The sum of three consecutive whole numbers is 105. Find the numbers.

The particular solution to the differential equation 7y'' + 8y' - 9y = 0, with initial values y(2) = 2 and y'(2) = 4, is \((15e^{2/7} - 14e^{-18/7}) / (15e^{4/7}) * e^{x} + (14e^{18/7} - e^[2/7}) / (15e^{4/7}) * e^{-9x/7}\). It can be obtained by solving the equation using the real distinct roots method and applying the given initial values.

To solve the differential equation, we assume a particular solution of the form \(y = e^{rx}\), where r is the root of the characteristic equation \(7r^2 + 8r - 9 = 0\).

By solving the characteristic equation, we find two real distinct roots: \(r_1 = 1\) and \(r_2 = -9\)/7.

Using these roots, we can write the general solution of the differential equation as \(y = C_1e^{r_1x} + C_2e^{r_2x}\), where \(C_1\) and \(C_2\) are constants to be determined.

Applying the initial values, y(2) = 2 and y'(2) = 4, we can form a system of equations to find the values of \(C_1\) and \(C_2\).

Solving the system of equations, we find \(C_1 = (15e^{2/7} - 14e^{-18/7}) / (15e^{4/7})\) and \(C_2 = (14e^{18/7} - e^{2/7}) / (15e^{4/7})\).

Therefore, the particular solution to the given differential equation, with the given initial values, is \(y = (15e^{2/7} - 14e^{-18/7}) / (15e^{4/7}) * e^{x} + (14e^{18/7} - e^{2/7}) / (15e^{4/7}) * e^{-9x/7}\).

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The 45% represents a descriptive statistic. Descriptive statistics are used to describe or summarize characteristics of a sample or population. In this case, the percentage of students living in the dormitories (45%) is a descriptive statistic that provides information about the sample of 800 students.

Descriptive statistics involve organizing, summarizing, and presenting data in a meaningful way. They are used to describe various aspects of a dataset, such as central tendency (mean, median, mode) and dispersion (variance, standard deviation). In this case, the percentage of students living in the dormitories (45%) is a descriptive statistic that describes the proportion of students in the sample who live in the dormitories.

Statistical inference, on the other hand, involves making conclusions or predictions about a population based on data from a sample. It uses techniques such as hypothesis testing and confidence intervals to make inferences about the population parameters.

In summary, the 45% represents a descriptive statistic as it provides information about the proportion of students living in the dormitories based on the sample of 800 students. It is not an example of statistical inference, a population, or a sample.

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The trigonometric function is given as

Apply the half angle identity to find the value of tan 75 ,

Here,

Now rationalize the function.

Again simplify the trigonometric function,

Hence the answer is 3.732.

a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

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Answer:

A. $21.59

Step-by-step explanation:

$151.13 ÷ 7 tons= $21.59 each per ton

From the given symmetry the given figure has point and rotational symmetry.

As given in the question,

Figure is attached.

The attached figure is having two arrows clockwise and anticlockwise.

So the given figure has point symmetry.

Given figure does not have line symmetry.

So the given figure has rotational symmetry.

Therefore, the given figure has point and rotational symmetry.

The above question is incomplete, the complete question is:

Determine whether the figure has line, point, and/or rotational symmetry. Check all that apply. (1 point)

Line

Point

Rotational

None

Figure is attached.

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As per given by the question,

There are given that Helen earns per hours rate is $14.75.

That means, the rgular rate is $14.75 per hour.

Now,

To calculate the employees overtime, multiply their regular rate by 1.5.

Then,

She receives time-and-a-halfe pay menas, she receives over time pay.

So,

Helen earns doller with overtime is,

Now,

When she worked in 50 hours in a week .

Then,

The wages is,

So, Helen received wages whe she worked 50 hours in a week is 1106.25.

Hence, the option fifth is correct.

Answer:

it's 6

Step-by-step explanation:

B=7 and D=13, so 13-7= 6

Answer:

y = 3x + 1

Step-by-step explanation:

Given the following points (0, 1) and (1, 4),

Let x1 = 0

y1 = 1

x2 = 1

y2 = 4

We can solve for the solve for the slope using the following formula:

\(m = \frac{y2 - y1}{x2 - x1} = \frac{rise}{run} = \frac{4 - 1}{1 - 0} = \frac{3}{1} = 3\)

Next, the y-intercept is the value of y, when x = 0. Looking at one of the given points, (0, 1) we can see that the value of y when x = 0 is 1.

