The curl and the divergence of the vector field is illustrated below.
The term vector in math contains both position and magnitude.
Here we need to find the curl and the divergence of the vector field.
While we looking into the given question, we have the function
=> F(x, y, z) = <ex, exy, exyz>
AS per the concept of convergence, here we have consider that F=⟨P,Q,R⟩ is a vector field in R3 and Px, Qy, and Rz all exist here then the divergence of F is defined by as,
=> div F = Px + Qy + Rz
=> div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z.
The term curl in vector field is defined as a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space
And the curl of the vector field is calculated as,
=> curl F = (Ry−Qz)i + (Pz−Rx)j + (Qx−Py)k
=> curl F = (∂R/∂y−∂Q/∂z)i + (∂P/∂z−∂R/∂x)j + (∂Q/∂x−∂P/∂y)k.
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!Please Help.! I'm falling behind in the math and don't how to do this.
Answer:
m = 12
Step-by-step explanation:
The equation is y=mx +b
Where m is the slope
So, in this case slope is 12
12 is an integer, so my answer is correct!
What is the solution to the system of equations 3x 2y Z 7 5x 5y 4z 3 3x 2y 3z 1?
The answer is x = 4
y = -1
z = -3
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1
________
Let's take the first and the third equation, multiply the first one by (-1) and sum them up:
3x+2y+z=7
3x+2y+3z=1
____
-3x-2y-z=-7
3x+2y+3z=1
____
2z = -6
z = -6/2
z = -3
Substitute z in all equations:
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1
______
3x + 2y - 3 = 7
5x + 5y - 12 = 3
3x + 2y - 9 = 1
______
3x + 2y = 10
5x + 5y = 15
3x + 2y = 10
The first and the third equations are the same, so one can be excluded:
3x + 2y = 10
5x + 5y = 15
Multiply the first equation by -5 and the second equation by 2 and sum them up:
-15x - 10y = -50
10x + 10y = 30
_________
-5x = -20
x = -20/-5
x = 4
Substitute x:
3x + 2y = 10
12 + 2y = 10
2y = 10 - 12
2y = -2
y = -2/2
y = -1
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Why is it called a real number?
A set of all rational and irrational numbers is called the real numbers. All real numbers can be plotted on the number line. It is not imaginary number which cannot be quantified. It is denoted by capital Latin letter R.
Rational numbers are number that can be expressed as p/q where p and q are integers and value of q not equal to 0.
For example, -3/4, 5/3, 6/1.
Irrational numbers are not rational numbers but they can be plotted on the number line. It cannot be expressed as a simple ratio.
For example π, √2, -√7.
But √(-7) is an imaginary number.
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the school of business has 3 fax machines. the toner in each machine needs to be changed after about 5 hours of use. there is one unit secretary who is responsible for the fax machine maintenance. it takes him 15 minutes to replace the toner cartridge. what is the average time spent in the system? a. 0.2749 hrs b. 0.0142 hrs c. 0.1563 hrs d. 0.0249 hrs e. none of the above
The average time spent in the system which consists three fax machines is 0.026470 hour. So, option (e) none of the above is right here.
What is Queuing System?The M/M/1 queuing system is a single-server, infinite-capacity system in which the arrival interval is exponentially distributed with the parameter lambda and the service time is also exponentially distributed with the parameter. If the number of servers is maximum and all are equal, this model is considered an M/M/C queue.
We have, total number of fax machine in a business school is equals to three.
The toner of each machine needs to be changed in 5 hours of use . Time taken by secretary to replace toner cartridge = 15 minutes
We have to calculate average time spent in the system. fax machines , k = 3
Service person , R = 1
Arrival rate, λ = 3/5per hour = 0.6/hour
Service rate, μ =( 60/15) per hour
= 4/hour
Now, using the equation of finite population model M/M/1, the average time spent to maintain the fax machines in system is ,
L = λ² /μ (μ - λ )
plugging the value of μ and λ in above formula we get, L = (0.6)²/4(4-0.6)
= 0.36/13.6 = 0.026470
So, required answer is 0.026470 hour .
