$630,463.17
The revenue function in dollars from the sale of x campers is given by:
R(x) = 66,000x + 46,000(10+x)^(-1) - 8000
We can simplify this function as follows:
R(x) = 66,000x + 46,000/(10+x) - 8000
= 66,000x + 4600/(1+x/10) - 8000
To find the x-value that maximizes revenue, we need to find the critical points of the function R(x) and then determine whether each critical point corresponds to a local maximum, local minimum, or neither.
Taking the derivative of R(x) with respect to x, we get:
R'(x) = 66,000 - 4600/(1+x/10)^2
Setting R'(x) equal to zero, we get:
66,000 - 4600/(1+x/10)^2 = 0
Multiplying both sides by (1+x/10)^2, we get:
66,000(1+x/10)^2 - 4600 = 0
Expanding and simplifying, we get:
(x+10)^2 = 44/3
Taking the square root of both sides, we get:
x+10 = ±(2*sqrt(11))/3
Subtracting 10 from both sides, we get:
x = -10 ± (2*sqrt(11))/3
So the critical points of R(x) are:
x = -10 + (2sqrt(11))/3 and x = -10 - (2sqrt(11))/3
To determine whether each critical point corresponds to a local maximum, local minimum, or neither, we can use the second derivative test. Taking the second derivative of R(x), we get:
R''(x) = 9200/(1+x/10)^3
At the critical point x = -10 + (2*sqrt(11))/3, we have:
R''(-10 + (2sqrt(11))/3) = 9200/(1+(-10+(2sqrt(11))/3)/10)^3
= 9200/(1+2*sqrt(11)/30)^3
≈ -318.68
Since R''(-10 + (2sqrt(11))/3) is negative, the critical point x = -10 + (2sqrt(11))/3 corresponds to a local maximum of R(x).
Similarly, at the critical point x = -10 - (2*sqrt(11))/3, we have:
R''(-10 - (2sqrt(11))/3) = 9200/(1+(-10-(2sqrt(11))/3)/10)^3
= 9200/(1-2*sqrt(11)/30)^3
≈ 318.68
Since R''(-10 - (2sqrt(11))/3) is positive, the critical point x = -10 - (2sqrt(11))/3 corresponds to a local minimum of R(x).
Therefore, the x-value that maximizes revenue is x = -10 + (2*sqrt(11))/3, and the maximum revenue is:
R(-10 + (2sqrt(11))/3) = 66,000(-10 + (2sqrt(11))/3) + 46,000/(10-10+(2*sqrt(11))/3) - 8000
≈ $630,463.17
Learn more about revenue
brainly.com/question/8645356
#SPJ11
your very smart if you help
a + 26 = 180 (linear pair)
a = 180 - 26
a = 154°
Kayak rental company A charges an initial fee of $12 plus $3.25 for every hour spent kayaking. Kayak rental company B charges $9.25 for every hour spent kayaking. A customer finds that after h hours, the kayak rental companies will cost the same. Which equation represents this situation? Responses 3.25h+12=9.25h , 3.25 h plus 12 equals 9.25 h, 9.25h+3.25h=12 , 9.25 h plus 3.25 h equals 12, 9.25h=12−3.75h , 9.25 h equals 12 minus 3.75 h, 3.25h=12+9.25h
Answer: 3.25h + 12= 9.25
Step-by-step explanation:
12 is the initial fee which we will just add to our answer
3.25 is the rate per hour, it is being multiplied by the number of hours.
the number of hour it took to reach the same cost is not told so we will just put a variable.
What is this answer to this
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{4}}} \implies \cfrac{-12 +16}{4} \implies \cfrac{ 4 }{ 4 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-16)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{4}) \implies y +16 = 1 ( x -4) \\\\\\ y+16=x-4\implies y=x-20\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Let X be a random variable with EXP < and let Y = [X]. Suppose that X has a Lebesgue density symmetric about 0. Show that X and Y are uncorrelated, but they are not independent.
The value of Y is not independent of the value of X, and so X and Y are not independent.
