Given f(x) = 2x - 1 and g(x) = x² + 5, find i)fg(x)

ii) gf(x)​

The number of ways to chose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office is 11880.

If the person cannot hold more than one office.

Then the number of ways of selecting a president, vice president, secretary and treasurer of the club from the club consisting of 12 member is given by the permutation ¹²P₄.

Because we have to select four member out of 12,

So, solving further,

= ¹²P₄

= 12!/(12-4)!

= 12!/8!

= 12 x 11 x 10 x 9

= 11880.

So, there are a total of 11880 ways to chose the members.

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Complete question - A club has 12 members A president, a vice president, a secretary, and a treasurer are to be chosen from these members. A member cannot serve for more than one position. In how many ways can this be down?

By the Lacey Act, it can be concluded that

Whole animals and plants, live specimens, and falsely labelled parts or products are all prohibited under the Lacey Act

What is initial Lacey Act?

There are many wild animals in United States of America that were illegally smuggled, traded or sold. Lacey Act is a conservation law which is passed in the United States of America that stops the illegal trading, smuggling and selling of these wild animals.

Whole animals and plants, live specimens, and falsely labelled parts or products are all prohibited under the Lacey Act

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Each month we have to deposit 1389 of amount and we get interest of 30000

percentage, a relative value indicating hundredth parts of any quantity.

Given 500000 to be in our account in retirement of 30 years.

We need to find how much we have to deposit each month.

We know that in a year there are 12 months.

For 30 years the number of months are 12×30=360

So Now divide 500000 by 360 to find each month deposit

500000/360=1388.8

So each month one has to deposit 1389 into account.

Now if account earns 6% of interest. We need to find how much amount we earned.

6% is converted to decimal by dividing 6 by 100

0.06

Now multiply with 500000

0.06×500000

30000

Hence, each month we have to deposit 1389 of amount and we get interest of 30000.

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If the length of the room in drawing is 3 inches, then the actual length of the room is 24 feet

The scale of the drawing of a hotel = 1 inch : 8 feet

The length of the room in the hotel in the drawing = 3 inches

Consider the actual length of the room as x

Then the proportion will be

1 inch / 8 feet = 3 inches / x feet

Cross multiply the terms and find the value of x

1 × x = 3 × 8

Multiply the numbers

x = 24 feet

Hence, if the length of the room in drawing is 3 inches, then the actual length of the room is 24 feet

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The surface area of the solid pyramids are as follows;

First figure; 436 square units

Second figure; 319 square units

Third figure; 673 square units

A pyramid is a shape that consists of a polygon base and side faces that are triangular.

First figure

The figure is a pentagonal pyramid of height 8 units and side length of 10 units

The apothem, a, can be obtained from the formula;

[tex]a = \dfrac{s}{2\cdot tan \left(\dfrac{180}{n} \right)}[/tex]

s = 10

n = 5

[tex]a = \dfrac{10}{2\cdot tan \left(\dfrac{180}{5} \right)} \approx 6.88[/tex]

Slant height ≈ √(8² + 6.88²) ≈ 10.55

Area of the 5 triangles = 5 × (1/2) × 10 × 10.55 ≈ 263.75

Area of pentagonal base ≈ (1/2) × 6.88 × 5 × 10 = 172
Area of the figure ≈ 263.75 + 172 ≈ 436

Second figure;

Square pyramid

n = 4

When s = 8, we get;

[tex]a = \dfrac{12}{2\cdot tan \left(\dfrac{180}{4} \right)} =6[/tex]

Slant height of the 8 units long side = √(6² + 10²) ≈ 11.66

Area of two of the four triangle surfaces = 2×(1/2)×8 ×11.66≈ 93.28

When s = 12 we get;

[tex]a = \dfrac{8}{2\cdot tan \left(\dfrac{180}{4} \right)} =4[/tex]

Slant height of the 12 units long side = √(4² + 10²) ≈ 10.77

Area of two of the four triangle surfaces = 2×(1/2)×12 × 10.77 ≈ 129.24

Area of the rectangular base = 12 × 8 = 96

Area of the figure = 93.28 + 129.24 + 96 ≈ 319

Third figure

Octagonal pyramid

n = 8

s = 8

[tex]a = \dfrac{8}{2\cdot tan \left(\dfrac{180}{8} \right)}\approx 9.66[/tex]

Slant height = √(9.66² + 6²) ≈ 11.37

Area of the 8 triangles = 8 × (1/2) × 8 × 11.37 ≈ 363.84

Area of the octagonal base = 2×(1 + √2)×s²

Therefore;

2×(1 + √2)×8² ≈ 309.02

Area of the figure ≈ 363.84 + 309.02 ≈ 673

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The value of the expression will be;

⇒ 2y + 1

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (2x - 3y - 5) - (2x - 5y - 6)

Now,

Solve the expression as;

The expression is,

⇒ (2x - 3y - 5) - (2x - 5y - 6)

⇒ 2x - 3y - 5 - 2x + 5y + 6

⇒ 2x - 2x - 3y + 5y - 5 + 6

⇒ 2y + 1

Thus, The value of the expression will be;

⇒ 2y + 1

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A plaintiff who sues on the basis of disparate-treatment discrimination in hiring must make out a prima facie case of illegal discrimination and will win in the absence of a legally acceptable employer defense. True

Disparate treatment discrimination refers to the form of discrimination from an employer who blatantly treats an employee, or a potential employee differently based on the individual’s race, religion, color, sex, national origin, etc. It is intentional employment discrimination. A plaintiff who sues on the basis of disparate-treatment discrimination in hiring must make out a prima facie case. Prima facie case refers to a cause of action or defense that is sufficiently established by a party's evidence to justify a verdict in their favor, provided such evidence is not rebutted by the other party. The facts of the case are assumed to be true unless contradicted by evidence, hence if the plaintiff has produced sufficient evidence of their claim that the case will be decided for the plaintiff unless the defendant produces evidence to rebut it. To establish prima facie case, the plaintiff must be a member of the a protected class, must have applied and was qualified for the job in question, was rejected by the employer, and employer continued to seek applicants for the position or filled the position with a person not in a protected class. If plaintiff establishes all of this, burden now falls on employer as they must then prove their reasoning.

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The population difference within the pair is normal.

The population distribution of mice with and without diabetes are identical.

mRNA population distribution for mice with diabetes is shifted relative to the population distribution for mice without diabetes.

Conclusion,

the two population has same shape , the two samples are independent  simple random samples  and the two samples are paired , the population means are the same .

Hence, each of the two population distribution is normal.

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Answer:

Step-by-step explanation: 1 of them

The value of  x is 46.6 degree

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

tan θ = opposite /adjacent = 5.7/5.4 = 1.0555

θ = arctan ( 1.0555 ) = 46.6 degree = x

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The angular momentum of the earth in its orbit around the sun is compared with the angular momentum of earth on its axis as below :

Earth's radius is 6.38 x 106 meters, its mass is 5.97 x 1024 kg, and its orbital radius is 1.5 x 1011 meters. The period of the earth's rotation is 24 hours, or 86400 seconds. The period of its revolution is one year, or 3.156 x 107.

Finding the angular momentum entails

L = mE x r2 x w L = 2.6742 x 1040kg.m2.s-1

I= 2/5M.R2 L8= 7.07 x 1023kg.m2.s-1 for a homogeneous sphere with mass M, radius R, and an axis through its center.

Earth's angular momentum in a circular orbit around the sun is measured at Li=2.6742 x 1040 kg.m2.s-1.

Given that the radius of the planet is so small in comparison to the distance from the sun, it makes sense to model the earth as a particle.

L8= 7.07 x 1023 kg.m2.s-1 is the size of the earth's angular momentum as a result of its revolution around an axis passing through the north and south poles.

Parameters and Calculations:

Earth's mass, mE, is 5.97 x 1024 kg, and its radius, R,

the earth's orbital parameters are as follows: RE= 6.38 x 106 m, r= 1.5 x 1011 m, t=24h = 86400 s, and t=1 year = 3.156 x 107

Finding the angular momentum entails

L=mexr2xw where

L = 2.6742 x 10-40 kg/m2/s-1

For a homogeneous sphere with mass M, radius R, and a central axis,

I= 2/5M.R^2

L8 = 7.07 x 1023 kg/m2/s-1

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The two companies will charge the same for 20 tons of sugar and the cost when the two companies charge the same is calculated to be $9510

The amount of sugar for which the charge will be equal can be determined by using an algebraic expression as follows;

5495 + 200.75x = 7500 + 100.50x

Here x represents tons of sugar

200.75x - 100.50x = 7500 - 5495

100.25x = 2005

x = 2005 ÷ 100.25

x = 20

Hence for 20 tons of sugar, the two companies will charge the same. Now by substituting the value of x = 20, the cost when the two companies charge the same can be determined as follows;

5495 + 200.75x = 5495 + 200.75 (20) = 5495 + 4015 = $9510

Hence $9510 is the cost when the two companies charge the same.

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For the given problem the p - value is 0.0697.

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: Dean Halverson recently read that full-time college students study 20 hours each week.

She decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week.

A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks.

It was found that the average number of hours that the 35 students studied each week was 21.1 hours.

The sample standard deviation of 4.3 hours.