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The speed of a runner increased steadily during the first three seconds of a race. her speed at half-second intervals is given in the table. find lower and upper estimates for the distance that she traveled during these three seconds.
t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0
V (ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2
She can only move a certain distance in three seconds, with a lower distance of 33.45 feet and a upper distance of 43.45 feet.
The first three seconds of a race saw a runner's speed rapidly grow.
The time is therefore 3 seconds.
The table provides her speed at half-second intervals.
We are aware,
Speed = Distance / Time
Similarly
Distance = Speed × Time
t equals 0.5 seconds
Then, the lower distance traveled overall is equal to 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).
Terms are multiplied and added.
= 0.5 × 66.9
= 33.45 feet
The upper distance traveled is equal to 0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)
= 0.5 × 86.9
= 43.45 feet
As a result, Her lower distance in three seconds is therefore 33.45 feet, and her upper distance in three seconds is 43.45 feet.
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What is the sum of 182330+23 ?
18 25/33
18 13/30
19 13/30
19 25/33
❗quick please❗
Answer:
19 and 13/30
Step-by-step explanation:
First make 2/3 have a common denominator with 23/30
You can do this by multiplying the numerator and denominator of 2/3 to get 20/30
Now add
20/30 + 23/30 = 43/ 30
Simplify this fraction
1 and 13/30
add this to 18
18 + 1 and 13/30 = 19 and 13/30
Aiden misses 20% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 54?
Answer: 270
Step-by-step explanation:
20 percent = 2/5
Times 54 or 54/1 with 2/5
You should get 270. So Aiden missed 270 free throws.
Hope This Helps:)!A student randomly guesses on 10 true or false questions. Use the binomial model to find the probability that the student gets 7 out of the 10 questions right.
As per the binomial distribution, the probability that the student gets 7 out of the 10 questions right is 0.1171875
The term binomial distribution refers a probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.
Here we have given that the student randomly guesses on 10 true or false questions
And we have to use the binomial model to find the probability that the student gets 7 out of the 10 questions right.
While we looking into the given question, the thing we have identified are listed as follows:
Number of questions = 10
Number of right answer = 7
The probability of getting right answer = 1/2
The probability of getting wrong answer = 1/2
Now, as per the binomial distribution formula it can be written as,
=> P(r) = [10!/7!(10-7)!] x [1/2]⁷ x [1/2]¹⁰⁻⁷
When we simplify this one, then we get,
=> P(r) = 0.1171875
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What is the slope of 3x 5y =- 15?
Answer:
m = -3/5
Step-by-step explanation:
We have to get to the equation y = mx + b
3x 5y = -15
We subtract 3x from both sides
5y = -3x - 15
Then we divided by 5 into both sides
y = -3/5x - 3
We know our equation is y = mx + b
m = the slope
b = y-intercept
The slope is -3/5
Select all the points that segment ge¯¯¯¯¯ contains. triangle d e f with sides d e and e f congruent. segment e g is drawn from vertex e to base d f such that it bisects the base. segment e g also divides the vertex angle d e f into two angles, d e g with measure 3 y plus 4, and f e g with measure 5 y minus 10.
The segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts.
The points that segment e g contains are the points e and g.
Segment e g bisects triangle d e f, which means that it cuts the triangle into two equal parts. This means that the two sides d e and e f are congruent, and that the vertex angle d e f is divided into two equal angles, d e g with measure 3 y plus 4, and f e g with measure 5 y minus 10.
This can be expressed using the following formula:
Let d e = x
Then d e g = 3x + 4
f e g = 5x - 10
and d e + e f + f e g = 180°
Substituting the values for d e g and f e g, we get:
3x + 4 + x + 5x - 10 = 180°
9x = 196
x = 21.77
Therefore, the length of the sides d e and e f is 21.77.
Since segment e g bisects the base d f, it divides the base into two equal parts, each of length 10.88. The segment e g also divides the vertex angle d e f into two angles, d e g with measure 3 x + 4 = 67.33, and f e g with measure 5 x - 10 = 108.67.
Therefore, segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts. The segment also divides the vertex angle d e f into two angles, d e g with measure 67.33, and f e g with measure 108.67.
