What is the inverse of the function, f(x)=2x−1‾‾‾‾‾‾√3−3?
Responses

f−1(x)=(x+3)3−12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x plus 3 close parentheses cubed minus 1 over denominator 2 end fraction

f−1(x)=(x−3)3−12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x minus 3 close parentheses cubed minus 1 over denominator 2 end fraction

f−1(x)=(x−3)3+12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x minus 3 close parentheses cubed plus 1 over denominator 2 end fraction

f−1(x)=(x+3)3+12

Okay, here are the steps to solve this problem:

* The recipe calls for 3/4 teaspoon of cinnamon for every 4 cups of granola mix.

* So for 1 cup of granula mix, you need 3/4 / 4 = 3/12 teaspoon of cinnamon.

* For 12 cups of granula mix, you would need 12 * (3/12) = 3 teaspoons of cinnamon.

Therefore, for 12 cups of granola mix you would need 3 teaspoons of cinnamon.

Answer:

Approximately 15.7 ft

Step-by-step explanation:

We want to find the circumference of the circle

C = pi * diameter

C = pi *5

C = 5pi ft or approximately 15.7 ft

The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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Answer:

The Correct answer is B

Step-by-step explanation:

Answer:

2/3 or 67%

Step-by-step explanation:

To find the exact probability for you to reach into the orange balls you'll have to do a data table on which you'll include how many orange balls are by the total amount of balls that are within the urn.

For example:
The urn contains:

* 10 red balls
* 20 yellow balls
* 60 orange balls

Total amount of balls that you have on the urn is 90, you'll get this result by doing a simple addition of the table of content.

Afterwards, we have to find the probability, so you will have to take the amount of orange balls (which is 60) and divide it by 90 (Which is the total amount of balls you have on the urn).

60/90

A quick tip for you to do this on a simplified manner is by dividing the numerator and the denominator by their greatest common divisor (Which in this case is 30) (30x2 = 60) (30x3 = 90)

60/90 = (60 divided 30) / (90 divided 30) = 2/3

To resolve this problem, we get that the probability of selecting an orange ball is 2/3 or approximately 0.67 which we'll simplify to 67%

I hope this helped you

The volume of the given right cone is approximately 597.9 cubic units.

In this problem, we are going to find the volume of a right cone. A cone is a three-dimensional object that has a circular base and tapers to a point. The term "right" means that the axis of the cone is perpendicular to its base. The formula for the volume of a right cone is V = (1/3)πr²h, where V is the volume, r is the radius of the circular base, and h is the height of the cone.

Now, let's apply this formula to the given cone. We are given that the radius of the circular base is 16 and the height of the cone is 7. So, we can substitute these values into the formula to get:

V = (1/3)π(16)²(7) V = (1/3)π(256)(7) V = (1/3)(1,792π) V ≈ 597.9

We round our answer to the nearest tenth as requested. So, the final answer is V ≈ 597.9.

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If both Tony and Marcus work on the job and the cost of labor is $48.00 per hour then labor estimate for the job is $576.00.

Marcus: 1 slab / 9 hours = 1/9 slab per hour

Tony: 1 slab / 3 hours = 1/3 slab per hour

The total amount of work they can do in one hour is the sum of their individual rates:

Marcus and Tony: 1/9 + 1/3 = 4/9 slab per hour

So together, Marcus and Tony can lay 4/9 of a slab per hour.

time = work / rate

time = 1 / (4/9) = 2.25 hours

total labor cost = hours worked x cost per hour

The total number of hours worked is the sum of the hours worked by Marcus and Tony:

total hours worked = 9 hours + 3 hours = 12 hours

The cost per hour is $48.00, so the labor estimate for the job is:

total labor cost = 12 hours x $48.00/hour

= $576.00

Therefore, the labor estimate for the job is $576.00.

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The angle measures of w and x are given as follows:

In this problem we have an isosceles triangle, meaning that two of the side lengths, along with two of the angle measures, are congruent.

The congruent side lengths are given as follows:

SR and RQ.

