I am struggling… find the domain and range of the polynomial function. Write your answer in interval notation!

Answer: a=7.6

Step-by-step explanation:

solve for angle C:

[tex]\frac{sinc}{5} =\frac{sin120}{11}[/tex]

[tex]11sinc=5sin120[/tex]

[tex]C=23.2[/tex]

solve for A:

=180-(120+23.2)

=36.8

solve for a:

Using the law of sines

[tex]\frac{sin120}{11} =\frac{sin36.8}{a}[/tex]

[tex]asin120=11sin36.8[/tex]

[tex]a=7.6[/tex]

In order to have a potential value of $12,000 at a simple rate of interest of 8.0% after 6 years, the current value you must invest is therefore approximately $8,108.11.

A formula called Simple Interest (S.I.) is used to determine how much interest will be charged on a certain principal sum of money at a specific interest rate. For instance, if a person borrows Rs. 5000 for two years at a rate of 10 p.a., they will be compelled to pay S.I. on the whole amount borrowed during those two years.

For simple interest, use the formula:

A = P(1 + rt)

where r is the interest rate, t is the amount of time in years, A represents the future value, P is indeed the present value, and so on.

This formula can be changed to account for P:

P = A / (1 + rt)

By entering the specified values, we obtain:

P = 12,000 / (1 + 0.08 x 6)

P = 12,000 / 1.48

P = $8,108.11

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The probability that at least 4 buyers would prefer green among the 16 selected is approximately 0.1031.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

This problem can be modeled as a binomial distribution with n = 16 trials and p = 0.3 probability of success (preferring green).

Let X be the number of buyers who prefer green among the 16 selected. We need to find P(X ≥ 4).

Using a binomial probability table or calculator, we can find:

P(X ≥ 4) = 1 - P(X < 4)

= 1 - P(X ≤ 3)

= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.1233 + 0.2854 + 0.3028 + 0.1854]

= 0.1031 (rounded to 4 decimal places)

Therefore, the probability that at least 4 buyers would prefer green among the 16 selected is approximately 0.1031.

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Chance is 1/10

Given that the die has 20 different numbers, ranging from 1-20, we are to determine the chance that the top side will be either a 9 or a 10.When throwing a die with a different number of faces or sides, each face has an equal chance of showing up as the top side. Thus, to determine the chance that the top side will be either a 9 or a 10, we need to find the probability of rolling a 9 or 10.To calculate the probability of a single event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. Thus, in this case, the probability of rolling a 9 or a 10 would be:Probability of rolling a 9 or a 10= number of favorable outcomes/ total number of possible outcomesNumber of favorable outcomes: 2 (since there are only 2 sides of the die that have a 9 or a 10)Total number of possible outcomes: 20 (since there are 20 different numbers on the die)Probability of rolling a 9 or a 10 = 2/20 = 1/10Therefore, the chance that the top side will be either a 9 or a 10 is 1/10.

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In response to the stated question, we may state that As a result, the prism value of x is around 6.432 cm.

A prism is a polyhedron with either an n-sided polygonal basis, a second base that is a shifted copy of the original base, and n extra faces (essentially all parallelograms), with two connecting the corresponding sides of the base. Any cross sections those are parallel to the base are translations of it. A prism is a three separate, solid, three-dimensional object with two faces. It has the same merge, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with out any bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by planes that are obliquely oriented to one another. A typical prism has two triangular faces and parallel square faces. They are made of either glass or metal.

Two congruent triangles and three rectangular faces make up the right triangular prism.

L is the length of the rectangular faces.

W is the width of the rectangular faces.

H is the height of the rectangular faces and the prism.

B is the triangle's base.

x is the height of the triangles.

SA = 2B + PH

B = 1/2 * base * height

B = 1/2 * 13 cm * x = 6.5x cm²

P = 13 cm + 5 cm + x = 18 cm + x

SA = 2B + PH

376.8 cm² = 2(6.5x cm²) + (18 cm + x)(12 cm)

376.8 cm² = 13x cm² + (18 cm)(12 cm) + 12x cm²

376.8 cm² = 25x cm² + 216 cm²

25x cm² = 376.8 cm² - 216 cm²

25x cm² = 160.8 cm²

x = 6.432 cm

As a result, the value of x is around 6.432 cm.

