In the accompanying diagram, the width of the inner rectangle is represented by 2 - 3 and the length by 2+3. The width of the
outer rectangle is represented by 3 - 4 and the length by 32 +4.
x + 3
x-3
|3x - 4
3x + 4
Part A
Write an expression to represent the area of the larger rectangle.
Part B
Write an expression to represent the area of the smaller rectangle,
x2
Part
Express the area of the region inside the larger rectangle by outside the smaller rectangle as a polynomial in terms of x.

Answer:

The time that elapses before the players collide is 4.59 secs

Step-by-step explanation:

The distance between the two players is 41 meters. Hence, they would have total distance of 41 meters by the time they collide.

We can write that

S₁ + S₂ = 41 m

Where S₁ is the distance covered by Player 1 before collision

and S₂ is the distance covered by Player 2 before collision

From one of the equations of kinematics for linear motion,

\(S = ut\) + \(\frac{1}{2} at^{2}\)

Where \(S\) is distance

\(u\) is the initial velocity

\(a\) is acceleration

and \(t\) is time

Since the players collide at the same time, then time spent by player 1 before collision equals time spent by player 2 before collision

That is, t₁ = t₂ = t

Where t₁ is the time spent by player 1

and t₂ is the time spent by player 2

For player 1

\(S\) = S₁

\(u\) = 0 m/s ( The player starts at rest)

\(a\) = 2.2 m/s²

Then,

S₁ = \(0(t)\) + \(\frac{1}{2} (2.2)t^{2}\)

S₁ = \(1.1t^{2}\)

\(t^{2} = \frac{S_{1} }{1.1}\)

For player 2

\(S\) = S₂

\(u\) = 0 m/s ( The player starts at rest)

\(a\) = 1.7 m/s²

Then,

S₂ = \(0(t)\) + \(\frac{1}{2} (1.7)t^{2}\)

S₂ = \(0.85t^{2}\)

\(t^{2} = \frac{S_{2} }{0.85}\)

Since the time spent by both players is equal, We can  write that

\(t^{2}\) = \(t^{2}\)

Then,

\(\frac{S_{1} }{1.1} = \frac{S_{2} }{0.85}\)

\(0.85S_{1} = 1.1S_{2}\)

From, S₁ + S₂ = 41 m

S₂ = 41  - S₁

Then,

\(0.85S_{1} = 1.1 ( 41 -S_{1} )\)

\(0.85S_{1} = 45.1 - 1.1S_{1}\)

\(0.85S_{1} + 1.1S_{1} = 45.1 \\1.95S_{1} = 45.1\\S_{1} = \frac{45.1}{1.95} \\S_{1} = 23.13 m\)

This is the distance covered by the first player. We can then put this value into \(t^{2} = \frac{S_{1} }{1.1}\) to determine how much time elapses before the players collide.

\(t^{2} = \frac{S_{1} }{1.1}\)

\(t^{2} = \frac{23.13 }{1.1}\)

\(t^{2} = 21.03\\t = \sqrt{21.03} \\t = 4.59 secs\)

Hence, the time that elapses before the players collide is 4.59 secs

Answer:

$986.84

Step-by-step explanation:

exchange rate is the rate at which one currency is exchanged for another currency

Amount of dollars bought = amount of RS / selling rate

75,000 / 76 = $986.84

Answer:

90 point

Step-by-step explanation:

they have to be equel

hotel elegance

30 for signing up

15 per night

45 point 1 night and signing up

90-45= 45

45÷15=3

3nights

hotel paradiso

10 signing up

20 per night

30 for signing up and 1 night

90-30=60

60÷20= 3

3nights

if he spends 3 night at the hotel he will get the same points

The answer to the question is (a) 1.440.The critical value that would be used to obtain an 80% confidence interval for the mean of a Normally distributed population, given an SRS of six observations, would be 1.440.

To calculate the critical value for an 80% confidence interval, we need to use the t-distribution. The t-distribution is used when the sample size is small (less than 30) or when the population standard deviation is unknown.  For an 80% confidence interval with 5 degrees of freedom (6-1=5), the critical value is 1.440, according to the t-distribution table. This means that if we take multiple samples of the same size from the same population and construct 80% confidence intervals for each sample, approximately 80% of the intervals would contain the true population mean.

To obtain the critical value for an 80% confidence interval for the mean of a Normally distributed population, given an SRS of six observations, we need to use the t-distribution. The t-distribution is used when the sample size is small (less than 30) or when the population standard deviation is unknown.  To determine the critical value, we first need to calculate the degrees of freedom, which is the sample size minus one. In this case, the degrees of freedom would be 5 (6-1=5). We then need to look up the corresponding t-value from the t-distribution table for an 80% confidence level and 5 degrees of freedom. Using the t-distribution table, we can find that the critical value for an 80% confidence interval with 5 degrees of freedom is 1.440.

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Answer:

(6,-2.5)

Step-by-step explanation:

The formula for the midpoint between two points is:

\((\frac{x_{1} + x_{2}}{2},\frac{y_{1}+y_{2}}{2})\)

Now we substitute

We have than (9, -1) is \((x_{1}, y_{1})\) and (3, - 4) is \((x_{2}, y_{2})\)

So:

\((\frac{(9) + (3)}{2},\frac{(-1)+(-4)}{2})\\\\(-1) + (-4) = -5\\9 + 3 = 12\\\)

So, we have:

\((\frac{12}{2}, \frac{-5}{2})\\\\12 / 2 = 6\\-5 / 2 = -2.5\\\\(6, -2.5)\)

I can do a graphic explanation if you want.

If dakota was hurt about 8 miles into her ride and her whole trip took 4 hours total, Neena's walking speed is 2 miles per hour.

Let's assume that Neena's walking speed is "x" miles per hour. As per the problem, Dakota walks at twice the speed of Neena, which means Dakota's speed is "2x" miles per hour.

Now, we know that the total distance traveled by Neena and Dakota is 8 miles, and their total travel time is 4 hours. We can set up the following equation using the distance formula:

distance = speed x time

For Neena:

distance = x * t₁

For Dakota:

distance = 2x * t₂

Total distance = 8 miles

Total time = t₁ + t₂ = 4 hours

Substituting the distance and time values, we get:

x * t₁ + 2x * t₂ = 8

t₁ + t₂ = 4

Solving for t₁, we get:

t₁ = 4 - t₂

Substituting this in the first equation and simplifying, we get:

x * (4 - t₂) + 2x * t₂ = 8

4x = 8

x = 2

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Answer:

(x - 6)(x + 2)

Step-by-step explanation:

Given

x² - 4x - 12

Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 4)

The factors are - 6 and + 2, since

- 6 × 2 = - 12 and - 6 + 2 = - 4 , thus

x² - 4x - 12 = (x - 6)(x + 2) ← in factored form

Answer:

So the solution to the system of equations is (x,y) = (3,-2).

Step-by-step explanation:

To solve for x and y using substitution, we can first substitute y=-2 into the second equation to find the value of x, and then use that to find y.

Starting with the second equation:

4x - 3(-2) = 18

Expanding the -3(-2) using the distributive property:

4x + 6 = 18

Subtracting 6 from both sides:

4x = 12

Dividing both sides by 4:

x = 3

Now that we have x = 3, we can substitute that back into the first equation to find y:

y = -2

So the solution to the system of equations is (x,y) = (3,-2).

The probability 11.1% of domestic airfares within the United States are $250 or less.

The formula for the z score is -

z = (x - μ)/σ

In which,

Substitute the value in formula.

P(x ≤ 250) = (250 - 385)/100

P(x ≤ 250) = -1.22

Select the p value from negative z score table;

P(x ≤ 250) = 0.111

P(x ≤ 250) = 11.1%

Thus, 11.1% of domestic flights within the United States are $250 or less.

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By answering the above question, we may state that probability  As a result, there is a 60% chance that Mitsugu will have a quiz on Wednesday, Thursday, or Friday.

Mathematicians use probability theory to determine the chance that an event will occur or a statement is true. A probability of about 0 reflects how probable an event appears to occur, whereas a risk is a value between 0 and 1, where 1 suggests certainty. Probability is a mathematical representation of the likelihood that a specific event will take place. Other ways to express probabilities are as integers between 0 and 1 or as percentages between 0% and 100%. the ratio of events among equally likely options that lead to a certain event to all other outcomes.

We must sum the chances that Mitsugu will have a test on each of the following days in order to determine the likelihood that Mitsugu will test on Wednesday, Thursday, or Friday:

Wednesday or Thursday or Friday equals Wednesday plus Thursday plus Friday (Friday)

We can see from the given table that there is a 0.2 percent chance of a quiz on Wednesday, a 0.15 percent chance on Thursday, and a 0.25 percent chance on Friday. Hence, we may enter the following numbers in the formula above:

P(Thursday, Friday, or Wednesday) = 0.2 + 0.15 + 0.25 = 0.6

As a result, there is a 60% chance that Mitsugu will have a quiz on Wednesday, Thursday, or Friday.

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Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope

Answer:

4445.5 lbs

Step-by-step explanation:

1 ton is 2,000 pounds

Answer:

300 009 =

three hundred thousand nine

Step-by-step explanation:

hope it helps an u said the ans

a) The center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

b) We have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

(a) Deriving the class equation of a finite group G involves partitioning the group into conjugacy classes. Conjugacy classes are sets of elements in the group that are related by conjugation, where two elements a and b are conjugate if there exists an element g in G such that b = gag^(-1).

To derive the class equation, we start by considering the group G and its conjugacy classes. Let [a] denote the conjugacy class containing the element a. The class equation is given by:

|G| = |Z(G)| + ∑ |[a]|

where |G| is the order of the group G, |Z(G)| is the order of the center of G (the set of elements that commute with all other elements in G), and the summation is taken over all distinct conjugacy classes [a].

The center of a group, Z(G), is the set of elements that commute with all other elements in G. It can be written as:

Z(G) = {z in G | gz = zg for all g in G}

The order of Z(G), denoted |Z(G)|, is the number of elements in the center of G.

The conjugacy classes [a] can be determined by finding representatives from each class. A representative of a conjugacy class is an element that cannot be written as a conjugate of any other element in the class. The number of distinct conjugacy classes is equal to the number of distinct representatives.

By finding the center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

(b) To prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique, we need to show two implications: if it is normal, then it is unique, and if it is unique, then it is normal.

If a Sylow p-subgroup is normal, then it is unique:

Assume that P is a normal Sylow p-subgroup of G. Let Q be another Sylow p-subgroup of G. Since P is normal, P is a subgroup of the normalizer of P in G, denoted N_G(P). Since Q is also a Sylow p-subgroup, Q is a subgroup of the normalizer of Q in G, denoted N_G(Q). Since the normalizer is a subgroup of G, we have P ⊆ N_G(P) ⊆ G and Q ⊆ N_G(Q) ⊆ G. Since P and Q are both Sylow p-subgroups, they have the same order, which implies |P| = |Q|. However, since P and Q are subgroups of G with the same order and P is normal, P = N_G(P) = Q. Hence, if a Sylow p-subgroup is normal, it is unique.

If a Sylow p-subgroup is unique, then it is normal:

Assume that P is a unique Sylow p-subgroup of G. Let Q be any Sylow p-subgroup of G. Since P is unique, P = Q. Therefore, P is equal to any Sylow p-subgroup of G, including Q. Hence, P is normal.

Therefore, we have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

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1- A = 23.55

2- In the 7th payment, the interest is $50 and the principal is $193.55.

To find the value of A, we can use the formula for calculating the monthly payment on a loan. Given that you took a loan of $5000 for 24 months at an interest rate of 1% per month, we can substitute these values into the formula. By doing so, we find that A is equal to $23.55.

To determine the interest and principal in the 7th payment, we need to understand how loan payments are typically structured. Each monthly payment consists of both interest and principal components. Initially, the interest portion is higher, while the principal portion gradually increases over time.

In this case, we know the loan amount is $5000, and the loan term is 24 months. To find the interest and principal in the 7th payment, we need to calculate the remaining balance after the 6th payment.

To calculate the remaining balance after the 6th payment, we subtract the total amount paid from the initial loan amount. The total amount paid after 6 payments can be calculated by multiplying the monthly payment (A) by the number of payments (6). In this case, 6 * $23.55 equals $141.30.

Next, we subtract the total amount paid ($141.30) from the initial loan amount ($5000) to get the remaining balance, which is $4858.70.

Now, we can calculate the interest in the 7th payment. Since the interest rate is 1% per month, the interest for the 7th payment can be found by multiplying the remaining balance ($4858.70) by 1% (0.01), resulting in $48.59. Therefore, the interest in the 7th payment is $48.59.

To find the principal in the 7th payment, we subtract the interest ($48.59) from the monthly payment ($23.55). This gives us $174.96. However, we need to adjust the principal amount to match the remaining balance after the 6th payment. Therefore, we subtract the remaining balance after the 6th payment ($4858.70) from $174.96 to find the adjusted principal, which is $193.55.

In summary, in the 7th payment, the interest is $48.59 and the principal is $193.55.

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Answer:

The last one

Step-by-step explanation:

Answer:6 should be right

Step-by-step explanation: since the absolute value of -6 is 6, it satisfies the equation

|-6|=6

6 is less than or EQUAL to 6

The (0, 3] is taken out of the picture leaving you with B.

We have given that,

Machine 1 can complete a task in x hours while an upgraded machine (machine 2) needs 9 fewer hours.

We have to determine the,

The plant manager knows the two machines will take at least 6 hours, as represented by the inequality

after you find the intervals.

you also need to consider that the plant manager knows the two machines will take at least 6 hours.

so (0, 3] is taken out of the picture leaving you with B.

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Answer:

7/8 ingridents

Step-by-step explanation:

If you're working with improper fractions where the numerators are larger than the denominators, make the denominators the same. Then add the numerators. If you're adding mixed numbers, turn them into improper fractions and make each fraction equivalent. This will make it easy to add the fractions together.

Mark me brainliest!

Answer:

Step-by-step explanation:

1/8x1/4x1/2=1/64

Answer:

x = 9

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle is

Parallel to the third side

then the 2 angles are same- side interior angles and sum to 180° , that is

16x - 33 + 8x - 3 = 180

24x - 36 = 180 ( add 36 to both sides )

24x = 216 ( divide both sides by 24 )

x = 9

Numbers play a crucial role in helping us predict the ebbs and flows in our lives. They are used to measure and quantify patterns and cycles that occur in our daily lives, such as circadian rhythms.

Circadian rhythms are the physical, mental, and behavioral changes that follow a 24-hour cycle, responding primarily to light and darkness in an organism's environment. Numbers help us measure and track these rhythms, allowing us to predict when we will feel awake or sleepy, hungry or full, and so on.

For example, we know that the average human circadian rhythm is 24.2 hours, and that our bodies produce the hormone melatonin at night to help us sleep. By measuring and tracking these numbers, we can predict when we will feel tired and need to sleep, and when we will feel awake and alert.

Numbers also help us predict other patterns in our lives, such as our menstrual cycles, the best times to exercise, and when we are most likely to get sick. By tracking and measuring these numbers, we can better understand and predict the ebbs and flows in our lives and make more informed decisions about our health and well-being.

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A single payment of approximately $289.16 is required today to settle the two scheduled debt payments of $600 each, due three months and six months from now.

The future value (FV) of the first payment of $600 due in three months can be calculated as FV = PV(1 + rt), where PV is the present value (single payment today), r is the interest rate, and t is the time period. In this case, the time period is three months, which is equivalent to 0.25 years, and the interest rate is 10% or 0.10.
Similarly, the future value of the second payment of $600 due in six months can also be calculated using the same formula, but with a time period of six months or 0.5 years.
To find the single payment required today to settle both payments, we add the future values of the two payments:
FV = PV(1 + rt) + PV(1 + rt)
Substituting the values into the equation, we get:
$600 = PV(1 + 0.10 * 0.25) + PV(1 + 0.10 * 0.5)
Simplifying further, we have:
$600 = PV(1 + 0.025) + PV(1 + 0.05)
$600 = 1.025PV + 1.05PV
$600 = 2.075PV
Dividing both sides of the equation by 2.075, we find:
PV = $600 / 2.075
PV ≈ $289.16
Therefore, a single payment of approximately $289.16 is required today to settle the two scheduled debt payments of $600 each, due three months and six months from now.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The length of line segment K′N′ from the trapezoid KLMN cannot be determined based on the given information. More information is needed to answer this question accurately.

The length of line segment K′N′ will be the same as the length of line segment KN in the original trapezoid KLMN. This is because a reflection across the x- or y-axis does not change the length of any line segments, it only changes their position.

To find the length of line segment KN, we can use the distance formula:

KN = √((x2 - x1)² + (y2 - y1)²)

Where x1 and y1 are the coordinates of point K, and x2 and y2 are the coordinates of point N.

Without knowing the coordinates of points K and N, it is not possible to determine the length of line segment KN or K′N′. Therefore, more information is needed to answer this question accurately.

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Answer:

4.75

graph picture is attached.

press or click on the picture to see the whole graph

Step-by-step explanation:

put 1 where x is

y = 4 + (0.75*1)

y = 4 + .75

y = 4.75

number next to x is the SLOPE

The correct line of code that completes this operator which transforms a Point by dx and dy is shown below: Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Note that the function operator+ takes two arguments: an integer dx and an integer dy.

The function returns a point, which is created by adding dx to x and dy to y.The completed code is shown below:class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Therefore, the correct answer is: `Point(x_+dx,y_+dy)`

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To prove that \(\mathbf{x = \frac{62}{9}}\) given that \(9(x+6)-41=75\), the following are the missing statements and reasons for the stated proof:

Statement 1: \(9(x+6) - 41=75\)

Reason: Given

Statement 2: \(9(x+6) = 116\)

Reason: Addition Property of Equality

Statement 3: \(9x + 54 = 116\)

Reason: Distributive Property

Statement 4: \(9x = 62\)

Reason: Subtraction Property of Equality

Statement 5: \(x = \frac{54}{6}\)

Reason: Division Property of Equality

Given the algebraic equation, 9(x+6) − 41 = 75, to prove that x = 62/9, we would solve the equation using several properties as shown below:

Statement 1: \(9(x+6) - 41=75\)

Reason: Given (You first of all state what is given)

Statement 2: \(9(x+6) = 116\)

Reason: Addition Property of Equality

This is arrived at as shown below:

\(9(x+6) - 41 + 41 =75 + 41\\\\9(x+6) = 116\)

Statement 3: \(9x + 54 = 116\)

Reason: Distributive Property

This is arrived at as shown below:

\(9 \times x + 9 \times 6 = 116\\\\9x + 54 = 116\)

Statement 4: \(9x = 62\)

Reason: Subtraction Property of Equality

This is arrived at as shown below:

\(9x + 54 - 54 = 116 - 54\\\\9x = 62\)

Statement 5: \(x = \frac{54}{6}\)

Reason: Division Property of Equality

This is arrived at as shown below:

\(9x = 62\\\\\mathbf{x = \frac{62}{9}}\)

In summary, to prove that \(\mathbf{x = \frac{62}{9}}\) given that \(9(x+6)-41=75\), the following are the missing statements and reasons for the stated proof:

Statement 1: \(9(x+6) - 41=75\)

Reason: Given

Statement 2: \(9(x+6) = 116\)

Reason: Addition Property of Equality

Statement 3: \(9x + 54 = 116\)

Reason: Distributive Property

Statement 4: \(9x = 62\)

Reason: Subtraction Property of Equality

Statement 5: \(x = \frac{54}{6}\)

Reason: Division Property of Equality

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The two probabilities for events U and V are:

A) P(U and V) = 0

B) P(U or V) =  0.67

We know that if two events A and B are mutually exclusive events, then these two events can't occur at the same time, this means that:

P(A and B) is always zero, and:

P(A or B) = P(A) + P(B)

Here we know the probabilities:

P(U)= 0.38

P(V) = 0.29

Then we can write:

P(U and V) = 0  (by definition)

And:

P(U or V) = P(U) + P(V) = 0.38 + 0.29 = 0.67

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The productivity of the truck in bank measure is most nearly 32.3 (option C).

To calculate the productivity of the truck in bank measure, we need to convert the loose density to bank density. Bank measure refers to the volume of material when it is compacted or in its natural state, while loose measure refers to the volume of material when it is loose or not compacted.

The formula to convert loose density to bank density is as follows:

Bank Density = Loose Density / (1 + Moisture Content)

Since the moisture content is not provided in the question, we assume it to be zero for simplicity. Therefore, the bank density is equal to the loose density.

Next, we need to calculate the truck's productivity in bank measure. The formula for productivity is:

Productivity = Truck Capacity / Cycle Time

However, the truck capacity and cycle time are not provided in the question. Therefore, we cannot directly calculate the productivity.

Given that we have the specifications of the truck's density, we can make an estimation based on industry standards. A common truck capacity for earth hauling is around 20 cubic yards. The cycle time can vary depending on factors such as loading and dumping time, travel distance, and road conditions. For estimation purposes, let's assume a cycle time of 30 minutes (0.5 hours).

Using these values, we can calculate the productivity as follows:

Productivity = Truck Capacity / Cycle Time

Productivity = 20 / 0.5

Productivity = 40 cubic yards per hour

However, the productivity is measured in bank measure (yd³/hr), so we need to adjust the result based on the bank density.

Adjusted Productivity = Productivity * (Loose Density / Bank Density)

Adjusted Productivity = 40 * (100 / 110)

Adjusted Productivity ≈ 32.3 cubic yards per hour (bank measure)

Therefore, the productivity of the truck in bank measure is most nearly 32.3 (option C).

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The factors of the expression specified is given by: Option B: \((2x^2 - 1)(2x^2 + 1)(4x^4 + 1)\)

If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

\(a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\)

Suppose two numbers are there as 'a' and 'b'.

Then, we get:

\((a+b)(a-b) = a(a-b) + b(a-b) = a^2 -ab + ab - b^2 = a^2 - b^2\\(a+b)(a-b) = a^2 - b^2\)

For the considered case, factoring the considered expression \(16x^8 - 1\) by rewriting it as:

\(16x^8 - 1 = (4 \times 4 \times x^4 \times x^4) - 1^2 = (4x^4)^2 -1^2\\\\\\\)

Now, since we've got \((a+b)(a-b) = a^2 - b^2\), therefore,

\(16x^8 - 1 = (4x^4)^2 -1^2\\16x^8 - 1 = (4x^4 +1 )(4x^4 - 1)\)

The second term can also be factored using same property, as shown below:

\(16x^8 - 1 = (4x^4 +1 )(4x^4 - 1) = (4x^4 + 1)((2x^2)^2 - 1^2) \\16x^8 - 1 = (4x^4 + 1)(2x^2 + 1)(2x^2 - 1)\\\\\text{Rearranging the terms, we get}\\16x^8 - 1 = (2x^2 - 1)(2x^2 + 1)(4x^4 + 1)\)

Therefore, the factors of the expression specified is given by: Option B: \((2x^2 - 1)(2x^2 + 1)(4x^4 + 1)\)

Learn more about exponentiation here:

https://brainly.com/question/15722035

Answer:

Option B

Step-by-step explanation:

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