This function gives the same result as the previous function we derived, but it expresses the calculation as a composition of the two separate functions that represent each raise separately.
What is function?A function is a set of instructions or statements that perform a specific task or computation and returns a value or result. In programming, a function is typically defined using a specific syntax and can be called or invoked by other parts of the program to carry out a particular operation.
Functions are used in programming to break down complex tasks into smaller, more manageable pieces of code, which can then be reused in multiple parts of the program. They can also help to improve the organization, readability, and maintainability of code.
by the question.
let the worker's original hourly wage be represented by the variable x. Then the function for the worker's new hourly wage when the 20% raise is applied before the $2 raise can be expressed as follows:
[tex]f(x) = (1.20x) + 2[/tex]
In this function, the expression (1.20x) represents the worker's hourly wage after the 20% raise is applied, and the additional $2 raise is added to this amount to determine the final hourly wage.
We can also express this function using function composition notation. Let g(x) represent the function that applies the 20% raise to the worker's hourly wage and let h(x) represent the function that adds the $2 raise to the resulting hourly wage. Then we have:
[tex]g(x) = 1.20x[/tex]
[tex]h(x) = x + 2[/tex]
Using function composition, we can write the function for the worker's new hourly wage as:
[tex]f(x) = h(g(x)) = h(1.20x) = 1.20x + 2[/tex]
To learn more about function:
https://brainly.com/question/21145944
#SPJ1
Which of the following statements is equivalent to saying that there is a 50% increase in the cost of a movie? Circle all that apply. a. The new cost of the movie is twice the old cost. b. The new cost of the movie is one and a half times the old cost. C. The increase in the cost of the movie is half the original cost. d. The increase in the cost of the movie is half the new cost. e. The cost of the movie doubled.
All of the statements are equivalent to saying that there is a 50% increase in the cost of a movie.
The formula for calculating a percentage increase is:
Percentage increase = (New Value - Original Value) ÷ Original Value x 100
In this case, we can say that the original value is the cost of the movie before the increase, and the new value is the cost of the movie after the increase. Let's say the original cost of the movie is $10. Then the percentage increase is 50%.
We can calculate the new cost of the movie as follows:
New Cost = Original Cost + (Original Cost x Percentage Increase)
New Cost = 10 + (10 x 0.50)
New Cost = 10 + 5
New Cost = 15
Therefore, we can say that the new cost of the movie is 15, which is one and a half times the original cost of $10. The increase in the cost of the movie is 5, which is half the original cost of $10. The cost of the movie did double, from the original cost of $10 to the new cost of 15.
Learn more about percentage here:
https://brainly.com/question/16797504
#SPJ4
define average case complexity. derive an expression for the average case com- plexity of binary search.
The average case complexity is a measure of the expected performance of an algorithm when the input is chosen randomly. The average case complexity of binary search is O(log n), where n is the size of the input.
Average case complexity is a measure of the expected running time of an algorithm when it is run on inputs that are drawn randomly from a specified probability distribution. The average case complexity provides a more realistic estimate of the performance of an algorithm in real-world scenarios.
For binary search, the average case complexity can be derived by considering the probability distribution of the search key in the sorted input array. Assuming a uniform distribution of search keys, the probability of finding a key at any position in the array is 1/n, where n is the size of the array.
Let T(n) be the average case time complexity of binary search on an input array of size n. In the best case, the search key is found in the middle of the array in O(1) time. In the worst case, the search key is not present in the array, and the algorithm performs O(log n) comparisons.
In the average case, the probability of finding the key at any position is 1/n, and the number of comparisons required to find the key is proportional to the distance between the key and the middle of the array. Therefore, the average number of comparisons required in the average case is:
1/n * (1 + 2 + ... + n-1) = (n-1)/2n
Thus, the average case time complexity of binary search is O((n-1)/2n) = O(log n), which is the same as the worst-case time complexity.
Learn more about complexity of binary search here: brainly.com/question/29734003
#SPJ4
For your monthly budget: for each $15 earned, only $4 can be spent on fast food. If your paycheck is $1850 and you spent $400 on fast food, which sentence correctly describes your spending compared to your budget?