Let X be a random variable with EXP <∞ and let Y = [X]. Since X has a Lebesgue density symmetric about 0, we know that E[X] = 0. Therefore, E[XY] = E[X[X]] = E[X²] = Var[X] + E[X]² = Var[X].
Since X and Y are uncorrelated, we have E[XY] - E[X]E[Y] = 0, which implies that E[XY] = E[X]E[Y] = 0*E[Y] = 0. Therefore, X and Y are uncorrelated.
However, X and Y are not independent because the value of Y depends on the value of X. For example, if X = 1.5, then Y = 1, but if X = -1.5, then Y = -2. Therefore, the value of Y is not independent of the value of X, and so X and Y are not independent.
Lear more about Random variable
brainly.com/question/17238189
#SPJ11
f(x)=x4−19x3+135x2+2- Fiat the toe crical nambersa,boff′(that is, the values at whichf′′′is zero or undetined) and lat thoir euact values in tho fiet colume of the tibie below (a ancendeng order,a
The critical numbers of f''(x) are 5 and 4.5.
To find the critical numbers of f(x), we need to first find the derivative of f(x) and then set it equal to zero. The derivative of f(x) is f'(x) = 4x3 - 57x2 + 270x. Setting this equal to zero gives us:
4x3 - 57x2 + 270x = 0
Factoring out an x gives us:
x(4x2 - 57x + 270) = 0
Using the quadratic formula, we can find the values of x that make this equation true:
x = (-(-57) ± √((-57)2 - 4(4)(270)))/(2(4))
x = (57 ± √(3249 - 4320))/8
x = (57 ± √(-1071))/8
x = (57 ± i√1071)/8
Since the values of x are complex, there are no real critical numbers of f(x).
The second derivative of f(x) is f''(x) = 12x2 - 114x + 270. Setting this equal to zero gives us:
12x2 - 114x + 270 = 0
Using the quadratic formula, we can find the values of x that make this equation true:
x = (-( -114) ± √((-114)2 - 4(12)(270)))/(2(12))
x = (114 ± √(12996 - 12960))/24
x = (114 ± √36)/24
x = (114 ± 6)/24
x = 5 or x = 4.5
The table below shows the critical numbers of f(x) and f''(x) in ascending order:
| Critical Number | f(x) | f''(x) |
|-----------------|------|--------|
| 4.5 | N/A | 0 |
| 5 | N/A | 0 |
To know more about derivative click on below link:
https://brainly.com/question/25324584#
#SPJ11
In the same year, at the Avondale golf club, there are 12 women and 56 men members. Write the ratio of women: men, in its simplest form.
Answer:
3:14
for every 3 women, there is 14 men
Step-by-step explanation:
The figure shown is a rhombus. Find the length of ST.
The length of ST is 57 unit.
What is Perimeter?A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or length. The circumference of a circle or an ellipse is its perimeter.
As, we know that the four sides of Rhombus are equal.
So, TR = QR
-x+ 68 = 5x + 2
-x - 5x = 2 - 68
-6x = - 66
x= -66/ (-6)
x= 11
So, the length of ST = 5x+ 2 = -x+ 68 = 57 unit
Learn more about Perimeter here:
https://brainly.com/question/6465134
#SPJ1
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x) = x2 + 3, g(x) = x + 4 f(g(x)) = g(f(x)) =
f(g(x))=x² + 8x +19 ; g(f(x))=x² + 7 are the value of the asked functions
explanation:-
the given functions are: f(x) = x² + 3 and g(x) = x + 4
f(g(x)) = f(x + 4) = (x + 4)² + 3 = x² + 16 + 8x +3 = x² + 8x +19
g(f(x)) = g(x² + 3) = x ²+ 3 + 4 = x² + 7
learn more about functions here. https://brainly.in/question/51284326
#SPJ11
The state capitals of Santa Fe, Oklahoma City, and Austin are shown in the map below. Abbreviating the cities by their first letter, write a mathematical statement using the Triangle Inequality Theorem to prove the distance from Santa Fe to Austin to Oklahoma City is greater than the distance from Santa Fe to Oklahoma City. (PLEASE HELPPPPP!!)
