We can describe 3x - 2 as an expression. How can we describe the parts of the expression that the arrows point to? 3x - 2​

[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }.[/tex]

[tex]f(x)=2x+\frac{3}{5} \\ \\[/tex]

[tex]y=2x+\frac{3}{5} \\ \\[/tex]

[tex]x=2y+\frac{3}{5} \\ \\[/tex]

[tex]x-\frac{3}{5} =2y+\frac{3}{5} -\frac{3}{5} \\\\x-\frac{3}{5} =2y[/tex]

[tex]\frac{x-\frac{3}{5}}{2} =\frac{2y}{2} \\ \\\frac{x-\frac{3}{5}}{2} =y[/tex]

[tex]y =\frac{x-\frac{3}{5}}{2}[/tex]

[tex]y =\frac{x}{2} -\frac{\frac{3}{5} }{2}[/tex]

[tex]y =\frac{x}{2} -\frac{3}{5} }*\frac{1}{2} \\ \\y =\frac{x}{2} -\frac{3*1}{5*2} }\\ \\y =\frac{x}{2} -\frac{3}{10} }[/tex]

[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }[/tex].

To verify if this is the correct expression for the inverse of the function, simply see if the "x" values and "y" values of the function are inverses as well. For example, a value of x = 2 returns 4.6 on the original function. Therefore, the inverse function should return 2 when a value of x = 4.6 is used. Check the attached image to see this comparison using the table of values of the original function and it's inverse.

Hello and greetings KingDanny2xx.

Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.

 [tex]\boldsymbol{\sf{f(x)=2x+\dfrac{3}{5} }}[/tex]

We substitute f(x) for y.

          [tex]\boldsymbol{\sf{y=2x+\dfrac{3}{5} }}[/tex]

We interchange x and y.

       [tex]\boldsymbol{\sf{x=2y+\dfrac{3}{5} }}[/tex]

We interchange the sides of the equation. We want to swap sides because mathematicians agreed to the convention that the unknown variable in equations and inequalities must always be on the left-hand side.

If there is a variable on both sides, we do it to facilitate a later calculation.

        [tex]\boldsymbol{\sf{2y+\dfrac{3}{5}=x }}[/tex]

We multiply both sides of the equation by 5. We want to multiply an equation to get rid of fractions and/or rational expressions, doing a lot more calculations later.

Both sides of the equation must be multiplied by the same value to preserve equality between all sides, according to the Multiplication Property of Equality.

        [tex]\boldsymbol{\sf{5\left(2y+\dfrac{3}{5}\right)=5x }}[/tex]

We distribute the 5 to the terms in parentheses. The distributive property is that each term in an expression between parentheses is multiplied by the expression outside the parentheses.

          [tex]\boldsymbol{\sf{5x2y+5x\dfrac{3}{5} =5x}}[/tex]

We calculate the product.

            [tex]\boldsymbol{\sf{10y+\not{5}x\dfrac{3}{\not{5}}=5x }}[/tex]

We cancel the greatest common divisor 5.

            [tex]\boldsymbol{\sf{10y+3=5x}}[/tex]

We move the constant to the right side and change its sign. We want to move a constant to the right because it is customary for constants in equations to be on the right hand side.

The sign of the constant must be changed because in the process of "moving the constant", we are adding its opposite to both sides.

We move the constant to the right by adding its opposite to both sides.

     [tex]\boldsymbol{\sf{10y+3-3=5x-3}}[/tex]

Since two opposite numbers add up to 0, we remove them from the expression. The additive inverse property states that two opposite numbers add up to 0.

Since adding or subtracting 0 doesn't change the value of the expression, we can simply remove them.

      [tex]\boldsymbol{\sf{10y=5x-3}}[/tex]

We divide both sides of the equation by 10. We want to divide an equation to isolate the unknown variable on one side or to transform the equation in a certain way.

Both sides of the equation must be divided by the same number to preserve equality between the sides, according to the Division Property of Equality.

         [tex]\boldsymbol{\sf{10y\div10=(5x-3)\div10}}[/tex]

Any equation divided by itself is equal to 1.

         [tex]\boldsymbol{\sf{y=(5x-3)\div10}}[/tex]

We distribute the 10 to the terms in parentheses. The distributive property is that each term of an expression between the parentheses is multiplied by the expression that is outside the parentheses.

