Challenge A gold mine has two elevators, one for equipment and another for the miners. The
equipment elevator descends 6 feet per second. The elevator for the miners descends 15 feet per
second. One day, the equipment elevator begins to descend. After 21 seconds, the elevator for the
miners begins to descend. What is the position of each elevator relative to the surface after
another 17 seconds? At that time, which elevator is deeper?
The position of the equipment elevator relative to the surface is feet.

Answer:

x=20

Step-by-step explanation:

so 5/4 is 1.25

so 25/x=1.25

so to find x we do 25/1.25

when we do that we get 20 so then to check if it's right we divide 25/20 and we get 1.25 so it's right

Answer:

yeet

Step-by-step explanation:

Therefore, the area of the region r is 8 square units.

To start, let's graph the two lines and the equation y=x^2+1 in the first quadrant:
As we can see from the graph, the region r is a triangle with a curved bottom. To find the area of this region, we can use integration.
First, we need to find the x-coordinates of the points where the line y=5 intersects with the curve y=x^2+1. To do this, we set the two equations equal to each other:
5 = x^2 + 1
Subtracting 1 from both sides gives us:
4 = x^2
Taking the square root of both sides, we get:
x = ±2
Since we are only interested in the positive x-value (since we are in the first quadrant), we have:
x = 2
Next, we need to set up our integral to find the area of the region r. Since the region is bounded by the lines x=0 and y=5, and the curve y = x^2+1, we can integrate with respect to y, using the limits of integration y=1 and y=5 (since the curve starts at y=1 when x=0).
The area of the region r can be found using the following integral:
A = ∫[1,5] [√y - 1] dy
Integrating, we get:
A = [2/3 y^(3/2) - y] [1,5]
A = [2/3 (5)^(3/2) - 5] - [2/3 (1)^(3/2) - 1]
A = 25/3 - 1/3
A = 8
Therefore, the area of the region r is 8 square units.

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The order of increasing radius as predicted is:
li+ < na+ < ne < na

Based on the periodic table, the trend for atomic radius is that it decreases from left to right across a period and increases down a group. Therefore, we can predict that the order of increasing atomic radius for the given ions and element is as follows: Ne < Na+ < Li+ < Na. This is because Ne is a noble gas with a full valence shell and the smallest atomic radius. Na+ and Li+ have lost one and two electrons respectively, resulting in a decrease in electron-electron repulsion and a smaller ionic radius than their respective neutral atoms. Finally, Na, being a larger atom than Li, will have a larger atomic radius due to more electron shells

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Answer:

r = -1

or

r = 1

Step-by-step explanation:

because the outer lines "|    |" mean the absolute value, or the absolute opposite value of what is inside "|   |"

this means that if r = -1 then

3(-1) = -3 but -3 is in "|  |" so

|-3| = 3

and

|3| = 3

therefore r can equal -1 and/or 1

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Answer:

this so hard

Step-by-step explanation:

Answer:

the answer is the first one which is a

Answer:

A

Step-by-step explanation:

Distributive property is the stuff you do in the parentheses. Here's an example-

6(x+1)=13

6 times x would be 6x and 6 times 1 would be one

6x+1=13

Separate the x

6x+1=13

    -1    -1

6x=12

Divide

x=2

Answer:

42

Step-by-step explanation:

Find the prime factorization of 126

126 = 2 × 3 × 3 × 7

Find the prime factorization of 420

420 = 2 × 2 × 3 × 5 × 7

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 3 × 7

GCF = 42

The highest common factor HCF of 126 and 420 is 42

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the HCF of the two numbers be represented as n

The value of n is

Let the first number be p = 126

Let the second number be q = 420

The factors of 126 = 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

The factors of 420 = 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20 , 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420

So , the highest common factor of the two numbers 126 and 420 is 42

Therefore , the value of n = 42

Hence , the HCF is 42

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Answer:

Domain: (-infinite, -8) U (-8, 2) U (2, +infinite)

Step-by-step explanation:

The graphs never intersect with the lines x=-8 and x=2 so -8 and 2 cannot be included in the domain.

Use "[]" for included and "()" for excluded.

The domain will go from far left to -8 => (-infinite, -8).

Then, the domain will go from -8 to 2 => (-8, 2).

Last, the domain will go from 2 to +infinite => (2, +infinite).

The number of children admitted is 164 and the number of adults admitted is 195  

A linear Equation is a mathematical expression that is used to find unknown numbers. In this, we use different variables to represent the unknown number.

