3. Find the composition (f ∘ g)(–2) for the functions f(x) = 2x + 1 and g(x) = x2 – 3.

SHOW YOUR WORK PLEASE

It be concluded that figure A and figure C are showing similar triangle but they are not congruent.

If two triangles are similar then they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are said to be similar figures.

Similarity of two triangles mean when two triangles satisfy the AAA property that is when three angles of one triangle is equivalent to angles with another triangle.

Here for the figure A and C they satisfy the AAA property.

Hence it be concluded that figure A and figure C are showing similar triangle but they are not congruent. The triangles have same shape but not in same size.

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Answer:

x = 3 + √(22/3) and x = 3 - √(22/3).

Step-by-step explanation:

Step 1: Divide both sides by the coefficient of x^2 to get the coefficient of x^2 equal to 1.

3x^2 - 18x + 5 = 0

x^2 - 6x + 5/3 = 0

Step 2: Move the constant term to the right-hand side of the equation.

x^2 - 6x = -5/3

Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation.

x^2 - 6x + 9 = -5/3 + 9

(x - 3)^2 = 22/3

Step 4: Solve for x by taking the square root of both sides of the equation.

x - 3 = ±√(22/3)

x = 3 ± √(22/3)

The statement can be linked to a theorem in geometry known as the "double angle rotation theorem". According to this theorem, if a geometric figure has symmetry about a straight line, and that line intersects another straight line at a point, then the symmetry of the figure about the second line is equivalent to a rotation of twice the angle from the first line to the second line, that is about the point of intersection.

In simple terms, the double angle rotation theorem means that if we can have a geometric figure that is symmetric about a line L1, and L2 is another line that intersects L1 at a point P, then we can rotate the figure about point P by twice the angle formed between L1 and L2 to get the same symmetry about the line L2.

The application of this theorem applies to various aspects of geometry that include transformational geometry and symmetry.

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3/8. If the spinner does not land on yellow, the probability it will land on blue is 3/8.

We must first establish the total number of potential outcomes before we can compute the likelihood that the spinner will land on blue in the event that it doesn't land on yellow. There are only 5 potential outcomes as we know the spinner did not rest on yellow.

Two of those five probability are blue. Given that the spinner did not fall on yellow, the likelihood that it will land on blue is 2/5, or 3/8 in decimal notation. This computation accounts for the fact that the sample space has been decreased from 6 to 5 possibilities owing to the elimination of yellow. We calculate the likelihood of 3/8 by dividing the number of favourable outcomes (2) by the total number of potential outcomes (5).

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An equation that represent the data in the table shown is: D. y = 2x + 3.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 3)/(0 - 1)

Slope (m) = -2/-1

Slope (m) = 2

Based on the information provided above at point (0, 3), an equation that models the line is represented by this mathematical equation;

y = mx + c

y = 2x + 3

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Answer:

It will take them 9756 minutes

Step-by-step explanation:

10 students take 813

How do you get from 10 to 120?

times 10 by 12

Now times 813 by 12

9756

Answer:

(a) 7

(b) 7

(c) 27

The property of addition used in all three equations is the associative property, which allows us to regroup the numbers being added without changing their sum.

Elaine needs tο buy 350 inches οf fabric fοr her windοws.

A fractiοn represents a part οf a number οr any number οf equal parts. There is a fractiοn, cοntaining numeratοr(upper value) and denοminatοr(lοwer value).

If each windοw is 35 inches wide, then the tοtal width οf fabric Elaine needs is:

Tοtal width = 4 windοws x 35 inches per windοw

Tοtal width = 140 inches

Fabric = 2 1/2 x Tοtal width

Tο simplify this, we can first cοnvert the mixed number tο an imprοper fractiοn: 2 1/2 = 5/2

Then, we can multiply this fractiοn by the tοtal width:

Fabric = 5/2 x Tοtal width

Substituting the value οf Tοtal width, we get:

Fabric = 5/2 x 140 inches

Fabric = 350 inches

Therefοre, Elaine needs tο buy 350 inches οf fabric fοr her windοws.

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The square root function always returns a non-negative value, the range of f(x) is R: [0, ∞).

It is the set of values of the variable for which the function has a valid output.

To find the domain and range of the function f(x) = [tex]sqrt(x^2 - 49)[/tex], we need to consider the possible values of x that make the function well-defined and the corresponding values of f(x) that the function can take.

The function f(x) is defined if the argument inside the square root is non-negative, that is, [tex]x^2 - 49[/tex] ≥ 0. This inequality can be solved as:

(x - 7)(x + 7) ≥ 0

The solution to this inequality is x ≤ -7 or x ≥ 7, so the domain of the function is D: (-∞, -7] ∪ [7, ∞).

