May any kind soul teach me on how to do this primary six math question .

[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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Answer:

95,367,431,640,625 (or approximately 9.5 x 10^13)

Step-by-step explanation:

If there are 5 choices for each question in a 20-question multiple-choice test, then there are 5 possible answers for each question. To find the total number of ways to answer the test, we need to multiply the number of choices for each question together.

Therefore, the total number of ways to answer the 20-question multiple-choice test is:

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5

which is equal to 95,367,431,640,625 (or approximately 9.5 x 10^13) ways to answer the test.

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]

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.

The linear regression equation is defined as follows:

C. ŷ = 6.5x − 279.1

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for this problem are given on the table as follows:

(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).

Inserting these points into a calculator, the line of best fit is given as follows:

ŷ = 6.5x − 279.1

Meaning that the correct statement is given by option C.

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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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Answer: there you go :)

Step-by-step explanation:

Its D, 90-20=70 ft traveled downwards

The difference between  the Statue of Liberty compared to other outdoor statues is that it is made of copper which is option C.

The Statue of Liberty is a colossal neoclassical sculpture located on Liberty Island in New York Harbor in the United States. It was a gift from the people of France to the people of the United States, dedicated on October 28, 1886, and has since become one of the most recognizable symbols of the United States and its ideals of freedom and democracy.

The statue was designed by French sculptor Frédéric-Auguste Bartholdi, with the help of engineer Gustave Eiffel. The statue depicts a female figure dressed in a flowing robe and holding a torch in one hand and a tablet in the other, upon which is inscribed the date of the American Declaration of Independence (July 4, 1776).

The Statue of Liberty is unique among outdoor statues in that it is made of copper sheets that have oxidized over time to form a green patina. This patina has become an iconic symbol of the statue and is a result of the natural process of copper corrosion. The statue was originally a shiny brown color, but the oxidation of the copper has gradually changed its appearance over time.

Therefore, while the Statue of Liberty is also located in a park and on a pedestal, and it is larger than many outdoor statues, these characteristics are not unique to the statue and can be found in other outdoor statues as well.

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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.

Answer:

Step-by-step explanation:

To determine if the job is complete, we need to add up the fractions of the decoration that each person put up:

Anna: 2/5

Manna: 1/4

Hanna: 3/10

Now we can find the total fraction of the decoration that they put up by adding these fractions:

2/5 + 1/4 + 3/10 = 16/40 + 10/40 + 12/40 = 38/40

So they have completed 38/40 of the decoration. To find the fraction of the job that is still left to do, we can subtract this from 1:

1 - 38/40 = 2/40

Therefore, there is still 2/40 of the decoration left to do, or 1/20 of the total job.

Answer:

a = 4x with a small 3 at the top ( x with a small 4 at the top + 3x ) with a small 30 + 3

b = B = 6x with a small 17 at the top + 192x with a small 15 at the top + 2520x with a small 13 at the top + 17280x with a small 11 at the top + 64800x with a small 9 at the top + 124416x with a small 7 at the top + 93312 with a small 5 at the top

sorry but I don't know c

Step-by-step explanation:

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:

Ricky is taller by 11 inches ( a)

Step-by-step explanation:

1 foot = 12 inches

5 feet= 60 inches

Ticky is 68 inches

Ricky is 79 inches

ricky-Ticky=  79- 68= 11 inchesss!

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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If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, the missing measures are m<ADC = 90°, m<BAC = 24°, m<CDB = 240°, and m<AEB = 132°.

The Pythagorean theorem is a fundamental theorem in geometry that says that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

That is to say mathematically,

[tex]a^{2} + b^{2} = c^{2}[/tex]

where a and b are the lengths of the two sides of the triangle (the sides adjacent to the right angle), and c is the length of the hypotenuse.

Thus, substituting our values for this formula,

[tex]x^{2} +9^{2} =22[/tex]

[tex]x^{2} +81= 484[/tex]

[tex]x^{2} = 484-81[/tex]

[tex]x^{2} =403[/tex]

[tex]x=20.1[/tex] = AB

Thus,

BC = 9

AB = 20.1

BD= 22

EC = 11

m<ADC = 90°

m<BAC = 24° (90-66)

m<CDB = 240°

m<AEB = 132° (180-24-24)

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You asked an incomplete question. The complete question reads;

If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, find each missing measure. I also attached an image of the question.

Below are some general reasons why a questionnaire might not be suitable:

Poorly constructed questions: If the questions in the questionnaire are not clear, ambiguous, leading, or biased, then the responses obtained may not be accurate or reliable. Poorly constructed questions may also lead to confusion, misunderstandings, and errors.

Lastly Inadequate sampling: If the sampling technique used to select respondents is not representative of the target population, then the results obtained may not be generalizable or applicable to the larger population. The sample size and composition may also affect the validity and reliability of the results.

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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:

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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:

(1) 63 odd - and - 28 even

(2) 49 odd - and - 76 even

Step-by-step explanation:

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.

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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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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Part A: distance travelled by athlete when she reaches her maximum is 1.3 m.

Part B: her maximum height: 5 m.

Th equation is-

y = -1.2x² + 3.12x +3.

horizontal distance - x

Part A: distance travelled by athlete when she reaches her maximum:

Comparing given equation with standard form of quadratic equation:

x = -b/a

x = -3.12/2(-1.2) = 1.3

Thus, distance travelled by athlete when she traveled horizontally and reaches her maximum of 1.3 m.

Part B: her maximum height:

y = -1.2x² + 3.12x +3.

Put x = 1.3

y = -1.2(1.3)² + 3.12(1.3) +3.

On solving:

y = 5.028

y = 5 m

Thus, her maximum height, round to the nearest tenth of a meter is 5 m.

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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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y = $100.00 - $10.00x is the equation for the total amount of money in the savings account after x weeks.

The y-intercept represents the initial deposit of $100.00 and the slope is -10

a. Let's call the amount of money saved each week "s" and

let's call the total amount of money in the savings account after "x" weeks "y".

Since the amount saved each week is the same, we can express the total amount of money in the savings account as:

y = $100.00 + sx

We know that at the end of the 5th week, the total amount in the savings account is $50.00. So we can set up the following equation:

$50.00 = $100.00 + 5s

solving for s:

$50.00 - $100.00 = 5s

-$50.00 = 5s

-10 = s

So the equation for the total amount of money in the savings account after x weeks is:

y = $100.00 - $10.00x

b. In the context of this problem, the slope represents the amount of money that is saved each week.

In this case, the slope is -10, meaning that $10.00 is saved each week. The y-intercept represents the initial deposit of $100.00.

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Answer: d is the answer

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