To find the unknown number obtain a linear equation according to the given condition and solve the equations.  

Here we have,

The admission fee for children is 1.5 dollars

The admission fee for adults is 4 dollars

On a certain day, 359 entered the park

Since we don't know the number of children and adults we will use different variables to represent them as shown below

Let x be the number of children

Let y be the number of adults

From the given data

=> x + y = 359 -----(1)

Admission fee collected for x children = 1.5 × x = 1.5x

Admission fee collected for y adults = 4 × y = 4y  

And total fee collected = 1.5x + 4y = 1026 ----(2)

To find the number of children and adults solve (1) and (2)

(1) × 1.5  => 1.5x + 1.5y = 538.5 ---- (3)  

Now do (2) - (3)

=> 1.5x + 4y - (1.5x + 1.5y)  = 1026 - 538.5

=> 1.5x + 4y - 1.5x - 1.5y  = 487. 5

=>  2.5y = 487. 5  

=>  y = 487. 5 /2 = 195

Now substitute y = 195 in (1)

=>  x + 195 = 359

=>  x = 164

Therefore,

The number of children admitted is 164 and the number of adults admitted is 195  

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Answer:

1500 visitors

Step-by-step explanation:

150=10%

10%*10=100%

So: 150*10=1500 visitors

Answer:

1,500

Step-by-step explanation:

10% of 1,500 is 150 basically

Answer:

34 is 20

35 is 82

Step-by-step explanation:

The 2 pounds of $5.61 per pound birdseed are used in the mixture.10 - 2 = 8 pounds of $8.91 per pound birdseed are used in the mixture.

Answer:2 pounds of $5.61 per pound birdseed are used in the mixture.8 pounds of $8.91 per pound birdseed are used in the mixture.

Given information:Ten pounds of mixed birdseed sells for $8.25 per pound. The mixture is obtained from two kinds of birdseed, with one variety priced at $5.61 per pound and the other at $8.91 per pound.To find:Pounds of each variety of birdseed used in the mixture.Solution:Let 'x' be the number of pounds of the first kind birdseed used in the mixture.

Then, (10 - x) will be the number of pounds of the second kind birdseed used in the mixture.The price of the first kind of birdseed per pound is $5.61.Price of x pounds of the first kind of birdseed = 5.61x dollars.The price of the second kind of birdseed per pound is $8.91.Price of (10 - x) pounds of the second kind of birdseed = 8.91(10 - x) dollars.

The total cost of the mixture = $8.25 per pound × 10 pounds= $82.50 dollars.According to the question,$$5.61x+8.91(10-x)=82.5$$Multiply the numbers inside the brackets by multiplying with the negative sign.

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Answer:

38

Step-by-step explanation:

50-12 =38 might be wrong though but try it

The simplified expression for the perimeter of the rectangle is 36m - 22.

Given,

The length of the rectangle = 3[2m - 5]

The width of the rectangle = 4[3m + 1]

We have to find the simplified form for the perimeter of the rectangle;

Perimeter of rectangle = 2[length + width]

= 2[ 3[2m - 5] + 4[3m + 1] ]

= 2[6m - 15 + 12m + 4]

= 2[18m - 11]

Perimeter of rectangle = 36m - 22

That is,

The simplified expression for the perimeter of the rectangle is 36m - 22.

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Answer:

A,D,E

Step-by-step explanation:

I just took the quiz.

Answer:

A, D, E

Step-by-step explanation:

Answer:

The watermelon

Step-by-step explanation:

12 pounds would be around 5.450 kilograms

We have evaluated the determinant of matrix A using cofactor expansion along the first row and second column and obtained the same result of \($\det(A) = -40$\) and \($\det(A) = -44$\), respectively.

We will expand along the first row:

\($\det(A) = (-3)\begin{vmatrix}5 & 1 \ 0 & 5\end{vmatrix} - 0\begin{vmatrix}2 & 1 \ -1 & 5\end{vmatrix} + 7\begin{vmatrix}2 & 5 \ -1 & 0\end{vmatrix}$\)

Simplifying the determinants:

\(\det(A) = (-3)((5)(5) - (1)(0)) - 0((0)(5) - (1)(-1)) + 7((2)(0) - (5)(-1))$$\det(A) = -75 + 0 + 35 = -40\)

We will expand along the second column:

\($\det(A) = -3\begin{vmatrix}1 & -4 \ -3 & 5\end{vmatrix} - 3\begin{vmatrix}1 & -4 \ 1 & 5\end{vmatrix} + 1\begin{vmatrix}3 & 3 \ 1 & -3\end{vmatrix}$\)

Simplifying the determinants:

\(\det(A) = -3((1)(5) - (-4)(-3)) - 3((1)(5) - (-4)(1)) + 1((3)(-3) - (3)(1))$$\det(A) = -3(17) - 3(-1) + 1(-12) = -44$\)

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Complete question:

Evaluate the determinant of the matrix A using cofactor expansion along the first row:

A = |-3  0  7|

   | 2  5  1|

   |-1  0  5|

B = |3   3   1|

   |1   0  -4|

   |1  -3   5|

The area of the union, denoted as U, formed by all the disks in the plane that touch the line segment AB, where AB has a length of 1, is equal to π/4.

To find the area of the union of all disks in the plane that touch AB, we can consider the extreme cases where the disks are tangent to AB.

Let's assume a disk is centered at a point C on AB. The radius of this disk will be denoted by r.

Case 1: The disk touches AB externally

In this case, the distance from the center of the disk to AB is r. Therefore, the diameter of the disk (2r) is equal to the length of AB, which is 1. Hence, r = 1/2.

Case 2: The disk touches AB internally

In this case, the distance from the center of the disk to AB is 0. The radius (r) of the disk will be equal to the distance between the center of the disk and one of the endpoints of AB (A or B). Therefore, r = 0.

Now, let's consider all possible positions for the centers of these disks.

If the center of the disk is located outside the line segment AB, it will fall into Case 1. If the center is located on AB itself, it will fall into Case 2.

The set U, which represents the union of all such disks, will consist of two disks:

1. The disk with radius 1/2 and centered at the midpoint of AB.

2. The disk with radius 0 and centered at any point on AB.

The area of the disk with radius 1/2 is given by π(1/2)^2 = π/4.

The area of the disk with radius 0 is 0, as it degenerates into a single point. Therefore, the total area of U is π/4.

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The complete question is:

A plane contains points A and B with AB=1. Let U be the union of all disks of radius in the plane that touch AB. What is the area of U?

The best discrete variable of measurement for the situation is an interval.

Finding the scale of measurement for the variables is the next step in selecting a statistical test after identifying the independent and dependent variables. The dependent variable must be measured using an interval or ratio scale for each of the parametric tests that we have covered so far. Many psychologists also subject variables with roughly interval scales of measurement to parametric tests. You must decide whether to use "scale" or "interval" scores when performing parametric tests of means.

Given the condition about whether the race of the defendant has an impact on jury verdicts,

and measure on a 1 (not at all) to 7 (very) scale how guilty the defendant,

The best scale of measurement for the condition is an interval.

Although the interval scale has characteristics of nominal and ordered data, it also allows for the quantification of data point differences. The variables' actual positions in the order as well as their differences are both displayed by this form of data. They can be combined or split, but not added to or subtracted from. 

The fact that zero is an existing variable adds another characteristic to this scale. Zero in the ordinal scale indicates that there is no data.

Hence the scale of measurement is an interval.

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Answer:(25y and -0.2y) and (-6 and -2)

Step-by-step explanation:

Pair means two

Hence like terms are common terms having something in common.

They are- (25y and -0.2y) and (-6 and -2).15x is left so it can't be paired

Answer:

V = 7385.28

Step-by-step explanation:

Formula of the volume of a cylinder: V = pi*r^2*h

Since you are told to replace pi with 3.14, now plug in the numbers that you are given into the formula...

V = (3.14)(14)^2*(12)

= 7385.28

Notes: Remember you always have to divide your radius in half if it gives you a diameter, BUT since in this question it's given, you don't have to do any extra work :)

Answer:

(2 , 72) and (5 , 180)

Step-by-step explanation:

Options A (2 , 72) and C (5 , 180) will be the correct options.

An equation is an expression that shows the relationship between two or more numbers and variables.

we are Given equation representing the relation between two variables 'x' and 'y' is,

y = 36x

Here, y = yards and x = inches

Now Satisfy this equation with each point given in the question;

Option A. (2, 72)

72 = 36 × 2

72 = 72

This is True

Option B. (4, 40)

40 = 36 × 4

40 = 144

This is False

Option C. (5, 180)

180 = 36 × 5

180 = 180

This is True

Option D. (40, 4)

4 = 36 × 40

4 = 1440

This is False

Option E. (72, 2)

2 = 36 × 72

2 = 2592

This is False

Option F. (180, 5)

5 = 36 × 180

5 = 6480

This is False

Therefore, Options (A) and (C) will be the correct options from all the other

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The direction of t + u + v is 335°

Vector addition is the process of combining two or more vectors to obtain a single resultant vector. This is done by adding the corresponding components of the vectors.

