Which of the following expressions represents “5 less than 3 times the number m”?

• 3m- 5
• 5m- 3
• 5-3m
• 3-5m

The correct option is option( A).

Using the property of Obtuse Triangle, the triangle with sides { 8, 10, 14 } is an Obtuse Triangle.

Obtuse Triangle:

An obtuse triangle is a triangle with one interior angle greater than 90 degrees. In geometry, a triangle is represented as a closed 2D figure with three sides of equal or unequal length and three angles of equal or unequal measurements.

Obtuse triangle property:

we have given the sides of triangle so, we use the fourth property for check the triangle formed by given sides are obtuse triangle or not .

8² + 10² = 164; 14² = 196 -> obtuse

9² + 12² = 225; 15² = 225 -> not obtuse

10² + 14²= 296 ; 17²= 289 --> not obtuse

12² + 15² = 369; 19²= 361 --> not obtuse

Hence, the required triangle is triangle with sides 8, 10, 14.

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Complete Question:

which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle

A. 8, 10, 14

B. 9, 12, 15

C. 10, 14, 17

D. 12, 15, 19

Answer: the answer is A 8, 10, 14.

Step-by-step explanation: it show below.

Answer:

Please open the attachment below to find the work and solution to the problem.

The ratio of AB to AC and the ratio of AD to DC is 1 : 2 each respectively. They are equivalent ratios.

A ratio means a comparison of two different quantities while proportion is an equality of two ratios.

Ratio of AB to AC = 5 in : 10 in

= 5 / 10

= 1 / 2

= 1 : 2

Ratio of AD to DC = 4 in : 8 in

= 4 / 8

= 1 / 2

= 1 : 2

Therefore, the ratio of AB to AC and the ratio of AD to DC is 1 : 2 each respectively. They are equivalent ratios.

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The differential form of the integral sin x cos x dx is sin²x/2 + C.

Differential form:

Differential form provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds.

Given,

Here we need to find the differential form in the integral is  sin x cos x dx.

Here we have the integral form,

=> ∫ sin x cos x dx

Now, we have to substitute

=> u = sin(x) ⟶ du/dx

=> cos(x) ⟶ dx = 1 / cos(x)du

So, it can be written as,

=> ∫ u du

By apply power rule, then we get.

=> u²/2 +C

Apply the value of u as sin x, then we get,

=> sin²x/2 + C

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We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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The equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\\)

As we can see in the graph the line goes from (-6, 0) and (0, 3)

Finding the slope:

\(\rm m =\dfrac{3-0}{0-(-6)}\\\)

m = 3/6 = 1/2

y = mx + c

y = (1/2)x + c

c is the y-intercept

c = 3

The equation:

y = (1/2)x + 3

Thus, the equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

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The probability a selected person is both tall and fat is 0.341

From the question, the given parameters are

People = 100

Fat = 55

Tall = 62

So, the individual probabilities are

P(Fat) = 55/100

P(Tall) = 62/100

Evaluate

P(Fat) = 0.55

P(Tall) = 0.62

The probability a person is both tall and fat is

P(Fat and Tall) = P(Fat) * P(Tall)

So, we have

P(Fat and Tall) = 0.55 *  0.62

Evaluate

P(Fat and Tall) = 0.341

Hence, the probability is 0.341

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Answer:

Which equation could Payton solve to determine the number of packages of black  T-shirts, b, he bought?

3b + 4(5) = 38

A political scientist surveyed 28 of the current 101 representatives in a state's congress.

The size of the sample is 28.

Sample size :

A sample is a small part of a population chosen for statistical research.

The sample size refers to the number of individuals in a sample, as the name suggests.

It has a significant impact on the data's accuracy and precision.

A larger sample size will reduce the sampling error, allowing the findings to be more accurate.

A political scientist has surveyed 28 of the current 101 representatives in a state's congress.

So, the size of the sample is 28.

The size of the sample is the number of participants in a study who are selected from the population.

To assess results, researchers use data from a sample of a population.

Sample size determines the accuracy of survey findings.

