A fence must be built to enclose a rectangular area of 5000 ft^2. Fencing material costs $3 per foot for the two sides facing north and south and $6 per foot for the other two sides. Find the cost of the least expensive fence. The cost of the least expensive fence is $ (Simplify your answer.)

The gardener used 40.5 gallons of gasoline in his lawn mowers in the one month.

Let's say the amount of gasoline used in the lawn mowers is x gallons.

Then, the rest of the gasoline (61.5 - x) would have been used for other purposes.

Since the total amount of gasoline used is 61.5 gallons, we can set up an equation:

x + (61.5 - x) = 61.5

Simplifying this equation, we get:

x + 61.5 - x = 61.5

Combining like terms, we get:

61.5 = 61.5

This equation is true, so we know that our assumption that x is the amount of gasoline used in the lawn mowers is correct.

Therefore, the gardener used x = 40.5 gallons of gasoline in his lawn mowers in the one month.

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The letters of all applicable properties Linear ,Nonlinear ,Separable ,Homogeneous

i) y′ = 3xy/(x^2 -5xy)

Linear,

Separable

ii) y′ = x^3 y^2

Nonlinear,

Separable.

iii) y′ = xy

Separable,

Homogeneous

iv) y′ = y/x

Separable,

Homogeneous

v) y′ = ex

Nonlinear

vi) y′ + 3xy = tan^-1(x)

Linear

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Answer:

n=26

n=33

Step-by-step explanation:

The edge length is 22 inches, the rate at which the cube's volume is changing is 1056 cubic inches/second.

Given that a cube's surface area increases at a rate of 32 square inches per second and the edge length is 22 inches, the rate of change of the cube's volume is required to be determined. Here, the surface area of a cube is given by:SA = 6a²Differentiating w.r.t time t, we have: d/dt (SA) = d/dt (6a²)⇒ d(SA)/dt = 12a da/dt Also, the volume of a cube is given by: V = a³

Differentiating w.r.t time t, we have: d/dt (V) = d/dt (a³)⇒ d(V)/dt = 3a² da/dt. It is given that d(SA)/dt = 32 square inches per second When the edge length is 22 inches, then a = 22 inches. Putting the values in the above equations, we get: d(SA)/dt = 12a da/dt⇒ 32 = 12(22) da/dt⇒ da/dt = 4/3 inches/second d(V)/dt = 3a² da/dt⇒ d(V)/dt = 3(22²) (4/3)⇒ d(V)/dt = 1056 cubic inches/second.

Therefore, when the edge length is 22 inches, the rate at which the cube's volume is changing is 1056 cubic inches/second.

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high length:6mletngh of shadow =2~3mø is angle ofelevation

Step-by-step explanation:

hope it helps

The molar volume of ethane at 300 K and 200 atm, calculated using the Van der Waals equation of state, is approximately 0.109 L/mol.

To calculate the molar volume, we need to solve the cubic equation obtained from the expanded Van der Waals equation of state:

V^3 - (b + pRT)V^2 + (pa)V - pab = 0

Given the values of a = 5.5088 L^2 atm mol^(-2) and b = 0.065144 L mol^(-1) for ethane gas, and the temperature T = 300 K and pressure p = 200 atm, we can substitute these values into the cubic equation.

Substituting the values into the equation, we have:

V^3 - (0.065144 + (200)(0.0821)(300))V^2 + (5.5088)(200)V - (200)(0.065144)(5.5088) = 0

Solving this cubic equation, we find that one of the roots corresponds to the molar volume of ethane at the given conditions, which is approximately 0.109 L/mol.

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After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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To calculate the expected value of perfect information (EVPI) for the given payoff table, we first need to determine the expected value with perfect information (EVWPI) and then subtract the maximum expected value under the current decision-making scenario.

Therefore, the expected value of perfect information (EVPI) for this payoff table is approximately -$9.08. This value represents the potential benefit of having perfect information about the states of nature in making decisions, taking into account the difference between the best decision under perfect information and the best decision without perfect information.

