Answers
\(f'(2) = -\frac{3}{16}\\\)
Step-by-step explanation:Given:
\(f(x) = \frac{3}{x +2}\\\)
Recall:
\(\frac{\text{d}}{\text{d}x}f(x) = f'(x)\\\)
\(\frac{\text{d}}{\text{d}x}(\frac{f(x)}{g(x)}) = \frac{f'(x)g(x) -f(x)g'(x)}{g(x)^2}\\\)
If we want to solve for \(f'(2)\), we must first find how \(f'(x)\) will be defined.
\(f'(x) = \frac{\text{d}}{\text{d}x}f(x) \\ f'(x) = \frac{\text{d}}{\text{d}x}(\frac{3}{x +2}) \\ f'(x) = \frac{3' \cdot (x +2) -3 \cdot (x +2)'}{(x +2)^2} \\ f'(x) = \frac{0(x +2) -3(1)}{(x +2)^2} \\ f'(x) = \frac{-3}{(x +2)^2} \\ f'(x) = -\frac{3}{(x +2)^2}\)
Now we can evaluate \(f'(2)\).
\(f'(2) = -\frac{3}{(2 +2)^2} \\ f'(2) = -\frac{3}{(4)^2} \\ f'(2) = -\frac{3}{16}\)
Related Questions
y= -x^2+10x-25 in factored form and what is the x intercept
Answers
Step-by-step explanation:
X-intercept, y = 0
0 = -x² + 10x - 25
-x² + 10x - 25 = 0
-(x² - 10x + 25) = 0
x² - 10x + 25 = 0
(x - 5)(x - 5) = 0
x = 5
(5,0)
PLSSSSSSSSSSS HELPPPPPPPPPP OMG PLSSSSSSSS HELPPPPPP
Answers
Answer:
A
Step-by-step explanation:
You can see they are multiplying x by 3 every time.
Answer:
A) y=3x
Step-by-step explanation:
find the pattern between x and y. if we try using the equation y=3x, plug in the values to check if its correct.
input(x) = 2
output(y)=6
6=3(2)
6=6
what is f(-1) for the graph shown below?
Please help
Answers
Answer:
f(-1)= -3
Step-by-step explanation:
We all know f(x) = y
Since x= -1, y= -3 as per given in the graph, so
f(-1)=-3
The options are: 3/10, 65%, 3/7, 70%
Answers
Answer:
70%
Step-by-step explanation:
there are 20 total marbles and only 14 are not blue so 14/20 = 7/10 = 70%
Can you find the surface area and volume pls? ITS WORTH 50 points
Answers
Answer:
Solution given:
r=4in
h=4in
surface area=2πr(r+h)=2π*4(4+4)=64π or201.06ft²
Volume=πr²h=π*4²*4=64π or 201.06ft³
51. MULTIPLE CHOICE Which of the following numbers is not prime?
(Skills Review Handbook)
A 1
B 2
C 3
D 5
Answers
PLEASE HELP IM GETTING TIMED 8. The graph shows the relationship between the depth of a diver and the time that has passed .
Which function best represents the relationship shown in the graph ?
A. y = 10x - 15
B. y = 2x - 15
С. y = - 10x - 15
D.y=-15x-10
Answers
Answer:
C
Step-by-step explanation:
Glad I could help!
Answer:
c
Step-by-step explanation:
rise/run
-20/2=-10 for the slope
3.5. x (5.8 - 7.09)?
Answers
Answer:
-4.51500
Step-by-step explanation:
Answer:
-4.515
Step-by-step explanation:
Assuming the "x" is multiplication, 5.8-7.09=-1.29, then 3.5*(-1.29)=-4.515
What is the meaning of "all free variables of a formula ϕ(u1, . . . , un) are among u1, . . . , un"?
Answers
The phrase "all free variables of a formula ϕ(u1, . . . , un) are among u1, . . . , un" refers to a property of a logical formula ϕ with variables u1, u2, ..., un. In logic and formal systems, variables are used to represent unspecified elements or objects.
What does the phrase imply?When a variable is considered "free" in a formula, it means that it is not bound by any quantifiers or other logical operators in the formula. In other words, it is a variable that is not restricted in any way within the formula.
The given statement implies that all the free variables in the formula ϕ(u1, . . . , un) are explicitly listed among the variables u1, u2, ..., un. In other words, the formula ϕ does not contain any additional free variables beyond the ones explicitly mentioned.
Learn more about variable on
https://brainly.com/question/28248724
#SPJ1
Solve for x.
√10x−29=x−2
Enter your answers in the boxes.
Answers
Answer:
x = 11, 3
Step-by-step explanation:
√(10x - 29) = x - 2
(√(10x - 29))² = (x - 2)²
10x - 29 = x² - 4x + 4
-10x + 29 -10x + 29
x² - 14x + 33
(x - 11) (x - 3)
x - 11 = 0; x - 3 = 0
+ 11 +11 +3 +3
x = 11 x = 3
I hope this helps!
Identify a pattern in the given list of numbers. Then use this pattern to find the next number.
1, 1, 1, 2, 1, 4, 1,
Answers
The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2
By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.
The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.
Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:
1 + 1 = 2
Hence, based on the observed pattern, the next number in the sequence is 2.
Therefore, the completed list of numbers would be:
1, 1, 1, 2, 1, 4, 1, 2
For more such questions on numbers visit:
https://brainly.com/question/24644930
#SPJ8
1. -4x +5 > -5
I need help
Answers
Step-by-step explanation:
-4x+5>-5
-5 -5
-4x>-10
/-4 /-4
x<2/5
You switch the sign whenever you divide a negative. In this case, we did, so instead of it being x>2/5, the answer is x<2/5.
hope it helps! :3
Answer:
x<5/2
Step-by-step explanation:
help the work hurts meee!!!!!!!!!!!!! and show thee work
Answers
12 in is 1 ft, 5 in is ~0.41 ft, 13 in is ~1.08 ft
16 oz is 1 lb, 9 oz is ~0.56 lbs, 18 oz is ~1.13 lbs
1.The base length of a rectangle is multiplied by 8. How does this affect the area?
A. area is 2x bigger
B. area is 4x bigger
C. area is 8x bigger
D. area is 16x bigger
2.The base length and the width length of a rectangle are both multiplied by 4. How does this affect the area?
A. area is 2x bigger
B. area is 4x bigger
C. area is 8x bigger
D. area is 16x bigger
3.The radius of a circle is tripled. How does this affect the area?
A. area is 3x bigger
B. area is 6x bigger
C. area is 9x bigger
D. area is 18x bigger
Answers
Answer:
2x bigger
Step-by-step explanation:
because if you split the rectange in half, it would be 2x?
Answer:
1. A 2. A? I think. 3. C
Step-by-step explanation:
27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
Answers
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
Learn more about determining the percentage at https://brainly.com/question/24877689.
#SPJ1
Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
Answers
1. A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
In this case, the spinner's outcome of landing on region three is independent of landing on region six. Each spin is unrelated to the previous spin, and the outcome of one region does not affect the outcome of the other region. Therefore, the events are independent. The probability of landing on both region three and region six is the product of their individual probabilities: 1/8 * 1/8 = 1/64.
2. A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?
In this scenario, the events are overlapping. A jersey can be both purple and have a number greater than 5 at the same time. Therefore, the probability of it being purple or having a number greater than 5 is the sum of their individual probabilities, minus the probability of the overlapping event (purple jerseys with a number greater than 5). There are 4 purple jerseys out of 10 total jerseys, and there is 1 jersey with a number greater than 5 out of 10. However, there is one jersey that satisfies both conditions (purple and number greater than 5), so we need to subtract it from the sum. So the probability is (4/10 + 1/10) - (1/10) = 4/10 = 2/5.
3. A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?
In this scenario, the events are mutually exclusive. A chocolate cannot be both a milk chocolate and have no peanuts inside at the same time. Therefore, the probability of it being a milk chocolate or having no peanuts inside is the sum of their individual probabilities. There are 6 milk chocolates out of 10 total chocolates, and there are 7 chocolates without peanuts out of 10. So the probability is 6/10 + 7/10 = 13/10, which is greater than 1. However, probabilities cannot exceed 1, so we need to take the maximum value of 1. Therefore, the probability is 1.
4. You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?
In this case, the events are independent. The outcome of the coin flip does not affect the outcome of the die roll. The probability of the coin landing heads up is 1/2, and the probability of the die showing an even number is 1/2. To find the probability of both events occurring, we multiply their individual probabilities: 1/2 * 1/2 = 1/4.
I hope this clarifies the nature of each event. Let me know if you have any further questions!
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
solve: 2/x+3 - 1/x = -4/x^2+3x
You must show your work and enter your answer below.
Answers
The solution of the linear equation is determined as x = -4.
What is the solution of the linear equation?
The solution of the linear equation is calculated by applying the following method as follows;
The given linear equation;
2/x+3 - 1/x = -4/x² +3x
We can start by simplifying the equation and getting rid of the fractions.
