how do i find the inverse of f(x)=\(\sqrt[3]{5x+5}\)
Answers
The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
What is inverse of function?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).Change y in for the f(x) :
y = ∛5x + 5
Switch the x and y
x³ = 5y + 5
x³ - 5 = 5y
y = ( x³ - 5 ) / 5
f⁻¹ = ( x³ - 5 ) / 5
Hence, The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
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Related Questions
A statistical test always produces evidence, but never _________.
Answers
A statistical test always produces evidence, but never complete evidence.
What is a statistical test ?A statistical test is a way to determine if a claim (like a hypothesis) about a quantitative attribute of a population is true or not. As a result, it serves as a tool for making quantitative assessments of a process or processes.
The objective is to determine whether there is enough evidence to "reject" a process theory or hypothesis. In other words, a statistical test will always yield evidence, but this evidence is never a full indicator; it is either sufficient or it is not.
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Find the polar coordinates of rectangular coordinates (-√2,1). Limit θ to the interval [0,2pi) and round 2 dceimal places if needed
Answers
The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.
To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:
r = √(x² + y²)
θ = tan^⁻1(y/x)
Plugging in the given values of (-√2,1), we get:
r = √((-√2)² + 1²) = √(2 + 1) = √3
θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians
Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:
θ ≈ 2.0344 + π ≈ 5.1779 radians
Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).
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PLS HELP ME WITH THIS
you need to use the y=mx+b
Answers
Hello!
What is a slope-intercept line:
\(y = mx + b\)
m: slope\(slope = \dfrac{y_2-y_1}{x_2-x_1} =\frac{-4--2}{3-0} =-\dfrac{2}{3}\)
y-intercept or point whose x-coordinate is '0'==> value of y-intercept is '-2'
Thus the equation is \(y=-\dfrac{2}{3}x-2\)
Hope that helps!
Answer: y=-2/3x-2
Step-by-step explanation:
1) Draw a triangle from one point to the next point.
For this example, I will use (-3,0) and (0,-2).
You can see that the number goes down 2 and right 3. From this, you can conclude that the rate is -2/3 using the equation rise/run.
2) Find the y-intercept
Looking at the graph, you can find that the y-intercept is (0,-2).
3) Fill in the y=mx+b
y=-2/3x-2
Last week, the Tasha Cola company had sales of $2,346.87. This week, the company had sales of $8,867.14. Which is the best estimate of the company’s total sales for both weeks?
Answers
Answer:
$11,200 or $11,000
Step-by-step explanation:
The amounts are approximately $2,300 and $8,900 which add up to $11,200.
Answer: $11,200 or $11,000
It seems there are choices for this problem, but you did not include them, so I can't tell the exact correct answer.
-1/4 plus 3/5
Answer or else
Answers
The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.
To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.
The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:
-1/4 = -5/20
3/5 = 12/20
Now that the fractions have the same denominator, we can add them:
-5/20 + 12/20 = (-5 + 12)/20 = 7/20
Therefore, -1/4 + 3/5 is equal to 7/20.
To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.
Thus, the final answer is 7/20.
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Choose 1 answer:
(Choice A)
Add 10 to the input to get the output.
(Choice B)
Multiply the input by 2 to get the output.
(Choice C)
Multiply the input by 3. Then subtract 5 from the result to get the output.
Answers
Answer:
its multiply by 2
Step-by-step explanation:
the reason for this is because 5 x 2=10
10 x 2 =20
15 x 3 = 30
may i have brainliest
The product of 2 more than 5 times a number and 4 less than three times a number
Answers
Sorry I'm not sure if I'm right just my thinking...
set the number to be x so that (5x+2)(3x-4)??
A standard die is rolled. Find the probability that the number rolled is greater than 3
. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Rolling a number higher than 3 has a 2/6 or 1/3 chance of happening. Another way to say this is to round a decimal to the closest millionth, which is \(0.333333\) .
What is the fraction in the lowest terms?A standard die has 6 sides, labelled with the numbers 1 through 6. When the die is rolled, each side has an equal probability of landing face up.
Since we want to find the probability of rolling a number greater than 3, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
When you roll a standard die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Since we want to find the probability of rolling a number greater than 3, we need to count how many of these outcomes satisfy that condition.
Therefore, the probability of rolling a number greater than 3 is 2/6 or 1/3. Alternatively, we could express this as a decimal rounded to the nearest millionth, which would be \(0.333333\) .
