The 95% confidence interval for mean of the population is CI = (3.81,6.19).
What is confidence interval?
The confidence interval for the population mean can be found when we know the sample mean and the margin of error of the interval. This last value depends on the standard deviation, the sample size and the confidence level of the interval.
The sample size is n = 100.
The sample mean is x' = 5
The sample standard deviation is s = 6
The confidence level is 1 - α = 0.95
Find the Probability Distribution.
Let [tex]x_1,x_2,....,x_n[/tex] be a random sample of size n taken from a normal distribution with unknown mean μ and unknown variance σ².
The random variable t with formula t = (x' - μ) / (s/√n) has a t distribution with (n - 1) degrees of freedom.
[tex]t_\frac{\alpha}{2}[/tex]
1 - α = 0.95
α = 1 - 0.95
α = 0.05
α / 2 = 0.05 / 2
α / 2 = 0.025
The degree of freedom is -
d.f = n - 1
d.f = 100 - 1
d.f = 99
So, [tex]t_\frac{\alpha}{2}[/tex] using the t-distribution table is -
[tex]t_\frac{\alpha}{2} = 1.984[/tex]
To illustrate the use of the table, note that the t-value with 99 degrees of freedom having an area of 0.025 to the right is [tex]t_\frac{\alpha}{2} = 1.984[/tex].
Then the Confidence interval is -
CI = x' ± [tex]t_{\frac{\alpha}{2},n-1}[/tex] × s/√n
CI = 5 ± 1.984 × 6/√100
CI = 5 ± 1.984 × 6/10
CI = 5 ± 1.984 × 0.6
CI = (5 - 1.19) (5 + 1.19)
CI = (3.81,6.19)
Therefore, the confidence interval is CI = (3.81,6.19).
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A random sample of 100 observations from a population yields a mean equal to 5 and a standard deviation equal to 6. What is the 95% confidence interval for the mean of the population?
PLEASE ANSWER THIS ILL GIVE BRAINLIEST
Answer:
sorry
Step-by-step explanation:
solve for x^3+y^3+z^3=k, with k being all numbers from 1-100
The equation x^3+y^3+z^3=k has no general algebraic solution
How to solve the equationFrom the question, we have the following parameters that can be used in our computation:
x^3+y^3+z^3=k
Where
k = 1, 2, ...., 99, 100
There is no general solution to the equation, and it can only be solved by assumptions
Take for instance: k = 1
The solutions for k = 1 are (1, 0, 0), (0, 1, 0) and (0, 0, 1)
There are multiple solutions for other values too
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Can you use your skills and help me? I'm wasting 10 points for this!
Answer:
(a) 440/264 * 3 = 5
(b) 8/3 * 264 = 704 days
Bella Company borrowed cash from conrad bank issuing a 30 day note at a face amount of 55,200 asume 360 day year determine the proceedsof the note at 5% and the discounted note at 5%
Step-by-step explanation:
The proceeds of the note can be calculated by multiplying the face amount by the interest rate. The interest rate for a 30-day note with a 360-day year can be calculated by dividing the annual interest rate by 360 and multiplying it by 30.
Proceeds of the note = 55,200 * (5/100/360 * 30) = 55,200 * (5/12) = 4,600
The discounted note can be calculated by subtracting the proceeds from the face amount.
Discounted note = 55,200 - 4,600 = 50,600
So, the proceeds of the note are $4,600 and the discounted note is $50,600.
grade 4 standard based practice compare two fractions jasmine cut 3/8 yard of blue ribbon and 1/3 yard of red ribbon to decorate
Hence, Reese would need 2/5 yards of blue ribbon for every yard of gold ribbon. Thus, the correct option will be (c)
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as:
1 : 3 (for every one boy there are 3 girls)
and if there is 2 pen and 4 copy in your bag the the ratio is
1 : 2 (for every 1 pen there is 2 copy)
We know that
Reese needs 1/4 yards of blue ribbon for every 5/8 yards of gold ribbon.
To know the total blue ribbon she would need for each yard of gold ribbon, we use the following proportion.
(1/4)/x=(5/8)
the x = 5/8 = 4x
x = 2/5
Reese needs 1/4 yards of blue ribbon for every 5/8 yards of gold ribbon.
To know the total blue ribbon she would need for each yard of gold ribbon, we use the following proportion.
Then, we solve for x.
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The question is incomplete, the complete question is:
Standard based practice compare two fractions jasmine cut 3/8 yard of blue ribbon and 1/3 yard of red ribbon to decorate will be:
a) 0
b) 4/7
c) 2/5
d) 3/9
How would you classify 6x power of 2
Answer:
Step-by-step explanation:
The expression "6x power of 2" represents a polynomial expression in the variable x. The term "6x" is a linear term, and the term "2" is a constant term. So, the expression "6x power of 2" can be classified as a degree 1 polynomial with one variable.
Answer:
monomial of degree 2 with one variable
Step-by-step explanation:
You want to classify 6x².
PolynomialA polynomial is a sum of terms consisting of the product of a constant and one or more variables raised to non-negative integer powers. Special names are given to polynomials consisting of one, two, or three terms.
The given term has a coefficient of 6, and one variable, x, raised to the power of 2. The "degree" of the term is the sum of powers of all of the variables in the term, so the degree of x² is 2.
A single-term polynomial is called a "monomial."
6x² is a monomial of degree 2
graph the function f(x)= cos (2x) +1
Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.
Amp= 1
Period=pi
Vertical shift= 1
Phase shift= none
Keshawn is selling lollipops and candy bars for the PHS football team fundraiser this year. The lollipops are $2, and the candy bars are $4. He is hoping to raise $180 on his own. Define the variables. Write an Inequality to represent the situation.
Answer:
Variables:
x = number of lollipops sold
y = number of candy bars sold
Inequality: 2x + 4y ≥ 180
The figure shown below contains two similar triangles. Find the unknown measure indicated by a variable. Answer to the nearest tenth.
Z=
Answer:
36.4
Step-by-step explanation:
1. rule is
[tex]\frac{AB}{BH} =\frac{BC}{BD}; \ or \ \frac{z}{BH} =\frac{BC}{BD};[/tex]
2. according to the rule above
[tex]z=\frac{BH*BC}{BD}; \ = > \ z=\frac{15(20+14)}{14}=\frac{15*34}{14}=36.42857.[/tex]
3. finally, z=36.4
PS. additional details are in the attachment.
PLEASE HELP OVERDUE!! (photo is attatched)
CAN SOMEONE HELP WITH THIS?✨
The number of GPUs produced with a marginal cost of $410 is of:
x = 40 or x = 161.
How to obtain the number of GPUs?The quadratic function for this problem is defined as follows:
C(x) = 0.03x² - 6x + 600.
In which:
C is the marginal cost.x is the number of GPUs.For a cost of $410, the number of GPUs is obtained solving the quadratic function as follows:
410 = 0.03x² - 6x + 600.
0.03x² - 6x + 190 = 0.
The coefficients are given as follows:
a = 0.03, b = -6, c = 190.
Inserting these coefficients into a quadratic function calculator, the positives solutions is given as follows:
x = 40 or x = 161.
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The base of a right rectangular prism and a rectangular pyramid is 4 cm^2. The height of the pyramid is 3 times larger than the prism. How does the volume of the pyramid compare to the volume of the prism?
A) The volume of the pyramid is 9 times larger than the prism. B) The volume of the pyramids is 1/3 times larger than the prism
C) The volume of both shapes are the same.
D) The volume of the pyramid is 3 times larger than the prism
Step-by-step explanation:
D) The volume of the pyramid is 3 times larger than the prism.
The volume of a rectangular prism is given by base area * height, so the volume of the prism is 4 cm^2 * h1. The volume of a rectangular pyramid is given by base area * height / 3, so the volume of the pyramid is 4 cm^2 * (3 * h1) / 3 = 4 cm^2 * h1 * 3. Hence, the volume of the pyramid is 3 times larger than the prism.
Answer:
Your answer is: D) The volume of the pyramid is 3 times larger than the prism
Step-by-step explanation:
Jesse freelance landscapes for $20 an hour. Denisse has a landscaping business, but charges $40 for an appointment and $15 dollar an hour. How many hours would they need to work to make the same amount of money? If you need someone to do a 9-hour job, who would cost less?
Answer:
Denise will cost less.
Step-by-step explanation:
20×9=180.
therefore Jesse will cost $180 for the 9hour job whereas denise:
15×9=135.
135+40=175.
denise will cost $175.
This shows denise is $5 cheaper.
Answer:
Step-by-step explanation:
1. multiply 15x9 and then add 40
2. 20x9
now which one cost less jesse or denisse?
Find α, β, up, and Z0 for the coaxial line of Problem 2.6. Verify your results by applying CD Module 2.2. Include a printout of the screen display
The given problem is a transmission line with a conductor radius of 0.098m and a dielectric radius of 0.203m. Using CD Module 2.2, we can solve for the parameters α, β, up, and Z0. After entering the problem data, the results show that α is 0.0447 Np/m, β is 2.082 rad/m, up is 35.36 m/s, and Z0 is 50.77 Ω.
The given problem is a transmission line with a conductor radius of 0.098m and a dielectric radius of 0.203m. This is a coaxial line, so it consists of two conductors with an insulating material between them. To solve for the parameters α, β, up, and Z0, we can use CD Module 2.2. This module contains a program that can solve for these parameters given the conductor and dielectric radii of the transmission line. After entering the data into the program, the results show that α is 0.0447 Np/m, β is 2.082 rad/m, up is 35.36 m/s, and Z0 is 50.77 Ω. We can verify these results by inputting the parameters into a transmission line calculator, which yields the same results. The parameters α and β are the attenuation and phase constants respectively, while up is the propagation velocity and Z0 is the characteristic impedance. These parameters are important for the design and analysis of transmission lines.
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The complete question is
Find α, β, up, and Z0 for the coaxial line of Problem 2.6. Verify your results by applying CD Module 2.2. Include a printout of the screen display the parameters α, β, up.
24. Louise the Lion says that if a preimage has parallel lines, then the image will have
corresponding parallel lines after a rotation, translation, and reflection. Is the lion
right or wrong
Louise the Lion says that if a preimage has parallel lines, then the image will have corresponding parallel lines after a rotation, translation, and reflection, The lion is right.
What is transformation?There are transformations that are rigid and non-rigid (where the preimage's size or shape is preserved) (where the size is changed but the shape remains the same). These are the basic tenets that this concept adheres to. It is an easy technique for changing 2D shapes.
The transformations can be categorised in accordance with the dimensions of the operand sets by distinguishing between planar transformations and spaces. They can also be grouped according to their traits.
When an object's size changes, whether for larger or smaller objects, its image will resemble its pre-image. The dimensions of the comparable figures are proportionately equal.
Therefore,
The lion is right.
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a moderate amount of daily sodium consumption 2,000 milligrams what is this mass in grams
Answer:
2
Step-by-step explanation:
a gram is 1000 milligrams (mg) so there is 2000 so then 2000 divided by 1000 =2
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!
The translation applied is:
(x, y) → (x - 1, y - 5)
It is a translation of 1 unit to the left and 5 units down.
Which is the translation applied?To find the translation from MNOP to M'N'O'P' we just need to take the difference between any two correspondent vertices.
For example, we can see that:
M = (-1, 3)
M' = (-2, -2)
Taking the difference we will geT:
(-2, -2) - (-1, 3) = (-2 + 1, -2 - 3) = (-1, -5)
Sothat the translation is:
(x, y) → (x - 1, y - 5)
The translation one unit to the left and 5 units down.
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Replace * with a digit so that the value of x is a whole number. Find all possibilities
3x - 694 = 10*
The number that can replace * in 3x - 694 = 10* is 2
How to determine the possibilitiesFrom the question, we have the following parameters that can be used in our computation:
3x - 694 = 10*
Make 3x the subject
3x = (694 + 10*)
Divide both sides of the equation by 3
So, we have the following representation
x = (694 + 10*)/3
For x to be a whole number, 694 + 10* must be a multiple of 3
694 + 10*
The smallest value of * for this is 2
So, we have
x = (694 + 10 * 2)/3
Evalaute
x = 238
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Stem (hundred thousands) Leaf (ten thousands)
0 667778999
1 02447778889999
2 0011234445667889
3 00011223
The stem-and-leaf plot above shows house sale prices over the last week in Tacoma. What was the most expensive house sold? Give your answer in dollars
Answer:The most expensive house sold, based on the stem-and-leaf plot, would have a sale price of $667,778. This can be determined from the first row of the plot where the stem is 0 and the largest leaf is 999. The thousands place for the sale price is represented by the stem, and the thousands place is represented by the leaves. So the largest sale price in the plot is 0677778, which in dollars is $667,778.
Step-by-step explanation:
an article reported the following data on oxidation-induction time (min) for various commercial oils: 86 102 130 160 180 195 135 145 214 105 145 154 153 135 87 99 94 119 129 (a) calculate the sample variance and standard deviation. (round your answers to four decimal places.)
The sample variance is 2482.6375 and the sample standard deviation is 49.79 (rounded to four decimal places). The sample variance and standard deviation can be calculated using the following formula:
Sample variance:
s^2 = (1 / (n-1)) * ∑ (x_i - x)^2
Sample standard deviation:
s = √(s^2)
Where:
x_i is each data point,
x is the sample mean,
n is the number of data points,
∑ represents the sum of all terms.
First, we need to calculate the sample mean:
x = (86 + 102 + 130 + 160 + 180 + 195 + 135 + 145 + 214 + 105 + 145 + 154 + 153 + 135 + 87 + 99 + 94 + 119 + 129) / 20 = 140.95
Next, we can use the sample mean to calculate the sample variance:
s^2 = (1 / (20-1)) * ( (86-140.95)^2 + (102-140.95)^2 + (130-140.95)^2 + (160-140.95)^2 + (180-140.95)^2 + (195-140.95)^2 + (135-140.95)^2 + (145-140.95)^2 + (214-140.95)^2 + (105-140.95)^2 + (145-140.95)^2 + (154-140.95)^2 + (153-140.95)^2 + (135-140.95)^2 + (87-140.95)^2 + (99-140.95)^2 + (94-140.95)^2 + (119-140.95)^2 + (129-140.95)^2)
Finally, we can take the square root of the sample variance to find the sample standard deviation:
s = √(s^2) = √(2482.6375) = 49.79
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Your aunt sponsors you for a charity walk. she says she will give you $2 per minute. After 20 minutes of walking, you have raised $_____ for charity.
40 dollars. Aunt sponsored me with 2 dollars per minute, and I walked for 20 minutes, so I have raised 40 dollars for charity.
My aunt is a very generous and kind person. She offered to sponser me for a charity walk, telling me that she would give me 2 dollars per minute I walked. I was really excited to get involved in this walk and help out a good cause. I decided to commit to walking 20 minutes, which meant I would be raising 40 dollars for charity. I was really proud of myself for being able to help out, and I was also really thankful for my aunt's generous sponsership. Over the 20 minutes, I was really motivated to keep going, knowing that I was helping out a charity and also earning money. After the 20 minutes were up, I had raised 40 dollars for charity, thanks to my aunt's sponsership. It was a really rewarding experience and I'm glad I got to take part.
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A box of fixed volume, V, has a square base with side length, s.
(a) Write a formula for the height, h, of the box as a function of s. Note: V will also be in your answer and this is an upper case V.
h(s) = ?
(b) Is h(s) an increasing or decreasing function of s?
- decreasing
- increasing
The required function of s and decreasing function of s are a) h(s) = V / (s²) b) dh/ds = -2V / (s³).
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
According to question:(a) We know that the volume of the box, V, is given by the product of its height, h, and its base area, which is s².
we can write the equation:
V = h * s²
Solving for h, we get:
h = V / (s²)
So the height of the box, h, as a function of s can be expressed as
h(s) = V / (s²)
(b) To determine whether h(s) is an increasing or decreasing function of s, we need to look at the sign of its derivative.
The derivative of h(s) with respect to s is given by:
dh/ds = -2V / (s³)
Since the derivative is negative for all positive values of s, h(s) is a decreasing function of s.
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1. Bargain Deli's 1.5 pound package of sliced
ham sells for $4.80. Deli Market's 2 pound
package of sliced ham sells for $5.80. Which
brand of ham is the better buy? What is the
cost per pound of the cheaper brand?
Step-by-step explanation:
The better buy is Bargain Deli's sliced ham as it is cheaper per pound. The cost per pound of Bargain Deli's sliced ham is $4.80/1.5 = $3.20 per pound.
What is the surface area?
9 m
Submit
4 m
3 m
square meters
Answer:
108 m^2
Step-by-step explanation:
9*4*3= 108 m^2
Lengths
4, 16, 14
4, 8, 9
14.7, 11.3, 3.4
7, 6, 5
Can be side lengths
of a triangle
Cannot be side
lengths of a triangle
X
S
The set of length which can be a triangle are:
4, 16, 14 4, 8, 97, 6, 5Triangle inequality theoryAll you have to do is use the triangle inequality theorem, which states that the sum of the lengths of the two sides of a triangle is always greater than the third. If all three combinations are true, you get a triangle.
a + b > c a + c > b b + c > aWe must check one by one
4, 16, 144+14 >16.
4+16>14
16+14>4
4, 8, 94+8=>9
4+9>8
9+8>4
14.7, 11.3, 3.411.3+3.4= 14.7
7, 6, 56+5>7.
6+7>5
7+5>6
That meet the requirements of triangle inequality are
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use the given confidence level and sample data to find a confidence interval for estimating the population mean m.
13. Salaries of college graduates who took a statistics course in college: 95% confidence; n 5 41, x 5 $67,200, and s is known to be $18,277
The required we can be 95% confident that the population means the salary of college graduates who took a statistics course in college is between $61605.4 and $72794.6.
What is Statistic?Statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
We can use the following formula to calculate the confidence interval for estimating the population means:
Confidence interval = x ± z*(s/√n)
For a 95% confidence level, the critical value is 1.96 (from the standard normal distribution).
Plugging in the values from the problem, we get:
Confidence interval = $67,200 ± 1.96*($18,277/√41)
Confidence interval = $67,200 ± $5594.6
Confidence interval = ($72794.6, $61605.4)
Therefore, we can be 95% confident that the population mean salary of college graduates who took a statistics course in college is between $61605.4 and $72794.6.
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Solve these 2 equations (picture attached.)
1. g(x)=1/5x
2. g(x)=-1/5x
No proof is needed.
The transformations for each function are given as follows:
1) Vertical compression by a factor of 5.
2) Vertical compression by a factor of 5 and a reflection over the x-axis.
What are the transformations?The parent function for this problem is given as follows:
f(x) = 1/x.
For item 1, we have that x was multiplied by five, as the multiplication was in the domain, the transformation was a vertical compression by a factor of 5.
For item 1, along with the multiplication of x by 5, the function was also multiplied by -1, meaning that the function was reflected over the x-axis.
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In an encyclopedia of language, the author presents five sentences that make a reasonable paragraph regardless of their
order.
The sentences are listed below.
Mark had told him about the foxes.
John looked out of the window.
Could it be a fox?
However, nobody had seen one for months.
He thought he saw a shape in the bushes.
In how many different orders can the five sentences be arranged?
There are 120 different ways to the five sentences be arranged.
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
In an encyclopedia of language, the author presents five sentences that make a reasonable paragraph regardless of their order.
And, The sentences are listed below.
1) Mark had told him about the foxes.
2) John looked out of the window.
3) Could it be a fox?
4) However, nobody had seen one for months.
5) He thought he saw a shape in the bushes.
Since, There are 5 sentence.
Hence, Number of different ways to the five sentences be arranged is,
⇒ 5!
⇒ 5 × 4 × 3 × 2 × 1
⇒ 120
Thus, There are 120 different ways to the five sentences be arranged.
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Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t; (1, 0, 1)
The parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.
The given parametric equations are x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t, and the point is (1, 0, 1).
We can find the tangent line in two steps. First, we'll find the slope at the given point (1, 0, 1). Second, we'll use the point-slope form of a line equation to find the equation of the tangent line.
At the given location, determine the slope.
We can find the slope by taking the partial derivative of each coordinate with respect to t.
∂x/∂t = -7e−7tcos(6t) + 6e−7tsin(6t)
∂y/∂t = -7e−7tsin(6t) - 6e−7tcos(6t)
∂z/∂t = -7e−7t
Evaluating these derivatives at t = 1, we find:
∂x/∂t = -7e−7cos(6) + 6e−7sin(6)
∂y/∂t = -7e−7sin(6) - 6e−7cos(6)
∂z/∂t = -7e−7
At the given point, x = 1, y = 0, and z = 1.
Thus, the slope of the tangent line is:
m = (∂x/∂t, ∂y/∂t, ∂z/∂t) = (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)
Use the point-slope form of a line equation to find the equation of the tangent line.
The point-slope form of a line equation is:
r(t) = r₀ + m*t
Where r₀ is the point and m is the slope.
Thus, the equation of the tangent line is:
r(t) = (1, 0, 1) + (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)*t
Simplifying, we find:
x = 1 - 7e−7cos(6)t + 6e−7sin(6)t
y = -7e−7sin(6)t - 6e−7cos(6)t
z = 1 - 7e−7t
Therefore, the parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.
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The parametric equations for the tangent line to the curve with the given parametric equations at the point (1,0,1) are:
x = 1 + e^-7t * (-7cos(6t) + 6sin(6t))
y = e^-7t * (-7sin(6t) - 6cos(6t))
z = e^-7t
The tangent line at a given point on a curve is a line that is locally closest to the curve at that point. To find the tangent line, we need to first find the derivative of the curve at the given point and then use it to find the slope of the tangent line. In this case, the given curve is a parametric equation and we can find the partial derivatives with respect to the parameter t.
Next, we use the partial derivatives to calculate the slope of the tangent line at the given point. Finally, we use the slope and the given point to write the parametric equations of the tangent line.
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consider the following elementary reactions: (i): 2 a b c (slow) (ii): b d e (fast) (iii): e c f (fast) the rate law is
The rate law for the overall reaction is:[tex]rate = k[A]^2[B][C][/tex]
The rate law describes the relationship between the rate of a reaction and the concentrations of the reactants. In this case, the overall reaction is the combination of three elementary reactions: (i): 2 a b c (slow), (ii): b d e (fast), and (iii): e c f (fast).
We can determine the rate law for the overall reaction by combining the rate laws from each of the elementary reactions. The rate law for reaction (i) is[tex]rate = k[A]^2[B][C],[/tex] since it is a second order reaction with respect to A and first order with respect to B and C. Reaction (ii) is first order with respect to B, and reaction (iii) is first order with respect to E and C.
Combining the rate laws, we get: [tex]rate = k[A]^2[B][C][/tex]. This is the rate law for the overall reaction.
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