Let ƒ: [0, 1] → R be a function. For each n € N, partition [0, 1] into n equal subintervals and suppose that for each n the up- per and lower sums are given by Un = 1+ and Ln 1 = 2 n n respectively. 1 Is f integrable? If so, what is f(x) da? Explain your answer. 1, x = [0,1) 2, X = 1 (i) What is Ln (as a function of n)? (ii) What is Un (as a function of n)? (iii) Use your answers to (i) and (ii) to calculate g(x) dx.

The denominator is negative, we know that the system is unstable and there is no minimum number of servers that can guarantee a stable system.

To determine the minimum number of servers needed, we can use the following formula:

\(N = (p^2 + p) / (2(1 - p))\)

where N is the number of servers, ρ is the utilization factor, which is equal to the ratio of the average service time (5 minutes) to the interarrival time (2 minutes), or ρ = 5/2 = 2.5, and the denominator is equal to the average number of customers in the system.

Plugging in the values, we get:

\(N = (2.5^2 + 2.5) / (2(1 - 2.5))\)

N = 6.25 / (-3)

Since the denominator is negative, we know that the system is unstable and there is no minimum number of servers that can guarantee a stable system. This means that either the interarrival time or the processing time needs to be adjusted to achieve a stable system.

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First we need to solve for n, likte this:

In a graph, n would look like a line, which value is always 14, like this:

Volumes of the cylinder are given by:

(A) (1) Volume = 2486.88 cubic in.

(2) Volume = 108518.4 cubic ft.

(3) Volume = 47608.68 cubic yd.

(B) (4) Volume = 508.68 cubic ft.

(5) Volume = 8490.56 cubic yd.

(6) Volume = 43407.36 cubic in.

(7) Volume = 9420 cubic ft.

(8) Volume of cylindrical flower vase = 1105.28 cubic in.

Surface Area of the Cylinder are given by:

(1) Surface Area = 113.04 square in.

(2) Surface Area = 1444.4 square ft.

(3) Surface Area = 678.24 square yd.

(4) Surface Area = 1130.4 square yd.

(5) Surface Area = 602.88 square in.

(6) Surface Area = 1055.04 square ft.

(7) Surface Area = 1570 square ft.

(8) Surface Area = 791.28 square yd.

(9) Surface Area = 326.56 square in.

We know that the volume of a cylinder with radius 'r' and height 'h' is given by,

V = 2πr²h

(A) (1) From the figure, radius = 6 in and height = 11 in.

So the volume = 2π(6)²*11 = 2486.88 cubic in.

(2) Radius = 24 ft. and height = 30 ft.

Hence, the volume of cylinder = 2π(24)²*30 = 108518.4 cubic ft.

(3) Radius = 19 yd. and height = 21 yd.

Hence, the volume of cylinder = 2π(19)²*21 = 47608.68 cubic yd.

(B) (4) Radius = 3 ft. and height = 9 ft.

Hence, the volume of cylinder = 2π(3)²*9 = 508.68 cubic ft.

(5) Radius = 13 yd. and height = 8 yd.

Hence, the volume of cylinder = 2π(13)²*8 = 8490.56 cubic yd.

(6) Radius = 16 in. and height = 27 in.

Hence, the volume of cylinder = 2π(16)²*27 = 43407.36 cubic in.

(7) Radius = 10 ft. and height = 15 ft.

Hence, the volume of cylinder = 2π(10)²*15 = 9420 cubic ft.

(8) Cylindrical flower vase is 11 inch tall and radius of vase is 4 inches.

The volume of flower vase = 2π(4)²*11 = 1105.28 cubic in.

   Now we know that the surface area of a Cylinder with radius 'r' and height 'h' is given by,

S = 2πrh + 2πr²

(1) Radius = 2 in. and Height = 7 in.

Hence the surface area = 2π*2*7 + 2π(2)² = 113.04 square in.

(2) Radius = 10 ft. and Height = 13 ft.

Hence the surface area = 2π*10*13 + 2π(10)² = 1444.4 square ft.

(3) Radius = 6 yd. and Height = 12 yd.

