I need help!
Comepare each pair of fractions using Greater than sign , less than sign and equal to.

The required answer is TRUE. ∇·(∇×F) = 0 for any vector field of the form F = Fi + Gj.

Explanation:

TRUE. ∇·(∇×F) = 0 for any vector field of the form F = Fi + Gj.
To show this is true, we can use vector calculus identities. First, we can expand the curl of F:
∇×F = (∂G/∂x - ∂F/∂y)k
where k is the unit vector in the z-direction.
Next, we can take the divergence of this expression:
∇·(∇×F) = ∇·(∂G/∂x - ∂F/∂y)k
Using the identity ∇·(fA) = f(∇·A) + A·(∇f), we can simplify this expression:
∇·(∇×F) = (∇·∂G/∂x - ∇·∂F/∂y)k
But the divergence of a component function is simply the second partial derivative with respect to that variable, so we can further simplify:
∇·(∇×F) = (∂²G/∂x² + ∂²F/∂y²)k
no z-component in the original vector field F, the partial derivatives with respect to z will be zero.

Since F is of the form F = Fi + Gj, we know that it has no z-component, and therefore the divergence of (∇×F) must also have no z-component. But the only z-component in the expression we just derived is k, so it must be zero. Therefore,
∇·(∇×F) = 0
for any vector field of the form F = Fi + Gj.

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Answer:14.48

sorry if it is wrong.

Step-by-step explanation:0.25*57.90=14.475

I would greatly appreciate if you can give this the brainliest answer crown!

Step-by-step explanation:

The heights range from 132cm to 162 cm

3 children are taller than 150cm

9 children are shorter than 144cm

149.5cm is the median height

Managers and other decision makers are urged to be creative during step 2, which involves the process of establishing numerous alternative goals.

Numerous indicates a big amount. Despite the fact that you only have two feet, the word "many" might be used to describe the limitless number of pairs of shoes you own. The terms choice, election, option, preference, and selection can also be used to describe alternatives.

The report contains many of errors. The book contains numerous examples of plagiarism. All around the country are his innumerable progeny.

The numerous awards that are hung on the walls serve as visual proof of his huge accomplishment. She has proven her worth on numerous occasions. Alternative and alternate are phrases that are essentially synonymous.

Both expressions, which date from the middle of the 16th century, provide possibilities in addition to those that are initially suggested: an alternative perspective or proposal.

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The area of parallelogram ACEF for the given perimeter 198 is equal to  486 square units.

For parallelogram ACEF,

Perimeter of the parallelogram ACEF = 198 units.

To find the area of parallelogram ACEF,

we need to know the base and height of the parallelogram.

The perimeter and the lengths of two adjacent sides BF and DF.

Let us denote the length of BF as b and the length of DF as d.

The perimeter of a parallelogram is ,

Perimeter = 2(Base + Side)

198 = 2(Base + b + d) ...(1)

Also BF = 6 and DF = 12,

so substitute these values into equation (1),

⇒198 = 2(Base + 6 + 12)

⇒198 = 2(Base + 18)

Now,  solve for Base + 18,

⇒(Base + 18) = 198 / 2

⇒Base + 18 = 99

⇒Base = 99 - 18

⇒Base = 81

Now that the base length = 81,

Find the height of the parallelogram.

The height is the perpendicular distance between the base and the opposite side.

Since opposite sides of a parallelogram are parallel and congruent, the height is equal to the distance between BF and DE.

The distance between BF and DE is,

Height = DE - BF

⇒Height = d - b

⇒Height = 12 - 6

⇒Height = 6

Finally, calculate the area of the parallelogram using the formula,

Area = Base × Height

⇒ Area = 81 × 6

⇒ Area = 486

Therefore, the area of parallelogram ACEF is 486 square units.

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Answer: \(30, 35\ mph\)

Step-by-step explanation:

Given

Truck can travel 150 miles while car can travel 175 miles in same time

If the speed of truck is 5 mph slower than the car

Suppose the speed of car is \(x\ mph\), speed of truck would be \(x-5\)

For same time

\(\Rightarrow \dfrac{150}{x-5}=\dfrac{175}{x}\\\\\Rightarrow 6x=7(x-5)\\\Rightarrow 6x=7x-35\\\Rightarrow x=35\ mph\)

Speed of truck is \(x-5=30\ mph\)

Speed of car \(x=35\ mph\)

Answer:

x=2/5

Step-by-step explanation:

did the equation

Answer:

2y=5x+2c

Step-by-step explanation:

Applying the exterior angle of a triangle theorem, m∠G = 40°.

