he three data sets have the same mean and range, but is the variation the same? Prove your answer by computing the standard deviation. Assume the data were obtained from samples. (a) 4, 5, 11, 13, 13, 14 (b) 5, 7, 10, 10, 13, 15 (c) 3, 10, 11, 11, 12, 13

The coordinates of the fourth vertex are (0, -4).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;

Midpoint = [(3 - 6)/2, (6 - 6)/2]

Midpoint = [-3/2, 0/2]

Midpoint = (-1.5, 0).

For the fourth vertex, we have:

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(-1.5, 0) = [(-3 + x₂)/2, (4 + y₂)/2]

-3 + x₂ = 2(-1.5)

x₂ = -3 + 3

x₂ = 0.

4 + y₂ = 0

y₂ = -4.

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Answer: 18 boxes per hour

Step-by-step explanation:

72 divided by 4 is 18

Answer:

Answer D is correct

Step-by-step explanation:

As a result, the particle's velocity changes as time passes. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3.

A mathematical equation, such as 6 x 4 = 12 x 2, states that two numbers or values are equivalent. a meaningful noun. When several or even more components need to be taken into account simultaneously in order to comprehend or describe the entire situation, an equation is used.

The derivatives of the displacing equation with time as a parameter is the particle's velocity.

v = ds/dt = d/dt (2/t²) = -4/t³

As a result, the particle's velocity at times t = a, t = 1, t = 2, and t = 3 is as follows:

v(a) = -4/a³

v(1) = -4/1³ = -4 m/s

v(2) = -4/2³ = -0.5 m/s

v(3) = -4/3³ = -0.15 m/s

The particle's velocity consequently varies over time. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3. Due to the fact also that velocity is negative for any and all values of t, the particle is travelling in the reverse way (i.e., to the left).

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Answer:

Net profit is the amount of money that a company has earned after deducting all of its expenses, taxes, and other costs from its total revenue. It is the final result of a company's income statement, which shows the revenue, expenses, gains, and losses incurred during a specific period of time, typically a year. Net profit is often used as a key measure of a company's financial performance and is a crucial metric for investors and stakeholders in evaluating the success of a business.

Step-by-step explanation:

Answer:53

Step-by-step explanation:

Answer:

7.75 ; 7.81 ; 7.77 ; 7.84

Answer:

140in^2

Step-by-step explanation:

Split the area into 3 different shapes, and solve for the area of each (see picture below)

For the first area, the left triangle, we have a length of 4 and a height of 7. So we're going to multiply these two numbers together, then divide by 2 since we're only solving for the area of a triangle and not a rectangle. This gives us 14in^2.

Next, we can simply multiply 15 by 7 to get an area of 105in^2, since this is a rectangle.

For the last area, we can do the same thing as the first. Multiply 6 by 7, then divide by 2, giving us 21in^2.

Finally, we can add up all of these areas to get the total area, and our final answer:

14+105+21=140in^2

Answer:

212.5ft^2

Step-by-step explanation:

First, go ahead and find the area of the total square. To do this, multiply the length by the height (15*15) to get 225. This is not our final answer, but it will help us solve the problem later.

Next, we need to find the area of the lower-left triangle that is cut off. To do this, we will find the side lengths of just that section. Because the left side of the square and the right side are the same total length, we can just subtract 10 from 15 to get a length of 5.

Now, to find the area of the triangle we will use b*h/2:

5*5/2=12.5

All that's left is to subtract this area from the initial area (225) to get our final answer of 212.5ft^2.

Answer:

Step-by-step explanation:

(a) Since the current entering and leaving the intersection of wires must be equal, we have:

x + y = 18 (current entering the top intersection)

z + w = 18 (current leaving the top intersection)

x + z = 9 (current entering the bottom intersection)

y + w = 9 (current leaving the bottom intersection)

We can solve this system of equations using substitution or elimination. For example, we can eliminate w by adding the first two equations and subtracting the last two equations:

2x + 2y + 2z = 36

2y + 2z - 2x = 0

2z - 2x = 9

Solving for z in terms of x, we get:

z = (x + 9/2)

Substituting this into the first equation, we get:

x + y = 18

Substituting z in terms of x into the second equation, we get:

w = (18 - z) = (18 - x - 9/2) = (27/2 - x)

Therefore, the solution in terms of x, y, z, and w is:

(x, y, z, w) = (x, 18 - x, x + 9/2, 27/2 - x)

(b) To know all of the currents exactly, we need to measure the current in any one wire that is not already determined by the system of equations. From part (a), we see that w is determined in terms of x, y, and z. Therefore, we should measure the current in wire x or y to know all of the currents exactly.

Answer:

The answer that you are looking for is 70º

Step-by-step explanation:

Usually, in three-sided figures, there is a total of 3 angles all adding up to 180º.

So in turn, since most quadrilaterals are made up of 2 triangles all the sides have to equal to 360º.

We can use the equation 360 = 110×2+q2

To find the value of q.

