2. for each infinite sequence suggested below, give its generating function in closed form, i.e., not as an infinite sum. (use the most obvious choice of form for the general term of each sequence.)

Answer:

You can see the graph in the picture attached.

Answer: The amount of money needed to be given to the server is $30 and 23 cents.

Since tax is 6%, hence:

Total bill including tax = $28.52 + 6% of $28.52 = $30.23

The amount of money needed to be given to the server is $30 and 23 cents.

Therefore the denominations needed for this is one $20 bill, two $10 bills and 23 pennies.

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Step-by-step explanation:

A cubicle-filled office may also be referred to as a "sea of cubicles," "cube farm," or "pods" such as a 4-pod or 8-pod of cubes.

In the given question we have to explain about  a group of cubicles.

A cubicle-filled office may also be referred to as a "sea of cubicles," "cube farm," or "pods" such as a 4-pod or 8-pod of cubes.

A cubicle is a type of office workspace that is partially enclosed and divided from adjacent workspaces by partitions that are typically 5 to 6 feet (1.5 to 1.8 metres) tall. Its objective is to shield managers and office workers from the sights and sounds of an open workspace so they can focus with fewer interruptions. Walls, work areas, compartments, cabinets, and bookcases are just a few of the modular components that make up cubicles, which can be arranged anyway the user sees fit.

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The equation which can be used to find the amount of time Hiroshi spends on his math homework is 1/4(x + 30 + 60) = x

According to the question,

Let total time Hiroshi spent on his homework be "y"

Total time spent on history homework = 30 minutes

Total time spent on English homework = 60 minutes

It is given that the time spent on math homework is x

and Also that One fourth of his total homework time is spent on math

=> x = 1/4y

=> 4x = y ----------(1)

Also , Sum of time taken in different homework will be equal total time y

=> 30 + 60 + x = y --------(2)

Substituting the values of x from equation (1) in equation (2)

=> 30 + 60 + x = 4x

divide by 4

=> 1/4(x + 30 + 60) = x is equation

=> x + 30 + 60 = 4x

=> 3x = 90

=> x = 90/3

=> x = 30 minutes

Total time taken in doing homework is 120 minutes

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A gate has a standard key pad with the digits 0 through 9. How many possible code combinations are there if the code is 4 digits long.

There are 10,000 different code combinations.

We have given that,

A gate has standard key pad with digits 0-9 ..

we have to make a 4 digit code with 10 possible digits (0-9) and first one cannot be zero .

but digits can't be repeat.

put down 5 blank spaces on paper and then put the number of combinations in each space.

the first digit can not be 0, so there are 9 possible combinations (1-9).

The second digit cannot be the same as the first digit, but it can be 0, so there are 9 combinations.

The third digit cannot be either the first or the second digit and thus there are 8 combinations.

The fourth digit has 7 combinations.

numbers of combinations you should have

9×9×8×7 = 4536

hence, total possible combination are 4536.

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The equation that represents the function g , the result of the transformation is g(x) = -(1/2)tanx     .

In the question ,

the parent function is given to be tangent ,

let the the parent function be denoted by "f" ,

So , f(x) = tanx,

given that the function is horizontally compressed by a factor of 1/2 ,

that means the function is multiplied by 1/2 ,

So ,g(x) = (1/2)tanx

also given that it is reflected over the x axis ,

reflection over x axis means , multiplying it by -1,

So , g(x) = -(1/2)tanx .

Therefore , the function g is g(x) = -(1/2)tanx  .

The given question is incomplete , the complete question is

The parent tangent function is horizontally compressed by a factor of 1/2 and reflected over the x-axis. Write an equation to represent function g, the result of this transformation ?

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Answer:

g(x)=-tan(2x)

Step-by-step explanation:

Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

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The main advantages of using a random forest versus a single decision tree is that Random forest algorithm avoids and prevents overfitting by using multiple trees.

Random forest replaces the data used to build the tree and also the explanatory variables are bootstrapped so that partition is not done on the same important variable whereas  decision trees do not follow this algorithm. Bootstrapping reduces bias and variance both which makes the model more robust and accurate.

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Symptoms of an allergic reactions:

Allergies cause your body to react to normally harmless things like pollen, dust, and animal dander. Symptoms can be mild, but can be very serious for some people.

allergen he can enter the body in four different ways.

Allergy symptoms vary from person to person, and the substances that trigger the allergic reaction may also be different.

If you have a runny or stuffy nose after a few minutes of walking, you may have allergic rhinitis. This is our reaction to tiny particles in the air we breathe.

Sneezing doesn't seem to be a big deal. However, it can be a mild early sign of a serious allergy, even the foods you eat.Your sneezing can also be quickly replaced by more serious symptoms.

Occasional itchy or watery eyes can occur for many reasons. But it could be something more serious, like a drug allergy.

Strange changes can be signs of a severe allergic reaction to food or drugs. You may notice sudden wheezing. Or you just feel like you can't breathe.

Rash may be itchy, painful, warm, bumpy, or blistered. They are a common result of allergic reactions to pet dander, chemicals, foods, drugs, or cosmetics.

A sudden drop in blood pressure can make you feel like you're going to pass out. The whole body may become weak or confused. this is a serious situation.

If your mouth, lips, or tongue are swollen for no apparent reason, this may be angioedema, a sign of an allergic reaction. It's not necessarily serious.

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Step-by-step explanation:

just like with every equation. we move things around by applying the same operations to both sides.

-4(y + 3) + 35 > 4(6 - y)

-4y - 12 + 35 > 24 - 4y

23 > 24

that is always false (23 is never larger than 24).

so, there is no solution.

Answer:

4.65[tex]m^{2}[/tex]

Step-by-step explanation:

the outlier is 28.4

add up all the numbers

3.7+5.2+3.8+5.5+4.2+5.5 = 27.9

divide by 6 (because there are 6 numbers)

27.9/6=4.65

Answer:

-0.5

Step-by-step explanation:

To find the middle of two numbers you can add them together then divide by two. Here you would do -7 + 6 which equals -1

The divide by 2 which equals -0.5

The number of pounds would 12 bearings weigh are 26.39615 pounds.

A ratio in mathematics represents the number of times one number contains another. For instance, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the lemon-to-orange ratio is 6:8 (or 3:4), while the orange-to-fruit ratio is 8:14. (or 4:7).

Ratios are mathematical expressions that compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula is A/B.

Machine                       Weigh

 1          --------------->    1 kg=2.20462 pounds

 7         ---------------->   15.4 pounds

 12        ---------------->   ?

If  6 machine -------- 13.19538

    5 machine ------- ?

x=(5×13.19538)/6

x=10.00615

∴ 12 machines bearings=15.4+10.99615pounds

=26.39615 pounds

The number of pounds would 12 bearings weigh are 26.39615 pounds

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Equation which represents a line that has a slope of 1/3 and passes through the point (-2,1) is:

[tex]y=\frac{1}{3} x+\frac{5}{3}[/tex]

What is the Equation of a Line?

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

Let the equation of line be y=mx+c

Where m is the slope and c is the y-intercept

⇒ m=1/3

and The line passes through (-2,1)

Putting it in the equation

[tex]\begin{aligned}&1=\frac{1}{3} \times-2+c \\&c=1+\frac{2}{3} \\&c=\frac{5}{3}\end{aligned}[/tex]

Hence,

An equation that represents a line that has a slope of 1/3 and passes through the point (-2,1) is: [tex]y=\frac{1}{3} x+\frac{5}{3}[/tex]

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The cubic polynomial can be computed using the following formula if the zeros of a cubic polynomial's product and sum are known: (x - sum of zeros) (x² + product of zeros) is a cubic polynomial.

A three-degree polynomial is referred to as a cubic polynomial. The cubic polynomial can be computed using the following formula if the zeros of a cubic polynomial's product and sum are known:

cubic function = (x - sum of zeros)

(x² + zero product)

For instance, the cubic polynomial is (x + 1)(x2 - 4) if the product of the zeros is 4 and the total of the zeros is -1.

The cubic polynomial is illustrative of:

ax³ + bx² + cx + d = 0

In the general case, where a, b, c, and d are constants.

The product of the zeros is given by: d/a ,

The zeros' sum is given by : - b/a.

These numbers are substituted into the cubic polynomial's general equation to produce the following result:

ax³ + bx² + cx + d = a(x³ + (-b/a)x² + (d/a)x)

= a(x³ - bx + d)

Therefore, if the product and sum of the zeros are known, the cubic polynomial may be obtained.

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Alexander's petrol better value for money and 30 litres of petrol cost from the cheaper petrol station  is £36.

Given:

Lois £17.40 for 12 litres of petrol Alexander £22.80 for 19 litres of petrol​.

a)

Lios money for 1 liter is:

= 17.40/12

= 1740/100/12

= 1740*1/100*12

= £1.45

Alexander money for 1 liter is:

= 22.80/19

= £1.2

From this alexander petrol better value for money.

b)

= 30 liters*alexander petrol cost for 1 liter

= 30*1.2

=  £36.

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The exclusive right to distribute, exhibit, perform, or reproduce an original work in copies, as well as the right to create derivative works based on the original work, is known as copyright. This assertion is true.

A bundle of legal privileges known as copyrights automatically belongs to everyone who produces an original work of authorship, such as a piece of literature, film, music, or software. These privileges include the ability to copy, create derivative works from, distribute, perform, and show the work in public.

The following exclusive rights belong to copyright owners exclusively, according American copyright law: Create phonorecords or duplicates of the material. Make works based on the original work. distribute copies or phonorecords of the work to the public by selling, transferring ownership, leasing, renting, or borrowing.

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Step-by-step explanation:

1)

to finish the work in 30 days, 9 workers are needed.

that means one worker can do 1/9 of the work in 30 days, and therefore 1/9 / 30 = 1/270 of the work in one day.

that means we need 270 workdays to finish the work.

to get the work done in 18 days we need therefore

270/18 = 15 workers

2)

you mention only 3 things (emergency, Tracey insurance and mutual fund) but the ratio covers 4.

what is missing ?

without that information this cannot be solved.

but this is what you do, when you find the 4th thing :

the ratio 9 : 5 : 4 : 7 tells us that the whole (P5000) is split into 9+5+4+7 = 25 parts.

each part is therefore worth 5000/25 = P200.

so, whatever is represented by 9 parts gets 9×200 = P1800.

whatever is represented by 5 parts gets 5×200 = P1000.

whatever is represented by 4 parts gets 4×200 = P800.

and whatever is represented by 7 parts gets 7×200 = P1400.

To maintain AED and its supplies;-

Given,

AED;-

When a person is having a sudden cardiac arrest, an AED, or automated external defibrillator, is used to assist them. It is an advanced but simple to use medical equipment that can analyze the heart's rhythm and, if necessary, provide an electrical shock, or defibrillation, to aid in the heart's re-establishment of an efficient rhythm.

Here,

To maintain AED and its supplies;-

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Answer:

AD is Congruent to BC and it's given, (given just means that it was already said or stated, and you don't need to do the work to find it) Angle DAC would be congruent to angle BAC (if that doesn't work, rearrange them to look like angle CAB). AC would be congruent to DB. Triangle ADC would be congruent to triangle BCD by (since i don't know exactly which way the letters are arranged is would either be SAS or SSA) and that's because you know two of the sides are congruent to each other and one angle.

I tried hard to sketch out what the shape looked like based on the information given, and that's because I need a visual of what the shape looks like. Sorry, this took so long to answer.

The blanks are filled in below and completed the proof.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

AD is congruent to BC.

AD is parallel to BC.

Now,

Since AD is parallel to BC, alternate interior angles AD and BC are congruent.

AC is congruent to AC since segments are congruent to themselves.

Along with the given information that AD is congruent to BC, triangle ADC is congruent to triangle CBA by the Side-Angle-Side Triangle Congruence theorem.

Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle DCA is congruent to angle BAC.

Since those alternate interior angles are congruent. AB must be parallel to CD.

Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, ABCD is a parallelogram.

Thus,

The blanks are filled in above.

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The linear system of equation y = -12x and 4x+2y= -8 has only one solution at 0.4,-4.8) .

The linear equation is  y = -12x and 4x+2y = -8

Now we solve the equations by substitution:

Using the value of y from the first equation and substituting in the second equation we get:

4x+2y = -8

or, 4x + 2(-12x)= -8

or, 4x -24x = -8

or, -20 x = -8

or, x = 0.4

At x=0.4 , y = -4.8

Hence solution is (0.4,-4.8) which represents the point of intersection of the two lines.

The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." Unknown variables are used as one or more variables in linear equations to model real-world issues.

The solutions are the points at which the lines or planes used to describe the linear equations intersect or meet. The set of values for each variable in a system of linear equations is known as the solution set.

Disclaimer: the complete question is :

How many solutions does this linear system have y = -12x and 4x+2y= -8 have?

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The fraction that is greater than 3/4 is B. 10/12

It should be noted that a fraction has a numerator and denominator and is expressed as a/b..

It should be noted that 5/8 in percentage will be:

= 5/8 × 100

= 62.5%

10/12 will be:

= 10/12 × 100

= 83.3%

7/16 will be:

= 7/16 × 100

= 700/16

= 43.75%

Therefore, the fraction greater is 10/12.

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The required three additional points that the line have slope (-7, -7) and m=2 passes through are (0,7), (2,11) and (1,9).

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

we are given with the point (-7,-7) and m = 2(which is not given in this question so this question is incomplete)

now

first construct a linear equation using point(-7,-7) and m=2

(y−y1)=m(x−x1)

and we have

x1=-7, y1=-7

(y+7)=2(x+7)

(y+7)=2x+14

y=2x+7

Now, we can substitute values for x and y to find 3 additional points that lie on this line.

and after drawing graph we'll get the points:

(0,7), (2,11) and (1,9)

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The output of the function when input is -3 is 3.

A function relates each element of a set with exactly one element of another set (possibly the same set).

In a simpler term function relates input and output.

The inputs or the independent variables are on the x axis while the output or dependent variable of a function is on the y-axis.

Therefore, let's trace the y output value for an input value of -3.

Therefore, the output function when input is -3 is 3.

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The  expression whose value is twice the value of the element in the 3rd row and the 2nd column will be x [2][1] × 2

Given,

In the question:

A two-dimensional array x of doubles

Write an expression whose value is twice the value of the element in the 3rd row and the 2nd column.

Now, According to the question:

A two-dimensional array x of doubles

The value of the element in the 3rd row and the 2nd column.

Also, Value is twice of an element.

The expression will be :

=> x [2][1] × 2

Hence, The  expression whose value is twice the value of the element in the 3rd row and the 2nd column will be x [2][1] × 2

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The graph of the function is given in attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is f(x) = x² + 3

f of x equal to x square plus three

f(x) = x² + 3

y= x² + 3

Select a few x values, and plug them into the equation to find the corresponding  y values.

x       0      1       2       3       4

y        3      4      7      12      19

Hence, the graph of the function is given in attachment.

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Examples of complex fraction are [tex]\frac{\frac{1}{4}}{\frac{3}{8}}[/tex], [tex]\frac{\frac{1}{3}}{9}[/tex], [tex]\frac{4}{\frac{2}{5}}[/tex] etc.

The first and most common way to represent a fraction is with [tex]\frac{a}{b}[/tex]

Where 'a' is the numerator and 'b' is the denominator.. A horizontal bar separates the numerator and denominator.

A complex fraction is one that contains fractions in the numerator, denominator, or both.

some examples of complex fractions are:

[tex]\frac{\frac{1}{4}}{\frac{3}{8}}[/tex] , [tex]\frac{\frac{1}{3}}{9}[/tex] , [tex]\frac{4}{\frac{2}{5}}[/tex] etc.

Thus, an example of complex fraction is [tex]\frac{4}{\frac{2}{5}}[/tex].

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(a) The number of people expected to have blood type O+ among 40 randomly selected people  is 14 .

(b) the standard deviation of number of people who have blood type O+ among 40 people is 3.0166 .

In the question ,

it is given that ,

probability that the person has blood group of type O+ is (p) = 0.35

the number of people randomly selected is (n) = 40 people ,

So , Number of people expected to have blood type O+ among 40 randomly selected people = Mean of the binomial distribution .

= n × p

= 40 × 0.35
= 14

So ,The standard deviation of the number of people expected to have blood type O+ among 40 randomly selected people = √(n × p × q)

= √(40 × 0.35 × (1-0.35))

= √(40 × 0.35 × 0.65)

= 3.0166

Therefore , (a) The number of people expected to have blood type O+ among 40 randomly selected people  is 14 .

(b) the standard deviation of number of people who have blood type O+ among 40 people is 3.0166 .

The given question  is incomplete , the complete question is

If the probability that a person has blood type O+ is 0.35 and you have 40 randomly selected people ,

(a) About how many would you expect to have blood type O+ ?

(b) What is the standard deviation of the number of people who would have blood type O+ among the 40 people ?

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For the non negative number, the first number of rows of pascal's triangle is attached below.

Non negative number:

Non negative number means the number which is either zero or a positive number.

Given,

Here we have a non-negative integer number of rows, And we have to generate the first number of rows of pascal's triangle And in pascal's triangle, each number is the sum of the two numbers directly above it.

Before make the pascal's triangle,

We know that the given condition is each number is the sum of the two numbers directly above it.

Based on these condition, we have plotted the following pascal's triangle.

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Answer:

x= [tex]5\frac{1}{7} or \frac{36}{7}[/tex]

y=7

Step-by-step explanation:

we use comparing fractions for this since we know the bottom sides for both triangles we will use that

4/7=x/9

cross multiply

4(9)=7x

36=7x

/7.  /7

36/7=x

5 1/7=x

now to find y we do same thing

4/7=4/y

cross multiply

4y=7(4)

4y=28

/4.  /4

y=7

hopes this helps please mark brainliest