∮c (z(z+1)(2-3z) - dz) = 2πi ×0 = 0
Therefore, the value of the given integral is zero.
To evaluate the integral ∮c (z(z+1)(2-3z) - dz), where c is the circle |z| = 2, we can apply Cauchy's residue theorem. This theorem states that if f(z) is an analytic function inside a simple closed contour C, except for isolated singularities at points a₁, a₂, ..., aₙ, then the integral of f(z) around C is equal to 2πi times the sum of the residues of f(z) at the singularities inside C.
In this case, the function f(z) = z(z+1)(2-3z) has singularities at z = 0, z = -1, and z = 2/3 (roots of the quadratic term and the denominator). However, only the singularity at z = -1 lies within the contour |z| = 2.
To find the residue at z = -1, we can calculate the limit:
Res(-1) = lim(z->-1) (z+1)(z(z+1)(2-3z))
Simplifying the expression:
Res(-1) = lim(z->-1) (z+1)(2z² - z - 2)
= lim(z->-1) (2z³ + z² - 2z - z² - z - 2)
= lim(z->-1) (2z³ - z - 3z - 2)
Evaluating the limit:
Res(-1) = 2(-1)³ - (-1) - 3(-1) - 2
= -2 + 1 + 3 - 2
= 0
Since the residue at z = -1 is zero, the integral around the contour |z| = 2 is also zero:
∮c (z(z+1)(2-3z) - dz) = 2πi× 0
= 0
Therefore, the value of the given integral is zero.
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Solve for .
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
43 +4 < 92 +8
Answer:
[tex]x > -\frac{24}{19}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{3}x + 4 < \frac{9}{2}x + 8[/tex]
Required
Solve for x
Collect like terms
[tex]\frac{4}{3}x - \frac{9}{2}x < 8-4[/tex]
[tex]\frac{4}{3}x - \frac{9}{2}x < 4[/tex]
Take LCM
[tex]\frac{8x - 27x}{6} < 4[/tex]
[tex]\frac{-19x}{6} < 4[/tex]
Multiply by 6
[tex]6 * \frac{-19x}{6} < 4 * 6[/tex]
[tex]-19x < 24[/tex]
Divide by -19
[tex]x > -\frac{24}{19}[/tex]
-48+6
+(-3)(-4) (-2)
-7
Answer:
-73
Step-by-step explanation:
-48+6-24-7 = -73
[tex] {2x}^{2} - 5x + 3[/tex]
Experimental Probability is ___________ .
a . our prediction
b. data from our experiment
Answer:
its B
Step-by-step explanation:
Answer:
b. data from our experiment
Step-by-step explanation:
Find the area of the shaded sector below.
Answer:
9.07571212
Step-by-step explanation:
To solve this we first need to find the area of the circle, r squared times pi
4 x 4 x pi = 50.2654825
Now we multiply this by 65/360, 50.2654825 x 65/360 = 9.07571212
The shaded sector covers 9.07571212 square inches.
(っ◔◡◔)っ ♥ Hope It Helps & Please Consider Giving Brainliest♥
Khan khan khan khan
Answer:
11
Step-by-step explanation:
it says motor cycles combined with garbage so add both of them then subtract that from the bull dosers
motor =18
garbage=4
18+4=22
bulldosers=11
22-11= 11 more
Answer:
11
Step-by-step explanation:
HELP ASAP PLEASE ILL MARK BRAINLIEST AND RATE 5 STARS PLEASEEE
A survey about the student government program at a school finds the following results:
190 students like the program
135 students think the program is unnecessary
220 students plan on running for student government next year.
If a circle graph were made from this data, what would the measure of the central angle be for the group that likes the program? Round your answer to the nearest whole number. Make Sure To Show Your Steps
Answer: 126 degrees
there are 360 degrees in a circle.