Therefore, the y-intercept is (0, 1), or b = 1.

Given our slope, m = 3, and y-intercept, b = 1:

Our linear equation in slope-intercept form, y = mx + b is:

y = 3x + 1

Answer:

send u questioonn

Step-by-step explanation:

properly

Answer:

To find the area of a quarter circle, find the area of the whole circle by using the formula A = pi * r^2 and then divide by 4. To find the perimeter of the quarter circle, find the circumference of the whole circle, divide by 4, and then add the radius twice.

The area of a house advertised as 1920 square feet under roof is approximately 178.37 square meters.

To convert the area from square feet to square meters, we can use the conversion factor 1 square meter = 10.764 square feet.

By dividing the area in square feet by this conversion factor, we can obtain the equivalent area in square meters.

Given that the house is advertised as having 1920 square feet under roof, we can calculate the area in square meters as follows:

Area in square meters = 1920 square feet / 10.764 square feet per square meter

Area in square meters ≈ 178.37 square meters

Therefore, the area of the house is approximately 178.37 square meters.

It's important to note that this conversion assumes a simple conversion factor and does not account for other factors such as the shape or layout of the house.

Additionally, this conversion provides an approximate value as it is based on a conversion factor that may vary slightly depending on the specific conversion rate used.

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Answer:

-1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-1

The proof of det(A) = a₁det(M₁1) - a2 det(B) where a₁ is the first element of the first row of A and M₁₁ is the principal minor of A  is done.

Given information:

A symmetric tridiagonal matrix A is given.The matrix B is formed from A by deleting the first two rows and columns.

To prove: det(A) = a₁det(M₁1) - a2 det(B) where a₁ is the first element of the first row of A and M₁₁ is the principal minor of A obtained by deleting its first row and first column.

For any matrix A with an element ai, j not equal to zero, there is a cofactor Cij.

The adjugate of A is the transpose of the matrix of cofactors.

In other words, given a matrix A with an element ai, j, we define the minor Mi, j to be the determinant of the submatrix obtained by deleting the ith row and jth column, and the cofactor Cij to be (-1)^(i+j)Mi, j.

We can then define the adjugate matrix of A as the transpose of the matrix of cofactors of A.

Let A be the tridiagonal matrix and B be the matrix obtained from A by deleting the first two rows and columns.

So, det(A) is the sum of the products of the elements of any row or column of A with their corresponding cofactors.

If we choose the first column and compute the cofactors of the first two elements, we get:

a₁C₁,₁ - a₂C₂,₁ = a₁det(M₁,₁) - a₂det(M₂,₁)

Also, C₁,₁ = det(B), C₂,₁ = -a₂, and

det(M₁,₁) = a₁.

Hence,a₁det(M₁,₁) - a₂det(M₂,₁) = a₁a₁ - a₂(-a₂)

= a₁² + a₂² ≥ 0

Therefore, det(A) ≥ 0.

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The value of x in the given pentagon can be calculated by summing up the interior angles and setting it equal to 540 degrees.

To find the value of x in the given pentagon, we can use the fact that the sum of the interior angles of a polygon with n sides is equal to (n-2) x 180 degrees. Since a pentagon has 5 sides, its sum of interior angles is (5-2) x 180 = 540 degrees.

We can use this information to solve for x in the given pentagon by summing up the other four angles (given in degrees) and setting the sum equal to 540 - x. Solving for x gives us the value of x in the pentagon. Understanding the properties of polygons, such as the sum of their interior angles, is important in geometry and can help in calculating their angles, areas, and perimeters.