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Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all 9 people in the group would be $81. This includes an entrance ticket and a $3 skate rental fee for each person. Which equation can you use to find t, the cost of each entrance ticket? How much does each entrance ticket cost? $
Answers
The cost of the entrance ticket is $6.
The equation that can be used to represent the information in the question is:
Total cost = (number of students x entrance fee) + (cost to rent a skate x number of students)
$81 = 9t + ($3 x 9)
$81 =9t + $27
In order to determine the value of t, the following steps would be taken:
Combine similar terms
$81 - $27 = 9t
Subtract similar terms
54 = 9t
Divide both sides of the equation by 9
t = $6
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What is the range of the function f(x)=2x^3−3x for the domain {−1, 1, 2}?
Answers
The range of the function is {1,-1,10} for function f(x)=2x³−3x .
What is a function?A relation is a function if it has only One y-value for each x-value.
In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.
The given function is f(x)=2x³−3x
The domain is {-1,1,2}
Now f(-1)=2(-1)³-3(-1)
=-2+3=1
f(1)=2(1)³-3(1)=2-3=-1
f(2)=2(2)³-3(2)=16-6=10
Hence, the range of the function is {1,-1,10} for f(x)=2x³−3x .
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Which of the following best describes the equation below? y=2/5x-12 A. neither linear nor nonlinear B. linear C. both linear and nonlinear D. nonlinear
Answers
Answer:
B. Linear
Step-by-step explanation:
Q is the midpoint of PR. If PQ = 8x+11 and QR = 14x-1, what is the value of x?
Answers
Answer:
x=2
Step-by-step explanation:
PQ =QR if Q is the midpoint
8x+11 = 14x-1
Subtract 8x from each side
8x+11 -8x = 14x-1-8x
11 = 6x-1
Add 1 to each side
11+1 = 6x-1+1
12 = 6x
Divide each side by 6
12/6 = 6x/6
2 =x
For the following word problems, first write a system of equations then solve for full marks.
3. The perimeter of a rectangle is 64 cm. Twice the width is 4 cm more than the length.
Find the dimensions of the rectangle.
Answers
The length of rectangle is 20cm and width is 12cm.
Let the length is x cm and width is y cm.
then perimeter 2(x+y) =64 cm
=> x+y = 64/2 = 32
=> x + y = 32 .............(1)
and according to question twice the width is 4cm more than length so,
2y = x + 4
=> 2y -x = 4 .............(2)
now we add these two equation to find the value of x and y.
3y = 36
=> y = 12
now put the value of y on any equation to find value of x ,
x +12 = 32
=> x = 32 -12 = 20
so, the length of rectangle is 20cm and width is 12cm.
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Joyce saved $220 on an item that was 75% off what was the original price
Answers
Answer:
$880
Step-by-step explanation:
Use the equation:
\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.
220=(1-0.75)x
simplify parenthesis terms
220=0.25x
divide both sides by 0.25
880=x
So, the original price was $880.
Hope this helps! :)
A ball bounces to a height of 6.7 feet on the first bounce. Each subsequent bounce reaches a height that is 81% of the previous bounce. What is the height, in feet, of the sixth bounce? Round your answer to the thousandths place. 1.892 ft 2.336 ft 2.650 ft 5.427 ft
Answers
On the 1st bounce, height = 6.7 feet
We were not given the inital height of the ball before the 1st bounce
2nd bounce:
height = 0.81 of the previous bounce
height = 0.81(6.7)
3rd bounce:
height = 0.81 of the previous bounce
previous bounce = 0.81(6.7)
height = 0.81(0.81 × 6.7)
We can derive a formula for the nth bounce:
\(\begin{gathered} \text{height = 6.7(0.81)}^{n\text{ - 1}} \\ h(n)\text{ = 6.7(0.81)}^{n\text{ - 1}} \\ To\text{ check:} \\ \text{when n = 1} \\ h(1)\text{ = 6.7(0.81)}^{1\text{ - 1}}\text{ = 6.7 ft} \end{gathered}\)For the sixth bounce, height:
\(\begin{gathered} h(n)=6.7(0.81)^{n-1} \\ \text{when n = 6} \\ h(6)=6.7(0.81)^{6-1} \\ h(6)=6.7(0.81)^5 \\ h(6)\text{ = 2.336 ft }(\text{option B)} \end{gathered}\)Find the circumference of the circle in terms of π. C= mi (Type an exact answer in terms of π.)
