seat for every game they plan to attend. Single-game tickets may not be available, or if they are, may be for an unfavorable seat.

Season tickets often provide a discount compared to single-game tickets, and they save the fan time and effort to look for individual tickets. Additionally, season tickets holders are typically given priority seating options for post-season games and have access to exclusive team events and merchandise discounts.To sum up, you should recommend purchasing season tickets to the average local baseball fan since they plan to attend 67 games during the season.

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The rectangular equation given is x + 7√(x² + y²) = x² + y², which can be converted to the polar equation r = 7 - cos(θ).

Using the trigonometric identity cos(θ) = x/r, we can write:

r = 7 - x/r

Multiplying both sides by r, we get:

r² = 7r - x

Using the polar to rectangular conversion formulae x = r cos(θ) and y = r sin(θ), we can express r in terms of x and y:

r² = x² + y²

Substituting r² = x² + y² into the previous equation, we get:

x² + y² = 7r - x

Substituting cos(θ) = x/r, we can write:

x = r cos(θ)

Substituting this into the previous equation, we get:

x² + y² = 7r - r cos(θ)

Simplifying, we get:

x² + y² = 7√(x² + y²) - x

Rearranging, we get:

x + 7√(x² + y²) = x² + y²

This is the rectangular form of the polar equation r = 7 - cos(θ).

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Therefore, the mean is 3.00, the degrees of freedom is 4, the variance is 2.5, and the standard deviation is approximately 1.58.

To calculate the mean, we add up all the scores and divide by the number of scores:

Mean = (4 + 1 + 3 + 5 + 2) / 5 = 15 / 5 = 3

To calculate the degrees of freedom (df), we subtract 1 from the sample size:

df = n - 1 = 5 - 1 = 4

To calculate the variance, we first calculate the deviation of each score from the mean:

(4 - 3)^2 = 1

(1 - 3)^2 = 4

(3 - 3)^2 = 0

(5 - 3)^2 = 4

(2 - 3)^2 = 1

Then we add up these deviations and divide by the degrees of freedom:

Variance = Σ (X - M)^2 / df = (1 + 4 + 0 + 4 + 1) / 4 = 2.5

To calculate the standard deviation, we take the square root of the variance:

Standard deviation = √2.5 ≈ 1.58

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The sum of the arithmetic sequence 4, 11, 18, 25, ..., 249 is 4554 and there are 36 terms in the sequence.

(a) To determine the number of terms in the sum, we can find the pattern in the terms.  we observe that each term is obtained by adding 7 to the previous term. Starting from 4 and incrementing by 7, we can write the sequence of terms as 4, 11, 18, 25, ..., and so on.

To find the number of terms, we need to determine the value of n in the equation 4 + 7(n-1) = 249. Solving this equation, we find n = 36. There are 36 terms in the sum.

(b) To compute the sum using a technique discussed in this section, we can use the formula for the sum of an arithmetic series. The formula is given by Sn = (n/2)(2a + (n-1)d), where Sn represents the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, the first term a is 4, the number of terms n is 36, and the common difference d is 7.

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The following pseudocode determines whether UVT is the singular value decomposition (SVD) of matrix A, utilizing the given function eigs(X) to compute eigenvectors and eigenvalues.

The pseudocode begins by checking the dimensions of U, V, and A to ensure they conform to the requirements of an SVD. If the dimensions are incompatible, an error message is printed, and the program exits. Next, the product of U and VT is computed without using direct multiplication. The eigs function is then used to calculate the eigenvectors E and eigenvalues F for the matrix UV_transpose. Afterward, the product of E, F, and the transpose of E is computed, providing EFE_transpose. The dimensions of A and EFE_transpose are compared, and if they differ, an error message is printed, and the program exits. Finally, the elements of A and EFE_transpose are compared within a small tolerance. If all elements fall within the tolerance, it is concluded that UVT is the SVD of A. Conversely, if any element lies outside the tolerance, it is determined that UVT is not the SVD of A.

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Answer:

n^3*a_n ≈ (1/27) * n^3 → non-zero limit

Step-by-step explanation:

We have the sequence given by a_n = (5+3n)^(-3), and we want to find a value of k such that n^k*a_n has a finite non-zero limit as n approaches infinity.

