According to the problem-solving strategies you learned in this lesson, what
should you do after you've gathered your resources on a problem?
A. Check your answers and present the solution.
B. Come to an answer.
C. Gather your resources again.
OD. Understand the problem.

The hexagonal close-packed lattice has the highest packing efficiency, which is 74.05%.

This is because in a hexagonal close-packed lattice, the packing of atoms is such that each atom is surrounded by six other atoms, arranged in a hexagonal arrangement. This creates a very efficient packing of atoms. The maximum number of atoms that can be packed in a given unit cell is achieved with this lattice structure.In a simple cubic lattice, each atom is surrounded by eight other atoms arranged in a cube, which is slightly less efficient than the hexagonal close-packed lattice. The packing efficiency for a simple cubic lattice is 68.8%. The body-centred cubic lattice has the least efficient packing of atoms, with a packing efficiency of 60.9%. In this lattice, each atom is surrounded by eight other atoms, arranged in a cube and the central atom is shared by eight other unit cells.

In conclusion, the hexagonal close-packed lattice has the highest packing efficiency of 74.05%, followed by the simple cubic lattice with 68.8% and the body-centred cubic lattice with 60.9%.

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Answer:

See below.

Step-by-step explanation:

(a)

To multiply two polynomials, multiply every term of the first polynomial by every term of the second polynomial. Then combine like terms.

\( (\dfrac{1}{2}x - \dfrac{1}{4})(5x^2 - 2x + 6) = \)

\( = \dfrac{1}{2}x \times 5x^2 - \dfrac{1}{2}x \times 2x + \dfrac{1}{2}x \times 6 - \dfrac{1}{4} \times 5x^2 + \dfrac{1}{4} \times 2x - \dfrac{1}{4} \times 6 \)

\(= \dfrac{5}{2}x^3 - x^2 + 3x - \dfrac{5}{4}x^2 + \dfrac{1}{2}x - \dfrac{3}{2}\)

\( = \dfrac{5}{2}x^3 - \dfrac{9}{4}x^2 + \dfrac{7}{2}x - \dfrac{3}{2} \)

(b)

No. Since the binomials are different, the product of two different binomials and the same trinomial will give different results.

Answer: -3

Step-by-step explanation: the number before x is the slope

Answer: So the length of one side of the triangular-shaped walking path is 330 feet.

Step-by-step explanation:

The perimeter of the triangular-shaped walking path is 990 feet, and the length of one side is represented by x. We can write an equation to find x using the formula for the perimeter of a triangle:

P = a + b + c

Where P is the perimeter, and a, b, and c are the lengths of the sides of the triangle. Since one of the sides is represented by x, the equation can be written as:

990 = x + x + x

Simplifying the equation, we can find the value of x:

990 = 3x

Dividing both sides by 3, we get:

330 = x

So the length of one side of the triangular-shaped walking path is 330 feet.

Answer:

Work the problem backward

Step-by-step explanation:

instead of 10-x=25 do 25-10 = x So yeah that should give you the variable X

Answer:

-15

Step-by-step explanation:

10-x=25

take away 10 from both sides of the equation.

-x = 15

divide by - (-1) to get x

x = -15

The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

Given the following data: Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min.

Its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.

The pile is 10 ft high.

To determine how fast the height of the pile is increasing, we need to differentiate the formula for the volume of a cone with respect to time.

We know that the volume of a cone is given by: \(V = (1/3)πr²h\)

We are given that the base diameter and the height of the cone are always equal, so we can write: r = (d/2)and h = d

where d is the diameter of the base of the cone.

The volume of the cone is given by: V = (1/3)π(d/2)²d

Simplifying, we get:\(V = (1/12)πd³\)

Differentiating both sides with respect to time, we get:

dV/dt = (1/4)πd² (dd/dt)

We are given that dV/dt = 30 ft³/min, and we want to find dd/dt when h = 10 ft.

Substituting V = (1/3)π(10/2)²(10)

= (1/3)π(25)(10)

= (250/3)π and d = 10,

we get:

30 = (1/4)π(10²)(dd/dt)

Simplifying, we get:

dd/dt = 12/π

The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

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The notation "||v||" typically refers to the Euclidean norm (also known as the magnitude or length) of a vector v in a Euclidean space. The Euclidean norm of a vector v in n-dimensional space is defined as the square root of the sum of the squares of its components:

||v|| = sqrt(v1^2 + v2^2 + ... + vn^2)

Given that ||v|| = 8, we can find the Euclidean norm of -7v as follows:

||-7v|| = 7 * ||-v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2)

Since -v has the same magnitude as v but points in the opposite direction, we can replace each vi in the above expression with -vi:

||-7v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2) = 7 * sqrt(v1^2 + v2^2 + ... + vn^2)

But we know that ||v|| = sqrt(v1^2 + v2^2 + ... + vn^2) = 8, so we can substitute:

||-7v|| = 7 * ||v|| = 7 * 8 = 56

Therefore, ||-7v|| is 56.

Answer:

m<PXQ Is Acute

m<QXN is Obtuse

Step-by-step explanation:

Acute Angles are lsss than 90⁰

Obtuse Angles are greater than 90⁰

Right angles are exactly 90⁰

Answer:

1/7

Step-by-step explanation:

If one child was born on a Monday, then we don't have to consider that when solving the question, as it asks if both children were born on a Monday.

Thus, we only need to find the probability that the second child is born on a Monday. Since there are 7 days in a week and equally likely that the child is born on any day, then the probability of the child being born on a Monday would be 1/7.

Answer: The answer is 48          

Step-by-step explanation:

(60*100)/125=48

The 100 percent is 48 and the 125 percent of 48 is 60 .

Answer:

48

Step-by-step explanation:

"What is 60 is 125% of"

Put this sentence into an expression.  The wording is awkward in the question.  " . . is 60 is 125% of" is not a complete sentence.   I believe it is asking what number results in 60 when we take 125% of it.  I'll rephrase it as "125% of what number is 60."  Please check my logic on this interpretation.

Write this as an expression, using N for the unknown "number:"

 125% (N) = 60

(1.25N) = 60

N = 60/1.25

N = 48

125% of 48 is 60  

Answer:

he is not correct because k could be equal to any whole number

there fore no matter what number you subtract 3.5 from it couldnt be a whole number (that includes 21)

By applying the simple concept of algebra, the equation showing the number of Kenny's baseball cards (b) is b = 82 + 159. So it can be concluded that the number of Kenny's baseball cards is 241 cards.

The use of algebra in everyday life.

Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used, starting from simple mathematical operations, to financial planning, calculating time/mileage, and so on.

In the above questions, we can take some notes as follows:

Baseball cards sold (x) = 82 cards.

Remaining baseball cards (y) = 159 cards.

The number of baseball cards owned by Kenny (b):

b = x + y

  = 159 + 82

  = 241 cards

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The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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Answer:

3 apples for 1.29

Step-by-step explanation:

If you divide 1.29 by 3, you will get 0.43 which means each apple then costs 0.43 each. This is less than 0.45 so it is the better value.

Answer:

$1.29 for 3

Step-by-step explanation:

The reason is that $0.45 per apple means for every apple, you have to pay $0.45. That eventually is going to start to add up. $1.29 for 3 means that you are paying $0.43 for 3, which means that you are saving money.

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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The critical point of the function f(x,y) = xy*e^(-(x^2 + y^2)/2) is (0,0). The critical points of a function occur where the gradient is zero or undefined.

To find the critical points of f(x,y), we need to calculate the partial derivatives with respect to x and y and set them equal to zero.

Let's find the partial derivatives:

∂f/∂x = ye^(-(x^2 + y^2)/2) - xy^2e^(-(x^2 + y^2)/2)

∂f/∂y = xe^(-(x^2 + y^2)/2) - xy^2e^(-(x^2 + y^2)/2)

Setting both partial derivatives to zero, we have:

ye^(-(x^2 + y^2)/2) - xy^2e^(-(x^2 + y^2)/2) = 0     ...(1)

xe^(-(x^2 + y^2)/2) - xy^2e^(-(x^2 + y^2)/2) = 0     ...(2)

From equation (2), we can simplify it as:

x = xy^2                  ...(3)

Plugging this into equation (1), we get:

ye^(-(x^2 + y^2)/2) - (xy^2)^2e^(-(x^2 + y^2)/2) = 0

ye^(-(x^2 + y^2)/2) - x^2y^4e^(-(x^2 + y^2)/2) = 0

Factoring out ye^(-(x^2 + y^2)/2), we have:

ye^(-(x^2 + y^2)/2)(1 - xy^2e^(-(x^2 + y^2)/2)) = 0

This equation holds true if either ye^(-(x^2 + y^2)/2) = 0 or 1 - xy^2e^(-(x^2 + y^2)/2) = 0.

The first equation, ye^(-(x^2 + y^2)/2) = 0, implies y = 0.

The second equation, 1 - xy^2e^(-(x^2 + y^2)/2) = 0, implies x = 0 or y = ±1.

Considering these results, we can see that the only critical point that satisfies both equations is (0,0). Therefore, (0,0) is the critical point of the function f(x,y)=xye^(-(x^2 + y^2)/2).

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Answer:

it should be 1571.19

Step-by-step explanation:

If you combine the you just need to add them using the amount under weekly 584+987.19= 1571.19 weekly

THe closest answer i got was 18122

Answer:

1 (2/3) or 1.66666667

Step-by-step explanation:

The slope of a line is found by using the equation :

y2 - y 1 / x2 - x1

So all we have to do is plug in our values given.

To find which belongs with which variable (such as x2 or y1), we do the following:

We know that the coordinates of a point are represented by (x, y). So we must assign a number to each points number.

(2, 8) will be x1 and y1.

(5, 13) will be x2 and y2

Plug in the values :

13 - 8 = 5

5 - 2 = 3

5 / 3 = 1 (2/3)

So, the slope of the line is 1.66666667 or 1 and (2/3)s

Answer:

Step-by-step explanation:

2010.2/380= 5.29

Answer:

5.29  = 20.102 / 3.8.

Step-by-step explanation:

529 × 3.8 = 2010.2

So 529 = 2010.2 / 3.8

We need 5.29 on the left so we divide both sides by 100:

5.29 = 2010.2 / (3.8*100)

5.29  = 20.102 / 3.8

Answer:

x=25

Step-by-step explanation:

divide each side by 5

125/5=25

It is an illustration of theoretical probability.

Theoretical probability establishes the probability of certain events occurring.

The ratio of the entire number of conceivable possibilities to the intended outcome is known as theoretical probability.

In this case, the intended consequence is earning a 2, which is only one of the six potential possibilities. The possibility of receiving a 2 is.

Observance determines empirical probability. Nothing about the observing of the specified episode is indicated in the question, hence it is not an empirical probability.

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The additive inverse of 6/5 is -6/5. The reason is that when you add a number and its additive inverse, the result is always zero: 6/5 + (-6/5) = 0.

In mathematics, when we have a fraction with a negative numerator and a negative denominator, we can simplify the fraction by dividing both the numerator and denominator by the greatest common factor (GCF) of the absolute values of the numerator and denominator. This process does not change the sign of the fraction.

In the case of -6/-5, the absolute value of the numerator is 6 and the absolute value of the denominator is 5, and the GCF of 6 and 5 is 1. Dividing both the numerator and denominator by 1 gives us -6/-5, which is equivalent to 6/5, with the negative sign indicating that the fraction is negative.

So the negative or additive inverse of -6/-5 is simply its equivalent positive fraction, which is 6/5. This is because the additive inverse of any fraction is a fraction that, when added to the original fraction, results in 0. In this case, adding -6/-5 and 6/5 results in 0.

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Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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Answer:

Part A:

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom

Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.    

Step-by-step explanation:

Answer:

392000

Step-by-step explanation:A=p(1+

The equation 24÷4=6 can be thought of as 24 broken into 4 groups of 6 each. This can be shown mathematically as follows: 24/4 = 6.

The division 24 ÷ 4 = 6 can be represented as 24 divided into 4 groups of 6 each. Therefore, each group contains 6 elements.

Another way to represent this division is by using a division box. In this case, 24 is the dividend, 4 is the divisor, and 6 is the quotient. Here's how to write it in the division box format:``` 6|24----4```The divisor is outside the division box, while the dividend is inside the division box. Then, we divide 24 by 4 to obtain 6. Therefore, 24 ÷ 4 = 6.

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Relating the coordinates, it is found that the coordinate of B is -2.

-----------------------

The distance between A and B is 1/3 of AC, thus:

\(x + 9 = \frac{21}{3}\)

\(x + 9 = 7\)

\(x = -2\)

The coordinate of B is -2.

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