Ethan is planning for his retirement. He has narrowed it down to two investment options. The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years. The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years. If both compound interest at a rate of 2.5%, determine which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account. Round your final answer to the nearest cent.

Answer:

Step-by-step explanation:d = 14t + 21t = 35t

So, after 3 hours, the distance between the boats will be:

d = 35 * 3 = 105 miles

Therefore, the Serenity and the Mystic will be 105 miles apart after traveling for 3 hours.

The system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

Equation modelling is the process of writing a given mathematical statement (or word problem) in the form of a mathematical equation for the correct analysis of the given problem (or situation).

Given is that Jordan's t-shirt business sells long sleeve shirts for $18 and short sleeve shirts for $13. He needs to make at least $350 to buy a new heat press machine.

Let {S} represent the short sleeves and {L} represents the long sleeves. So, we can model the equations as -

S + L < 30

13S + 18L ≥ 350

Therefore, the system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

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The measure of angle NOP is found by solving an equation that is obtained by using the fact that the sum of the angles in a triangle is 180 degrees. The solution is m∠NOP to obtain the answer of 53.13 degrees.

In the problem, we are given a triangle NOP, where \overline{NP} is extended through point P to point Q. We are given the measures of three angles: m∠OPQ, m∠PNO, and m∠NOP.

We are asked to find the measure of angle NOP.To find the measure of angle NOP, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So, we add up the measures of the three angles we know:

m∠OPQ + m∠PNO + m∠NOP = 180

We are given the measures of m∠OPQ, m∠PNO, and m∠NOP in terms of x. We substitute these values and get an equation in terms of x:

(9x-19) + (2x+5) + (3x+16) = 180

Simplifying the left side of the equation, we combine like terms:

14x + 2 = 180

We can then isolate x by subtracting 2 from both sides of the equation:

14x = 178

And then we can solve for x by dividing both sides of the equation by 14:

x = 12.71

Now that we know x, we can use it to find the measure of angle NOP, which is what we were asked to do. We substitute x = 12.71 into the equation for m∠NOP:

m∠NOP = 3x + 16 = 3(12.71) + 16 = 53.13

Therefore, the measure of angle NOP is 53.13 degrees.

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The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The equations are given below.

y = 2x + 56       ....1

y = 9x               ....2

From equations 1 and 2, then we have

9x = 2x + 56

7x = 56

 x = 8

Then the value of the variable 'y' is given as,

y = 9(8)

y = 72

The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).

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Answer:

34 bricks is the greatest amount Mary could have used

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

so im a little confused  3,5203,5203, is not a proper number and there is not enought yards to make a full mile could you reword it?

Step-by-step explanation:

Answer:

Step-by-step explanation:

percentages are usually out of 100.

so you are turning 1/5 to x out of 100.

we can do thismany ways; i will be doing a ratio.

1:5

to

x:100

we can see that 5 times 20 equals 100, therefore, 1 times 20 would equal x.

so 20/100 is equal to 1/5.

Answer:

percentages are .so you are turning 1/5 to x out of 100. we can do this many way; I will be doing a ratio. of 1:5tox:100we can see that 5 times 20 equals 100, therefore, 1 time 20 would equal x.so 20/100 is equal to 1/5.

A quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. The value "59%" is a statistic.

In this scenario, a sample of the quarterback's passes was taken during the championship football game, and the completion percentage was calculated based on that sample. Since the percentage was calculated based on a sample, it is a statistic. A parameter, on the other hand, is a value that describes a characteristic of an entire population. For example, if we were to consider the completion percentage of all quarterbacks in the league, then the mean or median completion percentage would be a parameter because it would describe a characteristic of the entire population of quarterbacks. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.

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Complete Question

Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. Is the value a parameter or a statistic?

Overall, the article has given me a deeper appreciation for the role that statistics plays in the political landscape.