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\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=65\pi \end{cases}\implies 65\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi}\cdot 65\pi =r^3 \\\\\\ \cfrac{195}{4}=r^3\implies \sqrt[3]{\cfrac{195}{4}}=r\implies 3.65\approx r\)

Answer:

46°

Step-by-step explanation:

from large triangle:

let the third unknown angle be 'a'

then,

a+x+7+85=180

a=88-x

now,from small triangle,

let the third unknown angle be 'b'

then,

b+x+2x=180

b=180-3x

b=a (vertically opposite angles)

then,

180-3x=88-x

2x=92

x=46

Answer:

12

Step-by-step explanation:

Answer: B

Step-by-step explanation:

because I took this test

Answer:

3(h + 6)

Step-by-step explanation:

Since we are starting with

h•3 + 6•3, try to see that there are two terms here h•3 and 6•3. In both of these terms is the factor 3. We can factor out the 3. This leaves behind (h + 6).

h•3 + 6•3

= 3(h + 6)

Its like "un-distributive" property. (this is not a technical term)

Answer: 38 miles per gallon ; 342 miles.

Step-by-step explanation:

The miles/gallon that he got on the trip will be:

= 228/6

= 38 miles per gallon.

When he used 9 gallons of gas, the distance travelled will be:

= 38 × 9

= 342 miles

Answer:

Question :

Jamar drove 228 miles and used 6 gallons of gas.

Solution :

a) How many miles/gallon did he get on the trip?

\({\implies{\sf{\dfrac{228}{6}}}}\)

\({\implies{\sf{ \cancel{\dfrac{228}{6}}}}}\)

\({\implies{\sf{\underline{\underline{\red{36 \: miles/gallon}}}}}}\)

Hence, he get 38 miles/gallon for his trip.

\(\rule{200}2\)

b) On another trip, he used 9 gallons of gas. How far did he travel?

\({\implies{\sf{38 \times 9}}}\)

\({\implies{\sf{\underline{\underline{\red{342 \: miles}}}}}}\)

Hence, he traveled 342 miles by using o gallon og gas.

\(\underline{\rule{220pt}{3pt}}\)

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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Answer:The answe would be 5 cause the 0 doesn't count

Step-by-step explanation:

Answer:

y = 0.30x + 200 and The price of airfare increases by $0.30 for each mile traveled.  

Step-by-step explanation:

the person above is incorrect

Answer:

y = 0.30x + 200

Step-by-step explanation:

Hope that helped :)

Yes, every rational function has a vertical asymptote.

A rational function is defined as a fraction of two polynomials such as P(x)/Q(x) where Q(x) ≠ 0.

A vertical asymptote is a vertical line that the graph of a function approaches but never touches.

It happens when the denominator of a rational function Q(x) = 0, so the fraction becomes undefined.

Therefore, the denominator of a rational function becomes zero at some point or several points in its domain, which results in a vertical asymptote.

For example, consider the following rational function f(x) = (3x² - 5x + 2)/(x - 1)(x + 2)

The denominator (x - 1)(x + 2) becomes zero when x = 1 or x = -2, so the rational function has two vertical asymptotes at x = 1 and x = -2.

Therefore, it can be concluded that every rational function has a vertical asymptote.

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For an integral value of \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ \) and

\(I_2 = \int_{ 1}^{-2} f(x)dx = -10 \\ \), the computed value of integral \(\int_{ 1}^{3} f(x)dx\) is equals to the -6. So, option(c) is right one.

In mathematics, an integral is the continuous process of a sum, which is used to calculate areas, volumes, and their properties. Integration is a way to sum up parts to the whole.

We have an integral say \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ \)

\(I_2 = \int_{ 1}^{-2} f(x)dx = 10 \\ \)

We have to determine value of \(\int_{ 1}^{3} f(x)dx\).

Using the properties of integral, consider integral \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18\\ \)

from distribution property, \(I_1 = \int_{ -2}^{3} 2f(x) dx + \int_{ -2}^{3} 2 dx = 18 \\ \)

\(2 \int_{ -2}^{3} f(x) dx + [ 2x]_{ -2}^{3} = 18\)

\(2 \int_{ -2}^{3} f(x) dx + 10 = 18\)

\(2 \int_{ -2}^{3} f(x) dx = 8\)

\(\int_{ -2}^{3} f(x) dx = 4\)

Now, consider the required integral and rewrite, \(\int_{ 1}^{3} f(x)dx = \int_{ 1}^{-2} f(x)dx + \int_{ -2}^{3} f(x)dx \\ \)

Substitute all known values of integrals

\(\int_{ 1}^{3} f(x)dx = 10 + 4 = 14 \)

Hence, required value is 14.

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Isolationism is what identified America in that moment.

Hope this helps!

Have a fabulous day!

Answer:

Step-by-step explanation:

Answer:

The answer is letter D.

why?

Step-by-step explanation:

Id.k -_-

j0ke

=

2

π

r

=

2

π

3

≈

18.84956

and that's it

HOPE IT HELPS

(FROM CROSS)

Answer:

A

Step-by-step explanation:

The student must have thought that every single arrowhead is a line of symmetry, so since there are 10 arrowheads, there must be 10 lines of symmetry. This is incorrect because if you look closely at the diagram, each line has 2 arrowheads, so the student is overcounting by a factor of 2. They should have just counted the number of lines, not arrowheads. Therefore, there must be 10/2 = 5 lines of symmetry, not 10. Hope this helps!

Answer:

\( \sqrt[3]{1000} = 10\)

So the radius of the sphere is 10/2 = 5 inches.

The volume of this sphere is

(4/3)π(5³) = 500π/3 cubic inches.

Answer: To check a solution, you can substitute the solutions into the equations and verify that both equations are true.

Step-by-step explanation:

Answer:

c or d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Slope- intercept form:

In the process of solving it was found that:

The equation therefore is:

Correct choice is D

To solve the system of equations using elimination, we can manipulate the equations by adding or subtracting them to eliminate one variable at a time.

12. Given the equations:

2x - 5y = -12

4x + 5y = 6

Adding these two equations eliminates the variable y:

(2x - 5y) + (4x + 5y) = -12 + 6

6x = -6

x = -1

Substituting the value of x into either of the original equations, we can solve for y:

2(-1) - 5y = -12

-2 - 5y = -12

-5y = -10

y = 2

Therefore, the solution to the system of equations is x = -1 and y = 2.

13. Given the equations:

3x - 4y = -8

3x - y = 10

Subtracting the second equation from the first equation eliminates the variable x:

(3x - 4y) - (3x - y) = -8 - 10

3y = -18

y = -6

Substituting the value of y into either of the original equations, we can solve for x:

3x - (-6) = 10

3x + 6 = 10

3x = 4

x = 4/3

Therefore, the solution to the system of equations is x = 4/3 and y = -6.

The remaining systems of equations can be solved using a similar approach by applying the elimination method to eliminate one variable at a time and then solving for the remaining variables.

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Answer:

83.2 miles

Step-by-step explanation:

what i had to do was multiply 7.3 by 13 and that was 94.9 that was as close as i could get it to 100 so i then multipled 6.4 by 13 and got 83,2 miles

The algebraic expression that corresponds to the sentence "I think of a number, subtract 4, then divide by three" is given as follows:

(n - 4)/3.

The sentence for this problem is given as follows:

"I think of a number, subtract 4, then divide by three".

The number is unknown, hence the variable used to represent the number is given by n.

Then the subtraction of the number n by 4 is represented by the expression presented as follows:

n - 4.

The division of the entire expression by 3 means that the parenthesis has to be applied to (n - 4), due to the precedence of operators, hence:

(n - 4)/3.

The problem asks for the algebraic expression that represents the sentence.

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Answer:

to get your answer you have to. Then after that, and finally