The questions below can be answered by collecting data. Data related to which question is most likely to show variability?

For the system of equations 2y = 2x and y = x, there are infinite number of solutions.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The system of equations given by 2y = 2x and y = x can be solved by substituting y = x into the first equation -

2y = 2x

Substituting y = x, we get -

2x = 2x

Now, on simplifying, we get -

x = x

The equation x = x is true for all values of x.

Therefore, there are infinitely many solutions to this system of equations.

In geometric terms, the two equations represent two lines in the coordinate plane that intersect at every point on the line y = x.

Therefore, the number of solutions is infinite.

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Answer: top two goes together, middle left goes to bottom right, bottom left goes to middle right

Step-by-step explanation:

Substitute x for an easy number like 2 and solve.

x - 2/3 - 1/2x = 1/2x - 2/3

x - 1/2 - 3/4x = 1/4x- 1/2

1/3x - 3/4 - 2/3x = -1/3x - 3/4

A finite sequence is a sequence with a finite number of elements, that is, a sequence that has a definite beginning and end.

In mathematics, a sequence is a set of numbers, arranged in a particular order. Each number in the sequence is called a term or element of the sequence, and is identified by its position or index in the sequence. For example, the sequence of natural numbers 1, 2, 3, 4, 5, ... can be represented as {a_n}, where a_1 = 1, a_2 = 2, a_3 = 3, and so on.

A sequence can be either finite or infinite. A finite sequence has a fixed number of terms, while an infinite sequence continues indefinitely. A sequence can also be arithmetic, geometric, or neither.

An arithmetic sequence is a sequence in which each term is obtained by adding a constant value, called the common difference, to the previous term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3.

In mathematics, a sequence is an ordered list of elements, typically numbers or other mathematical objects, that are written in a particular order. A finite sequence is a sequence with a finite number of elements, that is, a sequence that has a definite beginning and end.

For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of five elements. The first element is 1, the second element is 2, and so on, until the last element, which is 5. The sequence {1, 1/2, 1/4, 1/8, 1/16} is another example of a finite sequence, this time of decreasing terms.

Finite sequences are used in many areas of mathematics, including algebra, calculus, and number theory. They are often studied in their own right, and their properties and patterns can be used to solve problems and prove theorems.

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The radius of the Earth's orbit around the sun is approximately 93 million miles.

To calculate the circumference of the Earth's orbit, we can use the formula:

C = 2πr

where C is the circumference and r is the radius. Plugging in the value for the radius, we get:

C = 2π(93,000,000) = 584,336,000 miles

So the Earth travels approximately 584,336,000 miles in one orbit around the sun.

The speed of the Earth in its orbit around the sun can be calculated using the formula:

v = 2πr/T

where v is the velocity, r is the radius, and T is the period (the time it takes for the Earth to complete one orbit). The period of the Earth's orbit is approximately 365.25 days, or 31,557,600 seconds.

Plugging in the values, we get:

v = 2π(93,000,000)/(31,557,600) = 29,784 miles per hour

So the Earth travels at approximately 29,784 miles per hour in its orbit around the sun.

The amount after 10 years will be obtained by continuous compounding is $2443.1.

The formula for the continuous compounding:

A = P[tex]e^{rt}[/tex]

A = amount after compounding.

P = principal $2000

r = rate of interest 2%

t = time 10 years

Then,

A = 2000* [tex]2.72^{0.02*10}[/tex]

A = 2000* 1.22155

A = 2443.1

Thus, the amount after 10 years will be obtained by continuous compounding is $2443.1.

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The expression that completes the equation the result of 30/100 + 9/10 is 1.2.

The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. When attempting to solve problems containing two linear equations, this form is also quite helpful.

We must multiply the values of 30 and 100, then add the resulting product to the resulting product of the values of 9 and 10 in order to complete the equation 30 100 + 9 10.

The result of multiplying 30 by 100 is:

30 x 100 = 3000

The result of adding 9 and 10 is:

9 x 10 = 90

Thus, we must combine these two items to finish the equation:

3000 + 90 = 3090

30100 + 910 = 3090, which is the expression that completes the equation.

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the complete question is:

complete the equation

[tex]\frac{30}{100}+\frac{9}{10}[/tex]

Answer:

The answer is 39/100

Step-by-step explanation: Nothing more.

AB/BC = DE/EF

35/15 = DE/60

DE = 35*60 / 15

DE = 140

answer

A 140

Answer: Supplementary   x=2

Step-by-step explanation:

supplementary adds up to 180

complementary adds up to 90

Answer:

  C.  396

Step-by-step explanation:

You want the LCM of 4, 18, and 44.

You can find the least common multiple by considering the unique factors to their highest powers.

  4 = 2^2

  18 = 2·3^2

  44 = 2^2·11

The unique factors are 2, 3, 11, and their highest powers are 2, 2, and 1, respectively. The LCM is ...

  2² × 3² × 11 = 396

__

Check

  396 = 4·99 = 18·22 = 44·9 . . . . . 99, 22, and 9 have no common factors

The number of runners who are expected to finish the race, given the probability of finishing and the number who registered is 1, 375 runners.

The probability of a runner finishing the race is 11/12. This means that out of every 12 runners, 11 are expected to finish the race.

We know that 11 out of 12 runners are expected to finish the race, so we can write:

11/12 = x/1,500

11 × 1,500 = 12 × x

16,500 = 12x

x ≈ 1,375

Therefore, approximately 1375 runners are expected to finish the race out of 1500 runners.

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Answer:

Experimental Procedure:

Materials:

Piece of wood

Electronic balance

Bunsen burner

Heat-resistant mat

Stopwatch or timer

Safety goggles

Lab coat

Safety Precautions:

Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.

Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.

Use the Bunsen burner only under adult supervision.

Be cautious when handling hot objects, and allow them to cool before touching.

Procedure:

Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.

Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.

Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).

After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.

Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.

Calculate the difference between the initial and final mass of the wood, and record it in the table.

Repeat steps 1-6 three times to obtain three sets of data.

Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.

Conclusion:

If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.

Answer:

2.83333 pounds of flour in each container

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.

To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).

by the question.

a. x-3.5>6.9

x>6.9+3.5

x>10.4

b. 6.4>x+3.1

x[tex]\geq 32[/tex]

c. x/4≤8

x≤32

d. 2/3x≤-10

x≤-15

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Answer:

a) To find the probability that a randomly chosen student completes the activity in less than 30.1 seconds, we need to standardize the value using the formula z = (x - mu) / sigma, where x is the time taken, mu is the mean, sigma is the standard deviation, and z is the standard normal variable.

z = (30.1 - 34.7) / 7.6 = -0.6053

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than -0.6053 is 0.2739.

Therefore, the probability that a randomly chosen student completes the activity in less than 30.1 seconds is 0.2739.

b) To find the probability that a randomly chosen student completes the activity in more than 38.1 seconds, we need to standardize the value using the same formula.

z = (38.1 - 34.7) / 7.6 = 0.4474

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than 0.4474 is 0.3274.

Therefore, the probability that a randomly chosen student completes the activity in more than 38.1 seconds is 0.3274.

c) To find the proportion of students taking between 30.9 and 38.5 seconds, we need to standardize both values and then find the area between them in the standard normal distribution.

z1 = (30.9 - 34.7) / 7.6 = -0.5

z2 = (38.5 - 34.7) / 7.6 = 0.5

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being between -0.5 and 0.5 is 0.3830.

Therefore, the proportion of students taking between 30.9 and 38.5 seconds to complete the activity is 0.3830.

d) To find the time taken by 90% of all students to finish the activity, we need to find the z-value corresponding to the 90th percentile of the standard normal distribution using a standard normal distribution table or calculator.

The z-value corresponding to the 90th percentile is approximately 1.28.

Now, we can use the formula z = (x - mu) / sigma to find the corresponding time value.

1.28 = (x - 34.7) / 7.6

x - 34.7 = 1.28 * 7.6

x - 34.7 = 9.728

x = 44.428

Therefore, 90% of all students finish the activity in less than 44.428 seconds.

1. The longest side is side 2 (4√5). 2. a² = 50, b² = 80, c² = 12.

3. Since a² + b² < c², the triangle is obtuse.

An obtuse triangle is a triangle with one angle greater than 90 degrees.

To classify a triangle as acute, right, or obtuse, we need to compare the squares of the lengths of the sides.

In this case, a² = 50, b² = 80, and c² = 12.

If a² + b² < c², the triangle is obtuse.

If a² + b² = c², the triangle is right.

And if a² + b² > c², the triangle is acute.

