Given the function f(x) = 3 (x - 9) + 6 which of the following represents f-1 (x)?
Answers
Answer:
\(f^{-1}\)(x) = \(\frac{1}{3}\) x + 7
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 3(x - 9) + 6 ← distribute and simplify right side
y = 3x - 27 + 6 = 3x - 21 ( add 21 to both sides )
y + 21 = 3x ( divide all terms by 3 )
\(\frac{1}{3}\) y + 7 = x
Change y back into terms of x with x = \(f^{-1}\)(x) , thus
\(f^{-1}\)(x) = \(\frac{1}{3}\) x + 7
Related Questions
y= -5x-9 (slope) I NEED HELP
Answers
Answer:
-5 is the slope
Step-by-step explanation:
if there's a number in front of x, it's most likely the slope.
I need help with this
Answers
The measures of dispersion mean , median , mode and range of the data are 3.79, 2, 2 and 9.75 respectively
The meanThe mean is the ratio of the sum of all the values and the number of values in the dataset .
The mean = (1 + 0.8 + 2 + 2.5 + 1.5 + 5 + 10 + 5.1 + 3 + 2.25 + 0.5 + 0.25 + 1.8 + 4.1 + 2 + 2 + 7) / 14 = 3.79
The medianThis is the middle value of the distribution after it has been rearranged in order of magnitude.
Rearranged data : 0.25, 0.5, 1, 1.5, 1.8, 2, 2, 2, 2.25, 3, 4.1, 5, 5.1, 7, 10
median = 2
The modeThis is the most frequently occurring value in the dataset . The modal value here is 2 with a frequency of 4
Mode = 2
The RangeThis is the difference between the maximum and minimum values
Range = 10 - 0.25 = 9.75
Therefore, the range of the data is 9.75
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Even though I already got the question right,I need someone to show the work on how to get the answer for this question.
Answers
Given
Answer
\(\begin{gathered} \sin x=\frac{P}{H} \\ \sin x=\frac{5}{8.3} \\ x=\sin ^{-1}(\frac{5}{8.3}) \end{gathered}\)Which is triangle 2
What is the most widely used probability model for continuous numerical variables?.
Answers
In statistics, the normal probability distribution is the most often used continuous probability distribution.
A simple mathematical process transforms any value from a classical probability distribution to its normal distribution equivalent, including mean and standard deviation.
To determine the required probability, the normal distribution table is employed.
The geometric, behavioral, and negative binomial probabilities are all common as discrete distributions. The regular, logarithm, exponential, chi-square, beta, t, and F distributions are examples of common continuous distributions.
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I need help with my homework please help
Answers
The formulas for the rigid transformations of the figures are listed below:
Case 1: (x, y) → (x - 10, y + 9)
Case 2: (x, y) → (- y, x)
Case 3: (x, y) → (- x, y)
Case 4: (x, y) → (- y, x)
Case 5: (x, y) → (x, - y)
Case 6: (x, y) → (x, y + 10)
How to determine the transformation rule for each case
In this question we find six cases of rigid transformations applied on figures. The most common rigid transformations are listed below:
Translation: (x, y) → (x + a, y + b), where a, b are real numbers.Reflection about x-axis: (x, y) → (x, - y)Reflection about y-axis: (x, y) → (- x, y) Rotation: (x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ), where θ is the angle of rotation.Then, by direct inspection, we derive the following rigid transformations:
Case 1 (Translation)
(x, y) → (x - 10, y + 9)
Case 2 (Rotation)
(x, y) → (x · cos (- 270°) - y · sin (- 270°), x · sin (- 270°) + y · cos (- 270°))
(x, y) → (- y, x)
Case 3 (Reflection about y-axis)
(x, y) → (- x, y)
Case 4 (Rotation)
(x, y) → (x · cos 90° - y · sin 90°, x · sin 90° + y · cos 90°)
(x, y) → (- y, x)
Case 5 (Reflection about x-axis)
(x, y) → (x, - y)
Case 6 (Translation)
(x, y) → (x, y + 10)
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A firework rocket consists of a cone stacked on top of a cylinder where the radius of the cone and the cylinder are equal the diameter of the cylindrical base of the rocket is 8 in and the height of the cylinder is 5 in while the height of the cone is 3 in
Answers
Answer:
Surface area of the rocket = 76π
Step-by-step explanation:
Given:
Diameter = 8 in
Radius of cylinder = 4 in
Radius of cone = 4 in
Height of the cylinder = 5 in
Height of the cone = 3 in
Find:
Surface area of the rocket.
