A gold mine has two​ elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 13 feet per second. One​ day, the equipment elevator begins to descend. After 33 ​seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 12 ​seconds? At that​ time, which elevator is​ deeper?

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

X = 20

Y = 10√3 or 17.32 or 17.3

Steps given below in the image,

I hope my answer helps you.

Answer:

x = 20

y = 17.32

Step-by-step explanation:

\(10 = x \cos 60 \degree \\ \\ \implies \: 10 = x \times \frac{1}{2} \\ \\ \implies \: 10 \times 2= x \\ \\ \implies \: \huge{ \boxed{x = 20}} \\ \\ y = 10 \tan \: 60 \degree \\ \\ \implies \: y = 10 \times \sqrt{3} \\ \\\implies \: y = 10 \times 1.732 \\ \\\implies \: \huge{ \boxed{ y = 17.32}}\)

In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata. The type of sampling used in this scenario is stratified sampling.

Stratified sampling is a sampling method where the population is divided into homogeneous subgroups or strata, and individuals are randomly selected from each stratum in proportion to their representation in the population. In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata.

By randomly selecting a proportionate number of individuals from each group, Christopher ensures that both varsity and junior varsity athletes are represented in the sample, maintaining the proportional representation of each group in the population. This method allows for more accurate and representative results by capturing the characteristics of both groups separately.


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Answer:

36.3%

Step-by-step explanation:

Solving our equation

r = 907 / ( 5000 × 0.5 ) = 0.3628

r = 0.3628

converting r decimal to a percentage

R = 0.3628 * 100 = 36.28%/year

The interest rate required to

accumulate simple interest of $ 907.00

from a principal of $ 5,000.00

over 0.5 years (6 months) is 36.28% per year.

The annual simple interest rate to the nearest tenth of a percent is 36%

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given after 6 months which is 1/2 or 0.5 years the simple interest earned annually on an investment of $5000 was $907, we have to determine r.

∴ SI = (p×r×t)/100

907 = (5000×r×0.5)/100.

907 = 50×0.5×r.

r = 907/(50×0.5).

r = 907/25.

r = 36.28 %.

Which is 36% rounded to the nearest tenth.

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Answer:

16 - x = -2

16 + 2 = x

x = 18

hope it helps!

Answer:

x=4

Step-by-step explanation:

The value of x for the given polygon is 126º.

The given pentagon with angles (x-30)°, (x-30)°, (x-30)°, x° and x°.

We need to find the value of x.

A pentagon is a flat 2D shape that has five sides and five vertices.

The word “pentagon” comes from the Greek word “pentagons”, which means “five-angled”. A regular pentagon has five internal angles that form corners. The angles in all the corners add up to 540º.

Now, (x-30)°+(x-30)°+(x-30)°+x°+x°=540º

⇒5x-90=540

⇒5x=630

⇒x=126º

Therefore, the value of x for the given polygon is 126º.

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Answer:

you can literally look these up and you get step by step answers

Step-by-step explanation:

Answer:

152.3 approximately

Step-by-step explanation:

A polygon with 13 sides (and angles too) would be called tridecagon

Now, the sum of interior angles in a polygon is calculated by dividing the number of angles minus 2 by 180 [(n-2)*180]

(13-2)/180 = 1.980 and to find what is the measure of one angle, we divide the sum by the number of angles the polygon has

1.980/13 = 152.3 approximately

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

Answer:

First number is x

Second number is y

Step-by-step explanation:

x = 2y + 1

x + y = 25

(2y + 1) + y = 25

3y = 24

y=24/3

y = 8

x = 2(8) + 1

x = 16+1

x=17

Hope this helps!!

Answer: A parabola can be defined as the set of all points that are equidistant from a focus and a directrix. Based on the information provided, the focus of the parabola is (0, 4) and the directrix is y =.

The parabola will open upwards or downwards depending on the location of the focus and the directrix. Since the focus is at (0, 4), and the directrix is at y =, the parabola must open upwards. The axis of symmetry of the parabola will pass through the focus and will be perpendicular to the directrix.

Without more information, it is not possible to fully determine the shape and equation of the parabola. The shape of the parabola and its equation can be found by using the focus and directrix and other information, such as the vertex or a point on the parabola.

Step-by-step explanation:

The standard deviation of the number of incorrect answers in an exam will be equal to 1.12.

If a student randomly guesses on an exam containing 5 true or false questions, the number of incorrect answers will follow a binomial distribution with n = 5 (the number of questions) and p = 0.5 (the probability of guessing incorrectly on each question). The standard deviation of a binomial distribution is given by the formula:

sd = √(np(1-p))

Plugging in the values n = 5 and p = 0.5, we get:

sd = √(50.5(1-0.5)) = √(50.50.5) = √(1.25) = 1.12

Rounding to two decimal places, the standard deviation of the number of incorrect answers is 1.12.

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The answer is the system of equations is x = 0.290566 and

y = 40.603774.

To solve this system of equations using a matrix, we have to write it in the form AX = B, where A will be coefficient matrix, X will be variable matrix, and B, constant matrix.

The system of equations is:

                                     y = 650x + 175

                                     y = 25,080 - 120x

To write it in matrix form, arrange coefficients and constants as follows:

| 650 -1 | | x | | 175 |

| -120 1 | * | y | = | 25,080 |

So, coefficient matrix A is:  | 650 -1 |

                                                  | -120 1 |

Variable matrix X is: | x |

                                         | y |

And constant matrix B is: | 175 |

                                                | 25,080 |

The coefficients in the first column of the matrix are coefficient of x in each equation, and coefficients in the second one are the coefficients of y. The constants in the matrix are constants from each equation.

To solve for X, we use matrix algebra to isolate X. First, we have find the inverse of matrix A:

\(A^{-1 }\) = (1 / det(A)) * adj(A)

where, det(A) is determinant of A, and adj(A) represents adjugated of A (the transpose of the co-factor matrix of A).

We can calculate these as follows:

det(A) = (650 * 1) - (-120 *(-1)) = 530

adj(A) = | 1 120 |

          = |-1 650 |

So \(A^{-1 }\)  = (1 / 530) * | 1 120 |

            = | 0.001887 0.226415 |

   \(A^{-1 }\)   = |-1 650 | |-0.001887 1.226415|

Now we can solve for X:

X = \(A^{-1 }\)* B

X = | 0.001887 0.226415 | * | 175 |

  = | 0.290566 |

  = |-0.001887 1.226415 | | 25,080 | | 40.603774|

So, the system of equations is x = 0.290566 and y = 40.603774.

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Final answer:

The given matrix does not match either the first equation 'y = 650x + 175' nor the second equation 'y = 25,080 - 120x'. There's a discrepancy between the coefficients given in the matrix and those in the equations.

Explanation:

The first step is to express both equations in terms of y to match the matrix provided. However, the equations already match this format.

The first equation is y = 650x + 175, so if we place the terms in matrix form, we'll get: Column 1 as -650 (the coefficient of x) and Column 2 as 1 (the coefficient of y) and Column 3 as -175 (the constant).

For the second equation, which is y = 25,080 - 120x, again converting all terms as per the columns in matrix form, the coefficients will be Row 2 - Column 1 as 120 (the coefficient of x), Column 2 as 1 (the coefficient of y), and Column 3 as 25,080 (the constant).

Given that the matrix provided doesn't match either of these equations, there must be a mistake in the matrix or in these equations.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

(1, -2), (4, 1)

Step-by-step explanation:

Here we want to solve the system of equations:

y = x^2 - 4*x + 1

y = x - 3

First, we can see that in both parts we have isolated the variable "y", so we can just write:

x - 3 = y = x^2 - 4*x + 1 = y

removing the "y"s, we get:

x - 3 = x^2 - 4*x + 1

Now we can solve this for x

0 = x^2 - 4*x + 1 - x + 3

0 = x^2 - 5*x + 4

This is a quadratic equation, the solutions are given by the Bhaskara's formula, that says that for a general quadratic equation:

0 = a*x^2 + b*x + c

The solutions are given by:

\(x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}\)

So for the case of our equation:

0 =x^2 - 5*x + 4

The solutions are given by:

\(x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*1*4} }{2*1} = \frac{5 \pm 3}{2}\)

So the two solutions are:

x₁ = (5 + 3)/2 = 4

x₂ = (5 - 3)/2 = 1

To find the ordered pair, we need to replace these values in one of the equations of the system, let's use the second:

y = x₁ - 3 = 4 - 3 = 1

Then we have one solution at (4, 1)

And for the other:

y = x₂ - 3 = 1 - 3 = -2

then the ordered pair is (1, -2)

Now we want to write from least to greatest with respect to the x-coordinate, then the correct order is:

(1, -2), (4, 1)

a) the population cannot be negative, the limiting population is 4300.

b)the population is increasing when 0 < p < 4300 and decreases when p > 4300.

c)the equilibrium solutions are p = 0 and p = 4300.

(a) To determine when the population is increasing or decreasing, we need to look at the sign of dp/dt.

\(\frac{dp}{dt} = 1.2p(1 - \frac{p}{4300})\)

For dp/dt to be positive (i.e. population is increasing),

we need\(1 - \frac{p}{4300} > 0, or \ p < 4300.\)

For dp/dt to be negative (i.e. population is decreasing),

we need\(1 - \frac{p}{4300} < 0, or p > 4300.\)

Therefore, the population is increasing when 0 < p < 4300 and decreases when p > 4300.

(b) To find the limiting population, we need to find the value of p as t approaches infinity.

As t approaches infinity,\(\frac{dp}{dt}\)approaches 0. Therefore, we can set \(\frac{dp}{dt}\) = 0 and solve for p.

0 = 1.2p(1 - p/4300)

Simplifying, we get:

0 = p(1 - p/4300)

So, either p = 0 or 1 - p/4300 = 0.

Solving for p, we get:

p = 0 or p = 4300.

Since the population cannot be negative, the limiting population is 4300.

(c) Equilibrium solutions occur when\(dp/dt = 0.\)We already found the equilibrium solutions in part (b): p = 0 and p = 4300.

Therefore, the equilibrium solutions are p = 0 and p = 4300.

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a)  The population is increasing when 0 < p < 4300, and  decreasing when p > 4300.

b)  The population cannot be negative, the limiting population is 4300.

c)  these are the equilibrium solutions.  At p = 0, the population is not

increasing or decreasing, and at p = 4300,  the population is decreasing

but not changing in size.

(a) To determine when the population is increasing or decreasing, we

need to find the sign of dp/dt. We have:

dp/dt = 1.2p(1 - p/4300)

This expression is positive when 1 - p/4300 > 0, i.e., when p < 4300, and

negative when 1 - p/4300 < 0, i.e., when p > 4300.

Therefore, the population is increasing when 0 < p < 4300, and

decreasing when p > 4300.

(b) To find the limiting population, we need to solve for p as t approaches infinity. To do this, we set dp/dt = 0 and solve for p:

1.2p(1 - p/4300) = 0

This equation has two solutions: p = 0 and p = 4300. Since the population cannot be negative, the limiting population is 4300.

(c) To find the equilibrium solutions, we need to solve for p when dp/dt = 0. We already found that the only solutions to dp/dt = 0 are p = 0 and

p = 4300.

Therefore, these are the equilibrium solutions.

At p = 0, the population is not increasing or decreasing, and at p = 4300,

the population is decreasing but not changing in size.

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Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

In plan A,

    Plans for saving = $500

  Amount of saving each week = $20

∴ Number of weeks needed to make goal = (500 ÷ 20) (by using division)

                                                                       = 25

In plan B,

    Plans for saving = $500

   Amount of saving each week = $30

∴ Number of weeks needed to make goal = (500 ÷ 30) (by using division)

                                                                       = 17

In plan C,

    Plans for saving = $500

   Amount of saving each week = $40

∴ Number of weeks needed to make goal = (500 ÷ 40) (by using division)

                                                                       = 13

In plan D,

    Plans for saving = $500

   Amount of saving each week = $50

∴ Number of weeks needed to make goal = (500 ÷ 50) (by using division)

                                                                       = 10

So, Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

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The length (or combined diameters) of three pennies is approximately 5.715 centimeters.

To calculate the length (or combined diameters) of three pennies, we need to first determine the total diameter of the three coins. Each penny has a diameter of 0.75 inches, so if we add up the diameters of three pennies, we get:

3 x 0.75 inches = 2.25 inches

Now, to convert inches to centimeters, we need to use a conversion factor. The conversion factor for inches to centimeters is 2.54 centimeters per inch. So, we can convert the total diameter of three pennies from inches to centimeters by multiplying it by the conversion factor:

2.25 inches x 2.54 centimeters per inch = 5.715 centimeters

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Answer:

J=17

Step-by-step explanation:

J/-2 + 7 = -12

multiply both sides by -2 to cancel out the J/-2 and turn it into J + 7 = 24

transfer the 7 to the other side to get J = 24 - 7

J = 17

hopefully this helps.

The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

We have first three colour Green that is g1 , g2 and g3

And We have next three colour red that is r1 , r2 and r3

The probability that all adjacent points differ in colour = 3! * \(^{4}C_{3}\) 3! / 6!

=> \(\frac{ 3! * 4! *3!}{6!}\)

=> \(\frac{1}{5}\)

The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

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The number of ways to select a simple random sample of size 5 from a population of 7 children in a family is equal to 21ways.

As given in the question,

Number of children in the family 'n' = 7

Number of simple random sample of size  = 5  ( without replacement )

Number of ways to select the children defines a population

= ⁷C₅

= ( 7! ) / ( 7 - 5 )! ( 5! )

= ( 7 × 6 × 5! )/ ( 2! ) ( 5! )

= 7 × 3

= 21 ways

Therefore, the number of ways to select children of simple random sample of size 5 is equal to 21ways.

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Answer:

Just Search For Polygon Ethereum In Trust Wallet And It Would Pop Out.

Step-by-step explanation:

After It Pops Out, Enable The Polygon Ethereum

The estimated value of the square root of √57 is 7.5496

Square root:

Square root means inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

The square root of a natural number is a value, which can be written in the form of

y = √a.

It means ‘y’ is equal to the square root of a, where ‘a’ is any natural number.

Given,

√57

Here we need to determine the two consecutive whole numbers that it lies between. Write the two numbers and explain the process you used to select them.

To solve this one then we have to expand the given term like the following,

=> √57 = √(19 x 3)

We know that the values of

√3 = 1.732

and the value of

√19 = 4.35889

So, the value of

=> √(19 x 3) = 4.35889 x 1.732

=> 7.5496

Therefore, the value of √57 is 7.5496.

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The pool dimensions are approximately 12.22 by 21.22 feet.

To start, we know that the pool must be a 77 sq ft rectangle, so we can use the formula for the area of a rectangle (length x width = area) to solve for the dimensions.

77 = length x width

Next, we know that the fenced off plot is a 17 by 26 feet rectangle. We can use this information to set up an equation for the distance between the pool and the fence:

17 - 2x = length
26 - 2x = width

We also know that the fence should be twice as far away on the end where the lifeguard chair will be located, so we can set up another equation:

17 - 4x = length (on the side with the lifeguard chair)

Now we can substitute the expressions for length and width into the formula for the area of a rectangle:

77 = (17 - 2x)(26 - 2x)

Expanding the expression on the right side, we get:

77 = 442 - 86x + 4x^2

Rearranging and simplifying, we get a quadratic equation:

4x^2 - 86x + 365 = 0

Using the quadratic formula, we can solve for x:

x = (86 +/- sqrt(86^2 - 4(4)(365))) / (2(4))

x = (86 +/- sqrt(55284)) / 8

x = (86 +/- 234.85) / 8

x = 36.86 or 2.39

We can ignore the negative value, so x = 2.39 feet.

Now we can use the equations for length and width to solve for the dimensions of the pool:

length = 17 - 2x = 17 - 2(2.39) = 12.22 feet
width = 26 - 2x (except on the side with the lifeguard chair, where it is 4x) = 26 - 2(2.39) = 21.22 feet

So the pool dimensions are approximately 12.22 by 21.22 feet.

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Answer:

The sales tax percentage is 2%.

Step-by-step explanation:

With the information provided, you can find the sales tax percentage by subtracting the retail price from the amount the customer paid and dividing that by the retail price. Then, you have to multiply the result by 100.

((58.14-57)/57)*100= (1.14/57)*100=0.02*100= 2%

According to this, the answer is that the sales tax percentage is 2%.

K-Means uses Euclidean distance. The output includes average and maximum distances, separation, and convergence after iterations related to the number of starting seeds.

In the output of a K-Means cluster analysis, "Ave Distance" refers to the average distance between the data points and their assigned cluster centroids.

"Max Distance" represents the maximum distance between any data point and its assigned centroid. "Separation" indicates the distance between the centroids of different clusters, reflecting how well-separated the clusters are.

Convergence in K-Means clustering refers to the point when the algorithm reaches stability and the cluster assignments no longer change significantly.

When the video mentions convergence after 4 iterations, it means that after four rounds of updating cluster assignments and re-computing centroids, the algorithm has achieved a stable result.

The "Number of starting seeds" option determines how many initial random seeds are used for the algorithm, and it can affect the number of iterations needed for convergence. Increasing the number of starting seeds may result in faster convergence as it explores different initial configurations.

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Solution, Diameter = 30\(radius = \frac{diameter}{2} = \frac{30}{2} = 15 \\ \)

Now, []area = \pi {r}^{2} \)\( = 3.14 \times 15 \times 15\)\( = 706.5 \)Hence the area is 706.5now........\(circumference = 2 \: \pi\: r\)\( = 2 \times 3.14 \times 15\)\( = 94.2\)hence the answer is 94.2...

Solution,

Diameter = 30

\(radius = \frac{diameter}{2} = \frac{30}{2} = 15 \\ \)

Now,

\(area = \pi {r}^{2} \)

\( = 3.14 \times 15 \times 15\)

\( = 706.5 \)

Hence the area is 706.5

now........

\(=Circumference = 2 \: \pi\: r\)

\( = 2 \times 3.14 \times 15\)

\( = 94.2\)

hence the answer is 94.2...

Answer:

x = 4, y = 5.

Step-by-step explanation:

4x-2=3y-1

y+3=3x-4

Rearranging:

4x - 3y =  1       (A)

-3x + y = -7      (B)

Multiply  B by 3:

-9x + 3y = -21   (C)
Adding A and C:

-5x = -20

x = 4

Substitute for x in equation A:

4(4) - 3y = 1

3y = 15

y = 5.