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There is only one possible triangle that can be drawn with one angle measuring 30 deg and another measuring 110°. This is because all triangles have a sum of 180° for the three angles.

Triangle is a three-sided polygon with three straight sides that intersect at three vertices. It is one of the basic shapes in geometry, and is considered to be a building block of other shapes. Triangles can be classified according to their sides, angles, and area. The most common types of triangles are equilateral, isosceles, and scalene triangles, which are classified according to the length of their sides. Triangles can also be classified according to their angles, as acute, right, and obtuse triangles, which are classified according to the size of their angles. Additionally, the area of a triangle is determined by its base, height, and side lengths.

Therefore if one angle is 30° and the other is 110°, the third angle must be 40° for the triangle to be valid.

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False. For two triangles to be similar, the angles must be equal. The angles of the two triangles given do not match, so the triangles are not similar.

An angle is a geometrical figure that is formed by two lines or rays that have a common endpoint. It is a measure of the amount of turn between the two lines or rays. Angles are typically measured in degrees, with a full angle measuring 360 degrees. Angles can also be measured in radians, with a full angle measuring 2π radians. Angles are used in math and science to describe position and orientation. Common examples of angles include right angles, acute angles, obtuse angles, and straight angles. Angles can be used to calculate the area of polygons, measure the slope of a line, and determine the force of friction.

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Complete Question:
A triangle has angles that measure 45° and 65°. A second triangle has angles that measure 110° and 30°. These two triangles are similar. O True O False

The characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

In a polynomial expression, a coefficient is the numerical factor that is multiplied by a variable or variables raised to a certain power. In the expression 5.1xy - 4x + y - 1.5, the coefficient 5.1 is multiplied by the variables x and y, raised to the first power. Therefore, the term 5.1xy consists of the coefficient 5.1 and the variables x and y.

In contrast, the other terms in the polynomial do not have a coefficient that contains a decimal or a fraction. The term -4x has a coefficient of -4, the term y has a coefficient of 1, and the constant term -1.5 has a coefficient of -1.5.

Thus, the characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

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When the width of a rectangle is increasing at a rate, and the length increases at a rate, the rate at which the area increases can be determined by multiplying the rates of the width and the length.

When the width and length of a rectangle increase at certain rates, the area of the rectangle also changes at a specific rate. The rate of change of the area is determined by multiplying the rates of change of the width and length.

This is because the area of a rectangle is calculated by multiplying its width and length, and therefore any change in either dimension affects the overall area. The product of the rates of change of the width and length gives the overall rate of change of the area.

Therefore, the rate at which the area is increasing when the width of a rectangle is increasing at a rate, while the length increases at a rate can be calculated using the above formula.

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The sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1.

The formula for the sum of an infinite geometric series when |x| < 1 is given as:

S = a/(1-r)

We have a = 1 and r = x/1.

S = 1/(1-x) + 2x/(1-x)² + 3x²/(1-x)³ + 4x³/(1-x)⁴ + ...

we multiply both sides of this equation by (1-x)²,

S(1-x)² = (1-x) + 2x + 3x²(1-x) + 4x³(1-x)² + ...

S(1-x)² = 1 + x + x² + x³ + ...    eqn (1)

Using the formula for the sum of an infinite geometric series when |x| < 1, we have:

1/(1-x) = 1 + x + x² + x³ + ...

Substituting this into equation (1), we get:

S(1-x)² = 1/(1-x)

S = 1/[(1-x)²]

In conclusion, the sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1

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The relative frequency of the event "spin a 2" is given as follows:

0.2.

To calculate the relative frequency of an event, you need to divide the number of times the event occurs by the total number of events in the data-set.

Hence the formula to calculate the relative frequency is presented as follows:

Relative frequency = (Number of times the event occurs) / (Total number of events)

From the table, the parameters for the event "spin a 2" are given as follows:

Hence the relative frequency is given as follows:

10/50 = 0.2.

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Answer: 2.8%

Step-by-step explanation: 2.8%

£80 :))

Answer:50

Step-by-step

Answer:

Answer is D

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between −50 and 0 is 50

Answer:

The balanced equation that represents an endothermic reaction is:

2 CH4 (g) + 2 O2 (g) → 2 CO2 (g) + 2 H2O (g)

This is because the reactants (CH4 and O2) have a higher bond energy than the products (CO2 and H2O), meaning that energy must be absorbed in order to break the bonds and form the products. As a result, the reaction is endothermic.