Computation:
Slant hight = \(\sqrt{4^2 + 3^2}\)
Slant hight = 5 in
Surface area of the rocket = Surface area of cylinder + Surface area of cone + Area of circle
Surface area of the rocket = 2πrh + πrl + πr²
Surface area of the rocket = 2π(4)(5) + (π)(4)(5) + (π)(4)²
Surface area of the rocket = 40π + 20π + 16π
Surface area of the rocket = 76π
4. Consider the ground state of the Harmonic Oscillator with the potential in the k standard form V = x² so the potential well is centered at x = 0. 2 (a) Evaluate the values of (x²) and σ₂ = √
Answers
(a) To evaluate (x^2) for the ground state of the Harmonic Oscillator, we need to integrate x^2 multiplied by the square of the absolute value of the wavefunction ψ0(x).
(b) The expectation value of p^2 for the ground state of the Harmonic Oscillator is simply the eigenvalue corresponding to the momentum operator squared.
(c) By calculating the uncertainties in position (Δx) and momentum (Δp) for the ground state, we can verify that their product satisfies Heisenberg's uncertainty principle, Δx · Δp ≥ ħ/2.
(a) In the ground state of the Harmonic Oscillator, the wavefunction is given by \(\psi_0(x) = \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{2\sigma^2}}\), where \(\sigma\) is the standard deviation.
To evaluate \((x^2)\), we need to find the expectation value of \(x^2\) with respect to the wavefunction \(\psi_0(x)\). Using the formula for the expectation value, we have:
\((x^2) = \int_{-\infty}^{\infty} x^2 \left|\psi_0(x)\right|^2 dx\)
Substituting the given wavefunction, we have:
\((x^2) = \int_{-\infty}^{\infty} x^2 \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{\sigma^2}} dx\)
Evaluating this integral gives us the value of \((x^2)\) for the ground state of the Harmonic Oscillator.
To evaluate \(\sigma_2\), we can simply take the square root of \((x^2)\) and subtract the expectation value of \(x\) squared, \((x)^2\).
(b) To evaluate \((p^2)\), we need to find the expectation value of \(p^2\) with respect to the wavefunction \(\psi_0(x)\). However, in this case, it is clear that the ground state of the Harmonic Oscillator is an eigenstate of the momentum operator, \(p\). Therefore, the expectation value of \(p^2\) for this state will simply be the eigenvalue corresponding to the momentum operator squared.
(c) The Heisenberg's uncertainty principle states that the product of the uncertainties in position and momentum (\(\Delta x\) and \(\Delta p\)) is bounded by a minimum value: \(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\).
To show that the uncertainty product satisfies the uncertainty principle, we need to calculate \(\Delta x\) and \(\Delta p\) for the ground state of the Harmonic Oscillator and verify that their product is greater than or equal to \(\frac{\hbar}{2}\).
If the ground state wavefunction \(\psi_0(x)\) is a Gaussian function, then the uncertainties \(\Delta x\) and \(\Delta p\) can be related to the standard deviation \(\sigma\) as follows:
\(\Delta x = \sigma\)
\(\Delta p = \frac{\hbar}{2\sigma}\)
By substituting these values into the uncertainty product inequality, we can verify that it satisfies the Heisenberg's uncertainty principle.
Regarding the statement \((x) = 0\) and \((p) = 0\) for this problem, it seems incorrect. The ground state of the Harmonic Oscillator does not have zero uncertainties in position or momentum. Both \(\Delta x\) and \(\Delta p\) will have non-zero values.
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Tara, Inc. is authorized to issue 5,000,000 shares of $20 par common stock. 500,000 shares of stock were originally sold for $50 per share. The stock is currently selling for $40 per share and Tara has decided to repurchase 12,000 shares of stock. When Tara, Inc. repurchases their own stock, how much gain or loss will the company recognize on its income statement?
A. $120,000 gain B. $120,000 loss C. $360,000 gain D. $-0-
Answers
The closest option is D. $-0
To determine the gain or loss on the repurchase of stock, we need to compare the repurchase price with the original sale price.
Original sale price: 500,000 shares * $50 per share = $25,000,000
Repurchase price: 12,000 shares * $40 per share = $480,000
To calculate the gain or loss, we subtract the repurchase price from the original sale price:
Gain or Loss = Original Sale Price - Repurchase Price
= $25,000,000 - $480,000
= $24,520,000
Since the result is a positive value, it represents a gain. Therefore, the company will recognize a gain of $24,520,000 on its income statement.
The given options do not include this exact amount, so the closest option is D. $-0-. However, it is important to note that the gain is not zero but rather $24,520,000.
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you intend to estimate a population mean with a confidence interval. you believe the population to have a normal distribution. your sample size is 15. find the critical value that corresponds to a confidence level of 90%. (report answer accurate to three decimal places with appropriate rounding.)
Answers
The critical value that corresponds to a confidence level of 90 % [1.34503037 , ∞ ).