H0: μ = 20

H0: μ > 20

n = 35

X bar = 21.1

s = 4.3

Test statistics = t = (X bar - μ) / (s / √n)

                            = (21.1 - 20) / (4.3 / √35)

                          t = 1.5134

P value = df = n - 1 = 35 - 1 = 34

P([tex]t_3_4[/tex] > 1.5134) = 0.0697

Hence, the p - value is 0.0697.

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The area of the figure that is given in the image below is: 26.13 ft².

To find the area of a composite figure, find the area of each of the shapes that make up the composite figure, then add their areas together.

Given the composite figure as shown in the diagram below, it consists of a triangle and a half circle (semicircle). To find the area of the composite figure, find the area of the triangle and that of the semicircle.

Area of triangle = 1/2 × base × height = 1/2 × 6 × 4

Area of triangle = 1/2 × 24

Area of triangle = 12 ft²

Area of semicircle = 1/2 × π × r² = 1/2 × 3.14 × 3²

= 14.13 ft²

Area of the composite figure = 12 + 14.13 = 26.13 ft².

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The slope of line  y = - 2x is found to be -2 by comparing it with the equation of line.

The given equation is y = - 2x.

Comparing it with the equation of line y = mx, we get,

Slope(m) = -2

Therefore, the slope of line  y = - 2x is found to be -2 by comparing it with the equation of line.

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Depth first search (DFS) is an algorithm for reversing traversing or searching tree or graph data structures.

If there are two vertex-disjoint paths connecting any two vertices, the graph is biconnected .A straightforward cycle passes through any two vertices in a biconnected graph.

If a connected graph is connected but does not have any Articulation Points, it is Biconnected .In a graph, we mostly need to check two things.

1.The chart is associated.

2.There isn't enunciation point in diagram.

DFS traversal commences at any vertex. We check to see if there is an articulation point during DFS traversal .

The graph is biconnected if no articulation points are found. Lastly, we must determine whether DFS was able to reach all vertices. The graph would not even be connected if none of its vertices could be reached.

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The Two-Sample Z-Tests remain valid because the two mistakes offset each other.

The Two-Sample Z-Tests is used to compare the means of two samples to determine whether it is feasible that they come from the same population. The null hypothesis is: the population means are equal.

A Z-Test can only be used when the population standard deviation is known and the sample size is 30 data points or larger. If not, a T-Test should be used.

Practically, the Two-Sample Z-Tests is not used often, because the two population standard deviations σ 1 and σ 2 are usually unspecified. Alternately, sample standard deviations and the T‐distribution are used.

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By substituting the point and slope we know, we can solve for b (the y-intercept.) This will allow us to write the full equation, as we already know the slope.

Solving for B

Set up equation                                                                   y = mx + b

Substitute                                                                             5 = -5(-4) + b

Simplify                                                                                 5 = 20 + b

                                                                                            -20 -20  

Solve                                                                                    -15 = b

Writing the Equation

Set up equation                                                                   y = mx + b

Substitute                                                                             y = -5x - 15

Solve                                                                                    y = -5x - 15

Check:

We can check if our equation is right by graphing it. In this graph, you can see it has a slope of -5 and goes through the point (-4,5). Therefore, our answer is correct:

Answer:

1930,00

Step-by-step explanation:

Gross income - expenses = net income

The value of cost of all the product is 32.50

The amount a buyer pays for a good or service is known as the selling price. It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of competing companies in the market.

Formulas and Calculations for Sale Prices Percent Off Price Formula

List price - (List price x (percentage / 100)) = Discounted price

For instance, the sale price is 25% off the list price of $130.

Divide 25% by 100 to get the decimal equivalent: 25/100 = 0.25

Divide the list price by the decimal percent: 130*0.25 = 32.50

Subtract the amount of the discount from the list price: 130 - 32.50 = 97.50

Using the formula:

130 - (130*(25/100)) =

\s130 - (130*0.25) =

       \s130 - 32.50 = 97.50

25% off $130 is $97.50

Formula for Fractional Off Price

List price - Discounted price (List price x fraction)

Example: The sale price is one-third of the list price of $120.

Divide the list price by the fractional discount: 120*1/3 = 40

Subtract the amount of the discount from the list price: 120 - 40 = 80

Using the formula:

120 - (120*1/3) = \s120 - 40 = 80

1/3 off $120 is $80

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The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Then the equation is given as,

(x + 12) / (x + 5) = (x + 5) / x

Simplify the equation, then we have

(x + 12) / (x + 5) = (x + 5) / x

x² + 12x = (x + 5)²

x² + 12x = x² + 10x + 25

12x - 10x = 25

Further, simplify the equation, then we have

2x = 25

x = 25/2

x = 12.5

The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.

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The real distance between the ship and the base is 35 km and the measure of the bearing of B from S would be; 70 degrees.

Scale factor is the factor which is used to enlarge or smaller the original figure. Scale factor is the ratio of representation measurement of the figure to the original figures.

The figure represent the position of the ship(S) and the marine base(B).

a) Real distance between the ship and the base is;

When the distance from ship and the base is measured by rules. It comes out 3.5 cm.

The scale of the diagram is 1 cm, represents 10 km. Thus,

BS = 10/ 1 x 3.5

BS = 35 km

b) Measure the bearing of B from S

With the help of compass, the bearing angle of B from S is measured as the given;

Angle BSN = 70 degree

Thus, the real distance between the ship and the base is 35 km and the measure of the bearing of B from S would be; 70 degrees.

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Answer:

Step-by-step explanation:

x=(y-7)/

The value of x is 10.

Parallel lines are those straight lines that are always the same distance apart from each other. Parallel lines never meet, no matter how much they are extended.

Given that, three lines parallel to each other,

We know, segments in parallel lines are in equal proportion,

5/4 = (2x-10)8

10 = 2x-10

2x = 20

x = 10

Hence, the value of x is 10.

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The concept to graph a linear equation is explained below.

To make a line you really want two focuses. Then you can define a boundary through those two focuses. The x and y factors in the direct condition address the x and y facilitates on a diagram. In the event that you plug in a number for x, you can compute the relating number for y.

As examined, direct chart frames a straight line and indicated by a situation; y=mx+c. where m is the slope of the diagram and c is the y-block of the chart. The angle between any two focuses (x1, y1) and (x2, y2) are any two focuses on the direct or straight line

Steps to graph linear equation,

Step 1: Find the line slope and the y-intercept form of the line

Step 2: Graph the y-intercept of linear equation

Step 3: Find another point on the linear line using the slope

Step 4: Draw a linear equation of line that passes through the points

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The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) [tex]\sqrt{x + 5}[/tex]

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) [tex]\sqrt{\dfrac{5}{x} } +3= 17[/tex]

[tex]\sqrt{\dfrac{5}{x} }= 17-3 =14[/tex]

[tex]\dfrac{5}{x} }=14^2=196[/tex]

[tex]x = \dfrac{5}{196}[/tex]

9e) [tex]\sqrt{\dfrac{4}{x} } = 1[/tex]

[tex]\dfrac{4}{x} } = 1^2[/tex]

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) [tex]\sqrt{\dfrac{0.6}{36} }[/tex]

[tex]\sqrt{\dfrac{0.6}{36} }[/tex] = [tex]\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13[/tex]

9h) [tex]\sqrt{\dfrac{4-10}{0.01} }[/tex]

[tex]\sqrt{\dfrac{4-10}{0.01} }[/tex]= √(-600) = √(-1)·√(600) = i·10·√6

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Answer:

Explanation:

First step is to multiply the expression in brackets on the left side by 0.5

0.5(x+8)=x−4

Now we can move the unknown x to left side and the numbers to right side

x+4=x−4

The last equality is false, so the original equation has no solutions.

x−x=−4−40=−8

Cross-sectional pattern is not present in a time series. A time series is a sequence of data points measured at equally spaced time intervals.

A pattern is a repeat or uniformity in a collection of items or events. It is the typical manner in which something is carried out or occurs. Visual patterns, behavioral patterns, and language patterns are only a few examples of patterns. In the context of data analysis, patterns relate to regularities or trends in the data that may be utilized to anticipate outcomes or pinpoint connections between various variables. For instance, a time series of stock prices may show a definite upward trend, demonstrating the stock's increasing worth. To forecast the stock's future performance and guide investment choices, a pattern in this data may be found.

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Both the positive and the negative equations are set up to check the same distance from zero.

Absolute value refers to the distance of a number from zero regardless of the direction, which is indicated by the signs (positive if to the right of zero, and negative if to its left).

When solving absolute value equations, we must provide all possible answers that are of the same distance from zero. That means solving for the positive equation, which gives us the number to the right of zero, as well as solving for the negative equation, which gives us the number to the left of zero with the given distance (absolute value).

Therefore, both the positive and the negative equations are set up to check the same distance from zero.

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The purpose of controlling is to monitor performance and take corrective action as needed to ensure that objectives are met.

Performance refers to how effective or successful someone or something is in doing something. The capacity of a corporation to adopt optimal organization with the goal of providing a product or service that satisfies the expectations of consumers and customers determines business performance, which is strongly related to commercial effectiveness. Employee Engagement and Productivity are Improved by Performance Management. Employees who are actively involved in their work environments stay longer and produce better outcomes. Increasing employee engagement is essential to increasing output and maximizing return on investment.

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