The First step to do is to simplify all terms with 110×2 being equal to 220 and q2 staying the same.

We then use the opposite symbol to remove 220 leaving q2 by itself while 360 is subtracted by 220 and turned into 140.

The only thing left to do is to do the opposite operation of multiplying, which is dividing and dividing both sides by 2 leaving q = 70.

You can find the equation below:
360 =  110×2+q2
360 =  220 + q2
-220 = -220 + q2
 140 = q2
  ÷2 = ÷2
  70 = q

I hope this was helpful!

The total amount that Rahul will have is 108,006.20.

Compound interest is a type of interest where the interest earned on a principal amount is added to the principal, and the new total amount becomes the basis for calculating interest in the next period.

In other words, the interest is earned not only on the principal amount but also on the accumulated interest.

The formula for compound interest is:

Here we have, Rahul's plans to invest $25,000 in a retirement account that compounds 6% monthly.

From the data,

The principal amount, P = 25000

Rate of interest, r = 6% = 6/100 = 0.06

Time period, t = 25 years  

Number of compounds, n = 12  [ Since compounded annually ]

By using the formula, A = P (1 + r/n)^(n×t)  

A = 25000 [ 1 + 0.6/12]⁽¹²ˣ²⁵⁾

A = 25000 [ 1 + 0.005]⁽³⁰⁰⁾

A = 25000 [1.005]⁽³⁰⁰⁾  

A = 108,006.20 (rounded to the nearest cent)  

Therefore,

The total amount that Rahul will have is 108,006.20.

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Answer:281.92 cm

Step-by-step explanation:

ok so we have a triangle and the area of a triangle is bh/2 so 12.8x8.81/2= 56.384 and since we have 5 of these 56.384x5=281.92Cm

Therefore , the solution of the given problem of equation comes out to be  the system of equations has an answer of x = -20 and y = 10.

The same letter is frequently used in mathematical formulas to attempt to enforce variable uniformity among two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using the outcome y + 6 = 12 as an example, the normalise divides the numbers 12 and b + 6 into 2 parts. The relationship between each symbol component and the amount of lines can be found. A symbol's meaning typically runs counter to itself.

Here,

The set of linear equations can be used to find the values of x and y:

144x + 288y = 1440 \s28x + 84y = 280

By dividing both parts of the second equation by 28, we can begin by making it simpler:

x + 3y = 10

Then, by separating x, we can use this equation to solve for x in terms of y:

x = 10 - 3y

In order to simplify the first problem, we can use this expression in place of x:

=>  144(10 - 3y) + 288y = 1440

=>  1440 - 432y + 288y = 1440

=>  -144y = -1440

=>  y = 10

Given that y = 10, we can solve for x by substituting this number into the equation x + 3y = 10:

=>  x + 3(10) = 10

=>  x + 30 = 10

=> x = -20

As a result, the system of equations has an answer of x = -20 and y = 10.

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Answer:

y = 3/5x - 3

Step-by-step explanation:

slope (m) of line perpendicular to y = -5/3x is 3/5, the negative reciprocal of -5/3

use the point (5, 0) and the point-slope form to find b, the y-intercept:  

y - 0 = 3/5(x - 5)

y = 3/5x - 15/5

y = 3/5x - 3   equation is now in the slope-intercept form

The key features of the graph are

If the graph has a local maximum

From the given graph, we can see that:

The graph has a maximum (momentarily) at x = 1

This means that "yes", the function has a local maximum at x = 1

The local maximum

In (a), we have

x = 1

The y coordinates at this point is

y = 1

So, the local maximum is y = 1

The decreasing interval

From the graph, we can see that the y values decrease from -∝ till x = -1 and also decrease from x = 1 till ∝

The function type

Based on the appearance of the graph, the function is an odd function

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The the estimated answer is 42 and the actual answer is 41.91. The answer 41.91 is very close to the estimated answer of 42, so it looks sensible.

When rounding to one significant figure, we keep only the leftmost digit that is not zero. Therefore, rounding 33.72 and 8.19 to one significant figure gives 34 and 8 respectively so the estimated answer is;

34 + 8 = 42

Actual answer answer is derived as;

33.72 + 8.19 = 41.91

In conclusion, the estimated answer is 42 and the actual answer is 41.91. The answer 41.91 is very close to the estimated answer of 42, so it looks sensible.

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Answer:

-csc^2 θ = dθ/dt = 1/5 (dx/dt)

or

3.49 km/min

Step-by-step explanation:

dx/dt

- 5cosec^2 θ * (rate of change of angle of elevation)

- 5 cosec^2 (π/3) * (-π/6)

(5π/6) * (4/3)

= 10π/9 km/min. = 3.49 km/min

Substituting the values shows that the point that lies on the exponential function are

We can use substitution to determine which ordered pairs lie on the graph of the exponential function f(x) = 3(4)^2x.

For the first ordered pair (0, 3),

f(0) = 3(4)^2(0) = 3(1) = 3

(0, 3) lies on the graph of the exponential function.