        [tex]\boldsymbol{\sf{y=5x\div10-3\div10 }}[/tex]

We write the division as a fraction. A fraction is another way of writing division.

One more way to remember it is the division symbol.

We notice that the division symbol looks like a fraction where the dots represent the numerator and denominator.

         [tex]\boldsymbol{\sf{y=\dfrac{5}{10}x-3\div10 \iff y=\dfrac{\not{5}}{\not{10}}x-\dfrac{3}{10} }}[/tex]

We divide by the common factor 5. The object of canceling a common factor is to rewrite a fraction in the simplest form to facilitate a later calculation.

We can cancel a common factor because it will still represent the same value.

         [tex]\boldsymbol{\sf{y=\dfrac{1}{2}x-\dfrac{3}{10} }}[/tex]

Substitute y for f⁻¹ (x). Substitution means to replace one algebraic expression with another or with a specific value.

         [tex]\boldsymbol{\sf{f^{-1}(x)=\dfrac{x}{2}-\dfrac{3}{10} }}[/tex]

Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.

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Therefore , the solution of the given problem of area comes out to be  a.720 sq. ft, b.$227.94 , c.64,800 BTUs. and d.2,592 sq in.

Calculating how much space would be needed to fully enclose its exterior will reveal its overall size. The neighboring area is considered when selecting a comparable good for the rectangular design. The surface area of something determines its overall measurements. The number of sides between a cuboid's four trapezoidal shapes determines how much water it can hold.

Here,

A.

=>  2(144 sq. ft.) + 2(162 sq. ft.) =  720 sq. ft.

b.

16 *  18 = 288 square feet

The entire region that needs painting is:

=> 720 square feet +  288 square feet = 1008 square feet.

We need to apply two layers of paint to the following surface area:

=>  2 * 1008 square feet =  2016 square feet.

5.04 gallons are obtained by multiplying 2016 square feet by 400 square feet per gallon.

=> $6 liters* $37.99/gallon = $227.94

c. 16 feet by 18 feet by 9 feet equals 2,592 cubic feet

As a result, the room's necessary cooling capacity is:

=> 2,592 cubic feet*25 BTUs per cubic foot =  64,800 BTUs.

Rounding up to the next greatest thousand BTUs, we need an air conditioner with a capacity of 65,000 BTUs.

d.

=> 16 ft x 144 sq in/ft = 2,304 sq in by

=>  18 ft x 144 sq in/ft = 2,592 sq in

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Opens down with a vertex at (3, −8)

Term οr phrase used tο describe the factοrs Geοrge is "quality οf life."

In grammar, a phrase—called expressiοn in sοme cοntexts—is a grοup οf wοrds οr singular wοrd acting as a grammatical unit. Fοr instance, the English expressiοn "the very happy squirrel" is a nοun phrase which cοntains the adjective phrase "very happy".

Phrases can cοnsist οf a single wοrd οr a cοmplete sentence. In theοretical linguistics, phrases are οften analysed as units οf syntactic structure such as a cοnstituent. An adjective phrase is a phrase that mοdifies (explains) a nοun.

The term used tο describe the factοrs Geοrge is cοnsidering is "quality οf life."

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Juan paid Rs. 4.35 for the grapes. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, frequently referred to as "arithmetic operations," are claimed to be able to explain all real numbers. The four mathematical operations that come after division, multiplication, addition, and subtraction are quotient, product, sum, and difference.

We are given that Juan bought 24 ounces of grapes and the grapes cost 2.90 per pound.

We know that 1 pound = 16 ounces.

So, 24 ounces = 1.5 pounds

Now, using multiplication operation, we get

⇒ 1.5 * 2.9 = Rs. 4.35

Hence, Juan paid Rs. 4.35 for the grapes.

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There would be $2203.50 in Stony's account by September 2020 using simple interest formula.

As the bank charges an annual 8% simple interest, we may apply the following formula:

Simple interest is calculated as follows: Principle is the initial investment, Rate is the annual interest rate, and Time is the duration in years.

Here, the principal (P) is $1575, the interest rate (r) is 8%, and the time (t) is 5 since we need to know how much money Stony will have in his account by September 2020, which is five years from now.

