what is the inverse of the function f (x) = 1/3x-5

Answer:

0.2x-0.8

Step-by-step explanation:

In 0.2(x-4), you can multiply 0.2(The number outside of the parentheses) by the numbers inside the parentheses. So, it would be 0.2*x-0.2*4, which is 0.2x-0.2(4), which is 0.2x-0.8.

The student can take 8 months of lessons if he has $649 to spend on lessons and the book.

The arithmetic action of division is the opposite of multiplication. It is employed to determine how frequently one quantity is included within another. Divide the dividend by the divisor to execute a division, which can be represented with the division symbol () or a fraction bar (/). The outcome of division is the quotient, which shows how many times the dividend can be divided by the divisor. For instance, if you divide 8 apples into 4 equal portions, each portion would include 2 apples.

First, let's find the total cost of the lessons by multiplying the cost per month by the number of months:

$78/month × n months = $78n, where n is the number of months of lessons.

Next, we add the cost of the book to find the total cost:

$78n + $25 = $649.

Now, we can solve for n by subtracting the cost of the book from both sides of the equation:

$78n = $649 - $25 = $624.

Finally, we divide both sides of the equation by 78 to find the number of months of lessons:

n = $624 ÷ $78/month = 8 months.

So, the student can take 8 months of lessons if he has $649 to spend on lessons and the book.

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The simplified expression of 1+sin^2-cos^x / 2sin^2x  issin^2(x) / 2(1 + cos(x)) + 1 / 2(1 - cos(x))

To simplify this expression, we can first simplify the numerator by combining the terms inside the parentheses:

1 + sin^2(x) - cos(x) = sin^2(x) + 1 - cos(x)

Next, we can factor the denominator trigonometric identity sin^2(x) + cos^2(x) = 1:

2 sin^2(x) = 2(1 - cos^2(x)) = 2 - 2cos^2(x)

Now we can substitute these simplified expressions into the original expression:

(1 + sin^2(x) - cos(x)) / (2 sin^2(x))

= (sin^2(x) + 1 - cos(x)) / (2 - 2cos^2(x))

= [(1 - cos(x)) + sin^2(x)] / [2(1 - cos(x))(1 + cos(x))]

1+sin^2-cos^x / 2sin^2x = [sin^2(x) / 2(1 + cos(x))] + [1 / 2(1 - cos(x))]

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Answer:

50% or 1/2

Step-by-step explanation:

Because there are 4 animals in the barn, if two animals leave (out of 4), then there are 50% of the animals in the barn and 50% of the animals leaving the barn.

Hope this helps! If you find my answer helpful, please consider marking brainliest! If you have any questions, feel free to ask in the comments!

Answer: 8.9 and 6.7

Step-by-step explanation:

These are right triangles, so you can use the Pythagorean theorem, a² + b² = c², where a and b are the legs, or shorter sides, of the triangle and c is the hypotenuse, or the longest side.

1. 4² + 8² = c²

16 + 64 = c²

80 = c²

c = √80

c = 8.9

2. 6² + 3² = c²

36 + 9 = c²

45 = c²

c = √45

c = 6.7

Answer:

see below

Step-by-step explanation:

(1+20%) * (1-20%) =1.2 *0.8 = 0.96

so it's the same as 1- 4% = 0.96

no

Answer:

  T = 79e^(-kt) +60

Step-by-step explanation:

You want the particular solution to the differential equation ...

  dT +k(T -60)dt = 0 . . . . T(0) = 139

This is a separable differential equation, so we can solve it by separating the variables and integrating each side:

  [tex]\dfrac{dT}{T-60}=-k\,dt\\\\\displaystyle \int{\dfrac{dT}{T-60}}=\int{-k}\,dt\\\\\ln{(T-60)}=-kt+C\\\\T-60=e^{-kt+C}=Ce^{-kt}\qquad\text{take antilogs; values of $C$ are different}[/tex]

Applying the initial condition, we have ...

  139 -60 = C = 79

Then the particular solution is ...

  [tex]\boxed{T=79e^{-kt}+60}[/tex]

Answer:

y=-3/2+3

Step-by-step explanation:

so you have to solve for y

The interquartile range is least affected by an outlying value in the data set of the range, interquartile range, and variance is True.

Max to min value is the range. Range can substantially change if there are any outliers.

Since the threshold values for Q3 and Q1 are not outliers, the IQR won't change.

Outliers cause variance to be misinterpreted since they vastly increase variance.

Interquartile range:

You may determine the spread of the midpoint of your distribution using the interquartile range.

The interquartile range contains half of the values for any distribution that is ordered from low to high. The first 25% of values are found in the first quartile (Q1), while the last 25% are found in the fourth quartile (Q4).

The third quartile (Q3) less the first quartile (Q1) is the interquartile range (Q1). This provides us with the data set's middle half's range.

The interquartile range is calculated using only 2 values, much like the range. The IQR, however, is less impacted by outliers because the two values are more likely to be average scores because they are drawn from the middle of the data set.