You have 78% of money left to spend on fast food in your budget ratio.
Yes, that is correct. Here's a step by step explanation of how to figure that out:
1. Calculate the total amount of fast food that can be spent in a month: $15 x 4 = $60.
2. Calculate the total amount of money left in the budget for fast food: $1850 - $60 = $1790.
3. Calculate the percentage of money left in the budget for fast food: ($1790/$1850) x 100 = 78%.
Question 17 (2 points)
Suppose that 10% of Peloton bikes are defective and should be replaced. Peloton
offers one-year warranties on their new bikes, and should a customer use the bike in
the first year and discover the defect, the bike will be replaced. Peloton also knows
that 75% of customers use the bike in the first year. What is the probability a
customer will actually make a valid warranty claim?
0.075
0.10
.175
0.75
As a result, the likelihood that a client will submit a legitimate warranty claim is: P(valid claim) = P(faulty and used) = P(faulty) * P(used) = 0.1 * 0.75 = 0.075
what is probability ?Chance is a way to gauge how likely something is to happen. A number between 0 and 1, where 0 denotes an impossibility and 1, a certainty, is used to describe it. If you flip a fair coin, for instance, the likelihood that it will land heads up is 0.5 because there are two equally probable outcomes (heads or tails). Similar to fair six-sided dice, only one of the six equally probable outcomes—rolling a 1, 2, 3, 4, 5, or 6—is a 4, so the probability of rolling a 4 is 1/6, or roughly 0.167.
given
Both the likelihood that a customer's bike is flawed and the likelihood that they will use the bike within the first year affect the likelihood that they will submit a legitimate warranty claim.
To determine the likelihood that both occurrences will occur simultaneously, we can use the probability multiplication rule:
P(used and faulty) = P(defective) * P (used)
10%, or 0.1, is the chance that a Peloton bicycle is broken. 75%, or 0.75, is the chance that a customer will use the bike in the first year.
As a result, the likelihood that a client will submit a legitimate warranty claim is: P(valid claim) = P(faulty and used) = P(faulty) * P(used) = 0.1 * 0.75 = 0.075 .
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
$9,300 is invested in an account earning 8.9% interest (APR), compounded daily. Write a function showing the value of the account after � t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
The function for the value of the account after t years can be written as:
V(t) = 93000(1.08900365)t
The coefficient of 1.08900365 is the annual growth rate (APR) compounded daily. After rounding to four decimal places, it becomes 1.0890.
The percentage of growth per year (APY) is 8.90%. This is the same as APR, but expressed as a percentage.
If 1/10 of my footy cards is 23, how many cards do I have?
Answer:230
Step-by-step explanation:
1.The volume of a toaster is 100 in . If the toaster is 2.5 inches wide and 4 inches high, how long is the toaster, in inches?
2. Find the volume of a cylinder with a diameter of 9 ft and a height of 1 ft.
Use 3.14 or the calculator value for pi and provide an answer accurate to the nearest tenth.
Answer:
10 in.
Step-by-step explanation:
V = LWH
100 = L × 2.5 × 4
L = 10
a system of equations is shown below.
y=3x+5
x + y=-7
Answer: x = -3, y = -4, or (-3, -4)
Step-by-step explanation:
To solve the system of equations, we can substitute the first equation into the second equation, replacing y with 3x + 5:
x + (3x + 5) = -7
Simplifying:
4x + 5 = -7
Subtracting 5 from both sides:
4x = -12
Dividing by 4:
x = -3
Now that we know x = -3, we can substitute that value into either of the original equations to find y:
y = 3(-3) + 5 = -4
Therefore, the solution to the system of equations is x = -3, y = -4, or (-3, -4).
(-2) to the second power - (-28) divided by 7
Answer:
≈ 4.57
Step-by-step explanation:
(-2) ^ 2 = 4
4 - (-28) = 4 + 28 = 32
32/7 ≈ 4.57
Graph the function to find the zeros. Rewrite the function with the polynomial in factored form.
y=x²+x-2
The zeros of the function are ? .
Therefore , the solution of the given problem of function comes out to be the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).
