Which choice is equivalent to the fraction below when x is an appropriate value? Hint: Rationalize the denominator and simplify.

The  mass converted value in the standard form using kilograms to pounds is given by ( 94.7988 ) pounds.

Standard formula which relates these two given quantities of mass are written as :

One kilogram is equivalent 2.205 pounds.

Now, substitutes the standard relation between the kilograms and the pounds to calculate the required value,

1 kilogram = 2.205 pounds

⇒ 43 kilograms = ( 43 ) × ( 2.205 ) pounds

⇒ 43 kilograms = ( 94.7988 ) pounds

Therefore, the converted value of 43 kilograms into the pounds is written as  ( 94.7988 ) pounds.

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Answer:

Yes, the set of rational expressions is closed under multiplication.

Step-by-step explanation:

A rational expression is a fraction of polynomials, where the numerator and denominator are both polynomials with coefficients in some field, such as rational numbers. When we multiply two rational expressions, we reproduce two fractions of polynomials.

To multiply two fractions, we multiply their numerators and denominators separately and then simplify the result if possible. When we multiply the numerators and denominators of two rational expressions, we get new polynomials, which are still polynomials with coefficients in the same field. Therefore, the multiplication result is still reasonable, and the set of rational expressions is closed under multiplication.

For example, consider the following two rational expressions:

(a + 1) / (b + 2) and (c - 3) / (d - 4)

Their product is:

[(a + 1) / (b + 2)] * [(c - 3) / (d - 4)]

= (a + 1)(c - 3) / (b + 2)(d - 4)

The result is still rational since the numerator and denominator are both polynomials with coefficients in the same field. Therefore, the set of logical expressions is closed under multiplication.

The function 1/5f(x) compares to the parent function f(x) given as follows:

Vertical shrink/compression by a factor of 1/4.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

For a vertical compression or stretch, the definitions are given as follows:

As k = 0.2 < 1, the transformation is a vertical shrink by a factor of 1/5.

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Answer:

-4a² + 7a + 4

Step-by-step explanation:

Subtract -4 + 3a² from 7a - a².

(7a - a²) - (-4 + 3a²) =

= 7a - a² + 4 - 3a²

= -4a² + 7a + 4

Therefore, based on their z-scores, Ryan is more likely to be accepted at his university of choice than Kyle, assuming that the admissions decision is based solely on their exam scores.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. The closer the probability is to 1, the more likely the event is to occur, while the closer it is to 0, the less likely it is to occur.

Here,

To determine which of the two students is more likely to be accepted at their university of choice, we need to compare their exam scores relative to the other students who took the same exam. We can use the concept of standard scores, also known as z-scores, to make this comparison.

The z-score of an observation x is the number of standard deviations that x is away from the mean of the population. It is calculated as:

z = (x - μ) / σ

where x is the observation, μ is the mean of the population, and σ is the standard deviation of the population.

For Kyle's exam, his z-score is:

z = (403 - 355) / 59 = 0.814

For Ryan's exam, his z-score is:

z = (45 - 27) / 4 = 4.5

A z-score of 0 means the observation is at the mean of the population, while a positive z-score means the observation is above the mean, and a negative z-score means the observation is below the mean.

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Answer: 40.6

Step-by-step explanation:

first you write the formula (a= a+b divided by 2 times h)

11+3 divided by 2 times 5.8

14 divided by 2 = 7 times 5.8

The correct answer is 40.6

Answer:

15

Step-by-step explanation:

q/4=60
Just divide 60 by 4. :)

When each vertex of the square is located on the circumference of the circle, each side of the square measures 5.971 cm.

As per Geometry and trigonometry, a square has equilateral triangle sides and four equal angles, making itself an equilateral quadrilateral. Other name for it is a triangle with two adjacent vertices that are the same length. An equilateral quadrant is one that has four equal ends and four equal angles, like a square. Angles that are 90 degrees or straight are square angles. The downtown's diagonals are also split at a right angles and are evenly spaced. a rectangle with approximately consecutive sides that is adjacent. a trapezoid with four equal sides and straight angles on all four sides. a parallelogram with two adjacent sides that seem to be equal and make a right angle. rhombus has straight sides.

given

If the square perfectly fits the circle, then the circle's diameter is the same as the square's diagonal. The square's diagonal also has a length of cm because each side of the square is cm long. The square's diagonal can be determined using the area of the circle, as shown below:

area = [tex]\pi[/tex]*r *r

r*r = 56/pi

r = 4.22

As the square's diagonal and the circle's diameter are equal, x = 5.971 cm.

When each vertex of the square is located on the circumference of the circle, each side of the square measures 5.971 cm.

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The value of 152 centimeter converted to feet is simply done by dividing the length value by 30.48 so we get 152 cm equal to 4.98 feet.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Use the following two formulae to translate from cm to feet and inches:

1 cm equals 0.3937 inches.

and

12 inches make one foot.

It goes like this:

70.86614 inches are equal to 180 cm (180 x 0.3937 inches).

60.86614 div. 12 = 5 and 60.86614 mod. 12 = 10.86614

hence, 180 centimetres equal 5 ft. 10.86614 inches.

To have this tool calculate something for you, input 180 cm above.

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The null hypothesis in a two-tailed test states that there is no significant difference or relationship between two variables being compared.

In hypothesis, the invalid speculation is an assertion about the populace that expects there is no massive distinction or connection between two factors. In a two-followed test, the invalid speculation expresses that there is no distinction or connection between the two gatherings being looked at. The two-followed test is utilized when we are keen on testing whether the mean of an example is essentially not the same as the mean of a populace, without determining a course. For instance, a two-followed test might be utilized to test whether another drug affects pulse, without determining whether it will increment or lessening circulatory strain. The elective speculation in a two-followed test is that there is a huge contrast or connection between the two gatherings.

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An online calculator for Rand McNally mileage is a tool that allows you to calculate the distance and travel time between two locations based on the Rand McNally Road Atlas.

An online calculator for Rand McNally mileage typically requires you to input the starting location and the destination and then provides an estimated distance and travel time based on data from the Rand McNally Road Atlas. Some calculators also allow you to adjust for factors such as traffic, tolls, and fuel consumption.

This type of calculator can be useful for planning road trips, estimating travel costs, and optimizing travel routes. It is often used by trucking companies, delivery services, and other businesses that rely on accurate mileage and travel time information.

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The binomial probability distribution is a ​Discrete probability distribution that describes probabilities for experiments in which there are two​ mutually exclusive outcome.

Discrete Probability Distribution:

A discrete probability distribution can be defined as a probability distribution that gives the probability that a discrete random variable has a given value. These distributions represent data with a finite number of possible outcomes. There are two conditions that a discrete probability distribution must satisfy.

1) 0 ≤ P(X = x) ≤ 1. This means that the probability of a discrete random variable X taking the exact value x is between 0 and 1.

2) ∑P(X = x)=1. The sum of all probabilities must be 1.

Mutually exclusive outcome:

Mutual Exclusive Outcome is a statistical term that describes two or more events that cannot occur simultaneously. It is commonly used to describe a situation where one result is replaced by another. For example, war and peace cannot coexist at the same time. This makes them mutually exclusive.

The concept of mutual exclusivity is often used in capital budgeting. A company may have to choose from several projects that, when completed, will add value to the company. Some of these projects are mutually exclusive.

For example, suppose a company has a budget of $50,000 for an expansion project. Projects A and B are mutually exclusive if available projects A and B each cost $40,000 and project C costs $10,000.

If a company is pursuing A, it cannot afford to bully B, and vice versa. Project C can be considered independent. Even if other projects go ahead, the company can still afford to do C. If neither A nor B accepts, the viability of C is not affected, and accepting C does not affect the viability of other projects.

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The expression for the measure of the given angle in the image of the circle with center O is [tex]\frac{arc UZW}{2}[/tex].

Remember that the angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference. According to this, we can deduce the following expression for the measure of the given angle:

[tex]m\angle UXY = \frac{arc UZW}{2}[/tex]

An angle is a figure in Plane Geometry generated by two rays or lines that share a common endpoint. The term "angle" is derived from the Latin word "angulus," which meaning "corner". The two rays are referred to as the sides of an angle, while the common terminus is referred to as the vertex. The angle in the plane does not need to be in Euclidean space.

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The measure of angle B is given as follows:

m < B = 172º.

Vertical angles are angles that are opposite by the same vertex in crossing segments, and these angles are congruent, meaning that they have the same measure.

For this problem, angles A and B are congruent, hence the value of x is obtained as follows:

8x - 20 = 7x + 4

x = 24.

Hence the measure of angle B is obtained as follows:

m < B = 8(24) - 20

m < B = 172º.

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Since triangle CDE is dilated by a scale factor of 2 to form triangle CDE, the measure of side EC is equal to 43 units.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

2 = 86/side EC

Side EC = 43 units.