A matched pairs experiment compares the taste of instant coffee with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 40 subjects who participate in the study, 14 prefer the instant coffee and the other 26 prefer fresh-brewed. Take p to be the proportion of the population that prefers fresh-brewed coffee. You might find a table of critical values useful. You can use table A or the bottom row of table D, but table D is easier.
Find a 95% confidence interval for p. 95% CI:_________
The 95% confidence interval for p is (0.47, 0.83)
Total subjects = 40
People preferring fresh brewed = 26
Calculating the sample proportion -
Sample proportion = Number of subjects preferring fresh brewed coffee / Total number of subjects
= 26 / 40
= 0.65
It is required to establish crucial values depending on chosen confidence level in order to generate the confidence interval. The z-value associated with a 97.5% cumulative probability to obtain a 95% confidence range is to be found. This is because the remaining 5% by 2 is divided to determine middle 95% of the standard normal distribution. The z-value for a 97.5% cumulative probability is around 1.96 using Table D or any other approach.
Using the formula for confidence interval -
[tex]CI = p + z x \sqrt ((px (1 - p) / n)[/tex]
Substituting the values -
[tex]CI = 0.65 ± 1.96 \sqrt{x} ((0.65 * (1 - 0.65)) / 40)[/tex]
[tex]= 0.65 ± 1.96 x \sqrt(0.2275 / 40)[/tex]
= 0.65 ± 1.96 x 0.0921
= 0.65 ± 0.1802
Rounding to two decimal places, the 95% confidence interval will be 0.47, 0.83)
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The speed of light is 3 × 108 meters per second. It take 1.82 × 102 seconds for light to reach Mars. What is the distance, in meters, between the sun and Mars? A 4.82 x 1016 B 4.82 x 1010 C 5.46 x 1016 D 5.46 x 1010
Answer:
D 5.46 x 10^10
Step-by-step explanation:
Recall that speed is the rate of change of distance with time and may be expressed mathematically as
speed = Distance/time
Distance = speed * time
Hence given that the speed of light
= 3 × 10^8 meters per second
Time taken for light to travel between the given distance
= 1.82 × 10^2 seconds
substituting the given values
Distance = 3 × 10^8 * 1.82 × 10^2
= 5.46 * 10^(8+2)
= 5.46 * 10^10 meters
In a survey, 25 people were asked how much they spent on their child's last birthday gift. The results were roughly bell- shaped with a mean of $39 and standard deviation of $20. Construct a confidence interval at a 80% confidence level. Give your answers to one decimal place. I Interpret your confidence interval in the context of this problem.
The confidence interval at an 80% confidence level is approximately $33.88 to $44.12.
To construct a confidence interval for the mean based on the given survey data, we can use the formula:
Confidence Interval = mean ± (critical value) * (standard deviation / √sample size)
In this case, the mean is $39, the standard deviation is $20, and the sample size is 25. The critical value corresponds to the desired confidence level, which is 80%. To determine the critical value, we can use a standard normal distribution table or a statistical calculator.
For an 80% confidence level, the critical value (z-score) is approximately 1.28.
Now, let's calculate the confidence interval:
Confidence Interval = $39 ± (1.28) * ($20 / √25)
= $39 ± (1.28) * ($20 / 5)
= $39 ± (1.28) * $4
= $39 ± $5.12
This means we can be 80% confident that the true mean amount spent on a child's last birthday gift falls within this range based on the given survey data.
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What is the value of x?
Answer. it is 5 or letter i
Answer:
The value of x is 5
Step-by-step explanation:
Using the linear pair theorem, both angles are supplementary and add up to 180 degrees. 180 minus 140 is 40. and 8 times 5 = 40. So x = 5.
pleas help thanks
5. Which term of the geometric sequence 1, 3,9, ... has a value of 19683? 14
The term of the geometric sequence 1, 3,9, ... which has a value of 19683 is :
To find which term of the geometric sequence has a value of 19683, we can use the formula for the nth term of a geometric sequence.
Here's the formula:
an = a₁ * r^(n - 1)
where an is the nth term of the sequence
a₁ is the first term of the sequence
r is the common ratio of the sequence
Given the sequence 1, 3, 9, ..., we can see that a₁ = 1 and r = 3.
To find the value of n that gives the term with a value of 19683, we can substitute these values into the formula and solve for n:
19683 = 1 * 3^(n - 1)
19683/1 = 3^(n - 1)
3^9 = 3^(n - 1)
Now we can equate the exponents:
9 = n - 1
n = 9 + 1
n = 10
Therefore, the 10th term of the geometric sequence 1, 3, 9, ... has a value of 19683. Thus, the answer is 10.
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sooooooooo
technically i've neevr lost a fight with a tiger
Answer:
oh thats cool
Step-by-step explanation:
If the half-life of a radioactive isotope is 3 million years,
what percent of the isotope is left after 6 million years?
- 50
- 25
- 12.5
- 6.75
After 6 million years, 25 percent of the radioactive isotope will be left.
The half-life of a radioactive isotope is the time it takes for half of the initial amount of the isotope to decay. In this case, the half-life is 3 million years. After the first half-life, half of the isotope will remain, which is 50 percent. After another 3 million years (a total of 6 million years), another half-life will have passed. Therefore, half of the remaining 50 percent will decay, leaving 25 percent of the original isotope.
To understand this further, let's consider the decay process. After the first 3 million years, 50 percent of the isotope will have decayed, leaving 50 percent. Then, after the next 3 million years, another 50 percent of the remaining isotope will decay, resulting in 25 percent remaining (50 percent of the original amount). This exponential decay pattern continues as each successive half-life cuts the remaining amount in half.
Therefore, after 6 million years, 25 percent of the radioactive isotope will be left, while 75 percent will have undergone radioactive decay.
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(b)
4 cm
a
3 cm
4 cm
15 cm
8 cm
Volume = 540 cm
Answer:
are you trying to look for the height or radius?
if you're looking for the height then you'll have to divide the volume by pi and the radius squared
if you're looking for the radius then you'll have to divide the volume by pu and the height and do the squareroot over the whole equation
Solve the initial value problem (2 x-6 xy + xy) dx + (1 - 3x2 + (2 + x?) y) dy = 0, y(1) = -4 and then provide the numerical value of lim y(x) rounded-off to FIVE significant figures. A student rounded-off the final answer to FIVE significant figures and found that the result was as follows (10 points): X+00 (your numerical answer for the limit must be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The implicit solution of the initial value problem is described by the equation as follows (mark a correct variant) (6 points): 3 xy - (x + 1) y2 + 9 x2 = 0 x² + x y + (2x + 10) y2 – 10 = 0; x2 - xy + (2x - 10) y2 + 12 = 0 2x2 – 3xy - (1 + x?)y2 + 19 = 0 x2 - xy + (2x - 10) y2 = 0 x2 + y - 3x"y +(1+) y2 – 33 = 0 2) The explicit solution for the value of y as the function of x is described by the explicit formula as follows (mark a correct variant) (4 points) y -1+3x_v719+8x2 + ** 2+x? y у -*-400-80x+41x2-3x3 40-5+x) -x-41x28x3 4-5+x) x+41x28x? 4-5+x) y = *-480-96x+41x2-3x3 y = 4-5+x) -1+3x2 + 7/1948x2 + x y = 2+x2 -3x - 76+93x2 +8x* у 2(1+x2) 2) The explicit solution for the value of y as the function of x is described by the explicit formula as follows (mark a correct variant) (4 points): y = -1+3x2-77/19+8x2+x 2+x2 y = y = 400-80x+41x2 - 8x? 4-5+x) -x-41x28x3 4(-5+x) x+41x2-8x3 4-5+x) Tut y = X 480-96x+41x2 - 8x3 y = 4-5+x) -1+3x² +17/19+8x2+x+ O y = 2+x2 -3x - 76+93x2 +8x4 y = 2(1+x²) 3x - 14+49x2 +36 x+ y = 2(1+x2)
The implicit solution to the initial value problem (2x − 6xy + xy)dx + (1 − 3x^2 + (2 + x^2)y)dy = 0 with y(1) = −4 is given by the equation:3xy − (x + 1)y^2 + 9x^2 = 0. The explicit solution for y as a function of x is given by the formula: y = (-1 + 3x^2 - 7/19 + 8x^2 + x)/(2 + x^2)The numerical value of lim y(x) rounded off to five significant figures is -1.3152.
