Express the greatest common divisor of each of these pairs of integers as a linear combination of these integers. a) 9, 11b) 33, 44 c) 35, 78 d) 21, 55 e) 101, 203 f) 124, 323 g) 2002, 2339 h) 3457, 4669 i) 10001, 13422

The condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).

In mathematics, a polynomial with integer values (also called a numerical polynomial) has an integer value for each integer n.

Contrary to popular belief, every polynomial with integer coefficients has integer values.

For instance, when t is an integer, the polynomial takes on integer values.

So, polynomials are the sums of terms of the form kˣⁿ, where k is any number and n is a positive integer.

A description of polynomials, such as the polynomial 3x+2x-5.

The concepts of degree, standard form, monomial, binomial, and trinomial are all covered in this section.

Therefore, the condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).

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Answer:

30 cm

Step-by-step explanation:

Make sure all units are the same!

P = Perimeter

A = Area

Formula used for similar figures:

\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)

\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)

Applying eq(ii):

∴\(\frac{25}{P_{2}} = \frac{10}{12}\)

Cross-multiplication is applied:

\((25)(12) = 10P_{2}\)

\(300 = 10P_{2}\)

\(P_{2}\) has to be isolated and made the subject of the equation:

\(P_{2} = \frac{300}{10}\)

∴Perimeter of second figure = 30 cm

Answer:

\( \sin( \frac{31\pi}{3} ) \)

= 0.537

Answer:

√3/2

Step-by-step explanation:

sin((31π/3)= sin( 10π + π/3)= sin(π/3) =√3/2

Main Answer: Marco is studying for an upcoming exam in his college algebra class. He should be aware that he should retrieve the information seven times before he stops studying it.

Supporting Explanation :According to the theory of the “Curve of Forgetting,” humans tend to forget around 50% of new information within the first hour. That’s why it’s important to review and study the same information multiple times in order to keep it in long-term memory. Retrieving information at least seven times can help to counteract the “Curve of Forgetting” and improve retention. Spacing out study sessions over a longer period of time also helps to increase retention and reduce the likelihood of forgetting. Thus, it is important for Marco to retrieve the information seven times before stopping to study.

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Answer:f(-4.3)=-12.9

Step-by-step explanation:

f(-4.3)=-4.3x3=-12.9

The circumference of a circle with a radius of 3 ft is greater than the distance around a semicircle with a diameter of 16 ft by approximately 2.84 ft.

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius. For the given circle with a radius of 3 ft, the circumference would be C = 2π(3) = 6π ft.

The distance around a semicircle is calculated by finding half the circumference of the corresponding full circle. In this case, the diameter of the semicircle is 16 ft, which means the corresponding full circle has a radius of 8 ft. The circumference of the full circle is C = 2π(8) = 16π ft. Therefore, the distance around the semicircle is half of that, which is 8π ft.

Comparing the two values, 6π ft is greater than 8π ft by approximately 2.84 ft. Hence, the circumference of the circle with radius 3 ft is greater than the distance around the semicircle with a diameter of 16 ft by approximately 2.84 ft.


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The bottleneck in the process is Station 5, with a processing time of 8 minutes. The capacity of the assembly line is approximately 1.76 toy trucks per hour.

a. The bottleneck in this process is the station with the longest processing time. In this case, Station 5 has the longest processing time of 8 minutes. The bottleneck is the station that limits the overall capacity of the assembly line because it takes the longest time to complete its task.

b. To calculate the capacity of the assembly line, we need to determine the cycle time, which is the time it takes for one complete cycle of the assembly line. The cycle time is equal to the sum of the processing times at each station. In this case:

Cycle time = 1 + 2 + 3 + 4 + 8 + 6 + 5 + 3 + 2 = 34 minutes

To calculate the capacity in toy trucks per hour, we need to convert the cycle time from minutes to hours:

Capacity = 60 minutes / 34 minutes = 1.76 toy trucks per hour

c. The direct labor cost for the toy truck with the current process can be calculated by multiplying the number of workers assigned to each station by their hourly wage, and then dividing it by the number of toy trucks produced per hour. Since there is one worker per station and each worker receives $15 per hour, the direct labor cost per toy truck can be calculated as follows:

Direct labor cost = (Number of workers × Hourly wage) / Capacity

= (9 workers × $15/hour) / 1.76 toy trucks per hour

≈ $80.68 per toy truck

d. If the work were organized in a work cell, with one worker performing all tasks, the direct labor cost would remain the same. Each worker would still receive $15 per hour, regardless of the number of tasks they perform. There would be no specialization gains in this scenario, so the direct labor cost per toy truck would still be approximately $80.68.

e. To determine the utilization of the worker in station 2, we need to compare the processing time at that station to the cycle time of the assembly line. The processing time at station 2 is 2 minutes, and the cycle time is calculated as 34 minutes (as mentioned in point b).

Utilization = Processing time at station 2 / Cycle time

= 2 minutes / 34 minutes

≈ 0.059 or 5.9%

This means that the worker in station 2 is only utilized for about 5.9% of the cycle time, indicating that they spend most of their time waiting for the other stations to complete their tasks.

f. With the reduced staffing from nine to six workers per shift, the tasks should be assigned to the six workers in the most efficient way possible. One possible assignment could be as follows:

Worker 1: Stations 1 and 2

Worker 2: Stations 3 and 4

Worker 3: Stations 5 and 6

Worker 4: Stations 7 and 8

Worker 5: Station 9

Worker 6: No assigned task (idle)

g. To calculate the new capacity of the line with six workers, we need to determine the total processing time for the new assignment. The total processing time would be the sum of the processing times at each station assigned to a worker:

Total processing time = 1 + 2 + 6 + 5 + 3 + 2 = 19 minutes

The new capacity of the line would be the reciprocal of the total processing time:

Capacity = 60 minutes / 19 minutes = 3.16 toy trucks per hour

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Answer:

Given that ,

Jo and Paul share sweets in the ratio 1:2

Let the sweets with Jo be " x " and let the sweets with Paul be " 2x "

Also ,

Paul gets 12 sweets.

\(\therefore \: 2x = 12 \\ \implies \: x = \cancel \frac{12}{2} \\ \\ \implies\boxed{ \: x = 6}\)

Therefore ,

Jo gets 6 sweets.

hope helpful! :)

Answer:6 sweets

Step-by-step explanation:

they both share sweets in ratio 1:2

paul have 12 sweets (double of jo sweets as given in ratio)

jo get 12/2=6 sweets

so total sweets = 18 sweets

Answer:

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

The given expression is that  -3ab

100-3*16=100-48=52

52 it is.

The Makespan is 790.

The Flow Time for Each Job is 70, 210, 410, 530, 690, 790.

The overall Average Flow Time is 450.

To compute the makespan, flow time for each job, and overall average flow time, we'll use the First-Come-First-Served (FCFS) scheduling algorithm.

Given the processing times for each job:

Job:      1    2    3    4    5    6

Time:    70  140  200  120  160  100

Makespan:

The makespan is the total time required to complete all jobs. It is the sum of the processing times for all jobs.

Makespan = 70 + 140 + 200 + 120 + 160 + 100 = 790

Flow Time for Each Job:

The flow time for a job is the time from when the job arrives until it is completed. For FCFS, it is simply the cumulative processing time of all the previous jobs plus the processing time of the current job.

Job:      1    2    3    4    5    6

Time:    70  140  200  120  160  100

Flow Time: 70, 210, 410, 530, 690, 790

Overall Average Flow Time:

To calculate the average flow time, we sum up the flow times for all the jobs and divide by the number of jobs.

Average Flow Time = (70 + 210 + 410 + 530 + 690 + 790) / 6 = 450

Therefore, Makespan: 790

Flow Time for Each Job: 70, 210, 410, 530, 690, 790

Overall Average Flow Time: 450

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Answer:

11/12

Step-by-step explanation:

There are 12 possibilities, 1 for each number. 1,2,3,4,5,6,7,8,9,10,11,12. The number 6 does not work which is just 1 possibility. 12-1 answer meet the condition, out of the 12 possibilities

g(x) is basically transformed f(x). First, let's focus on f(x) graph. Notice how the graph has slope of 1 and intersect y-axis at (0,0).

Which means that our equation for f(x) is:

\( \large{f(x) = x}\)

Now then we focus on g(x). g(x) is f(x+k). That means if f(x) = x then f(x+k) would mean substitute x = x+k in the equation.

\( \large{f(x + k) = x + k }\\ \large{g(x) = x + k}\)

Next, we want to find the value of k. In the slope-intercept form or y = mx+b where m = slope and b = y-intercept. Notice the g(x) graph and see that the graph intersects y-axis at (0,4). Therefore k = y-intercept = 4.

\( \large{g(x) = x + 4}\)

Answer

Answer: 4

Step-by-step explanation:

Based on the right triangle altitude theorem, the term that completes the equation is: a. YZ.

The right triangle altitude theorem state that when an altitude is drawn to from the vertex of a right triangle to intersect the opposite side perpendicularly, the length of the altitude would be equal to the geometric mean of the line segments that are formed by the altitude on the right triangle's hypotenuse.

In other words, the square of the length of the altitude equals the product of the line segments formed, according to the right triangle altitude theorem.

XZ = altitude

WY = hypotenuse

WZ and YZ are the line segments formed.

Therefore, the equation would be:

XZ² = (WZ)(YZ) [right triangle altitude theorem]

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The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.

The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated  instead of the radius, we have  to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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The molar solubility of Fe(OH)2 in pure water is approximately 2.77×10^(-6) mol/L based on the given Ksp value of 4.87×10^(-17).


The solubility product constant (Ksp) expresses the equilibrium constant for the dissolution of a sparingly soluble compound. For Fe(OH)2, the Ksp value of 4.87×10^(-17) indicates that only a small amount of Fe(OH)2 will dissolve in water.

To determine the molar solubility, we assume that x moles of Fe(OH)2 dissolve in water to form x moles of Fe^2+ and 2x moles of OH^- ions. Using the Ksp expression [Fe^2+][OH^-]^2 = 4.87×10^(-17) and substituting the molar solubility (x), we solve for x to find x = 2.77×10^(-6) mol/L. Thus, the molar solubility of Fe(OH)2 in pure water is approximately 2.77×10^(-6) mol/L.

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Answer:

its B

Step-by-step explanation:

Answer:

i got A for both of them ^^

for #1 you would do 8(1/2÷2)-(1/4+4)

and for #2 its 7(2.5) - (12/3+6)

Stack parameters and register parameters are different ways of passing function arguments in a programming language.

Each approach has its advantages, and the choice between them depends on various factors such as platform architecture, optimization goals, and calling conventions. However, some advantages of stack parameters over register parameters include:

Flexibility: Stack parameters allow for more flexibility in function calls, as they can accommodate a larger number of arguments compared to registers. Registers have limited availability, and if there are more arguments than available registers, the stack can be used to pass the remaining parameters.

Function Call Conventions: Many calling conventions dictate the use of the stack for passing parameters, making stack parameters more compatible with standard calling conventions across different platforms and compilers. Register parameters, on the other hand, may have stricter limitations or variations depending on the specific architecture or calling convention.

Function Composition: Using the stack for parameter passing allows for easier function composition and chaining. When functions call other functions, the stack-based parameter passing mechanism allows the callee function to easily access the arguments passed by the caller function, as they are stored in a well-defined and accessible location.

Optimized Register Usage: Register parameters are generally preferred when optimizing for performance, as they can provide faster access to the arguments due to the reduced memory access required. However, stack parameters can free up registers for other critical uses, such as storing frequently accessed variables or intermediate results.

Language Portability: Stack parameters are generally more portable across different programming languages, as register usage and availability can vary significantly. Using the stack for parameter passing ensures compatibility and consistency in function calls, regardless of the programming language used.

It's worth noting that the specific advantages may vary depending on the programming language, compiler, and target platform. Therefore, it is essential to consider the specific context and requirements when choosing between stack parameters and register parameters.

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Answer:

15x^2 + 23x = 4

Step-by-step explanation:

NOT BOX METHOD :

(-5x-1)(-3x-4)

=15x^2+20x+3x+4

=15x^2+23x+4

The formula for calculating the area of a triangle is:A = 1/2 bhWhere A = Area, b = Base and h = Height. Given that A = 16cm², h = 2.5cm, the base of the triangle can be calculated using the formula.

16cm² = 1/2 b × 2.5cmb × 2.5cm = 16cm²5cm² = 1/2 b5cm² × 2 = b, the base (b) of the triangle is equal to 10 cm.

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2.6

Given the expression;

Simplify the expression in the bracket to have:

Simplify the result to have;

Hence the result of the given function on simplification is 2.6

The graphics tool used to help determine whether a process is in control or out of control is a. control chart.

A graphical tool used to help determine whether a process is in control or out of control is a control chart. A control chart is a chart used to monitor the stability of a process over time and to distinguish between common cause and special cause variation. It displays data points in relation to upper and lower control limits, which are calculated using statistical methods.

The control chart provides a visual representation of the process and enables users to identify trends, shifts, or other patterns that may indicate that the process is out of control.

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Jada and Malik will have the same amount of money after approximately 9 weeks.

To calculate how much money Jada and Malik will have after 7 weeks, we need to consider their weekly earnings and existing savings.

Jada earns $15 per week mowing lawns and already has $50 in her savings account. Over 7 weeks, she will earn a total of 7 * $15 = $105 from mowing lawns. Adding her existing savings, Jada will have a total of $50 + $105 = $155 after 7 weeks.

Malik earns $10 per hour for the first hour of babysitting and already has $70 in his savings account. To calculate Malik's earnings, we need to know how many hours he babysits each week. Assuming he babysits for the same number of hours each week, let's say 3 hours, he will earn 3 * $10 = $30 per week. Over 7 weeks, Malik will earn a total of 7 * $30 = $210 from babysitting. Adding his existing savings, Malik will have a total of $70 + $210 = $280 after 7 weeks.

To determine when Jada and Malik will have the same amount of money, we need to set up an equation:

$155 (Jada's total after x weeks) = $280 (Malik's total after x weeks)

Simplifying the equation, we have:

155 + 15x = 280 + 30x

Rearranging the equation, we get:

15x - 30x = 280 - 155

-15x = 125

Dividing both sides by -15, we have:

x = -125 / -15 = 8.33

Since we can't have a fraction of a week, we round up to the nearest whole number.

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Answer:

Step-by-step explanation:

1. 8a = -2

  a = -2/8 =-1/4

2. -11b = -6

    b = 6/11

3. -2c = 16

    c = -8

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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Answer:

32

Step-by-step explanation:

Hope it helps!!

Answer:

Subtraction Property of Equality

Step-by-step explanation:

In the given equation, property of equality is being used is subtraction property of equality.

Given that, a= 2b, then a-c= 2b-c.

The Subtraction Property of Equality states that an equal value subtracted or removed from two equal items will result in a new equal amount. An equation is indicated with an equal sign separating two equivalent sides of a mathematical statement. The formula for the subtraction property is if a = b, then a - c = b - c.

Now,

a-c= 2b-c

Substitute a=2b in the given equation a-c= 2b-c, we get

2b-c=2b-c

Here, c is subtracted from equals

Therefore, in the given equation, property of equality is being used is subtraction property of equality.

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Answer:

r = 12

Step-by-step explanation:

DG + GM = DM , substitute values

r + 3 + 4r - 28 = 35 , that is

5r - 25 = 35 ( add 25 to both sides )

5r = 60 ( divide both sides by 5 )

r = 12

Answer:

D) y = (x+1)^2

Step-by-step explanation:

Given the graph, the y-intercept is 1, and the x-intercept is -1. Only equation that works is D:

When we plug in x=-1:

y=(-1+1)^2

y=0

This is shown on the graph

When we plug in y=1:

1=(x+1)^2

1=x+1

0=x

x=0

This shows up on the graph

Answer:

4/125

Step-by-step explanation:

The potential energy of the water in a lake is 57 trillion N × m, which is 57 trillion joules (J).

Gravitational potential energy applies in this situation. G P E = m g h is the formula for gravitational potential energy, where: mg stands for weight or mass times gravity (w). The height to which an object can fall before kinetic energy replaces potential energy is denoted by the symbol h. In the example of the lake, we first determine the amount of water using the equation for the volume of a typical cylinder in order to determine the weight of the cylinder: V cy l = π r²L , The weight density of the water per cubic foot, which is about 62 lb, can then be multiplied by this volume: W(water) = (Volume) (Density)

W (water) = (28,000,000 ft² ⋅ 40ft) ( 62 lb ÷ ft³ )

W (water) = 69,440,000,000 lb

To calculate the potential energy, multiply this weight by the height. GPE=mgh

GPE=Wh=(69,440,000,000lb)(600ft)

GPE=41,644,000,000,000ft⋅lb

matching the level of precision by rounding the response to two significant digits. 4.2X10¹³ft⋅lb , or 42 trillion ft-lb.

Because joules are measured in N × m units, multiply the result by fractional equivalencies. 42trillionft × lb × (4.45N ÷ lb) × (m ÷ 3.28ft)

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