What is function?All of the subjects, including actual and fictitious locales and arithmetic variable design, will be covered in the midterm exam questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Every postbox has a specific location that could serve as a refuge.
Here,
We can draw points for different values of x and y to graph the function => y = x² + x- 2:
|x| |y=x²+x-2|
|---|-----------|
|-3 | 4 |
|-2 | 0 |
|-1 | -2 |
|0 | -2 |
|1 | 0 |
|2 | 6 |
|3 | 12 |
We can use the elements in the table above to plot them on a graph and link them to create a parabolic shape.
We can search for the values of x where the function y = 0 to determine the function's zeros.
Using the zeros we discovered, we can recast the function as the polynomial in factored form is:
=> y = (x + 2)(x - 1)
Therefore, the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
What is the meaning of "symmetric group SX on X"?
The answer of the given question based on explaining the meaning of symmetric group Sₓ on X the answer is given below,
What is Permutation?In mathematics, permutation is way of arranging set of distinct objects in particular order. A permutation of set is bijection from the set to itself, meaning that each element in set is mapped to a unique element, and every element in set is mapped to exactly once. For example, the set {1, 2, 3} can be permuted in six different ways: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Permutations have important applications in group theory, combinatorics, and cryptography.
The symmetric group Sₓ on X is a group of permutations of a set X, where Sₓ is the set of all possible bijections from X to X. In other words, the elements of Sₓ are all possible ways of rearranging the elements of X, while still maintaining the structure of the set. A permutation is a bijection that maps each element of X to a unique element of X.
The order of the symmetric group Sₓ on X is the number of elements in X, denoted by |X|. The symmetric group has important applications in group theory, algebraic geometry, and combinatorics. It is also a fundamental concept in the study of abstract algebra and is used to study the properties of permutations, symmetry, and groups.
To know more about Bijection visit:
https://brainly.com/question/13012424
#SPJ1
The symmetric group S_X on a set X is the group of all permutations of the elements in X.
Describe Bijective Function?A bijective function, also known as a bijection, is a type of function in mathematics where every element in the domain (input) is paired with a unique element in the range (output), and every element in the range has a corresponding element in the domain. In other words, a bijection is both injective (one-to-one) and surjective (onto).
A function f: X → Y is said to be bijective if:
Every element in X is paired with a unique element in Y (one-to-one or injective). This means that no two elements in X are mapped to the same element in Y.
Every element in Y has a corresponding element in X (onto or surjective). This means that every element in Y is mapped to by at least one element in X.
A permutation of X is a bijective function that maps each element of X to a unique element of X. The symmetric group S_X contains all possible permutations of the elements of X, and the group operation is function composition.
In other words, if X is a set with n elements, then the symmetric group S_X contains all possible bijections from X to itself, which means there are n! (n factorial) elements in S_X. Each element in S_X represents a unique way to permute the elements in X.
For example, let X = {1, 2, 3}. The symmetric group S_X on X contains the following six elements (permutations):
The identity permutation: (1, 2, 3)The permutation that swaps 1 and 2: (2, 1, 3)The permutation that swaps 1 and 3: (3, 2, 1)The permutation that swaps 2 and 3: (1, 3, 2)The permutation that cycles the elements in a clockwise direction: (3, 1, 2)The permutation that cycles the elements in a counterclockwise direction: (2, 3, 1)These six permutations form a group under function composition, which is the symmetric group S_X on X.
To know more about permutations visit:
https://brainly.com/question/1216161
#SPJ1
a) find the probability the chosen person is a woman
b) find the probability the chosen person favors pink or purple
c) if the chosen person favors turquoise, what is the probability this person is a man?
The probability that the person chosen is a woman is 0.51.
The probability that the person chosen favors pink or purple is 0.67.
The probability that a person that favors turquoise is a man is 0.66.
What are the probabilities?Probability is the odds that a random event would occur. The odds that the event occurs has a probability value that lies between 0 and 1. The more likely it is that the event would happen, the closer the probability value would be to 1.
The probability that the person chosen is a woman = number of women / total number of people = 152 / 300 = 0.51.
The probability that the person chosen favors pink or purple = (number of people who favor pink / total number of people) + (total number of people that favor purple / total number of people) = (50 /300) + (50 / 300) = 0.67.
The probability that a person that favors turquoise is a man = men who favor turquoise / total number of people who favor turquoise = 79/120 = 0.66
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
Is the function represented by the following table linear, quadratic or exponential?
The function represented by the table is symmetric, and the values of y vary with the square of the corresponding values of x. Therefore, the function is exponential.
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value. It is a mathematical object that takes an input and produces an output. A function is often represented symbolically as f(x), where f is the name of the function and x is the input. The output value of the function depends on the input value, and the relationship between the input and output is determined by the rule of the function. Functions can be linear, quadratic, exponential, trigonometric, or many other types. They are used to model real-world phenomena and solve mathematical problems.
Here,
To determine if the function represented by the table is linear, quadratic, or exponential, we can plot the points on a graph and look at the pattern of the data.
x y
-2 12
-1 3
0 0
1 3
2 12
|
12 * * 12
| \ /
6 * *
| |
0 --*--*--*--*--*--*--*--*--
| |
* *
/ \ /
-6 * * *
|
-2 -1 0 1 2
Looking at the graph, we can see that the points do not fall on a straight line, so the function is not linear. Additionally, the curve of the points does not resemble a parabola, so the function is not quadratic. However, the points are symmetric around the y-axis, suggesting that the function may be exponential.
To confirm this, we can calculate the ratio of consecutive y-values:
12/3 = 4
3/0 = undefined
0/3 = 0
3/12 = 1/4
We can see that the ratio is not constant except for the first and last points, which have a ratio of 4. This suggests that the function is not purely exponential, but may have some other component.
To know more about function,
https://brainly.com/question/28193995
#SPJ1
dy If x = a sin 2t, y = a(cos 2t + log tan t), then find dx
Step-by-step explanation:
We have:
x = a sin 2t
Differentiating with respect to t, we get:
dx/dt = 2a cos 2t
Next, we have:
y = a(cos 2t + log tan t)
Differentiating with respect to t, we get:
dy/dt = -2a sin 2t + (1/tan t)(1/ln 10)
Using the identity:
sin^2 t + cos^2 t = 1
We have:
sin 2t = 2sin t cos t
And:
cos 2t = cos^2 t - sin^2 t
cos 2t = 2cos^2 t - 1
Using these identities, we can rewrite dx/dt and dy/dt in terms of x and y:
dx/dt = 2a sqrt(1 - x^2/a^2)
dy/dt = -2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t)
Therefore, we have:
dx/dy = dx/dt ÷ dy/dt
Substituting the expressions for dx/dt and dy/dt, we get:
dx/dy = (2a sqrt(1 - x^2/a^2)) / (-2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t))
Simplifying, we get:
dx/dy = (-2 sqrt(1 - x^2/a^2)) / (2 sqrt(1 - x^2/a^2) - (1/ln 10)(y - a cos 2t))
caculate the following multiplication
[tex]67 \times 12[/tex]
Answer:
804
Step-by-step explanation:
Just use a calculator.
TRUE OR FALSE to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.
The given statement 'to calculate the average of the numeric values in a list the first step is to get the sum of all the given values ' is a true.
Average of the numeric values in a list,
First step is to get the sum of values in the list.
It is not the total number of values.
Once we have the sum, we can divide it by the number of values to get the average.
Here is an example,
Suppose we have a list of numeric values are as follow,
[2, 4, 6, 8, 10].
To calculate the average of these values, we first find their sum,
2 + 4 + 6 + 8 + 10 = 30
Next,
divide the sum by the number of values in the list
Number of values = 5
30 / 5 = 6
This implies,
The average of the values in the list is 6.
Therefore, to get the average first step is to get the total of all values is true statement.
Learn more about average here
brainly.com/question/29635181
#SPJ4
Figure ABCD is a parallelogram.Parallelogram A B C D is shown. The length of A D is 5 x + 3 and the length of B C is 38.What is the value of x?6789
ABCD is a parallelogram, the value of x is 7
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.
The opposing sides of a parallelogram are equal and parallel.
AD = BC
5x + 3 = 38
Take 3 away from both sides.
5x + 3 - 3 = 38 - 3
5x = 35
Subtract 5 from both sides.
5x/5 = 35/5
x = 7
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
To know more about parallelogram, click the below link
https://brainly.com/question/24149031
#SPJ4
1 Which equations define y as a nonlinear
function of x? Select all that apply.
A. y = - 3/4x
B. y = 1/2x - 8
C. y = 5/x
D. y = -3 + 2x
E. y = 3x² - 2
The equations that define y as a nonlinear function of x are: C. y = 5/x and E. y = 3x² - 2
What is function?In mathematics, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule or a set of rules that assigns each input value exactly one output value. Functions can be represented using equations, graphs, or tables. They are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and finance.
Here,
A function is considered nonlinear if it does not have a constant rate of change or a straight-line graph. In other words, if the function does not follow a linear pattern.
A. y = -3/4x is a linear function because it has a constant rate of change of -3/4 and a straight-line graph.
B. y = 1/2x - 8 is a linear function because it has a constant rate of change of 1/2 and a straight-line graph.
C. y = 5/x is a nonlinear function because it does not have a constant rate of change and its graph is not a straight line. It is a hyperbola.
D. y = -3 + 2x is a linear function because it has a constant rate of change of 2 and a straight-line graph.
E. y = 3x² - 2 is a nonlinear function because it does not have a constant rate of change and its graph is a parabola.
Option A and D are linear functions, while option B is a linear function with a constant term.
To know more about function,
https://brainly.com/question/28193995
#SPJ1
What is these two answers? Can you help me to solve this question?
Answer:
258 m/s
250 m/s
Step-by-step explanation:
s = 2t³
s(5) = 2(5)³ = 250
s(8) = 2(8)³ = 1024
average = (s(8) - s(5))/(8 - 5) = (1024 - 250)/3 = 258 m/s
s(5) = 2(5)³ = 250 m/s
rewrite 0,26 as a proper fraction, show all steps
The fraction form of 0.26 is 13/50.
What is a fraction that is improper or proper?
When a fraction's numerator is less than its denominator and it doesn't contain any whole numbers, the fraction is said to be appropriate. When a fraction represents a number bigger than one, it is said to have an inappropriate fraction since the numerator is larger than the denominator.
When the numerator value is less than the denominator, the fraction is said to be appropriate. 23, 6/7, 8/9, and other correct fractions are examples.
The decimal is 0.26
= 26/100
= 13/50
Hence, The answer is 13/50
Learn more about proper fraction
brainly.com/question/1601136
#SPJ1
10 of 1710 of 17 Questions
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
Answer:
6)-56+567)-/(05(-)9
Step-by-step explanation:
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
The seventh grade class is putting on a variety show to raise money. It cost $500 to rent the banquet hall that they are going to use. If they charge $15 for each ticket, how many tickets do they need to sell in order to raise at least $1000?
Answer:
Step-by-step explanation:
First divide 1000 by 15 to find the amount
which is about 67 tickets.
Given the triangle below, what is mA, rounded to the nearest tenth? B 12 Triangle not drawn to scale A. 60.4° B. 2.2° 10 O C. 58.2° OD. 55.8° C SUBMIT
Answer:
C
Step-by-step explanation:
A gray squirrel population was introduced in a certain region 18 years ago. Biologists observe that the population doubles every six years, and now the population is 600. a) What was the initial squirrel population? b) What is the expected squirrel population t years after introduction? c) Estimate the expected squirrel population 10 years from now.
The initial squirrel population was 75. The squirrel population t years in an equation can be determined as P(t) = 75 * 2^(t/6). The expected squirrel population 10 years from now is 261.80.
A. Let initial squirrel population = x
It is given that the population doubles every six years.
so after 18 years, the population has doubled three times. So, the equation will be:
x * 2^3 = 60
x * 8 = 600
x = 75
The initial squirrel population was 75.
