The inverse function of f(x) = 9x - 2 is [tex]f^{(-1)x}[/tex] = (x + 2)/9. The inverse function of g(x) = 7x - 3 is [tex]g^{(-1)x}[/tex] = (x + 3)/7. The inverse function of h(x) = x - 3(5 - 4x) is [tex]h^{(-1)x}[/tex] = 13x - 15. The inverse function of j(x) = x + 5 is [tex]j^{(-1)x}[/tex] = x - 5.
Let's find the inverse functions for each given function:
a) f(x) = 9x - 2
To find the inverse function, we can follow these steps:
Replace f(x) with y: y = 9x - 2.
Swap x and y: x = 9y - 2.
Solve the equation for y: x + 2 = 9y.
Divide both sides by 9: (x + 2)/9 = y.
Replace y with [tex]f^{(-1)x}[/tex]: [tex]f^{(-1)x}[/tex]= (x + 2)/9.
Therefore, the inverse function of f(x) = 9x - 2 is [tex]f^{(-1)x}[/tex] = (x + 2)/9.
b) g(x) = 7x - 3
Following the same steps as above:
Replace g(x) with y: y = 7x - 3.
Swap x and y: x = 7y - 3.
Solve the equation for y: x + 3 = 7y.
Divide both sides by 7: (x + 3)/7 = y.
Replace y with [tex]g^{(-1)x}[/tex]: [tex]g^{(-1)x}[/tex]= (x + 3)/7.
Thus, the inverse function of g(x) = 7x - 3 is [tex]g^{(-1)x}[/tex] = (x + 3)/7.
c) h(x) = x - 3(5 - 4x)
Again, following the same steps:
Replace h(x) with y: y = x - 3(5 - 4x).
Swap x and y: x = y - 3(5 - 4x).
Solve the equation for y: x = y - 15 + 12x.
Collect like terms: 12x - y = 15 - x.
Solve for y: y = 12x + x - 15.
Combine like terms: y = 13x - 15.
Replace y with [tex]h^{(-1)x}[/tex]: [tex]h^{(-1)x}[/tex] = 13x - 15.
Thus, the inverse function of h(x) = x - 3(5 - 4x) is [tex]h^{(-1)x}[/tex] = 13x - 15.
d) j(x) = x + 5
Following the same steps as before:
Replace j(x) with y: y = x + 5.
Swap x and y: x = y + 5.
Solve the equation for y: y = x - 5.
Replace y with[tex]j^{(-1)x}[/tex]: [tex]j^{(-1)x}[/tex] = x - 5.
Therefore, the inverse function of j(x) = x + 5 is [tex]j^{(-1)x}[/tex] = x - 5.
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JK and LM are perpendicular diameters of a circle. They are each 12 inches long. What is the approximate length of chord LK? With Explanation Please
Answer:
8.5 inches
Step-by-step explanation:
Let the center of the circle = C
Now CK = CL = 6
Using Pythagoras theorem
LK^2 = CL^2 + CK^2
= 6^2 +6^2
= 36 + 36
= 72
LK = 72 ^1/2
= ( 36*2)^1/2
= 6(2)^1/2
= 8.5 inches
In how many ways can 6 adults and 3 children stand together in a line so that no two children are next to each other?
There are 25,200 different ways in which 6 adults and 3 children can stand together in a line such that no two children are next to each other.
To determine the number of ways in which 6 adults and 3 children can stand together in a line such that no two children are next to each other, we can use the concept of permutations.
Let's consider the adults and children as distinct entities. First, we will calculate the number of ways to arrange the adults in a line, and then we will insert the children into the gaps between the adults.
Step 1: Arrange the adults
Since there are 6 adults, there are 6! (6 factorial) ways to arrange them in a line.
Step 2: Insert the children
Now, we have 7 possible positions between the adults where the children can be inserted. These positions include the spaces before the first adult, between each pair of adjacent adults, and after the last adult.
To ensure that no two children are next to each other, we need to choose 3 distinct positions out of the 7 available positions. This can be done in 7C3 ways, which represents the combination of 7 positions taken 3 at a time.
Using the formula for combinations, 7C3 can be calculated as follows:
7C3 = 7! / (3! * (7-3)!)
= 7! / (3! * 4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35
Step 3: Multiply the results
Finally, we multiply the number of ways to arrange the adults (6!) by the number of ways to insert the children (35) to obtain the total number of arrangements:
Total number of arrangements = 6! * 35
= 720 * 35
= 25,200
Therefore, there are 25,200 different ways in which 6 adults and 3 children can stand together in a line such that no two children are next to each other.
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David had $35 to spend at the fair. If the admission to the fair is $4.5 and the rides cost $1.50 each, what is the greatest number of rides David can go on?
Answer:
20 rides
Step-by-step explanation:
35-4.5=30.5
20*1.5=30 and 30 plus 4.5 equals 34.5
If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent. True or False?
The statement "If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent" is true.
Let's understand why?
Explanation:
An argument with a tautology conclusion is an argument that arrives at a conclusion that is always true, regardless of the truth values of the premises. In other words, it is impossible for the premises to be true while the conclusion is false.
This means that any attempt to find a counterexample that disproves the conclusion will always fail, as there is no possible scenario in which the conclusion is false.
The counterexample set of an argument is the set of all possible scenarios in which the premises are true but the conclusion is false. If the conclusion is a tautology, then there is no possible scenario in which the conclusion is false, and thus the counterexample set is empty. An empty counterexample set is equivalent to an inconsistent counterexample set, as it means that there is no consistent scenario in which the conclusion is false.
Therefore, if the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent.
Hence, the statement is true.
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I dont know this someone please answer this and show work and FAST! My teacher will call on me soon
Answer:
I can' see this. Can you show it closer? Please!
Step-by-step explanation:
Answer:
ok maybe itll work with this???
Step-by-step explanation:
file:///C:/Users/apple/Downloads/13f2bddc55b71689635395017a167da1%20(1).pdf
I hope it workksss
convert 123 percent into fraction
1.23 is a decimaland 123/100 OR 123% is the percentage for 123/100.
HOW TO WRITE 123/100 AS A DECMAL?
Step-by-step explanation:
Fraction=123/101
Decmial=1.21782
percentage=121.782%
In a study by a researcher, the Poisson distribution was used to model the number of patients per month referrea to an oncologist. The researchers use a rate of 16 patients per month that are referred to the oncologist. Calculate the probability that in a month:
a) exactly 10 patients are referred to an oncologist. -
b) between five and 15 inclusive are referred to an oncologist.
c) more than 10 are referred to an oncologist
The probability that exactly 10 patients are referred to an oncologist in a month is 0.036
The probability that between five and 15 inclusive are referred to an oncologist in a month is 0.98.
The probability that more than 10 patients are referred to an oncologist in a month is 0.873
Given:
A researcher used Poisson distribution to model the number of patients per month referred to an oncologist. The researcher uses a rate of 16 patients per month. We have to find the probabilities for different conditions:
a) The probability of exactly 10 patients are referred to an oncologist.
b) The probability that between five and 15 inclusive are referred to an oncologist.
c) The probability that more than 10 are referred to an oncologist.
Solution:
a) The number of patients referred to an oncologist per month follows Poisson distribution with parameter λ = 16.
The probability of exactly 10 patients are referred to an oncologist is:
`P(X = 10) = e^(-λ) * (λ^x) / x!` = `e^(-16) * (16^10) / 10! = 0.036`
Therefore, the probability that exactly 10 patients are referred to an oncologist in a month is 0.036.
b) The probability that between five and 15 inclusive are referred to an oncologist is:
`P(5 ≤ X ≤ 15) = P(X ≤ 15) - P(X ≤ 4)``= ∑_(x=0)^4 (e^(-16) * (16^x) / x!) + ∑_(x=5)^15 (e^(-16) * (16^x) / x!)`≈ 0.98
Therefore, the probability that between five and 15 inclusive are referred to an oncologist in a month is 0.98.
c) The probability that more than 10 are referred to an oncologist is:
`P(X > 10) = 1 - P(X ≤ 10)` `= 1 - ∑_(x=0)^10 (e^(-16) * (16^x) / x!)` ≈ 0.873
Therefore, the probability that more than 10 patients are referred to an oncologist in a month is 0.873.
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Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid singularity statement please help
Answer:
Not similar
Step-by-step explanation:
anybody can help me with this
Answer:
the answer is a/ 21 kilometers
The animal department wants to estimate the kangaroo population. So they marked 30 kangaroos with paint. These kangaroos were then released into the jungle. After four months 600 kangaroos were caught. Among these Kangaroo, 18 were marked. To the nearest whole number,what is the best estimate for the kangaroo population?
Answer:
1000
Step-by-step explanation:
From the above question
We have the following parameters
30 were intially Marked
600 were caught and out of it 18 was marked
The formula for the best estimate of the population is calculated as:
Total population = Initial marked kangaroo × Number of caught kangaroo/Number of kangaroo marked after they were caught
= 30 × 600/18
= 1000
Answer:
kangaroos are found in austraillia i don't kno where in austrailla u can find one but they are cute as a pumpkin
Step-by-step explanation:
find the solution to mx cx kx=f(t) for an arbitrary function f(t), x(0)=0, x'(0)=0
Step-by-step explanation:
The given equation `mx cx kx=f(t)` is a second-order linear differential equation with constant coefficients. The general solution to this type of equation is given by the sum of the complementary solution `x_c(t)` and the particular solution `x_p(t)`.
The complementary solution x_c(t) is the solution to the associated homogeneous equation mx cx kx=0. The characteristic equation for this homogeneous equation is mr^2 + cr + k = 0. Solving this quadratic equation gives two roots r_1 and r_2. The complementary solution can then be written as x_c(t) = C_1e^(r_1t) + C_2e^(r_2t).
The particular solution x_p(t) depends on the form of the function f(t). There are several methods for finding the particular solution, such as undetermined coefficients or variation of parameters.
Once the complementary and particular solutions are found, the general solution to the given differential equation is given by x(t) = x_c(t) + x_p(t). The constants C_1 and C_2 can then be determined using the initial conditions x(0)=0 and x'(0)=0.
Without more information about the function f(t), it is not possible to find a more specific solution to the given differential equation.
someone helpp!!!!!!!
Answer:
the rate of change is 3
Step-by-step explanation:
if im wrong im sorry but if im right give me brainliest
Franco Co-operation makes iron benches, they want to move their production unit to a new location. The new production plant will cost SAR 200000 to construct Variable costs of production of each bench are SAR 200 and the selling price of each bench is SAR 250. Determine the break-even point for bench production at the new plant?
The break-even point for bench production at the new plant is 4000 units.
The new production plant of Franco Cooperation will cost SAR 200000 to construct.
The variable costs of production of each bench are SAR 200. The selling price of each bench is SAR 250. We can find out the break-even point of bench production at the new plant by using the break-even formula.
Break-even point (in units) = Fixed costs / Contribution margin per unitWhere,
F = Fixed costs
P = Price per unit
V = Variable cost per unit
Contribution margin per unit = Price per unit - Variable cost per unit
First, let's calculate the contribution margin per unit.
P = Selling price of each bench = SAR 250V = Variable cost per unit = SAR 200
Contribution margin per unit = P - V= SAR 250 - SAR 200= SAR 50
Now, let's calculate the break-even point.
Fixed costs (F) = Cost of constructing the new plant= SAR 200000
Contribution margin per unit = SAR 50
Break-even point (in units) = F / Contribution margin per unit= SAR 200000 / SAR 50= 4000.
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The break-even point for bench production at the new plant can be found by dividing the fixed costs by the contribution margin per unit.
The break-even point for bench production at the new plant is 4000 benches.
To determine the break-even point, we need to calculate the contribution margin per unit. Contribution margin per unit is the amount left over after deducting the variable costs from the selling price. It is also called unit contribution margin. Therefore, the contribution margin per unit = Selling price per unit - Variable cost per unit
= SAR 250 - SAR 200
= SAR 50
Now, we can use the formula to calculate the break-even point:
Break-even point = Fixed costs / Contribution margin per unit
Fixed costs = cost of new production plant
= SAR 200000
Contribution margin per unit = SAR 50
Therefore, Break-even point = SAR 200000 / SAR 50
= 4000 benches
The break-even point for bench production at the new plant is 4000 benches.
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25 points. Get it before the mod sees it!
gogogogo lol
Answer:
yy
Step-by-step explanation:
bi
Jerry ordered 4 items online. He is charged $2.91 per pound for shipping. The items weighed 4.3 pounds, 2 pounds, 3.8 pounds, and 5.9 pounds. How much will he be charged for shipping? (Round to the nearest cent).
Answer:
46.56 pounds
Step-by-step explanation:
Given data
4.3 pounds
2 pounds
3.8 pounds, and
5.9 pounds
Let us find the total weight of all the items
=4.3+2+3.8+5.9
=16 pounds
We are told that he is charged $2.91 per pound for shipping
Hence the cost of shipping 16 pounds is
=2.91*16
=46.56 pounds
clients with a quickbooks online plus subscription can create 400 ungrouped tags and 1000 grouped tags distributed among up to 40 tag answer
Clients with a QuickBooks Online Plus subscription have the ability to create a total of 400 ungrouped tags and 1000 grouped tags, which can be distributed among up to 40 tag categories.
QuickBooks Online Plus offers users the flexibility to categorize transactions using tags. Tags are a way to organize and track transactions based on specific criteria or categories. There are two types of tags available: ungrouped tags and grouped tags.
With a QuickBooks Online Plus subscription, clients can create a maximum of 400 ungrouped tags. These tags can be assigned to individual transactions to provide additional information or categorization. Clients can create up to 40 tag categories and distribute the 1000 grouped tags among these categories.
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HEY GUYS COULD YOU HELP ME WITH THESE TWO QUESTIONS!!! DON'T WORRY YOU'LL GET YOUR POINTS!!
Answer:
i am unsure
Step-by-step explanation:
I HEART POINTS
Ali travelled 75% of her journey to work by taxi. If his total journey is 12km, what distance did she travel by taxi? don't send in file please
how do i do this question? i got it wrong and im confused how
Answer:
im pretty sure youre right :/ dont know why it marked you as wrong
Answer:
I think its F im not sure but i did 12x12 witch is 144 the rest is self explanory
Step-by-step explanation:
7. The short sides of a parallelogram are both 12.0 cm. The acute angles
of the parallelogram are 65°, and the short diagonal is 15.0 cm.
Determine the length of the long sides of the parallelogram. Round
your answer to the nearest tenth of a centimetre.
Please help explain this question
The length of the longest side of the parallelogram is 14.7 cm.
We have,
Let's denote the length of the long sides of the parallelogram as L.
In a parallelogram, the opposite sides are congruent, so both long sides have the same length.
The Law of Cosines states:
c² = a² + b² - 2ab cos(C)
Where:
c is the length of the side opposite the angle C,
a and b are the lengths of the other two sides,
C is the measure of the angle opposite side c.
The short sides of the parallelogram are 12.0 cm, and the acute angle is 65°.
Applying the Law of Cosines to find the length of the long side:
[tex]L^2 = 12^2 + 12^2 - 2 * 12 * 12 * cos(65)\\L^2 = 144 + 144 - 288 * cos(65)\\L^2 = 288 - 288 * cos(65)\\L = \sqrt{(288 - 288 * cos(65))}\\L = 14.7 cm[/tex]
(rounded to the nearest tenth of a centimeter)
Thus,
The length of the longest side of the parallelogram is 14.7 cm.
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calculate the value of x for the following polygon
(answers me or i'll throw oli london at you )
Answer:
X = 60 degrees
Answer
80°
Step by Explanation:
the angle right to 60°= 180-60 (linear pair)
= 120°
total angle of 5 sided polygon= 540°
540° = x + 110° + 130° + 100° + 120°
540° = x + 460°
x= 540° - 460°
x = 80°
A critical component in a circuit will work properly only if 3 other components all work properly. The probabilities of a failure for the 3 other components are 0.008, 0.015, and 0.022. Find the probability that at least 1 of these 3 components will fail.
Note: Round using three significant figures, if necessary
Answer: Probability that one of the three components will fail is about 0.045.
Step-by-step explanation:
Can some plz help me
Answer: red 36 m
Step-by-step explanation: base plus base = 18 / 2 = 9 * 4 = 36 m
Answer:
36 m²
Step-by-step explanation:
To answer this question you will need the equation to find the area of a trapezium:
[tex]\frac{(a + b)}{c}[/tex] × height
Substitute the figures into the equation:
[tex]\frac{(6+12)}{2}[/tex] × 4
6+12= 18
After substituting use BIDMAS/ PETMAS to solve
18÷2= 9
9×4= 36 m²
Greyson and Preston have a piece of paper that is 10 inches by 9 inches. What is the area of the paper?
Answer:
90
Step-by-step explanation:
please help me .......
Select the function that represents the simple interest formula.
A. A) = P(1 + )- 1, where n is a positive integer
O
B. A(n) = P+ (n-1);• P, where n is a positive integer
O
C. An) = n + (-1). P, where n is a positive integer
O
D. A(n) = (1 - 1)(P:n)', where nis any real number
Answer:
B. A(n) = P + (n-1)i*P
Step-by-step explanation:
The formula to determine the simple interest formula is given below:
Simple interest = P×r × t
where
P denotes the principal
r denotes the rate of interest
And, t denotes the number of years
Now we replace i with the t
So,
SI = Pni
Now for n-1 years, the simple interest is
SI = P(n - 1)×i
So, the total amount would be
A(n) = P + (n - 1)i × P
Question 11 i’m confused
is (x 7) a factor of f(x) = x3 − 3x2 2x − 8? explain your reasoning.
(x + 7) is a factor of f(x) = x^3 - 3x^2 + 2x - 8. By using synthetic division, we find that the remainder is 0.
To determine if (x + 7) is a factor of the polynomial f(x) = x^3 - 3x^2 + 2x - 8, we can use synthetic division.
Performing synthetic division with the divisor (x + 7), we set up the division as follows:
-7 | 1 -3 2 -8
|_________________
1 -10 72 -520
The numbers in the bottom row of the synthetic division represent the coefficients of the quotient polynomial. In this case, the quotient polynomial is 1x^2 - 10x + 72, and the remainder is -520.
Since the remainder is not zero, (x + 7) is not a factor of f(x). If (x + 7) were a factor, the remainder would be zero.
Therefore, (x + 7) is not a factor of f(x) = x^3 - 3x^2 + 2x - 8.
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The following scatter plot depicts the number of chicken pox cases after 1988. The variable x represents the number of years after 1988. The variable y represents the number of cases in thousands.
A graph has number of years after 1988 on the x-axis, and reported cases (thousands) on the y-axis. Points trend on a negative line.
Does there appear to be a linear relationship? Explain your answer.
a.
Yes, there is a linear relationship. The data appears to have a negative correlation.
b.
Yes, there is a linear relationship. The data appears to have a positive correlation.
c.
No, there is not a linear relationship. The data seems random.
d.
No, there is not a linear relationship. There is no line which goes through all the points.
Answer: D
Step-by-step explanation: On Edge2021
Please help me with the question please ASAP I’ll mark u as a brnlist
*2 questions
Answer:
First answer is 76.50 and the second one is scale factor of 1/2
Step-by-step explanation: Mark brainlist or im deleting my answer :)
Answer:
scale factor = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{WX}{AB}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]
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1 pizza costs $12.75 and feeds 4
To feed 24 students he needs 24 ÷ 4 = 6 pizzas , then
6 cost = 6 × $12.75 = $76.50