Let's simplify the expression n^k*a_n:

n^k*a_n = n^k*(5+3n)^(-3)

We can rewrite this as:

n^k*a_n = [n/(5+3n)]^3 * [1/(n^(-k))]

Using the fact that 1/(n^(-k)) = n^k, we can further simplify this to:

n^k*a_n = [n/(5+3n)]^3 * n^k

We want this expression to have a finite non-zero limit as n approaches infinity. For this to be true, we need the first factor, [n/(5+3n)]^3, to approach a finite non-zero constant as n approaches infinity.

To see why this is the case, note that as n gets large, the 3n term dominates the denominator and we have:

[n/(5+3n)]^3 ≈ [n/(3n)]^3 = (1/27) * n^(-3)

So we need k = 3 for n^k*a_n to have a finite non-zero limit. Specifically, as n approaches infinity, we have:

n^3*a_n ≈ (1/27) * n^3 → non-zero constant.

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The line integral of this vector which lies between the points. f = x i +y j , from (2, 0) to (8, 0) is 30.

To calculate the line integral of the vector field F(x, y) = xi + yj along the line between the points (2, 0) and (8, 0), we can parameterize the line segment and then evaluate the integral.

1. Parameterize the line segment:
Let r(t) = (1-t)(2, 0) + t(8, 0) for 0 ≤ t ≤ 1.

Then r(t) = (2 + 6t, 0).

2. Find the derivative of the parameterization:
r'(t) = (6, 0)

3. Evaluate the vector field F along the line segment:
F(r(t)) = (2 + 6t)i + (0)j

4. Take the dot product of F(r(t)) and r'(t):
F(r(t)) • r'(t) = (2 + 6t)(6) + (0)(0) = 12 + 36t

5. Integrate the dot product over the interval [0, 1]:
∫(12 + 36t) dt from 0 to 1 = [12t + 18t^2] evaluated from 0 to 1 = 12(1) + 18(1)^2 - 0 = 12 + 18 = 30

The line integral of the vector field along the line between the given points is 30.

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The total number of posts in the fence is 300.

A community garden is surrounded by a fence. The total length of the fence is 3000 feet. For every 40 8 PM defense, there are four posts.

To find the total number of posts in the fence, first, we need to find out the number of fence segments. Each segment has 1 post at the start and 1 post at the end. The number of posts between any two segments is given by 40/4 = 10 posts per segment.

We can then use this information to solve the problem as follows:Let the number of fence segments be n.Each segment is 8 pm = 1/3 day long.The total length of the fence is 3000 feet.So, the length of one segment of the fence = (3000/n) feet.There are 10 posts per segment.

So, the number of posts in one segment of the fence = 10 x (1/3) = (10/3) posts.Since there is one post at the start and end of each segment, the total number of posts in one segment of the fence = (10/3) + 2 = (16/3) posts.

So, the total number of posts in the fence, n = Total length of the fence / Length of one segmentNumber of segments = n = 3000 / (3000/n)Number of segments = n = (3000 * n) / 3000Number of segments = n = n

Number of segments = n²

Number of segments = 900/16 = 56.25 ~ 56

The total number of posts in the fence = Number of segments x Number of posts per segmentTotal number of posts = 56 x (16/3)Total number of posts = 299.67 ~ 300 posts.

Therefore, the total number of posts in the fence is 300.

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Mrs. Falkener has written a company report every 3 months for the last 6 years, resulting in a total of 24 reports. Among these reports, 2/3 of them show the company earning more money than it spends. Therefore, 1/3 of the reports, or 8 reports, show the company spending more money than it earns.

In 6 years, there are 12 quarters since there are 4 quarters in a year. Mrs. Falkener has written a company report every 3 months, which means there are 12 * 3 = 36 periods in total. However, since each report covers a 3-month period, the total number of reports is 36 / 3 = 12.

Given that 2/3 of the reports show the company earning more money than it spends, we can calculate the number of reports showing the company spending more money than it earns. Since 2/3 of the reports represent the earnings being greater, the remaining 1/3 represents the expenses being greater. Therefore, 1/3 of 12 reports is 12 * (1/3) = 4 reports.

In conclusion, among the 24 company reports written by Mrs. Falkener in the last 6 years, 2/3 of them, or 16 reports, show the company earning more money than it spends. The remaining 1/3, or 8 reports, show the company spending more money than it earns.

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c-9 would be an equation that means 9 less than c

The smallest number of pigeons in the pigeonhole that contains the most number of pigeons is 2341.

To determine the smallest number of pigeons in the pigeonhole that contains the most number of pigeons, we can use the pigeonhole principle.

The pigeonhole principle states that if you distribute more than m objects into m pigeonholes, then at least one pigeonhole must contain more than one object.

In this case, we have 32761 pigeons and 14 pigeonholes. To minimize the number of pigeons in the pigeonhole that contains the most, we want to distribute the pigeons as evenly as possible.

Dividing 32761 by 14, we get:

32761 / 14 = 2340 remainder 1

This means we can evenly distribute 2340 pigeons to each of the 14 pigeonholes, leaving 1 pigeon remaining.

To minimize the number of pigeons in the pigeonhole that contains the most, we distribute the remaining 1 pigeon to one of the pigeonholes, resulting in the exact integer is 2341.

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The rent of the apartment during the 9th year of living in the apartment is approximately1538.54.

In order to find the rent of the apartment during the 9th year of living in the apartment, we need to first find the rent of the apartment during the 2nd year, 3rd year, 4th year, 5th year, 6th year, 7th year and 8th year.

Rent of apartment during the second year

Rent during the second year = (1 + 0.095) x 800

Rent during the second year = 1.095 x 800

Rent during the second year = $876

Rent of apartment during the third year

Rent during the third year = (1 + 0.095) x 876

Rent during the third year = 1.095 x 876

Rent during the third year = $955.62

Rent of apartment during the fourth year

Rent during the fourth year = (1 + 0.095) x 955.62

Rent during the fourth year = 1.095 x 955.62

Rent during the fourth year = $1043.78

Rent of apartment during the fifth year

Rent during the fifth year = (1 + 0.095) x 1043.78

Rent during the fifth year = 1.095 x 1043.78

Rent during the fifth year = $1141.08

Rent of apartment during the sixth year

Rent during the sixth year = (1 + 0.095) x 1141.08

Rent during the sixth year = 1.095 x 1141.08

Rent during the sixth year = $1248.07

Rent of apartment during the seventh year

Rent during the seventh year = (1 + 0.095) x 1248.07

Rent during the seventh year = 1.095 x 1248.07

Rent during the seventh year = $1365.54

Rent of apartment during the eighth year

Rent during the eighth year = (1 + 0.095) x 1365.54

Rent during the eighth year = 1.095 x 1365.54

Rent during the eighth year = $1494.96

Rent of apartment during the ninth year

Rent during the ninth year = (1 + 0.095) x 1494.96

Rent during the ninth year = 1.095 x 1494.96

Rent during the ninth year = $1538.54

Therefore, the rent of the apartment during the 9th year of living in the apartment is approximately 1538.54.

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So, the inequality which represents the situation is 7.5h + 30 ≥ 300, where h ≥ 36. Hence, the answer is B.

Given: Chris works at a bookstore and earns $7. 50 per hour plus a $2 bonus for each book she sells. Chris sold 15 books. The total earning of Chris,E(h) = 7.5h + 2 × 15 = 7.5h + 30 dollars where h is the number of hours worked by Chris .In order to find out the minimum hours she has to work to earn at least $300, we have to solve the inequality:7.5h + 30 ≥ 300 ⇒ 7.5h ≥ 270 ⇒ h ≥ 36.

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The distance traveled by the car when the tire makes one complete turn is 56.52 inches. The distance traveled by the car is equivalent to the wheel's circumference.

Given that the diameter of a wheel is 18 inches and the value of Pi is 3.14. To find the distance traveled by the car when the tire makes one complete turn, we need to find the circumference of the wheel.

Circumference of a wheel = πd, where d is the diameter of the wheel. Substituting the given values in the above formula, we get:

Circumference of a wheel = πd

                                 = 3.14 × 18

                                 = 56.52 inches.

Therefore, the distance traveled by the car when the tire makes one complete turn is 56.52 inches. When a wheel rolls over a surface, it creates a circular path. The length of this circular path is known as the wheel's circumference. It is directly proportional to the diameter of the wheel.

A larger diameter wheel covers a larger distance in one complete turn. Similarly, a smaller diameter wheel covers a smaller distance in one complete turn. Therefore, to find the distance covered by a car when the tire makes one complete turn, we need to find the wheel's circumference. The formula to find the wheel's circumference is πd, where d is the diameter of the wheel. The value of Pi is generally considered as 3.14.

The wheel's circumference is 56.52 inches. Therefore, the distance traveled by the car when the tire makes one complete turn is 56.52 inches.

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