A pool measuring 18 meters by 30 meters is surrounded by a path of uniform width, as shown in the
figure. If the area of the pool and the path combined is 1900 square meters, what is the width of
the path?

The maximum height of the ladder on the wall is given as follows:

h = 8.7 m.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 60º, the parameters are given as follows:

Hence the maximum height is obtained as follows:

tan(60º) = h/5

h = 5 x tangent of 60 degrees

h = 8.7 m.

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Answer:

Step-by-step explanation:

We can start by solving the second equation for y:

1/2y - x = 1

1/2y = x + 1

y = 2x + 2

Now we can substitute this expression for y into the first equation:

y = 2 - 6x

2x + 2 = 2 - 6x

Adding 6x to both sides, we get:

8x + 2 = 2

Subtracting 2 from both sides, we get:

8x = -0

Dividing both sides by 8, we get:

x = 0

Now we can use this value of x to find y:

y = 2x + 2

y = 2(0) + 2

y = 2

Therefore, the solution to the system of equations is x=0 and y=2.

The sum of geometric series 3+2.55+2.1675+1.842375+...

Hence, the correct option is B.

To find the sum of a geometric series, we can use the formula

S = a(1 - [tex]r^{n}[/tex]) / (1 - r)

Where

S = sum of the geometric series

a = first term of the series

r = common ratio of the series

n = number of terms in the series

In this case, we can see that the first term is 3 and the common ratio is 2.55/3 = 0.85. We can also see that there are an infinite number of terms in the series.

Using the formula for an infinite geometric series, we can simplify the formula to

S = a / (1 - r)

By putting these values we have, we get

S = 3 / (1 - 0.85) = 20.

Hence, the sum of the geometric series is 20.

Hence, the correct option is B.

The question is incomplete and the complete question is '' FIND THE SUM OF GEOMETRIC SERIES 3+2.55+2.1675+1.842375+...

A. 8

B. 20

C. 12

D. 4 ''

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We can eulerize this graph in the most efficient way possible by making these vertices have even degree through  adding  an edge between them.

We can Eulerize a graph by ensuring  to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.

A good method to do this is by  adding  edges between pairs of vertices that have odd degree until all vertices have even degree.

In the scenario above,  all the  vertices have odd degree except for the first and last vertices. To make these vertices have even degree, we go ahead and add an edge between them.

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The correlation coefficient between the minutes the actor appeared shirtless in a film and the film's opening weekend gross is 0.75.

In this scenario, the minutes shirtless (x) would be plotted on the x-axis of the scatter plot while the open weekend gross (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the minutes shirtless (x) and the open weekend gross (y), an equation for the linear regression is given by:

y = 10.83 + 0.86x

Correlation coefficient, r = 0.7488571925 ≈ 0.75

In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is approximately greater than 0.7;

0.7＜|r| ≤ 1   (strong correlation)

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The estimated rating of chips whose cost is $1.10 is 2.25.

From the question, we have the following parameters that can be used in our computation:

y = 2.5x - 0.5

To estimate the rating of chips whose cost is $1.10, we can substitute x = 1.10 into the equation y = 2.5x - 0.5 and solve for y.

y = 2.5x - 0.5

y = 2.5(1.10) - 0.5

y = 2.75 - 0.5

y = 2.25

Therefore, the estimated rating of chips whose cost is $1.10 is 2.25. Rounded to the nearest hundredth, it is 2.25.

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Answer:

----------------------

To solve this problem, we can use a system of equations with two variables:

We have two equations based on the given information:

Solve the first equation for x:

Substitute the expression for x into the second equation:

Simplify and solve for y:

Substitute the value of y back into the expression for x:

So, you should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.

Answer:

Step-by-step explanation:

You should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.

The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.

We have,

Let's first find the probability of selecting a male smoker and then the probability of selecting a female smoker.

P(Male smoker) = Number of male smokers / Total number of male students

P(Male smoker) = 29 / (29 + 262)

P(Male smoker) = 0.10

Similarly, the probability of selecting a female smoker is:

P(Female smoker) = Number of female smokers / Total number of female students

P(Female smoker) = 40 / (40 + 360)

P(Female smoker) = 0.10

Now, we can find the probability of selecting both a male smoker and a female smoker by multiplying the probabilities:

P(Both smokers) = P(Male smoker) x P(Female smoker)

P(Both smokers) = 0.10 x 0.10

P(Both smokers) = 0.01

Therefore,

The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.

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The equation of the line that is perpendicular to the line passing through the points (-3, 10) and (3, 8) is y = 3x + 9.