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Answer:

Step-by-step explanation:

Let the original cost be x

The shoppers get 10% of the original price

Therefore the equation to find final cost =

Discount: 10x/100

Final Cost: 90x/100

Mark brainliest for further answers :)

The value of teh probability P(Financial Aid | Graduate) is 0.72

The probability is represented as:

P(Financial Aid | Graduate)

The probability is calculated as:

P(Financial Aid | Graduate) = (Financial Aid and Graduate)/(Graduate)

Using the values on the table, we have:

P(Financial Aid | Graduate) = (1879)/(1879 + 731)

Evaluate

P(Financial Aid | Graduate) = 0.72

Hence, the value of teh probability P(Financial Aid | Graduate) is 0.72

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Answer:it is the fist car

Step-by-step explanation:

Because im so fudgen smart

Answer:

n=3 (there's no way I can explain this I can only give you the answer)

Step-by-step explanation:

As a result, the area of the surface formed by rotating the given curve about the x-axis throughout the period [9, 20] is 864π.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

The area of the surface generated when a curve is revolved about an axis is known as the surface area of revolution and can be calculated using the formula:

A = 2π ∫ y dx

where y is the equation of the curve being revolved and the integral is taken over the interval [a,b] in which the curve is being revolved.

In this case, the curve is given by y = 8√x on the interval [9, 20]. So, the surface area of revolution is:

A = 2π ∫_9^20 8√x dx

This integral can be evaluated using substitution. Let u = √x, so that du = dx / 2√x and x = u^2. Then:

A = 2π ∫_3^4 8u * 2u du

= 2π * 8 * ∫_3^4 u^2 du

= 2π * 8 * [u^3/3]_3^4

= 2π * 8 * (64/3 - 27/3)

= 2π * 8 * (37/3)

= 864π

So, the area of the surface generated when the given curve is revolved about the x-axis over the interval [9, 20] is 864π.

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When we have no information about the expected values (E) or variances (Var) of random variables X and Y due to the ignorance of their probability density functions (PDFs) or probability mass functions (PMFs), we can still make use of the assumption that X and Y are independent and identically distributed (i.i.d.). By relying solely on the i.i.d. assumption, we can estimate the expected values and variances of X and Y.

In the absence of knowledge about the specific PDF/PMF of X and Y, the i.i.d. assumption allows us to treat X and Y as if they were drawn from the same distribution with unknown parameters. This assumption enables us to employ certain statistical techniques and properties that are applicable to i.i.d. random variables.

To estimate the expected values of X and Y (E(X) and E(Y)), we can calculate the sample means of a sample drawn from each variable. Under the i.i.d. assumption, the sample means should provide reasonable approximations of the true expected values.

Similarly, to estimate the variances of X and Y (Var(X) and Var(Y)), we can calculate the sample variances of samples drawn from each variable. Again, assuming independence and identical distribution, the sample variances can be used as estimators of the true variances.

It is important to note that these estimations rely solely on the i.i.d. assumption and do not take into account any specific characteristics of the unknown distributions of X and Y. They serve as basic estimators in the absence of additional information about the PDFs/PMFs.

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The cost of each lily is $3.25, and the cost of each rose is $6.50 according to the first arrangement and second arrangement.

Let's assume the cost of each lily is represented by "L" and the cost of each rose is represented by "R." Based on the given information, we can form a system of linear equations.

From the first arrangement, we know that 5 lilies and 1 rose cost $19.75. This can be written as the equation 5L + R = 19.75.

From the second arrangement, we know that 6 lilies and 3 roses cost $27.75. This can be written as the equation 6L + 3R = 27.75.

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

Multiply the first equation by 3 and the second equation by -1 to eliminate the R term:

15L + 3R = 59.25

-6L - 3R = -27.75

Adding the equations, we get:

9L = 31.50

Divide both sides by 9:

L = 3.50

Now substitute the value of L back into one of the original equations. Let's use the first equation:

5(3.50) + R = 19.75

17.50 + R = 19.75

Subtract 17.50 from both sides:

R = 2.25

Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.

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Answer:

X=2

Step-by-step explanation:

Answer:

1. 80%

2. 11.7

3. 37.5%

4. 12%

5. D diesel

1. $12.8

2. 0.025

3. $1,133.44

4. 120 people

5. 75 people

Answer:

1. 80

2. 11.7

3. 6%

4. $39

5. B

To analyze the variables Birth Rate and Death Rate at the same time the scatter plot would be appropriate to use.

