In centimeters, what is the unknown length in this right triangle?
61 cm
60 cm

The volume of the cube expressed as a fraction will be 27x³y³ / 64.

Given that:

Volume, V = (0.75xy)³

It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the cube expressed as a fraction is calculated as,

V = (0.75xy)³

V = (3xy/4)³

V = 27x³y³ / 64

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The general solution of the differential equation y''(x) + y(x) = sec(x) tan(x) is y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x); here c₁ and c₂ are constants.

To solve the differential equation y''(x) + y(x) = sec(x) tan(x) using variation of parameters, we first need to find the solutions to the homogeneous equation y''(x) + y(x) = 0.

The auxiliary equation for the homogeneous equation is r² + 1 = 0, which has complex roots r = ±i.

The corresponding solutions to the homogeneous equation are y₁(x) = cos(x) and y₂(x) = sin(x).

Next, we need to find the particular solution using the method of variation of parameters. Let's assume the particular solution has the form y_p(x) = u(x)cos(x) + v(x)sin(x).

Now, we need to find u(x) and v(x) by substituting this form into the original differential equation and solving for u'(x) and v'(x).

Differentiating y_p(x), we get y_p'(x) = u'(x)cos(x) - u(x)sin(x) + v'(x)sin(x) + v(x)cos(x).

Taking the second derivative, y_p''(x) = -u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x).

Substituting these derivatives into the original differential equation, we have:

(-u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x)) + (u(x)cos(x) + v(x)sin(x)) = sec(x)tan(x).

Simplifying, we get:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x).

To find u'(x) and v'(x), we solve the following system of equations:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x),

u(x)cos(x) + v(x)sin(x) = 0.

We can solve this system using various methods such as substitution or elimination.

Solving the system, we find:

u'(x) = sin(x)sec(x),

v'(x) = -cos(x)sec(x).

Integrating these expressions, we obtain:

u(x) = -ln|sec(x) + tan(x)| + C₁,

v(x) = -ln|sec(x) + tan(x)| + C₂.

Finally, the particular solution is given by:

y_p(x) = (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

The general solution to the differential equation is the sum of the homogeneous and particular solutions:

y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

Here, c₁ and c₂ are constants.

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Answer:

-3

Step-by-step explanation:

     Let x = the number

Then 3x = its triple, and the condition is:

x - 8 < 3x

Subtract x from each side

-8 < 2x

Divide each side by 2

-4 < x

Reverse the inequality

x > -4

The smallest integer greater than -4 is -3.

Check:

-3 - 8 < 3(-3)

-11 < -9

It checks.

Answer:

The intersection is at (0,1)

Step-by-step explanation:

Answer: 1.44pi

Step-by-step explanation: just plug in 1.2 for r in a=pi(r^2)

Answer:

B. 1 horse per 20 pounds hay

C. YEs, an equation that can represent this is y=20x where x is the number of horses and y is the hay. Because i can make an equation that works for any value in this table, it is proportional.

Step-by-step explanation:

Answer: a) 1 2 3 4 5 6 7

20 40 60 80 100 120 140

b) 20 pounds of hay/horse

c) Yes. An increase in 1 horse results to an equivalent increase of 20 pounds of hay.

Step-by-step explanation:

Answer:

three thirds is one whole

Step-by-step explanation:

The answer is 18 because three thirds is one whole which in this case is 18! Have a nice day!

Answer:

Step-by-step explanation:

gradient = 5 = [k-(-1)]/[6-2]

[k+1]/4 = 5

k+1=20

k=19

The value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5 is found to be 19 by using the formula for gradient and solving the resulting equation for k.

To find the value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5, we'll use the formula for gradient, which is (y2 - y1) / (x2 - x1).

The given points can be substituted into the formula as follows: The gradient (m) is 5. The point A(2, -1) will be x1 and y1, and point B(6, k) will be x2 and y2. Now, we set up the formula as follows: 5 = (k - (-1)) / (6 - 2).

By simplifying, the equation becomes 5 = (k + 1) / 4. To find the value of k, we just need to solve this equation for k, which is done by multiplying both sides of the equation by 4 (to get rid of the denominator on the right side) and then subtracting 1 from both sides to isolate k. So, the equation becomes: k = 5 * 4 - 1. After carrying out the multiplication and subtraction, we find that k = 20 - 1 = 19.

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The equation of line that has a slope of 2 and passes through the point (-3,4) will be;

⇒ y = 2x + 10

Option B is true.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line = (-3, 4)

Slope of the line = 2

Since, The equation of line that has a slope of 2 and passes through the point (-3,4) will be;

⇒ y - y₁ = m (x - x₁)

⇒ y - 4 = 2 (x - (-3))

⇒ y - 4 = 2 (x + 3)

⇒ y - 4 = 2x + 6

Add 4 both side;

⇒ y - 4 + 4 = 2x + 6 + 4

⇒ y = 2x + 10

Thus, The equation of line that has a slope of 2 and passes through the point (-3,4) will be;

⇒ y = 2x + 10

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Answer:

37.5 km2 ...............

Answer:

The GCF of both is g^3

Step-by-step explanation:

Here, we are asked to give the greatest common factor of g^3 and g^15

In simpler terms we want to find that biggest term that could divide both values.

Mathematically, since g^3 is itself a factor of g^15, then we can conclude that the GCF of both is g^3

To estimate the mean number of pages per book in the fiction section of the large school library, we can use a t-test. A t-test is a statistical method for determining the probability that a given sample of data comes from a population with a certain mean value.

Given that the sample size is 35 and the standard deviation is 47.6 pages per book, we can use the t-distribution table to find the t-value for a 99% confidence level.

The t-value for a 99% confidence level and 34 degrees of freedom (sample size - 1) is 2.021.

With this information, we can construct a confidence interval for the mean number of pages per book in the fiction section of the large school library. The confidence interval is given by:

Sample mean ± t-value * (Standard deviation / √Sample size)

Therefore, the confidence interval for the mean number of pages per book in the fiction section of the large school library is:

291.8 ± 2.021 * (47.6 / √35)

The margin of error is approximately 12.2 pages per book.

So the mean number of pages per book in the fiction section of the large school library is between 279.6 and 304 pages per book with a 99% confidence level.

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

To classify a triangle by its angles and sides, we can use the properties and definitions of different types of triangles. Let's analyze the given triangle with sides measuring 8, 11, and 12 and angles measuring 45 degrees, 65 degrees, and 70 degrees.

Classification by angles:

Acute Triangle: An acute triangle has all three angles less than 90 degrees.

Obtuse Triangle: An obtuse triangle has one angle greater than 90 degrees.

Right Triangle: A right triangle has one angle exactly 90 degrees.

Based on the given angles of 45 degrees, 65 degrees, and 70 degrees, none of them are greater than 90 degrees, so we can classify the triangle as an Acute Triangle.

Classification by sides:

Equilateral Triangle: An equilateral triangle has all three sides of equal length.

Isosceles Triangle: An isosceles triangle has two sides of equal length.

Scalene Triangle: A scalene triangle has all three sides of different lengths.

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

In summary, based on the given measurements, the triangle can be classified as an Acute Scalene Triangle. We determined this by comparing the angles to the definitions of acute, obtuse, and right triangles, and comparing the side lengths to the definitions of equilateral, isosceles, and scalene triangles.

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To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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You may not cross a single broken white or yellow line, when doing so would interfere with traffic unless it is safe to do so and without interfering with traffic.  

The yellow line on the road serves as a barrier between opposing lanes of traffic as a traffic safety measure. It is intended to alert drivers to the fact that they are moving in the opposite directions and should keep a safe distance while driving.

The yellow line is typically placed in the centre of the road to indicate the separation of traffic. On highways and interstates, the yellow line is frequently used to mark the separation between two lanes of traffic moving in the same direction.

Drivers should always follow the yellow line and never cross it because doing so can be risky and result in accidents. The yellow line can also be used to show when passing other vehicles is dangerous.

On the driver's side, it is prohibited to pass other cars when a yellow line is interrupted by a solid line. Overall, the yellow line is an important safety measure for drivers to be aware of and obey when on the road.

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A sample size of 1500 or 10000 is generally sufficient for a reasonably accurate poll if proper methodology and random sampling techniques are utilized.

The correct answer is option A and B.

Determining a sufficient sample size for a reasonably accurate poll requires considering several factors: the population size, desired margin of error, confidence level, and expected variability within the population.

To calculate the sample size, we can use the formula:

n = (\(Z^2 * p * (1-p)) / (E^2)\)

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level

p = estimated proportion or expected prevalence in the population

E = desired margin of error

For example, let's assume we want a 95% confidence level, a margin of error of 5%, and an estimated prevalence of 50% (which provides the maximum required sample size). Plugging these values into the formula, we have:

Z = 1.96 (corresponding to a 95% confidence level)

E = 0.05 (5% margin of error)

p = 0.5 (estimated prevalence)

n = (\(1.96^2\) * 0.5 * (1-0.5)) / (0.05^2)

n = (3.8416 * 0.25) / 0.0025

n = 0.9604 / 0.0025

n = 384.16

Therefore, the required sample size would be approximately 384. This calculation assumes a worst-case scenario (p = 0.5) to ensure a conservative sample size estimate.

