What is the value of the power?

As each side of the cube has a surface area of 24in².the total amount of wrapping paper needed is 64in².

Surface area is the total area of a three-dimensional object's surface, including the area of its faces and any curved surfaces.

To calculate the amount of wrapping paper needed for the cube, we can use the formula for the surface area of a cube:

SA = 6 x (side)²

In this case, the side of the cube is 2in,

so the SA = 6 x (2in)² = 24in²

To get the amount of wrapping paper needed, we would need to multiply this by 4, as each side of the cube has a surface area of 24in².

Therefore, the total amount of wrapping paper needed is

24in² x 4 = 96in²

To convert this to a square, we would need to divide it by 4, as each side of the square is equal in length.

Therefore, the total amount of wrapping paper needed is

96in² / 4

= 24in x 4

= 64in².

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The C program for RK 4th order .

C program,

#include<stdio.h>

//differential equation "dy/dx = (y-2*x*y)"

float f(float x, float y)

{

return(y-2*x*y);

}

int main()

{

// Finds value of y for a given x using step size h

int i,n;

float x0,y0,x,h,k1,k2,k3,k4;

printf("Enter the value of x:");

scanf("%f",&x);

//initial value y0 at x0.

printf("Enter the initial value of x & y:");

scanf("%f%f",&x0,&y0);

//step size

printf("Enter the value of h:");

scanf("%f",&h);

//prints the initial value of y at x and step size.

printf("x0=%f\t yo=%f\t h=%f\n",x0,y0,h);

//Count number of iterations using step size or

//step height h

n=(x-x0)/h;

// Iterate for number of iterations

for(i=1;i<=n;i++)

{

//Apply Runge Kutta Formulas to find

//next value of y

k1 = h*f(x0,y0);

k2 = h*f(x0+h/2,y0+k1/2);

k3 = h*f(x0+h/2,y0+k2/2);

k4 = h*f(x0+h,y0+k3);

//Update next value of y

y0 = y0+(k1+2*k2+2*k3+k4)/6;

//Update next value of x

x0=x0+h;

}

//print the value of y at entered value of x.

printf("at x=%f\t,y=%f\n",x,y0);

return 0;

}

Solution of DE,

y' = y - 2xy, y(0) = 1

The task is to find value of unknown function y at a given point x.

Below is the formula used to compute next value yn+1 from previous value yn. The value of n are 0, 1, 2, 3, ….(x – x0)/h.

Here h is step height and xn+1 = x0 + h

\(K_{1} = h f(x_{n} ,y_{n} )\)

\(K_{2} = hf( x_{n} + h/2 , y_{n} + K_{1}/2 )\)

Thus,

\(y_{n+1} = y_{n} + K_{1} / 6 + K_{2} / 3 + K_{3} / 3 + K_{4} / 6 +O(h^{5} )\)

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Answer:3x+140

Step-by-step explanation:

Answer:

23x+120

Step-by-step explanation:

3x+20x+120

Combine Like Terms:

=3x+20x+120

=(3x+20x)+(120)

=23x+120

Answer:

omg I absolutely love your profile picture:)

In this study, 60 undergraduate students were recruited to examine the effect of recycling on the amount of wrapping paper used to wrap a gift. The students were randomly assigned to one of two rooms, one with a recycling bin and one with a trash bin.

The researchers, who were secretly interested in measuring the amount of paper used, found that the students in the room with the recycling bin used significantly more paper than those in the room with the trash bin. This experiment suggests that the presence of a recycling bin may not have a significant effect on reducing the amount of wrapping paper used.

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a. There are no real solutions to the equation. Therefore, there is no value of α for which P(-1 < X < 2) = 0.75.

b. The value of parameter α for  P(|X| < 1) = P(|X| > 2) is 4

a. We know that for a uniform distribution over (−α,α), the probability density function is given by f(x) = 1/(2α) for −α ≤ x ≤ α and zero otherwise. Thus, the probability of the event (-1 < X < 2) can be computed as:

P(-1 < X < 2) = ∫(-1)²/(2α) dx + ∫2²/(2α) dx

= (1/2α) ∫(-1)² dx + (1/2α) ∫2² dx

= (1/2α) [x]₋₁¹ + (1/2α) [x]²₂

= (1/2α) (2α - 1) + (1/2α) (4 - α²)

= (3 + α²)/(4α)

We want this probability to be 0.75. So, we solve the equation (3 + α²)/(4α) = 0.75 for α:

(3 + α²)/(4α) = 0.75

=> 3 + α² = 3α

=> α² - 3α + 3 = 0

This is a quadratic equation in α with discriminant:

Δ = b² - 4ac

= (-3)² - 4(1)(3)

= 9 - 12

= -3

Since Δ is negative, there are no real solutions to the equation. Therefore, there is no value of α for which P(-1 < X < 2) = 0.75.

b. The pdf of a uniform distribution is given by:

f(x) = 1/(b-a), for a ≤ x ≤ b

In this case, a = -α and b = α. Therefore,

f(x) = 1/(2α), for -α ≤ x ≤ α

Now we can calculate the probabilities as follows:

P(|X| < 1) = P(-1 < X < 1) = ∫(-1 to 1) f(x) dx = ∫(-1 to 1) 1/(2α) dx = 1/(2α) * [x]_(-1 to 1) = 1/α

P(|X| > 2) = P(X < -2 or X > 2) = P(X > 2) + P(X < -2) = ∫(2 to α) f(x) dx + ∫(-α to -2) f(x) dx = ∫(2 to α) 1/(2α) dx + ∫(-α to -2) 1/(2α) dx = 1/4

Therefore, we need to find α such that P(|X| < 1) = P(|X| > 2) = 1/4.

From P(|X| < 1) = 1/α, we get α = 1/P(|X| < 1) = 1/(1/4) = 4.

From P(|X| > 2) = 1/4, we get the same value of α = 4.

Hence, α = 4 satisfies both conditions.

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Answer:

576

Step-by-step explanation:

64×9 = 576

72×8= 576

The LCM of both numbers is 576

Answer:

Step-by-step explanation:

It will be the least common multiple of 64 and 72 days

64 = 2 * 2 * 2 * 2 * 2 * 2 = 2⁶

72 = 2*2*2*3*3 = 2³ * 3²

LCM = 2⁶ * 3² = 64 * 9 =  576

Both will meet each other again 576 days

Jutin chooses a function J(x) = 3x - 1 that when he uses the number 7 as an input, then the output is 20.

As per the given data, Jutin chooses a function in which he uses the number 7 as an input, then the output is 20.

Here we have to determine which function Jutin has to use.

Now we have to substitute the value that x = 7 in all the given functions.

First function:

F(x) = 2\(x^{5}\)

F(7) = 2 \((7)^{5}\)

F(7) = 2 (16807)

F(7) = 33614 which is not equal to 20.

Second function:

G(x) = \(x^{2}\) - 19

F(7) = \((7)^{2}\) - 19

F(7) = 49 - 19

F(7) = 30 which is not equal to 20.

Third function:

H(x) = 13 - x

H(7) = 13 - 7

H(7) = 6 which is not equal to 20.

Fourth function:

J(x) = 3x - 1

J(7) = 3(7) - 1

J(7) = 21 - 1

J(7) = 20

The correct function is J(x) = 3x - 1

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Answer:

3/4x-2

Step-by-step explanation:

3−4=8

∴3=4+8

∴4=3−8

∴=14(3−8)=34−2

Answer + Step By Step:

Answer:

\(f^{-1}(x)=\sqrt{x+4}+1\)

Step-by-step explanation:

\(f(x)=(x-1)^2-4\\y=(x-1)^2-4\\\)

Swap x and y and solve for y:

\(x=(y-1)^2-4\\x+4=(y-1)^2\\\sqrt{x+4}=y-1\\\sqrt{x+4}+1=y\\f^{-1}(x)=\sqrt{x+4}+1\)

Hence, the inverse function is \(f^{-1}(x)=\sqrt{x+4}+1\)

Answer:

parallel

Step-by-step explanation:

Answer:

0.0131086142

Step-by-step explanation:

I just put in the calculator.

Answer:

F(2x^2) = 8x^2 + 6

Step-by-step explanation:

F (g(x))

= F(2x^2) = 4 (2x^2) + 6

= F(2x^2) = 8x^2 + 6

Answer:

1st option

Step-by-step explanation:

turn 15% into a decimal:

%15 -> 0.15

multiply $7 by 0.15 then add together:

7 x 0.15 = 1.05

$7 + $1.05 = $8.05

20 hours x $8.05 hour = $161

$161 x 10 weeks = $1610 total by the end of summer

the question does not say how many hours she works normally so the answer might be off...

if she continued with $7, assuming she works 20 hours/week:

20 hours x $7 = $140

$140 x 10 weeks = $1400

$1400 + $200 = $1600 total by the end of summer

The first option

Current:

[] $7 an hour

[] 20 hours worked a week

[] 10 weeks of summer

First option:

20 hours a week with 15% raise

-> $7 * 1.15 raise = $8.05

-> $8.05 * 20 hours = $161

-> $161 * 10 weeks = $1,610

-> She will earn $1,610 with the first option

Second option:

Normal working with a $200 cash bonus

-> $7 * 20 hours = $140

-> $140 * 10 weeks = $1,400

-> $1,400 + $200 = $,1600

-> She will earn $,1600 with the second option

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.

- Heather

Answer:

Don caught 3.6 kg and Dan caught 0.6 kg.

Step-by-step explanation:

Set up a system of equations:

Don's fish is the variable a and Dan's fish is the variable b.

a + b = 4.2 (1)

a=6b          (2)

We can substitute a in the first equation using the second equation, so:

6b + b = 4.2

7b = 4.2

b = 0.6 kg

Dan caught 0.6 kg. Then, we can use equation 2 to find how much Don caught.

a = 6 x 0.6

a = 3.6

Don caught 3.6 kg.

Option (c) 26.7% of the global oceans are Marine Protected Areas (MPAs). Marine Protected Areas (MPAs) are designated areas in the oceans that are set aside for conservation and management purposes.

They are intended to protect and preserve marine ecosystems, biodiversity, and various species. MPAs can have different levels of restrictions and regulations, depending on their specific objectives and conservation goals.

As of the current knowledge cutoff in September 2021, approximately 26.7% of the global oceans are designated as Marine Protected Areas. This means that a significant portion of the world's oceans has some form of protection and management in place to safeguard marine life and habitats. The establishment and expansion of MPAs have been driven by international agreements and initiatives, as well as national efforts by individual countries to conserve marine resources and promote sustainable practices.

It is worth noting that the percentage of MPAs in the global oceans may change over time as new areas are designated or existing MPAs are expanded. Therefore, it is important to refer to the most up-to-date data and reports from reputable sources to get the most accurate and current information on the extent of Marine Protected Areas worldwide.

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The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.

So, we need to find out the year in which the population will fall below 100 pheasants per hectare.

First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.

Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.

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Answer:

it is 1.08

Step-by-step explanation:

it was this on khan

Answer:

It costs $0.49 for each avocado and $0.36 for each tomato.

Step-by-step explanation:

This is a system of equations problem.

Let x represent the avocados and y represent tomatoes:

4x + 5y = 3.76  <--- scenario 1

6x + 3y = 4.02 <---- scenario 2

If we graph these out on a graphing calculator, the lines will intersept at point (0.49,0.36)

The x coordinate represents how much it costs for each avacado and the y coordinate represents how much it costs for each tomato

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer: X = -2/5

Step-by-step explanation:

Answer:

This has already been answered correctly (x = -2/5), but I'll add the steps required to arrive at that conclusion.

Step-by-step explanation:

Solving 2(5x+3)=2 requires that we use the order of operations, or PEDMAS, in going through the steps.  PEDMAS is the acronym for Parentheses, Exponents, Division, Multiplication, Addition and Subtraction.  These are the order in which math operations should be done when solving equations.  This provides the "rules of the road" when interpreting how equations were meant to be read.

2(5x+3)=2    

1.  Parentheses:  First, we should complete whatever is inside a set of parentheses, in this case (5x+3).  There is nothing we can do with (5x+3) so go to the next step.

2. Exponents:  none here, so continue

3.  Division:  none here, so continue

4.  Multiplication:  We can do the term 2(5x+3) by multiplying the 2 times each of the values within the parentheses.

        2(5x+3) = 10x + 6

We now have:

         10x + 6 = 2

5.  Addition/Subtraction:  Subtract 6 from both sides:

         10x + 6 - 6 = 2 - 6

         10x = - 4

We've gone through PEDMAS once, so start over again since we are still looking for the value of x.

The only operation left is to divide both sides by 10:

     10x = -4

      10x/10 = -4/10

   x= - 4/10 or -2/5

In general, PEDMAS works quite well.  It defines how to interpret the manner in which equations are written.  If there is any remaining ambiguity, always work from left to right.  Solve the portion on the left first, then move right.  

Also, it is always good, and edifying, to try the solution to see if the equation works for that solution.  We can ask "Does a value of x=-(2/5)  give the answer of "2" when used in 2(5x+3)?

   2(5x+3)        

   2(5*(-2/5) + 3) =  2?                 for x = -(2/5)

    2(5*(-2/5) + 3) =  2?  

Use PEDMAS:

     2(5*(-0.4) + 3) =  2?

     2(-2 + 3) = 2?

      2(1)  = 2?                     YES, -(2/5) is correct

Il faut calculer la différence entre les deux nombres, la diviser par l'ancienne valeur, puis multiplier par 100 pour obtenir le pourcentage.

La différence entre les deux nombres est :

28 - 20 = 8

L'ancienne valeur est 20, donc nous avons :

(8 / 20) x 100 = 0.4 x 100 = 40

Le pourcentage d'augmentation est donc de 40%. Le lanceur de baseball a augmenté son nombre de victoires de 40% par rapport à l'année précédente.

The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

Given,

A spherical golf ball is measured to have a radius of $$5 mm, with a possible measurement error of $$0.1 mm

How to determine the volume

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

r is the radius of the sphere

pi takes the value 3.14

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

v = 4/ 3 (392.5)

v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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The equation which represents a cost function with a greater hourly rate than these charges is; C > 28 + 35h. The table required is therefore the table which represents the given function.

According to the question;

On this note, for one hour, the charge is; $63.

In essence, the table represents a cost function with a greater hourly rate than these charges will be;

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Answer:

n = 3

Step-by-step explanation:

8 = 2(n + 1)

8 = 2n + 2

6 = 2n

n = 3

The percentage of their matches that SPARX FC have is lost 35% of their matches.

The percentage of matches lost by SPARX FC is calculated using the formula below:

Total number of matches played = 7 + 6 + 7

Total number of matches played = 20

Number of matches lost = 7

Percentage of matches lost = (7 / 20) * 100

Percentage of matches lost = 35%

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1) The probability density function is 1 - ∫[0, 1200] f(x) dx.

2) The probability density function is  1 - ∫[0, 1200] f(x) dx.

To estimate the probability that the total life of all components will exceed 1200, we need to consider two scenarios: one with exponentially distributed lifetimes and another with uniformly distributed lifetimes.

1) Exponentially Distributed Lifetimes:

Given that the lifetime of component i is exponentially distributed with a mean of 10 + i/10, we can calculate the failure rate (λ) for each component as λ = 1 / mean.

The total life of all components can be modeled as a sum of exponentially distributed random variables. Since the sum of exponential random variables follows a gamma distribution, we can use the gamma distribution to estimate the probability.

Let's denote the lifetime of component i as Xi, and the total life of all components as T = X1 + X2 + ... + X100.

The mean of the gamma distribution for the total life is given by E(T) = Σ(E(Xi)) = Σ(1 / λi), where λi is the failure rate of component i.

1.1 Calculation:

The probability that the total life of all components will exceed 1200 can be estimated as follows:

P(T > 1200) = 1 - P(T ≤ 1200)

= 1 - ∫[0, 1200] f(x) dx,

where f(x) is the probability density function of the gamma distribution with appropriate parameters.

2) Uniformly Distributed Lifetimes:

Given that the lifetime of component i is uniformly distributed over (0, 20 + i/5), we can calculate the mean lifetime for each component using the formula for the mean of a continuous uniform distribution: mean = (a + b) / 2, where a and b are the endpoints of the distribution.

The total life of all components can be modeled as the sum of uniformly distributed random variables. Since the sum of uniform random variables follows a Irwin-Hall distribution, we can use the Irwin-Hall distribution to estimate the probability.

Again, let's denote the lifetime of component i as Xi, and the total life of all components as T = X1 + X2 + ... + X100.

The mean of the Irwin-Hall distribution for the total life is given by E(T) = Σ(E(Xi)) = Σ((a + b) / 2), where a and b are the endpoints of the uniform distribution for each component.

2.1 Calculation:

Similarly, we can estimate the probability that the total life of all components will exceed 1200 using the Irwin-Hall distribution:

P(T > 1200) = 1 - P(T ≤ 1200)

= 1 - ∫[0, 1200] f(x) dx,

where f(x) is the probability density function of the Irwin-Hall distribution with appropriate parameters.

Correct Question :

We have 100 components that we will put in use in a sequential fashion. That is, component 1 is initially put in use, and upon failure, it is replaced by component 2, which is itself replaced upon failure by component 3, and so on. If the lifetime of component i is exponentially distributed with mean 10 + i/ 10, i = 1, . . . , 100, estimate the probability that the total life of all components will exceed 1200. Now repeat when the life distribution of component i is uniformly distributed over ( 0, 20 + i/ 5), i = 1, . . . , 100.

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Answer:

$125

Step-by-step explanation:

if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price

let a = original price

this equation can be used to represent the question

a x 0.8 = 100 ]]divide both sides by 0.8

a = 100 / 0.8 = 125

Answer:

10x^(2)-4x

Step-by-step explanation: