show that 2 mn = 1 m (m n 2 ) 1 n (m n 2 ) and use this identity to obtain the unit fraction decompositions of 2 7, 2 35, and 2 91 as given in the 2/n table in the rhind mathematical papyrus.

The number of hours for both the motorcycles to meet is given by the equation T = 4 hours

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of the motorcycle 1 = 55 mph

Let the speed of the motorcycle 2 = 70 mph

Let the total distance between them be D = 500 miles

Now , the number of hours for them to meet be T

So , the distance traveled by motorcycle 1 d = 55T

The distance traveled by motorcycle 2 = ( 500 - d ) = 70T

Substituting the values in the equation , we get

( 500 - d ) = 70T

500 - 55T = 70T

Adding 55T on both sides of the equation , we get

500 = 125T

Divide by 125 on both sides of the equation , we get

T = 500/125

T = 4 hours

Hence , the number of hours is 4 hours

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Answer:

y=1/5x

That's the answer with the other point at (0,0)

Step-by-step explanation:

Thomas has 10 pound of meat. He used 0.14 pound of meat to make one hamburger, he can make 71 hamburger with the meat he has.

Thomas has in total 10 pounds of meat

In making one hamburger 0.14 pound of meat is used,

So the amount of hamburger made with the remaining meat is

10 - 0.14 = 9.86 pound

So, 9.86/0.14 = 70.42 ≈ 70.

So in total of 70 Hamburgers can be made with the meat Thomas has.

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences. Measurement, then, is the process of establishing how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind.

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As per the equation, we are able to calculate the total cost of sundae being $17.

To calculate,

Per person cost × number of people = cost of sundaes

4.25 × 4 = 17

One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction. Divide a rational expression by multiplying the first fraction by its reciprocal. We factor everything and search for common factors after rewriting the division as multiplication of the first expression by the reciprocal of the second. rational arguments are divided. A division problem has three main components: the dividend, the divisor, and the quotient. That which will be divided is the dividend. The number of "people" into which the number is divided is referred to as the divisor. The ratio is the response.

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The distance between the van and Hartville is changing at a rate of 39.42 miles per hour.

This is because the van has traveled 126 miles due west at a rate of 30 miles per hour, meaning it is now 63 miles away from Hartville. If the van continues travelling due west at a rate of 30 miles per hour, then it will take another 2 hours to reach Hartville. Thus, the distance between the van and Hartville is changing at a rate of 63 miles divided by 2 hours, or 39.42 miles per hour.

The distance between the van and Hartville is changing as the van travels due west at a rate of 30 miles per hour. After travelling 126 miles, the van will be 63 miles away from Hartville. This means that the distance between the van and Hartville is decreasing at a rate of 63 miles divided by the amount of time it takes for the van to reach Hartville, which is 2 hours.

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the 12th term of the geometric sequence will be 97656250.

What is geometric sequence?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

The terms are given 2,10,50...

a = 2

r = 10/2 = 5

The 12th term will be= 2*(5)[tex])^{11}[/tex] = 2 * 48828125= 97656250

Hence, the 12th term of the geometric sequence will be 97656250.

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The equation representing the cost of a bag is 2x + 18 = $68 and for each bag Britney has to pay $25.

Let us consider  'x' be the total cost representing amount of money to check each bag under the weight limit.

Additional amount to pay per bag for over weight limit is equal to $9

Total amount paid by Britney to check both the bags = $68

Equation represents the cost of bags is equal to :

2x + 2(9) = $68

⇒ 2x + 18 = $68

⇒ 2x = $68 - $ 18

⇒ 2x = $50

⇒ x = $50 / 2

⇒ x = $25

Therefore, the equation which represents the cost of a bag is 2x + 18 = $68 and cost for each bag is $25.

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The number of casual jeans sold was 81 and the number of dress jeans sold was 40.5 (rounded to 41).

        $45x + $55x/2 = $4,060

        $45x + $55x/2 = $4,060

        $45x + $55x/2 = $4,060

        $100x/2 = $4,060

        $100x = $8,120

        x = 81

So from above calculation, we got that the number of casual jeans sold was 81 and the number of dress jeans sold was 81/2 = 40.5 (rounded to 41).

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The derivatives of tan^2(x) and sec^2(x) are the same because they are related by the identity tan^2(x) = sec^2(x) - 1.

By using the chain rule, the derivative of tan^2(x) can be found by first finding the derivative of tan(x), then squaring it. The derivative of sec^2(x) can also be found using the chain rule, by first finding the derivative of sec(x), then squaring it.

Since tan^2(x) and sec^2(x) are related by a constant difference, their derivatives will be the same. This means that the rate of change of tan^2(x) with respect to x will be equal to the rate of change of sec^2(x) with respect to x. This is a useful relationship because it allows us to relate the derivatives of two important trigonometric functions, making it easier to integrate or differentiate expressions involving them.

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If I lose half each week there is no value to reach "0" so we approximate the value to be less than 1, and the weekly amount is:

7 weeks

   Fractions are also called fractional numbers and are defined as an expressed numerical value that denotes a division and is expressed in the form:

x/y

Where:

x = numerator or dividing

y = denominator or divisor.

If the initial value we have is $100 and we determine its half, which is one week of expenses, we are left with the following:

$100 * 1/2 = $50

$50 * 1/2 = $25

$25 * 1/2 = $12.5

$12.5 * 1/2 = $6.25

$6.25 * 1/2 = $3.125

$3.125 * 1/2 = $1.5625

$1.5625 * 1/2= $0.78125

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Answer:

total number of cherries=780

number of cherries on the plate=145

number of cherries on the bowl is 4 times the number of cherry in the plate=145×4=580

number of cherry in the cup =580+145-780=45

Salut/Hello!

Answer: 70, 11, 91

Step-by-step explanation:
g - gumball
/ - fraction line
=> - results

The current total of gumballs = 200 - 25 = 175 gumballs

There are ? red gumballs in the machine:
red g/175 gumballs = 10/25 (the probability of a red gumball to fall in a sample)
red g/175 = 0.4 => 175 x 0.4 = 70 red gumballs

There are ? more green gumballs than white gumballs in the machine:
First, we need to find both green and white gumballs.

green g/175 gumballs = 5/25
green g/175 = 0.2 => 175 x 0.2 = 35 green gumballs

white g/175 gumballs = 2/25
white g/175 = 0.08 => 175 x 0.08 = 14 white gumballs

35 - 14 = 11 more green gumballs than white gumballs

There are ? gumballs that are either blue or green in the machine.

blue g/175 gumballs = 8/25
blue g/175 = 0.32 => 175 x 0.32 = 56 blue gumballs
or
175 - (70 red g + 35 green g + 14 white g) = 175 - 119 = 56 blue gumballs

35 green g + 56 blue g = 91 gumballs that are either blue or green


How do you find the probability?

It's simple, pretend like you have a dice. A dice has 6 faces and you need a six to (example) get out of Jail. You have 6 faces but you only need one, so the probability you get a 6 is 1/6 = 0.1(6)
But let's say you have 2 dices and you need both to be 6 to get out of jail. well thats 1/6 x 1/6 which is equal to 1/36  = 0.02(7)

In the problem, we have the sample of 25 gumballs in which 10 are red.
The probability a red gumball to fall is 10/25 = 0.4 (as calculated above)


I hope it was helpful! :]

The numerical value of x and y in the right triangle are 8√5 and 8 respectively.

The figure in the diagram is a right angle triangle.

Using the trigonometric ratios;

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Next, we determine the value of x.

sin( θ ) = Opposite / Hypotenuse

sin( 60 ) = x / 16

x = sin( 60 ) × 16

x = 8√5

For y;

cos( θ ) = Adjacent / Hypotenuse

cos( 60 ) = y / 16

y = cos( 60 ) × 16

y = 8.

Therefore, the value of x is 8√5 and y is 8.

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Answer: Alan would have to sell less than 540 boxes.

Step-by-step explanation:

The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

Qualities and their permutations, theorems and surrounding structures, morphologies and their placements, and locations where they can be encountered are all included in the study of mathematics. The association between a group of inputs, of which each has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a requires great, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on procedures, one-to-one functions, several more functions, within functions, and on functions.

given

The slope formula, (y2-y1)/, states that the average rate of change is the ratio of the change in y to the change in x.

(x2-x1) We have f(x), which is equivalent to byt but instead of y.

f(-2) - f (0)  /   -2

= f(14+4 + 5 ) + 5 / -2

28 / - 2

= -14

The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

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The domain of the function is {-2, -1, 0, 1, 2}

The domain

This is the elements in the set A

So, we have

Domain =  {-2, -1, 0, 1, 2}

The range

To do this we calculate the value of the function at each x value

So, we have

y = -(-2)³ + 2 = 10

y = -(-1)³ + 2 = 3

y = -(0)³ + 2 = 2

y = -(1)³ + 2 = 1

y = -(2)³ + 2 = -6

So, the range is

Range = {10, 3, 2, 1, -6}

If it is a function

The relation is a function

Because each x value have unique y values

So, the notation is

f(x) = -x³ + 2

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Answer:

c=42

Step-by-step explanation:

have a good day!

The functions in memory is more likely to be the Interrupt Service Routine (ISR) for handling system calls are f4 and f8

What is Interrupt Service Routine?

A software function known as an interrupt service routine (ISR) is called upon by hardware in response to an interrupt. An interrupt is examined by ISR, which decides how to handle it, executes the handling, and then returns a logical interrupt value. The ISR alerts the kernel with a return value if no more handling is necessary.

Reason:

Sending a Unix signal to the process that developed a variant allows for the handling of several variations. The intended action is delayed until the process receives a signal, allowing the kernel to evaluate other requests swiftly.

This approach does not accommodate interruptions since they typically occur after the associated process has ceased and the wholly unrelated process is running, as in the case of a process seeking a data transfer. Sending a Unix signal to the active process is therefore improper.

The handling of disruptions relies on the nature of interruption. We will categorize the three basic types of interruption for our needs as follows:

I/O causes disruptions.

The relevant interference handle should ask the I/O device to determine the best course of action if it needs attention. This kind of interruption is covered in the recently updated section "I / O Disorder Management."

Time is of the essence.

The kernel is informed that the deadline has passed by a specified timer, either an APIC timer or an external timer, by use of this type of interference. The majority of these illnesses are addressed as I/O disorders.

Another CPU multiprocessor system is interrupted by an interprocessor when its CPU is uninstalled. In the recently published section "Interprocessor Interrupt Handling," we conceal such interruptions.

Managing I/O Disruption

The I/O interfering adapter should typically be adaptable enough to support many devices simultaneously. For instance, many devices might share an IRQ line in the PCI bus architecture. This indicates that the interference vector alone does not provide a complete picture. The identical vector 43 is equipped with a USB port and sound card in the example displayed in Table 4-3. However, when their IRQ line is shared with other devices, several hardware components prevalent in earlier PC systems (such ISA) do not operate consistently.

The following list discusses two distinct methods for obtaining the bothersome handle's flexibility.

shared IRQ

Multiple interference lines are produced by the intrusion (ISRs). Each ISR is a feature connected to a single shared IRQ line device. Each ISR is carried out to see if its device requires attention because it is impossible to know in advance which device to issue an IRQ for. If it does, the ISR completes all the tasks that must be completed when the device generates interference.

When a disruption occurs, not all activities should be executed immediately. In actuality, not every activity should be performed near the distraction handle. Because the signals on the relevant IRQ line are momentarily disregarded while the interfering host is active, long-term non-processing performance should be delayed. Most crucially, even if system suspension is disabled, the disruptive host's process must continue in TASK RUNNING state. As a result, interference managers are unable to carry out any blocking operations like I/O disk performance. Linux divides post-disruption activities into the following three groups:

Actions that are crucial, such admitting PIC interference, redistributing the PIC or device controller, or updating the device's data acquisition and processor. Because it must be completed as soon as possible, this can be done rapidly and extremely swiftly. Sensitive actions are carried out when hidden interference is disabled inside the immediate disruption holder.

Not attentive

modifying data structures that are solely visible to the processor, for example (for example, reading a scan code after a push-key keyboard). These acts are turned into a short remedy with enabled distractions because they can also be swiftly stopped.

It is not indirectly transferred.

similar as replicating the bar's content in the process space (for example, sending the keyboard line bar to the end management process). Since the interested process will constantly be waiting for the data, this can be postponed for a long period without having an impact on kernel performance. The various tasks covered in the next section, "Softirqs and Tasklets," are used to carry out the actions that can be responded arbitrarily.

The functions f4 and f8 that handle system calls are more likely to be Interrupt Service Routines (ISRs) in memory.

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Answer:

slope = -3

Step-by-step explanation:

Note the slope-intercept form: y = mx + b , in which:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

~

In the case of the given line:

y = mx + b

y = (-3)x + (6)

Note what values and sign are in each given variable:

y = y

m = slope = -3

x = x

b = y-intercept = 6

∴ -3 is your answer for slope.

~

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The scale factor is 3.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

From the graph the dimension of triangle STU is

SU = 5 units

TU = 3 units

ST = 2 units

and, dimension of triangle S'T'U' is

S'U' = 15 units

T'U' = 9 units

S'T' = 6 units

so, the Scale factor is

S'U' / SU = 15 / 5

S'U' / SU = 3

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Consequently, point N's ordered pair is (2,6).  A pair that has two values stated in a specific order between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate

N's coordinates are: (-2,-6)

To create point N', point N is reflected over the y-axis.

Point N is then created by reflecting point N' over the x-axis ".

To locate: The ordered pair describing N's location ".

Solution:

Point N's coordinates are (-2,-6). To create point N', point N is reflected over the y-axis.

[tex]& (x, y) \rightarrow(-x, y) \\[/tex]

[tex]& N(-2,-6) \rightarrow N^{\prime}(2,-6)[/tex]

Point N is then created by reflecting point N' over the x-axis.

[tex]& (x, y) \rightarrow(x,-y) \\[/tex]

[tex]& N^{\prime}(2,-6) \rightarrow N^{\prime \prime}(2,6)[/tex]

Consequently, point N's ordered pair is (2,6)

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The value of x and y in the given triangle is 4 and 6 respectively.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

The two triangles are similar. Using the rule of similar triangles we have:

4/ 6 = y / y+3

4(y + 3) = 6y

4y + 12 = 6y

12 = 2y

y = 6

Similarly, using the rule of similar triangles we have:

4/6 = x/6

(4)(6) = 6x

24 = 6x

x = 4

Hence, the value of x and y in the given triangle is 4 and 6 respectively.

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Answer:
The value of f(-0.5) is approximately 0.63

Step-by-step explanation:

An exponential function is of the form f(x) = a^x, where a is a constant. Since we know the values of f(−1) and f(0), we can use them to find the value of a.

From f(−1) = 4, we have:

4 = a^(-1)

From f(0) = 18, we have:

18 = a^0

Dividing the two equations, we have:

a = sqrt(18)

Now that we know the value of a, we can substitute it into the exponential function to find f(−0.5):

f(-0.5) = a^(-0.5) = sqrt(18)^(-0.5) = (4.242640687119285)^(-0.5) = 0.6324555320336758

to the nearest hundredth, it would be 0.63

10) The factor of the expression (x³ + 7x² + 6x) is,

⇒ x (x + 1) (x + 6)

11) The value of a in factor of (x² - 16x + 63) is, - 9

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

10) The expression is,

⇒ x³ + 7x² + 6x

11) The expression is,

⇒ x² - 16x + 63

Now, We can factor as;

10) The expression is,

⇒ x³ + 7x² + 6x

⇒ x (x² + 7x + 6)

⇒ x (x² + 6x + x + 6)

⇒ x (x (x + 6) + 1 (x + 6))

⇒ x (x + 1) (x + 6)

11) The expression is,

⇒ x² - 16x + 63

⇒ x² - 9x - 7x + 63

⇒ x (x - 9) - 7 (x - 9)

⇒ (x - 7) (x - 9)

Hence, By compare the factors (x - 7) (x + a), we get;

⇒ a = - 9

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The value of the correlation coefficient for the number of baggage handlers and the number of arriving passengers is 0.842.

Therefore the answer is D. 0.842

The correlation coefficient is a measure of the strength of the linear relationship between two variables. It is a value between -1 and 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

In this case, the output from the regression equation analysis states that the correlation coefficient is √0.709 = 0.842, which means that there is a strong positive linear relationship between the number of baggage handlers and the number of arriving passengers. A correlation coefficient of 0.842 is considered a strong positive relationship.

In this case, an increase in the number of arriving passengers is associated with an increase in the number of baggage handlers needed, as reflected by the positive correlation coefficient.

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The leading coefficient, degree and end behaviour are realised for the following polynomials.

What is the leading coefficient?

The leading term is the term containing the highest power of the variable: the term with the highest degree. The leading coefficient is the coefficient of the leading term.

Leading coefficients are the numbers written in front of the variable with the largest exponent. Just like regular coefficients, they can be positive, negative, real, or imaginary as well as whole numbers, fractions or decimals. In a polynomial, the leading term is the term with the highest power of x.

For the given question:

a) -4x⁴-3x³+x²+4

Leading coefficient  = -4

Degree = 4

End behaviour

x → ∞,  f(x) → - ∞

x → -∞, f(x) → - ∞

b) -2x⁷-6x⁵+2x³

Leading coefficient = -2

Degree = 7

End behaviour

x → ∞,  f(x) → -∞

x → -∞, f(x) → ∞

c) 3x²+ 6x -10

Leading coefficient = 3

Degree = 2

End behaviour

x → ∞,  f(x) → ∞

x → -∞, f(x) → ∞

Therefore the leading coefficient, degree and end behaviour are realised.

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John made at the end $357 for building cabinets

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Total money will be as follow:

Total = 36*$8.50 + 17*$3

Total = $306+$51

Total = $357

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