Given that f(x)=x+4 and g (x)=3x/x+1 (1) determine the value of f(9)​

By using the concept of function, it can be calculated that

[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, the function is

[tex]f(x) = 2x + \frac{4}{3}\\[/tex]

Let f(x) = y

[tex]2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\[/tex]

6x + 4 = 3y

6x = 3y - 4

[tex]x = \frac{3y - 4}{6}[/tex]

[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]

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The partial fraction form of the given fraction [x+5/(x-7)(x-5)] is

[A/(x-7)+B/(x-5)].

So, the fraction is:

We know that:

Use the same identity to get the partial fraction of the given fraction as follows:

Therefore, the partial fraction form of the given fraction [x+5/(x-7)(x-5)] is [A/(x-7) + B/(x-5)].

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The Total Probability is 4/663 and 35/2652

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. An event's probability is a number between 0 and 1.

Solution:

We know that there are 52 cards in a deck of cards.

So, probability of getting a king = 4/52 = 1/13

And probability of getting a 7 after drawing a king is 4/51,

this is because one card is drawn out from the deck and there are only 51 cards left in the deck.

Total Probability = 1*4/13*51 = 4/663

In the secon case, there are two possibilities,

It can be the kling drawn might be of spade or not

Case 1: When King drawn is of Spade

Probaility of drawing a King of Spade = 1/52

Probability of drawing a Spade after King of Spade is drawn = 11/51

Total Probaility = 1*11/52*51 = 11/2652

Case 2: When King drawn is not of Spade

Probability of drawing a King not of Spade = 2/52

Probability of drawing a Spade after drawing the King = 12/51

Total Probability = 2*12/51*52 = 24/2652

Total Probability of drawing a king and spade = 11/2652 + 24/2652 = 35/2652

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The passage of journal entries to record the transactions, using the perpetual system of inventory with the First-in, First-out (FIFO) method, is as follows:

Account Titles                                 Debit        Credit

Inventory                                     $300,000

Accounts Payable (Indiana International) $300,000

Accounts Receivable

(Ceridian Corporation)            $100,000

Sales Revenue                                           $100,000

Cost of goods sold                   $60,000

Inventory                                                    $60,000

Cash                                       $275,000

Sales Revenue                                        $275,000

Cost of goods sold               $150,000

Inventory                                                 $150,000

Accounts Payable

(Indiana International)       $300,000

Cash                                                       $300,000

Inventory                            $360,000

Cash                                                      $360,000

Cash                                     $60,000

Sales Revenue                                     $60,000

Cost of goods sold            $30,000

Inventory                                              $30,000

Inventory $300,000 Accounts Payable (Indiana International) $300,000

Accounts Receivable (Ceridian Corporation) $100,000 Sales Revenue $100,000

Cost of goods sold $60,000 Inventory $60,000

Cash $275,000 Sales Revenue $275,000

Cost of goods sold $150,000 Inventory $150,000

Accounts Payable (Indiana International) $300,000 Cash $300,000

Inventory $360,000 Cash $360,000

Cash $60,000 Sales Revenue $60,000

Cost of goods sold $30,000 Inventory $30,000

Thus, with the perpetual system using FIFO, inventory movements are recorded in the Inventory account as they occur and not at the period's end.

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Answer:

depends on how many sections there are

Step-by-step explanation:

if there were 2 then it would be one foot 4 sections equal 2 and so on. the ratio for this 2:1 meaning there has to be 2 sections for there to be one foot.

89.81% of 2.16 million is 1.94 million.

In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. After dividing a number by its whole, multiply it by 100 to determine its percentage. As a result, the percentage refers to a component per 100. The word "percent" denotes a percentage of 100.

To calculate a group's share of the total in terms of 100, use the percentage formula. Using this method, you may represent a number as a fraction of 100. You'll see that the approach below may be used to rapidly calculate each of the the percentages:

(Value/Total Value) x 100 = %

According to the question,

(x/100) 2.16 = 1.94

x = 1.94 (100)/ 2.16

x = 194/ 2.16

x = 89.81 %

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[tex]{ \pink{ \boxed{ \red{ \sf{f(4) = - 7}}}}}[/tex]

Step-by-step explanation:

[tex]{ \green{ \sf{f(x) = { - x}^{3} + 3 {x}^{2} + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = ( { - 4})^{3} + 3( {4})^{2} + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = - 64 + 3(16) + 9}}}[/tex]

[tex]{ \green{ \sf{ f(4) = - 64 + 48 + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = - 64 + 57}}}[/tex]

[tex]{ \blue{ \boxed{ \orange{ \sf{f(4) = - 7}}}}}[/tex]

The two numbers that are compatible are 0.25 and 8. The property which helps to calculate it is commutative property.

What is the commutative property?

This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution.

Given numerical expression is (0.25 x 12.3) x 8.