To find a line that is perpendicular to another line, we need to use the fact that the slopes of the two lines are negative reciprocals of each other.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the slope formula:

slope = (y₂ - y₁)/(x₂ - x₁)

Therefore, the slope of the line passing through the points (-3, 10) and (3, 8) can be found as follows:

slope = (8 - 10)/(3 - (-3)) = -1/3

Now, to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope -1/3, which is 3.

Therefore, the slope of the line perpendicular to the given line is 3.

Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form of a linear equation is:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is any point on the line.

We know the slope of the perpendicular line is 3, and we can choose any point on the line. Let's choose the midpoint of the given points (-3, 10) and (3, 8), which is

=> ((-3+3)/2, (10+8)/2) = (0, 9).

So, using the point-slope form of the equation with m = 3 and (x1, y1) = (0, 9), we get:

y - 9 = 3(x - 0)

Simplifying this equation, we get:

y = 3x + 9

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Phil owns a ranch business and uses four-wheelers to do much of his work the allowable depreciation for year 2 is $4,096.

To calculate the allowable depreciation for year 2, we need to determine the depreciation basis of the four-wheeler and then apply the appropriate MACRS depreciation rate.

The depreciation basis is the original cost of the asset minus any Section 179 expense deduction and any bonus depreciation claimed.

Since we are ignoring these deductions in this case, the depreciation basis is simply the original cost of the four-wheeler:

Depreciation Basis = $12,800

To determine the MACRS depreciation rate for year 2, we need to consult Table 2 from the MACRS tables, which gives the percentage rates for assets in the 5-year class for each year of the recovery period. According to Table 2, the depreciation rate for year 2 is 32%.

Using this information, we can calculate the allowable depreciation for year 2 as follows:

Depreciation for Year 2 = Depreciation Basis × MACRS Depreciation Rate for Year 2

Depreciation for Year 2 = $12,800 × 32%

Depreciation for Year 2 = $4,096

Therefore, the allowable depreciation for year 2 is $4,096.

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The hiking trial at the state park that is the longest would be D. Hilltop

To find the hiking trail that is longest, convert the lengths shown to one form so as to see which is the longest.

Mammoth = 8.005 kilometers

Brookside = 8. 7 kilometers

Wild Rose = 8, 080 meters = 8. 08 kilometers

Hilltop = 8 kilometers 800 meters = 8. 8 kilometers

This then shows that the hiking trail that is the longest in the state park is the Hilltop trail which goes for 8. 8 kilometers.

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Answer:

x^(y^3-1) / -2xy

Step-by-step explanation:

4x^y^3 = 4x^(y^3)

-8x^2y = -8x^2y^1

= 4x^(y^3) / -8x^2y^1

= (4x^(y^3) / 4xy) / (-8x^2y^1 / 4xy)

= x^(y^3-1) / -2xy

Answer:

Step-by-step explanation:

The meaning of the given statement is concept of a cyclic subgroup in group theory.

What is cyclic group?

In group theory, a cyclic group is a group that can be generated by a single element. That is, it is a group that is generated by a single element a, where any element of the group can be expressed as a power of a.

The order of a cyclic group is equal to the order of its generator. If the generator has order n, then the cyclic group has n elements. The group operation in a cyclic group can be either additive or multiplicative, depending on the notation used.

The statement defines a cyclic subgroup is a subgroup of a group that is generated by a single element. The element used to generate the subgroup is called the generator of the cyclic subgroup. The set of all powers of the generator, including the inverse powers and the identity element, forms the cyclic subgroup.

In other words, the cyclic subgroup generated by an element a of a group is the smallest subgroup that contains a. It consists of all possible combinations of a and its inverse under the group operation.

A group or subgroup is called cyclic when it can be generated by a single element. In other words, if every element of the group can be expressed as a power of a single element, then the group is cyclic.

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The height of box for the given cuboid satisfied the relation through which the volume of cuboid is satisfied is,  height = x+2

What about volume of cuboid?

A cuboid is a three-dimensional shape that has six rectangular faces, where each face has four sides and four right  angles. The volume of a cuboid is the amount of space that it occupies in three-dimensional space. It is measured in cubic units.

The formula to calculate the volume of a cuboid is given by multiplying its length, width, and height.

Volume of cuboid = Length x Width x Height

The volume of a cuboid can be used to determine the amount of space that it can hold or the amount of material required to fill it.

The volume of a cuboid can be calculated by multiplying its length, width, and height.

If the length of the cuboid is represented by "l", the width by "w", and the height by "h", then the volume can be calculated using the formula:

Volume of cuboid = l x w x h

According to the given information:

As, we know that the volume of cuboid = length x breath x height

Given volume of cuboid is = [tex]x^{3} + 6x^{2} +11x^{} + 6[/tex]

And width = x + 1 and length = x + 3.

Volume of cuboid = length x breath x height

⇒ [tex]x^{3} + 6x^{2} +11x^{} + 6[/tex] = (x + 1)(x + 3) x height

⇒ height = [tex]\frac{x^{3} + 6x^{2} +11x^{} + 6}{(x+1)(x+3)}[/tex]

⇒ height = [tex]\frac{(x+1)(x+2)(x+3)}{(x+1)(x+3)}[/tex]

⇒ height = (x+2)

So, the height of the given cuboid is (x+2)

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Answer:

C. d= 163t represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours. This is because Rajindri earns $163 for every two hours that she works, which means she earns $81.50 for each hour that she works. Therefore, the equation that relates the number of dollars earned to the number of hours worked is d = 163t.

Step-by-step explanation:

Answer:

32[tex]a^{35}[/tex]

Step-by-step explanation:

using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]

[tex](2a^3a^4)^{5}[/tex]

= (2[tex]a^{(3+4)}[/tex] )^5

= [tex](2a^7)^{5}[/tex]

raise each term inside the parenthesis to power 5

= [tex]2^{5}[/tex] × [tex]a^{7(5)}[/tex]

= 32[tex]a^{35}[/tex]

Answer:

32[tex]a^{35}[/tex]

Step-by-step explanation:

using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]

[tex](2a^3a^4)^{5}[/tex]

= (2[tex]a^{(3+4)}[/tex] )^5

= [tex](2a^7)^{5}[/tex]

raise each term inside the parenthesis to power 5

= [tex]2^{5}[/tex] × [tex]a^{7(5)}[/tex]

= 32[tex]a^{35}[/tex]

Answer:

7.5 kilometers

Step-by-step explanation:

[tex]\frac{40}{5}[/tex] = [tex]\frac{60}{x}[/tex]

[tex]\frac{40}{5}[/tex] can be simplified to 8

8 = [tex]\frac{60}{x}[/tex]  Multiply both sides by x

8x = 60  Divide both sides by 8

[tex]\frac{8x}{8}[/tex] = [tex]\frac{60}{8}[/tex]

x = 7.5

Helping in the name of Jesus.

Answer:

400% of 2 is 8, so it would be less than 10

Step-by-step explanation:

Group work and group discussion are discouraged is a factor that does not fit into the environment for doing mathematics

The mathematics scope can differ contingent upon a person's exact circumstances in addition to their individual preferences. As a whole, however, math is customarily studied and exercised within tranquil and absorbed settings that allow for intensive thought processes. A few typical conundrums for executing mathematics tasks encompass:

Libraries: Many mathematicians affectionately flock to libraries for their serene environment furthermore the availability of learning materials and related informational sources. University-focused facilities usually brag extensive selections of mathematics books as well as magazines.

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Answer:

MN and ML are on the same straight line.

Answer:

17.023413

Step-by-step explanation:17.023413

Answer:

They barter, or trade (without using money). Economic systems are based on customs, traditions, and beliefs of the past.

Step-by-step explanation: -

The frequency of the wave is 2.62 Hz

Answer: 2304.0 cm³

Step-by-step explanation: V = length x width x height

V = 18 cm x 8 cm x 16 cm

V = 2304 cm³

The statement on theoretical probabilities is True.

Theoretical probabilities, referred to as classical probabilities, are utilized when we can suppose that each conceivable result has an equal chance of happening.

Typically, this is observed in games of luck like tossing a coin or rolling dice, where the chances of every possible outcome are equivalent. Such scenarios permit one to use probability principles and determine the probability of each outcome transpiring.

For instance, with fair coins, it's reasonable to assert that there's an even likelihood for heads or tails, setting both probabilities at 1/2.

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The angle that is supplementary to the angle DEA is angle DEC

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have

Angle = DEA

As a general rule;

Two angles are said to be supplementary if their sum add up tp 180 degrees

This means that the angles are on a straight line

The angle are on the same straight line with ange DEA is DEC

Hence, the angle is angle DEC

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Step-by-step explanation:

Subtract the 99 from 949 then    divide by 2

949-99= 425 dollars = price of dryer

( then washer is  425 + 99 )