Intermediate results obtained during the process include: implicit solution of initial value problem and explicit solution for y as a function of x. The implicit solution of the initial value problem is described by the equation:3 xy - (x + 1) y2 + 9 x2 = 0. The explicit solution for y as a function of x is given by the formula: y = (-1 + 3x^2 - 7/19 + 8x^2 + x)/(2 + x^2).
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HElp pls :((((((((((((
Answer:Just add them all
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
First you have to find the percentage of pan crust to all the other crusts to do this you add all the crusts together:
397+220+167+196 = 980
Then divide 196 by 980:
196/980 = .2 or 20%
Then multiply 400 by 20%
400*20% = 80
The point p=(x,1/2)
Lies in the unit circle shown below what is the value of X in simplest
"Let C be a semialgebra on a set X. Let A = {0} U {U}=1 A; : n E N, {A1, ... , An} C C, disjoint}. = : In other words, A consists of the empty set and all finite, disjoint unions of sets in C. Prove that A is an algebra on X.
"
The set A, defined as A = {∅} ∪ {⋃_{i=1}^n Ai : n ∈ ℕ, {Ai} ⊆ C, disjoint}, is proven to be an algebra on a set X.
To prove that A is an algebra, we need to show that it satisfies three conditions: (1) X ∈ A, (2) for any set A ∈ A, its complement X\A also belongs to A, and (3) for any sets A, B ∈ A, their union A ∪ B also belongs to A.
First, the empty set ∅ is included in A by definition. Second, let A be any set in A, represented as A = ⋃_{i=1}^n Ai, where {Ai} is a collection of disjoint sets from C. Then, the complement of A is X\A, which can be represented as X\A = ⋃_{i=1}^n (X\Ai). Since each Ai is in C, their complements X\Ai are also in C, implying X\A is a disjoint union of sets from C and therefore belongs to A.
Lastly, let A and B be two sets in A, represented as A = ⋃_{i=1}^n Ai and B = ⋃_{j=1}^m Bj. The union of A and B is A ∪ B = ⋃_{i=1}^n Ai ∪ ⋃_{j=1}^m Bj. Since Ai and Bj are disjoint sets from C, their union Ai ∪ Bj is also in C. Thus, A ∪ B is a disjoint union of sets from C and belongs to A.
By satisfying all three conditions, A is proven to be an algebra on X.
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If
y=∑n=0[infinity]cnxny=∑n=0[infinity]cnxn
is a solution of the differential equation
y′′+(3x−1)y′−1y=0,y″+(3x−1)y′−1y=0,
then its coefficients cncn are related by the equation
cn+2=cn+2= cn+1cn+1 + cncn .