Hence the surface area = 2π*6*12 + 2π(6)² = 678.24 square yd.

(4) Radius = 9 yd. and Height = 11 yd.

Hence the surface area = 2π*9*11 + 2π*9² = 1130.4 square yd.

(5) Radius = 6 in. and Height = 10 in.

Hence the surface area = 2π*6*10 + 2π(6)² = 602.88 square in.

(6) Radius = 8 ft. and Height = 13 ft.

Hence the surface area = 2π*8*13 + 2π(8)² = 1055.04 square ft.

(7) Radius = 10 ft. and Height = 15 ft.

Hence the surface area = 2π*10*15 + 2π(10)² = 1570 square ft.

(8) Radius = 6 yd. and Height = 15 yd.

Hence the surface area = 2π*6*15 + 2π(6)² = 791.28 square yd.

(9) Radius = 4 in. and Height = 9 in.

Hence the surface area = 2π*4*9 + 2π(4)² = 326.56 square in.

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Answer:

120 cubic cm

Step-by-step explanation:

formula is b*h. the base can be found by l*w/2. the area of the base is 12. 12*10 is 120 cm

Answer:

\(120 cm^3\)

Step-by-step explanation:

area of triangular base times the height will give the volume

(1/2 × 6 × 4)(10)

12×10 = \(120 cm^3\)

Answer:

I think B is the correct answer, sorry im not very good with math tho.

Step-by-step explanation:

Sorry if its incorrect

Answer:

16

Step-by-step explanation:

let boys equal to 5x

and girls equal to 4x

so 4x+5x=36

X=4

so boys are 5*4

boys are 20

and girls are 16

so boys are 4 more than girls

Answer:

16 girls

Step-by-step explanation:

boys : girls : total

5          4        5+4 = 9

take the total number of people and divide by 9

36/9 = 4

Each number should be multiplied by 4

boys : girls : total

5*4        4*4     9*4

20          16        36

There are 16 girls

Answer: C. 78%

Step-by-step explanation:

simply divide 7 by 9 and move the decimal two places to the right and round!

Answer:

The coordinates of the point equidistant from the position of the three students is (-3, 1).

The equation of the locus of the circular path is:

\(x^2+y^2+6x-2y-15=0\)

Step-by-step explanation:

The point that is equidistant from the three students is the circumcenter of the triangle formed by the three students.

The circumcenter of a triangle is the point at which the perpendicular bisectors of the sides of the triangle intersect.

Label the vertices of the triangle:

We only need to find the perpendicular bisectors of two of the sides.

To find the perpendicular bisectors, first find the slope of the two lines by using the slope formula:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

The slope of AB is:

\(m_{AB}=\dfrac{y_B-y_A}{x_B-x_A}=\dfrac{-4-5}{-3-(-6)}=\dfrac{-9}{3}=-3\)

Therefore, the slope of the perpendicular bisector of AB is 1/3.

The slope of AC is:

\(m_{AC}=\dfrac{y_C-y_A}{x_C-x_A}=\dfrac{1-5}{2-(-6)}=\dfrac{-4}{8}=-\dfrac{1}{2}\)

Therefore, the slope of the perpendicular bisector of AC is 2.

Now find the midpoints of two of the line segments by using the midpoint formula:

\((x_m,y_m)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

The midpoint of AB is:

\(\implies \left(\dfrac{x_A+x_B}{2},\dfrac{y_A+y_B}{2}\right)=\left(\dfrac{-6+(-3)}{2},\dfrac{5+(-4)}{2}\right)=\left(-\dfrac{9}{2},\dfrac{1}{2}\right)\)

The midpoint of AC is:

\(\implies \left(\dfrac{x_A+x_C}{2},\dfrac{y_A+y_C}{2}\right)=\left(\dfrac{-6+2}{2},\dfrac{5+1}{2}\right)=\left(-2,3\right)\)

Now we can create equations for the perpendicular bisectors of AB and AC by substituting the found slopes and midpoints into the point-slope formula:

\(y-y_1=m(x-x_1)\)