Answers
The circumference of a circle is given by:
\(C=\pi D\)In this case the diameter of the circle is 30, therefore the circumference is:
\(C=30\pi\)Points P and S are located the same distance from 0 on the
number line shown.
Answers
The expression which has a negative value according to the number line drawn in the task content where points P and S are as given is; Choice D; P + 1.
Which expression has a negative value according to the number line drawn in the task content?It follows from the task content that the expression which has a negative value among the given answer choices is to be identified.
As evident in the number line, the number S is greater than 1, and hence, is a positive number.
Also, the number P is less than -1 and hence, is a negative number.
Since, the task content requires that the expression with negative value be identified, it follows that the required expression is; Choice D.
This follows from the fact that, hypothetically, the value of P is -1.8, hence; P + 1 = -1.8 + 1
= -0.8
Ultimately, The expression which has a negative value according to the number line drawn in the task content where points P and S are as given is; Choice D; P + 1.
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According to a poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1,200 Americans is selected. Complete parts (a) through (d) below.
a. What percentage of the sample would we expect to report being afflicted by stress?
Answers
The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%
How to calculate the percentage afflicted by stress?The percentage of a data set is when part of the data is represented per 100 with a symbol of %.
It was stated in the question that 80% of Americans report being afflicted by stress.
Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.
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For Field Day, the 72 students in fourth grade will be divided into tears with the same number of students on each team. The 60 students in third grade will be divided into teams that each have the same number of students as the fourth grade teams. What is the largest number of students that a team could have? Help meeee
Answers
We do this because the factors are the numbers determining the number of people and the number of teams, for example if they used the factors 6 and 10 for 60, they would make 6 teams of 10 people. And since factors are whole numbers, it makes sense for people and doesn’t cut ppl in half.
So the greatest factor that 72 and 60 gave have in common is 12, bc 5 x 12 is 60 and 6 x 12 is 72, and they don’t have other factors in common that are higher than 12.
This means that 12 is the answer, bc it’s the largest number of students that a team could have, in both the fourth and third grades.
a ball is thrown up vertically. after t seconds, it's height (in feet) is given by the function h (t)=96t-16t^2 . after how long will it reach its maximum height
Answers
The time taken to reaches its maximum height is 3s.
In the question,
It is given that,
Height, h(t) = \(96t - 16t^{2}\)
The maximum value of the function is obtained if the first derivative of the function h (t) = 0.
\(\frac{dh(t)}{dt} = 96 - 32t = 0\)
⇒ \(t = 3\)
So, time taken to reach its max height is 3 seconds.
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y bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expens prepare bank reconcilation
Answers
The adjusted bank balance after reconciling is Br. 5,224.42.
How the bank reconciliation will be prepared?To prepare the bank reconciliation, we have to analyze the differences between the bank statement balance and the company's ledger balance.
Details
Bank statement balance of Br. 4,964.47 at July 31.
Add: Deposit made after banking hours Br. 410.90
New balance: Br. 5,375.37.
Deduct Erroneously charged check of Br. 79
New balance Br. 5,296.37.
Deduct Outstanding checks:
Check No. 801 of Br. 100.00 (issued on June 15).
Check No. 888 of Br. 10.25 (issued on July 24).
Check No. 890 of Br. 294.50 (issued on July 27).
Check No. 891 of Br. 205.00 (issued on July 30).
Total outstanding checks: Br. 609.75.
New balance: Br. 4,686.62.
Deduct: Incorrectly charged amount of Br. 120.
Add: Correct amount of Br. 210.
Add: Proceeds from the collection Br. 500.
Add: Interest earned on the account balance Br. 24.75.
Deduct: Returned check of Br. 10
Deduct: Fee charged by the bank for handling the collection Br. 5.00.
Deduct: Check from customer John Br. 50.25.
Deduct the service charge by the bank for the month of July of Br. 12.70.
New balance: Br. 5,224.42.
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Mrs. marks has to pay if she drives 300 miles. 25 + 0.30*m=
Answers
Answer:25.3
Step-by-step explanation:
Because your adding 25 to 0 and leaving the decimal point and taking away 0 from 30
Twice the difference of m and 12 gives 72.
translate to algebraic equation
Answers
Answer:
\(2(m - 12) = 72\)
Step-by-step explanation:
Part 1) "The difference of m and 12"
This simply means subtracting 12 from m. Therefore, we get \((m - 12)\).
Part 2) "Twice the difference of m and 12"
This means we should double the same difference we got in Part 1. Therefore, we get \(2(m - 12)\).
Part 3) "gives 72"
Finally, we are given that the algebraic expression we found under Part 2 should be equal to 72. Therefore, we get \(2(m - 12) = 72\)
When using the scanning objective (4X), how long would the entire ocular micrometer ruler be in millimeters?2.5 mm
Answers
The entire ocular micrometer ruler be in millimeters 2.3mm
Determine the size of an object/cell? Once the field of view is calculated for your microscope, you will be able determine the size of the objects that you are looking at.You will need to count (or estimate) how many cells will fit across the diameter of the field of view.To get the average size of one cell, you will divide the field of view by the number of cells that would fit across the diameterTo convert the diameter from millimeters to micrometers, multiply the diameter by 1000For the scanning objective (4X),
the objective is the scanning power, The, power is 4X and the Diameter in mm is 2.3mm
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Between 6pm and 7pm, 5 mystery novels, 3 non-fiction books, 7 picture books, and 2 science fiction novels were returned to the library. What is the experimental probability that the next book returned to the library is a picture book?
Answers
Match the situation with its probability.
Answers
The given probabilities are as follows:
Spinner landing on at least one A = 7/16Spinner landing on C and D in any order = 1/8Spinner landing on two Bs = 1/16Spinner landing on C on the second spin = 1/4What are the probabilities?The probabilities are determined using the formula below:
Probability = number of expected outcome / number of total outcomesSpinner landing on at least one A:
number of at least one A = 7
Spinner landing on at least one A = 7/16
Spinner landing on C and D in any order:
number of landing on C and D in any order = 2
Spinner landing on C and D in any order = 2/16
Spinner landing on C and D in any order = 1/8
Spinner landing on two Bs:
number of landing on two Bs = 1
Spinner landing on two Bs = 1/16
Spinner landing on C on the second spin:
Number of landing on C on the second spin = 4
Spinner landing on C on the second spin = 1/4
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I need it done very quick pls help
Answers
You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years of ownership. Since you are particularly interested in the Toyota Camry, you decide to estimate the resale value of the Camry with a 90% confidence interval. You manage to randomly obtain data on 17 recently resold 5 year old Toyota Camrys. These 17 cars were resold at an average price of $12,400. Assume the resale value of the Camry after 5 years of ownership is normally distributed.
Write the formula that should be used to calculate the 90% confidence interval for the true mean resale value of the Camry after 5 years of ownership.
If the 90% confidence interval for the true mean resale value of the Camry after 5 years of ownership is from $12,103 to $12,697, what is the value for the sample standard deviation of the 17 cars in the sample? Assume all values below are rounded to the nearest dollar.
a) $625
b) $701
c) $744
d) Can't answer the question based on the information given.
e) None of the above are correct.
Answers
Answer:
b) $701
Step-by-step explanation:
We want to find the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 17 - 1 = 16
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 16 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.746.
If the 90% confidence interval for the true mean resale value of the Camry after 5 years of ownership is from $12,103 to $12,697.
The margin of error is half this difference. So
\(M = \frac{12697-12103}{2} = 297\)
Margin of error formula:
\(M = T\frac{s}{\sqrt{n}}\)
In which s is the standard deviation of the sample and n is the size of the sample.
In this question:
\(T = 1.746, M = 297, n = 17\)
We use this to find s, which is the sample standard deviation. So
\(M = T\frac{s}{\sqrt{n}}\)
\(297 = 1.746\frac{s}{\sqrt{17}}\)
\(s = \frac{297*\sqrt{17}}{1.746}\)
\(s = 701.35\)
To the nearest dollar, $701 and the answer is given by option b.
-5(x+1)= - 3(2x-2)
x= 11
X=-3
x=3
x= -11 please help quick!!!
Answers
Help me with thisPlease explain in a non-complicated way with as little steps as possible. Thank you.
Answers
Simplify the expression inside the [ ] symbols using the law of signs:
\(\lbrack-2-(+3)\rbrack=\lbrack-2-3\rbrack=\lbrack-5\rbrack\)Therefore:
\(25-\lbrack-2-(+3)\rbrack^2=25-\lbrack-5\rbrack^2\)Notice that (-5)^2=+25. Then:
\(25-\lbrack-5\rbrack^2=25-(+25)\)Then, there are two expression which are equivalent to the given expression:
Option a)
\(25-(+25)\)Option d)
\(25-\lbrack-5\rbrack^2\)