Write the correct order of letters to the finish line Example ABCGH​

The divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

To find the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k, you need to take the divergence operator (∇ · F).

The divergence of a vector field in Cartesian coordinates is given by the following formula:

∇ · F = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z),

where Fx, Fy, and Fz are the x, y, and z components of the vector field F, respectively.

In this case, we have:

Fx = (5x^2 + 7 - sin(xz)),

Fy = 0, and

Fz = (5x^2 + 7 - sin(xz)).

Taking the partial derivatives, we get:

∂Fx/∂x = 10x - zcos(xz),

∂Fy/∂y = 0, and

∂Fz/∂z = 10x - zcos(xz).

Now, substituting these derivatives into the divergence formula, we have:

∇ · F = (10x - zcos(xz)) + 0 + (10x - zcos(xz)).

Simplifying further, we get:

∇ · F = 20x - 2zcos(xz).

Therefore, the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

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Answer: B= 12 15

Step-by-step explanation:

The given ratios are

A) 2 3= 2: 3  already in its simplest form

B)  12 15 =12:15 Changing to its simplest form, we divide both by 3 giving us           4:5

C)  18 27 =18: 27  Changing to its simplest form, we divide both numbers by 9 giving us =2:3        

D)6 9=6:9  Changing to its simplest form, we divide both by 3 giving us  

       2:3

Therefore the ratio not equivalent to other three is 12:15

Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.



Historical scientists deal with falsification by employing rigorous methodologies and critical analysis of evidence. They strive to gather as much relevant data as possible to test hypotheses and theories. This is done through meticulous research, including the examination of primary sources, archaeological artifacts, historical records, and other forms of evidence. Historical scientists also engage in peer review and scholarly discourse to subject their findings to scrutiny and criticism.

The mechanism used by historical scientists to falsify hypotheses involves a combination of evidence-based reasoning and the application of established principles of historical analysis. They aim to construct coherent and logical explanations that are supported by the available evidence. If a hypothesis fails to withstand scrutiny or is contradicted by new evidence, it is considered falsified or in need of revision. Historical scientists constantly reassess and refine their hypotheses based on new discoveries, reinterpretation of existing evidence, and advancements in research techniques. This iterative process helps to refine our understanding of the past and ensures that historical knowledge remains dynamic and subject to revision.

Therefore, Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.

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The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.

1: We can use the formula to calculate the present value of the annuity:

P = A x [1 - (1+i)^-n] / i

Where

P = Present Value

A = Annuity

i = Interest Raten = Number of payments

2: Calculate the present value of each payment using the formula:

P1 = 25000 / (1.06)⁵

P2 = 25000 / (1.06)⁶

P3 = 25000 / (1.06)⁷

P4 = 25000 / (1.06)⁸

P5 = 25000 / (1.06)⁹

P6 = 25000 / (1.06)¹⁰

P7 = 25000 / (1.06)¹¹

P8 = 25000 / (1.06)¹²

3: Substitute the values into the formula to find the present value:

P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8

P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)

P = 158620.39

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The highest temperature recorded was 415°F(maximum).

At its lowest, the temperature is 385°F(minimum).

The function of absolute value calculates the separation between a point and an origin.

A less-than-compound inequality is represented by:

\( |x| \leq a\)

then the solution is

\( - a \leq \: x \: \leq \: a\)

according to the question

Temperature T is set to 400°F with a tolerance of 15°F, meaning that the absolute difference between T and 400°F may not be greater than 15°F; in other words:

\( |T - 400| \leq \: 15\)

now apply the solution

\( - 15 \leq \: T - 400 \leq \:15\)

then simplify this

\(T - 400 \ge \: - 15 \\ T \geq \: - 15 + 400 \\ T \geq \: 385\)

\(T - 400 \leq \: 15 \\ T \leq \: 15 + 400 \\ T \leq \: 415\)

Hence, The highest temperature recorded was 415°F(maximum).

At its lowest, the temperature is 385°F(minimum).

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An inscribed angle is formed by two chords of a circle that intersect at a vertex located on the circle.

The angle itself is formed by the two sides of the angle, which are the line segments connecting the vertex to the endpoints of the chords. The property that makes inscribed angles interesting is that the measure of an inscribed angle is half the measure of the intercepted arc on the circle.

This relationship holds true for any inscribed angle in a circle, making it a useful concept in geometry for solving problems involving angles, arcs, and circles.

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Answer:

32

Step-by-step explanation:

In ΔLMK

short leg /long leg = 18/24

In ΔLMJ

short leg /long leg = 24/JK

Now we make them equal

(18/24) = (24/JK), cross multiply

  18·JK = 24², divide both sides by 18

      JK = 24²/18

     JK = 32

Answer:

3.82 in

Step-by-step explanation:

Answer:

Step-by-step explanation:

By using the Pythagorean theorem:

b^2+3^2=5^2
b^2+9=25

b=sqrt (25-9)

b=sqrt(16)

b=4

=> 4^2+7^2=c^2
16+49=c^2
65=c^2
=>c=sqrt(65)

c = (approximately) 8

Answer:

Relation 1 & 2 are functions

Relation 3 & 4 are not functions

Step-by-step explanation:

For a relation to be a function every x must have one and only one y

This is not true for relation 3 which has 2 y's at x = m and 2 y's at x = v

This is also not true for relation 4 which has 2 y's at x = 4

Answer: Line BC and Line DE

Step-by-step explanation:

In geometry terms, we can say that for any set of two points, we always can find a line that passes through them.

For example, in the image, we can see two lines (but actually we could make more with those points)

We can see a line that connects points B and C, and we can call that line as:

Line BC

We also can see a line that connects the points D and E, we can call this line as:

Line DE

So the two lines are: Line BC and Line DE

The average time it takes to rent a video tape is 0.141 minutes.

Given data:Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).
Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, we need to determine the average time it takes to rent a video tape.
Let us assume λ = 12 and μ = 3 × 8.15 = 24.45
Average time it takes to rent a video tape = 1 / (μ - λ/n)
Where, n = number of servers⇒ Average time it takes to rent a video tape = 1 / (24.45 - 12/3)⇒ Average time it takes to rent a video tape = 1 / 8.45⇒ Average time it takes to rent a video tape = 0.1185 minutes = 0.141 rounded to three decimal places.

Thus, the average time it takes to rent a video tape is 0.141 minutes.

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Answer:

x = ± 3

Step-by-step explanation:

given y varies as \(\frac{1}{x^2}\) , then

y = k × \(\frac{1}{x^2}\) = \(\frac{k}{x^2}\) ← k is the constant of variation

to find k use the condition x = 2 , y = 1

1 = \(\frac{k}{2^2}\) = \(\frac{k}{4}\) ( multiply both sides by 4 )

4 = k

y = \(\frac{4}{x^2}\) ← equation of variation

when y = \(\frac{4}{9}\) , then

\(\frac{4}{9}\) = \(\frac{4}{x^2}\) ( cross- multiply )

4x² = 36 ( divide both sides by 4 )

x² = 9 ( take square root of both sides )

x = ± \(\sqrt{9}\) = ± 3

Answer:

no

Step-by-step explanation:

it would be 87.5

Kellen will pay approximately $11.07 in interest over 6 months if she continues to pay $100 per month.

To calculate the interest Kellen will pay in 6 months, we first need to calculate her monthly interest fee, that's 4.9% APR divided by using 12 months:

monthly interest fee = 4.9% / 12 = 0.4083%

We also want to calculate the full amount of time Kellen will take to pay off her debt, which is 6 months. we will then use this records to calculate the closing stability on her credit score card after 6 months of paying $100 in step with month:

overall payments = 6 x $100 = $600

remaining stability = $5,877 - $600 = $5,277

Next, we want to calculate the each day periodic charge, that's the monthly interest rate divided with the aid of the variety of days in a billing cycle (35 days):

daily periodic rate = 0.4083% / 35 = 0.0117%

Finally, we are able to use the method for finance charge to calculate the quantity of interest Kellen pays in 6 months:

Finance charge = closing balance x daily periodic rate x number of days in 6 months

Finance charge = $5,277 x 0.0117% x 180

Finance charge = $11.07

Therefore, Kellen will pay approximately $11.07 in interest over 6 months if she continues to pay $100 per month.

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Answer: A. -2.2 B. -2.7

Step-by-step explanation: To find the rate of change is y2-y1/x2-x1.

For A y2=184.3, y1=140.3 x2=0 and x1=20. 184.3-140.3 will give you 44. 0-20 is -20. So 44 divided by -20 is -2.7.

For B its the same thing: y2=109.3, y1=28.3, x2=30, and x1=60. 109.3-28.3 is 81 and 30-60 is -30. 81 divided by -30 is -2.7.

The geometric cumulative distribution function should be used.

The geometric cumulative distribution is a discrete likelihood conveyance where the random variable demonstrates the quantity of the Bernoulli trial expected to get the primary achievement. A Bernoulli trial is an experiment that can have just two potential results, ie., achievement or disappointment. All in all, in a mathematical dispersion, a Bernoulli trial is rehashed until a triumph is gotten and afterward halted. Here we are interested in the first success in the three chances, which is completely specified with the distribution function of a geometric distribution, and because the question asked for the probability of having a hand with five cards in the same suit in one of the first three hands. Hence the correct option is the cumulative distribution function.

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Answer:

Step-by-step explanation:

t=3

Answer:

prime number is 17 and the square number is 16 if you subtract them you get 1 .

Use the distance formula to solve for the direct distance from (4,-4) up to (-14,8)

Since 1 grid is equal to 0.125 miles. Multiply the distance in units and we get

Rounding to 2 decimal places, the direct distance is 2.70 miles.

Answer:

3

Step-by-step explanation:

\(18*\frac{1}{6} \\\\3\)

Answer:

=3x

Step-by-step explanation:

18x^1 / 6

=3x

The two pieces of paper of an art project one piece was 3/8 foot long and the other was 7/18 foot long, we will write these fraction in decimal form is 0.375 and 0.388888889 by Division Method.

Given,

          Length of one Piece of paper = 3/8 foot

          Length of other Piece of paper = 7/18 foot

We know,

                Division Method,

               for one piece of paper,

                       Divisor = 8                  

                       Dividend = 3

           Length of one piece of paper is  = 3 ÷ 8

                                                              = 0.375

         for other piece of paper,

                       Divisor = 18              

                       Dividend = 7

              Length of one piece of paper is  = 7 ÷ 18

                                                                  = 0.388888889

we will write these fraction in decimal form is 0.375 and 0.388888889 by Division Method

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Answer:

4:1

Step-by-step explanation:

The ratio at first would be 48:12, after this to simplify it we need to find the gcf (greatest/biggest common factor), which is 12. Dividing 48 by 12 gives us 4 and dividing 12 by 12 gives us 1, thus making the ratio 4:1

Answer:

2b

Step-by-step explanation:

To find the expected number of times Joan rolls a 3, we use the formula for mean of a binomial distribution.

The correct option is, option (C) 6.

The probability of rolling a number 3 on any given roll is 1/4

If Joan rolls the die 20 times, the number of times she rolls a 3 will follow a binomial distribution with n = 20 (number of trials) and p = 1/4 (probability of success).

The formula for the probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (the number of times Joan rolls a 3), k is the number of successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of rolling a 3 exactly k times out of 20 rolls:

P(X=k) = (20 choose k) * (1/4)^k * (3/4)^(20-k)

To find the expected number of times Joan rolls a 3, we can use the formula for the mean of a binomial distribution:

E(X) = n * p

In this case, E(X) = 20 * 1/4 = 5

Therefore, the expected number of times Joan rolls a 3 is 5.

Since the possible answers are integers, the closest answer to 5 is 6. Therefore, the answer is (C) 6.

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we conclude that at 5:00 p.m. there are 8 more inches of snow than at 8:00 a.m.

We know that at 8:00 a.m. there were t inches of snow in the ground.

At 5:00 p.m. there were 3t inches of snow in the ground.

Then the difference between the heights of the snow is:

3t- t = 2t

And we know that at 5:00 p.m. there were 12 inches of snow then we can solve the linear equation for t:

3t = 12in

t = (12in)/3 = 4 in

Replacing that in the difference of heights:

2t = 2*4in = 8in

From this, we conclude that at 5:00 p.m. there are 8 more inches of snow than at 8:00 a.m.

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Given:

Cost to rent a raft = $7 per person

Number of people a raft can hold = 6

Lunch cost = $3 per raft

To find:

The total cost for a group of 6.

Solution:

A raft can hold 6 people. So, one raft is required for group of 6.

Lunch cost = $3

Cost to rent a raft for one person = $7

Cost to rent a raft for 6 person = 6 × $7 = $42

Now,

Total cost = Lunch cost + Cost to rent a raft for 6 person

                = $3 + $42

                = $45

Therefore, the total cost for a group of 6 is $45.

Answer:

C. 8

Step-by-step explanation:

This then simplifies to (10^1 times 5 ^ -1)cubed. 5^-1 is 1/5, and 10^1 is 10. 10 times 1/5 is 2, and 2^3 is equal to 8.