B. Let squirrel population t years = P(t)
It is given that the population doubles every six years, then the equation will be written as:
P(t) = 75 * 2^(t/6)
C. To calculate the estimation of squirrel population 10 years from now,
t = 10 can be substituted in the above equation.
P(10) = 75 * 2^(10/6)
P(10) = 261.80
Therefore, we can conclude that the expected squirrel population 10 years from now is 261.80.
To learn more about population estimation
https://brainly.com/question/30509475
#SPJ4
what is the x intercept of the equation y=10x−32
The x-intercept is (3.2, 0), and the y-intercept is (0, -32) if the equation of the line is y = 10x - 32.
Answer: x= 3.2
Step-by-step explanation:
by graphing we can see where the line crosses the x axis at 3.2
I attached a graph to show you this method
to solve algebraically, y = 10x - 32 is your equation
put this in standard form ax + by = c
-10x + y = -32
to solve for x, substitute 0 for y and solve
-10x + 0 = -32
divide both sides by -10
-10/-10 x = -32/ -10
x = 3.2
If y= cos x - sin x /cos x + sin x then dy /dx is :
Answer:
Step-by-step explanation:
We can find dy/dx by differentiating y with respect to x using the quotient rule.
First, we need to rewrite y using the trigonometric identity for the tangent of the difference of two angles:
y = (cos x - sin x)/(cos x + sin x) = [(cos x - sin x)/(cos x + sin x)] * [(cos x - sin x)/(cos x - sin x)]
y = (cos^2 x - 2cos x sin x + sin^2 x)/(cos^2 x - 2sin x cos x + sin^2 x)
y = (cos 2x - sin 2x)/(cos 2x + sin 2x)
Now we can apply the quotient rule:
dy/dx = [(-sin 2x - cos 2x)(cos 2x + sin 2x) - (cos 2x - sin 2x)(-sin 2x + cos 2x)]/(cos 2x + sin 2x)^2
dy/dx = (-sin^2 2x - cos^2 2x - 2sin 2x cos 2x + sin^2 2x + cos^2 2x + 2sin 2x cos 2x)/(cos 2x + sin 2x)^2
dy/dx = 0/(cos 2x + sin 2x)^2
Therefore, dy/dx = 0.
Orders arriving at a website follows a Poisson distribution. Assume that on average there are 12 orders per hour. (a) What is the probability of no orders in five minutes? (b) What is the probability of 3 or more orders in five minutes? (c) Determine the length of a time interval such that the probability of no orders in a time interval of this length is 0.001.
a) The probability of no orders in 5 minutes is calculated to be 0.36788.
b) The probability of three or more orders in 5 minutes is calculated to be 0.08.
c) The length of the time interval such that the probability of no orders in a time interval of this length is 0.001 is calculated to be 34.5 min.
X is assumed to be the poisson's distribution where λ = 12 orders per hour.
a) At T = 1/12 hours which is 5 min, probability of no orders,
P (X = 0) = e^(-12/12) = 0.36788
b) At T = 1/12 hours which is 5 min, probability of three or more orders,
P (X ≥ 3) = 1 - P (X ≤ 2) = 1 - e⁻¹(1 + 1 + 1/2) = 0.08
c) Let us find the interval T for which:
P (X = 0) = 0.001
e^(-12T) = 0.001
Solving the equation for T we have,
T = -1/12 ln(0.001) = 0.5756 hours = 34.5 min
To know more about probability:
https://brainly.com/question/22714682
#SPJ4
Consider a Poisson probability distribution with λ = 2.8. Determine the following probabilities.
a) P(x = 5)
b) P(x > 6)
c) P(x ≤3)
Answer:
a) Using the Poisson probability formula:P(x = 5) = (e^(-λ) * λ^x) / x!
P(x = 5) = (e^(-2.8) * 2.8^5) / 5!
P(x = 5) ≈ 0.1008
b) P(x > 6) = 1 - P(x ≤ 6)
We can find P(x ≤ 6) using the cumulative Poisson probability formula:
P(x ≤ 6) = Σ (e^(-λ) * λ^x) / x!
P(x ≤ 6) = (e^(-2.8) * 2.8^0) / 0! + (e^(-2.8) * 2.8^1) / 1! + (e^(-2.8) * 2.8^2) / 2! + (e^(-2.8) * 2.8^3) / 3! + (e^(-2.8) * 2.8^4) / 4! + (e^(-2.8) * 2.8^5) / 5! + (e^(-2.8) * 2.8^6) / 6!
P(x ≤ 6) ≈ 0.8581
Therefore,
P(x > 6) = 1 - P(x ≤ 6)
P(x > 6) ≈ 0.1419
c) P(x ≤ 3) = Σ (e^(-λ) * λ^x) / x!
P(x ≤ 3) = (e^(-2.8) * 2.8^0) / 0! + (e^(-2.8) * 2.8^1) / 1! + (e^(-2.8) * 2.8^2) / 2! + (e^(-2.8) * 2.8^3) / 3!
P(x ≤ 3) ≈ 0.4232
54.2 consider the competing species model, equaltion 54.1 sketch the phase plane and the trajectories of both population
To sketch the phase plane and trajectories of both populations in the competing species model, plot the population of one species on the x-axis and the population of the other species on the y-axis. Then, plot the isoclines and use them to determine the direction and stability of the population trajectories.
The competing species model is a system of two differential equations that describe the population dynamics of two species competing for the same resources. To sketch the phase plane and trajectories, plot the population of one species on the x-axis and the population of the other species on the y-axis. Then, plot the isoclines, which are curves that represent the values of one species' population at which the other species' population does not change.
The isoclines are found by setting each differential equation to zero and solving for one population in terms of the other. For example, the isocline for species 1 is found by setting dN1/dt = 0 and solving for N2. The resulting equation gives the values of N2 at which the population of species 1 does not change. Plotting these curves on the phase plane divides it into regions where the population of each species increases or decreases.
The direction and stability of the population trajectories can be determined by analyzing the slope of the vector field, which represents the rate of change of the population at each point in the phase plane. Trajectories move in the direction of the vector field, and their stability depends on the curvature of the isoclines. If the isoclines intersect at a single point, it is a stable equilibrium where both populations coexist. If they intersect at multiple points, the stable equilibrium depends on the initial conditions of the populations. If they do not intersect, one species will eventually drive the other to extinction.
To know more on competing species model
https://brainly.com/question/15100592
#SPJ4
--The question is incomplete, answering to the question below--
"Consider the competing species model, how to sketch the phase plane and the trajectories of both population"
Given that the point (-24, 7) is on the terminal side of an angle, theta , find the exact value of the following: sin(θ)= cos(θ)= tan(θ)= csc(θ)= sec(θ)= cot(θ)=
Point (-24,7) on terminal side on angle theta having trigonometric ratio equals to,
sin(θ) = 7/25 csc(θ) = 25/7
cos(θ) = -24/25 sec(θ) = -25/24
tan(θ) = -7/24 cot(θ) = -24/7
Values of the trigonometric functions for an angle θ.
In standard position with the given point (-24, 7) on its terminal side.
Hypotenuse of the right triangle formed by the angle and its terminal side using the Pythagorean theorem,
Hypotenuse = √((-24)^2 + 7^2)
⇒Hypotenuse = √(576 + 49)
⇒Hypotenuse = √(625)
⇒Hypotenuse = 25
Signs of the sine, cosine, tangent, cosecant, secant, and cotangent based on the quadrant in which the angle lies.
x-coordinate is negative and the y-coordinate is positive, the angle is in the second quadrant.
This implies,
sin(θ) = 7/25
cos(θ) = -24/25
tan(θ) = -7/24
csc(θ) = 25/7
sec(θ) = -25/24
cot(θ) = -24/7
cosecant, secant, and cotangent are the reciprocals of the corresponding sine, cosine, and tangent values.
Therefore, the exact values of trigonometric ratios for the given point are,
sin(θ) = 7/25 csc(θ) = 25/7
cos(θ) = -24/25 sec(θ) = -25/24
tan(θ) = -7/24 cot(θ) = -24/7
learn more about point here
brainly.com/question/30465906
#SPJ4