Multiplying every term by x will help us achieve that:
2 + 3x - 1 = -4/x + 3x²
Simplifying further:
2 + 3x - 1 = (-4 + 3x²) / x
Combining like terms:
3x + 1 = (-4 + 3x²) / x
(x)(3x + 1) = -4 + 3x²
3x² + x = -4 + 3x²
We can subtract 3x² from both sides:
x = -4
Learn more about linear equations here: https://brainly.com/question/28732353
#SPJ1
y = 5x − 2
y = −3x + 6
Answers
The solution of the given system of equations is (1, 3).
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given is a system of two equations, we will find its solution
The equations are,
y = 5x − 2
y = −3x + 6
We will first find solution by equating the equations because, the LHS are equal,
Therefore,
5x-2 = -3x+6
8x = 8
x = 1
Put x = 1 in any equation, to get the value of y,
y = 5(1)-2
y = 5-2
y = 3
Therefore, the solution of the equation is (1, 3)
We can also find the solution by plotting the graph of the equation, the lines where intersects gives the solution of the equation, (refer to graph attached)
The lines are intersecting at (1, 3) therefore, (1, 3) is the solution of the equations,
Hence, the solution of the given system of equations is (1, 3).
Learn more about system of equations, click;
https://brainly.com/question/90105
#SPJ1
The question is incomplete, so I solved for,
Find the solution of the system of equations y = 5x − 2
y = −3x + 6
Fargus deposits $366 in a savings account at City BankThe account pays an annual interest rate of 5 percent She makes no other deposits or withdrawalsAfter three months the interest is calculated. How much simple interest does her money
Answers
The Simple interest after three month $423.70
What is Simple Interest ?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
If she deposits $366 in the account and you receive interest, you must first calculate the interest for the current year before adding the sum to calculate the interest for the following month.
for instance, deposit plus interest equals the new amount for month one, month one amount plus interest equals amount for month two, and month two amount plus interest equals amount for month three.
The total would thus be $423.70 for the following month:
month 1
366+ (366*.05)=x
366+18.3=x
month 2
384.30+(384.30*.05)=x
384.30+19.22=x
month 3
403.52+(403.52*.05)=x
403.52+20.18=x
423.7 = x
Thus, total amount then would be $423.70
To know more about Simple Interest click on the link
https://brainly.com/question/25793394
#SPJ10
The friends collected a total of 43 shells on the beach. Paula collected x shells. Bethany collected 3 less than twice as many shells as Paula. Jerrell collected 2 more than half as many shells as Paula. How many shells did Paula collect?
A. 8 shells
B. 12 Shells
C. 21 shells
D. 29 Shells
Answers
Answer:
12
Step-by-step explanation:
The number of shells collected by Paula is 12 shells
The correct answer is B.
The given expression:
total number of shells collected by the friends, t = 43 shells
number of shells collected by Paula = x
number of shell collected by Bethany = 2x - 3
number of shell collected by Jerrell = \(\frac{x}{2} + 2\)
To find:
the number of shells collected by PaulaThe number of shells collected by Paula is calculated as follows:
\(x + (2x-3 ) + (\frac{x}{2} + 2) = 43\\\\3x + \frac{x}{2} - 1 = 43\\\\\frac{6x + x}{2} = 43 + 1\\\\\frac{7x}{2} = 44\\\\7x = 88\\\\x = \frac{88}{7} \\\\x \approx 12 \ shells\)
Thus, the number of shells collected by Paula is 12 shells
Learn more here: https://brainly.com/question/16889590
In a certain year, the percent of persons (ages five and older) in each state who speak a language at home other than English was approximately exponentially distributed with a mean of 9.456. Suppose we randomly pick a state. Part (a) Define the random variable X. the age of persons in each state who speak a language at home other than English the percent of persons (ages five and older) in each state who speak a language at home other than English the number of persons (ages five and older) in each state who speak a language at home other than English the percent of persons (ages five and older) in each state who only speak English at home Part (b) Is X continuous or discrete? continuous discrete Part (c) Give the distribution of X. (Round your answer to four decimal places.) X ~ ? Part (d) Enter an exact number as an integer, fraction, or decimal. = Part (e) Enter an exact number as an integer, fraction, or decimal. =
Answers
Answer:
this is a really long paragrah 0-0
Step-by-step explanation:
very long paragraph
Which equation is graphed here?
Answers
Answer:
Y=5 X=1 multiply them bother
Step-by-step explanation:
in a science experiment, Judah is tracking the height of a small tree. At the beginning, the tree measured 32 inches. Six weeks later, The tree measures 36 inches. What is the percent increase in the tree's height? Please help!.
Answers
We can say that the tree's height increased by 12.5% over the course of the six-week experiment.
To calculate the percent increase in the tree's height, we need to find the difference between its new height and its old height, and then express that difference as a percentage of the old height.