The range of the function is the set of all possible values that the function can take. Since the square root function always returns a non-negative value, the range of f(x) is R: [0, ∞).

Therefore, the correct answer is (B) D: (-∞, -7] ∪ [7, ∞), R: [0, ∞).

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Answer:65

Step-by-step explanation:

This test is left-tailed and the test statistic is -1.53

Since the alternative hypothesis is that less than 10% of treated subjects experienced headaches, and this is a lower bound, the test is left-tailed.

To find the test statistic, we first need to calculate the expected number of subjects who would experience headaches if the null hypothesis were true (i.e., if the true proportion were 10%). This is found by multiplying the total number of treated subjects by the hypothesized proportion:

Expected number of subjects with headaches = 0.10 * 288 = 28.8

We then use the formula for the z-score of a sample proportion:

z = (p - P) / √(P(1 - P) / n)

where p is the sample proportion (21/288), P is the hypothesized proportion (0.10), and n is the sample size (288).

Plugging in the values, we get:

z = (0.073 - 0.10) / √(0.10 * 0.90 / 288) = -1.53

Therefore, the test statistic is z = -1.53.

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a. The function that models the fox population t years after 2000 is:

[tex]p(t) = 12500 * e^{(0.05t)[/tex]

b. The estimated fox population in the year 2008 is 19121 (rounded to the nearest integer).

Amοng the crucial kinds are: When there is a mapping fοr a range fοr each dοmain between twο sets, this is knοwn as an injective functiοn οr οne tο οne functiοn. When mοre than οne element is transferred frοm dοmain tο range, the functiοn is said tο be surjective οr tο be an οntο functiοn

(a) Since the fox population has a continuous growth rate of 5% per year, the population can be modeled using the exponential growth formula:

[tex]p(t) = p(0) * e^{(rt)[/tex]

where p(0) is the initial population, r is the continuous growth rate (expressed as a decimal), t is the time elapsed in years, and e is the mathematical constant e ≈ 2.71828.

Using the given information, we have:

p(0) = 12500 (the population in the year 2000)

r = 0.05 (the continuous growth rate)

Therefore, the function that models the fox population t years after 2000 is:

[tex]p(t) = 12500 * e^{(0.05t)[/tex]

(b) To estimate the fox population in the year 2008, we need to find the value of p(8) using the function from part (a):

[tex]p(8) = 12500 * e^{(0.05*8)} = 19121[/tex]

Therefore, the estimated fox population in the year 2008 is 19121 (rounded to the nearest integer).

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Answer:After layla adds a tip, the price of the item is $16.20. The percent of the tip is 10 %

Step-by-step explanation:

What is a tip?

A tip is a gift or a sum of money placed or given for a service performed or anticipated, by extension, a form of gratuity. Even if the service is poor, it's recommended you leave at least 10 percent.

How to calculate a tip?

There are four ways of calculating a tip:

Method 1: Move over the decimal in the bill total and then double that number.

Method 2: Multiply the tax of the bill by two.

Method 3: Double the pretax bill and then move the decimal over one space.

Method 4: Determine 10% of the bill and add half

The required solution of the given inequality is {m | 6 ≤ m < 9}.

In mathematics, inequality is a statement of an order relationship between two numbers or algebraic expressions that is greater than, greater than or equal to, less than, or less than or equal to.

According to question:

We can solve the inequality as follows:

3 + m ≥ 9 or 1 + 2m < 19

Subtracting 3 from both sides of the first inequality, we get:

m ≥ 6

Subtracting 1 from both sides of the second inequality and then dividing by 2, we get:

m < 9

Putting these two inequalities together, we get:

6 ≤ m < 9

This is the solution in interval notation. To write it in set-builder notation, we can use the following notation:

{m | 6 ≤ m < 9}

This means the set of all values of m such that m is greater than or equal to 6, and less than 9.

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Answer: What is minor arc and major arc?

Image result for 1. Name a minor arc. 2. Name a major arc. 3. Name a point of tangency. 4. Name a radius.

Every pair of endpoints defines two arcs. An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.

Step-by-step explanation:

The area of the regular polygon and rounded  to the nearest hundredth is 200 sq. units.

How to find the area of any polygon?

Area of Regular Polygon Formula = [tex]\frac{l^2n}{4tan\left(\frac{180}{n}\right)}[/tex] Square units

Length of side of the regular polygon is 5.2 and have n= 9 sides

Let's say, Area is A for the polygon,

[tex]A = \frac{(5.2)^2 \times 9}{4 tan\left(\frac{180}{9}\right)}\\\\A= 167.16\ sq.\ units\\A= 200\ sq.\ units\ (round-off\ to\ nearest\ hundred)[/tex]

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area is approximately 158.72 square centimeters

To find the area of a regular octagon with a given side length and apothem, we can use the formula:

Area = (1/2) × Perimeter × Apothem

where Perimeter is the total length of all the sides of the octagon.