Based on the given options:

- A sample size of 1500 exceeds the required sample size, providing a reasonably accurate poll.

- A sample size of 10000 is more than sufficient and would yield an even more accurate poll.

- Sampling 10 percent of the population can be considered sufficient, depending on the total population size.

- Sampling 100 percent of the population would provide the most accurate results, but it is usually impractical or impossible.

In conclusion, both a sample size of 1500 and 10000 are correct answer making option A and B the correct answer.

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The question probable may be:

Which of the following sample sizes is sufficient to have a reasonably accurate poll? Group of answer choices:

A. 1500

B. 10000

C. 10 percent of the population

D. 100 percent of the population

Answer:

6

Step-by-step explanation:

Add three to both sides

Subtract 2x from both sides

2x=12

Divide by 2

X=6

Answer:

x = 6

Step-by-step explanation:

4x - 3 = 2x + 9

2x = 12

x = 6

If the slope of a line is 90 over 510, then the line is a straight line passing through the origin, and it has a slope of 90/510.

This can be written as y = (90/510)x, where x is the independent variable and y is the dependent variable.

The equation of the line is y = (90/510)x or y = 0.176x, where 0.176 is the slope of the line.

This means that for every unit increase in x, the value of y increases by 0.176.

To graph this line, we need to plot a few points that lie on the line.

We can choose any two points, but it's best to choose points that are easy to work with.

Let's choose x = 0 and x = 10. When x = 0, y = (90/510)(0) = 0. When x = 10, y = (90/510)(10) = 1.57.

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The coefficient of determination, r, is the amount of variation in the observed values of the response variable that is explained by the regression line.

About Coefficient of Determination:

When forecasting the result of an event, the coefficient of determination is a statistical measurement that looks at how variations in one variable may be explained by differences in a second variable.

In other words, the coefficient of determination, r, which is more frequently used to refer to the strength of a linear relationship between two variables, is a crucial tool for researchers when undertaking trend analysis.

For illustration, this coefficient of determination might be used to consider the possibility that a woman would give birth to her child on a specific date in the future if she became pregnant on a specific day. This metric's objective in this situation is to determine the relationship between the connected occurrences of conception and birth.

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Answer:

A

Step-by-step explanation:

A is between -3 and -4

Answer:

y = 1/4 +3

Step-by-step explanation:

Answer:

try y>-1/5

Step-by-step explanation:

Normal or natural variations in the quality of production output that are due purely to chance are common causes.

According to the statement

we have to tell about the that cause which effect the quality and production output in the normal and natural variation.

So, For this purpose, we know that the

Common cause variation is present when the control chart of a process measure shows a random pattern of variation with all points within the control limits. When a control chart shows common cause variation, a process measure is said to be in statistical control or stable.

And due to this cause there is a lot of effect on the natural variations in the quality of production output.

So, Normal or natural variations in the quality of production output that are due purely to chance are common causes.

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The margin error is 6.

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor.

A higher error indicates a high chance that the result of the sample reported may not be the true reflection of the whole population. A higher margin indicates that the survey results may stray from the actual views of the total population. On the other hand, a smaller margin indicates that the results are close to the true reflection of the total population, which builds more confidence in the survey.

The margin of error is equal to half the width of the entire confidence interval.

The margin error is:

\(\frac{66-54}{2}= \frac{12}{2} = 6%\)

Thus, the margin error is 6.

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Answer:

0.0069444444

Step-by-step explanation:

Answer:

A) 60 girls B)80 boys

Step-by-step explanation:

Pretend that the ratio is a fraction. If there are 4 boys for every 4 girls, than pretend that you add the 4 and the 3 together, thus giving you 7 as your denominator. Start with the girls, giving you a fraction of 3/7, multiply by 140, you get 60 as the number of girls. 140-60=80, giving you 80 boys.

A statement which best describes the function that represents the situation include the following: A) It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.

In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.

This ultimately implies that, a linear function has the same (constant) slope or ratio of change and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

In this context, we have the following linear function;

F = 0.75x

where:

F represents the final cost in dollars.

x represents the price on the tag in dollars.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

v = 10

Step-by-step explanation:

2 = v - 8

add 8 to both sides

10 = v

Answer:

I am not good at this but a good app for math is Math

way

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