greatest common factor of 14xy2 and 28x2y

In the given triangle, α is equal to 67.36°.

What is a triangle's definition?

A triangle is a two-dimensional closed geometric form that has three sides, three angles, and three vertices (corners). It is the most basic polygon, produced by joining any three non-collinear points in a plane. The sum all angles of a triangle is always 180°. Triangles are classed according to their side length (equilateral, isosceles, or scalene) and angle measurement (acute, right, or obtuse).

Now,

Using Trigonometric functions

We can use the sine function

So,

Sin α=Perpendicular/Hypotenuse

Sin α = 12/13

α=67.36°

Hence,

           The value of α will be 67.36°.

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The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

The initial node represents the decision whether to invest in the development of the microbiological product.

The two possible outcomes are a successful development or failure after 2 years.

(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.

Starting from the end nodes and working backwards, we have:

For large-scale production with high sales:

Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m

For large-scale production with low sales:

Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m

For small-scale production with high sales:

Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m

For small-scale production with low sales:

Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m

At the 2-year node, the expected value for a successful development is:

For large-scale production:

Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m

For small-scale production:

Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m

Finally, at the initial node, the expected value for investing in the development is:

Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m

Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.

(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:

Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp

Setting this equal to zero and solving for p, we get:

p = 1

Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.

(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.

The utilities are increasing and concave, indicating diminishing marginal utility of money.

This means that the new owner is risk-averse.

The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.

To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.

If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.

If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.

If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.

If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.

If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.

Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

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16.) Mean average deviation= option C

17.) Range of a data set = option E.

18.) First quartile = opinion AB

19.) Second quartile = option B

20.) Third quartile = option A

21.) Interquartile range = option D

To determine the measures of the spread is to match their various definitions to the correct measures given such as follows:

16.) Mean average deviation: The average deviation of data from the mean.

17.) Range of a data set : The difference between the highest value and the lowest value in a numerical data set.

18.) First quartile: The median in the lower half.

19.) Second quartile: The median value in a data set.

20.) Third quartile: The median in the upper half.

21.) Interquartile range: The distance between the first and the third quartile.

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The quotient function of f(x) and g(x) is given as follows:

(f/g)(x) = 3x^(3/4).

The functions in the context of this problem are defined as follows:

When we want to divide two functions, we just divide each other, hence:

(f/g)(x) = f(x)/g(x) = 3x/x^(1/4).

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

x/x^(1/4) = x^(1 - 1/4) = x^(3/4).

Hence the function is:

(f/g)(x) = 3x^(3/4).

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The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.

In the event that a monopolistic firm takes over superbly competitive advertising, we would anticipate seeing the advertising cost of the great rise and the amount sold drop.

Be that as it may, when a monopolistic firm takes over the showcase, it picks up showcase control and the capacity to impact the cost. The monopolist can charge a better cost than the competitive advertising cost since there are no near substitutes for its item. As the monopolist raises the cost, the amount requested will drop, as customers switch to substitutes or decrease their utilization of the item.

we would anticipate seeing the advertising cost of the great rise and the amount sold fall as the monopolist tries to extend benefits by raising costs. This is often in differentiating from impeccably competitive advertising.

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x=47°

The degree of a triangle is equal to 180°.

Since a triange=180°, you would subtract 180 by 102+31 because the other two angles are 102° and 31°.

180-102-31=47°

Therefore the answer would be x=47°

Answer:  the solution for y in terms of x is y = (-1/4)x - 8.

Step-by-step explanation: In order to obtain a solution for y in the given equation of 4y = -x - 32, it is imperative to achieve the isolation of y on a singular side of the equation. To accomplish this task, it is possible to perform division on both sides of the equation by a factor of 4:

The given equation 4y/4 = (-x - 32)/4 can be expressed in an academic manner as follows: The given equation reveals that the quotient of 4y divided by 4 is equivalent to the quotient of the opposite of x added to negative 32, also divided by 4.