Using the Triangle Inequality Theorem the correct option is [tex]$SA + AO > SO$[/tex].
What is triangle inequality theorem?
The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. In mathematical notation, for a triangle with sides of lengths a, b, and c, this can be written as:
a + b > c
b + c > a
a + c > b
The correct mathematical statement using the Triangle Inequality Theorem to prove the distance from Santa Fe to Austin to Oklahoma City is greater than the distance from Santa Fe to Oklahoma City is:
[tex]$SA + AO > SO$[/tex]
where:
SA is the distance from Santa Fe to Austin
AO is the distance from Austin to Oklahoma City
SO is the distance from Santa Fe to Oklahoma City
This inequality states that the sum of the distances from Santa Fe to Austin and from Austin to Oklahoma City is greater than the distance from Santa Fe to Oklahoma City.
Therefore the correct option is [tex]$SA + AO > SO$[/tex].
To learn more about triangle inequality theorem visit:
https://brainly.com/question/1163433
#SPJ1
Find the point (x, y) on the unit circle that corresponds to the real number t. ON THE BLANK WRITE DOWN sqrt(2) for √2 or sqrt(3) for √3. t = 5????/6 the corresponding (x,y) is
The point (x, y) on the unit circle that corresponds to the real number t = 5π/6 is (-√3/2, 1/2).
The point (x, y) on the unit circle that corresponds to the real number t can be found using the following equations:
x = cos(t)
y = sin(t)
Since t = 5π/6, we can plug this value into the equations to find x and y:
x = cos(5π/6) = -√3/2
y = sin(5π/6) = 1/2
Therefore, the point (x, y) on the unit circle that corresponds to the real number t = 5π/6 is (-√3/2, 1/2).
Note: The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of the coordinate plane. The x-coordinate of a point on the unit circle corresponds to the cosine of the angle formed by the positive x-axis and the radius connecting the origin to the point, while the y-coordinate corresponds to the sine of this angle.
For more about circle:
https://brainly.com/question/29142813
#SPJ11
The ratio of roses to carnations in a floral shop is 1:4. If there are 240 carnations, how many roses are there?
Using the ratio, there are 60 roses in the floral shop.
To find the number of roses in the floral shop, we can use the ratio given in the question. The ratio of roses to carnations is 1:4, which means that for every 1 rose, there are 4 carnations.
If there are 240 carnations, we can use cross multiplication to find the number of roses.
1/4 = x/240
Cross multiplying gives us:
4x = 240
Solving for x, we get:
x = 240/4
x = 60
In conclusion, if the ratio of roses to carnations in a floral shop is 1:4 and there are 240 carnations, there are 60 roses.
Know more about ratio here:
https://brainly.com/question/12024093
#SPJ11
Given a line and a point, not on the line, there is one and only _____ line which passes through the given point and______ is to the given line.
A. one, parallel
B. one, perpendicular
C. two, parallel
D. two, perpendicular
Given a line and a point, not on the line, there is one and only one line which passes through the given point and is perpendicular to the given line. The correct answer is B.
A line and a point not on the line are given. We are asked to find the one and only line that passes through the given point and is perpendicular to the given line. The line that passes through the given point and is perpendicular to the given line is known as the perpendicular bisector.
The perpendicular bisector passes through the midpoint of the line segment formed by the two endpoints of the given line. Therefore, the answer is B. There is one and only one line that passes through the given point and is perpendicular to the given line. Therefore the correct answer of this question is option B
Know more about line segment here:
https://brainly.com/question/30072605
#SPJ11
HELP!!
One cubic foot of water is equivalent to 7.48 gallons. If the capacity of the fish tank is 100 gallons, find the maximum possible height for the fish tank. Round your answer to the nearest thousandth of an inch.
Show your work.
The height of the fish tank should be approximately 1.981 feet which is also equivalent to 23.772 inches.
What is the maximum possible height for the fish tank?As desired capacity of the fish tank is 100 gallons, and 7.48 gallons of water are equivalent to 1 cubic foot, the desired volume of the fish tank is (100 / 7.48) cubic feet, or approximately 13.369 cubic feet.
The desired volume is stated as a number of cubic feet so the known dimensions of the fish tank must be converted from inches to feet.
length = 54 inches = 4.5 feet
width = 18 inches = 1.5 feet
The formula for the volume V of a rectangular prism with length l, width w, and height h is V = lwh. We will substitute the known dimensions into the formula and solve for h.
V = ℓwh
13.369 ≈ 4.5 × 1.5 × h
13.369 ≈ 6.75h
h ≈ 13.369 / 6.75
h ≈ 1.981
Read more about height
brainly.com/question/1739912
#SPJ1
The delgados obtained an instrument loan of $12,000 from the credit union to pay for their son's tuitions. They obtained the loan at an apr of 10 percent and agreed to repay the loan in 12 mounths what is the finance charge the
The Finance Charge for the Delgados obtained for an instrument is $1200 to repay the loan in 12 months.
The given data is as follows:
Instrument loan = $12,000
Loan at APR = 10%
Number of months = 12 Months
The finance charge is calculated by using the formula,
Finance charge = Loan amount x APR x No' of months to repayment / No' of months in a year
Finance charge = ($12,000 x 10% x 12) / 12
Finance charge = 14400 / 12
Finance charge = $ 1200
Therefore we can conclude that the Finance charge for the Delgados obtained for an instrument is $1200.
To learn more about finance charge
brainly.com/question/3436429
#SPJ4
Given n points P1, P2, ..., Pn in d-dimensional space, the objective of the 3-center problem is to choose three center points ci, C2, C3 from the list of n given points so that the maximum distance between any point and its closest center is minimized. Mathematically speaking, we wish to choose three center points ci, C2, C3 to minimize the following cost function. cost(C1,C2,C3) = max min(||Pi – c1 ||?, ||P; – c2||2, ||Pi – c3||2) - (1) 1 1. Write a brute force algorithm that solves the 3-center problem. A brute force algorithm is an algorithm that solves a problem by trying every possibility. Be sure that your algorithm specifies enough detail so that it will be relatively easy for you to translate it into C source code. What is the computational complexity of your algorithm in terms of the number of input points n? For example, recall that bubble sort is O(n^2).
O(n
A brute force algorithm for the 3-center problem would involve trying every combination of three points in the set of given points, calculating the cost for each combination using Equation (1), and then returning the combination with the minimum cost. The algorithm can be expressed as follows:
The computational complexity of this algorithm is O(n
combinations of three points from a set of n points.
Learn more about brute force algorithm
brainly.com/question/28197566
#SPJ11
A quant is instructed to investigate the relationship between the size of a bond issue y and its trading volumes (value traded) x. Consider the data for 7 bonds:
x 20 30 40 50 60 70 80
y 10 12 30 40 48 60 75
(a) (i) Construct a scatterplot of these data.
(ii) What does the scatter plot suggest about the relationship between x and y?
(b) A linear model of the form y = α + βx + ε is fitted to the data, where the error terms (ε) independently follow a N(0, σ^2 ) distribution with the variance σ^2 being an unknown parameter.
(i) Determine the fitted line of the regression model.
(ii) Predict y when x = 250.
(c) A partially completed ANOVA table for this regression analysis is given below.
Source of variation sums of squares Degrees of freedom Mean Squares F-Value
Regression 3410 A D E
Error 59 B C
Total 3469 6
(i) Determine the missing values A, B, C, D and E in the table.
(ii) Determine an estimate of the variance σ 2 based on the above table.
(iii) Perform an F-test to test the null hypothesis that there is no linear relationship between x and y, based on the above table.
(d) (i) Dertemine the percentage of variation in y explained by x.
(ii) Calculate the coefficient of correlation and give an interpretation.
coefficient of correlation is 0.82
a) (i) The scatter plot of the data given is:
(ii) The scatter plot suggests that there is a positive linear relationship between x and y, as the data points move in an upward trend.
b) (i) The fitted line of the regression model is: y = 2.06 + 0.68x
(ii) When x = 250, the predicted value of y is 165.0
(iii) Missing values A, B, C, D, and E in the table are:
A = 3410, B = 5, C = 1, D = 5, E = 6.59
(iv) An estimate of the variance σ2 is 5.98
c) (i) The F-value for the F-test is 6.59, and the p-value is 0.02. This suggests that there is a significant linear relationship between x and y, as the p-value is less than 0.05.
(ii) The percentage of variation in y explained by x is 68.1%.
(iii) The coefficient of correlation is 0.82, indicating that there is a strong positive linear relationship between x and y.
Learn more about regression model
brainly.com/question/14983410
#SPJ11
Solve for x. If there is more than one solution, separate the solutions (1)/(x-6)+(x)/(x)=(-9x+3)/(2)
The value of x for this solution is x = -2, 3, -3.
To solve for x, we need to combine like terms and then isolate x on one side of the equation. Here are the steps:
1. Multiply both sides of the equation by the common denominator of (x)(x-6)(2) to eliminate the fractions:
(1)(x)(2) + (x)(x-6)(2) = (-9x+3)(x)(x-6)
2x + 2x^2 - 12x = -9x^3 + 3x^2 - 54x + 18
2. Combine like terms:
2x^2 - 10x = -9x^3 + 3x^2 - 54x + 18
3. Move all terms to one side of the equation:
9x^3 - x^2 + 44x - 18 = 0
4. Use the Rational Root Theorem to find possible solutions:
The possible rational roots are ±1, ±2, ±3, ±6, ±9, ±18
5. Use synthetic division to test the possible roots and find the actual solutions:
When we divide by -2, we get a remainder of 0, so -2 is a solution.
When we divide by 3, we get a remainder of 0, so 3 is a solution.
When we divide by -3, we get a remainder of 0, so -3 is a solution.
6. The solutions are x = -2, x = 3, and x = -3.
So the final answer is:
x = -2, 3, -3
Learn more about equation: https://brainly.com/question/29657992
#SPJ11
rections: Circle the correct answer unless the problem What is the value of (mn)/(r^(2)) if m=7,n=18 and r=6 ? A. 3.5
The correct answer is A. 3.5.
The value of [tex](mn)/(r^(2))[/tex] if m=7, n=18, and r=6 can be found by plugging in the given values into the equation and simplifying.
Step 1: Plug in the given values:
[tex](mn)/(r^(2)) = (7*18)/(6^(2))[/tex]
Step 2: Simplify the equation:
[tex](7*18)/(6^(2)) = (126)/(36)[/tex]
Step 3: Simplify further:
(126)/(36) = 3.5
To know more about equation refer to-
brainly.com/question/29657992#
#SPJ11
5) A decade of inflation
a) Suppose the annual inflation rate was 3% for 10 years in a row. What was the inflation rate for that decade?
b) Find the inflation rate for the decade from 1960 to 1970. If the inflation rate had been the same for each year in that decade, what would that annual rate have been? The answer to part a) will help you with this problem. This might be difficult depending on your math background, but try to be creative.
The inflation rate for that decade will be 34.39%. If the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.
a) If the annual inflation rate was 3% for 10 years in a row, the inflation rate for that decade would be 34.39%. This is calculated by using the formula (1 + annual inflation rate)^number of years - 1. So in this case, it would be (1 + 0.03)^10 - 1 = 0.3439 or 34.39%.
b) To find the inflation rate for the decade from 1960 to 1970, we need to know the Consumer Price Index (CPI) for both years. The CPI for 1960 was 29.6 and the CPI for 1970 was 38.8.
We can use the formula (CPI in later year/CPI in earlier year)^(1/number of years) - 1 to find the annual inflation rate.
So in this case, it would be (38.8/29.6)^(1/10) - 1 = 0.0279 or 2.79%. Therefore, if the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.
Learn more about inflation at https://brainly.com/question/14405066
#SPJ11
Given sin tetha= -12/13 and tetha is in the 4rd quadrant, find the following using Double Angle 13 identities. Show all work/formulas and give answers in exact form (no decimals). a. sin2tetha b. cos2tetha
Given sin θ = -12/13 and θ is in the 4th quadrant, we can use the double angle identities to find sin 2θ and cos 2θ. The double angle identities are:
sin 2θ = 2sin θcos θ
cos 2θ = cos^2 θ - sin^2 θ
First, we need to find cos θ. Since θ is in the 4th quadrant, we know that cos θ is positive. Using the Pythagorean identity, we can find cos θ:
sin^2 θ + cos^2 θ = 1
(-12/13)^2 + cos^2 θ = 1
144/169 + cos^2 θ = 1
cos^2 θ = 25/169
cos θ = 5/13
Now, we can use the double angle identities to find sin 2θ and cos 2θ:
sin 2θ = 2sin θcos θ = 2(-12/13)(5/13) = -120/169
cos 2θ = cos^2 θ - sin^2 θ = (5/13)^2 - (-12/13)^2 = -119/169
Therefore, the answers are:
a. sin 2θ = -120/169
b. cos 2θ = -119/169
Learn more about quadrant
brainly.com/question/7196312
#SPJ11
8:02 PM Wed Feb 22 L Allie Stevenson's practice S.12 Properties of logarithms: mixed review Rewrite the logarithmic expression as a single logarithm with the same base. Assume all expressions exist and are well-defined. Simplify any fractions. 2log_(w)x+4log_(w)2x
The simplified expression is log_(w)(16x^6)
To rewrite the logarithmic expression as a single logarithm with the same base, we need to use the properties of logarithms. The properties we will use are:
1) log_b(x)+log_b(y) = log_b(xy)
2) a*log_b(x) = log_b(x^a)
Using the first property, we can combine the two terms with the same base:
2log_(w)x+4log_(w)2x = log_(w)x^2+log_(w)(2x)^4
Using the second property, we can simplify the exponents:
log_(w)x^2+log_(w)(2x)^4 = log_(w)x^2+log_(w)16x^4
Using the first property again, we can combine the two terms with the same base:
log_(w)x^2+log_(w)16x^4 = log_(w)(x^2*16x^4)
Simplifying the expression inside the logarithm:
log_(w)(x^2*16x^4) = log_(w)(16x^6)
Therefore, the final expression is:
2log_(w)x+4log_(w)2x = log_(w)(16x^6)
Answer: log_(w)(16x^6)
To know more about logarithmic expression click on below link:
https://brainly.com/question/24211708#
#SPJ11
Choose all the due process rights that are found in the 6th Amendment.
A)
the right to be assisted by counsel
B)
the right to a speedy and public trial
C)
the right to confront and cross-examine witnesses
D)
the right to not be 'deprived of life, liberty or property without due process
of law
E
the right of the people to be secure in their persons, houses, papers, and
effects, against unreasonable searches and seizures
The due process rights found in the 6th Amendment are: the right to be assisted by counsel, the right to a speedy and public trial, and the right to confront and cross-examine witnesses. Option A, B, C are correct.
The right to assistance of counsel - this means that a defendant has the right to be represented by an attorney, who can help them prepare their defense, cross-examine witnesses, and navigate the complexities of the criminal justice system.
The right to a speedy and public trial - this means that a defendant has the right to a trial that is conducted promptly and is open to the public, so that justice can be done fairly and transparently.
The right to confront witnesses - this means that a defendant has the right to cross-examine witnesses who testify against them in court, in order to test their credibility and the accuracy of their testimony.
Option D is a due process right found in the 5th Amendment, while option E is a right found in the 4th Amendment.
Hence, A. B. C. the right to be assisted by counsel, right to a speedy and public trial, right to confront and cross-examine witnesses is the correct option.
To know more about Amendment here
https://brainly.com/question/12124635
#SPJ4
\[ \begin{array}{l} f(x)=2 x^{2}+5 \\ f-1(x)= \end{array} \] fx domain \( f x \) range \[ \begin{array}{l} f(x)=\frac{1}{2} x+4 \\ g(x)-6 x-2 \\ f \circ g(x)= \\ g \circ f(x)= \\ f(x)=\frac{1}{x-9} \\
The f(g(x)) is equal to 72x^2+48x+9 and g(f(x)) is equal to 3x+22.
To provide an accurate answer, it's important to first understand what the question is asking for. From the given information, it appears that there are several different parts to this question, so I will address each one individually.
1. Finding f-1(x)
To find the inverse of f(x), we can switch the x and y values and solve for y.
\begin{align*}
f(x) &= 2x^2+5 \\
y &= 2x^2+5 \\
x &= 2y^2+5 \\
2y^2 &= x-5 \\
y &= \sqrt{\frac{x-5}{2}} \\
f^{-1}(x) &= \sqrt{\frac{x-5}{2}}
\end{align*}
Therefore, f-1(x) is equal to √((x-5)/2).
2. Determining fx domain and range
The domain of f(x) is all real numbers since there are no restrictions on the input value x. However, the range of f(x) is limited by the fact that 2x^2+5 is always greater than or equal to 5. Therefore, the range of f(x) is [5,∞).
3. Finding f(g(x)) and g(f(x))
To find f(g(x)), we first need to substitute g(x) into f(x) wherever x appears:
\begin{align*}
f(g(x)) &= 2(g(x))^2+5 \\
&= 2(6x+2)^2+5 \\
&= 72x^2+48x+9
\end{align*}
To find g(f(x)), we first need to substitute f(x) into g(x) wherever x appears:
\begin{align*}
g(f(x)) &= 6f(x)-2 \\
&= 6\left(\frac{1}{2}x+4\right)-2 \\
&= 3x+22
\end{align*}
Therefore, f(g(x)) is equal to 72x^2+48x+9 and g(f(x)) is equal to 3x+22.
4. Explaining f(x)=1/(x-9)
The function f(x)=1/(x-9) is a rational function with a vertical asymptote at x=9. This means that as x approaches 9 from either direction, the function values become increasingly large (either positive or negative infinity).
The domain of f(x) is all real numbers except for x=9 (since dividing by zero is undefined). The range of f(x) is all real numbers except for zero (since 1/0 is undefined).I hope this helps! Let me know if you have any further questions.
Learn more about Equal
brainly.com/question/12323068
#SPJ11
can some one please help me with this
We can rewrite the inequality as:
95 ≤ u ≤ 155
How to solve the inequality?Here we have the absolute value inequality:
|125 - u| ≤ 30
Where the variable is u.
The absolute value can be decomposed into two inequalities:
(125 - u) ≤ 30
(125 - u) ≥ -30
Solving these two we will get:
125 - 30 ≤ u
125 + 30 ≥ u
Then the compound inequality is:
95 ≤ u ≤ 155
Learn more about inequalities at:
https://brainly.com/question/24372553
#SPJ1
What is 1/1 of a full rotation?
Answer:
Try out
Step-by-step explanation:
1/4
1/2
1
1 1/2
Answer: 360 degrees
So basically when you spin around you make 360 degrees lol.
please help and hurry i really need help and i also need to know where to drag the bar to it will only let me move it past 10 not before 10
The answer of the given question based on statistical measures the answer is, Min: 2,Max: 15,Med: 8,Q1: 4,Q3: 13.
What is Statistics?Statistics is branch of mathematics that deals with collection, analysis, interpretation, presentation, and organization of the data. It provides way to summarize and describe numerical information in meaningful way, and it enables us to make the informed decisions based on that information. Statistics is used in many things , including business, finance, health, engineering, social sciences, and more.
To create the box and whisker plot:
Draw a number line that includes all the data points.
Mark the minimum and maximum values with a horizontal line.
Locate the median and draw a vertical line through it.
Draw a box from the first quartile (Q1) to the third quartile (Q3).
Draw whiskers from the box to the minimum and maximum values.
Here is the completed box and whisker plot:
O
1
2 3 4 5 6 7 8
|--------|
9
10 11 12 13 14 15 16 17 18
|--------------|
X
The box represents the middle 50% of the data, with the bottom of the box at Q1 and the top of the box at Q3. The median is marked by a vertical line inside the box. The whiskers extend from the box to the minimum and maximum values, with any data points outside the whiskers shown as individual points (outliers).
To know more about Median visit:
https://brainly.com/question/3515636
#SPJ1
Tim wants to watch 23 seasons of a series, each season has 11 episodes and each episode is 11 minutes, how many minutes does he have to watch of the series?
Answer: 2783 minutes
Step-by-step explanation:
Answer:
2783
Step-by-step explanation:
Since there is 11 episodes in each season and there is 23 seasons we multiply and get 253 so 253 episodes and each one has 11 minutes so 11 x 253 which is 2783
Use Pascal’s Triangle to determine the fifth term of the expansion of (x − 5)6
The fifth term of the expansion of (x − 5)⁶ is found as: 937x².
Explain about the Pascal’s Triangle?The Pascal triangle has a lengthy history. It may be traced back to India's Pingala people in the second century BC, who also knew various other binomial formulas at the same time.
Using the binomial series:
(n C r) = n! / (r1(n - r)!
Given equation: (x − 5)⁶
On comparing:
a = x, b = -5 and n = 6
x⁶ + (6C1).x⁶.(-5)¹ + (6C2).x⁴.(-5)² + (6C3)x⁴(-5)³ + (6C4).x²(-5)⁴ + (6C5).x¹.(-5)⁵ + (-5)
Using binomial calculator to solve the expression as;
x⁶ - 30x⁵ + 375x⁴ - 2500x³ + 937x² - 1870x + 15625
Thus, the fifth term of the expansion of (x − 5)⁶ is found as: 937x².
Know more about Pascal’s Triangle,
https://brainly.com/question/13670757
#SPJ1
A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling. 10 tickets, they were still at a net loss of
$800 (due to the production costs). They sold each ticket for
$70
Let y represent the net profit (in dollars) when they have sold. X tickets. Complete the equation for the relationship between the net profit and number of tickets sold. Y=
The equation for the relationship between the net profit and the number of tickets sold is Y= 70x - 1500.
We are aware that the group charges $70 for each ticket and that after selling 10 tickets, there was a net loss of $800. Thus, the sum of the proceeds from the sale of the ten tickets was:
10 tickets sold for $70 each will bring in a total of $700.
The total production expenses must have been: Given that the net loss was $800:
Costs of production in total are $700 + $800 = $1500.
Let x be the number of purchased tickets. The sum of the sales of x tickets is:
Selling x tickets will bring in a total of $70.
The sum of the revenue less the sum of the production costs is the net profit:
All revenue minus all costs of production equals net profit.
[tex]Y = x × $70 - $1500[/tex]
Thus, the following equation represents the connection between the net profit and the number of tickets sold:
Y = 70x - 1500
learn more about net profit
brainly.com/question/22024991
#SPJ4
50 points pls help it’s math
The inequalities seen on Cartesian plane are - 2 · x + y > 1 and - (1 / 2) · x + y ≤ 2, respectively.
How to determine the inequalities representing a graph
In this problem we find two graphs by inequalities on Cartesian plane, whose definitions are listed below:
Case 19:
f(x) > y
Case 20:
f(x) ≤ y
Each inequality has a function of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptAnd the slope can be determined by secant line formula:
m = Δy / Δx
Now we proceed to determine each inequality:
Case 1:
Slope
m = 4 / 2
m = 2
Intercept
b = 1
Inequality
y > 2 · x + 1
- 2 · x + y > 1
Case 2:
Slope
m = 1 / 2
Intercept
b = 2
Inequality
y ≤ (1 / 2) · x + 2
- (1 / 2) · x + y ≤ 2
To learn more on inequalities: https://brainly.com/question/27989101
#SPJ1