Convert 36000cm^2 to m^2

Answer:

1/27

Step-by-step explanation:

A die has a 1/3 chance per roll of landing on a number greater than 4.

Three rolls would be represented by (1/3)^3 or 1/3 x 1/3 x 1/3, equal to 1/27.

Hope this helped!

the equation line perpendicular to r is  y = 3x +12.

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The eqaution of the line r passing through (6,6) and (-3,3)

y-3 = (\(\frac{3-6}{-3-6}\)) (x+3)

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

So the slope is -1/3

For a line perpendicular, the slope will be 3.

So the equation of the line perpendicular can be written as y-3 = 3(x+3)

or y = 3x +12

Hence the equation line perpendicular to r is  y = 3x +12.

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Using the washer method, the volume of the solid generated by revolving the region enclosed by the triangle with vertices (3,2),(4,3), and (3,3) about the y-axis is 0 units.

We need to find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (3,2),(4,3), and (3,3) about the y-axis. The triangle with vertices (3,2),(4,3), and (3,3) is shown below:

The triangle is enclosed by the lines x = 3, y = 2, y = x - 1.

Since the region is revolved about the y-axis, the method of cylindrical shells cannot be used. Thus, we use the washer method to find the volume of the solid. This method involves taking vertical slices, so we need to integrate with respect to x.Let us consider an infinitesimal slice of width dx at a distance x from the y-axis. The slice is a washer with inner radius x - 1 and outer radius 2 - x. The height of the washer is the difference in y-coordinates of the points on the two bounding curves. The points are:

x = x, y = x - 1 (on the line y = x - 1)

x = x, y = 3 - x (on the line y = 3 - x)

Thus, the height of the washer is (3 - x) - (x - 1) = 4 - 2x.

The area of the washer is: π [(2 - x)² - (x - 1)²] = π (3 - 2x) dx

Hence, the volume of the solid is: V = ∫ 0 ³π (3 - 2x) dx

V = π ∫ 0 ³ (3 - 2x) dx

V = π [(3x - x²)] [0, ³]

V = π [(9 - 9) - (0 - 0)]V = 0

Therefore, the volume of the solid generated by revolving the region enclosed by the triangle with vertices (3,2),(4,3), and (3,3) about the y-axis is 0 units.

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Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

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The value of 6 divided by 396 is 0.1515.

Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The primary purpose of division is to determine how many equal groups are formed or how many people are in each group when equitably sharing.

The steps include:

Step 1: Take the first digit of the dividend from the left.

Step 2: Divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and then write the difference below.

Step 4: Bring down the next digit of the dividend.

In this case, 6/396 will give the value illustrated above.

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Andace needs to score at least 98 on her fifth exam to have an average of 90 or better for the five exams.

To find out what score Andace needs to get on the fifth exam, we can use the formula for the average (also known as the mean):

Average = (sum of all scores) / (number of scores)

We know that Andace needs an average of 90 or better for the five exams. Therefore, the sum of all five scores must be at least 450 (90 multiplied by 5).

The sum of Andace's first four scores is:

96 + 84 + 95 + 82 = 357

To get an average of 90 or better for the five exams, Andace needs to get a total of:

450 - 357 = 93

on her fifth exam.

Since she has already taken four exams and the maximum score she can get on her fifth exam is 100, we can subtract her first four scores from 93 to find out what she needs to score on her fifth exam:

93 - 96 - 84 - 95 - 82 = -164

Since it's not possible for Andace to score a negative number on her fifth exam, we can conclude that she needs to score at least 98 (93 - 5) to have an average of 90 or better for the five exams.

In conclusion, Andace needs to score at least 98 on her fifth exam to have an average of 90 or better for all five exams.


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The answer for the differential equation is:

f(theta) = -sin(theta) - cos(theta) + 4*theta + 2

To solve for f(theta), we need to integrate twice since f''(theta) is given.

First, we integrate f''(theta) with respect to theta to get:

f'(theta) = -cos(theta) + sin(theta) + C₁

where C₁ is an arbitrary constant of integration.

Next, we integrate f'(theta) with respect to theta to get:

f(theta) = -sin(theta) - cos(theta) + C₁*theta + C₂

where C₂ is another arbitrary constant of integration.