Answer:

I believe the answer would be 30 people.

Step-by-step explanation:

To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.

we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.

In the row-wise identical matrix, all entries in each row are the same, but the entries in different rows can be different.

In the column-wise identical matrix, all entries in each column are the same, but the entries in different columns can be different.

Thus, we can say that the entries in the matrix are highly constrained, with only one unique value per row or column. The matrix is usually denoted as a scalar multiple of the identity matrix or a vector of constants, depending on whether it is row-wise or column-wise identical.

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The probability that a randomly selected gas station in Russia charges more than the mean price in the United States is quite low.

This is because the prices of gas in Russia are typically much lower than the mean price of gas in the United States. The average cost of gasoline in Russia is around $0.50 per liter while in the United States, the average price of gas is around $1.78 per liter.

To explain further, the cost of living in Russia is lower than the cost of living in the United States. This means that there is more disposable income for people living in Russia and as a result, the price of gas is much lower than in the United States.

In addition, the cost of transportation and other production costs are lower in Russia than in the United States, which also keeps the prices of gas in Russia lower.

All of these factors make it unlikely that a randomly selected gas station in Russia would be charging more than the mean price in the United States.

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The unit digit of the given sum [tex]1998^{1999}-1999^{1998}[/tex] is one according to the one's place of 8 and 9 powers.

Here, we need to find the unit digit of [tex]1998^{1999}[/tex] :

8 power of any dight will give us the unit digit of 8, 4, 2 and 6.

Here 8 has power 9.

Then the unit place of the sum will be equal to 2.

Similarly, we need to find the sum of other one.

Other sum: [tex]1999^{1998}[/tex]

9 power of 8

9 power of odd numbers will give 9 as unit digit.

9 power of even numbers will give 1 as unit digit.

Here, we have 8 as power the, we will get the unit digit as 1.

Now we need to simplify the sum.

Unit digit of  [tex]1998^{1999}-1999^{1998}[/tex] is equal to 2 - 1 = 1.

The unit digit of the given sum [tex]1998^{1999}-1999^{1998}[/tex] is one.

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A random variable is a variable whose possible values are determined by chance, while a discrete random variable can only take on certain values, and a continuous random variable can take on any value within a given range

There are two types of random variables: discrete random variables and continuous random variables.

The difference between these two types of random variables is as follows:

Discrete random variables: A discrete random variable is one that can only take on a finite or countably infinite number of distinct values. These values are usually represented by integers.

Examples of discrete random variables include the number of students in a class, the number of cars in a parking lot, or the number of heads that come up when a coin is flipped. In other words, a discrete random variable is one that can be counted.

Continuous random variables: A continuous random variable is one that can take on an infinite number of values, and these values can be represented by any real number within a given interval.

Examples of continuous random variables include height, weight, temperature, and time. In other words, a continuous random variable is one that can be measured.

Continuous random variables are usually represented by a function called the probability density function, which describes the likelihood of any given value occurring within the given interval.


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Answer:

꧁. ꧂

Step-by-step explanation:

꧁. ꧂꧁. ꧂

The additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes is 21.54 minutes (rounded to two decimal places).

Given that: Initial temperature of the liquid, T₁ = 170°F.Final temperature of the liquid, T₂ = 35°F.Constant temperature of the freezer, T = 25°F.

Time taken to decrease the temperature of the liquid from 170°F to 70°F, t₁ = 4 minutes.

The rate of change of temperature, R = (T₁ - T) / t₁ = (170°F - 25°F) / 4 minutes = 111.25°F/minute.

In the freezer, the rate of change of temperature is constant. Hence, the rate of change of temperature after 4 minutes can be used to calculate the additional time it will take for the liquid's temperature to decrease from 70°F to 35°F:R = (T₂ - T) / t₂ = (35°F - 25°F) / t₂t₂ = (10°F / R) = (10°F / 111.25°F/minute) = 0.089728 minutes ≈ 5.38 seconds.

Adding this time to the initial 4 minutes, we have the additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes: t = t₁ + t₂ = 4 minutes + 0.089728 minutes ≈ 4.089728 minutes or 4 minutes 5.38 seconds.

The additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes is 21.54 minutes (rounded to two decimal places).

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Direct variation means the ratio of y to x is constant.

y1/x1 = y2/x2 ⇒

y2 = (x2/x1) y1

Plug in

x1 = 3

y1 = 7

x2 = 7

and get y2.

The percentage of adults who planned to file their taxes electronically is approximately 63%.

A random telephone survey of 1,051 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. The survey results showed that 664 of those surveyed planned to file their taxes electronically.

Total number of adults surveyed = 1,051

Number of adults who planned to file their taxes electronically = 664

Percentage of adults who planned to file their taxes electronically is;

= (Number of adults who planned to file their taxes electronically / Total number of adults surveyed) x 100%

=(664/1051) x 100%

= 63.16 %

Therefore, the percentage of adults who planned to file their taxes electronically is approximately 63%.

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The equivalent expression for 2(n+2) is 2n +4.

Equivalent expressions are expressions that have the same effect even though they look different. If two algebraic expressions are equivalent, then both expressions have the same value when we insert the same value for the variable.

Problems with equivalent expressions often have simple and complex expressions. Check which complex expression is equivalent to a simple expression:

(1) Divide any coefficient: a(bx±c) = abx± aca, open parenthesis, b, x, addition and subtraction, c, close parenthesis, equals , a , b, x, plus or minus, a, c.

(2) Combine all like terms on both sides of the equation: the x term and the constant.

(3) Arrange the terms in the same order, usually the term x precedes the constant.

(4) Two expressions are equivalent if all their terms are identical.

The given expression is : 2(n+2)

Multiplying the expression by 2 : 2n+4

Here, 2n + 4 is the equivalent expression.

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The relationship between the types of quadrilaterals such as rectangles, trapezoids and rhombi can be quantified in terms of sides and angles.

Rectangles and trapezoids

Squares and rhombi

Squares and trapezoids

Rhombi and trapezoids

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The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 22.21 and the sum of squares due to error (sse) is 6.89 will be 15.32.

To find the Sum of Squares due to Regression (SSR), we use the formula:

SST = SSR + SSE

Rearranging the equation to obtain SSR, we get:

SSR = SST - SSE

[tex]$\begin{aligned}SSR&= SST - SSE \\&= 22.21 - 6.89 \\&= 15.32\end{aligned}$[/tex]

Therefore, the value of the Sum of Squares due to Regression (SSR) is 15.32, given the Total Sum of Squares (SST) is 22.21 and the Sum of Squares due to Error (SSE) is 6.89.

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The first step in conducting exploratory research is to conduct a literature search. (Option 3)

Exploratory research is a type of research design used when the researcher has little or no knowledge about the research problem. The purpose of exploratory research is to gain a better understanding of the problem, identify potential research questions, and develop a hypothesis or research design.

The first step in exploratory research is to conduct a literature search, which involves reviewing existing research and publications related to the research problem. This helps the researcher to identify key concepts and theories related to the problem, as well as to identify any gaps or limitations in the existing research.

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Complete Question:

in general, the first step in conducting exploratory research is to___.

group of answer choices

The required medians of the triangle intersect at the point [tex]\left(4,\frac{10}{3}\right)$[/tex].

The medians of a triangle intersect at a point known as the centroid. To find the centroid of a triangle, we need to find the average of the x-coordinates and the average of the y-coordinates of its vertices.

Let the vertices of the triangle be A(0,0), B(5,0), and C(7,5). Then the midpoint of AB is

[tex]\left(\frac{0+5}{2},\frac{0+0}{2}\right) = (2.5,0)$[/tex],

the midpoint of BC is [tex]\left(\frac{5+7}{2},\frac{0+5}{2}\right) = (6,2.5)$[/tex], and the midpoint of CA is

[tex]\left(\frac{0+7}{2},\frac{0+5}{2}\right) = (3.5,2.5)$[/tex]

Therefore, the centroid of the triangle is:

[tex]$\begin{align*}\left(\frac{0+5+7}{3},\frac{0+5+5}{3}\right) &= \left(\frac{12}{3},\frac{10}{3}\right) \&= \left(4,\frac{10}{3}\right)\end{align*}[/tex]

So the medians of the triangle intersect at the point [tex]\left(4,\frac{10}{3}\right)$[/tex].

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