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The largest area that can be enclosed by a fence of 240 m and a wall is 7200m²

It is given that the rectangular area will be fenced up against a long rectangular wall. Therefore, the fencing will be done on just three sides.

Let one side be x

Then the side opposite to it must be x cm as well

The sum of the three sides should be equal to 240 m

Hence the third side must be 240 - 2x m

Therefore the area of the region fenced must be

A = x(240 - 2x)

or, A = 240x - 2x²

Now we need to maximize the above equation

Taking the first derivative zero we get

A' = 0

or, 240 - 4x = 0

or, 60 - x = 0

or, x = 60

Now we will test whether the above output is maximum or not. The second derivative of A is

A'' = -4

Since A'' is a constant function,

Now, A''(60) = -4

Therefore, the maximum side will have lengths of 60 m and 120 m.

Hence the largest area that can be enclosed with the fence is

60 X 120 m²

= 7200 m²

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Answer:

2160°

Step-by-step explanation:

We have,

Number of Sides, n = 14

So,

Sum of all interior angle = pi ( n - 2 )

or, Sum of all interior angle = pi ( 14 - 2 )

or, Sum of all interior angle = 12 pi radians.

We know,

1 radian = ( 180 / pi ) (degree)

or, 12 radians = 2160 (degree)

The account balance at the end of two years (eight quarters) is $866.24.

Suki earned $66.24 interest during that time.

What do you mean by interest rate?

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.

According to data in the given question,

We have:

Placed amount= A= $800

Interest rate (quarterly)= r= 4%

Time= t = 2 years

Now, we will using the formula below:

[tex]A=P(1+\frac{r}{n} )^{nt}\\=800(1+\frac{0.04}{4} )^{4*2}\\=800(1+0.01 )^{8}\\=800(1.0828)\\=866.24[/tex]

So, the account balance at the end of two years (eight quarters) is $866.24.

Then, we have to determine the earned interest during that time,

Earned interest= A-P

= 866.24 - 800

= 66.24

Therefore, she earned $66.24 interest during that time.

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The circumference is 27.004 and the Area is 58.0586 calculated for the circle with radius of 4.3 and π = 3.14

The circumference of a is the arc length of the circle with the formula 2πr. While the area of a circle is calculated with formula πr²

Given radius r = 4.3 and π = 3.14

circumference = 2 × 3.14 × 4.3

circumference = 27.004

Area of the circle = 3.14 × 4.3²

Area of the circle = 3.14 × 4.3 × 4.3

Area of the circle = 58.0586

Therefore, the circumference and area of the circle with radius of 4.3 is 27.004 and 58.0586 respectively.

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This proves that the sum of 1/2n(n+1) + 1/2(n+1)(n+2) is always a square number.

When a number is multiplied by itself, the result is a square number. As an illustration, 25 is a square number as it is composed of 5 groups of 5, or 5 x 5. A square number, sometimes known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number as it equals 32 and is represented by the symbols 3.

Here,

Find the sum:

=1/2n(n+1) + 1/2(n+1)(n+2)

=1/2(n² + n) + 1/2(n² + 3n + 2)

=1/2(n² + n + n² + 3n + 2)

=1/2(2n² + 4n + 2)

=n² + 2n + 1

=(n + 1)²

This demonstrates that 1/2n(n+1) + 1/2(n+1)(n+2) is always a square number when added together.

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The length of BC rounded to 3 decimal places is 4.307 meters.

It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the base and perpendicular. Mathematically -

h² = p² + b²

We have the following length and angle as shown in the figure -

[x] = AB = 8.1

θ = ∠BAC = 28°

Using the tangent rule we can write -

tanθ = BC/AB

BC = AB tanθ

BC = 8.1 x tan(28°)

BC = 4.307

Therefore, the length of BC rounded to 3 decimal places is 4.307 meters.

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The explicit formula for the arithmetic sequence an = 15 + 5(n - 1) in function form is; aₙ = 5n + 10

The explicit formula for an arithmetic sequence is usually expressed as;

an = a + (n - 1)d

It could also be that any term of the sequence can be computed, without even knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic sequence.

We are given that the arithmetic sequence is represented by;

aₙ = 15 + 5(n - 1)

To write in function form, we apply distributive property to the terms within the bracket (parentheses) to get:

aₙ = 15 + 5n - 5

Rearranging gives us;

aₙ = 15 - 5 + 5n

aₙ = 5n + 10

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Complete question is;

Which represents the explicit formula for the arithmetic sequence an=15+5(n−1) in function form?

A

f(n)=5n+15

B

f(n)=n+20

C

f(n)=5n+10

D

f(n)=n+10

The linear equation representing the total amount of money Felipe makes every month be

y = x + 1000

Given, Felipe is paid $1,000 every month plus an additional bonus for every tractor he sells, x.

Let the total amount of money be, y

as, felipe gets a fixed amount i.e. $1000 every month.

now, let felipe gets 'x' amount as the additional bonus.

So, the linear equation be,

y = 1000 + x

Hence, the linear equation representing the total amount of money Felipe makes every month be

y = x + 1000

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The measurement closest to the side of this sign is 15 inch.

Area of Square is a², where 'a' is the length of a side of a square.

The Area of square is 219 in²,

Therefore, a²=219

Adding square roots to both sides..

√a² = √219

a = 14.798

    =15 inches (nearest value)

Hence, the closest value of the side is 15 inches.

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The 90% confidence interval for the mean is (264.6935,275.5065)

A confidence interval (CI) in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified confidence level; the 95% confidence level is the most frequent, but other levels, such as 90% or 99%, are occasionally used. The confidence level denotes the long-run proportion of related CIs that include the true value of the parameter. For example, 95% of all intervals generated at the 95% level should contain the parameter's true value.

From the given data ,

Sample mean = X = 270.1

Sample standard deviation = s = 9.3268

n = 10

Therefore , the 90% confidence interval for the mean is ,

[tex]\bar{X}[/tex]±[tex]t_{n-1,\alpha /2}[/tex](s/√n)

270.1 ± [tex]t_{10-1.0.10/2}[/tex](9.3268/√10)

270.1 ±1.8331 ×2.9494

270.1 ± 5.4065

(264.6935,275.5065)

Therefore, the 90% confidence interval for the mean is (264.6935,275.5065)

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The complete question is:

"The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport. 269 255 267 285 274 275 266 258 271 281

(a) Compute a 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles. (Round your answers to three decimal places.)"

The expression equivalent to (5z² + 3z + 2)² is 25x⁴ + 30z³ + 29z² + 12z + 4.

The correct answer option is option D

(5z² + 3z + 2)²

(5z² + 3z + 2) (5z² + 3z + 2)

= 25z⁴ + 15z³ + 10z² + 15z³ + 9z² + 6z + 10z² + 6z + 4

= 25x⁴ + 15z³ + 15z³ + 10z² + 9z² + 10z² + 6z + 6z + 4

= 25x⁴ + 30z³ + 29z² + 12z + 4

In conclusion, the equivalent expression is 25x⁴ + 30z³ + 29z² + 12z + 4.

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I would choose the western side to climb because it is less steep then others.

In mathematics, a line's steepness is determined by its slope (or gradient). The slope is the ratio of any two points on a line's vertical and horizontal distances. A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical. If a line rises from left to right, it is said to be increasing.

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The probability of getting a number < 9 is 28/37.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. It has a range from 0 to 1.

Probability(Event) = Favorable Outcomes / Total Outcomes

Main Body:

Total numbers on the spinner greater than 9  = 37 - 10 + 1 = 28

(we are subtracting 10 because we need number that is greater than 10.)

and adding 1 because both the ends of interval is counted.

total numbers on spinner =37

P( x>9) = 28/37.

Hence the probability of getting a number greater than 9 on spinning is 28/37.

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Answer:

I can’t be confident at all; this is about as close to a random guess as you can get.

Step-by-step explanation:

A correlation coefficient of 0 ⇔ no linear relationship

Answer:y=-6x+34

Step-by-step explanation: I hope this helps

The original Length is, 6500 m.

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x is 6.215 km and the total time taken for the whole journey is 3.61 hours.

Boat's speed in still water = u = 4 km/h

Speed of stream = v

Distance between A and B = 5 km

Upstream speed = u - v

                            = 4 - v

Time taken = [tex]T_{1}[/tex] = [tex]\frac{5}{4-v}[/tex]

Downstream speed = x = u + v

                                       = 4 + v

Time taken = [tex]T_{2}[/tex] = [tex]\frac{5}{4+v}[/tex]

According to question,

      [tex]T_{1}= T_{2}+2[/tex]

    [tex]\frac{5}{4-v}=\frac{5}{4+v}+2[/tex]

    [tex]\frac{5}{4-v}=\frac{5+2(4+v)}{4+v}[/tex]

    [tex]\frac{5}{4-v}=\frac{5+8+2v}{4+v}[/tex]

5(4+v) = (13+2v)(4-v)

20+2v = -2[tex]v^{2}[/tex]-5v+52

[tex]2v^{2}+10v-32 = 0[/tex]

[tex]v^{2}+5v-16 = 0[/tex]

v = 2.215 or -7.215

Speed can't be negative.

Therefore, v = 2.215

Upstream speed = 4 - 2.215

                            = 1.785 km/h

Downstream speed = 4 + 2.215

                                 = 6.215 km/h

[tex]T_{2}[/tex] = 5/6.215

    = 0.805 h

[tex]T_{1}[/tex] = 2 + 0.805

   = 2.805 h

Total time = 2.805 + 0.805

                 = 3.61 h

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The solutions of the expressions -(-1), -|-1|, -|1|, |1|, and |-1| are 1, -1, -1, 1, and 1.

We are given five expressions. An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. The first expression is -(-1). The simplified solution of the first expression is 1. The second expression is -|-1|. The simplified solution of the first expression is -1. The third expression is -|1|. The simplified solution of the first expression is -1. The fourth expression is |1|. The simplified solution of the first expression is 1. The fifth expression is |-1|. The simplified solution of the first expression is 1.

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Answer:

Step-by-step explanation:

Inverse matrix:

The equivalent Algebraic Expression is represented by  [ (1.5)³/(1.3)⁴ ]⁻⁶  .

An Algebraic Expression is defined as an expression that is made up of constants and variable and joined by mathematical operators .

In the question ,

a expression is expressed in words , we have to write an equivalent expression for it .

the statement 1.5 cubed is (1.5)³

1.5 cubed over 1.3 is = (1.5)³/1.3

1.5 cubed over 1.3 raised to the fourth power = (1.5)³/(1.3)⁴

and all raised to the power of negative six = [ (1.5)³/(1.3)⁴ ]⁻⁶

Therefore , The equivalent Algebraic Expression is represented by  [ (1.5)³/(1.3)⁴ ]⁻⁶  .

The given question is incomplete , the complete question is

Write an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six ?

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The R means Revolution, T means taper and I means inch. The correct option is B.

Given that in machine tool feed rate or dimensional change notation, dimensional distance i related to rotation or travel change.

We want to find the expression R, T and I.

Machining center programmers specify spindle speed in revolutions per minute (RPM). Feedrates per minute are often given in either inches per minute (ipm) or millimeters per minute (mmpm).

From the above definition, we get that R means Revolution, I means inch and T means taper.

Hence, The expressions R means revolution, T means taper and I means inch for the three of the more common notation are IPM, IPR, or TPI.

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The probability that a randomly selected sample mean will be more than $100 = 0.14082.

We are given that according to a research​ institution, the average hotel price in a certain year was $97.00.

Assume the population standard deviation is $18.00 and that a random sample of 40 hotels was selected.

Here, Mean = μ = $97.00  and  Standard deviation = σ = $18 and  n = 40

(a) Standard error of the mean = σ/[tex]\sqrt{n}[/tex] = 18/[tex]\sqrt{40}[/tex] = 2.74

(b) Let X bar = Sample Mean

The z score probability distribution for sample mean is ;

          Z = Xbar-μ/ σ/[tex]\sqrt{n}[/tex] ~ N(0,1)

So, Probability that the sample mean will be less than $102 = P(X bar < $102)

P(X bar < 102) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] < 102 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z < 0.74) = 0.7704

(c) Probability that the sample mean will be more than $104 =P(X bar > $104)

=  P(X bar > 104) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] < 104 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z > 1.47) = 1 - P(Z <= 1.47)

= 1 - 0.92922 = 0.0708

(d) Probability that the sample mean will be between $99 and $100 is given by = P($99 < X bar < $100) = P(X bar < $100) - P(X bar <= $99)

= P(X bar < 100) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] < 100 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z < 0.01) = 0.50399

= P(X bar <= 99) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] <= 99 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z <= -0.35) = 1 - P(Z <= 0.35)

= 1 - 0.63683 = 0.36317

Therefore, P($99 < X bar < $100) = 0.50399 - 0.36317 = 0.14082 .

Hence the answer is the probability that a randomly selected sample mean will be more than $100 = 0.14082.

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Answer: y=2/3x-8

Step-by-step explanation:

Insert the given information into the y=Mx+b equation

The value of x that makes m || n is x = 20

acc to our question-

Solving this for ''x'' :.

The value of x that makes the opposite inner angles congruents (making 3x° congruent to 2x+20°) is x = 20.

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The original price of each sketchbook is $6

Mr. Olin bought 6 sketchbooks for the students in his art class.

If the sketchbooks cost $18 total before tax

Each sketchbook was on sale for $3 off

We need to calculate the original price of each sketch book.

If the sketchbooks cost $18 total before tax

Cost of each text book = total cost / number of sketchbooks

= 18/6 = 3

Cost of each sketch book is $3

Each sketchbook was on sale for $3 off

Cost price = original price = discount

3 = original price - 3

original price = 6

Therefore, the original price of each sketchbook is $6

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1 Quintal can be carried for Rs 180 to the same direction.

Given that the charge of 0.25 quintal to a certain distance is Rs 45.

With Rs 45, 0.25 quintals can be carried.

With Rs 1, 0.25/45 quintals can be carried in same direction.

With Rs 180, (0.25*180)/45 = 1 quintal can be carried in same direction.

Hence 1 Quintal can be carried for Rs 180 to the same direction.

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The image of point (8,4) after translation is (-6,0).

What is image of a point?

A transformation where a point is moved across a certain line, called the line of reflection, to appear at an equal distance.

Main Body:

Given point is (8,4)

Translation in the point is left 2 units, down 4 units.

so left- right translation is done on x-axis where moving left means subtracting is while up - down translation is done on y- axis where moving down means subtracting.

Which means 2 units will be subtracted from x-axis and 4 units from y-axis

New point = (8-2 ,4-4)

                 = (6,0)

Image of point (6,0) according to y-axis will be (-6,0).

Hence image point is (-6,0)

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a. The equation that has one solution will be;

⇒ x + 3 = 4x

b. The equation that has no solution will be;

⇒ x + 3 = x

c. The equation that has infinitely many solution will be;

⇒ x + 3 = 3 (x/3 + 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x + 3

Now,

Use the expression x + 3, we can find as;

Let us defined an expression as;

⇒ x + 3 = 4x

Solve for x as;

⇒ x + 3 = 4x

⇒ x + 3 - 4x = 0

⇒ - 3x = - 3

⇒ x = 1

Hence, The equation has one solution.

Let us defined an expression as;

⇒ x + 3 = x

Solve as;

⇒ x + 3 = x

Subtract x both side, we get;

⇒ x + 3 - x = x - x

⇒  3 ≠ 0

Thus, The equation has no solution.

Let us defined an expression as;

⇒ x + 3 = 3 (x/3 + 1)

Solve as;

⇒ x + 3 = 3 (x/3 + 1)

⇒ x + 3 = 3x/3 + 3

⇒ x + 3 = x + 3

Subtract x we get;

⇒  3 = 3

Thus, The equation has infinitely many solution.

Therefore,

a. The equation that has one solution will be;

⇒ x + 3 = 4x

b. The equation that has no solution will be;

⇒ x + 3 = x

c. The equation that has infinitely many solution will be;

⇒ x + 3 = 3 (x/3 + 1)

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Answer:

1/ x+3 = 4x

2/ x=x

3/ x+3 = 3

Step-by-step explanation:

Hope you find it helpful!

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Answer: y = -x-1

Step-by-step explanation:

Answer:  f=15h+200

Step-by-step explanation:

h=hours
15$ and hour
mutiply hours and dollars add base pay
f for total money made :)