In this triangle, a² + b² = 50 + 80 = 130, which is less than c² = 12. Therefore, the triangle is obtuse. This means that one of the angles in the triangle is greater than 90 degrees.

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Answer:

4.

a-9=15

or. a=15+9

or. a=24

5.

n-9=13

or. n=13+9

or. n=22

6.

b-8=9

or. b=9+8

or. b=17

7

x-5=16

or. X=16+5

or X=21

8

n-6=17

or. n= 17+6

or. n=23

Step-by-step explanation:

minus sign changes into plus sign when changing sides

The maximum height οf the rοcket is 16 feet.

A system οf equatiοns in algebra is made up οf twο οr mοre equatiοns that are sοlved tοgether. "A grοup οf equatiοns satisfied by the same set οf variables are called a system οf linear equatiοns. Finding the values οf the variables emplοyed in the system οf equatiοns is the first step tοwards sοlving it.

While maintaining the balance οf the equatiοns οn bοth sides, we cοmpute the values οf the unknοwn variables. Finding a variable whοse value makes the cοnditiοn οf all the given equatiοns true is the primary gοal οf sοlving an equatiοn system.

(x - 2)(x - 5) = 0

Sο x = 2 οr x = 5.

If x = 2, then frοm the equatiοn οf the flare, we have y = -2 + 14 = 12.

If x = 5, then frοm the equatiοn οf the flare, we have y = -5 + 14 = 9.

Sο the twο οbjects intersect at the pοints (2, 12) and (5, 9).

Tο find the maximum height οf the rοcket, we can use the fοrmula fοr the x-cοοrdinate οf the vertex οf a parabοla:

x = -b/2a

In this case, a = -1 and b = 8, sο we have:

x = -8/-2 = 4

Sο the rοcket reaches its maximum height at x = 4. Tο find the maximum height, we can substitute x = 4 intο the equatiοn fοr the rοcket:

[tex]y = -4^2 + 8(4) = 16[/tex]

Sο the maximum height οf the rοcket is 16 feet.

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The experimental probability that the next piece of jewelry sold will be a bracelet is of 11/26.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

For the experimental probability that the next piece of jewelry sold will be a bracelet, the outcomes are given as follows:

Hence the experimental probability that the next piece of jewelry sold will be a bracelet is obtained as follows:

p = 22/52

p = 11/26.

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Mr. Allen's annual salary in the year 2007 was $90,000.

Given that, mr. Allen has a wife and three children. His monthly salary during the year 2007 was $7500.

To calculate Mr. Allen's annual salary, we need to multiply his monthly salary by the number of months in a year:

Annual salary = Monthly salary × Number of months in a year

Since Mr. Allen's monthly salary in 2007 was $7500 and there are 12 months in a year, his annual salary can be calculated as:

Annual salary = Monthly salary × Number of months in a year

Annual salary = $7500 × 12 months

Annual salary = $90,000

Therefore, his annual salary was $90,000.

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Answer: A.   -2√7

Step-by-step explanation:

3√7 - 5√7

= -2√7

Answer:x=11.42

Step-by-step explanation:

[tex]\frac{35}{20} =\frac{20}{x}[/tex]

[tex]35x=400[/tex]

[tex]X=11.42[/tex]

Answer:

To calculate the payback period (PBP) for this project, we need to determine how long it will take for the initial cash outlay of $40,000 to be recovered from the after-tax cash flows.

Year 1 cash flow = $10,000

Year 2 cash flow = $12,000

Year 3 cash flow = $15,000

Year 4 cash flow = $10,000

Year 5 cash flow = $7,000

Total cash inflows for year 1 and year 2 = $10,000 + $12,000 = $22,000

Total cash inflows for year 3 = $15,000

Total cash inflows for year 4 = $10,000

Total cash inflows for year 5 = $7,000

Cumulative cash inflows for year 1 and year 2 = $22,000

Cumulative cash inflows for year 3 = $37,000

Cumulative cash inflows for year 4 = $47,000

Cumulative cash inflows for year 5 = $54,000

It can be seen that the cumulative cash inflows reach the initial cash outlay of $40,000 after year 2, and therefore the payback period for this project is 2 years. Since the payback period is less than the maximum PBP of 3.5 years set by management, this project can be considered acceptable.

So, Hodgman Honest should recommend that Basket Wonders should accept this project as it has a payback period of only 2 years, which is less than the maximum PBP of 3.5 years set by management.