We may calculate Stony's interest earnings over a five-year period using the simple interest formula:

Interest is calculated as follows: $1575 x 0.08 x 5 = $628.50

Stony's account will therefore have the following balance by September 2020: Total Amount = Principal + Interest = $1575 + $628.50 = $2203.50

Therefore by September 2020, Stony would have $2203.50 in his account.

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This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get , x ≈ 1.29

Tο sοlve linear equatiοns with fractiοns, we need tο multiply bοth sides οf the equatiοn by the least cοmmοn multiple (LCM) οf all the denοminatοrs tο eliminate the fractiοns¹.

When an equatiοn invοlves fractiοns οn bοth sides, multiply each side by the denοminatοrs' lοwest cοmmοn multiple (LCM).

The LCM οf 4 and 3 is 12. Multiplying bοth sides by 12, we get:

12(x - (3x-2)/4) = 12((6-5x)/3)

Simplifying, we get:

12x - 3(3x-2) = 4(6-5x)

Expanding and cοllecting like terms, we get:

-6x + 6 = -20x + 24

Adding 20x tο bοth sides, we get:

14x + 6 = 24

Subtracting 6 frοm bοth sides, we get:

14x = <cοde>**18**</cοde>

Dividing bοth sides by <cοde>**14**</cοde>, we get:

<cοde>**x = 18/14**</cοde>

This is an imprοper fractiοn. Tο simplify it, we divide the numeratοr by the denοminatοr and get:

<cοde>**x = <u>9</u>/<u>7</u>**</cοde>

This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get:

x ≈ 1.29

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Answer:

49

Step-by-step explanation:

P: Parenthesis

E: Exponent

M: Multiplication

D: Division

A: Addition

S: Subtraction

Start by solving what is inside the parenthesis first:

Next, solve for the exponent:

7² (which means 7 multiplied by itself twice)

Now you can multiply 49 and 4:

49 × 4 = 196

Finally, divide 196 by 4:

196 ÷ 4 = 49

Therefore, the answer to the expression 7² (4) ÷ 4 is 49.

Answer:

To find the perimeter of the quadrilateral, we need to find the distance between its vertices and then add them up. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the distance between each pair of adjacent vertices:

Distance between (-3, 1) and (2, 1):

d = sqrt((2 - (-3))^2 + (1 - 1)^2) = sqrt(25) = 5

Distance between (2, 1) and (2, -2):

d = sqrt((2 - 2)^2 + (-2 - 1)^2) = sqrt(9) = 3

Distance between (2, -2) and (-3, -2):

d = sqrt((-3 - 2)^2 + (-2 - (-2))^2) = sqrt(25) = 5

Distance between (-3, -2) and (-3, 1):

d = sqrt((-3 - (-3))^2 + (1 - (-2))^2) = sqrt(9) = 3

Now we can add up these distances to get the perimeter:

perimeter = 5 + 3 + 5 + 3 = 16

Therefore, the perimeter of the quadrilateral is 16 units.

Note that in the above Theoretical Probability prompt, the P(A, D) if two cards are randomly selected with replacement is 2/9. (Option C)

Theoretical probability is a branch of mathematics that deals with predicting the likelihood of events based on mathematical reasoning and assumptions, rather than empirical evidence or observations.

Where it is required to determine the P(A, D) if two cards are randomly selected from cards (A,D,D) with replacement:

P (A) = 1/3

P (D) = 2/3


Thus, P (A, D) = 1/3 * 2/3

= 1/3 × 2/3

= (1×2) / (3×3)

= 2/9

Thus, it is correct to state that the probability, if two cards A, and D are randomly selected with replacement is 2/9. (Option C)

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Answer:

the bottle will last approximately 12.5 days if the patient takes 2 teaspoons (10 mL) of Mucinex 4 times a day as ordered.

Step-by-step explanation:

Assuming that one teaspoon is equivalent to 5 milliliters (mL), then 2 teaspoons would be 10 mL. Therefore, the patient will be taking a total of 10 mL four times a day, which is 40 mL per day.

Since the bottle contains 500 mL, we can calculate how long the bottle will last by dividing the total volume of the bottle by the daily dose:

Number of days = Total volume of bottle / Daily dose

Number of days = 500 mL / 40 mL per day

Number of days = 12.5 days

Therefore, the bottle will last approximately 12.5 days if the patient takes 2 teaspoons (10 mL) of Mucinex 4 times a day as ordered.