First remove the parenthesis from the numerical expression:

(0.25 x 12.3) x 8 = 0.25 x 12.3 x 8

Now apply commutative property:

(0.25 x 12.3) x 8 = (0.25 x 8) x 12.3

(0.25 x 12.3) x 8 = 2.00 x 12.3

(0.25 x 12.3) x 8 = 24.6

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Answer:

b=3x+y

Step-by-step explanation:

y=-3x+b

get b by itself on one side

y+3x=b

The rearranged equation, [tex]b = Y + 3x[/tex], allows us to determine the value of b based on the given values of Y and x.

Rearranging an equation involves manipulating the terms and variables in order to isolate a specific variable or simplify the equation. The goal is to rewrite the equation in a different form while maintaining equality.

In the context of solving the equation [tex]Y = -3x + b[/tex] for b, rearranging the equation means moving the terms around so that b is isolated on one side of the equation. This is done by performing inverse operations on the equation.

Starting with [tex]Y = -3x + b[/tex], we want to isolate b. To do this, we need to move the [tex]-3x[/tex] term to the other side of the equation.

By subtracting [tex]-3x[/tex] from both sides, we can eliminate the -3x term on the right-hand side. The equation becomes [tex]Y - (-3x) = b[/tex].

Simplifying further, [tex]Y + 3x = b[/tex]. Now, b is isolated on one side of the equation.

Therefore, the rearranged equation, [tex]b = Y + 3x[/tex], allows us to determine the value of b based on the given values of Y and x.

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The expression (2/3)² when simplified by repeated multiplication is 4/9

From the question. the expression is given as

(2/3)²

We start by rewriting the expression using repeated multiplication

This in other words means that:

We rewrite the (2/3)² as repeated multiplication

To do this, we apply the exponent rule of indices

This rule states that:

a^m = a * a * a .... in m places

So, we have

(2/3)² = (2/3) x (2/3)

Evaluate the products

(2/3)² = 4/9

Hence, the equivalent expression is 4/9

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Answer: 25.949%

Step-by-step explanation:

Answer:

Step-by-step explanation:

1

y-6 = -2/5(x-(-5)
y - 6 = -2/5(x+5)

y -6 = -2/5 x -2

y = -2/5 x -2 + 6

y = -2/5 x + 4

2

y-6 = 5/2 (x-(-5)

y-6 = 5/2 (x+5)

y - 6 = 5/2 x + 25/2

y = 5/2 x + 25/2 + 6

y = 5/2 x  + (25+12)/2

y = 5/2 x + 37/2

If a person deposits $8,000 into a savings account at 6.5% interest compounded quarterly for 12 years, the balance (future value) will be $17,342.70.

The future value is the compounded present value of an investment for a future period.

The future value can be computed using the FV formula, table, or an online finance calculator as below.

N (# of periods) = 48 quarters (12 years x 4)

I/Y (Interest per year) = 6.5%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $17,342.70

Total Interest = $9,342.70

Thus, the future value of a present investment of $8,000 at 6.5% interest compounded quarterly for 12 years is $17,342.70.

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Answer:

557.143

Step-by-step explanation:

195 / 35% = 557.14

Answer: 0.5

Step-by-step explanation:

1.45*0.34 = 0.493

Rounded to the tenth place is 0.5

The probability that George will win is 1/10 and the probability that Julia will win is 1/20.

So, calculate the probability as follows:

We know,

(A) George's probability of winning:

(B) Julia's probability of winning:

Therefore, the probability that George will win is 1/10 and the probability that Julia will win is 1/20.

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Answer:

No value of a will work.

Step-by-step explanation:

let me explain,

given values of a are1,2,3

checking these values of a ,

(1)³=125

1=125 (not true)

(2)³=125

8=125 (not true)

(3)³=125

27=125 (not true)

the correct value of a which makes this equation true is 5. let me make you clear,

(5)³=125

125=125 (true).

The solution to the given inequality 3 - x ≤ 19

or - x ≥ 24 is x ≥ -16 or x ≤ -24

An inequality is a statement that is of two quantities; one is specifically less than or greater than another. Inequality symbols are:

3 - x ≤ 19

or

- x ≥ 24

3 - x ≤ 19

-x ≤ 19 - 3

- x ≤ 16

divide both sides by -1

x ≤ 16/-1

x ≥ -16

or

- x ≥ 24

x ≥ 24/-1

x ≤ -24

In conclusion, the solution to the inequality is given by x ≥ -16 or x ≤ -24

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The triangle in option (a) is an equilateral triangle in option (b) is isosceles and the triangle in option (c) is a scalene triangle.

A triangle is a 3-sided shape occasionally referred to as a triangle. Every triangle has three sides and three angles, some of which may be the same.

An equilateral triangle is a triangle whose all sides are equal.

As below the triangle in option (a) with the purple marks has all sides are same thus it will be equilateral.

An isosceles triangle is a triangle whose two sides are the same.