According to the exterior angle theorem of a triangle, we have the following equation that is derived:

11x - 4 + 55 = 23x + 3

11x + 51 = 23x + 3

11x - 23x = -51 + 3

-12x = -48

-12x/-12 = -48/-12

x = 4

m∠G = 11x - 4 = 11(4) - 4

m∠G = 40°

Thus, applying the exterior angle of a triangle theorem, m∠G = 40°.

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\(f(x,y) =tan(x) + y\) and u is the unit vector in the direction of (-2,0). Then

(a) \(f(x,y) = tan(x) + y - sqrt(4)\)

(b) \(f(0.9, 9) = 7.813\)

(c) \(fu = (-1.077,-0.5)\)

The gradient of f at the point (4,4) is \((∂f/∂x, ∂f/∂y)\) evaluated at (4,4), which is \((sec^2(4), 1)\).

(a) \(f(x,y) = tan(x) + y - sqrt(4)\)

(b) \(f(0.9, 9) = tan(0.9) + 9 - 2 = 7.813\)

(c)\(fu = (0.9,9) = (∂f/∂x, ∂f/∂y) . u = (sec^2(0.9) * (-2), 1) . (-2/sqrt(4)) = (-1.077,-0.5)\)

The gradient of f at a point (x,y) is defined as the vector\((∂f/∂x, ∂f/∂y\)).

At the point (4,4), the partial derivative of f with respect to x,\((∂f/∂x),\) is \(sec^2(4)\) and the partial derivative of f with respect to y,\((∂f/∂y)\), is 1. Therefore, the gradient of f at (4,4) is \((sec^2(4), 1)\).

The gradient of a function gives the direction of maximum increase at a point and is orthogonal to the level curves (contours) of the function.

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In a binary search, the number of comparisons required to find a value depends on the size of the list and the position of the desired value within the list.

In this case, the list contains 15 numbers, and we are searching for the value 61.

The binary search algorithm works by repeatedly dividing the list in half and comparing the desired value with the middle element. Based on the comparison, the search continues in the lower or upper half of the remaining list until the desired value is found.

In this specific case, the value 61 is located in the second half of the list. The search would begin by comparing 61 with the middle element, which is 49. Since 61 is greater than 49, the search continues in the upper half. The next comparison would be made with the middle element of the upper half, which is 65. Again, 61 is smaller than 65, so the search proceeds in the lower half. Finally, the value 61 is found after one more comparison with the middle element of the remaining list, which is 54.

Therefore, it would take a total of 3 comparisons to find the value 61 using a binary search in this list of numbers.

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The required number of ways the 6 medals can be distributed among boys and girls is 14400 ways.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
10 boys and 11 girls are competing, Number different ways, the six medals possibly be given out is,
= 10C3 × 10C3
= 14400

The required number of ways the 6 medals can be distributed among boys and girls is 14400 ways.

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Answer: $75.92

Step-by-step explanation:

pls mark me branliest

The textbook b has the highest median review score of 7, it is the most popular textbook among the three.

To find the most popular textbook among the three, we will find the median review score of each textbook and then compare them. Since each textbook has a different number of reviews, we will find the median using the following steps:

Put all the reviews in numerical order.

Find the middle value. If there is an odd number of reviews, this is the median score. If there is an even number of reviews, take the average of the two middle scores.

To find the median review score of textbook a:

2, 6, 6, 7, 7, 8, 9

Putting the scores in order: 2, 6, 6, 7, 7, 8, 9

The median is the fourth score, which is 7. Therefore, the median review score of textbook a is 7.

To find the median review score of textbook b:

4, 4, 6, 8, 8, 9, 10

Putting the scores in order: 4, 4, 6, 8, 8, 9, 10

The middle two scores are 6 and 8, so we take their average: (6 + 8) / 2 = 7

Therefore, the median review score of textbook b is 7.

To find the median review score of textbook c:

5, 5, 6, 6, 6, 7, 10

Putting the scores in order: 5, 5, 6, 6, 6, 7, 10

The middle score is 6. Therefore, the median review score of textbook c is 6.

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Answer: C perpendicular

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

     This is not a unit rate because neither of the rates are equal to 1. A unit rate, for example, could be 25 ft per second.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

The probability that a randomly chosen member of the society has a grade point average between 3 and 3.2 is 0.2 or 20%.

