Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Find a function f such that F = ∇f. f(x, y, z) = (b) Use part (a) to evaluate C ∇f · dr along the given curve C.

Answer:

\(Unit\ Charge = -6\ units\)

Step-by-step explanation:

Question is incomplete; However, the missing part of the question will most likely be to calculate the charges on each particle.

If that is the case;

\(Tota\l Charges = -42\ units\)

We'll get the unit charge when we divide by 7.

This is so because, they all have the same charge.

\(Unit\ Charge = -42\ units/7\)

\(Unit\ Charge = -6\ units\)

Hence;

the unit charge is -6 units

Answer:

the unit charge is -6 units

Step-by-step explanation:

If NP and QS are parallel lines and ∠NOM = 130° then the value of ∠POM is 50°.

Parallel lines are two or more lines in a plane that do not intersect, regardless of how far apart they are.

Despite being located at different distances from one another, parallel lines always have the same slope, which is the same steepness and direction.

Since NP and QS are parallel lines, we have:

∠NOM + ∠MOP = 180° (because NOM and MOP are on a straight line)

Also, the alternate interior angles NOM and POM are equal, so:

∠NOM = ∠POM

Substituting this into the first equation gives:

∠POM + ∠MOP = 180°

We can now solve for ∠POM by substituting the given value:

130° + ∠POM = 180°

∠POM = 50°

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A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.

A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.

This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.

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A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.

A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.

Cone volume is calculated using the method V=1/3πhr².

Given that,

diameter(d) = 16 cm

radius (r) = d/2 = 8 cm

volume = 320π cubic centimeters

πr²h/3 = 320π

or, [π × (8)² × h]/3 = 320π

or,  h = (3 × 320)/(8)²

or, h = 15 cm

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Answer:

\(\displaystyle d \approx 3.6\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Reading a Cartesian Plane

Algebra II

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point A(-2, 1)

Point B(1, -1)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

3.6 units

Step-by-step explanation:

Point A --> \(x_{1} \\\) = -2 , \(y_{1}\) = 1

Point B --> \(x_{2}\) = 1   , \(y_{2}\) = -1

AB =

\(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 } \\\sqrt{[1 - (-2)]^2 + [(-1) - 1]^2} \\\sqrt{3^2 + (-2)^2} \\\sqrt{9 + 4} \\ \sqrt{13} \\3.605\)

distance between AB can be rounded to 3.6 units

Hope it helps.

Answer:

Option D. x = 8 is correct

Step-by-step explanation:

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

\(\fbox \colorbox{black}{ \colorbox{white}{x} \:  \:  \: \:  \: \: \colorbox{white}{=}  \:    \:   + \colorbox{white}{8}}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's solve for x ~

now, subtract 3 from both sides ~

hence, x = 8 ~

The factor of the function will be (4x - 3) and (3x + 1). The graph of the function is shown below.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The function is given below.

g(x) = 5x - 12x² + 3

Then the function can be written as

g(x) = - 12x² + 5x + 3

Then the factor of the function will be

g(x) = 0

Then we have

   - 12x² + 5x + 3 = 0

       12x² - 5x - 3 = 0

12x² - 9x + 4x - 3 = 0

    (4x - 3)(3x + 1) = 0

                         x = -0.33 and 0.75

Then the graph of the equation will be given below.

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The point 0.3 lies on right side and -5/2 lies on left side on number line.

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.

The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line.

Given:

we have to plot -5/2 and 0.3 on the number line

Now, writing -5/2 in decimal to plot on number line

-5/2 = -2.5

So, 0.3 lies on the right side of the zero between 0 and 1.

-2.5 lies on the left side of the zero between -2 and -3.

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Answer:

see below

Step-by-step explanation:

will be of the form xxxx3.x    '3' will be just to the left of the decimal point

Answer:

H0:μ=18, Ha:μ<18

H0:μ=11.3, Ha:μ<11.3

H0:μ=3.7, Ha:μ<3.7

Step-by-step explanation:

A left tailed test is a type of test usually taken from the alternative hypothesis that includes only one of either the less than or greater than options and not both.

A left tailed test corresponds with the less than option and in this case study, the left tailed test are:

H0:μ=18, Ha:μ<18

H0:μ=11.3, Ha:μ<11.3

H0:μ=3.7, Ha:μ<3.7

Answer:

= 4

Step-by-step explanation:

first lets find the value of x in 3x+2=5/9

3x+2=5/9

3x = \(\frac{5}{9}\) -2

3x = \(\frac{3}{9}\)

3x = \(\frac{1}{2}\)

x = \(\frac{1}{2 * 3\\ }\)

x = \(\frac{1}{6}\)

\(\frac{1}{6}\) can also be written as \(6^{-1}\)

−3x+8

-3 (\(\frac{1}{6}\)) +8

\(\frac{-3}{6}\) +8

= 4

The value of f(g(1) from the table of functions is given as 1.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

when x = 1

g(x) = 3

or f(g(1) = f(3) = 1

The value of f(g(1) from the table of functions is given as 1.

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Answer:

Step-by-step explanation:

2517.02

Answer:

No

Step-by-step explanation:

To determine whether the given set of ordered pairs {(49,13),(61,36),(10,27),(76,52),(23,52)} represents a function, check if each x-value is associated with a unique y-value.

Check the x-values in the set: 49, 61, 10, 76, and 23. There are no repeated x-values.  Still need to check if each x-value has a unique corresponding y-value.

Check the y-values: 13, 36, 27, 52, and 52. There is one repeated y-value, 52, for the pairs (76, 52) and (23, 52).

Conclusion: the y-value 52 is associated with 2 different x-values, therefore the given set of ordered pairs does not represent a function.

The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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Answer:

35x²- 18x -8

Step-by-step explanation:

5x × 7x= 35x²

5x × 2= 10x

-4 × 7x= -28x

-4 × 2= -8

*combine like terms

35x² + 10x -28x -8

10x - 28x= -18x

35x²- 18x -8

\(\bf{(5x-4)(7x+2) }\)

\(\bf{5x(7x+2)-4(7x+2) }\)

\(\bf{35x^{2} +10x-4(7x+2)}\)

\(\bf{35x^{2} +10x-28x-8 }\)

\(\bf{\red{35x^{2} -18x-8 \ \ \Rightarrow \ \ \ Answer }}\)

yeahStep-by-step explanation:

Answer:

4%

Step-by-step explanation:

To find the sales tax rate you need to divide the tax amount by the item amount so in this case it is 13.60/340 with an answer of 0.04 meaning the tax rate is 4%. Hope this helps!

Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of \(a^{2}\) + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

\(3x^{2}\) - 2 = -5x
\(3x^{2}\) + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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Answer:

Step-by-step explanation:

(–3s + 2t)(4s – t)

= -3s (4s - t) + 2t(4s - t)

\( = - 12 {s}^{2} + 3st + 8st - 2 {t}^{2} \)

\( = - 12 {s}^{2} + 11st - 2 {t}^{2} (ans)\)

Answer: -12s^2 + 11st -2t^2

Step-by-step explanation:

= (-3s + 2t)(4s - t)

= -12s^2 + 3st + 8st -2t^2

= -12s^2 + 11st -2t^2

Answer Provided by GauthMath please heart and comment thanks if you like.

The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.

Let's start the proof:

1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.

2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.

3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.

4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).

5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.

6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.

7. Now, we need to show that arc DE + arc FG = 360∘.

8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.

9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.

10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.

11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.

12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.

13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.

14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.

15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.

16. Simplifying, we have 90∘ = 180∘, which is a true statement.

17. Therefore, we have proven that m∠D + m∠F = 180∘.

Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

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Answer:

A is the most appropriate answer.

Step-by-step explanation:

if the fact that A occurs does not affect the probability or possibility of B occurring.

Answer: C is the correct answer!I don't feel like explaining. sorry.Please let me know if I am wrong.

The table is completed as follows using the double-declining-balance method of depreciation:

Year Cost   Accumulated  Book Value  Depreciation Accumulated  Book

                   Depreciation        B.O.Y         Expense     Depreciation  Value

                        B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000          $0           $30,000         $12,000         $12,000  $18,000

2   $30,000    $12,000          $18,000         $7,200           $19,200  $10,800

3   $30,000   $19,200          $10,800           $4,320          $23,520   $6,480

The double-declining-balance approach is what?

The double-declining-balance method is one of the depreciation techniques in use, however it adds additional costs in the first years of an asset's life.

In this depreciation method, the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2, is twice.

At the conclusion of each year, the leftover balance for the depreciation charge is adjusted using the double rate.

The difference between the closing balance from the previous year and the residual value is used to determine the depreciation charge for the most recent year.

Auto  = $30,000

Estimated useful life = 5 years

Residual = $800

Depreciable amount = $30,000 - $800 = 29,200

Straight-line depreciation rate = 100/5 = 20%

Double-declining depreciation rate =20% x 2 = 40%

Depreciation Expense:

1st year = 30,000 x 40/100 = 12,000

2nd year = 18,000 x 40/100 = 7,200

3rd year = 10,800 x 40/100 = 4,320

4th year = 6,480 x 40/100 = 2,592

5th year = 3,888 x 40/100 = 1,555

Year Cost   Accumulated  Book Value  Depreciation Accumulated Book

                   Depreciation        B.O.Y         Expense      Depreciation   Value

                        B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000          $0           $30,000         $12,000         $12,000  $18,000

2   $30,000    $12,000          $18,000         $7,200           $19,200  $10,800

3   $30,000   $19,200          $10,800           $4,320          $23,520   $6,480

4   $30,000  $23,520          $6,480           $2,592           $26,112   $3,888

5  $30,000  $26,112            $3,888          $1555           $27,667     $2,332

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Answer:6

18 as a product of its prime factors is 2*3*3 while 60 is 2*2*3*5 therefore considering common factors between both numbers we can see that there's one pair of two visible in both products and one pair of three we multiply both of these common values to get the final gcf which is 3*2=6

Answer:

\((a)\)  \(P(M\ or\ P\ or\ C) = 1.307\)

(b) See Explanation

Step-by-step explanation:

Given

\(P = 312\) ---- Professionals,

\(M = 470\) ----- Married persons,

\(C = 525\) ---- College graduates,

\(PCG = 42\)  ----- Professional college graduates,

\(MCG = 147\) ----- Married college graduates,

\(MP = 86\)  ---- Married professionals,

\(MPCG = 25\) ---- Married professional college graduates

\(Total =1000\)

Solving (a): P(M or P or C)

This is calculated as:

\(P(M\ or\ P\ or\ C) = P(M) + P(P) + P(C)\)

\(P(M\ or\ P\ or\ C) = \frac{n(M) + n(P) + n(C)}{Total}\)

\(P(M\ or\ P\ or\ C) = \frac{470 + 525 + 312}{1000}\)

\(P(M\ or\ P\ or\ C) = \frac{1307}{1000}\)

\(P(M\ or\ P\ or\ C) = 1.307\)

(b) In probabilities, the probability of an event or collection of events must not exceed 1 and must not go below 0.

In (a) above, the calculated probability exceeds 1.

Because of this single reason, the collected data is incorrect

The answer of given question is cosec θ is 5/2. sin θ is (√5/3).  cos θ is (1/4)√15.   cot θ is 2√3/3.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to calculate the measurements of angles and sides in triangles and to solve problems involving distances, heights, and angles.

1) We can use the fact that cosec θ is the reciprocal of sin θ:

cosec θ = 1/sin θ  cos θ is (1/4)√15.

Substituting the given value of sin θ:

cosec θ = 1/(2/5) = 5/2

Therefore, cosec θ is 5/2.

2) We can use the fact that cot θ is the reciprocal of tan θ:

cot θ = 1/tan θ

Substituting the given value of tan θ:

cot θ = 1/√(3/4) = 2/√3

To rationalize the denominator, we can multiply both the numerator and the denominator by √3:

cot θ = (2/√3) * (√3/√3) = 2√3/3

Therefore, cot θ is 2√3/3.

3) We can use the Pythagorean identity:

sin^2 θ + cos^2 θ = 1

Substituting the given value of sin θ:

(1/4)^2 + cos^2 θ = 1

Simplifying:

1/16 + cos^2 θ = 1

cos^2 θ = 1 - 1/16

cos^2 θ = 15/16

Taking the square root of both sides (since cosine is positive in the first quadrant where 0 < θ < π/2):

cos θ = √(15/16) = √15/4 = (1/4)√15

Therefore, cos θ is (1/4)√15.

We can use the Pythagorean identity:

sin^2 θ + cos^2 θ = 1

Substituting the given value of cos θ:

sin^2 θ + (2/3)^2 = 1

Simplifying:

sin^2 θ + 4/9 = 1

sin^2 θ = 1 - 4/9

sin^2 θ = 5/9

Taking the square root of both sides (since sine is positive in the second quadrant where 90° < θ < 180°):

sin θ = √(5/9) = (√5/3)

Therefore, sin θ is (√5/3).

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(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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