Answer:

3 final songs

Step-by-step explanation:

Answer: There will be 3 songs on the final CD.

Step-by-step explanation: The band expects to put 12 songs on their next CD. They write and record 25% more songs than they expect, which means they wrote and recorded 12 + (0.25 x 12) = 15 songs. During the editing process, 80% of the songs are removed. 80% of 15 is (0.80 x 15) = 12 songs. Subtracting the removed songs from the recorded songs, we get 15 - 12 = 3 songs that will be on the final CD. Therefore, there will be 3 songs on the final CD.

Answer:

(1) 63 odd - and - 28 even

(2) 49 odd - and - 76 even

Step-by-step explanation:

Answer: d is the answer

Step-by-step explanation: because if you do your math correctly it comes out to be 21/24

Step 1: To convert 1.33 repeating into a fraction, begin writing this simple equation:

n = 1.33 (equation 1)

Step 2: Notice that there are 2 digitss in the repeating block (33), so multiply both sides by 1 followed by 2 zeros, i.e., by 100.

100 × n = 133.333 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

100 × n = 133.333

 1 × n = 1.33

99 × n = 132

132

99

could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 33 (the GCF - greatest common factor).

n = 132

99

= 132 ÷ 33

99 ÷ 33

= 4

3

. So, 1.33 = 4/3

as the lowest possible fraction.

The probability that out of 8 workers, 3 will ride in carpools is 0.254.

What is probability?

The mathematical concept of probability is used to determine the likelihood of an event. It is solely useful for calculating the probability that an event will occur. From 0 to 1, where 0 represents impossibility and 1 represents a particular occurrence.

We are given that 30% of all commuters ride to work in carpools.

Now, if eight workers are selected, then the probability that three will ride in carpools is determined by using the following

P (X = 3) = [tex]n C_{x} p^{x} (1-p)^{(n-x)}[/tex]

We have n = 8, x = 3 and p = 0.3

So, using the formula, we get

⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (1-0.3)^{(8-3)}[/tex]

⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (0.7)^{(5)}[/tex]

⇒P (X = 3) = 56 *  [tex](0.3)^{3} (0.7)^{(5)}[/tex]

⇒P (X = 3) = 56 * 0.027 * 0.16807

⇒P (X = 3) = 0.254

Hence, the probability that out of 8 workers, 3 will ride in carpools is 0.254.

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The domain and the range of the relations are

What is domain?

In mathematics, the domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

In other words, the domain of a function is the set of values that can be plugged into the function and produce a valid output.

What is range?

In mathematics, the range of a function refers to the set of all possible output values (also known as the dependent variable) that the function can produce for a given input value from its domain.

In other words, the range of a function is the set of values that the function takes on as its input variable varies over its domain.

Using the above definitions, we have the domain and the range of the relations to be:

Graph 9:

Domain = [0, 6]

Range = [-3, 3]

Relation = Yes

Function = No

Graph 10:

Domain = (-∝, ∝)

Range = (-∝, ∝)

Relation = Yes

Function = Yes

Graph 11:

Domain = (-∝, ∝)

Range = [0, ∝)

Relation = Yes

Function = Yes

Graph 12:

Domain = [-3, 3]

Range = [-4, 4]

Relation = Yes

Function = No

Graph 13:

Domain = (-∝, ∝)

Range = [-2, 4]

Relation = Yes

Function = Yes

Graph 13:

Domain = (-∝, ∝)

Range: y = 1

Relation = Yes

Function = No

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actually, there are a total of "x" classrooms, which oddly enough is the 100%,  and we also know that 35% of that is 49, so

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 49& 35 \end{array} \implies \cfrac{x}{49}~~=~~\cfrac{100}{35} \\\\\\ \cfrac{ x }{ 49 } ~~=~~ \cfrac{ 20 }{ 7 }\implies 7x=980\implies x=\cfrac{980}{7}\implies x=140[/tex]

Therefore , the solution of the given problem of probability comes out to be the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.

The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.

Here,

The z-value for a chance of 0.20 in the right tail of the distribution can be found using a calculator or a standard normal distribution table.

The probability number in the right tail that is

=> closest to 0.20 using a standard normal distribution table is 0.1995.

This probability's equivalent z-value is roughly 0.84.

As an alternative, we can calculate the z-value using a computer. With a chance of 0.20, a mean of 0, and a standard deviation of 1, and the inverse normal function—also known as the normal quantile function—we obtain:

=> Z=invNorm(0.20) 0.84

As a result, the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.

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We have been given the function We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.

Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.

Therefore, the range of the function is given by y>0B is the correct option.

Answer:

Hope this helps

Step-by-step explanation:

the activity or occupation of keeping records of the financial affairs of a business.

Im not sure which bookkeeping you mean but bookkeeping focuses on recording and organising financial data.

Step-by-step explanation:

the 2 angles are supplementary. that means together they have 180°

4x + 29 = 180 - (12x + 55) = 180 - 12x - 55 = 125 - 12x

16x = 96

x = 96/16 = 6

Answer:

(a) Let X be the number of boxes that do not have any balls. We can calculate the probability that a particular box is empty, which is (1-p)^10, where p is the probability that a ball is put into that box. The expected number of boxes that are empty is then:

E(X) = 5(1-p)^10 (since each box has the same probability of being empty)

Substituting ∑(i = 1 to 5) p = 1, we get p = 1/5. Therefore,

E(X) = 5(1-1/5)^10 = 5(4/5)^10 ≈ 0.328

So, the expected number of boxes that do not have any balls is approximately 0.328.

(b) Let Y be the number of boxes that have exactly one ball. The probability that a particular box has exactly one ball is given by:

P(exactly one ball in a box) = 10p(1-p)^4

where p is the probability that a ball is put into that box. The expected number of boxes that have exactly one ball is then:

E(Y) = 5(10p(1-p)^4)

Substituting p = 1/5, we get:

E(Y) = 5(10/5^5) = 1/25

So, the expected number of boxes that have exactly one ball is 1/25.

Miguel has to put up the equation r = 72/16.

4.5% is the interest rate.

For calculating how long it would take for an investment to double in value, the rule of 72 is utilised. To get the doubling time, divide 72 by the interest rate.

To use the rule of 72, you simply divide the number 72 by the annual interest rate. For example, if the interest rate is 6%, the rule of 72 predicts that it will take approximately 12 years (72 ÷ 6 = 12) for the investment to double in value.

Part2:

equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires is n = 72 / r

Part3:

annual interest rate does Miguel need to double his money by the time he retire

r = 72 / n

72 / 16 = 4.5%

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Therefore, Kami has 9 different choices for her new shoe purchase, as listed above.

A mathematical equation is an expression that describes the relationship between two other expressions and is expressed as an equality on both sides of the equal to sign. The equation 3y = 16 is an illustration.

Kami has 3 choices for the color of her shoes and 3 choices for the type of heel, so the total number of possible shoe combinations is:

3 colors × 3 types of heels = 9 shoe combinations

The list of all possible choices for Kami's new shoe purchase is:

1.Black flat

2.Black small heel

3.Black high heel

4.White flat

5.White small heel

6.White high heel

7.Red flat

8.Red small heel

9.Red high heel

Therefore, Kami has 9 different choices for her new shoe purchase, as listed above.

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Answer:

36 square inches.

Step-by-step explanation:

volume is given by 1 by 3, into base into height is based. His height and volume and area of the base is given by area of the ashe area of the base is given by 3 into 60 by 5. As given in the question on solving it, we get it equals to 36 square inches.

Answer:

Step-by-step explanation:

You want the side lengths in a right triangle geometry when the altitude to the hypotenuse of length 25 cuts off a segment of length 6.

All of the right triangles in this configuration are similar. The proportional relationships between the sides give rise to three geometric mean relations.

In effect each of the segments x, y, z is the geometric mean of the two segments of the hypotenuse it touches.

  x = √(6·(25-6)) = √114 ≈ 10.68

  y = √(6·25) = 5√6 ≈ 12.25

  z = √((25 -6)·25) = 5√19 ≈ 21.79

__

Additional comment

To see how these arise, consider the ratio of long side to hypotenuse:

  z/25 = 19/z

  z² = 25·19

  z = √(25·19) . . . . . the geometric mean of 25 and 19

The "geometric mean" of n numbers is the n-th root of their product. For two numbers, it is the square root of their product.