We are given that the side length of the octagon is 5.2 cm and the apothem is 7.6 cm.

To find the perimeter of the octagon, we can use the fact that the octagon is a regular polygon and has eight equal sides. Thus:

Perimeter = 8 × side length = 8 × 5.2 cm = 41.6 cm

Now we can substitute the values we have into the formula to get:

Area = (1/2) × Perimeter × Apothem

Area = (1/2) × 41.6 cm × 7.6 cm

Area = 158.72 cm²

Therefore, the area of the regular octagon with a side length of 5.2 cm and an apothem of 7.6 cm is approximately 158.72 square centimeters.

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By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction is 8/21 .

To express a portion of a whole or the division of a quantity, use a fraction. It consists of a horizontal or slant line separating the two integers that make up the numerator and denominator. The total quantity of components in the whole is represented by the denominator, while the numerator is the number of equal parts that are being taken into account. As an illustration, the numerator and denominator of the fraction 3/4 are 3 and 4, respectively. Parts of a set, chunks of a pie, and ratios between quantities can all be represented using fractions. Using particular guidelines and algorithms, they can be multiplied, divided, added, or subtracted. To make calculations and comparisons simpler, fractions can be changed to decimals or percentages.

given

We combine the numerators and denominators together to multiply two fractions. So:

(4/9) x (6/7) = (4 x 6) / (9 x 7) = 24/63

By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction can be made simpler:

24/63 = (3 x 8) / (3 x 21) = 8/21

Because of this, 4/9 x 6/7 Equals 8/21.

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The measurement of angle EFG is 42.

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.

A straightforward illustration of a sector with a center angle of 180o is a protractor. The angle created by a circle's arc at its center is another way to describe the term "central angle."

We have a circle with center H and the central angle is 84 degrees

The central angle of the circle is double of circumference angle.

Then the measurement of angle EFG is 42.

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The terrarium has 594 cm³ volume of dirt.

What is volume?

Given the dimensions of the terrarium as h=12cm, l=22cm, and b=9cm, we can calculate the volume of the terrarium as follows:

Volume of terrarium = length x width x height

= 22 cm x 9 cm x 12 cm

= 2,376 cm³

Since the terrarium is filled 1/4 of the way with dirt, the volume of dirt is:

Volume of dirt = (1/4) x Volume of terrarium

= (1/4) x 2,376 cubic cm

= 594  cm³

Therefore, the terrarium has 594 cubic centimeters of dirt.

what is terrarium?

A terrarium is a sealed or partially enclosed glass container used to grow and display plants or small animals. It is typically made of clear glass or plastic and is designed to mimic a miniature ecosystem, providing a controlled environment for plants to grow and thrive. Terrariums are popular for indoor gardening and can be used to create a variety of landscapes, from tropical rainforests to desert landscapes. They require minimal maintenance and are an excellent way to bring a touch of nature into your home or office.

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Complete question is: A terrarium is filled 1/4 of the way with dirt. the  terrarium have 594 cubic centimeters of dirt.

The probability of picking a green card at random is 15/29.

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

The total number of cards in the deck is:

Red cards: 5

Blue cards: 9

Green cards: 15

So, the total number of cards in the deck is 5 + 9 + 15 = 29.

The probability of picking a green card at random is the ratio of the number of green cards to the total number of cards in the deck:

Probability of picking a green card = Number of green cards / Total number of cards

Probability of picking a green card = 15 / 29

Hence, the probability of picking a green card at random is 15/29.

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The dividend yield is 8.8%.

What is the marginal tax rate?

The ratio at which a person or corporation is taxed is known as the tax rate. Statutory, average, marginal, and effective tax rates are just a few of the ways that can be displayed. These rates can also be displayed using the inclusive and exclusive definitions of a tax base.

Here, we have

Given: Assume that Keisha's marginal tax rate is 40% and her tax rate on dividends is 15%. If a city of Atlanta bond pays 7.48% interest.

We have to find the dividend yield would a dividend-paying stock (with no growth potential) has to offer for Keisha to be indifferent between the two investments from a cash-flow perspective.

Dividend yield × (1 - tax rate) = Interest

Dividend yield × (1 - 0.15) = 7.48%

Dividend yield = 7.48%/0.85

Dividend yield = 8.8%

Hence, the dividend yield is 8.8%.

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a. The revenue functiοn R(x) = 75x - 3x² graph plοtted belοw.

b. Value οf x is 12.5 and maximum revenue prοduces $468.75

c. Whοlesale price/chip that prοduces the maximum revenue is $37.50

A cοmpany's οr business's revenue is the tοtal amοunt οf mοney it receives frοm sales οf its prοducts οr services οver a given time periοd.

a) Tο sketch a graph οf the revenue functiοn R(x), we first need tο calculate R(x) using the given fοrmula:

⇒ R(x) = x P(x)

⇒ R(x) = x(75 - 3x)

⇒ R(x) = 75x - 3x²

Nοw we can plοt this functiοn οn a rectangular cοοrdinate system. Belοw is an sketch οf the graph.

b) Taking the derivative οf R(x) and setting it equal tο 0:

⇒ R'(x) = 75 - 6x = 0

⇒ 6x = 75

⇒  x = 12.5

Sο, x = 12.5 is the value οf x that will prοduce the maximum revenue. Tο find the maximum revenue, we can substitute x = 12.5 intο the revenue functiοn R(x) = x (75 - 3x)

⇒ R(12.5) = 12.5 (75 - 3 (12.5)) = 468.75

⇒ R(12.5) = $ 468.75

Therefοre, the maximum revenue is $468.75

c) Tο find the whοlesale price per chip that prοduces the maximum revenue, we can substitute x = 12.5 intο the price functiοn, P(x) = 75 - 3x

⇒ P(12.5) = 75 - 3(12.5)

⇒ P(12.5) =  $37.50 per chip

Therefοre, the whοlesale price per chip that prοduces the maximum revenue is $37.50.

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Complete question:

The statement "a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left" and "a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y-axis and a dilation about the origin by a scale factor of 3/4" is correct of the question.

A polygon is a two-dimensional geometric shape that has three or more straight sides and angles. It is a closed shape, meaning that the sides connect to form a continuous boundary.

A polygon can have any number of sides, although polygons with three sides are called triangles, polygons with four sides are called quadrilaterals, and so on. The angles of a polygon are formed where two sides meet, and the sum of the interior angles of a polygon with n sides (n being greater than or equal to 3) is (n-2) times 180 degrees.

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We have shown that for any finite group G and any element r ∈ G, there exists a positive power of r that equals the inverse of r.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

To prove the statement, we need to show that there exists a positive power of r, say [tex]r^{k}[/tex], that equals the inverse of r, i.e.,  [tex]r^{k}[/tex], = [tex]r^{-1}[/tex].

Suppose all the powers of r are distinct, i.e.,  [tex]r^{n}[/tex]≠ [tex]r^{m}[/tex] for all n ≠ m in Z. Since G is finite, there are only finitely many powers, Since there are N+1 distinct elements in the set there must be some n,m ∈ {0,1,...,N} such that n < m and [tex]r^{n}[/tex] =  [tex]r^{m}[/tex]

Without loss of generality, assume n < m. Then we have:

[tex]r^{n}[/tex] =  [tex]r^{m}[/tex]

[tex]r^{m-n}[/tex]= 1

Let k = m - n > 0. Then we have:

[tex]r^{k}[/tex] = [tex]r^{m-n}[/tex]= 1

[tex]r^{-1}[/tex]= [tex]r^{(k-1)}[/tex]

Thus,  [tex]r^{k}[/tex] =  [tex]r^{(k-1)}[/tex], which is the desired result.

Therefore, we have shown that for any finite group G and any element r ∈ G, there exists a positive power of r that equals the inverse of r.

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Answer:

D) 105

Step-by-step explanation:

All 4 side shape's interior angle add up to 360

360 - 45 = 315

315 / 3 = 105

Enterprise ABC should invest in the production line of product X as it generates a positive net present value and an internal rate of return that is greater than ABC's cost of capital.

To determine if Enterprise ABC should invest in the production line of product X, we calculate the net present value (NPV) of the project using the given information and ABC's cost of capital of 9%. The initial investment is $2 billion, and the project generates an annual revenue of $1.2 billion with a variable cost of 40% of annual revenue and fixed cost of $100 million per year. The project has a useful life of 4 years and is depreciated using the straight-line method. The corporate income tax rate is 20% per year, payable in the year taxable income is generated.

Using a financial calculator, the NPV of the project is approximately $357.87 million, which is positive and indicates that the project generates a return that is greater than ABC's cost of capital. Additionally, the internal rate of return (IRR) of the project is approximately 12.21%, which is greater than ABC's cost of capital of 9%. Therefore, based on the method of internal rate of return (IRR), Enterprise ABC should invest in the production line of product X as it generates a positive net present value and an internal rate of return that is greater than ABC's cost of capital.

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