Hence the congruent angle measures are given as follows:

Hence angle w is given as follows:

w = 51º.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle x is given as follows:

x + 2 x 51 = 180

x = 180 - 102

x = 78º.

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Answer:

120 km²

Step-by-step explanation:

You just need to add all areas, (3×5) + (9×3) + (13×6) = 15 + 27 + 78 = 120

Answer:

x = - 12

Step-by-step explanation:

the central angle subtended by the arc with measure 45° are congruent, that is central angle is 45°

the 3 angles on the diameter then sum to 180° , that is

45 + 65 + x + 82 = 180

x + 192 = 180 ( subtract 192 from both sides )

x = - 12

Answer:

Option A is the correct choice that shows a function.

Step-by-step explanation:

What is a function?

A function is when there are no repeating "x" values.

For example:

These set of points: {(1,1), (1,2), (1,3), (1,4)} does not  show a function because there is repeating "x" values.

Option A shows that the points {(4,5), (5,5), (6,1), (8,2) is a function because there is no repeating "x" values.

The types of systems of linear equations are as follows:

Dependent: The system has infinitely many solutions. The graphs of the equations represent the same lines. Example:

. The system has infinitely many solutions.

Independent: The system has exactly one solution. The graphs of the equations intersect at a single point.

Inconsistent: The system has no solution. The graphs of the equations are parallel lines.

[tex]\textit{since we know that }\triangle FGH \cong \triangle CDE \\\\[-0.35em] ~\dotfill\\\\ HF=EC\implies -3s+44=-3t+50 \\\\\\ HG=ED\implies 6s=t+43\implies \boxed{6s-43=t} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{-3s+44=-3(6s-43)+50}\implies -3s+44=-18s+129+50 \\\\\\ 15s+44=129+50\implies 15s+44=179\implies 15s=135 \\\\\\ s=\cfrac{135}{15}\implies \boxed{s=9}\hspace{9em}\stackrel{ 6(9)-43 }{\boxed{t=11}}[/tex]

The value of x in the rectangle is,

⇒ x = 6

We have to given that;

Corresponding angles are,

⇒ (8x + 19)° and (21x - 13)°

Hence, We can say that;

⇒ (8x + 19)° + (21x - 13)° = 180°

⇒ 29x + 6 = 180

⇒ 29x = 174

⇒ x = 174/29

⇒ x = 6

Thus, The value of x in the rectangle is,

⇒ x = 6

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The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a positive actual number that is not exactly one.

A logarithm is the power to which a number must be raised in order to receive extra values. The simplest approach to express really large numbers is in this way. A number of important features of a logarithm demonstrate the fact that multiplication and division of logarithms can also be used to represent addition and subtraction logarithms.

The exponent by which base b must be raised to get a positive real number an is the logarithm of a positive real number a with regard to base b, a real number that is positive but not equal to one.

i.e., [tex]b^y=a[/tex] ⇔ [tex]log_b[/tex] a = y

In this case, "A" and "B" are two positive real numbers.

Y is an actual number.

Argument occurs inside the log as "a" by the name argument.

It is said that the base, or "b," is at the bottom of the log.

To put it another way, the logarithm provides a solution to the problem of "How many times is a number divided to get the other number?"

How numerous times must three be multiplied, for instance, to yield the number 27?

27 is the outcome of multiplying 3 times by 3.

Consequently, the logarithm is 3.

The logarithm form is written as follows:

[tex]log_3[/tex] (27) = 3 - equation 1

The base 3 logarithm of 27 is therefore 3.

It is also possible to write the above logarithm form as:

3x3x3 = 27

3³ = 27 - equation 2

Equations (1) and (2) are hence equivalent.

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The solution is,  the tangent of each angle that is not the right angle is:

angle tan A = 1.33

angle tan B = 0.75

Here, we have,

Given:

ABC is a right triangle.

angle ACB = 90

To find:

tan A

tan B

We know that tangent of an angle is given by the ratio

= opposite / adjacent

The opposite side and adjacent side is taken with respect to the angle for which the tangent is to be found.

tan A = BC/ AC

         = 8/6

         = 4/3

         = 1.33

and, tan B = AC/BC

                 = 6/8

                 =0.75

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Janeesa needs to drive about 6.9 mph faster than the speed limit to make it on time.