Larger samples lead to more reliable results because they represent the population more effectively.

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True

In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.

When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.

The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.

If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.

If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.

In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.

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The conjecture "A square number is either measurable by 4 or will be after the removal of a unit" is true. If a number is a perfect square, it can be expressed as either 4k or 4k+1 for some integer k.

However, if 4 is replaced by 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3.

To prove the conjecture that a square number is either divisible by 4 or will be after subtracting 1, we can consider two cases:

Case 1: Let's assume the square number is of the form 4k. In this case, the number is divisible by 4.

Case 2: Let's assume the square number is of the form 4k+1. In this case, if we subtract 1, we get 4k, which is divisible by 4.

Therefore, in both cases, the conjecture holds true.

However, if we replace 4 with 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3. For example, consider the square of 5, which is 25. This number is not divisible by 3. Similarly, the square of 2 is 4, which is also not divisible by 3. Hence, the conjecture does not hold when 4 is replaced by 3.

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Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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As there is a positive correlation between the variables, the correlation will be larger than 0 and less than 1. The correct option is 0< correlation <1.

Given that,

Linear association is measured via correlation. A trend line drawn through the scatter will indicate a relationship between an explanatory variable X and a response Y that is positive and growing but has some curvature

To find : The correlation

From the provided information,

The two variables are positively related.

The correlation coefficient takes a value from -1 to 1.

Since, the correlation between the variables is positive, therefore, the correlation will be greater than 0.

Thus, the correct option is 0<correlation<1.

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Answer:

Concept: Mathematical Comprehensive

General notes:

To show that the product of the sample observations is a sufficient statistic for θ > 0 in the case of a random sample taken from a gamma distribution with parameters α = θ and β = 6, we can use the factorization theorem for sufficient statistics.

Let's denote the random sample as X₁, X₂, ..., Xₙ, where each Xi is an independent and identically distributed random variable following a gamma distribution with parameters α = θ and β = 6.

The probability density function (pdf) of a gamma distribution with parameters α and β is given by:

f(x; α, β) = (1 / (β^α * Γ(α))) * (x^(α - 1)) * exp(-x / β)

where Γ(α) is the gamma function.

The joint pdf of the random sample can be expressed as:

f(x₁, x₂, ..., xₙ; α, β) = (1 / (β^(nα) * Γ(α)^n)) * (x₁ * x₂ * ... * xₙ)^(α - 1) * exp(-(x₁ + x₂ + ... + xₙ) / β)

By the factorization theorem, the product of the sample observations, denoted as T = x₁ * x₂ * ... * xₙ, is a sufficient statistic for θ if we can express the joint pdf as the product of two functions, one depending on the sample observations T and the other on the parameter θ.

Let's rewrite the joint pdf in terms of T:

f(x₁, x₂, ..., xₙ; α, β) = (1 / (β^(nα) * Γ(α)^n)) * T^(α - 1) * exp(-(x₁ + x₂ + ... + xₙ) / β)

Now, we can separate the terms depending on T and θ:

f(x₁, x₂, ..., xₙ; α, β) = (1 / (β^(nα) * Γ(α)^n)) * T^(α - 1) * exp(-(x₁ + x₂ + ... + xₙ) / β) = g(T; α) * h(x₁, x₂, ..., xₙ; β)

Here, we can observe that g(T; α) = (1 / (β^(nα) * Γ(α)^n)) * T^(α - 1) depends only on T and α, and h(x₁, x₂, ..., xₙ; β) = exp(-(x₁ + x₂ + ... + xₙ) / β) depends only on the sample observations and β.

Therefore, we have successfully factorized the joint pdf into two functions, one depending on T and α, and the other depending on the sample observations and β. This confirms that the product of the sample observations T = x₁ * x₂ * ... * xₙ is a sufficient statistic for the parameter θ when the random sample is taken from a gamma distribution with parameters α = θ and β = 6.

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Answer:

πd X 27.5

π X 29.5 X 27.5= 2548.61704

2548.62cm

The earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

a. The earnings per share for Company XYZ can be calculated by dividing the closing price by the P/E ratio. In this case, the closing price is $100.76 and the P/E ratio is 1525. Therefore, the earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

b. Based on the historical P/E ratio range of 12-14, the stock price of Company XYZ seems overpriced. The P/E ratio indicates the price investors are willing to pay for each dollar of earnings generated by the company. A higher P/E ratio suggests that investors have higher expectations for future earnings growth. In this case, the P/E ratio of 1525 is significantly higher than the historical range of 12-14, indicating that the stock is being valued at a much higher premium relative to its earnings. This suggests that the stock price may be inflated and not in line with the company's historical valuation metrics, indicating an overpriced condition.

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Answer:

$220

Step-by-step explanation:

first let's make the $12 bracelets as Type1 and the $8 bracelets as Type2,

then we calculate the amount she made by selling each type.

Eq.1 : No. of Type1 bracelets Selena made = 9

         Amount she sold them for = $12

         Amount she made by selling them = 9*12

                                                                                   = $108

Eq.2 : No. of Type2 bracelets Selena made = 14

          Amount she sold them for = $8

          Amount she made by selling them = 14*8

                                                                               = $112

Now we calculate the Total Amount she made

we add both of the amounts

$108 + $112

= $220

Hope this helps :)

The efficiency of the power screw in raising the load is approximately 6976%.

The efficiency of a power screw can be calculated using the formula: Efficiency = (Ideal Mechanical Advantage / Actual Mechanical Advantage) x 100% To find the Ideal Mechanical Advantage (IMA) of the screw, we can use the formula:

IMA = (π / tan(α)) x (π / 2) x (D / P)

Where: π is the mathematical constant pi (approximately 3.14159) tan(α) is the coefficient of friction (given as 0.20) D is the major diameter of the screw (given as 19 mm) P is the pitch of the screw, which can be calculated as (25.4 mm / number of threads per inch) First, let's calculate the pitch: Number of threads per inch = 6

Pitch = 25.4 mm / 6 = 4.23 mm (approximately)

Now, we can substitute the values into the formula to find IMA:

IMA = (π / tan(α)) x (π / 2) x (19 mm / 4.23 mm)

Using the given coefficient of friction, we have:

IMA = (π / 0.20) x (π / 2) x (19 mm / 4.23 mm)

Simplifying the equation, we get:

IMA = 9.87 x 1.57 x 4.49

Calculating IMA, we find:

IMA ≈ 69.76

Now, we need to find the Actual Mechanical Advantage (AMA), which can be calculated using the formula:

AMA = Load / Effort

Where:

Load is the weight being lifted (given as 17.80 kN)

Effort is the force applied to turn the screw

Since the screw is being used to lift the load, the Effort is equal to the load.

AMA = 17.80 kin / 17.80 kin

AMA = 1

Now, we can calculate the efficiency using the formula:

Efficiency = (IMA / AMA) x 100%

Efficiency = (69.76 / 1) x 100%

Efficiency ≈ 6976%

The efficiency of the power screw in raising the load is approximately 6976%.

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Answer:

Yes, negative 2 is bigger than negative six.

Answer:

(-2 is greater than -6 )it is the lower the it is such as -2 the way you know which is greater is by whatever negative is closer to 0 or to the positive numbers.

Step-by-step explanation:

Hope this heped!

Answer:

\(20\)

Step-by-step explanation:

\(5x+10 - x = 90\\\)

\(4x + 10 = 90\)

\(4x = 80\)

\(x = 20\)

\(\therefore\) the value of \(x\) is \(20\).

Hope this helps :)

Answer:

Tan(A) = \(\frac{8}{15}\)

Hope it helps!

Answer:

y = 0.5x - 3

Step-by-step explanation:

y = mx + b    (m is the slope of the line, and b the cross point over y-axis)

(x1, y1) = (6,0)

(x2, y2) = (0,-3)

m = (y2-y1)/(x2-x1)

m = (-3-0)/(0-6)

m = -3/-6

m= 1/2 = 0.5

b = -3

Answer:

There were 3 diamonds.