We start with the formula:
percent increase = (new value - old value) / old value * 100%
In this case, the old value is the height of the tree at the beginning of the experiment, which is 32 inches. The new value is the height of the tree six weeks later, which is 36 inches.
So, plugging in those values, we get:
percent increase = (36 - 32) / 32 * 100%
Simplifying this expression gives us:
percent increase = 4 / 32 * 100%
And when we evaluate that expression, we get:
percent increase = 12.5%
Therefore, the percent increase in the tree's height is 12.5%.
To learn more about tree's height please click on below link
https://brainly.com/question/25659489
#SPJ1
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answers
Answer:
(4,0) & (9,5)
Step-by-step explanation:
Where the equations cross are the solutions!
Hope this Helps! :)
Happy Studies
Round 607.5 to the nearest whole number.
Answers
607.5
.5 rounds up to 1
607+1=608
Answer:
608
Step-by-step explanation:
607.5 on a number line would be round 608
because 5 is rounded to 10 like that
Apply sam technique
Express each sum in sigma-notation
1 + 1/4 + 1/9 + 1/16 + ... + 1/400
Answers
9514 1404 393
Answer:
\(\displaystyle\sum\limits_{n=1}^{20}{\dfrac{1}{n^2}}\)
Step-by-step explanation:
We notice that the denominator of each term is the square of the term number, so the last term must be the 20th. The sum is then ...
\(\displaystyle\sum\limits_{n=1}^{20}{\dfrac{1}{n^2}}\)
A shirt and a tie together cost $58 the shirt cost $30 more than the type what is the cost of the shirt and dollars
Answers
Answer:
Shirt + tie = $ 58
shirth = 30 more than that of tie
let the price of tie be X
therefore the price of shirt = 30 + X
30 + X + X = 58
30 + 2x = 58
2x = 58 - 30
2x= 28
x = 14
x + 30
= 14 + 30
Cost of tie = $14 Cost of shirt = $44"Our new
training room can seat 150
employees. If 6 tables consisting of 6
chairs are now taken, what
percentage of our new facility's
seating is full?"
Employee: "At this point, we have
used up
of our new seating
capacity."
Answers
The percentage of our new facility's seating is full will be 76%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Initial value - Final value] / Initial value x 100
Our new training room can seat 150 employees.
If 6 tables consisting of 6 chairs are now taken.
Then the number of occupied seats by tables will be
⇒ 6 x 6
⇒ 36
Then the percentage of our new facility's seating is full will be
P = [(150 - 36) / 150] x 100
P = (114/150) x 100
P = 0.76 x 100
P = 76%
The percentage of our new facility's seating is full will be 76%.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ1
please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answers
Answer:
I think its C
Step-by-step explanation:
In a bank, 20 customers on the average, are served by a cashier in an hour. If
the service time has exponential distribution, what is the probability that;
(i) It will take more than 10 minutes to serve a customer?
(ii) A customer shall be free within 4 minutes
Answers
(i) The probability that it will take more than 10 minutes to serve a customer is approximately 0.1353.
(ii) The probability that a customer shall be free within 4 minutes is approximately 0.4866.
To solve this problem, we can use the exponential distribution formula. The exponential distribution is often used to model the time between events occurring at a constant average rate. In this case, we want to find the probability of specific service times.
Let's denote λ as the average number of customers served per hour. Given that 20 customers are served on average, we can determine λ by dividing the average number of customers by the time taken to serve them, which is 1 hour. Therefore, λ = 20 customers/hour.
Now, we can calculate the probability using the exponential distribution formula:
(i) To find the probability that it will take more than 10 minutes to serve a customer, we need to convert 10 minutes to hours, which is 10/60 = 1/6 hour. Let's call this value x.
The probability can be calculated as P(X > x) = 1 - P(X ≤ x), where X follows an exponential distribution with rate parameter λ.
P(X > 1/6) = 1 - P(X ≤ 1/6)
= 1 - (1 - \(e^{(-\lambda x))\) [Using the cumulative distribution function (CDF) of the exponential distribution]
= \(e^(- \lambda x)\)
= \(e^{(-20/6)\)
≈ 0.1353
(ii) To find the probability that a customer shall be free within 4 minutes, we convert 4 minutes to hours, which is 4/60 = 1/15 hour. Let's call this value y.
The probability can be calculated as P(X ≤ y), where X follows an exponential distribution with rate parameter λ.
P(X ≤ 1/15) = 1 - \(e^{(-\lambda y)\)
= 1 - \(e^{(-20/15)\)
≈ 0.4866
Therefore, the probability that a customer shall be free within 4 minutes is approximately 0.4866.
For more such questions on probability, click on:
https://brainly.com/question/251701
#SPJ8