Answer: D

Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis

To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.

The image undergoes a reflection at y=-3, Option D is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.

In the given figure the above image is original and it is flipped to form the image which is below the x axis.

In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

Hence, the image undergoes a reflection over y axis which is at y=-3.

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To simplify the expression 5^2 + 9^2, we can evaluate the squares of 5 and 9 and then add the results:

5^2 = 5 x 5 = 25

9^2 = 9 x 9 = 81

So, 5^2 + 9^2 = 25 + 81 = 106

Therefore, the simplified form of the expression 5^2 + 9^2 is 106.

Answer: x = -2, [tex]\frac{2 }{3}[/tex]

Step-by-step explanation:

     Given:

0 = –3x² – 4x + 4

    The quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

    Substitute known values:

* a = -3, b = -4, c = 4

[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-3)(4)} }{2(-3)}[/tex]

    Simplify with multiplication:

[tex]\displaystyle x=\frac{4\pm\sqrt{16+48} }{-6}[/tex]

    Simplify:

[tex]\displaystyle x=\frac{4\pm\sqrt{64} }{-6}[/tex]

[tex]\displaystyle x=\frac{4+8 }{-6}[/tex],    [tex]\displaystyle x=\frac{4-8 }{-6}[/tex]

[tex]\displaystyle x=\frac{12 }{-6}[/tex],    [tex]\displaystyle x=\frac{-4 }{-6}[/tex]

Hence, the system with nonlinear equations may contain one of these kinds of answers, depending on the particular equations and their graph.

Unable to form a straight line is a non-linear equation. With a fluctuating slope value, it resembles a graphed curve.

In general, there can be zero, one, many, or an infinite number of solutions to a system of nonlinear equations. It depends on the particular equations and how those interact with one another.

The problem has zero solutions if there are no values of the parameters that satisfy both equations, which occurs when the equations are inconsistant.

A single solution exists for the system if the equations cross at that point.

The system has multiple solutions if the equations cross more than once.

The system has an infinite number of solutions if the equations all describe the same curve.

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Answer:

Step-by-step explanation:

is a rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

Area = 1/2 b * h

Area =1/2 7 * 4

Area = 3.5 * 4

Area = 14 in²

So we have 7 in. and 4 in. so we just will mutilply It, So what we do here Is mutilply so we will do 7 x 4 = 28

So we have 28 then we mutilpy all of chocies to see which one Is 28.

A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

11 x 2=22 ❌ Not 28                                      

14 x 2 = 28 ✅ Is 28                                                                                                                                                            

22 x 2 = 44  ❌ Not 28

28 x 2 = 56  ❌ Not 28

A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

Area = 1/2 b * h ❌

 Area = 3.5 * 4  ❌            

 Area = 3.5 * 4  ❌      

 Area = 14 in²   ✅

We can compare the amount in the IRA at retirement to the total deposits made over the time period to determine if the interest earned has exceeded the amount deposited.

IRA is an acronym that stands for "Individual Retirement Account." It is a sort of investment account meant to assist individuals in saving for retirement. Individuals can deposit pre-tax income to an IRA, and the money in the account grows tax-free until taken in retirement.

Part 1: To calculate the amount that the IRA will contain when the person retires at age 65, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

In this situation, the individual establishes the IRA at age a, thus they have t = 65 - a years till retirement. Because the APR is expressed as a percentage, we must divide it by 100 to obtain the annual interest rate in decimal form. Because the individual deposits $d at the end of each month, n = 12 (monthly compounding) and the effective monthly interest rate is r/12.

Therefore, the amount of money in the IRA at retirement can be calculated as:

[tex]A = d * ((1 + r/12)^(12*(65-a)) - 1) / (r/12)[/tex]

Part 2 : We can compare the amount in the IRA at retirement to the total amount of deposits made over the time period. The total amount of deposits can be calculated as:

Total Deposits = 12 * (65-a) * d

The amount in the IRA upon retirement (estimated in Part 1) may then be compared to the total contributions made during the time period. If the amount in the IRA exceeds the total deposits, the interest generated has exceeded the entire deposits. If the amount in the IRA is less than the total deposits, the interest produced will not be sufficient to compensate for the amount contributed.

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Answer:

12,500 is 100%, or 1 in decimal terms. We calculate 5% by multiplying 12500 by 0.05.

This gives us a total of £625

Step-by-step explanation:

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