Step-by-step explanation:

\(\frac{Diamonds(D)}{Stars(S)}=\frac{3}{11}\)

Therefore, \(11D=3S\)

\(S=3D+2\)

Therefore,

\(\frac{11D}{3}=3D+2\)

\(11D=9D+6\)

\(2D=6\)

\(D=3\)

The given matrix is an elementary matrix that represents an elementary row operation of multiplying the second row by 4k. The determinant of this matrix is determinant of the original matrix, which is 4k.

Therefore, the determinant of the given elementary matrix is 4k.

To verify this result, we can also compute the determinant using the formula for a 3x3 matrix. The matrix obtained by applying the elementary row operation to the identity matrix is:

\(\left[\begin{array}{ccc}1&0&0\\0&4k&0\\0&0&1\end{array}\right]\)

The determinant of this matrix is calculated as: det(A) = 1 * (4k) * 1 - 0 * 0 * 0 - 0 * (4k) * 0 = 4k. So, the determinant of the given elementary matrix is indeed 4k, which matches our previous result.

In summary, the determinant of the elementary matrix is 4k, and this can be verified by calculating the determinant using the formula for a 3x3 matrix.

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Step-by-step explanation:

the slope of a line is the ratio "y coordinate change / x coordinate change" when going from one point to another on the line.

now, what I do in such a case, I look for points on the graph that have integer coordinates, as they are the essayist to read and then to calculate with.

I see e.g. (6, 10) and (10, 2).

now, when going from the first to the second point

x changes by +4 (from 6 to 10).

y changes by -8 (from 10 to 2).

so, the slope is -8/+4 = -2

The correct inequality is:  C) 2x + 5 > -1.

Given that, the solution set of an inequality is graphed on the number line below.  { -4, -3, -2, -1, 0, 1}.

Looking at the solution set, observe that all the values are less than or equal to 1.

The solution sets for each inequality:

A) 2x + 5 < -1:

Subtracting 5 from both sides:

2x < -6

Dividing both sides by 2:

x < -3

The solution set is (-∞, -3).

B) 2x + 5 > -1:

Subtracting 5 from both sides:

2x > -6

Dividing both sides by 2:

x > -3

The solution set is (-3, +∞).

C) 2x + 5 > -1:

Subtracting 5 from both sides:

2x > -6

Dividing both sides by 2: x > -3

The solution set is (-3, +∞).

D) 2x + 5 > -1 + 2:

Simplifying the right side:

2x + 5 > 1

Subtracting 5 from both sides:

2x > -4

Dividing both sides by 2: x > -2

The solution set is (-2, +∞).

Therefore, the solution sets are:

A) Solution set: (-∞, -3),

B) Solution set: (-3, +∞)

C) Solution set: (-3, +∞)

D) Solution set: (-2, +∞).

Hence, the correct inequality is:  C) 2x + 5 > -1.

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Answer:

Quadrant IV (4)

Step-by-step explanation:

I did the test and the other person was wrong.

The quadrant in which angle theta lie if csc theta < 0 and cot theta < 0 exists Quadrant IV (4).

Trigonometric Identities are equality conditions that hold for all possible values of the variables in the equation and use trigonometry functions. There exists numerous unique trigonometric identities that relate a triangle's side length and angle.

Sine, cosine, and tangent are the fundamental three operations in trigonometry. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical notions exists built.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These exists identities that, geometrically speaking, involve certain functions of one or more angles.

The quadrant in which angle theta lie if csc theta < 0 and cot theta < 0 exists Quadrant IV (4).

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

If the two angles have the same cosine values , then their reference angles must be complementary angles .

If two angles have the same cosine value, then it means that they have the same ratio of the adjacent side to the hypotenuse in a right triangle.

The reference angles of the two angles must be complementary angles, meaning they add up to 90 degrees or π/2 radians.

The reference angle is defined as the acute angle between the terminal side of the angle and the x-axis.

Since the adjacent sides of the two angles are equal, their terminal sides will intersect the y-axis at the same point which means that their reference angles must be complementary angles, since they share the same y-coordinate on the unit circle.

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