From the definition of the definite integral, we have lim _n →[infinity]3/n∑_k=1^n(6 k/n+sin(6 k π/n))=

The graph that matches the given linear inequality is (B) .

In the question ,

it is given that

the linear inequality is y \(>\) -x + 4

on rewriting the inequality

we get

x + y \(>\) 4

to plot the inequality , we need points to plot .

So ,when x = 0 , we have y = 4

and when y = 0 , we have x = 4

so the two points are (0,4) and (4,0) .

For shading the inequality , we put x = 0 and y = 0 ,

and get 0+0 > 4

0>4 , the result is False , So , the shaded region will be away from the origin which is shown in option (b) .

Therefore , The graph that matches the given linear inequality is (B) .

Learn more about Inequalities here

https://brainly.com/question/26591602

#SPJ1

The time it takes to read this question is a continuous random variable; the number of marshmallows that can fit into your mouth is a discrete random variable.

The time it takes for an individual to read a question can be considered as a continuous random variable. It is typically measured on a continuous scale and can take on any value within a given range. For example, it may take someone 10 seconds to read a question, while it might take another person 20 seconds. The time it takes to read a question can vary continuously.

On the other hand, the number of marshmallows that a person can fit into their mouth can be considered as a discrete random variable. It is measured on a discrete scale and can only take on whole number values. For instance, a person may be able to fit 2, 3, or 4 marshmallows into their mouth, but they cannot fit a fractional or continuous number of marshmallows. The number of marshmallows is limited to specific integer values, making it a discrete random variable.

for such more question on random variable

https://brainly.com/question/16730693

#SPJ11

The area of rectangle is found to be 117 sq. yd.

Let the length of rectangle be L:

The, the width is W + 4 = L

Perimeter = 2(length + width)

P = 2(L + B)

P = 2(W + 4 + W)

P = 2(2W + 4)

40 = 4W + 4

4W =36

W = 9

The, L = 9 + 4 = 13 yd.

Area = length * width

Area = 9*13

Area = 117

Thus, the area of rectangle is found to be 117 sq. yd.

To know more about the perimeter of the rectangle, here

https://brainly.com/question/10452031

#SPJ4

Answer:

Step-by-step explanation:

The perimeter of a rectangle is the total circumference of the rectangle.

Perimeter=2(Length + breadth)

Perimeter=40yd

Length=x+4 and breadth=x

40=2(x+x+4);

40=4x+8;

4x=32 and x=8yd

So, length=12yd and breadth=8yd.

Area = length*breadth

So Area = 12*8= 96ydsq

To know more about perimeter of rectangle: https://brainly.com/question/30243597

#SPJ4

Answer:

Step-by-step explanation:

7 feet   1 foot is 12 inches

7*12= 84 inches.

None of the choices are correct.

90 inches is 7.5 feet

62.5 inches is 5.2 feet

75 inches is 6.25 feet

Answer:

x³ + 11x² + 18x

Step-by-step explanation:

(x² + 2x)(x + 9)

Step 1: Distribute x²+2x into x + 9.

x³ + 2x² + 9x² + 18x

Step 2: Combine like terms.

x³ + 11x² + 18x

The area of this rectangle is x³ + 11x² + 18x.

Answer:

Area= height x width = (x + 9) (x^2 + 2x) = x^3 + 2x^2 + 9x^2 + 18x = x^3 + 11 x^2 + 18x

Step-by-step explanation:

The height is (x + 9) and the width is (x^2 + 2x) and the the area of the rectangle is equal to: Area= height x width = (x + 9) (x^2 + 2x) = x^3 + 2x^2 + 9x^2 + 18x = x^3 + 11 x^2 + 18x

The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

The figure is divided into two parts one is a rectangle and the second is a semicircle.