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Complete Question:

Triangle CDE is dilated by a scale factor of 2 to form triangle CDE . Side E'C' measures 86. What is the measure of side EC?

If y*=y1/2(y2+1) then -3(16* - 9*) = -10.5y1(y2 + 1), called polynomial.

A polynomial is an expression that consists of variables, numbers, and operations (like addition, subtraction, multiplication, and division). It is similar to a mathematical equation, but instead of an equals sign, it uses coefficients and variables in a power form. The power of a polynomial is determined by the highest power of the variables in the expression.

For example, if the polynomial is x2 + 5x + 2, then the power is 2. Polynomials are used in many areas of mathematics, such as calculus, algebra, and number theory.

If y*= y1/2(y2+1) then -3(16* - 9*)

= -3(16(y1/2(y2 + 1)) - 9(y1/2(y2 + 1)))

= -3(8y1(y2 + 1) - 4.5y1(y2 + 1))

= -3(3.5y1(y2 + 1))

= -10.5y1(y2 + 1)

In this problem, 16* is equal to 16(y1/2(y2 + 1)) and 9* is equal to 9(y1/2(y2 + 1)). When -3 is multiplied to 16* - 9*, the result is -3 times the difference of 16* and 9*. The expression then simplifies to -10.5y1(y2 + 1).

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Answer:

6) am - 2a - m + 2

7) bcx - bcy + x - y

Step-by-step explanation:

6) a(m - 2) - m + 2

am - 2a - m + 2

7) bc(x - y) + x - y

bcx - bcy + x - y

Answer:

120-90

=30

the change in stock price is $30 per share

The two smaller positive integers are:

m = 675

n = 45

And the sum is 675

We know that we have two positive integers, m and n.

And we know that:

3*m³ = 5*n⁵

One way of finding the numbers is evaluating one of the two in positive integers, until we get that the other one is also an integer.

For example,we can solve this for m to get:

m³ = (5/3)*n⁵

m = ∛((5/3)*n⁵)

Now just evaluate in different integer values of n.

if n = 3 we will get:

m = ∛((5/3)*3⁵) =  ∛(405) = 7.39

So this is not a solution.

Now I will use n = 45 = 5*3*3 (so all the exponents inside the cubic root are multiples of 3)

m = ∛((5/3)*(5*3²)⁵)

m = ∛(5⁶*3⁹) = 5²*3³ = 25*27 = 675

Then the sum is:

45 + 675 = 720

These is the smaller sum.

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1) The rate of growth for the honey bee population is approximately 10.1%, rounded to the nearest tenth.

2) The common ratio is approximately 1.101, rounded to the nearest thousandth.

We can use the formula for an explicit exponential model:

N = N0 × (1 + r)^t

where N0 is the initial population, r is the rate of growth (expressed as a decimal), t is the time elapsed (in years), and N is the final population.

We can use the given information to write two equations:

N0 = 3600

N = 25000

t = 12

Substituting these values into the formula, we get:

25000 = 3600 × (1 + r)^12

Solving for (1 + r), we get:

(1 + r)^12 = 25000/3600

(1 + r) = (25000/3600)^(1/12)

(1 + r) ≈ 1.101

r ≈ (1.101 - 1) × 100% ≈ 10.1%

Therefore, the rate of growth for the honey bee population is approximately 10.1%, rounded to the nearest tenth.

2) The common ratio is 1 + r, so

1 + r ≈ 1.101

Rounding to the nearest thousandth, we get:

1 + r ≈ 1.101

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The heart-shaped curve traced around a point on the circumference of a circle rolling completely around an equal fixed circle is called a "Cardioid."

A cardioid is a mathematical curve that is formed by tracing a point on a circle that rolls around another fixed circle. The term "cardioid" is derived from the Greek word "kardia," which means heart, as the curve resembles the shape of a heart. The cardioid curve has several interesting properties, including symmetry about a line called the "polar axis." The curve also has a "cusp" at the bottom point of the heart shape, where the curve changes direction abruptly. The length of the curve is four times the diameter of the rolling circle. Cardioids have applications in a variety of fields, including mathematics, physics, and engineering. They are used in the design of certain types of antennas, in the analysis of fluid flow, and in the study of planetary motion. They also have applications in the creation of heart-shaped designs in art and decoration. In summary, a cardioid is a heart-shaped curve that is formed by tracing a point on the circumference of a circle that rolls completely around an equal fixed circle. It has unique properties and applications in a variety of fields.

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The answer to 1/5 + 2/5 is 3/5

The volume of the rectangular prism is 480 cubic inches.

Volume is a three-dimensional space measurement. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Let's label the dimensions of the rectangular prism as length (l), width (w), and height (h).

From the given information, we know that the cross section formed by the horizontal plane and the prism is a rectangle with dimensions 8 in. and 12 in. This means that the length and width of the rectangular prism are at least 12 in. and 8 in., respectively.

Similarly, the cross section formed by the vertical plane and the prism is a rectangle with dimensions 5 in. and 8 in. This means that the height and width of the rectangular prism are at least 5 in. and 8 in., respectively.

Therefore, the faces of the rectangular prism are:

A face with dimensions l x w = 12 in. x 8 in.

A face with dimensions l x h = 12 in. x 5 in.

A face with dimensions w x h = 8 in. x 5 in.

To find the volume of the rectangular prism, we can use the formula:

Volume = length x width x height

Since we don't know the exact dimensions of the rectangular prism, we can use the minimum dimensions we found earlier. Therefore, the volume of the rectangular prism is:

Volume = 12 in. x 8 in. x 5 in. = 480 cubic inches

So the volume of the rectangular prism is 480 cubic inches.

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Transformations on a graph refer to changes made to the graph that affect its appearance or position without changing its underlying structure or properties.

Some common transformations on a graph include:

Translation: This involves shifting the entire graph horizontally or vertically without changing its size or shape. For example, if a point on the graph is originally located at (2,3), a translation by (4,-1) would move it to (6,2).

Scaling: This involves enlarging or shrinking the entire graph uniformly in all directions. For example, a scaling factor of 2 would double the distance between all points on the graph, while a scaling factor of 0.5 would halve it.

Reflection: This involves flipping the graph across an axis, such as the x-axis or y-axis. Reflections can also be performed across other lines, such as y = x or y = -x.

An overview on transformation was given as the information is incomplete.

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The length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle, we shall calculate for the length x and y by application of the trigonometric ratio of sine and cosine for the angle 45°.

sin 45° = y/9√2 {opposite/hypotenuse}

by cross multiplication

y = 9√2 × sin 45°

recall that sin 45° = √2/2

y = 9√2 × √2/2

y = 9m

cos 45° = x/9√2 {adjacent/hypotenuse}

by cross multiplication

x = 9√2 × cos 45°

recall that cos 45° = √2/2

x = 9√2 × √2/2

x = 9m

Therefore, the length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°.

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The probability that fewer than 3 of the elk survive to adulthood is

P(n < 3) = 0.8.

The probability of an event is a number that indicates how likely the event is to occur.

Given is that Biologists estimate that a randomly selected baby elk has a 44% probability of surviving to adulthood.

It is given that -

P{surviving to adulthood} = 44/100 = 0.4

For -

P(n < 3) = 0.4 + (0.4 + 0.4)/2

P(n < 3) = 0.4 + 0.4

P(n < 3) = 0.8

Therefore, the probability that fewer than 3 of the elk survive to adulthood is P(n < 3) = 0.8.

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Cost can refer to the amount of money or resources used in the production of a good or service, or the amount of money or resources used in the completion of a project. Generally, cost is the total amount of money or resources required to do something. Cost can be calculated by adding up the costs of each resource used or by multiplying the quantity of each resource used by the cost of that resource. Cost can also be determined by using a cost estimating technique, such as a cost-benefit analysis.

Nicole's equation: 7T + 7C = 63

Alberto's equation: 14T + C = 61

Cost of tulip bulb packages = (63 - 7C) / 7

To calculate the cost of tulip bulb packages, take the total amount of Nicole's sales ($63) and subtract the cost of the crocus bulb packages (7C). Then we divide the result by the number of tulip bulb packages (7).

Cost of crocus bulb packages = (61 - 14T) / 1

To calculate the cost of crocus bulb packages, take the total amount of Alberto's sales ($61) and subtract the cost of the tulip bulb packages (14T). Then we divide the result by the number of crocus bulb packages (1).

Cost of tulip bulb packages = $8.71

Cost of crocus bulb packages = $4.43

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The statements and reasons to complete the two column proof are given in the explanation.

Two triangles will only be similar if on comparing the corresponding length of their sides, there exist some common properties or relations. Though the triangles are similar, but not congruent.

The expected statements and reasons to complete the two column proof are:

      STATEMENT                      REASON

1. LQ II NP                               Given

2. <Q ≅ <N                             Alternate interior Angles

3. <L ≅ <P                              Alternate Interior Angles

4. ΔLMQ ~ ΔPMN                  Two pairs of corresponding angles are equal

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