To solve for C₁ and C₂, we use the initial conditions given:

f(0) = 2 => C₂ = 2

f'(0) = 2 => C₁ = 4

Therefore, the solution to the differential equation is:

f(theta) = -sin(theta) - cos(theta) + 4*theta + 2

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Answer:

30.00 – (1.79a + 0.36b + 2.99)

Step-by-step explanation:

you need to rest the amount of money pay.

There are two terms in the given expression 5xy²+ 35xy².

What is meant by term?

Terms comprise expressions. A term may be a constant, a variable, or a combination of variables and constants.

What is an example of a term?

It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase. Single-word examples: A single phrase is 3x.

There are two terms in the equation 5xyA ^2 + 35xyA^2 that is separated by an arithmetic operator +.

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The area of the circle in the graph is 113 square units.

Remember that for a circle of radius R, the area is given by the simple formula you can see below.

A = pi*R²

Where pi = 3.14, so we can use this formula to find the area of the circle.

On the diagram we can see that the radius of the circle is:

R = 6 units

Replacing that in the area formula we will get.

A = 3.14*(6 units)²

A = 113.04 units ²

The correct option is the third one.

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The probability that the sample mean would be less than 127 wpm if 84-speed typists are randomly selected is: 0.033625

What is Mean?

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally. The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean. When all of the values are organized in ascending order, the Median is the median value of the provided data. While the number in the list that is repeated a maximum of times is the mode.

We have

\(\mu=124\)  

\(\sigma=15\)

n=84

We want to find the probability that the sample mean would be greater than 127 WPM is

\(\begin{aligned}P(\bar{X} > 127) &=P\left(\frac{\bar{X}-\mu}{\sigma / \sqrt{n}} > \frac{127-124}{15 / \sqrt{84}}\right) \\&=P(Z > 1.83)\end{aligned}\)

\(=0.033625\)

The required probability is 0.0336.

Hence, The probability that the sample mean would be less than 127 wpm if 84-speed typists are randomly selected is: 0.033625

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Answer: 225 adult tickets, 375 student tickets

Step-by-step explanation:

a = adult tickets

s = student tickets

a + s = 600 (the adult and student ticket added together should equal 600)

6.00a + 4.50s = 3,037.50 ($6 multiply by the adult ticket plus $4.50 multiply by the student ticket should equal to 3,037.50)

a = -s + 600 (get one of the variable by itself by subtracting it from one side)

6 (-s + 600) + 4.5s = 3,037.5 (substitute the a for -s + 600)

-6s + 3600 + 4.5s = 3,037.5 (combine like terms)

-1.5s + 3600 = 3,037.5 (subtract 3600 from each side)

-1.5s = - 562.5 (divide -1.5 from each side)

s = 375

600 = 375 + a (substitute s for 375)

a = 225

Answer:

0.00000125(usual form)

Answer:

Step-by-step explanation:

total type of books are 4 types

the probability of one book is 60

so the probability of type of a book is 4/60=1/15

The interpretation of the slope is On average, for every additional year of age, bone density loss increases by approximately 0.41. (option a)

To calculate the least squares regression line, the data points are first plotted on a scatter plot. The line of best fit is then drawn through the data points such that the sum of the squared distances between the line and the data points is minimized. The slope of this line can be calculated using the following formula:

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

where n is the number of data points, Σ represents the sum of the values, x represents age, y represents bone density loss, and xy represents the product of x and y.

Using this formula, the slope for this data set can be calculated to be approximately 0.41. This means that, on average, for every additional year of age, bone density loss increases by approximately 0.41. In other words, the slope indicates a positive relationship between age and bone density loss, with bone density loss increasing as age increases.

Therefore, the correct answer is (a) On average, for every additional year of age, bone density loss increases by approximately 0.41.

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Complete Question:

Osteoporosis is a condition in which bone density decreases, often resulting in broken bones. Bone density usually peaks at age 30 and decreases thereafter. To understand more about the condition, a random sample of women aged 50 and over were recruited. Each woman's bone loss was recorded and the date is shown in this file. Create a scatter plot of these two variables, with age as the x variable and bone density loss as the y variable. Calculate the least squares regression line. What is your interpretation of the slope?

a. On average, for every additional year of age, bone density loss increases by approx 0.41.

b. On average, for every additional one point of bone density loss, age increases by approx 0.41.

c. On average, for every additional year of age, bone density loss increases by approx 6.9.

d. none of the above

Add a title to the dot plot that summarizes the variable being measured and the time period represented (in this case, "Bryan's Running Times over 10 Days").

However, I can describe how to create a dot plot for Bryan's data:

Choose a scale for the horizontal axis that covers the range of Bryan's running times. For example, if Bryan's shortest run was 20 minutes and his longest run was 40 minutes, you might choose a scale from 20 to 40 with tick marks at intervals of 2 or 5.

Label the horizontal axis with a title that indicates the variable being measured (in this case, "Minutes Run") and the unit of measurement (in this case, "Minutes").

Draw a vertical line for each data point in Bryan's data set at the appropriate location on the horizontal axis. For example, if Bryan ran for 35 minutes on the first day, draw a dot or small line segment above the tick mark at 35 on the horizontal axis.

Stack dots vertically for any repeated values of minutes run. For example, if Bryan ran for 30 minutes on two different days, draw two dots or line segments stacked vertically above the tick mark at 30 on the horizontal axis.

Label the vertical axis with a title that indicates the frequency of each value of minutes run (in this case, "Frequency") and the appropriate unit of measurement (in this case, "Days").

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To determine which location yields the higher profit per year, we need the specific data for the annual profit in each location. Please provide the annual profit values for the locations in question, and I will be able to calculate and compare the profit per year.

Without the necessary information regarding the annual profits of the locations, it is not possible to determine which location yields the higher profit per year. To make a meaningful comparison, we need the specific profit figures for each location. Once the annual profit values are provided, we can calculate the profit per year by dividing the total profit by the number of years.

Once the profit per year is calculated for each location, we can compare the values to determine which location has the higher profit per year. However, as the specific data regarding the annual profit in each location is missing, it is not feasible to provide a conclusive answer at this time. Please provide the annual profit figures for the locations in question, and I will be able to assist you further in determining which location yields the higher profit per year.

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The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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Answer:

A

Step-by-step explanation:

100% slope is -3 because you need to move down 3 times which is -3 and move to the right once which is 1

Slope= rise/run

Slope=-3/1 which equals -3

y-intercept= 2 because you just look at the y-axis and see any points that connects to it while the x is zero

Answer:

b=2

Step-by-step explanation:

subtract 2 on both sides (2b=4)

divide 2 on both sides (b=2)

Answer:

b = 2

Step-by-step explanation:

2b + 2 = 6

First, bring the 2 to the other side. To do this, subtract 2 on both sides

2b = 4

Now, divide to isolate b.

2b/2 = b

4/2 = 2

b = 2

The series 7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... is an alternating series, meaning that the signs of the terms alternate between positive and negative. To rewrite this series as a summation notation with an infinity symbol, we need to first determine the pattern of the denominator.

The denominators of the terms in the series are 8, 10, 12, 14, 16, .... We can see that the denominator of the nth term is 8 + 2(n-1), or 2n + 6.
Using this pattern, we can rewrite the series as:
7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... = ∑(-1)^(n-1) 7/(2n + 6) from n = 1 to infinity.
Therefore, the answer to your question is:
The series 7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... can be rewritten as ∑(-1)^(n-1) 7/(2n + 6) from n = 1 to infinity.

Rewriting the given series using summation notation. The series you provided is:
7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ...
This series can be rewritten using the summation notation as:
∑((-1)^(n-1) * 7/(6+2n)) from n=1 to infinity.

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Question:

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds.  Write an equation to determine how long it will take for the ball to reach the ground.

Answer:

\(t = 5.0625\)

Step-by-step explanation:

Given

\(h(t)=-16t^2+80t+5\)

Required

Find t when the ball hits the ground

This implies that h(t) = 0

So, we have:

\(0=-16t^2+80t+5\)

Reorder

\(-16t^2+80t+5 = 0\)

Using quadratic formula, we have:

\(t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\)

Where

\(a = -16\)      \(b =80\)      \(c = 5\)

So, we have:

\(t = \frac{-80\±\sqrt{80^2 - 4*-16*5}}{2*-16}\)

\(t = \frac{-80\±\sqrt{6400 +320}}{-32}\)

\(t = \frac{-80\±\sqrt{6720}}{-32}\)

\(t = \frac{-80\±82.0}{-32}\)

This gives:

\(t = \frac{-80+82.0}{-32}\) or \(t = \frac{-80-82.0}{-32}\)

\(t = \frac{2}{-32}\) or \(t = \frac{-162}{-32}\)

\(t = -\frac{2}{32}\) or \(t = \frac{162}{32}\)

But time can not be negative.

So, we have:

\(t = \frac{162}{32}\)

\(t = 5.0625\)

Hence, time to hit the ground is 5.0625 seconds

Answer:5

Step-by-step explanation:

w(n)=4-1

=5

In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

To evaluate the given iterated integral ∫∫R (1 - y²)/(9(x + y)) dA, where R is the region in the xy-plane bounded by the curves x = 0, y = 1, and 9(x + y) = 2, we can convert it to polar coordinates for easier computation.

In polar coordinates, we have x = rcos(θ) and y = rsin(θ), where r represents the distance from the origin and θ is the angle measured counter clockwise from the positive x-axis.

The integral becomes ∫∫R (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) r dr dθ. In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

In the given integral, we substitute x and y with their respective polar coordinate representations. The numerator becomes 1 - r²sin²(θ), and the denominator becomes 9(rcos(θ) + rsin(θ)). Multiplying the numerator and denominator by r, we have (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) = (1 - r²sin²(θ))/(9r(cos(θ) + sin(θ))). We then rewrite the double integral as two separate integrals: the outer integral with respect to θ and the inner integral with respect to r. The limits of integration for θ are 0 to π/2, while the limits for r are determined by the curve 0 = (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)).

We can simplify this curve to 2cos(θ) - 9sin(θ) = 9, which represents an ellipse in the xy-plane. The limits of r correspond to the radial distance within the ellipse for each value of θ. By evaluating the double integral using these limits, we can determine the result of the given iterated integral.

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Answer:

x=8/3

Step-by-step explanation:

12.5-4x=2x-3.5

12.5-4x-2x=-3.5

-4x-2x+3.5-12.5

-6x=-3.5-12.5

-6x=-16

thus getting x=8/3

Answer:

  zero

Step-by-step explanation:

You want the rate of change between the points (3, 1) and (4, 1).

The "rate of change" is also known as the "slope" of the line between the points. That is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For your points, this is ...

  m = (1 -1)/(4 -3) = 0/1 = 0

The rate of change is zero.

__

Additional comment

The y-value is constant. That means the equation of the line is y=1, a horizontal line. It does not rise or fall. Its rate of change is zero.

Answer:

Step-by-step explanation:

6x - 5 + 3x - 4 = 180     {Supplementary angles}

6x + 3x - 5 - 4 = 180

Combine like terms

9x - 9 = 180

Add 9 to both sides

9x = 180 + 9

9x = 189

Divide both sides by 9

 x = 189/9

x = 21

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The nswer is × = 21

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The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

To solve the system of equations using the weighted least squares method, we need to minimize the sum of the squared weighted residuals. Let's solve the problem using both the algebraic approach and matrices.

Algebraic Approach:

We have the following equations:

A + 2B = 10.50 + V1 ... (1)

2A - 3B = 5.55 + V2 ... (2)

2A - B = -10.50 + V3 ... (3)

To minimize the sum of squared weighted residuals, we square each equation and multiply them by their respective weights:

\(2^2 * (A + 2B - 10.50 - V1)^2\)

\(3^2 * (2A - 3B - 5.55 - V2)^2\\1^2 * (2A - B + 10.50 + V3)^2\)

Expanding and simplifying these equations, we get:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1)\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2)\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\\\)

Now, let's sum up these equations:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1) +\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2) +\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\int\limits^a_b {x} \, dx\)

Simplifying further, we obtain:

\(14A^2 + 31B^2 + 1113 + 14V1^2 + 33V2^2 + 14V3^2 + 14AB - 231A - 246B + 21V1 - 11.1V2 + 21V3 = 0\)

Now, we have a single equation with two unknowns, A and B. We can use various methods, such as substitution or elimination, to solve for A and B. Once the values of A and B are determined, we can substitute them back into the original equations to find the most probable values of A and B.

Matrix Approach:

We can rewrite the system of equations in matrix form as follows:

| 1 2 | | A | | 10.50 + V1 |

| 2 -3 | | B | = | 5.55 + V2 |

| 2 -1 | | -10.50 + V3 |

Let's denote the coefficient matrix as X, the variable matrix as Y, and the constant matrix as Z. Then the equation becomes:

X * Y = Z

To solve for Y, we can multiply both sides of the equation by the inverse of X:

X^(-1) * (X * Y) = X^(-1) * Z

Y = X^(-1) * Z

By calculating the inverse of X and multiplying it by Z, we can find the values of A and B.

Comparing Results:

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

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