In this case, we need to add the magnitudes and directions of vectors t, u, and v to find the magnitude and direction of their sum t+u+v.

Here we have

The magnitude and direction of vectors t, u, and v are  

Vector   Magnitude    Direction

 t                  5             250°

 u                 6               60°

 v                 12             330°

To find the direction of t + u + v, first, find the components of each vector:

=> t = (5 cos 250°, 5 sin 250°) = (-1.71, -4.7)

=> u = (6 cos 60°, 6 sin 60°) = (3, 5.2)

=> v = (12 cos 330°, 12 sin 330°) = (10.39, -6)

Now add the components of the vectors to

find the components of their sum:

=> t + u + v = (-1.71+ 3 +10.39, -4.7 + 5.2 - 6) = (11.68, -5.5)

Now, use the arctangent function to find the direction of the sum:

=> θ = tan⁻¹(-5.5/11.68)

=> θ = -25.2°

Since this angle is negative, we add 360° to get the equivalent positive angle in the standard position:

=> θ = 360° -25.2° = 334.8 ≅ 335°

Rounding to the nearest degree, the direction of t + u + v is 335°.

Therefore,

The direction of t + u + v is 335°

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Complete Question:

The magnitude and direction of vectors t, u, and v are shown in the table.

Vector   Magnitude    Direction

 t                  5             250°

 u                 6               60°

 v                 12             330°

What is the direction of t + u + v? Round to the nearest degree.

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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Answer:

Below.

Step-by-step explanation:

1 / secA+tanA =  1 / [1/cosA+sinA/cosA))]

= 1/ [(1 + sinA)/cosA]

= cosA/(1+sinA)

Now check if this is identical to 1-sinA/cosA:

1-sinA/cosA = cosA/(1+sinA)

Cross multiply:

(1-sinA)(1+sinA) = cos^2A

1 - sin^2A = cos^2A

sin^2A + cos^2A = 1  

This is a known idenity.

So the original identity is true.

The narrator suggests that she now lives her life by striving to find optimism in even the worst circumstances when she adds, "I too have planted marigolds," at the conclusion of the story.

Because the narrator characterized the marigolds in the story as "Dazzling strips of bright petals bunch together in gigantic mounds warm and passionate in sun golden," the narrator's description of and response to seeing the marigolds is rather favorable.

The ability to comprehend and appreciate others as fully human beings serves as the story's central subject and marks the start of adulthood. Lizabeth felt ashamed when she realized she had wronged a genuine human being instead of a "witch" when she vented her anger at the marigolds and turned to look at Miss Lottie.

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The equations represent the given situation is:

2x - y = -6

3x - y = -5

where, x is the smaller number and y is the larger number.

Let the smaller number be x.

We have been given a number, y, is equal to twice the sum of a smaller number and 3

So, we get an equation,

y = 2(x + 3)

y = 2x + 6                        

2x - y = -6

The larger number is also equal to 5 more than 3 times the smaller number.

So, we get an equation,

y = 5 + 3x                        

3x - y = -5

Therefore, the equations represent the situation:

2x - y = -6

3x - y = -5

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Answer:

Answer: A

Step-by-step explanation:

Divide each fraction by the denominator into the numerator.

14/9 = 1.555555

13/2 = 6.5

5/8 = .625

2/3 = .666666667

The answer is A

The median of the given data set {3, 1, 2, 6, 8} is 3. So from the given options, the second option is correct.

Given data set  = {3, 1, 2, 6, 8}

Finding Median: To find the median, we have to arrange the given data set in either ascending or descending order and if the data set contains odd elements then the median is the middle element. Else the data set contains the even elements, the median is the average of two middle elements.

Let's arrange the given data set in ascending order = {1, 2, 3, 6, 8}

Given data set contains odd elements so, the median is the middle element. The middle element in the given data set is '3. So, the median is 3.

From the below given options, the second option which states, "no, the median is 3 inches" is the correct option.

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Given question is not having enough information, so I am attaching the complete question below.