Area of figure = Area of rectangle + Area of a semicircle

Area of figure = L × B + (πr²/2)

A = 10 cm × 15 cm + (3.14 ×(5)^2/2)

A= 189.25 cm²

Hence the area of the shape will be 189.25 cm²

To learn more about the area, refer to the link;

https://brainly.com/question/11952845

#SPJ1

Answer: 0.65

Step-by-step explanation:

Two angles are said to be complementary angles when the sun of their angles will be equal to 90°. In this case, since the angle given is 75°, then the other angle will be:

= 90° - 75°

= 15°

Therefore, we'll then find the sine of 15° which will be:

= Sine 15°

= 0.65

Therefore, the correct option is A.

Answer: 7/12

Step-by-step explanation:

12/12-5/12=7/12

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is 18%.

To find the percent of the total area between two z-scores, we need to calculate the area under the standard normal curve between those two z-scores.

Using a standard normal distribution table or a statistical software, we can find the area to the left of each z-score and subtract the smaller area from the larger area to find the area between the z-scores.

For z = -1.5, the area to the left of z = -1.5 is approximately 0.0668.

For z = -0.7, the area to the left of z = -0.7 is approximately 0.2420.

The area between z = -1.5 and z = -0.7 is:

Area between z = -1.5 and z = -0.7 = Area to the left of z = -0.7 - Area to the left of z = -1.5

= 0.2420 - 0.0668

= 0.1752

To convert this area to a percentage, we multiply by 100:

Percentage of the total area between z = -1.5 and z = -0.7 = 0.1752 * 100 ≈ 17.52%

Rounding to the nearest integer, the percent of the total area between z = -1.5 and z = -0.7 is 18%.

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is approximately 18%.

To know more about percent , visit;

https://brainly.com/question/31323953

#SPJ11

Answer:

1. B: 47°

2. D: 41°

3. D: 22°

4. D: 80°

5. A: 32°

Step-by-step explanation:

Hope this helps!

Answer:

i think the answer is B

Step-by-step explanation:

sorry if this was wrong hoped i helped tho

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

The answer for the first one is 3 times

the answer for the second one is 9

Step-by-step explanation:

Answer:

25 cm^2

Step-by-step explanation:

The formula for the area of a triangle is \(1/2*base*height\).

We're given the base and height (altitude) in this question. The base is 10 cm and the height is 5 cm. All we have to do is plug them in to the formula now.

\(1/2*10*5\)

\(1/2*50\)

\(25\)

Answer: 334

Step-by-step explanation:

Cut the polygon into 2 pieces

Find the area of each rectangle and some it

7*10 = 70

24*(21-10) = 264

264 + 70 = 334

Answer:

334 ft²

Step-by-step explanation:

split the polygon into two

Area of A = 21 ft × 7 ft = 147 ft²

Area of B = (21 ft - 10 ft) × (24 ft - 7 ft)

Area of B = 11 ft × 17 ft = 187 ft²

Area of polygon = sum of Areas of A and B

147 ft² + 187 ft² = 334 ft²

The most common denominator of 892.5, 87.5, 4200, 396.25, and 5440 is 1000.

Least Common Denominator(LCD):

When two or more fractions have the same denominator, they are called common divisors. The least common divisor (LCD) is the smallest number that is a common divisor of a given set of fractions. For addition and subtraction of fractions and for comparing two or more fractions, the given fractions must have a common denominator.

Given by the question.

To Find:  the common denominator of these numbers; we have to represent them all as fractions with a common denominator.

First, we notice that 892.5 and 87.5 both have a denominator of 10. We can convert them to fractions with a denominator of 1000 as follows:

892.5 = 892.5/10 = 89.25/1000

87.5 = 87.5/10 = 8.75/1000

Next, we notice that 4200 and 5440 are both multiples of 10. We can convert them to fractions with a denominator of 1000 as follows:

4200 = 4200/10 = 420/100 = 42/10 = 42/1000

5440 = 5440/10 = 544/100 = 54.4/10 = 544/1000

Finally, 396.25 can be expressed directly as a fraction with a denominator of 1000:

396.25 = 396.25/1 = 39625/1000

Now that we have represented all numbers as fractions with a denominator of 1000, we can find their common denominator, which is 1000, by finding the least common multiple (LCM) of their denominators.

Learn more about Denominator:

https://brainly.com/question/7067665

#SPJ4

Answer: (If you are multiplying 1 2/3 by 1/3 this is for you.)

The simplest answer is 5/9.

Step-by-step explanation: First, turn the mixed number into an improper fraction. Ex: 1 2/3 --> 5/3 (The easiest way is to multiply your whole number by the denominator and add you answer to the numerator.

Ex: 1 x 3 (three is the denominator, one is the whole number.) Then add you answer to the numerator.

Ex: 3 is the answer for the multiplication step, 2 is the denominator. You sum is 5. Rewrite that as a fraction over the original denominator. You should get 5/3. Then last multiply your 2 fractions, 5/3 x 1/3 = 5/9.

Answer:

b=2 a=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 8x + 6

2(4x+3)

2.4x+2

2(2x +1)

Answer:

\(\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}\)

1. \(\boxed{Factorise \ = \ 8x + 6}\)

⎆To factorise this, you have to take the common factor out. In this case, it's 2.

\(8x + 6 \\ = 2(4x + 3)\)

\(\boxed{Answer \ = \ 2(4x + 3)}\)

2) \(\boxed{Factorise \ = \ 4x + 2}\)

⎆To factorise this, you have to take the common factor out. In this case also, it's 2.

\(4x + 2 \\ = 2(2x + 1)\)

\(\boxed{Answer \ = \ 2(2x + 1)}\)

____________________

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

ღ \(RainbowSalt2^{2}2^{2} \)

In this case, the displacement of the particle at time t is given by ∫ v(t) dt, and the displacement after 120 seconds is given by ∫_0^120 v(t) dt.

The integral of |v(t)| over the time interval [0, 120] gives the total distance traveled by the particle during that time.

Specifically, the value of the integral gives us the difference between the velocity of the particle at time t=120 and its velocity at time t=0.

a) The integral 120 ∫ v(t) dt represents the displacement of the particle from its starting point after 120 seconds, assuming that its initial displacement is zero. This can be seen by the fundamental theorem of calculus, which states that if F(x) is an antiderivative of f(x), then ∫ f(x) dx = F(b) - F(a), where a and b are the limits of integration. In this case, the displacement of the particle at time t is given by ∫ v(t) dt, and the displacement after 120 seconds is given by ∫_0^120 v(t) dt.

b) The integral 120 ∫ |v(t)| dt represents the distance that the particle travels in 120 seconds. This is because |v(t)| represents the magnitude of the velocity, or speed, of the particle at time t, regardless of its direction. Thus, the integral of |v(t)| over the time interval [0, 120] gives the total distance traveled by the particle during that time.

c) The integral 120 ∫ a(t) dt represents the change in velocity of the particle over the time interval [0, 120]. This can be seen by the fundamental theorem of calculus, which tells us that if f(x) is the derivative of g(x), then ∫ f(x) dx = g(x) + C, where C is a constant of integration. In this case, a(t) is the derivative of v(t), so the integral of a(t) over the time interval [0, 120] gives us the change in velocity of the particle during that time. Specifically, the value of the integral gives us the difference between the velocity of the particle at time t=120 and its velocity at time t=0.

To learn more about velocity visit:

https://brainly.com/question/18084516

#SPJ11

6. False. The present value (PV) is the initial investment or the amount invested in the stock, which is $7,500, not the amount received today ($8,050).

7. $1,200 represents the variable PMT (Payment). It represents the total dividends received over the four-year period.

8. The future value (FV) amount is $8,050, which is the amount received from selling the stock today.

9. It is not necessary to clear the TVM (Time Value of Money) registers when the calculations are completed, and you don't need to perform any further calculations.

10. True. When the "periods per year" register is set to 1, the periodic rate (interest rate) should be entered directly into the i-register as a decimal value, such as 0.05 for 5%.

Therefore, the PV is not $8,050 but $7,500, representing the initial investment. The variable $1,200 represents the PMT (payment) or the total dividends received. The FV amount is $8,050, the selling price of the stock. Clearing the TVM registers is not necessary after completing calculations, and when "periods per year" is set to 1, the periodic rate is entered directly into the i-register.

Learn more about initial investment visit:

https://brainly.com/question/29726908

#SPJ11

Answer:

3ZSM 1

Step-by-step explanation:

THE FASTEST LEARNING TO HAVE ANSWERS

Answer:

10-

Step-by-step explanation:

Answer:

Don’t really know what the question is, but these are the answers for x

The solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

To fathom the given differential equation, xy'' + y' = 0, we will begin by expecting a control arrangement of the frame y = ∑(n=0 to ∞) a_nx^n, where a_n speaks to the coefficients to be decided.

Separating y with regard to x, we get:

\(y' = ∑(n=0 to ∞) a_n(nx^[(n-1))] = ∑(n=0 to ∞) na_nx^[(n-1)]\)

Separating y' with regard to x, we get:

\(y'' = ∑(n=0 to ∞) n(n-1)a_nx^[(n-2)]\)

Presently, we substitute these expressions for y and its subsidiaries into the differential condition:

\(x(∑(n=0 to ∞) n(n-1)a_nx^[(n-2))] + (∑(n=0 to ∞) na_nx^[(n-1))] =\)

After improving terms, we have:

\(∑(n=0 to ∞) n(n-1)a_nx^[(n-1)] + ∑(n=0 to ∞) na_nx^[n] =\)

Another, we compare the coefficients of like powers of x to zero, coming about in a boundless arrangement of conditions:

For n = 0: + a_0 = (condition 1)

For n = 1: + a_1 = (condition 2)

For n ≥ 2: n(n-1)a_n + na_n = (condition 3)

Disentangling condition 3, we have:

\(n^[2a]_n - n(a_n) =\)

n(n-1)a_n - na_n =

n(n-1 - 1)a_n =

(n(n-2)a_n) =

From equation 1, a_0 = 0, and from equation 2, a_1 = 0.

For n ≥ 2, we have two conceivable outcomes:

n(n-2) = 0, which gives n = or n = 2.

a_n = (minor arrangement)

So, the solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

Learn more about differential equations here:

https://brainly.com/question/28099315

#SPJ1

The area of triangle ABC, given that angle A is 20 degrees, side b is 13 inches, and side c is 7 inches, is approximately 42 square inches (rounded to the nearest whole number).

To find the area of triangle ABC, we can use the formula:

Area = (1/2) * b * c * sin(A),

where A is the measure of angle A,

b is the length of side b,

c is the length of side c,

and sin(A) is the sine of angle A.

Given that A = 20 degrees, b = 13 inches, and c = 7 inches, we can substitute these values into the formula to calculate the area:

Area = (1/2) * 13 * 7 * sin(20)= 41.53≈42 square inches.

To learn more about triangle visit:

brainly.com/question/2773823

#SPJ11

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

\(dy/dx = x(1 + ln x) (x - 2)^2 / 2\)

\(y = 3√x(x − 2) * x^2 * (1 + ln(x))\)

To find the derivative of y using logarithmic differentiation.

The formula to be used is given below,

\(dy/dx = y * (ln(dy/dx))\) ........(1)

Take natural logarithms of both sides of the given equation to get the following equation,

\(ln(y) = ln(3√x(x − 2)) + ln(x^2) + ln(1 + ln(x))\)

Differentiate with respect to x on both sides of the above equation and simplify,

\(1/y * dy/dx = 1/3√x(x − 2) * 3/2 (x-2) * (1/x) + 2/x + 1/x (1/1 + ln(x))\)

\(dy/dx = y * (1/y * dy/dx)\)

\(dy/dx = 3√x(x − 2) * x^2 * (1 + ln(x)) * (1/3√x(x − 2) * 3/2 (x-2) * (1/x) + 2/x + 1/x (1/1 + ln(x)))\)

Thus, \(dy/dx = x(1 + ln x) (x - 2)^2 / 2\)

To know more about derivative refer here:

https://brainly.com/question/29144258#

#SPJ11

Answer:

acute

Step-by-step explanation:

Answer:

Complementary angle pair is here working