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Which of the following represents a linear inequality in open-sentence form? (Select all that apply.)
2x + 8 = 10y
2x - 7y > 10
8 + x > 5
3 < 5
Answer:
2x - 7y > 10
8 + x > 5
3 < 5
Step-by-step explanation:
The equations are
Ax + By + C < 0 or Ax + By + C > 0
There is no equal in a linear inequality
The first option 2x + 8 = 10y is an equation, so it is wrong. The other 3 are correct!
a statistics instructor wants to conduct a hypothesis test to determine if the mean number of credit hours taken by all ucf students is more than 11 hours. the instructor takes a sample of 27 ucf students and finds that they have a mean of 11.3 hours and a standard deviation of 3.0 hours. assume the population distribution of credit hours taken is approximately normal. what are the hypotheses for the test?
Hypotheses for the test are Null hypothesis and Alternative hypothesis
What is Hypothesis?
A hypothesis is an educated guess while using reasonable thinking, about the answer to a scientific question. Although it is not proof in an experiment, it is the predicted outcome of the experimentation. It can either be supported or not supported at all, but it depends on the data gathered.
The hypotheses for the test in this case are:
Null hypothesis (H0): The mean number of credit hours taken by all UCF students is not significantly different from 11 hours.
Alternative hypothesis (H1): The mean number of credit hours taken by all UCF students is significantly greater than 11 hours.
The null hypothesis represents the assumption that there is no difference between the mean number of credit hours taken by all UCF students and the value being tested (in this case, 11 hours). The alternative hypothesis is the opposite of the null hypothesis, and represents the claim that the mean number of credit hours taken by all UCF students is significantly different from 11 hours.
In this case, the instructor is specifically interested in testing whether the mean number of credit hours taken by all UCF students is significantly greater than 11 hours. Therefore, the alternative hypothesis is that the mean number of credit hours taken by all UCF students is significantly greater than 11 hours.
Hypotheses for the test are Null hypothesis and Alternative hypothesis
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Tori and Matias work as jewelers. Tori has an hourly wage of $24 and gets overtime for every hour she works over 40 hours. The overtime pay rate is 150% of the normal rate. Matias makes 5% commission on all jewelry he sells. Who earns more money in a week if Tori works 60 hours and Matias sells $21,000 worth of jewelry? Explain.
Tori earns more money.
How to find the commission rate?Add the sales income and the sales commission rate together to get the payable commission. A $10,000 product transaction would result in a $1,000 commission at a 10% commission rate.This is a pretty straightforward computation based on percentages. Simply take the selling price, multiply it by the commission rate, then divide the result by 100.Divide the base for that period by the appropriate commission rate to determine your commission for that period. For instance, if your commission rate is 5% and you generated $30,000 worth of sales between January 1 and January 15, you would multiply $30,000 by.05 to arrive at your $1,500 commission payout.Given data :
Tori : $24/h; 150% OT
Calculate Tori's overtime (OT) pay
Convert OT rate to decimals --> 150% = 1.
Tori's OT wage is 1.5*$24 = $36
Tori worked for 20h OT. (60h-40h = 20h)
(Regular pay X regular hours worked) + (OT wage X OT hours worked)
= ($24 X 40h) + ($36 X 20h)
= $1680
Matias : 5% commission
Convert 5% to decimals --> 0.05
(Jewelry sold) X (commission rate)
= $21000 X 0.05
= $1050
Since $1680 > $1080, Tori earns more.
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If f(x) is a third degree polynomial function and g(x) = f(−2x), which of the following is NOT true?
F f(x) and g(x) have the same x-intercepts.
G f(x) and g(x) have the same y-intercept.
H f(2) = g(−1)
J f(x) and g(x) have the same
number of zeros.
Answer:
F
Step-by-step explanation:
F. False. The graph of [tex]g[/tex] involved performing a horizontal compression on the graph of [tex]f[/tex].
G. True. Setting [tex]x=0[/tex] yields [tex]g(0)=f(0)[/tex].
H. True. Set [tex]x=-1[/tex].
J. True. The horizontal compression does not change the number of their roots, just the location.
What are the 3 types of triangle?