The coefficients cn are related by the equation:
cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn
To begin, we can substitute the expression for y into the differential equation and see if it satisfies the equation. Taking the first and second derivatives of y with respect to x, we find:
y' = ∑n=0[infinity]cnxn-1
y'' = ∑n=0[infinity]cn(n-1)xn-2
Substituting these expressions into the differential equation yields:
∑n=0[infinity]cn(n-1)xn-2 + (3x-1)∑n
=> 0[infinity]cnxn-1 - ∑n=0[infinity]cnxn+1 = 0
We can rearrange this equation to get:
∑n=0[infinity]cn(n+2)xn+1
=> ∑n=0[infinity]cn(n-1)xn-2 + (3x-1)∑n=0[infinity]cnxn
Now, we can compare the coefficients of xn+1 on both sides of the equation to get:
cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn
This is a recurrence relation for the coefficients cn. To see how it relates to the equation given in the question, we can substitute n+1 for n and simplify:
cn+3 = (n+2)(n+3)cn+2 + (3n+2)cn+1
Now we can substitute cn+1 from the original recurrence relation:
cn+3 = (n+2)(n+3)(n+1)cn+1 + (n+2)(n+3)cn + (3n+2)cn+1
Simplifying gives:
cn+3 = (n+2)(n+3)cn+2 + [(n+2)(n+3)(n+1) + 3n+2]cn+1
This is exactly the same recurrence relation as the one given in the question. Therefore, we can conclude that the coefficients cn are related by the equation:
cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn
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Help
I dont know the answer im not very smart
A survey of 879 supermarket employees revealed that 239 workers felt they were overqualified for the position. What is the best way to characterize the 879 employees?
Answer:
they doubt if they're qualified or not
Plz help is it the same?
Answer:
12.054 < 12.54
Step-by-step explanation:
12.054 is less than 12.54 because it has a zero in the tenths place, and 12.54 has a five in the tenths place! Always check the first spot after the decimal first. Best of luck<3
Answer:
12.054 < 12.54
Step-by-step explanation:
In an independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each treatment. If all three treatments have the same total. T1 T2 T3, what is SSbetween?
a. 0
b. 100
c. 10(3)
d. This cannot be determined from the information given.
The value obtained for SSbetween is 20. The correct answer is (b) 20.
To calculate the sum of squares between (SSbetween) for an analysis of variance (ANOVA), we need to determine the variation between the sample means of the different treatment conditions. The formula for SSbetween is as follows:
SSbetween = n * Σ(M - m)²
where n is the sample size for each treatment condition, M is the individual treatment condition mean, and m is the overall mean.
In this case, the sample size for each treatment condition is n = 10, and the treatment condition means are M1 = 1, M2 = 2, and M3 = 3.
To calculate SSbetween, we first find the overall mean (m) by taking the average of the treatment condition means:
m = (M1 + M2 + M3) / 3
m = (1 + 2 + 3) / 3
m = 6 / 3
m = 2
Now, we can calculate SSbetween:
SSbetween = n * Σ(M - m)²
SSbetween = 10 * [(1 - 2)² + (2 - 2)² + (3 - 2)²]
SSbetween = 10 * [(-1)² + (0)² + (1)²]
SSbetween = 10 * (1 + 0 + 1)
SSbetween = 10 * 2
SSbetween = 20
Therefore, the value obtained for SSbetween is 20. The correct answer is (b) 20.
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Incomplete question:
An independent-measures research study compares three treatment conditions using a sample of n = 10 in each treatment. For this study, the three sample means are M1 = 1, M2 = 2, and M3 = 3. For the ANOVA, what value would be obtained for SSbetween?
a.30
b.20
c.10
d. 2
If A = {3, 7, 9, 13, 22}, B = {5, 7, 14, 23, 31}, and C = {8, 9, 15, 23, 25, 31, 33}, then what is (A∪B)∩C?
(A∪B)∩C = {9, 23, 31}.
To find the intersection of the sets (A∪B) and C, we first need to determine the union of sets A and B. The union of two sets consists of all the unique elements present in both sets.
A∪B = {3, 5, 7, 9, 13, 14, 22, 23, 31}
Next, we find the intersection of the obtained union (A∪B) and set C. The intersection of two sets contains the elements that are common to both sets.
(A∪B)∩C = {9, 23, 31}
Therefore, the intersection of the sets (A∪B) and C is {9, 23, 31}. These are the elements that are present in both (A∪B) and C.