A scatter chart, also called as a scatter plot, is a graph that displays the correlation between two variables. They are a very effective type of chart because they enable viewers to see relationships or trends that would be nearly impossible to see in any other form right away.

Modern scatter charts are based on René Descartes' 17th-century cartesian coordinates system, albeit their exact origins are unknown. The majority of scatter plots used in science journals and publications may be found there.

One of the most adaptable and practical inventions in the history of statistical graphs is the scatter chart. This can seem like a bold statement, but scatter charts help make sense of muddled data. They are a tool for discovery as well as visualisation, which is a much bigger role for them.

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The range of the data is from 36 to 99.

I'd be glad to help you with that question. To answer it, I'll first explain what a stem-and-leaf plot is, and then I'll discuss how to use it to find the range of the data represented by it.A stem-and-leaf plot is a method of displaying quantitative data. The digits of the data are separated into two parts, the stem and the leaf. The stem consists of all digits except the last, and the leaf consists of the last digit. The stem-and-leaf plot is a way of organizing the data by sorting the stems into a column and listing the leaves for each stem in order. Here's an example of a stem-and-leaf plot:3 | 6 7 8 9 7 7 8 8 9 4 | 5 5 6 7 7 8 8 8 8 8 8 9 9 9In this example, the stems are 3 and 4, and the leaves are the second digits. For example, the first row represents data values between 36 and 39. There are 3 values in this range: 36, 37, and 39.To find the range of the data represented by the stem-and-leaf plot, we need to look at the smallest and largest values. The smallest value is the first number in the first row, which is 36. The largest value is the last number in the last row, which is 99.

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The valid C identifiers from the given options are (b) travel time, (d) number, (f) inchesinonecentimeter, (g) monthly pay, and (h) first.

In C programming, identifiers are names used to identify variables, functions, and other entities. They must follow certain rules to be considered valid. Here's an analysis of each option:

(a) firstc prog: Invalid identifier because it starts with a number, which is not allowed in C.

(b) travel time: Valid identifier because it consists of alphabetic characters and spaces are allowed.

(c) 3feetinayard: Invalid identifier because it starts with a number, which is not allowed in C.

(d) number: Valid identifier because it consists of alphabetic characters.

(e) cpp assignment: Invalid identifier because it contains a space, which is not allowed in C.

(f) inchesinonecentimeter: Valid identifier because it consists of alphabetic characters.

(g) monthly pay: Valid identifier because it consists of alphabetic characters and spaces are allowed.

(h) jack'shomework: Invalid identifier because it contains an apostrophe, which is not allowed in C.

To summarize, the valid C identifiers from the given options are (b) travel time, (d) number, (f) inchesinonecentimeter, (g) monthly pay, and (h) first.

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The solution set for the given graph is (2,1). The solution has been obtained using linear equations.

What is a linear equation?

It is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.

We are given two lines on the graph

The points of the red line are (3,0) and (0,3)

So, the equation of the line comes out to be

y=−x+3      ...(1)

The points of the blue line are (3,2) and (-1,-2)

So, the equation of the line comes out to be

y=x−1     ...(2)

To find the solution set, we need to solve the equations

Substituting (1) in (2), we get,

⇒−x+3 = x−1

⇒−2x = -4

⇒x = 2

So, y = 1

Hence, the solution set for the given graph is (2,1).

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The length of segment DE on the rectangle, considering the midpoint, is given as follows:

DE = 22.67.

The midpoint of a segment divides a segment into two segments of equal length, having half the length of the entire segment.

In this problem, the diagonal of the rectangle represented by segment AC has midpoint E, hence the measure of x is calculated as follows:

EC = AE.

The measures are as follows:

Hence:

7x - 3 = 4x + 8

7x - 4x = 8 + 3

3x = 11

x = 11/3.

Segment DE is also half of a diagonal, hence it's length is obtained with the numeric value of any segment EC or AE, as follows:

DE = EC = 7x - 3 = 7 x 11/3 - 3 = 77/3 - 9/3 = 68/3 = 22.67.

The rectangle is given by the image at the end of the answer.

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Answer:

In March he weighed 210 pounds

Step-by-step explanation:

In May he weighs 197.4 pounds