For the second ordered pair (1, 48)

f(1) = 3(4)^2(1) = 3(16) = 48

(1, 48) lies on the graph of the exponential function.

For the third ordered pair (1/2, 12),

f(1/2) = 3(4)^2(1/2) = 3(4) = 12

(1/2, 12) lies on the graph of the exponential function.

For the fourth ordered pair (.25, 8), :

f(0.25) = 3(4)^2(0.25) = 6

say that (0.25, 8) does not lie on the graph of the exponential function.

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Answer: 90%

Step-by-step explanation:

18/2=9

20/2=10

9 out of 10 is 90%

Answer: 81.82%

Step-by-step explanation: A percentage is a number or ratio that can be expressed as a fraction of 100.

here, we have,

given that,

In Mrs. Stone's class, 18 out of 22 students turned in their homework on time.

now,

the  percent of the class turned their homework in on time is,

18/22 * 100

=81.82%

The numbers 4 and 12  are not the best factors to use because they do not fully simplify the expression

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

Square root of 48

This can be expressed as

√48

Using Letty's solution, we have

√48 = √(4 * 12)

This gives

√48 = 2√12

So, we simplify again

√48 = 2√(4 * 3)

This gives

√48 = 4√3

Hence, the factors are not the best

Instead, she can use 16 and 3

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The order of operations (also known as BODMAS) should be used to evaluate this expression:

6 + 2*6 + 20/4 = 6 + 12 + 5 = 23

So the answer is 23.

Answer:

If the marlin weighs over 1,500 pounds, and it "dresses out two thirds of that," that means that the weight of the meat that can be harvested from the marlin is 2/3 of 1,500 pounds, or 1,000 pounds (since 2/3 x 1,500 = 1,000).

If the price per pound is thirty cents, then the total value of the meat is 1,000 x 0.30 = $300.

The answer as a fraction in lowest terms is 4/81, and the denominator is 81.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

There are 4 green card, 2 red cards, 3 blue cards

Now,

If the first card drawn is red and is replaced before the second draw, then the probability of drawing a red card on the second draw is the same as the probability of drawing a red card on the first draw, which is 2/9 (since there are 2 red cards out of a total of 9 cards).

To find the probability of drawing two red cards, we need to multiply the probability of drawing a red card on the first draw (which we know is 2/9) by the probability of drawing a red card on the second draw, which is also 2/9 (since the first card is replaced).

So the probability of drawing two red cards with replacement is:

(2/9) * (2/9) = 4/81

Therefore, the probability and denominator will be 4/81 and 81.

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Answer:

The answer is 1/25

Step-by-step explanation:

The triangle will have a perimeter of 19 units.

Triangle perimeter: The circumference of any two-dimensional figure is referred to as its perimeter. By adding the lengths of the sides, we can determine the perimeter of any closed shape. You will first learn what the perimeter is in this article.

For a triangle, the perimeter is the sum of all the sides of the triangle. To calculate the perimeter add all the sides of the triangle as below,

Perimeter = 4 + 6 + 9

Perimeter = 19 units

Therefore, the perimeter of the triangle is 19 units.

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The complete question is given below.

The sides lengths 4, 6, and 9 can be used to form the size of a triangle. Find the perimeter of the triangle.

Answer:

Step-by-step explanation:

gain

loss

gain loss

gain

Answer:

Gains : +1,+10,+3

loss: -3,-5,-9,-100

Step-by-step explanation: I think this question is basically just asking about givings examples of positive and negative numbers

The e values that satisfy the inequality 3e ≤ 6, are e = 1 and e = 2.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

To determine which values of e satisfy the inequality 3e ≤ 6, we can divide both sides by 3 -

3e/3 ≤ 6/3

e ≤ 2

Therefore, any value of e that is less than or equal to 2 will satisfy the inequality.

Out of the given choices, e = 1 and e = 2 satisfy the inequality, but e = 3 does not, because 3 is greater than 2.

Therefore, the correct answers are -

e = 1 and e = 2

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Answer:

The percentage increase is  21.4% increase

Given Data

Initial temperature =  12 1/4°F = 49/4 = 12.25°F

Final Temperature =  15 3/5°F = 78/5 = 15.6°F

We know that the expression for percentage increase is given as

Percent Increase = Increase/Final *100

Percent Increase = 15.6-12.25/15.6 *100

Percent Increase = 3.35/15.6 *100

Percent Increase = 0.214 *100

Percent Increase = 21.4%

Hence there is a 21.4% increase

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The missing term of question is "distance".

Distinct points refer to points that are not the same. In other words, if two or more points have different locations or coordinates, they are considered distinct points.

Distance is a measure of the length or space between two points, lines, or other objects. It is typically expressed as a non-negative number and can be determined using various formulas depending on the context and the nature of the objects being measured.

The missing term in the question is "distance". The sentence can be completed as:

"Between every pair of distinct points, there is a positive unique number called the "distance", which can be determined as the "absolute value of the difference" of the corresponding real numbers of the two points."

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Answer:

Step-by-step explanation:

37