Upon performing simplification, the expression on the right-hand side yields:

The equation y = (-1/4)x - 8 can be expressed in an academic manner as follows: The dependent variable y is equivalent to the product of the constant (-1/4) and the independent variable x, with an additional decrement of eight.

Answer:

6.8 ounces

To set up a hypothesis test for this production process, we need to define the null and alternative hypotheses. The null hypothesis (H0) is that the average amount of soda in each can is equal to 6.8 ounces, while the alternative hypothesis (Ha) is that the average amount of soda in each can is not equal to 6.8 ounces.

We can then collect data by taking regular random samples from the production process and calculate the sample mean and standard deviation. We can then perform a statistical test such as a t-test or z-test to determine whether we can reject or fail to reject the null hypothesis.

If we reject the null hypothesis, we can conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces. If we fail to reject the null hypothesis, we cannot conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces.

I hope this helps! Let me know if you have any other questions.

The length of v, to the nearest 10th of a centimeter is 2.2.

To find the length of side v in triangle UVW, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.

Using this formula, we have,

v/sin(m∠V) = w/sin(m∠W)

We know that w = 1.4 cm and m∠W = 63°. To find sin(m∠W), we can use a calculator,

sin(63°) ≈ 0.89

Substituting the values we know into the formula, we get,

v/sin(m∠V) = 1.4/0.89

To solve for v, we need to find sin(m∠V). We know that the sum of the angles in a triangle is 180°, so we can find m∠V by subtracting the measures of the other two angles from 180°,

m∠V = 180° - m∠U - m∠W

m∠V = 180° - 29° - 63°

m∠V = 88°

Now, we can substitute the value of sin(m∠V) into the equation and solve for v,

v/ sin(88°) = 1.4/0.89

v ≈ 2.2 cm

Therefore, the length of side v in triangle UVW is approximately 2.2 cm to the nearest tenth of a centimeter.

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Answer:

1.6

Step-by-step explanation: This is answer on DeltaMath

Answer:

17.2 hours, or 17 hours and 12 minutes

Step-by-step explanation:

If she reads 50 pages per hour, then 860/50 = 17.2

The absolute deviation for the observation of 16 in the data-set is given as follows:

5.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the mean of the data-set in this problem is given as follows:

(19 + 16 + 4 + 9 + 7)/5 = 11.

The absolute deviation of 16 is given by the difference between 16 and the mean of 11, hence:

16 - 11 = 5.

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The probability of reaching into the bucket and randomly drawing three balls numbered 4, 9, and 7 without replacement, in that order, is 1/990, which is a decimal rounded to the nearest millionth is 0.001.

The probability of drawing three balls numbered 4, 9, and 7 without replacement, in that order, can be found by multiplying the probabilities of drawing each ball in the correct order.

The probability of drawing the first ball, numbered 4, is 1/11, since there is only one ball numbered 4 out of 11 balls in the bucket.

After the first ball is drawn, there are 10 balls remaining in the bucket, and the probability of drawing the second ball, numbered 9, is 1/10, since there is only one ball numbered 9 remaining out of the 10 balls in the bucket.

After the first two balls are drawn, there are 9 balls remaining in the bucket, and the probability of drawing the third ball, numbered 7, is 1/9, since there is only one ball numbered 7 remaining out of the 9 balls in the bucket.

Therefore, the probability of drawing the balls numbered 4, 9, and 7 without replacement, in that order, is:

(1/11) * (1/10) * (1/9) = 1/990

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Answer:

the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line

Chad drinks  389.28  fluid ounces of water in 6 days.

A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.

An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.

given that,

chad drinks 64.88 fluid ounces of water per day,

so in 6 days

he will drink = 6 x water drink per day

= 6 x 64.88

= 389.28

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The range of f include the following: D. -5 ≤ f(x) ≤ 5.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-6, 5} or -6 ≤ x ≤ 5.

Range = {-5, 5} or -5 ≤ f(x) ≤ 5.

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The power series method can be used to solve a nonhomogeneous differential equation about an ordinary point by finding both a homogeneous and particular solution using a series expansion and the method of undetermined coefficients.

The power series method is a technique used to find a series solution of a differential equation. When applied to a nonhomogeneous differential equation, the method involves finding both a homogeneous solution and a particular solution.

Assuming that the nonhomogeneous differential equation has the form

y''(x) + p(x)y'(x) + q(x)y(x) = f(x)

where p(x), q(x), and f(x) are functions of x, we can begin by finding the solution to the associated homogeneous equation

y''(x) + p(x)y'(x) + q(x)y(x) = 0

Using the power series method, we can assume a solution of the form:

y(x) = a0 + a1(x - x0) + a2(x - x0)^2 + ...

where a0, a1, a2, ... are constants to be determined, and x0 is the ordinary point of the differential equation.

Next, we can find the coefficients of the power series by substituting the series solution into the differential equation and equating coefficients of like powers of (x-x0). This leads to a system of equations for the coefficients, which can be solved iteratively.

After finding the homogeneous solution, we can find a particular solution using a similar method. Assuming a particular solution of the form:

y(x) = u(x) + v(x)

where u(x) is a solution to the associated homogeneous equation, and v(x) is a particular solution to the nonhomogeneous equation, we can use the method of undetermined coefficients to find v(x). This involves assuming a form for v(x) based on the form of f(x), and then solving for its coefficients using the same technique as before.

Once we have found both the homogeneous and particular solutions, we can combine them to obtain the general solution to the nonhomogeneous differential equation.

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The total surface area of the given figure is 619.2 in², which is not listed in the provided options.

The surface area is known to be measure of the total area occupied by the surface of the object. Defining the surface area mathematically in the presence of a curved surface is better than defining the arc length of a one-dimensional curve, or the surface area of ​​a polyhedron (i.e. an object with flat polygonal faces). Much more complicated. For a smooth surface sphere such as the following, surface area is assigned using representation as a parametric surface. This surface definition is based on calculus and includes partial derivatives and double integrals.

The triangular face of the given figure represent an equilateral triangle of sides 12 in.

Area of the triangle = (√3/4) × a²

Area of the triangular face:

= (√3/4) × 12²

= (√3/4) × 144

= 57.6 in²

Area of the rectangle = Length × width

Area of the rectangular face:

= 12 × 14

= 168 in²

Area of the given figure:

= (2 × 57.6) + (3 × 168)

= 115.2 + 504

= 619.2 in²

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The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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The actual height of the statue is option C 231.2 feet.

A scale factor is a number used in mathematics to scale or multiply a quantity or measurement by another factor in order to establish a proportional relationship between two identical figures or objects.

In other terms, the scale factor is the ratio of the corresponding lengths, widths, or heights of the two figures or objects if they are similar, that is, they have the same shape but may range in size. This implies that you may determine the dimension of the second object by multiplying one dimension of one object by the scale factor.

Given that the scale factor is 230:1.

Thus,

actual height of statue / 230 = height of drawing / 1.2 feet

Now,

actual height of statue = (1.2 feet / 1.2 feet) * 230

actual height of statue = 230 feet

Hence, the actual height of the statue is option C 231.2 feet.

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The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:

P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)

where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.

Substituting the given probabilities into the formula, we get:

P(puncture or smashed corner) = 0.03 + 0.06 - 0.014

P(puncture or smashed corner) = 0.076

Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

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As per the unitary method, the list shows the number of each type of animal on this farm is

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

Let us start by assigning variables to each type of animal on the farm. Let's say the number of pigs is "x".

From the problem statement, we know that there are twice as many horses as pigs. Therefore, the number of horses would be 2x.

Further, we know that there are four times as many cows as horses. So, the number of cows would be 4 times the number of horses. Mathematically, we can represent it as:

Number of cows = 4 * Number of horses

Or, Number of cows = 4 * (2x) = 8x

Therefore, we have the number of each type of animal on the farm as follows:

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

This is the same ratio as we found using the unitary method.

Therefore, our solution is correct.

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The exponential function for the new participants is f(x) = 3 * 4^x

Let's start with the initial number of participants who sent selfies on Day 0.

We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.

On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.

We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.

Therefore, we can write an exponential function of the form:

f(x)=a * 4^x

Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.

We know that a = 12 from our earlier calculations.

So, we have

f(x) = 3 * 4^x

Hence, the function is f(x) = 3 * 4^x

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So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.

In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.

Here,

We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.

In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:

(x, y) → (x', y')

To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:

x' = x - 4

y' = y - 4

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The given statement about developing quantitative and measurable usability tests is true.

Use cases can help with developing quantitative and measurable usability tests. Use cases are scenarios that describe how a user might interact with a system or product in a specific situation.

By developing use cases, researchers can identify specific tasks that users may need to perform and design usability tests to measure how well users can perform those tasks.

This can help make the usability tests more objective and measurable, as researchers can use metrics such as completion rates, task time, and errors to assess the usability of the system or product.

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Answer:

B. 12x^2 + 31x + 20

Step-by-step explanation:

Use FOIL (First, Outer, Inner, Last)

(3x + 4)(4x + 5)

12x^2 + 15x +16x + 20

12x^2 + 31x + 20

Answer:

B

Step-by-step explanation:

You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x

Answer:

225 trains

Step-by-step explanation:

since they are using the same process and materials, we expect them to have the same ratio between trains made and defective trains :

600 / 30 = 20/1

one out of 20 is defect.

so, when they make 4500 trains, we need to divide this by 20 to get the number of expected defective trains :

4500 / 20 = 225

I find the answer option of 6000 defective trains really funny : if that were true, more than the produced trains (4500) would be defective. how ... ?

Answer:

[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6} & \text{Music} & \text{Gov} & \text{Theater} & \text{Sports} & \text{Total}\\\cline{1-6}\text{7th grade} & 42 & 12 & 20 & 58 & 132\\\cline{1-6}\text{8th grade} & 38 & 9 & 45 & 30 & 122\\\cline{1-6}\text{Total} & 80 & 21 & 65 & 88 & 254\\\cline{1-6}\end{array}[/tex]

"Gov" refers to "Student  Government".

==================================================

Explanation:

The rows are labeled "7th grade", "8th grade" and "Total".

The columns are labeled "Music", "Student  Government", "Theater", "Sports", and "Total".

I'll abbreviate "Student  Government" to "Gov" so that the table doesn't get too wide.

There are 254 students total. This value goes in the bottom right corner of the table. This is the grand total.

----------

We have 80 students in music. This value goes at the bottom of the "music" column since we're in a "total" row. Basically it's the total of all the music students regardless of grade.

Of those 80 students in music, 42 are in seventh grade. Write 42 in the first row of this column and 38 just underneath it (because 80-42 = 38). The two values 42 and 38 should add to the 80 mentioned.

----------

There are 21 students in student government. This value goes at the bottom of the "student government" column.

9 of these students are in eighth grade, so the remaining 21-9 = 12 must be in seventh grade.

----------

There are 65 students in theater. This value goes at the bottom of the "theater" column.

There are 20 such students in 7th grade and 45 in 8th grade (because 65-20 = 45).

----------

There are 88 students in sports.

30 are in 8th grade, so 88-30 = 58 must be in 7th.

----------

At this point, you should have these values along the bottom row:

80, 21, 65, 88, 254

The first four values (80, 21, 65, 88) should add to the grand total 254.

Along each row, add up the values to get the row total.

7th grade: 42 + 12 + 20 + 58 = 132

8th grade:  38 + 9 + 45 + 30 = 122

There are 132 seventh graders and 122 eighth graders.

Those subtotals add to 132+122 = 254 total students, which helps confirm we did things correctly.