Given:
you intend to estimate a population mean with a confidence interval. you believe the population to have a normal distribution. your sample size is 15. find the critical value that corresponds to a confidence level of 90%.
sample size n = 15
confidence interval ci = 90
we know that,
Degrees of freedom df = n - 1
here n = 15
df = n - 1
= 15 - 1
= 14
Using the graphical t value calculator:
with df = 14 significance level = 1 - 0.90 = 0.10
so t = [1.34503037 , ∞ )
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find the area of each figure
Answers
Answer:
A=120
B=20
C=20
Total area=160 cm2
This is really weird because the numbers dont look proportional to the shape but according to the data it should be correct :/
Answer:
Area of A=120cm²
Area of B=20cm²
Area of C=20cm²
Total area=160cm²
Step-by-step explanation:
For A
\(Length(l)=15cm\\Breadth(b)=8cm\\Now,\\Area=l*b\\Area=15cm*8cm=120cm^{2}\)
For B
\(Length(l)=5cm\\Breadth=12cm -8cm=4cm\\Now,\\Area=l*b\\Area=5cm*4cm\\Area=20cm^{2}\)
Area of C=20cm²
Total Area=160cm²
Children who have lost some baby teeth have better arithmetic skills than children who have not lost any baby teeth. In fact, the more baby teeth a child has lost, the better his/her arithmetic skills tend to be.
Which of the following statements is most likely true?
1. There is no correlation between arithmetic skills and losing baby teeth.
2. There is a correlation here, and losing baby teeth causes arithmetic skills to improve.
3. There is a correlation here, and improving arithmetic skills causes the loss of baby teeth.
4. There is a correlation here, but there is not a direct causal relationship between losing baby teeth and arithmetic skills.
Answers
Your friend loans you $20,000 for school. In five years he wants
$40,000 back. What is the interest rate he is charging you?
Remember to show your work.
Answers
The interest rate your friend is charging you for the $20,000 loan is 20% per year.
What is the interest rate on the loan?
The simple interest is expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is the interest rate and t is time.
Given that;
The Principal P = $20,000
Accrued amount A = $40,000
Elapsed time t = 5 years
Interest rate r =?
Plug these values into the above formula and solve for the interest rate r:
\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)
Converting r decimal to R a percentage
Rate R = 0.2 × 100%
Rate r = 20% per year
Therefore, the interest rate is 20% per year.
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I need help It’s honors 7 math pls help
Answers
Answer:
411,600.000× 10^3 OR 4.11600000×10^8
Step-by-step explanation:
The expontent seems to be 3 so you move the decimal point over <this way 3
if it is 8 you move it over this way < 8
Answer:
411,600.000× 10^3 OR 4.11600000×10^8
Step-by-step explanation:
The expontent seems to be 3 so you move the decimal point over <this way 3
if it is 8 you move it over this way < 8
Riley is building an ant farm for his school's science fair. He has enough materials to build a farm that is 550 square inches in total, 15 square inches of which will be taken up for food and water sources. Of the remaining available space, each ant needs at least 5 square inches to themselves. What is the maximum amount of ants Riley's ant farm can house
Answers
Answer:
991 Ants
Step-by-step explanation:
amount of area excluding the area needed for food and resources= 1000-9=991 Square inches
area each ant needs= 1 square inch
number of ants= 991÷1= 991 ants
Hazel McCurry offered $419,400 for a home that had been priced
at $439,500. The seller agreed to the offer. If she made a $44,000
down payment, what is the mortgage loan amount?
Answers
Answer:375,400
Step-by-step explanation:
419,400-44,000=375,400
find the square root of 5.494
\( \sqrt{5.494} \)
Answers
Answer:
the square root of 5.494 is 2.34
Step-by-step explanation:
The computation of the square root of 5.494 is as follows"
According to the question it is mentioned that
The number is 5.494
Now the square root of the above number is
\(\sqrt{5.494}\)
= 2.34
Hence, the square root of 5.494 is 2.34
Therefore the same is to be considered
A notebook costs £1.10, a pen costs 33p , a pencil costs 25p and a sharpener costs 79p. Remi buys 4 pencils, 1 pen, 2 sharpeners and some notebooks. He pays with £6 and receives 89p change. How many notebooks did he buy?
Answers
yes because the pencil of the epiosal makes it 35 degrees hot and the emeritals makes it long so he bought 5 notebooks
Melania is trying to estimate √30. she uses this table of values. What should she do next to find √30 to the nearest hundredth?
Answers
20 POINTS,RELATIONS OF A FUNCTION (picture provided)
Answers
Answer:
Step-by-step explanation:
The measure of angles of a PQR are in the ratio 2 : 3 : 5 the measure of largest angle.
A. 90°
B. 54°
C. 36°
D. 85°
Someone please help ne
Answers
if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then, p(b) =
Answers
The chance of the event B is 0.4 when using the probability for the two independent two event formula.
In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).
Events classified as independent do not depend on other events for their occurrence.
Event A's likelihood of happening is P(A)=0.65.
The likelihood of the two events A and B intersecting is P(A∩B)=0.26.
Given that the likelihood of the two independent events is:
P(A∩B) = P(A)⋅P(B)
Then the probability of the event B will be,
P(B) = P(A)/P(A∩B)
P(B) = 0.65/0.26
P(B) =0.4
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Solve this problem. The demand function for a certain book is given by the function x=D(p)=70e^−0.005p. Find the marginal demand.
Answers
Therefore, the marginal demand is given by the function\(dD(p)/dp = -0.35e^-0.005p.\)
Marginal demand refers to the change in the demand for a commodity resulting from a unit change in price, holding all other factors constant.
In this question, we have a demand function that gives us the number of copies of a certain book that would be sold at a certain price.
In other words, it refers to the derivative of the demand function with respect to price.
Marginal demand can be obtained by computing the derivative of the given demand function. Therefore, the marginal demand can be computed using the formula dD(p)/dp, where
\(D(p) = 70e^-0.005p.\)
Differentiating D(p) with respect to p gives:
dD(p)/dp = -0.005*70e^-0.005p
{Using chain rule,\(d/dp(e^u) = e^u * du/dx\), where u = -0.005p}
Thus, marginal demand is:
\(dD(p)/dp = -0.35e^-0.005p\)
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What are the units on each side of the equation gmm/x2 = mv2/x? (m and m are two different masses.)
Answers
In the given statement is:
Gravitational Force between two bodies at a distance x is given by:-
F = GmM/ x2 ; If a body of mass ' m' is revolving around the body of mass M and it's orbit is stationary then centrifugal force must be equal to the Gravitational Force i.e. Fg = mv2/x therefore FG = Fg i.e. GmM/ x2 =mv2/x; where v is the orbit motion of the orbiting body of mass.
Now, Let us understand the :
In mechanics, gravity, often known as gravitation, is the constant force of attraction occurring on all matter. It plays no part in shaping the interior features of common stuff because it is easily the weakest force known to exist in nature.
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PLEASE HELP
PLEASE HELP
PLEASE HELP
PLEASE HELPPPPPPPPPPPPPP
Answers
Answer: I think the perimeter is 17ab4
Step-by-step explanation:
What is the median of this data set? {22, 5, 9, 1, 7, 3) Enter your answer in the box median =
Answers
Answer:
7 is the answer to your question
solve this:
x2-2x-24=0
Answers
Answer:
Step-by-step explanation:
x^2-2x-24
(x-6)(x+4)
x= 6,-4
Answer:
x=6 or x= - 4
Step-by-step explanation:
Factorise x²-2x-24=0
(x+6)(x-4)=0
x+6=0 x-4=0
x= - 6 or x=4
6 The radius of the base of a cylinder is 39 in. and its height is 33 in.. Find the surface area of the cylinder in terms of s.
Answers
Answer:
17650 in².
Step-by-step explanation:
Given that the base of cylinder is 39 inch and it's height is 33inches . We need to find the surface area of the cylinder . So we know the TSA of cylinder as ,
\(\bf\implies TSA_{(cylinder)}= 2\pi r ( r + h ) \\\\\bf\implies TSA_{(cylinder)}= 2\pi 39 ( 39 + 33) in.^2\\\\\bf\implies TSA_{(cylinder)}= 2\times \dfrac{22}{7}\times 39 \times 72 \\\\\sf:\implies \boxed{\red{\bf TSA_{(cylinder)}= 17650 in^2}}\)
You are planning a vacation and have found a great rate on a hotel. The hotel is $99 per night, plus tax and a
resort fee. The expression 99(1.05)+ 25 represents the total cost of the hotel for nights. What is the tax
rate and the resort fee? Explain how you know
Answers
Answer:
resort fee is 25
tax rate is 1.05
Step-by-step explanation:
Can someone help me please
Answers
Answer: add 1
Step-by-step explanation:
71/2 + 125/8
193/5
191/8
203/5
201/8
Answers
Answer:
\(19 \frac{7}{8} = 19.87\)
Step-by-step explanation:
\(1. \: lcd = 8 \\ 2. \: \frac{71 \times 4}{2 \times 4} - \frac{125}{8} \\ 3. \: \frac{284}{8} - \frac{125}{8} \\ 4. \: \frac{284 - 125}{8} \\ 5. \: \frac{159}{8} \\ 6. \: 19 \frac{7}{8} = 19.87\)