The probability distribution function (pdf), f(x), for the grade point averages of the gourmet society can be represented by a uniform distribution between 2.5 and 3.5. In a uniform distribution, the probability density is constant within the range and zero outside the range. The formula for the pdf is:

f(x) = 1 / (b - a)

where a is the lower bound (2.5 in this case) and b is the upper bound (3.5 in this case). Therefore, for this scenario:

f(x) = 1 / (3.5 - 2.5) = 1

To find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2, we need to calculate the area under the probability distribution curve within that range. Since the probability density is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range is 3.2 - 3 = 0.2, and the total width of the distribution is 3.5 - 2.5 = 1. Therefore, the probability is:

Probability = (width of range) / (total width)

= 0.2 / 1

= 0.2

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The capitalized cost for the solid waste treatment plant, based on a 6% MARR, is approximately $579 million.

To calculate the capitalized cost for the solid waste treatment plant, we need to determine the present value of all the costs over the project's lifespan.

The costs involved in the project are as follows:

Initial installation cost: $35 million.

Minor repair and renovation (R&R) after 10 years: $14 million.

Major R&R after 20 years: $18 million.

Operating and maintenance (O&M) costs each year, increasing at a compound rate of 6% per year.

First, let's calculate the present value of the O&M costs over the 20-year period: Using the TVM Factor Table calculator, the present value factor for a 6% MARR and 20 years is 10.206.

The total O&M costs over 20 years can be calculated as follows: O&M costs for the first year: $3 million. O&M costs for the subsequent years: $3 million * (1 + 0.06) + $3 million * (1 + 0.06)^2 + ... + $3 million * (1 + 0.06)^19.

Using the formula for the sum of a geometric series, the O&M costs over the 20-year period can be calculated as: O&M costs = $3 million * (1 - (1 + 0.06)^20) / (1 - (1 + 0.06)) = $3 million * (1 - 1.418519) / (-0.06) = $3 million * (-0.418519) / (-0.06) = $2.91038 million.

Now, let's calculate the present value of the costs: Present value of the initial installation cost: $35 million.

Present value of the minor R&R cost after 10 years: $14 million * 10.206 (present value factor for 6% MARR and 10 years) = $142.884 million. Present value of the major R&R cost after 20 years: $18 million * 10.206^2 (present value factor for 6% MARR and 20 years) = $371.001 million.

Present value of the O&M costs: $2.91038 million * 10.206 = $29.721 million. Finally, the capitalized cost of the solid waste treatment plant is the sum of all the present values: Capitalized cost = $35 million + $142.884 million + $371.001 million + $29.721 million = $578.606 million.

Rounding the final answer to the nearest whole number, the capitalized cost for the solid waste treatment plant is $579 million.

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The complete question is:

A new solid waste treatment plant is to be constructed in Washington County. The initial installation will cost $35 million (M). After 10 years, minor repair and renovation (R&R) will occur at a cost of $14M will be required; after 20 years, a major R&R costing $18M will be required. The investment pattern will repeat every 20 years. Each year during the 20 -year period, operating and maintenance (O\&M) costs will occur. The first year, O\&M costs will total $3M. Thereafter, O\&M costs will increase at a compound rate of 6% per year. Based on a 6% MARR, what is the capitalized cost for the solid waste treatment plant? Click here to access the TVM Factor Table calculator. $ Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. The tolerance is ±25,000.

Answer:

8

Step-by-step explanation:

Answer: 8

Step-by-step explanation: To find this we just needed to identify the factors of both 24 and 32.

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer:

if ab= ac and bc= 9 then ba=ac so there for b and a are equivalent so ac=9

Step-by-step explanation:

The dataset for the problem is provided by the United States Social Security Administration which lists the frequency of each name given to girls and boys in the 2010s.

The provided version of the dataset only contains names used at least 25 times for at least one gender so far this decade. Following is a sample CSV file that shows some data:

Isabella,42567,Girl
Sophia,42261,Girl
Jacob,42164,Boy
Emma,35951,Girl
Ethan,34523,Boy
Mason,34195,Boy
William,34130,Boy
Olivia,34128,Girl
Jayden,33962,Boy
Ava,30765,Girl
The dataset will be used to answer some questions.

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Answer: 9 x + 7 /2

Step-by-step explanation:

Answer:

 8 + 9x

Step-by-step explanation:

This is an algebraic expression.  Our job here is to simplify it by combining like terms:  combine the x terms and then combine the constants:

-3x + 5 ¾ + 12x - 2.25, after combining the x terms, is

       5 ¾ +    9x - 2.25

Next, combine the constants.  It's easier to convert -2.25 to -2 1/4 and then

add this 2 1/4 to 5 3/4:  

             8 + 9x

Answer: 50 km

Step-by-step explanation: So the map has a scale of 1 cm: 20 km. Next, you look at how far they are apart and see if the scale and the distance on the map are the same measurement. In this case, they are both centimeters so they stay the same. Then, all you do is multiple the real size, 20 km, by  

2.5 /1 . Then, 20 x 2.5=50. So the answer is 50 km

The volume of the pot is = 731.2 cubic inches.

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.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Since the forms of various three-dimensional objects vary, so do their volumes.

According to our answer-

volume of a pot is = πr²h + 2πr³

22/7 * 698/3

731.2 cubic inches

Hence, The volume of the pot is = 731.2 cubic inches.

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As per the unitary method, Gordon is correct because the Gordon would charge more than Ironing Palace

In math the term unitary method is defined as the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.

Here we have given that the total weight of these shirts is 9. 5 kg.

And here we have also given that each shirt weighs 190 g.

And Gordon charges £38 to iron these shirts.

And the charges in the Ironing Palace is 90p for each.

Here we have to use the unitary method to calculate the values for each of them,

The Total cost for Gordon is calculated as,

=> 38 x (9.5 / 0.19)

=> 1900

And the total cost for Ironing Palace is calculated as,

=> 90 x 9.5

=> 855

Therefore, while we looking into the values we have identified that Gordon is correct.

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The solution x1(t) for the de-coupled RL-RC circuit can be found by solving the differential equation x1'(t) = A11 * x1(t), where A11 is a constant value.

To solve this differential equation, we can use separation of variables.

1. Begin by separating the variables by moving all terms involving x1(t) to one side of the equation and all terms involving t to the other side. This gives us:

x1'(t) / x1(t) = A11

2. Integrate both sides of the equation with respect to t:

∫ (x1'(t) / x1(t)) dt = ∫ A11 dt

3. On the left side, we have the integral of the derivative of x1(t) with respect to t, which is ln|x1(t)|. On the right side, we have A11 * t + C, where C is the constant of integration.

So the equation becomes:

ln|x1(t)| = A11 * t + C

4. To solve for x1(t), we can exponentiate both sides of the equation:

|x1(t)| = exp(A11 * t + C)

5. Taking the absolute value of x1(t) allows for both positive and negative solutions. To remove the absolute value, we consider two cases:

  - If x1(0) > 0, then x1(t) = exp(A11 * t + C)
  - If x1(0) < 0, then x1(t) = -exp(A11 * t + C)

  Here, x1(0) is denoted as x10.

Therefore, the solution x1(t) for the de-coupled RL-RC circuit, starting at t=0, is given by either x1(t) = exp(A11 * t + C) or x1(t) = -exp(A11 * t + C), depending on the initial condition x10.

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Answer:

29

Step-by-step explanation:

using Pythagorean theory.

equate it to the hypotenus.

thus- hyp sq=adjacent sq +opposite sq

Answer:

  a.  0

Step-by-step explanation:

You want the limit of (k(x) -h(x))/k(x) as x approaches 0 when k(x) = sin(x)/x {x≠0} and h(x)=x+1 {x<1}.

Since we're concerned about the limit as x → 0, we don't have to be concerned with the fact that the expression is undefined at x = 0.

The function h(x) is defined as h(0) = 1, so we can just be concerned with the value of ...

  lim[x→0] (k(x) -1)/k(x)

The limit of k(x) as x → 0 is 1, so this becomes ...

  lim[x→0] (k(x) -1)/k(x) = (1 -1)/1 = 0

At x=0, sin(x)/x is the indeterminate form 0/0, so its limit there can be found using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim[x→0] sin(x)/x = lim[x→0] cos(x)/1 = cos(0) = 1

The fact that k(0) = 0 is irrelevant with respect to this limit.

__

Additional comment

We like to use a graphing calculator to validate limit values. The attachment shows the various functions involved. It also shows that as x gets arbitrarily close to 0 from either direction, the value of g(x) does likewise. This is all that is required for (0, 0) to be declared the limit. The lack of definition of g(x) at x=0 simply means the relation has a (removable) discontinuity there.

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