What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48
Answers
Answer:
h(x) = 4x+48Step-by-step explanation:
Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.
Then we will make x the subject of the formula as shown:
y = 1/4x - 12
adding 12 to both sides we have;
y + 12= 1/4x - 12 + 12
y + 12 = 1/4x
Multiplying both sides by 4 we have;
4(y+12) = x
x = 4y + 48
Substituting y for x
y = 4x+48
f^-1(x) = 4x+48
h(x) = 4x+48
Thee final expression will give the inverse of the function
Answer:
h(x) = 4x+48
Step-by-step explanation:
Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.
Then we will make x the subject of the formula as shown:
y = 1/4x - 12
adding 12 to both sides we have;
y + 12= 1/4x - 12 + 12
y + 12 = 1/4x
Multiplying both sides by 4 we have;
4(y+12) = x
x = 4y + 48
Substituting y for x
y = 4x+48
f^-1(x) = 4x+48
h(x) = 4x+48
Thee final expression will give the inverse of the function
Related Questions
P(A | B) can be read as "the probability that B occurs given that A has
occurred."
A. True
B. False
Answers
Using conditional probability, it is found that P(A|B) is read as "the probability that A occurs given that B has occurred", hence the statement is:
B. False.
What is conditional probability?It is the probability of an event B occurring, considering that event A has occurred, and it represented by P(A|B).
Hence, following the same standard, P(B|A) is read as "the probability that A occurs given that B has occurred", which means that the statement is false and option B is correct.
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suppose electric power is supplied from two independent sources which work with probabilities 0.4, 0.5, respectively. if both sources are providing power enough power will be available with probability 1. if exactly one of them works there will be enough power with probability 0.6. of course, if none of them works the probability that there will be sufficient supply is o.
Answers
Answer:
What is the question
Step-by-step explanation:
3. Layla has a coin that has a 60% percent chance of showing heads each time it is flipped (realize that this is an unfair or biased coin). She is going to flip the coin 5 times. Let X represent the number of heads she gets. What is the probability that she gets more than 3 heads? You may round your answer to the nearest hundredth. P(X>3)=? 4. A surgical intervention results in increased quality of life in 60% of patients. If 20 patients undergo surgery, what is the probability that it is effective on 12 patients? 4. A surgical intervention results in increased quality of life in 60% of patients. If 20 patients undergo surgery, what is the probability that it is effective on 12 patients?
Answers
1. The probability that Layla gets more than 3 heads is 0.40 (rounded to the nearest hundredth).
P(X>3) = 0.40.Let X represent the number of heads Layla gets on flipping a coin that has a 60% chance of showing heads. She is going to flip the coin five times and we are supposed to find the probability that she gets more than 3 heads. The probability that Layla gets more than 3 heads is P(X>3).
Solution :We are given that the coin has a 60% chance of showing heads each time it is flipped. The probability of getting a head (success) is p = 0.6 and the probability of getting a tail (failure) is q = 0.4. As Layla is going to flip the coin five times, we have n = 5.On each flip, X can either be a head or a tail. Thus, X is a binomial random variable with parameters n = 5 and p = 0.6.P(X>3) can be calculated as:P(X > 3) = P(X = 4) + P(X = 5)P(X = 4) = nCx × p^x × q^(n-x) = 5C4 × 0.6^4 × 0.4^1 = 0.2592P(X = 5) = nCx × p^x × q^(n-x) = 5C5 × 0.6^5 × 0.4^0 = 0.07776P(X > 3) = P(X = 4) + P(X = 5) = 0.2592 + 0.07776 = 0.33696 ≈ 0.40
2. Probability of surgery being effective on 12 patients = 0.00000078643 and the probability that surgery is effective on at least 12 patients out of 20 is 0.1985502502.
Let p be the probability that a surgical intervention results in an increased quality of life in a patient, which is given as 60%. Let X be the number of patients out of 20 who have an increased quality of life after undergoing the surgery. We are supposed to find the probability that surgery is effective on 12 patients out of 20.
Solution :Let X be the number of patients out of 20 who have an increased quality of life after undergoing the surgery. Then X is a binomial random variable with parameters n = 20 and p = 0.6.The probability of surgery being effective on exactly 12 patients can be calculated as:P(X = 12) = nCx × p^x × q^(n-x) = 20C12 × 0.6^12 × 0.4^8 = 0.00000078643 (rounded to 11 decimal places)
The probability of surgery being effective on at least 12 patients can be calculated as:P(X ≥ 12) = P(X = 12) + P(X = 13) + ... + P(X = 20)Using a binomial probability distribution table, we can calculate this probability as:P(X ≥ 12) = 0.00000078643 + 0.0000105188 + 0.0000976064 + 0.0007052774 + 0.0038752048 + 0.0163110784 + 0.052553726 + 0.125428942 = 0.1985502502Therefore, the probability that surgery is effective on 12 patients out of 20 is 0.00000078643
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2/5(5 + x) = 8
What is x if the equation equals 8
Answers
Answer:
x=15
Step-by-step explanation:
which word is associated with multiplication when computing probabilities?
-or
-and
-disjoint
-not
Answers
When computing probability , the word 'and' is most commonly used with multiplication, while 'or', 'disjoint' and 'not' are also associated with it.
The word most commonly associated with multiplication when computing probabilities is ‘and’. This is because when computing a probability, we are often looking to calculate the likelihood of two or more events occurring simultaneously. The other words associated with multiplication when computing probability are ‘or’, ‘disjoint’ and ‘not’. The word ‘or’ is used when calculating the probability of either one event or another occurring. The word ‘disjoint’ is used when calculating the probability of two or more mutually exclusive events (events that cannot occur together). Finally, the word ‘not’ is used when calculating the probability of an event not occurring.
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If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
2) tanΘ=1
Answers
The angles Θ are:
Θ = 45°
Θ = 225°
If tan = 1, the angle can be found by taking the inverse tangent (or arctan) of 1.
Because tangent is positive in the first and third quadrants, we must examine angles ranging from 0° to 360° that fall within those quadrants:
We have the following in the first quadrant:
arctan(1) = 45° if tan = 1
We have the following in the third quadrant:
225° = tan = 1 + 180° = arctan(1)
As a result, the possible angles for are 45° and 225°, which satisfy the equation tan = 1.
As a result, the angles are:
Θ = 45°
Θ = 225°
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Find the measure of <1Justify your answer.
Answers
Answer:
its 75
Step-by-step explanation:
im in highschool and just did this a couple of weeks ago
its called alternate interior or alternate exterior. something like that but i know im right trust me. also pls mark me brainliest
in a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. a family has two children. if x is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls
Answers
Answer:
The sum of the probabilities of all possible outcomes must equal 1.
Step-by-step explanation:
To solve this problem, we can use the binomial distribution, since we have a fixed number of trials (two children) and each trial has two possible outcomes (boy or girl) with a known probability of success (0.48 for a girl).
Let X be the random variable representing the number of girls born to the family. Then X follows a binomial distribution with parameters n = 2 (the number of trials) and p = 0.48 (the probability of success). The probability mass function (PMF) of X is given by:
P(X = k) = (n choose k) * \(p^{k}\) * \((1 - p)^{(n - k)}\)
where (n choose k) = \(\frac{n! }{(k! * (n - k)!)}\) is the binomial coefficient.
To find the probability that the family has 0, 1, or 2 girls, we need to calculate the values of P(X = 0), P(X = 1), and P(X = 2):
P(X = 0) = (2 choose 0) * \(0.48^{0}\) * \(0.52^{2}\) = 0.2704
P(X = 1) = (2 choose 1) * \(0.48^{1}\) * \(0.52^{1\\}\) = 0.4992
P(X = 2) = (2 choose 2) * \(0.48^{2}\) * \(0.52^{0}\) = 0.2304
Therefore, the probability that the family has 0, 1, or 2 girls is:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2704 + 0.4992 + 0.2304 = 1
Note that the sum of the probabilities of all possible outcomes must equal 1.
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or the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert. here are the items to choose from. choice possible items appetizer chicken strips, shrimp cocktail, nachos salad garden, caesar, southwest entree lamb, roast turkey, grilled chicken, t-bone steak side dish pinto beans, rice, french fries, baked potato, corn dessert apple pie, brownies, chocolate cake, cheesecake how many dinner specials are possible?
Answers
There are 720 possible dinner specials.
To calculate the number of dinner specials, we need to multiply the number of options for each course.
For the appetizer, there are 3 options (chicken strips, shrimp cocktail, nachos).For the salad, there are 3 options (garden, caesar, southwest).For the entree, there are 4 options (lamb, roast turkey, grilled chicken, t-bone steak).For the side dish, there are 5 options (pinto beans, rice, french fries, baked potato, corn).For the dessert, there are 4 options (apple pie, brownies, chocolate cake, cheesecake).The number of dinner specials is the product of the number of options for each course:
So,
3 x 3 x 4 x 5 x 4 = 720 possibilities
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what two numbers can multiply to get 400 and add to get 8
Answers
Solving a system of equations we will see that the two numbers are:
4 - √384*i and 4 + √384*i.
How to find the two numbers?We want to find two numbers x and y such that the product is 400 and the sum is 8, then we can write a system of equations:
x*y = 400
x + y = 8
Let's isolate x on the second equation to geT:
x = 8 - y
And replace that in the first equation to get:
(8 - y)*y = 400
8y - y² = 400
Now we have the quadratic equation:
-y² + 8y - 400 = 0
Using the quadratic formula we will get:
\(y = \frac{-8 \pm \sqrt{8^2 - 4*(-1)*-400} }{2*-1} \\\\y = \frac{-8 \pm \sqrt{-1,536} }{-2} \\\\y = 4 \pm \sqrt{384}i\)
So there are two possible values of y.
if we take the first one, then:
y = 4 + √384*i
In this case the value of x will be:
x = 8 - y = 8 - (4 + √384*i) = 4 - √384*i
We got the other value for x.
So the two numbers are 4 - √384*i and 4 + √384*i.
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I need help with math homework hurry
Answers
Answer:ok?
Step-by-step explanation:
Show me it.
Answer:
show us
Step-by-step explanation:
show us us us us us us us
1 2. The original quantity is 5 and the new
quantity is 3. What is the percent
change? Is it an increase or decrease?
Answers
A wakeboard ramp has a rise of 3 feet and a run of 8 feet, what is the slope of the ramp? the slope of the wakeboard in our example was 3/5 how do the steepness of each ramp compare
Answers
Answer:
3/8
Step-by-step explanation:
slope = rise/run = 3/8
The following three points are the locations of important facilities in a transportation network: (26,16), (51,59), and (36,41). The coordinates are in miles. a. Calculate the Euclidean distances (in miles) between each of the three pairs of facilties. (Enter your responses rounded to wo decimal places.) dAB= miles; dBC= miles; dAC= miles. b. Calculate these distances using rectlinear distances. (Enter your responses as integers.) dAB= miles; dBC= miles, dAC= miles.
Answers
a. To calculate the Euclidean distances between the three pairs of facilities, we use the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points. Calculating the Euclidean distances:
dAB = sqrt((51 - 26)^2 + (59 - 16)^2) ≈ 47.39 miles
dBC = sqrt((36 - 51)^2 + (41 - 59)^2) ≈ 23.53 miles
dAC = sqrt((36 - 26)^2 + (41 - 16)^2) ≈ 25.00 miles
b. To calculate the rectilinear distances, we use the formula:
d = |x2 - x1| + |y2 - y1|
Calculating the rectilinear distances:
dAB = |51 - 26| + |59 - 16| = 25 + 43 = 68 miles
dBC = |36 - 51| + |41 - 59| = 15 + 18 = 33 miles
dAC = |36 - 26| + |41 - 16| = 10 + 25 = 35 miles
Therefore, the Euclidean distances are approximately dAB = 47.39 miles, dBC = 23.53 miles, and dAC = 25.00 miles. The rectilinear distances are dAB = 68 miles, dBC = 33 miles, and dAC = 35 miles.
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Assuming an individual has X hours per week during the summer to devote to taking classes or working for an employer. Also, assume that to receive at least a B or better, you must devote at least X hours per course per week (1 course = X hours per week, 2 courses = X hours per week, etc...) Explain why one faces a tradeoff between the number of courses and hours of work. Why would it be impossible to take X courses while working X hours per week? Why would taking one class and working X hours per week would result in large amount of free time?
Answers
One faces a tradeoff between the number of courses and hours of work due to limited available time. Taking X courses while working X hours per week is impossible as it exceeds the time constraint.
The tradeoff between the number of courses and hours of work arises due to the finite number of hours available in a week. Assuming an individual has X hours per week, this time must be divided between courses and work.
To achieve a B or better in a course, it is necessary to dedicate at least X hours per course per week. Therefore, taking X courses while working X hours per week would require dedicating X hours per course, resulting in a total time commitment exceeding the available X hours.
Conversely, if only one class is taken while working X hours per week, the time commitment for a single course is less than X hours. This scenario leaves a significant amount of free time remaining, as the total time dedicated to the course and work does not exhaust the available X hours.
In summary, the tradeoff occurs because the time available is limited, and the minimum time requirement per course restricts the number of courses that can be taken while maintaining a specific work schedule.
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Jackson makes fruit punch by mixing the ingredients listed below.
6 cups of orange juice
5 pints of fruit punch
8 cups of apple juice
How many quarts of fruit punch does Jackson make?
A.3
B.6
C.24
D.96
Answers
Answer: B
Step-by-step explanation:
First, let's convert the 5 pints of fruit punch to cups:
5 pints = 5 x 2 cups/pint = 10 cups
Now we can add up the cups of each ingredient:
6 cups of orange juice + 10 cups of fruit punch + 8 cups of apple juice = 24 cups
Since there are 4 cups in a quart, we can divide by 4 to get the number of quarts:
24 cups ÷ 4 cups/quart = 6 quarts
Therefore, Jackson makes 6 quarts of fruit punch.
Last Ss, super easy im just braindead
Answers
Answer:
the answer is 90
Step-by-step explanation:
equivalent fractions for 2 1/5 and 1 5/6
Answers
1 5/6: 11/6, 22/12, 33/18, 44/24, etc.
What are the steps on how to copy an angle? (Geometry)
Answers
Step-by-step explanation:
Make a point P that will be the vertex of the new angle.
From P, draw a ray PQ. ...
Place the compasses on point A, set to any convenient width.
Draw an arc across both sides of the angle, creating the points J and K as shown.
Hope this helps :)
you have added the fractions 2/5 and 4/10 by converting 2/5 into 4/10 so the denominators are the same. your addition has given you the total of 8/10. now what must you do?
Answers
Answer: Reduce the fraction to the simplest form.
Hope this helps :)
Step-by-step explanation:
8/10
/ 2
4/5
Can some on please explain
Answers
Answer:
ORange =1 -2
Step-by-step explanation:
Step-by-step explanation:
From the given figure , we can see that there are two angles whose measures are x and 2x - 30°. If we notice they are the angles on the same segment . ( Draw a line through the end points of the two lines , and they will be on the same chord) . And we know that angles of the same segment are equal . Therefore ,
\(\tt\to x = 2x - 30^o \\\\\tt\to 2x - x = 30^o \\\\\tt\to\boxed{\orange{\tt x = 30^o }}\)
This is our required answer.
A regression table mainly shows us Select one: a. How we should run the regression analysis.b. what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0)c. that the smallest coefficients always have the greatest impact on the dependent variable.d. if a large constant term is important.e. all of the above.
Answers
A regression table mainly shows us that what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0) .
A regression table is a statistical technique that describes how strongly a dependent variable and one or more independent variables are correlated (s). A field or variable you are attempting to predict or comprehend could be a dependent variable.
Regression allows researchers to predict or explain the variation in one variable based on another variable. The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.
What is interpretation of regression statistics table?
In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable. When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression.
A regression table primarily reveals the values of the coefficients as well as the significance of each coefficient (how likely it is that it will depart from 0).
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6. Suppose the block factory has only
boxes and stacks. How can it pack an
order for 3,630 blocks?
Answers
Answer:
2,064 i think
Step-by-step explanation:
What is the difference of the rational expression below?
3x/x+1 - 5/x
Answers
Answer:
3x%x+1-5/5
3× 5x
Step-by-step explanation:
3x-5x
35yx 53yx
list the clusters, gaps, outliers, and shape of this dot plot please!
Answers
Answer:
Cluster : 60,61,62,63
Gaps: 64,65 , 69,70
Outlier: 71
This is what I learned so don't blame me please!
Step-by-step explanation:
Cluster is numbers all on one side. Outlier can be the largest number or lowest. Normally the alone one.
laoalaifnwrohqefubihasojksbd j
Answers
Answer:
6
Step-by-step explanation:
Cross multiply to get
5x= 10(x-3)
5x= 10x -30
-5x= -30
x =6
Answer:
x = 6
Step-by-step explanation:
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
How many classes would Gina need to take for the total cost to be the same at both dance studios?
Answers
Answer:
10 classes
Step-by-step explanation:
Given equations in the question
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
Where,
x = number of classes
Equate the total cost at both dance studios
15x = 25 + 12.5x
Collect like terms
15x - 12.5x = 25
2.5x = 25
Divide both sides by 2.5
2.5x / 2.5 = 25 / 2.5
x = 10 classes
x = number of classes = 10
Answer:
AStep-by-step explanation:
Posting more questions so please go to my page if you know this thank you
Answers
Answer:
I'm thinking the answer is 76 but I could be wrong
Step-by-step explanation:
find the exact value of sec pi/4
Answers
Sec pi/4 is the value of secant trigonometric function for an angle equal to π/4. The value of sec pi/4 is √2 or 1.4142 (approx).
Square root of 0.0144
Answers
Step-by-step explanation:
The square root of 0.0144 is 0.12.
To find the square root of 0.0144, we can use a calculator or estimate it manually. One way to estimate the square root of 0.0144 is to recognize that it is very close to 0.01, which has a square root of 0.1. Since 0.0144 is slightly larger than 0.01, we can expect its square root to be slightly larger than 0.1.
To get a more precise answer, we can use a calculator or long division. Here's one way to do it:
- Write 0.0144 as a fraction: 0.0144 = 144/10000
- Take the square root of the numerator and denominator separately: sqrt(144)/sqrt(10000)
- Simplify the square roots: 12/100
- Reduce the fraction: 3/25
Therefore, the square root of 0.0144 is 0.12 or 3/25.