What is the  speed limit

To find out how fast Janeesa needs to drive to make it on time, one can use the formula:

distance = rate x time

In this case, the distance is 247.5 miles, the time is 4 hours, and the rate is what we're trying to find. Rearranging the formula to solve for rate, we get:

rate = distance / time

Plugging in the values we know, we get:

rate = 247.5 / 4 = 61.875

To know how much faster Janeesa needs to drive, one has to subtract the speed limit from the required speed:

Speed Difference = Required Speed - Speed Limit

= 61.875 mph - 55 mph

 = 6.875 mph

Therefore, Janeesa needs to drive approximately 6.9 mph faster than the speed limit to make it on time.

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Only first figure of graph have an Euler circuit.

We have to given that;

There are 3 graphs are shown in figure.

Since, A graph has an Euler circuit if and only if the degree of every vertex is even.

Hence, In first graph,

Every vertex have even degree with 2 or 4.

Thus, It shows an Euler circuit.

In second graph,

Some vertex have odd degree with 3.

Hence, It does not shown an Euler circuit.

In third graph,

Some vertex have odd degree with 3.

Hence, It does not shown an Euler circuit.

Thus, Only first figure of graph have an Euler circuit.

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Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

Based on an equation, the minimum number of years it will take the population of North Dakota to equal the population of South Dakota given the current rates of growth is 15.3 years.

An equation describes the equality or equivalence of two or more mathematical expressions.

Equations use the equal symbol (=), while mathematical expressions combine variables with numbers, constants, values, and mathematical operands.

The population of North Dakota in 2012 = 0.7 million

The yearly population growth rate = 0.028 million

The population of South Dakota in 2012 = 0.83 million

The annual population growth rate = 0.0195 million

Let the number of years for the populations to equal = x

0.7 + 0.028x = 0.83 + 0.0195x

0.0085x = 0.13

x = 15.3 years

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A website is selling barbecue grills for $94, but mentions that they originally cost $200 the discount, as a percentage, is 53%.

The discount is the difference between the original price and the discounted price.

Discount = $200 - $94 = $106

To find the percentage discount, we need to calculate what percentage of the original price the discount represents:

Percentage discount = (Discount/Original price) x 100%

Percentage discount = ($106/$200) x 100%

Percentage discount = 53%

Therefore, the discount, as a percentage, is 53%.

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The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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The balance on the loan at the end of month 4 is approximately $289,836.23.

We are given that;

Amount borrowed= $290,000

Time 25 years

Payment=  $1, 530.73

Now,

To calculate the balance on the loan at the end of month 4, we can use the following formula2:

Balance = (Loan amount - Debt payment) * (1 + Interest rate / 12) - Debt payment

Where:

Loan amount is the original amount borrowed ($290,000)

Debt payment is the amount of principal paid in each monthly payment ($564.06 for the first month and $565.94 for the second month)

Interest rate is the annual interest rate divided by 100 (0.04)

Plugging in the values, we get:

Balance = ($290,000 - $564.06) * (1 + 0.04 / 12) - $565.94 Balance = $289,435.94 * 1.003333 - $565.94 Balance = $290,402.17 - $565.94 Balance = $289,836.23

Therefore, by the interest the answer will be $289,836.23.

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The correlation coefficient for the data-set in this problem is given as follows:

r = 0.75.

To obtain the correlation coefficient of the data-set in this problem, we must insert the points of the data-set into a correlation coefficient calculator.

From the table, the points of the data-set are given as follows:

(0, 5.9), (0.8, 8.6), (1.3, 15.5), (1.6, 17.3), (13.3, 21.5).

Inserting these points into a calculator, the correlation coefficient is given as follows:

r = 0.75.

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Answer:

526.32

Step-by-step explanation:

Let's assume that the cost price of the bag is "C".

Selling Price = Cost Price - Loss

We get:

500 = C - 0.05C

500 = 0.95C

C = 500/0.95

C ≈ 526.32

Therefore, the cost price of the bag was approximately Rs 526.32.