In summary, (A∪B)∩C = {9, 23, 31}.
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i don't understand. please help
Answer: 5m
Step-by-step explanation:
The Initial water level means that level amount when the time equal to 0hrs, which is 5m.
Find the inverse of this function. Show your steps.
Hi, so, I'm like halfway done, but can you show me the steps to get to the inverse of this function, please? Also, is was what I have so far correct?
Thanks so much if you help!
Answer:
Step-by-step explanation:
First, replace f(x) with y . ...
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y . ...
Replace y with f−1(x) f − 1 ( x ) . ...
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
Janet's Co. has sales of $90,000, COGS of 80% of sales and operating expenses of $5,000. a. Find the gross and net profits. b. Find the rate of markup (based on cost). c. Find the percent net margin. 36
Janet's Co. has sales of $90,000, cost of goods sold (COGS) equal to 80% of sales, and operating expenses of $5,000. The task requires calculating the gross and net profits, the rate of markup based on cost, and the percent net margin.
a. The gross profit can be found by subtracting the COGS from the sales. In this case, the COGS is 80% of $90,000, which amounts to $72,000. Thus, the gross profit is $90,000 - $72,000 = $18,000. To calculate the net profit, we need to subtract the operating expenses from the gross profit. Therefore, the net profit is $18,000 - $5,000 = $13,000.
b. The rate of markup based on cost represents the percentage of profit added to the cost of goods sold. It can be calculated by dividing the gross profit by the COGS and multiplying by 100. In this case, the markup rate is ($18,000 / $72,000) * 100 = 25%.
c. The net margin is the percentage of net profit relative to the sales. It can be calculated by dividing the net profit by the sales and multiplying by 100. In this case, the net margin is ($13,000 / $90,000) * 100 = 14.44%.
In summary, Janet's Co. has a gross profit of $18,000 and a net profit of $13,000. The rate of markup based on cost is 25%, indicating the percentage of profit added to the cost of goods sold. The net margin, representing the percentage of net profit relative to sales, is 14.44%.
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2. kiran is flying a kite. he gets tired, so he stakes the kite into the ground. the kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. how high is the kite?
a. 9√3 feet
b. 9 feet
c. 18/√2 feet
d. 18/√3 feet
If kite is on a string that is 18 feet long, then the height of kite is (b) 9 feet.
In order to find the height of the kite, we use trigonometry. We know that the length of the string is 18 feet and the angle with the ground is 30 degrees, we use the Sine function to determine the height of the kite.
The formula to find the height is:
Height = (Length of string) × Sin(Angle),
Substituting the values,
We get,
Height = (18 feet) × Sin(30 degrees),
Using the value of Sine of 30 degrees as (0.5), we can calculate the height as :
Height = (18 feet) × (0.5),
= 9 feet
Therefore, the correct option is (b) 9 feet.
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Triangle Sums***GRADED 1 of 51 of 5 Items #1 Triangle RST is shown. What is the measure of ∠T? Record your answer and fill in the bubbles on the grid. Be sure to use correct place value.
Answer:
[tex]\angle T = 70[/tex]
Step-by-step explanation:
Given
[tex]\angle T= 2x[/tex]
[tex]\angle S= 75[/tex]
[tex]\angle R= x[/tex]
See attachment for triangle
Required
Calculate [tex]\angle T[/tex]
First, we add up the angles in the triangle;
[tex]\angle R + \angle S + \angle T = 180[/tex]
[tex]x + 75 + 2x = 180[/tex]
Collect like terms
[tex]x + 2x = 180 - 75[/tex]
[tex]3x = 105[/tex]
Solve for x
[tex]x = \frac{105}{3}[/tex]
[tex]x = 35[/tex]
Given that:
[tex]\angle T= 2x[/tex]
[tex]\angle T = 2 * 35[/tex]
[tex]\angle T = 70[/tex]