Step-by-step explanation:
obtuse-larger than 90 degrees
acute-smaller that 90 degrees
right-exactly 90 degrees
Whats a mean example?
The mean of the given data set is 29.5.
The term "mean" refers to the arithmetic average of the data set and is derived by dividing the total number of data points in the data set by the total number of data points. It is a data point that represents the average of all the data points in the collection.
Example :
Find the mean of the following data set.
10, 20, 36, 12, 35, 40, 36, 30, 36, 40
Given,
xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40
n = 10
Mean = ∑xi/n
= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10
= 295/10
= 29.5
Therefore, the mean of the given data set is 29.5.
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Find the mean of the following data set.
10, 20, 36, 12, 35, 40, 36, 30, 36, 40
Given,
xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40
n = 10
Mean = ∑xi/n
= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10
= 295/10
= 29.5
What is the base of x2?
The given expression x² is an algebraic expression where x is the base and 2 is the exponent.
Therefore, the answer is x.
In an expression aᵇ, a is the base and b is the exponent. Here the expression aᵇ implies the base a is multiplied b times. For example x² implies x multiplied twice, that is
x² = x × x
Base number is the number which is multiplied to itself and the exponent denotes the number of times it is multiplied to itself. For example
x⁰ = 1
x¹ = x
x² = x×x
x³ = x×x×x
x⁴ = x×x×x×x
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algebra 1 please help i will give brainliest :)
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. Determine how many children and adults attended?
What is the value of the current I?
The current value of "i" in the complex numbers is √(-1)
The value of I as current is expressed as Amperes
In order to know what "i" is and what its value is, we must first know what kind of number it is.
How is current expressed?The current is the flow of electric charge, it is denoted with the letter "I" and its unit of measure is Amperes, it can take any value even complex numbers.
Complex numbersComplex numbers are known as imaginary numbers and can be defined as an extension of the set of real numbers, since in its structure it has a real number followed by an imaginary number denoted with the letter "i".
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
√(-1) = i
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3,286-(1,221+217)…….
Answer:
1848
Step-by-step explanation:
teachers' salaries california and new york lead the list of average teachers' salaries. the california yearly average is while teachers in new york make an annual salary of . random samples of teachers from each state yielded the following. california new york sample mean population standard deviation use for the average teachers' salaries in california. at , is there a difference in means of the salaries?
Therefore, we lack adequate data to draw the conclusion that population means differ.
What does the test statistic actually mean?A result of a statistical test of a hypothesis is a number known as the test statistic. It displays how closely the distribution predicted by your observed data fit the null hypothesis of that statistical test.
Here,
First hypothesis : [tex]H_{0}[/tex] : u1 - u2 = 0
Alternate hypothesis : [tex]H_{A}[/tex]: u1 - u2 ≠ 0
for 0.1 level with two tail test , critical z = 1.645
Rule of Decision: [tex]H_{0}[/tex] Reject if the test statistic's absolute value is |z|>1.645
California , New York
x1 = 64510.00 x2 = 62900.00
n1 = 45 n2 = 45
σ1 = 8200.00 σ2 = 7800.00
std error σx1-x2=√(σ21/n1+σ22/n2)=[tex]\sqrt{(8200^2/45+7800^2/45) }[/tex]= 1687.0750
test stat z =(x1-x2-Δo)/σx1-x2 =(64510-62900)/1687.0750 = 0.95
We cannot reject the null hypothesis because the test statistic does not fall into the rejection zone.
Therefore, we lack adequate data to draw the conclusion that population means differ.
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Pleaseee help me out
If\(\triangle XYZ\sim\triangle EDFV), the measure of angle F is
Answer:
63 degrees
Step-by-step explanation:
similar triangles have the same angles.
XYZ is similar to EDF. Therefore the measure of angle Z is the same as angle F. The measure of angle Z is 63, so the measure of angle F is also 63.
Find the measure of each angle indicated. Round to the nearest tenth.
The measurement of angles are given as 20.92°, 40.83°, 57.76°, 71.17°, 26.21° and 44.7°respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The given problem can be solved by applying the trigonometric ratios to all of the triangle as follows,
(11) In the given triangle,
Sinθ = 5/14
=> θ = Sin⁻¹(5/14) = 20.92°
(12) In the given triangle,
Tanθ = 7/8.1
=> θ = Tan⁻¹(7/8.1) = 40.83°
(13) In the given triangle,
Cosθ = 8/15
=> θ = Cos⁻¹(8/15) = 57.76°
(14) In the given triangle,
Tanθ = 8.8/3
=> θ = Tan⁻¹(8.8/3) = 71.17°
(15) In the given triangle,
Tanθ = 6.4/13
=> θ = Tan⁻¹( 6.4/13) = 26.21°
(16) In the given triangle,
Tanθ =9.4/9.5
=> θ = Tan⁻¹( 9.4/9.5) = 44.7°
Hence, the measures of the angles indicated in the triangles are obtained as 20.92°, 40.83°, 57.76°, 71.17°, 26.21° and 44.7°respectively.
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What is the probability distribution of getting a sum of 4?
Probability of getting the sum as 4 when a pair of dice is rolled is 1/12.
Define probability.A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Value of probability can be greater than 1?No, probability is aways between 0 to 1.
Find total number of possible outcomes
Here it is given that a pair of dice is rolled
So the event points are
= { (1,1), (1,2), (1,3), (1,4),(1,5),(1,6),(2,1), (2,2), (2,3), (2,4),(2,5),(2,6),(3,1), (3,2), (3,3), (3,4),(3,5),(3,6),(4,1), (4,2), (4,3), (4,4),(4,5),(4,6),(5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2), (6,3), (6,4),(6,5),(6,6)}
So the total number of possible outcomes = 36
Let A be the event that of getting a sum of 4
So the event points are (1,3) , (2,2) , (3,1)
So total number of possible outcomes for the event A is 3
Hence the required probability= P(A)= no. of favorable cases to event A/total no of outcomes
=3/36
=1/12
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What is the multiplicative of 5?
Answer:
1/5 apparently
How do you simplify an equation?
Answer:
see explanation below
if you have any questions on equation you can send it to me
Step-by-step explanation:
We have various of ways in which we can simplify an equation
for example
simplify: 2x – 4 = 10
soln
2x – 4 = 10
since we are looking for x we need to collect like terms
2x = 10 + 4
2x = 14
Then we will divide both sides by 2 to get x
x = 14/2
x = 7
N.B:- after solving an equation if you want to check the answer just substitute for the value
2x – 4 = 10
2(7) – 4 = 10
14 – 4 = 10
10 = 10
LHS = RHS
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What additional information do you need to prove ∆ ABC ≅ ∆ def by the ASA postulate?
Answer:
⭐2 corresponding, congruent angles
⭐1 corresponding, congruent side length that is included between the 2 angles
Example (figures not drawn to scale);
Why is i squared equal to 1?
The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.
Given that,
We have to find why i squared is equal to negative 1.
We know that,
The imaginary numbers are denoted as i.
We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.
The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.
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A"B"C"D" is the image of ABCD after the composition of transformations
T(-2,0) R180° about the origin.
What is the sum of the x and y coordinates of D"
The sum of the x and y coordinates of D" is 6
How to determine the sum of the coordinatesFrom the question, we have the following parameters that can be used in our computation:
D = (-1, -3)
The transformation rule is given as
T(-2,0) R180° about the origin.
Mathematically, this can be represented as
(x, y) = (-x + 2, -y)
So, we have the following representation
D" = (1 + 2, 3)
Evaluate the like terms
D" = (3, 3)
When the coordinates are added, we have
Sum = 3 + 3
Evaluate
Sum = 6
Hence, the sum is 6
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Complete question
A"B"C"D" is the image of ABCD after the composition of transformations
T(-2,0) R180° about the origin.
What is the sum of the x and y coordinates of D" if the coordinate of point D is (-1, -3)?
What are the three identities?
Answer: (a+b)2 = a2 + b2 + 2ab., (a-b)2 = a2 + b2 – 2ab.,a2 – b2 = (a+b) (a-b)
Step-by-step explanation: