What is the least common multiple of 51, 68 and 85?

The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.

To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.

To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length) + 2(width)

Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:

2x + 2y = 60,000

To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:

60,000 - x = 3x + 2y

The total length of the three sides that are not the front is 3x + 2y.

Now we can calculate how much the builder will pay for each type of fence:

Total cost of the fence = $20x + $30x + $20y = $50x + $20y

To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.

However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:

This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.

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6.666666666666666 (6.6 repeating, I just don’t know how to use the sign online)

I multiplied 3 1/3 by 2

Answer:

[tex] \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]

Step-by-step explanation:

Slope-intercept is in form of y = mx + b where m is slope and b is y-intercept. We simply solve for y in term of x and then we will obtain the slope-intercept form.

Given the linear equation:

[tex] \displaystyle{3x + 2y = 2}[/tex]

First, subtract both sides by 3x:

[tex] \displaystyle{3x + 2y - 3x= - 3x + 2} \\ \\ \displaystyle{2y = - 3x + 2}[/tex]

Then divide both sides by 2:

[tex] \displaystyle{ \dfrac{2y}{2} = \dfrac{ - 3x + 2}{2}} \\ \\ \displaystyle{ y = \dfrac{ - 3x + 2}{2}}[/tex]

Separate fractions (Simplify):

[tex] \displaystyle{ y= \dfrac{ - 3x}{2} + \dfrac{2}{2}} \\ \\ \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]

And we have finally converted the equation to slope-intercept form.

The height of vase b is 34.56 cm.

In mathematics, volume is the space taken by an object.

V=pi*r²*h

Here, given that,

vase A has height 20cm =H

and volume 1500^3. =V

And, A & B similar vases.

Again, vase B has volume 2592cm^3 =v

let, h, the height of vase b.

both radius are equal

so, we get,  V/pi*H = v/pi*h

i.e. 1500/20=2592/h

so, h= 34.56 cm

Hence, the height of vase b is 34.56 cm.

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Among the given four options, the word that doesnot have similar meaning to condemn is "critique".

The word "condemn" means to express strong disapproval or criticism of something or someone, often in a formal or official manner. It can also mean to pronounce a judgment of guilt, especially in a court of law. It implies a severe judgment or punishment. Condemn also implies the declaration of something being morally wrong or unacceptable. It is a strong word that carries a sense of condemnation or blame.

The sentences are given below:

The word that does not have a similar meaning to "condemn" is "critique".

"Condemn" means to express strong disapproval of something or someone, often in a formal or official manner.

"Criticize" means to express disapproval or to find fault with something or someone

"Censure" means to express strong disapproval or criticism of something or someone, typically in a formal or official manner.

"Disparage" means to speak or write about in a negative way; to belittle or criticize.

"Critique" means to evaluate (a work of art, literary work, etc.) in terms of its strengths and weaknesses; to give an analysis or evaluation of something."Critique" is different because it is an analysis or evaluation of something, whereas the other words are about expressing disapproval or criticism.

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The value of x is 8 and  the measure of the two marked angles is  60°.

When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.

we know that ,

10x-20=7x+4   (it is corresponding opposite angle)

3x=24

x=8

the value of x is 8.

the measure of the two marked angles is 10*8-20= 80°-20°= 60°.

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The dots in the expression - 321⋅35⋅7⋅15 represents multiplication.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

From higher classes, we write a dot sign in between two terms to represent that the terms are being multiplied.

Given, - 321⋅35⋅7⋅15 this represents multiplication between the numbers

- 321, 35, 7, and 15.

The result of this product is,

- 321×35×7×15

= - 1,179,675.

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The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1

Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]

here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.

We need to find the sum.

We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1

We know that the formula of the sum of n-terms of a geometric sequence is:

[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]

For n = 21, r = -1 and a1 = 1

[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]

Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1

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At the given rate, we can say that they will walk 6 laps and run 10 laps for a total of 16 miles.

In a direct proportional relationship, we can say that the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

For the first question, we have that out of a total distance of 8 miles,  and we can see that;

Walk is 3/8 of the distance.

Run is 5/8 of the distance.

Thus, the proportional relationships for the distances are given as follows:

Walked = 3/8 x Total Distance.

Ran = 5/8 x Total Distance.

We are told that the total distance is 16 miles and so;

Walked: 3/8 * 16 = 6 laps

Ran: 5/8 * 16 = 10 laps

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Geometrically there are 16 different routes from A to B that use each road exactly once.

What is geometry?

The area of mathematics known as geometry is concerned with the dimensions, sizes, forms, and angles of a wide range of everyday objects. Geometry comes from the Ancient Greek terms "geo" and "metron," which both imply "measuring."

Keep in mind that cities C and E can be excluded from the count of paths because there is only one road that can lead out of either city if a path enters it. The geometric diagram is shown below.

Now move on to the casework. It's important to keep in mind that there are two routes from A to D, D to A, B to D, and D to B.

Case 1: A⇒D: If the path from D leads back to A, the subsequent path must go to B⇒D⇒B. The path ADABDB has 2×1×2=4 possible outcomes. The path must continue with either BDAB or BADB if it leads from B to D. There are 8 possibilities as 2×2×2=8. Therefore, there are 4+8=12 potential outcomes in this scenario.

Case 2: A⇒B: BDADB must be the next step on the path. There are 2×2=4 options in this situation.

Combining the two situations results in 12+4=16.

Therefore, there are 16 different routes.

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Answer:90

Step-by-step explanation:

The total surface area of a cone which has a base diameter of 7 cm and height of 8 cm is  126.5 cm ²

The total surface area of a cone can be found by the formula :

= (π x radius ²) + (π x radius x height )

Radius is half of diameter so :

= 7 / 2

= 3. 5 cm

The total surface area of the cone is;
= ( π x 3. 5 ²) + ( π x 3. 5 x  8)

= 38 . 5 + 88

= 126.5 cm ²

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A value calculator is a tool used to help assess the worth of an asset or investment.

The value calculator is designed to help individuals and businesses determine whether an asset or investment is a good value. The calculator takes into account various types of data, such as the current market value, expected future value, and any associated risk factors.

This data is then used to calculate the present value, which is the amount of money an asset or investment is worth today. The calculator also takes into account inflation and other factors that could affect the current value of the asset or investment.

The value calculator can be used to help individuals and businesses make informed decisions about their financial investments.

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Part A: Based on the text, an inference that can be made about laughter is that it can be a positive response to a situation or a way of expressing joy.

Inference is the process of drawing conclusions from given facts or evidence. It involves making a logical guess or assumption based on the available information. Inference requires the use of critical thinking to draw conclusions that are most likely to be accurate.

Part B:
Yes - Laughter is described as a response to a situation and can be a way of expressing joy.
No - There is no evidence that laughter is a negative response to a situation.

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The degree of x-x3 is 3, or 3. It is a cubic polynomial. The formula for the 33 matrix's distinctive polynomial is f() = det (A - I3).

A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients. It can be expressed using just the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that contains variables, constants, and exponents and is based on the operations of addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

[tex]x - x^3[/tex] has a degree of 3, or 3.

The polynomial is a cubic one.[tex]f() = det (A - I3)[/tex]is the formula for the characteristic polynomial of the 33 matrix.

The characteristic polynomial of the provided 33 matrix is [tex]f() = -3 + 3 + 2.[/tex]

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Answer:

y= 12

Step-by-step explanation:

3(-12)-24

-36-24

-12

Answer:

FALSE

Step-by-step explanation:

It is not necessarily true that ƒ(5)=8 just because ƒ(1)=0, ƒ(3)=0, and ƒ(4)=0. In fact, it is possible for ƒ(x) to be a cubic function and for ƒ(5) to equal any number, depending on the specific form of the function and the values of its coefficients.

Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.

A heptagon is a seven-sided polygon. To find the area of a regular heptagon, we can use the formula:

Area = (7/4) * (perimeter) * (apothem)

where "perimeter" is the length of the heptagon's circumference and "apothem" is the distance from the centre to the midpoint of one of its sides. The radius of the heptagon is the apothem, which is 27.87 cm.

The perimeter of the heptagon can be calculated by multiplying the length of one side by the number of sides:

Perimeter = 24.18 cm * 7 = 168.26 cm

Now we can substitute these values into the area formula:

Area = (7/4) * 168.26 * 27.87

Area = approximately 554.55 sq cm.

Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.

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By solving the expression (3x2 +4x − 15) ÷ (x +3) the quotient is 3x-5 and r=0

When solving a division problem, the quotient is obtained by dividing the dividend by the divisor.

Mathematically, we denote the outcome of this division by separating the quotient and remainder with a capital R. (see below). The entire number that results from simplifying a fraction is known as the quotient.

We can do it by long division method  the required quotient is 3x-5 and r=0

not 3x-1 , r=1

multiply the divisor with 3x we will get 3x²+9x to cancel out the first term of dividend.

Now after solving we will get -5x -15

Now, multiply the divisor by -5 we will get -5x-15 which will cancel the entire dividend.

So that the quotient is 3x-5 and r=0

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Answer:

There are always two possible outcomes H (heads) and T (tails) but the possible combination outcomes are HH, TT, HT, and TH

Step-by-step explanation:

It is just my common sense~

There is 8 possible outcomes.

As per the given conditions in the question, the amount of money that the second son was left with by the man is 2,40,000.

To add two fractions with different denominators, you must first find a common denominator. A common denominator is a number that is divisible by both denominators of the fractions. Once you have a common denominator, you can add the numerators of the fractions together and place the sum over the common denominator. Then simplify the fraction if possible.

The reciprocal of a fraction is another fraction whose numerator and denominator are flipped. For example, the reciprocal of the fraction 2/3 is 3/2. The product of a fraction and its reciprocal is always equal to 1. To find the reciprocal of a fraction, simply swap the numerator and denominator.

Considering the conditions given in the question,let us suppose that the third son was left with x part of the money,

so we can use the equation,

part of money left for fist son + part of money left for second son + part of money left for third son = total part of money

or, 1/2 + 3/8 + x = 1

therefore, x = 1/8

Also we know that the third son was left 80,000 ,

so 1/8 of total money = 80,000

therefore, total money = 80000 * 8 =6,40,000

Now the amount left for the second son is , 3/8 of total money

which is equal to , 3/8 of 6,40,000 = 2,40,000

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Answer:

Step-by-step explanation:

m∡IGH = ? m∡FGH = 141 degrees and m∡FGI = 72 degrees

therefore, m∡IGH = m∡FGH - m∡FGI = 141 - 72 =  69 degrees

The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the function:

y = -(x/3) + 2

At x = -3:

y = -((-3)/3) + 2 = 3

At x = 0:

y = -(0/3) + 2 = 2

At x = 3:

y = -(3/3) + 2 = 1

At x = 6:

y = -(6/3) + 2 = 0

The value of y when x = -3 is 3

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Unreasonable Time is the nest option for running the group raffle at an upcoming assembly to give away a prize.

As given that;

Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time.

Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time.

Your school is considering running the group raffle at an upcoming assembly to give away a prize.

We have to write a brief explanation of what advice you would give them.

We can use the unreasonable time because  running the group raffle at an upcoming assembly to give away a prize cannot complete their work is the given amount of time.

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Answer:

the value is 4

Step-by-step explanation:

The rate of increase of the radius is 0.025 in/sec.

A three-dimensional object with a sphere-like shape. A sphere has no vertices or edges, unlike other three-dimensional shapes. The distances between each point on its surface and its center are equal.

In other words, the distance between any two points on the surface and the sphere's center is equal. The formula for the Volume of the sphere is given by

Volume of sphere = (4/3)πr³

Where, r = radius of the sphere

Here we have

A sphere is increasing in volume at the rate of 20 in³/s.  

Here we need to find at what rate the radius of the sphere increases when the radius is 4 in.

Let v = Volume of the sphere at time t

=> Change in Volume = dv/dt  = 20

r = Radius of the sphere at time t

As we know, the Volume of the sphere, v = (4/3)πr³

Differentiate the Volume of the sphere with respect to t

=> dv/dt = (4/3)3πr³⁻¹)(dr/dt)

=> dv/dt = 4πr² (dr/dt)

=>  20 = 4πr² (dr/dt)  

=>  5 = πr² (dr/dt)  

Given that radius, r = 4

=> 5 = π4² (dr/dt)  

=> 5 = (22/7) 64 (dr/dt)  

=> 5 = 3.14(64) (dr/dt)  

=> dr/dt = (5/3.14 × 64)  

=> dr/dt = 0.024880573

=> dr/dt = 0.025

Therefore,

The rate of increase of the radius is 0.025 in/sec.

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Answer:

44.8

Step-by-step explanation:

44.4 - (-0.4) = 44.8

Marissa velocity while skateboarding is 162 meters per minute

An equation is used to show the relationship between numbers and variables.

Velocity is the ratio of displacement to time taken. It is a vector quantity (has magnitude and direction) and it is given by:

Velocity = displacement / time

Marissa travels 486 meters in 3 minutes, hence:

Velocity = displacement / time

Velocity = 486 m / 3 min = 162 meters per minute

The velocity is 162 meters per minute

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Answer: The correct answer is 2.7m/s

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

No, some people don't like certain things. It like saying that you pick five random people who are at a science fair and ask them if they like science, the answer would be yes, but if you went to Walmart and asked five random people if they liked science your answers would most likely end up being no. It's the same way looking at the magazines.

Answer: Breadth? Did you mean width? If so, the answer is 128cm

Step-by-step explanation:

Area = Width x Length

8x16=128