The IQR provides a reliable indicator of variability for both skewed and normal distributions.

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Answer:

All the answers are bolded in the step-by-step explanation.

Hope it helps :)

Step-by-step explanation:

The radius of the top of a cylinder is always the same length as the radius of the base of a cylinder.

Radius of the base of can A: 10 cm

Radius of the base of can B: 18 cm

To find the area of the bases, use the area formula that you put as your first answer.

Area of the base of can A:

[tex]A=\pi (10^{2} )[/tex]

[tex]A=100\pi[/tex]

[tex]A=314[/tex] cm (Assuming we're only using 3.14 and not any other decimals)

Area of the base of can B:

[tex]A=\pi (18^{2} )[/tex]

[tex]A=324\pi[/tex]

[tex]A=1017.36[/tex] cm (Again, assuming we're only using 3.14 and not any other decimals)

The base of can B has a greater Area

To find the height, look at the diagram

Height of can A: 28cm

Height of can B: 9cm

Can A has a greater height

To find the volume, use the equation that you put as your answer for question 2 or just multiply the area of the base times the height.

Volume of can A:

[tex]314*28=V[/tex]

[tex]V=8792[/tex]

Volume of can B:

[tex]1017.36*9=V[/tex]

[tex]V=9156.24[/tex]

Can B holds more paint

Answer:

Step-by-step explanation:

The tree is .0564 meters

Answer:

Step-by-step explanation:

de chill de chill

The balance after 6 years is $2108.

percentage, a relative value indicating hundredth parts of any quantity.

Given that savings account earns 4% annual simple interest.

The principal is $1700.

We need to find the balance after 6 years.

The formula for simple interest I=Prt

I = interest

P = principal ($1700)

r = annual interest rate (4%)

t = time in years (6)

So the interest earned in 6 years is:

I = 1700× 4×6 / 100 = $408

The balance after 6 years is the sum of the principal and the interest earned:

1700 + 408 = $2108.

Hence,  the balance after 6 years is $2108.

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Answer: 10π + 20, or 51.4159, cm

Step-by-step explanation:

The circumference of a circle is calculated using πd. Our d, or diameter, is 20, so the circumference of a full circle would be 20π. However, we only have half of a circle, so that number is halved, resulting in 10π. Now, we just have to add on the cross section, which is equal to the diameter, giving us 10π + 20, or 51.4159, cm.

The probability of winning the quiz is 0.19 or 19% when the contestant answers randomly to each question.

The number of possible outcomes for answering 3 multiple-choice questions with 3 choices each is [tex]3^3[/tex] = 27. Out of these 27 possible outcomes, 9 of them result in the contestant getting 2 or more questions correct.

So, the probability of winning the quiz can be calculated as follows:

P(Winning) = 9/27 = 1/3 = 0.3333...

Rounding to two decimal places, the probability of winning the quiz is approximately 0.33 or 33%.

However, since the contestant is answering randomly to each question, the probability of winning can also be expressed as the sum of the probabilities of getting exactly 2, or 3 questions right. This is calculated using the binomial distribution. The probability of getting exactly 2 questions right is:

The probability of getting exactly 3 questions right is:

The sum of these probabilities gives the total probability of winning:

Rounding to two decimal places, the probability of winning the quiz is approximately 0.19 or 19%.

Since the contestant is answering randomly to each question, the probability of winning is approximately 0.19 or 19%.

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the ordered pair will be (3,-1) lies in the inverse function.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

function g(x)=∛(x−4)

So the inverse of the function

g ¬(x) = x³+4

So the ordered pair will be (3,-1)

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No. A triangle cannot be formed with side lengths of 2, 4, and 5. option (d)

The sum of the lengths of the two shorter sides (2 + 4 = 6) must be greater than the length of the longest side (5). This is known as the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, to form a triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side. In this case, the two shorter sides do not meet this requirement, so it is not possible to form a triangle with these side lengths.

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Complete Question:

Is it possible to form a triangle with side lengths 2, 4, and 5? If so, will it be scalene, isosceles, or equilateral?

A.Yes; scalene

B. Yes; isosceles

C. Yes; equilateral

d. no

The options which are equal to, or a good estimate of the ratio include:

8 out of 1, 000 :

8 / 100 :

8 out of 1, 000 is a ratio that can be shown to be :

= 8 / 1, 000 x 100 %

= 0. 008 x 100 %

= 0. 8 %

0. 8 % is less than 1 %.

8 / 100 is a ratio that would be:

= 8 / 100 x 100 %

= 8 %

This is almost 10 % as it is 2 % away.

8 / 100 = 0. 08

2 / 25 = 0. 08

These two ratios are therefore equal.

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Answer:

  (d)  x-axis

Step-by-step explanation:

You want the line of reflection that transforms Z(10, -8) to Z'(10, 8).

The line of reflection is the perpendicular bisector of the segment between a point and its image.

Here, the segment ZZ' is on the vertical line x=10, so the bisector will be a horizontal line whose y-value is the average of the y-values of Z and Z':

  y = (-8 +8)/2 = 0/2 = 0

The line y=0 is the x-axis. The line of reflection is the x-axis.

__

Additional comment

Rather than go to the trouble of considering perpendicular bisectors, you can simply make use of your knowledge of reflection over the axes:

  (x, y) ⇒ (-x, y) . . . . reflection over the y-axis

  (x, y) ⇒ (x, -y) . . . . reflection over the x-axis   ←

  (x, y) ⇒ (-x, -y) . . . . reflection over both axes, or reflection across the origin

Answer:

 (d)  x-axis

Step-by-step explanation:

The test does not prove the alternative hypothesis correct, because of the possibility of rejecting the null hypothesis when the null hypothesis is true.

The test does not prove the alternative hypothesis correct, because when performing a hypothesis test, the null hypothesis is rejected in favor of the alternative hypothesis. However, rejecting the null does not necessarily mean that the alternative hypothesis is true. It is possible for the null hypothesis to be rejected even when it is true, due to the occurrence of random fluctuations. Therefore, the test does not prove that the alternative hypothesis is correct, as there is always a possibility that the null hypothesis is true despite being rejected. To prove that the alternative hypothesis is correct, a series of hypothesis tests must be conducted to show that the population parameter is consistent with the alternative hypothesis.

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Answer:

2793.75

Step-by-step explanation:

1350 - 175 = 1175

1175 / 4 = 293.75

Answer:

4 Lessons

Step-by-step explanation:

55 * 4 = 220   +     140    =    360

75 * 4 = 300   +      60    =     360

Price per lesson, times number of lessons, plus deposit cost, equals total amount when the lessons will be the same price.

Hope this helps!

The evaluation of expression is 5/4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The expression; ( 6^2 - 4^2 ) x ( 1/4 )^2

=( 6^2 - 4^2 ) x ( 1/4 )^2

=(36-16)*(1/16)

=20*1/16

=5/4

Therefore, the algebraic expression answer will be 5/4.

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Answer:

3.41

Step-by-step explanation:

41/12

a) The vertex-form definition of the quadratic function is given as follows: y = 1/3(x - 3)² + 5.

b) The rider's minimum height above the ground is of: 5 meters,

c) The horizontal distance is given as follows: x = 0 m and x = 6 m.

The quadratic function in the context of this problem is defined as follows:

y = x²/3- 2x + 8.

In which:

The coefficients are given as follows:

a = 1/3, b = -2, c = 8.

The x-coordinate of the vertex is given as follows:

x = -b/2a = -(-2)/(2/3) = 3.

Hence the y-coordinate of the vertex is given as follows:

y = (3)²/3 - 2(3) + 8 = 5 meters.

Hence the vertex-form definition of the equation is given as follows:

y = 1/3(x - 3)² + 5.

As the function is concave up, the minimum height is of 5 meters.

For the horizontal distance at a height of 8m, we have that:

x²/3 - 2x + 8 = 8

x²/3 - 2x = 0

x(x/3 - 2) = 0.

Hence:

x = 0 m and x = 6 m.

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Answer:

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).

Step-by-step explanation:

To find the inverse of F(x), we need to follow these steps:

Step 1: Replace F(x) with y:

y = 5x^2 - 10x + 7

Step 2: Solve for x in terms of y:

y = 5x^2 - 10x + 7

y - 7 = 5x^2 - 10x

5x^2 - 10x = y - 7

5(x^2 - 2x) = y - 7

Completing the square:

5(x^2 - 2x + 1) = y - 7 + 5

5(x - 1)^2 = y - 2

x - 1 = ±sqrt((y-2)/5)

x = 1 ± sqrt((y-2)/5)

Step 3: Replace x with F^-1(x):

F^-1(x) = 1 ± sqrt((x-2)/5)

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).

The lowest value of the equation is at x = -2 when (x + 2) = 0.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given the function,

x² + 4x + 2

to find the lowest value,

factorize the function,

x² + 4x + 2

add and subtract 4 from the function,

x² + 4x + 2 + 4 - 4

x² + 4x + 4 - 2

(x + 2)² - 2

here (x + 2)² is always positive,

and lower value will be x = -2 when (x  + 2)  = 0

Hence lowest value will be at x = -2.

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The correct question is,

Lowest value of  x² + 4x + 2.

The cost price of cloth that John bought per meter is Php 46.00 (Option C). To find the cost price per meter, divide the total cost by the number of meters of cloth.

In this case, the total cost is Php 425.50 and the number of meters is 9.25. By dividing the total cost by the number of meters, we get Php 46.00 per meter. This means that John paid Php 46.00 for every meter of cloth he bought. This is the cost price per meter and it is option C, Php 46.00.

The specific value that corresponds to the unit price that was purchased is reflected in retail systems by the cost price. In some stock market theories, this value is used to determine the value of stock holdings, and it is used as a key factor in determining profitability.

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Answer: 7

Step-by-step explanation: 13 + 7 = 20

Answer: 7

Step-by-step explanation:

q+13=20

subtract 13 on both sides and you get

q=7