The equation of the perpendicular bisector of AB is:

\(\implies y-\dfrac{1}{2}=\dfrac{1}{3}\left(x-\left(-\dfrac{9}{2}\right)\right)\)

\(\implies y-\dfrac{1}{2}=\dfrac{1}{3}x+\dfrac{3}{2}\)

\(\implies y=\dfrac{1}{3}x+2\)

The equation of the perpendicular bisector of AC is:

\(\implies y-3=2\left(x-\left(-2\right)\right)\)

\(\implies y-3=2x+4\)

\(\implies y=2x+7\)

Now we have equations for the perpendicular bisectors of two of the sides of the triangle, we can find the x-value of the point of intersection (the circumcenter) by equating the equations and solving for x:

\(\implies 2x+7=\dfrac{1}{3}x+2\)

\(\implies \dfrac{5}{3}x=-5\)

\(\implies x=-3\)

Substitute the found value of x into one of the equations and solve for y:

\(\implies y=2(-3)+7=1\)

Therefore, the coordinates of the point equidistant from the position of the three students is (-3, 1).

To find the equation of the locus of the circular path, we need to find the equation of the circle with center at (-3, 1) and radius equal to the distance from any of the three students to the center.

To find the radius of the circle, calculate the distance between the center (-3, 1) and one of the points using the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Therefore, the distance between the center (-3, 1) and point A (-6, 5) is:

\(\implies r=\sqrt{(-6-(-3))^2+(5-1)^2}\)

\(\implies r=\sqrt{(-3)^2+(4)^2}\)

\(\implies r=\sqrt{25}\)

\(\implies r=5\)

Finally, substitute the found center and radius into the general equation of a circle:

\((x-h)^2+(y-k)^2=r^2\)

where (h, k) is the center, and r is the radius.

Therefore, the equation of the circle is:

\((x+3)^2+(y-1)^2=25\)

Expanding to give the equation of the locus of the circular path:

\(\implies x^2+6x+9+y^2-2y+1=25\)

\(\implies x^2+y^2+6x-2y-15=0\)

Answer:

Step-by-step explanation:

39 + s = 39 + 808 = 847

39 + s = 847

39 + s for s=808 [what is the value of the expression?].

847

please look at the attached picture :)

Answer:

- 5

Step-by-step explanation:

Substitute x = - 2 into f(x)

f(- 2) = 2(- 2) - 1 = - 4 - 1 = - 5

g'(x) = 1/f'(g(x)) = 1/sin(g(x))

We know that g is the inverse function of f, which means that f(g(x)) = x for all x in the domain of g.

Taking the derivative of both sides of this equation with respect to x, we get:

f'(g(x)) * g'(x) = 1

We also know that f'(x) = sin(x). Substituting x with g(x), we get:

f'(g(x)) = sin(g(x))

Substituting this into the previous equation, we get:

sin(g(x)) * g'(x) = 1

Solving for g'(x), we get:

g'(x) = 1/sin(g(x))

Therefore, g'(x) is equal to the reciprocal of sin evaluated at g(x). It's worth noting that this expression is undefined whenever sin(g(x)) = 0, which occurs at integer multiples of π. So the domain of g'(x) is the set of all x such that g(x) is not an integer multiple of π.

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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Rewrite 20x¹y³ - 30x³4 using a common factor is \(20 x y^3-120 x^3\).

What is common factor?

A number's precise divisor is referred to as a factor. Every component of a number must be either less than or equal to the provided number; it cannot be bigger. Every number has two or more components, while some numbers have more. For instance, the factors of 6 are 1, 2, 3, and 6. Additionally, every number is a factor of 1 and every number is a factor in and of itself. The number of components that make up a particular number can be considered to be finite. Check each number's largest common factor as well.

\(\begin{aligned}& 20 x^1 y^3-30 x^3 \cdot 4 \\& x^1=x \\& 30 x^3 \cdot 4=120 x^3 \\& =20 x y^3-120 x^3\end{aligned}\)

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Answer:

=77 and the reserve is to get the answers

The least possible value of "b" is 3. Hence, when "a = 2" and "b = 3," we satisfy all the given conditions. Thus, the least possible value of "b" is 3.

Let's analyze the given information:

The integer "a" has 3 factors: 1, "a," and one other factor.

The integer "b" has "a" factors.

"b" is divisible by "a."

From these conditions, we can deduce that "a" must be a prime number. This is because a prime number only has two factors: 1 and itself.

Therefore, "a" must be the smallest prime number, which is 2. So, "a = 2."

Now, we need to find the least possible value of "b" given that "b" has 2 factors.

Since "b" has 2 factors, it can only be a prime number. The smallest prime number greater than 2 is 3.

Therefore, the least possible value of "b" is 3.

Hence, when "a = 2" and "b = 3," we satisfy all the given conditions. Thus, the least possible value of "b" is 3.

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a. the sum of the first 200 natural numbers is 20,100. b. when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

(a) To find the sum of the first 200 natural numbers, we can use the formula for the sum of an arithmetic series.

The sum of the first n natural numbers is given by the formula: Sn = (n/2)(a + l), where Sn represents the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, we want to find the sum of the first 200 natural numbers, so n = 200, a = 1 (the first natural number), and l = 200 (the last natural number).

Substituting these values into the formula, we have:

Sn = (200/2)(1 + 200)

  = 100(201)

  = 20,100

Therefore, the sum of the first 200 natural numbers is 20,100.

(b) The ball rebounds three-fourths of the distance it drops, so each time it hits the pavement, it travels a total distance of 1 + (3/4) = 1.75 times the distance it dropped.

For the 6th rebound, we need to find the distance the ball traveled when it hits the pavement.

Let's represent the initial drop distance as h (30 ft).

The total distance traveled after the 6th rebound is given by the sum of a geometric series:

Distance = h + h(3/4) + h(3/4)^2 + h(3/4)^3 + ... + h(3/4)^5 + h(3/4)^6

Using the formula for the sum of a geometric series, we can simplify this expression:

Distance = h * (1 - (3/4)^7) / (1 - 3/4)

Simplifying further:

Distance = h * (1 - (3/4)^7) / (1/4)

        = 4h * (1 - (3/4)^7)

        = 4 * 30 * (1 - (3/4)^7)

Calculating the value:

Distance ≈ 4 * 30 * (1 - 0.1335)

        ≈ 4 * 30 * 0.8665

        ≈ 104 ft

Therefore, when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

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Answer:

1) 2 days

2) 11 days

3) may 16

5) 5 days

6) may 29th

Step-by-step explanation:

if someone can, check out my recent questions too please

Answer: 6

Step-by-step explanation: n-3x6-6=6

Step-by-step explanation:

there is nothing to solve as there is no equation.

but we can simplify the expression :

2b - (-4b) = 2b + 4b = 6b

remember :

++ = +

+- = -

-+ = -

-- = +

Answer:

6b

Step-by-step explanation:

2b+4b (- - = +)

The answer is 6b

Without a clear pattern or rule from the given examples, it is difficult to determine the value of 1*7 in this problem.

This problem appears to involve some sort of pattern or rule that relates the multiplication of two numbers to a resulting value. Let's examine the given examples to try to identify the pattern:

5*3=4: The product of 5 and 3 is 15, but the answer is 4. This means that some sort of operation was performed on 15 to produce 4. One possibility is that the digits of 15 were added together: 1 + 5 = 6, and then the result was subtracted from 10: 10 - 6 = 4. So, this pattern involves adding the digits of the product and subtracting the result from 10.

2*8=2: The product of 2 and 8 is 16, but the answer is 2. Again, we need to perform an operation on 16 to get 2. One possibility is to divide 16 by the sum of the digits: 1 + 6 = 7, so 16 / 7 = 2.28 (rounded to 2 decimal places). However, this pattern doesn't quite fit the given examples perfectly, so there may be other rules or variations involved.

6*3=3: The product of 6 and 3 is 18, but the answer is 3. Applying the same approach as before, we could try dividing 18 by the product of the digits: 6 * 3 = 18, so 18 / 18 = 1. However, this pattern doesn't match the previous examples either.

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Answer:

A. 12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

9 + (1/2)⁴ · 48

Step 2: Evaluate

Given:

The function is:

\(h(x)=x^2-3x+5\)

To find:

The value of \(h(2x+1)\).

Solution:

We have,

\(h(x)=x^2-3x+5\)

Putting \(x=2x+1\), we get

\(h(2x+1)=(2x+1)^2-3(2x+1)+5\)

\(h(2x+1)=(2x)^2+2(2x)(1)+(1)^2-3(2x)-3(1)+5\)

\(h(2x+1)=4x^2+4x+1-6x-3+5\)

On combining like terms, we get

\(h(2x+1)=4x^2+(4x-6x)+(1-3+5)\)

\(h(2x+1)=4x^2-2x+3\)

Therefore, the required function is \(h(2x+1)=4x^2-2x+3\).

Answer:

Step-by-step explanation:

100 - 12 = 88

88:100

22:25

Answer:

88

Step-by-step explanation:

12-100=

88

I hope this helped

To find the probability of saving a total of $20, we need to calculate the probability of both scenarios happening and add them together.

Scenario 1: Camera gets a 10% discount and game gets no discount.
The probability of the camera getting a 10% discount is 0.2 (or 20%) since there is a 20% chance of getting a discount on any item.
The probability of the game getting no discount is 0.8 (or 80%) since there is an 80% chance of not getting a discount on any item.
So, the probability of this scenario happening is 0.2 * 0.8 = 0.16 (or 16%).

Scenario 2: Game gets a 25% discount and camera gets no discount.
The probability of the game getting a 25% discount is 0.25 (or 25%) since there is a 25% chance of getting a discount on any item.
The probability of the camera getting no discount is 0.8 (or 80%) since there is an 80% chance of not getting a discount on any item.
So, the probability of this scenario happening is 0.25 * 0.8 = 0.2 (or 20%).

Therefore, the probability of saving a total of $20 is the sum of the probabilities of both scenarios: 0.16 + 0.2 = 0.36 (or 36%).

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Answer:

$9.95

Step-by-step explanation:

Answer:

its 9.955

Step-by-step explanation:

39.82÷4

by calculator

When you buy 2 chickens and 3 boxes of stuffing with a 20-pound note, you will get a change of 4 pounds.

Given that you have a 20-pound note and you buy 2 chickens and 3 boxes of stuffing, we need to determine the total amount spent on these items. Let's assume that the price of each chicken is 5 pounds and the price of each box of stuffing is 2 pounds.

Therefore, the total cost of 2 chickens and 3 boxes of stuffing is given by;Total cost = (2 x 5) + (3 x 2) = 10 + 6 = 16 poundsTherefore, the change that you will get from a 20-pound note is;Change = 20 - 16 = 4 pounds.it's important to note that the cost of 2 chickens and 3 boxes of stuffing is given by the total of the prices of each item

. Therefore, the cost of 2 chickens is given by 2 x 5 = 10 pounds, while the cost of 3 boxes of stuffing is given by 3 x 2 = 6 pounds. The total cost is obtained by adding the cost of chickens and stuffing;Total cost = 10 + 6 = 16 poundsGiven that the amount paid is 20 pounds, the change is obtained by subtracting the total cost from the amount paid. Therefore, the change is 20 - 16 = 4 pounds.

In conclusion, when you buy 2 chickens and 3 boxes of stuffing with a 20-pound note, you will get a change of 4 pounds. The total cost is obtained by adding the price of chickens and stuffing, while the change is obtained by subtracting the total cost from the amount paid.

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Answer:

Step-by-step explanation:

The hypotenuse is 200 meters.

The angle making the ground and the Hypotenuse is 7 degrees.

The trig relationship needed is the cosine.

Cos(7) = x / 200        Multiply both sides by 200

200*cos(7) = x

200* 0.9925 = x

x = 198.51

The calculator held the actual answer of cos(7)

Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.

If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.

b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.

c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.

All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.

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