In option (b) triangle the (blue marked) has two equal sides thus it will be isosceles.

A scalene triangle is a triangle with all unequal lengths in option (c) (green mark) all sides are unequal.

Hence "The triangle in option (a) is an equilateral triangle in option (b) is isosceles and the triangle in option (c) is a scalene triangle".

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The polynomial in standard form is equal to 2 · x³ + 12 · x² - 64.

Cubic equations have three roots. In this problem we need to derive a cubic equations whose three real roots (r₁, r₂, r₃) and leading coefficient (a) are given. The procedure consists in substituting on factor form of a cubic polynomial and expanding the resulting expression until standard form is obtained.

First, substitute on the factor form of the cubic equation:

y = 2 · (x - 2) · (x + 4)²

Second, expand the polynomial until its standard form is found:

y = 2 · (x - 2) · (x² + 8 · x + 16)

y = 2 · (x³ + 8 · x² + 16 · x - 2 · x² - 16 · x - 32)

y = 2 · (x³ + 6 · x² - 32)

y = 2 · x³ + 12 · x² - 64

The polynomial is equivalent to 2 · x³ + 12 · x² - 64.

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The number of children in the school who speak a language other than English at home is 144.

The fraction of children who speak Polish is 1/6.

Percentage is the ratio of a quantity expressed as a number out of 100. Percentage is a measure of frequency. The sign that is used to represent percentage is %.

Number of children in the school who speak a language other than English at home = Percentage of the students who speak a language other than English x number of children

Number of children in the school who speak a language other than English at home = 45% x 320

Number of children in the school who speak a language other than English at home = 0.45 x 320 = 144

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

Fraction of the students who speak Polish = number of students that speak Polish / total number of students who speak a language other than English.

Fraction of the students who speak Polish = 24 / 144 = 1/6.

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The required sketch graph of given straight line is shown below in the image.

The general equation of line is written as Y = mx + c where, m is the gradient of straight line, c is the point where the line cut y-axis.

we have, line y = x - 1

So, slope of line is 1 and y-intercept is -1

Thus,required graph of straight line is

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The speed of the aircraft is 682 mph

Given that: A speed of 60 mph is equal to 88 ft/sec

If an aircraft travels at a speed of 1000 ft/sec, the speed to the nearest mile per hour can be calculated by using the unit  ratio of

of mph to ft/s, that is:

60/88 = m/1000

m = 6x1000/ 88 = 60000/88 = 682 mph

Therefore, the speed of the aircraft to the nearest mile per hour is 682 mph

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⇒[tex]3x^{2} -13x-10\\=3x^{2} -15x+2x-10\\=(3x^{2} -15x)+(2x-10)\\=3x(x-5)+2(x-5)\\=(x-5)(3x+2)[/tex]

⇒The answer is  (x-5)(3x+2)

With the help of substitution the answer to the equation is - (-9/2 , 5/2)

acc to our question -

Hence,The solution to the equation is (-9/2, 5/2) using substitution.

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With 95% confidence, the margin of error is 19.523, population mean is (253.477, 292.523) and the change in cost over the two-year period is 19.21%.

In the given question,

The average cost per night of a hotel room in New York City(y) = $273

Number of rooms in hotel(n) = 45.

The sample standard deviation(s) = $65

(a.) Now finding the margin of error, with 95%(0.95) confidence.

The formula of margin of error is

ME= [tex]z_{\alpha /2}\times \frac{s}{\sqrt n}[/tex]

Now find the value of [tex]z_{\alpha /2}[/tex].

[tex]\alpha[/tex] = 1-0.95

[tex]\alpha[/tex] = 0.05

[tex]\alpha[/tex]/2 = 0.05/2

[tex]\alpha[/tex]/2 = 0.025

Now the value of [tex]z_{\alpha /2}[/tex]

[tex]z_{\alpha /2}=z_{0.025}[/tex]

From the standard table of z is 2.015.

Now putting the value in formula

ME= 2.015 × 65/√45

ME= 2.015 × 65/6.708

ME= 2.015 × 9.689

ME= 19.523

Hence, with 95% confidence, the margin of error is 19.523.

(b) Now finding .the 95% confidence interval estimate of the population mean.

Population Mean = y ± ME

Population Mean = 273 ± 19.523

Population Mean = {(273-19.523), (273+19.523)}

Population Mean = (253.477, 292.523)

(c) Now two years ago the average cost of a hotel room in New York City was $229 then the change in cost over the two-year period is

The change in cost = difference between the cost/old cost

The change in cost = (273-229)/229 *100

The change in cost = 44/229 *100

The change in cost = 0.1921 *100

The change in cost = 19.21%

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Answer:

Can't be written as fraction

Step-by-step explanation:

Irrational Numbers are Real Numbers which are not rational , which means that it can't be written as fraction

Answer:

x³ - 8

Step-by-step explanation: