The weekly demand of a slow-moving product has the following probability mass function: Demand, Probability, fx) 0.2 0.4 1 2 0.3 3 0.1 4 or more 0 Use VLOOKUP to generate 25 random variates from this distribution

The particular solution of the differential equation in the integral form is

yp(x) = -2[G(x)]f(x) = -2G(x) ∫ f(t) dt + C

For finding a particular solution yp(x) of the given differential equation using the integral form, we can follow these steps:

yp(x) = G(x)f(x) ........... (1)

Given the differential equation is y" + 2y' + y = f(x)

Substituting yp(x) = G(x)f(x) into the differential equation, we get:

y" + 2y' + y = f(x)

By differentiating the expression for yp(x) twice, we gety

p'(x) = G'(x)f(x) + G(x)f'(x)

yp''(x) = G''(x)f(x) + 2G'(x)f'(x) + G(x)f''(x)

Substituting these values in the differential equation:

y''(x) + 2y'(x) + y(x) = yp''(x) + 2yp'(x) + yp(x) = [G''(x) + 2G'(x) + G(x)]f(x) + [2G'(x) + G(x)f''(x)]

When we compare the coefficient of f(x) on both sides of the equation. It is given that the function G(x) satisfies the equation G''(x) + 2G'(x) + G(x) = 0

Now,

[2G'(x) + G(x)]f''(x) + [G''(x) + 2G'(x) + G(x)]f(x) = f(x)

Substituting the given value of the differential equation, f(x) = fx) and simplifying the above expression, we get

[2G'(x) + G(x)]fx) = f(x)

Comparing the above expression with the given equation, we can obtain G(x) as

G(x) = -2G'(x)

Substituting this value in equation (1), we get

yp(x) = G(x)f(x) = -2G'(x)f(x)

So the required particular solution yp(x) of the given differential equation in integral form yp(x)-G(x, t)f(t) dt y" + 2y' + y = fx) is given as

yp(x) = -2[G(x)]f(x) = -2G(x) ∫ f(t) dt + C

where G(x) satisfies the equation G''(x) + 2G'(x) + G(x) = 0 and C is a constant of integration.

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Answer:

108,0000 liters

Step-by-step explanation:

It should be 108,0000 liters because if there are 60 seconds per minute and the pump was on for 39 mins, 60 x 30 = 1800  

Then 1800 seconds times 600 liters per second equals 108,0000 liters

The probability of getting exactly 3 heads when a penny is flipped 9 times is approximately 0.1641.

The expression that represents the probability of getting exactly 3 heads when a penny is flipped 9 times is:

p(3 successes) = (9 C 3) * (0.5)^3 * (0.5)^(9-3)

Where:

"p(3 successes)" represents the probability of getting 3 heads.

"9 C 3" represents the number of ways to choose 3 flips out of 9 flips (also known as the binomial coefficient). This is calculated as 9! / (3! * (9-3)!), which simplifies to 84.

"0.5" represents the probability of getting heads on a single flip of a fair penny.

"(0.5)^(9-3)" represents the probability of getting tails on the remaining 6 flips, since the probability of getting either heads or tails on a single flip is 0.5.

Simplifying the expression, we get:

p(3 successes) = (9 C 3) * (0.5)^9

p(3 successes) = (84) * (0.5)^9

p(3 successes) ≈ 0.1641

Therefore, the probability of getting exactly 3 heads when a penny is flipped 9 times is approximately 0.1641.

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Answer:

C

Step-by-step explanation:

it was correct for me on edge

The graph of h against m is plotted in form of a curve.

Given:

A tree branch is observed to bend as the fruit growing on it increases in size.

The height h in metres of the branch end above the ground is closely approximated by the function \(h=2-0.2*1.60^{0.2m}\) where m is the estimated mass, in kilograms, of fruit on the branch.

We have to sketch the graph of h against m.​

The x-axis represents the mass in kg while the y-axis represents the height of the branch above the ground in metres.

Hence a curved graph is obtained by plotting the function.

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Answer:

Giraffe

Step-by-step explanation:

I made the estimates into fractions and the Giraffes one was greater than the Zebra

The Zebra runs faster because the speed of the Zebra is 17 m/s and the speed of the Giraffe is 14 m/s.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

The table represents the top running speed for a zebra and a giraffe.

As we know,

The speed formula:

speed = distance/time

For Giraffe:

Speed (v) = 280/20 = 14 m/s

For Zebra:

Speed (V) = 204/12 = 17 m/s

V > v

Thus, the Zebra runs faster because the speed of the Zebra is 17 m/s and the speed of the Giraffe is 14 m/s.

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Answer:

To determine the number of sheets of cardboard in a stack, we need to use the information given in the problem.

We know that each sheet of cardboard is 1 inch thick, and 16 sheets are stacked on top of each other in packages. The height of each stack is 21 inches.

Using the model of a ruler, we can divide the height of the stack (21 inches) by the thickness of each sheet (1 inch) to find the number of sheets in the stack.

21 ÷ 1 = 21

So, there are 21 sheets of cardboard in a stack.

To write an expression that can be used to determine the number of sheets of cardboard in a stack, we can use:

Number of sheets = height of stack ÷ thickness of each sheet

Or, substituting the given values: Number of sheets = 21 ÷ 1 = 21

This expression is simply a representation of the model we used earlier. It shows that we can determine the number of sheets in a stack by dividing the height of the stack by the thickness of each sheet. In this case, the expression yields the same result as the model, which is 21 sheets.

Figure SPOT is translated unit(s) right and unit(s) up to the right move 8 and to the up move 9.

An effective method for beginning to make this idea clear for translating squares is to give them a slice-out shape to get across the page truly.

Afterward, kids need to figure out how to have the option to interpret a shape without this support.

while doing the above task, ideally, let's begin by putting the effective method for beginning making this idea clear for translating square is to give them a slice out shape to get across the page truly.

Afterward, kids need to figure out how to have the option to interpret a shape without this support.

while doing the above task, ideally, let's begin by putting the mark of your pencil on the upper left-hand corner of the shape and afterward dropping your pencil down 1 and right 2, then, at that point, plotting the primary place of your new shape with a dab.

You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.

To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (8, 9).  mark your pencil on the upper left-hand corner of the shape and afterward drop your pencil down 5 and right 6, then, at that point, plot the primary place of your new shape with a dab.

You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.

To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (5, 4), (6, 3), (5, 2), and (4, 3).

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domain is xand range is f(x)i.e 2

The interval notation that shows the domain and range of the function

f(x) = 2|x| is domain = (all real numbers) and range = (all real numbers)

The domain of a function is input values "x" for which the function f(x) exists while the range of a function is the output value for which a function exists.

Given the function f(x) = 2|x|

Since the input variable is a positive value, the domain of the value will exists on all real numbers. The domain in interval notation is expressed as

The output variable is a positive value, the range of the value will exists on all real numbers. The range in interval notation is expressed as

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Answer:

39) a) \(2^{1}\)= 2

     b) \(2^{3}\)= 2×2×2=8

     c)\(2^{t}\)

40) no

Step-by-step explanation:

40) both point A and B is below the point C. therefore it cannot pass through point c

The volume of the frustum of the right circular cone is approximately 21850.2 cubic units where  frustum of a cone is a three-dimensional geometric shape that is obtained by slicing a larger cone with a smaller cone parallel to the base.  

To find the volume of a frustum of a right circular cone, we can use the formula:

V = (1/3) * π * h * (r₁² + r₂² + (r₁ * r₂))

where V is the volume, h is the height, r₁ is the radius of the lower base, and r₂ is the radius of the top base.

Given the values:

h = 15

r₁ = 25

r₂ = 19

Substituting these values into the formula, we have:

V = (1/3) * π * 15 * (25² + 19² + (25 * 19))

Calculating the values inside the parentheses:

25² = 625

19² = 361

25 * 19 = 475

V = (1/3) * π * 15 * (625 + 361 + 475)

V = (1/3) * π * 15 * 1461

V = (1/3) * 15 * 1461 * π

V ≈ 21850.2 cubic units

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The volume of the frustum of the right circular cone is approximately 46455 cubic units.

To find the volume of a frustum of a right circular cone, we can use the formula:

V = (1/3) * π * h * (R² + r² + R*r)

where V is the volume, π is a constant approximately equal to 3.14, h is the height of the frustum, R is the radius of the lower base, and r is the radius of the top base.

Given that the height (h) is 15 units, the radius of the lower base (R) is 25 units, and the radius of the top base (r) is 19 units, we can substitute these values into the formula.

V = (1/3) * π * 15 * (25² + 19² + 25*19)

Simplifying this expression, we have:

V = (1/3) * π * 15 * (625 + 361 + 475)

V = (1/3) * π * 15 * 1461

V ≈ (1/3) * 3.14 * 15 * 1461

V ≈ 22/7 * 15 * 1461

V ≈ 46455

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Answer:

so i the answer is 216 only

Answer:

I would venture to say that puts the first option. I may be wrong but I'd doubt it.

Number line going from 0 to 6.5 in increments of 0.5. An arrow goes from 0 to 1.5 and from 1.5 to 4.

A number system is defined as a system of writing to express numbers.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

We need to find which number line represents 1.5 + 2.5

When we add 1.5 + 2.5

One point five plus two point five

4.

So number line going from 0 to 6.5 in increments of 0.5. An arrow goes from 0 to 1.5 and from 1.5 to 4.

Hence, number line going from 0 to 6.5 in increments of 0.5. An arrow goes from 0 to 1.5 and from 1.5 to 4.

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Answer:

c

Step-by-step explanation:

i think

Answer:

he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).

Step-by-step explanation:

Answer:

40.3174736 ≈ 40.31

Step-by-step explanation:

uhhhhhh yeahh

Answer:

the answer is 47

Step-by-step explanation:

subtract 133 from 180 and you get 47

The three functions that need to be ordered so that each one is Big-Oh of the next one are given below : log n2n4 log n nlog The correct order of these functions would be: nlog(n) << n^(1/2) << n^2 << n^(log(n)) << 2^n

Justification: To determine the order of these functions, let's first compare log n2 with n. As n tends to infinity, n increases much faster than log n2. Thus, n is the Big-Omega of log n2. We can write it as: log n2 = O(n).Next, let's compare n with 4 log n.

For large values of n, the term 4 log n is much smaller than n. Therefore, we can say:n = O(4 log n)Next, we need to compare 4 log n with nlogn. Using logarithmic identities, we can write 4 log n as log n^4. Now, let's compare this with nlogn:log n^4 = 4 log n = O(n log n)

Hence, we can say that 4 log n is Big-Oh of nlogn. Now, we need to compare nlogn with n^(logn). One way to compare these two functions is to take their ratio and see what happens as n tends to infinity: lim n→∞ (nlogn / n^(logn))= lim n→∞ (n^logn / n^(logn))= lim n→∞ n^0= 1

Thus, we can say that nlogn is Big-Oh of n^(logn).

Hence, the correct order of these functions is:log n2 << n << 4 log n << nlogn << n^(logn).

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Answer:

C

Step-by-step explanation:

cot =cos/sin =a/b

cos=a/b*sin

(sin-cos)/(sin+cos) =(sin-sin*a/b)(sin+sin*a/b)

=(1-a/b)/(a+a/b)

=(b-a)/(a+b)

Answer:

6^5 (6 to the 5th power)

Step-by-step explanation:

6 is being mulitiplied 5 times  

Answer: it would be 6 with the tiny 5 in the upper right hand corner.// the exponent is 5

Step-by-step explanation: I am not the best at explanations but i will try. It is because there are 5 sixes.

Null hypothesis states, the new incentive program will not have a significant effect on reducing employee sick leave (26%). The new incentive program will result in a significant reduction in employee sick leave (26%), alternative hypothesis.

Hypothesis testing typically involves determining the statistical significance of the observed data by comparing it to a null hypothesis.

The null hypothesis (H0) in this scenario could be stated as: "The introduction of the new incentive program for perfect attendance will not have a significant effect on reducing employee sick leave (26%)."

The alternative hypothesis (H1) would then be: "The introduction of the new incentive program for perfect attendance will result in a significant reduction in employee sick leave (26%)."

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Answer:

2nd no is corret

Step-by-step explanation:

as altitude is defined as a st. line meeting its base forming 90degree angle.

Answer:

I think the second answer, JH is an altitude of GJI, is the correct answer.

Step-by-step explanation:

Having JH be an altitude of GJI means that it makes a 90 degree angle. And to prove that it's a 90 degree angle we look at where it has the little squares. The squares represent 90 degrees.

Hope this helps!

Answer: C

Step-by-step explanation:

I got this right

Answer:

A

Step-by-step explanation:

Answer:

-3/7m=12

-3m/7=12 multiplying by 12 on both sides

-3m=12x7

-3m=84

divide by -3

-3m/-3= 84/-3

m= -28

Ans is A

Situation can be modeled by a linear function, A situation that involves a constant rate of change can be modeled by a linear function.

A linear function is a mathematical representation of a relationship between two variables that forms a straight line when plotted on a graph. It is characterized by a constant rate of change between the variables.

In a linear function, the dependent variable (y) changes at a constant rate for every unit change in the independent variable (x). This means that as x increases or decreases by a fixed amount, y also changes by a consistent amount.

Situations that exhibit a constant rate of change can be effectively modeled by linear functions.

Examples include scenarios such as distance traveled over time at a constant speed, the growth of a bank account with a fixed interest rate, or the cost of an item per unit.

In these cases, the relationship between the variables can be represented accurately using a linear equation or function.

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Situation can be modeled by a linear function, A situation that involves a constant rate of change can be modeled by a linear function.

A linear function is a mathematical representation of a relationship between two variables that forms a straight line when plotted on a graph. It is characterized by a constant rate of change between the variables.

In a linear function, the dependent variable (y) changes at a constant rate for every unit change in the independent variable (x). This means that as x increases or decreases by a fixed amount, y also changes by a consistent amount.

Situations that exhibit a constant rate of change can be effectively modeled by linear functions.

Examples include scenarios such as distance traveled over time at a constant speed, the growth of a bank account with a fixed interest rate, or the cost of an item per unit.

In these cases, the relationship between the variables can be represented accurately using a linear equation or function.

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Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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Answer:

\(12\) cm

Step-by-step explanation:

If Kelsey knit a total of \(6\) cm of scarf over \(2\) nights, then we know that she can knit \(\frac{6}{2}=3\) cm each night. Therefore, after \(4\) nights of knitting, Kelsey would have knit a total of \(3*4=12\) cm of scarf in total. Hope this helps!

Answer:

Step-by-step explanation:

3

What is Word Problem?

Word Problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equation to be solved.

How to determine this

When 3 yard of rope weigh 2 pounds

By interpreting the question

i.e 3 yards = 2 pounds

Then how much does 18 yards weigh

Let x represent the number of pounds

When 3 yards = 2 pounds

18 yards = x

x = 18 yards * 2 pounds/3 yards

x = 36/3 pounds

x = 12 pounds

For 16 yards,

When 3 yards = 2 pounds

16 yards = x

x = 16 yards * 2 pounds/3 yards

x = 32/3 pounds

x = 10 2/3 pounds

x = 10.67 pounds

For 14 yards,

When 3 yards = 2 pounds

14 yards = x

x = 14 yards * 2 pounds/3 yards

x = 28/3 pounds

x = 9 1/3 pounds

x = 9.33 pounds

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