If chicken wire comes in rolls that are 48 inches long, determine the smallest amount of rolls that will be needed to fence the garden

The area under the graph of the function f(x) = e^x over the interval [-2, 2] is approximately 13.77 square units.

To calculate the area under the graph of the function, we can use integration. In this case, we need to integrate the function f(x) = e^x with respect to x over the interval [-2, 2].

The definite integral represents the area under the curve between the given limits.

∫[a,b] e^x dx

Applying the integral, we have: ∫[-2,2] e^x dx

Using the rules of integration, we can evaluate this integral to find the area under the curve.

The antiderivative of e^x is e^x itself. Evaluating the integral at the upper and lower limits, we get: [e^x] from -2 to 2

Plugging in the values, we have: e^2 - e^(-2)

This is the exact answer in terms of e. To get the numerical approximation, you can substitute the value of e into the expression to get the approximate area.

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Answer:

\(\frac{4(x+8)}{5}\)

Answer:

17

Step-by-step explanation:

12 1/2-(-4 1/2)

12 1/2+ 4 1/2

17

Answer:

what are the answers?

Step-by-step explanation:

Otherwise it isn't answerable

Triangles A, B, and C have a scale factor less than 1 in common

The figure that completes the question is added as an attachment

From the figure, we can see that triangles A, B, and C are smaller than the original triangle i.e. the triangle D

This means that triangle D is dilated by a scale factor less than 1 to form each of these triangles

This has just a slight difference to (a)

From the figure, we can see that triangles E, F, and G are bigger than the original triangle i.e. the triangle D

This means that triangle D is dilated by a scale factor greater than 1 to form each of these triangles

The conclusion about the scale factors is that

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GIVEN

The function is given to be:

SOLUTION

The y-intercept of a function is the value of the function when x = 0.

Substitute for x = 0 into the function;

In coordinate form, the y-intercept of the function is (0, 4).

The LAST OPTION is correct.

A = old value = 3431

B = new value = 3732

C = percent change

C = [ (B-A)/A ] * 100%

C =  [ (3732-3431)/3431 ] * 100%

C = (301/3431) * 100%

C = 0.0877 * 100%

C = 8.77%

Note: if C was a negative value, then we'd have a percentage decrease

Answer:

1

Step-by-step explanation:

it goes up 1 over 1 so the slope is 1/1 or 1

By using the properties of the Fourier cosine transform and evaluating the integrals, the final result will be F[e^(-ax) * cos(ax)] = (a + ω)/(a^2 + ω^2)

(i) To find the Fourier cosine transform of e^(-ax) * cos(ax), we can use the definition of the Fourier cosine transform and perform the necessary calculations.

The Fourier cosine transform F[f(x)] of a function f(x) is given by:

F[f(x)] = ∫[0,∞] f(x) * cos(ωx) dx

In this case, f(x) = e^(-ax) * cos(ax). Substituting this into the Fourier cosine transform formula, we have:

F[e^(-ax) * cos(ax)] = ∫[0,∞] e^(-ax) * cos(ax) * cos(ωx) dx

To evaluate this integral, we can use trigonometric identities to simplify the integrand. By applying the double-angle formula for cosine, we get:

F[e^(-ax) * cos(ax)] = ∫[0,∞] e^(-ax) * (cos((a+ω)x) + cos((a-ω)x))/2 dx

Now we can split the integral into two parts:

F[e^(-ax) * cos(ax)] = (1/2) * ∫[0,∞] e^(-ax) * cos((a+ω)x) dx + (1/2) * ∫[0,∞] e^(-ax) * cos((a-ω)x) dx

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Answer:

198

Step-by-step explanation:

rectangular side (9,3)

9x3=27

27x2= 54 (because there's rectangular sides)

Square end(6,3)

6x3=18

18x2=36(two square sides)

top&bottom sides

6x9=54

54xsquared2=108(two sides)

add all together

54+36+108=198cm(squared)

To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:

1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n

Solution:

1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.

2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.

Now, we need to verify that the product of these series converges:

3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)

4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.

5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.

In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and

summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.

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Answer:

Step-by-step explanation:

1) e +3 ≥ 9

(e + 3) + (- 9) ≥ 9 + (- 9)

e + 3 - 9 ≥ 9 - 9

e ≥ 6

2) 21 ≥ 7i

7i ≤ 21

\(i\) E ( -\(_{ \infty}\) 3]

3) i - 13≥ 4

(i - 13) + 13 ≥ 4 + 13

\(i\) E( 17,\({ \infty}\))

4)  -8 ≥ i(-2)

-8 ≥ -i · 2

-8 ≥ -2i

\(i\) E [4, infinite)  (No solution)

Explanation

Step 1

to find the total area divide the figure

now, we need to find the area of the triangle

so, we need to find the hypotenuse of the triangle

so, the height of the triangle is 5 cm

Step 2

let

side of the square=6

heigth of the triangle=5

base of the triangle=6

I hope this helps you

Answer:

Jesse has the largest range between the two players. The difference between their ranges is 2.

Step-by-step explanation:

Jesse's range: 14

Barbara's range: 10

Range is determined by using the largest number and the smallest number in a set of integers and subtracting them. Jesse's highest number was 24, and his lowest would be 10. 24-10=14.

Barbara's highest score was 22, while her lowest was 12. 22-12=10.

subtracting Jesse's range from Barbara's range would equal 2.  

(please don't cook me if this is incorrect but i'm 97% sure i'm right)

The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Here, we have,

The Taylor series at x=0 for cos(x) is given by:

cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!

Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):

To find the Taylor series for the given function, we'll use power series operations.

We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.

Let's start with cos²((3πx)/2):

cos²((3πx)/2) = (cos((3πx)/2))²

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²

Expanding the square of the series, we get:

cos²((3πx)/2)

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Now, we'll multiply the x term to obtain the Taylor series for the given function:

x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Expanding the multiplication and rearranging the terms, we have:

x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

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Answer:

<7 58

<5 47

<6 75

<4 107

<8 73

<9 49

all triangles add up to 180 and all lines add up to 180

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Answer:

6

Step-by-step explanation:

Δy =6-0 =6

Δx = 2-1 =1

slope = 6/1 = 6

Answer:

Elle pourra réaliser 8 bouquets :

Chaque bouquet aura 2 fleurs rouges et 3 fleurs jaunes.

Explication:

Sara veut évidemment utiliser toutes les fleurs pour qu'il n'en reste pas. Elle doit trouver un nombre qui se divise en 16 et 24,

C'est juste une manière indirecte d'utiliser le HCF de 16 et 24, qui est 8.

16

=

2

×

8

24

=

3

×

8

Elle pourra réaliser 8 bouquets :

Chaque bouquet aura 2 fleurs rouges et 3 fleurs jaunes.

Step-by-step explanation:

The likelihood or probability that she will give the first student a blue calculator and the second student a yellow calculator is 6.6%.

The math teacher Mrs. Piatt has six black, nine yellow, and two blue calculators.

Therefore, the total number of calculators is 17.

The probability that she hands out a blue calculator to the first student is:

P₁ = Number of blue calculators/ Total number of calculator

P₁ = 2/17

Now, as a calculator is handed out to a student. Then the remaining number of calculators is 16.

Therefore, the probability that the second student gets a yellow calculator will:

P₂ = Number of yellow calculators/ Total number of calculators.

P₂ = 9/16

Therefore, the probability that she will hand out a blue calculator to the first student, then hand out a yellow calculator second will be:

P = P₁ × P₂

P = 2/17 × 9/16

P = 18/272

P = 0.06617647058

P = 6.6%

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There are 64 ways to choose a single class representative.

To find the total number of ways to choose a single class representative, we add the number of students in each college: 18 students from the College of Liberal Arts and Social Sciences, 19 students from the College of Education, and 27 students from the College of Science and Health.

This gives us a total of 18 + 19 + 27 = 64 students. To choose a single class representative, we can choose any one of these 64 students, so there are 64 ways to choose a single class representative.

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Answer:

C - Sarah reads 4 pages in the morning and 6 pages at night for two days.

Step-by-step explanation:

(4+6)*2

(10) - C is the only one where they (do) something that equals 10, and does it twice.

A - (6+2)*4

B - 4 + (6*2)

D - (4 + 6) + 2

In the language of modular arithmetic, we're given

\(x-3\equiv0\pmod7\implies x\equiv3\pmod7\)

\(y+3\equiv0\pmod7\implies y\equiv-3\equiv4\pmod7\)

Then x = 7a + 3 and y = 7b + 4 for integers a and b.

Substitute these into the quadratic expression and simplify:

\(x^2+xy+y^2+n\equiv0\pmod7\)

\((7a+3)^2+(7a+3)(7b+4)+(7b+4)^2+n\equiv0\pmod7\)

\(49a^2+42a+9+49ab+28a+21b+12+49b^2+56b+16+n \equiv 0\pmod7\)

\(37+n\equiv 0\pmod7\)

\(n\equiv-2\equiv5\pmod7\)

which means the smallest positive integer n we are looking for is 5.

There are 160 possibilities for area codes

We are required to find all the combinations for different area codes

It is given to us that the conditions for the tree digit area code are:

first digit could be any number from 4 through​ 8,

the second digit was either 4 5 6 or 7, and the third digit could be any number except 2 or 7

Using the conditions above, the digits which can be first digit of code = 4 through 8 =4,5,6,7,8

the digits which can be second digit of code= 4,5,6,7

the digits which can be third digit of code = 0,1,3,4,5,6,8,9

number of possibilities for first digit= 5

number of possibilities for second digit=4

number of possibilities for third digit= 8

Therefore, total number of possibilities of code   = number of possibilities of first digit x number of possibilities of second digit x number of possibilities of third digit = 5 x 4 x 8=160

Therefore, there are 160 possibilities for area codes

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Answer:

$8 for 3 pounds

cost for p pounds: 3.50p - 2.50

Step-by-step explanation:

Cost of 3 pounds:

Original cost = Cost per pound x 3

= 3.50 x 3

= 10.50

Coupon = 2.50

Final cost = Original cost - Coupon

= 10.50 - 2.50

= $8

Cost of p pounds:

Original cost = Cost per pound x p

= 3.50 x p

= 3.50p

Coupon = 2.50

Final Cost = Original Cost - Coupon

= 3.50p - 2.50

Ai Mi has to pay $8 to buy 3 pounds of chicken.  An expression for the cost to buy p pounds of chicken would be; 3.50p - 2.50

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The Cost of 3 pounds:

Thus Original cost = Cost per pound x 3

= 3.50 x 3

= 10.50

Also, we know that the Coupon cost is 2.50

The Final cost = Original cost - Coupon

= 10.50 - 2.50

= $8

Now Let the Cost of pounds is p

The Original cost = Cost per pound x p

= 3.50 x p

= 3.50p

Also the cost of the Coupon = 2.50

The Final Cost = Original Cost - Coupon

= 3.50p - 2.50

Hence, Ai Mi has to pay $8 to buy 3 pounds of chicken.  An expression for the cost to buy p pounds of chicken would be; 3.50p - 2.50

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Answer:

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

Step-by-step explanation:

The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.

For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

Answer:

you dont, just make a vertical line where you plotted your point

Step-by-step explanation:

I am going to explain this as best as i can because i dont really remember how to do this

My teacher taught it to me as:

y is fly

so when you get an equation like this but with a y you will plot the dot on the y axis and make a horizontal line

x is dive

when you get an equation like this one you will plot the dot (exactly how you did it) and make a vertical line on that dot

i dont really know how to explain so sorry if you dont understand, hope it helps

Answer:

18c

= 18(36)

=648

Hope this helps you

Answer:

Part H

How many holes need to be drilled for 36 parts? Show your work.

Step-by-step explanation:

18c

= 18(36)

= 648

Given:

The radius of the sphere is 4 cm.

To find: The volume of the sphere

Explanation:

The formula of the volume of a sphere is,

Substituting the values we get,

Final answer: The volume of the sphere is 267.95 cubic cm.