One statistical discussion that stood out to me was the concept of margin of error. This is a measure of the accuracy of a poll and is calculated by taking into account the sample size and the variability in responses. I now have a better understanding of how pollsters use this measure to determine the reliability of their results.

Additionally, the article highlighted the importance of understanding statistical significance, which refers to the likelihood that a particular result occurred by chance. This is an essential concept in statistics that helps to determine whether a particular result is reliable or not.

It has also emphasized the need to interpret polling data with caution and to be mindful of the potential for errors and biases.

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Answer:

0.0256x^4y^4

Step-by-step explanation:

If the sum of 3 consecutive even numbers is 114, we can represent the numbers as x, x+2, and x+4.

The sum of the three numbers is:

x + (x+2) + (x+4) = 3x + 6

We know that the sum is 114, so we can set up the equation:

3x + 6 = 114

Subtracting 6 from both sides gives:

3x = 108

Dividing both sides by 3 gives:

x = 36

Therefore, the three consecutive even numbers are 36, 38, and 40.

Answer:

37, 38, 39

Step-by-step explanation:

let the 3 consecutive numbers be

n , n + 1 , n + 2

then summing and equating to 114

n + n + 1 + n + 2 = 114

3n + 3 = 114 ( subtract 3 from both sides )

3n = 111 ( divide both sides by 3 )

n = 37

n + 1 = 37 + 1 = 38

n + 2 = 37 + 2 = 39

the 3 consecutive numbers are 37 , 38 , 39

Answer:

y = 43

Step-by-step explanation:

47° , y and 90° lie on the straight line AB and sum to 180° , that is

47 + y + 90 = 180

y + 137 = 180 ( subtract 137 from both sides )

y = 43

Answer:

14 bows

Step-by-step explanation:

.5 yards is need for one bow if you have 7 yards you have 14(.5) yards

easier way a half goes into 7, 14 times since 14 divide by two is 7

The different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.

The sector is essentially a section of a circle, and it may be described using the following three criteria:

The area of a disc that is surrounded by two radii and an arc is known as a circular sector.

The circle is divided into the Major Sector and the Minor Sector by a sector.

The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.

Given that,

Central angle = [tex]\frac{\pi}{6}[/tex].

The arc length is given as:

l = α/360 (2πr)

Where, α is the central angle.

Substitute the value of central angle we have:

l = (π/6)/360 2πr

l = 2π²r/ 2160

The sector area is given as:

A = α/360  πr²

A = (π/6)/360 πr²

A = π²r²/ 2160

Similarly, the arc length is given as:

l = π/3

Substituting the value of l in arc length we have:

π/3 = α/360 (2πr)

α = 360(π)/ 6πr

α = 60/r

The sector area is given as:

A = α/360  πr²

A = (60/r) 360 πr²

A = πr/60

Hence, the different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.

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The percent error in Rashida's measurement while measuring the length of the beam is 4.29%.

What is meant by percent error?

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. Percent errors show the magnitude of our measurement errors during an analysis procedure. We are getting close to the accepted or original value when the percent mistakes are smaller. The relative error is multiplied by 100 to get the percent error.

Given,

  The actual length of beam = 17 and 1/2 feet = 17.5 feet

The measured length of beam = 16 and 3/4 feet = 16.75 feet

The formula to find the percent error is as follows:

Percent error = [tex]|\frac{Measured\ value - Actual\ value}{Actual\ value} | * 100[/tex]

                   =  [tex]|\frac{16.75 - 17.5}{17.5} | * 100 =[/tex] 0.75/17.5 * 100 = 4.29%

Therefore the percent error in Rashida's measurement while measuring the length of the beam is 4.29%.

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Answer:

So, the rational number is [tex]\frac{52}{12}[/tex] .

Step-by-step explanation:

Let x be the other number.

We know ,

[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]

To find x, we need to convert both to have a common denominator.

So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex]  ,

[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]

After multiplication the fraction  [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex]  .

[tex]\frac{70}{360}[/tex]+ x =  [tex]\frac{56}{10}[/tex]

Now we have common denominator of 360in both fraction,

Now,

we can simplify the equation ,

[tex]\frac{70}{360}[/tex]  + x = [tex]\frac{56}{10}[/tex]

70 + 360x = 56 × 36

2520 + 360x = 2016

504 + 360x = 2016

360x = 1512

x = [tex]\frac{1512}{360}[/tex]

   =[tex]\frac{52}{12}[/tex]

So, the rational number is [tex]\frac{52}{12}[/tex] .

Answer:

x-8

Step-by-step explanation:

the answer is  x-8                                                             correct answer x-8

Answer:Mr. Jacob purchased 7 adult tickets at $7.50 each, and 4 child tickets at $5.00 each, for a total of 11 tickets at a cost of $65.

Step-by-step explanation:

Answer:

Answers are below ----v

Step-by-step explanation:

1. Clockwise

2. 3

3. (y, -x)

4. (3x,3y)

The shortest distance is 5.83 miles as we calculate this by distance formula.

A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:

PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

The school is located 5 miles west of your home the co ordinate is (-5,0)

The playground is 3 miles south of the school so co - ordinate is (0,-3)

shortest distance  = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

√([tex]5^{2} +3^{2}[/tex]) = √34

=5.830 miles

And this Question also can be do by right angle triangle method

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A type 1 hypervisor functions as a compact operating system and runs directly on the host's hardware, but a type 2 hypervisor operates as a software layer on operating system, similar to other computer programs.

Which is the safer hypervisor, type 1 or type 2, and why that is more superior?

Native hypervisors are a safer solution. They are not dependent on the underlying OS, unlike hosted hypervisors. If you are attacked, the bare-metal hypervisor will improve your chances (Type 1). Because of this reliance, the type 2 server loses efficiency, performance, and speed. A Type 1 hypervisor operates directly on the hardware of the host computer. These hypervisors interface directly with the host computer's CPU, RAM, and physical storage, making them typically quicker and more effective than Type 2 hypervisors. eliminate the requirement to travel through the OS layer.

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Answer:

1 -

12 - ?

4 - square root of 16

64 -

16 -

2.828 - square root of 8

Step-by-step explanation:"
I need more terms to match them.

The second option has the better value-for-money.

To find the price per gram, you need to take the quotient between the cost and the mass for each case.

The first brand costs $29.49 for 250 grams, then the cost is:

c = $29.49/250g = $0.12 per gram.

The other brand costs $69.99 for 750 grams, then the cost per gram is:

C = $69.99/750g = $0.09 per gram

We can see that the second option has the better vale-for-money.

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In the triangle LMN the length of the side l as per given measures of side and angles is equal to 42.4 inches ( nearest tenth )

In triangle LMN,

Let us consider side length opposite to ∠L, ∠M, and ∠N be l , m , and n respectively.

Measure of side m = 450 inches

Measure of ∠M = 74°

Measure of ∠N = 41°

Sum of all the angles in a triangle is equal to 180°

m ∠M + m ∠N + m ∠L = 180°

⇒ 74° + 41° + m ∠L = 180°

⇒ m ∠L = 180° - 115°

⇒ m ∠L = 65°

Using sine law of triangle we have,

sin L / l  = sin M / m = sin N / n

⇒sin L / l  = sin M / m

Substitute the value we get,

⇒ sin 65° / l  = sin 74° / 450

⇒ l = sin 65° × ( 450 / sin 74°)

⇒ l = 0.9063 × ( 450 / 0.9613 )

⇒ l = 42.43 inches

⇒ l = 42.4 inches ( nearest tenth )

Therefore, the measure of the side length l in a triangle LMN is equal to 42.4 inches ( nearest tenth ).

The above question is incomplete, the complete question is:

In ΔLMN, m = 450 inches,  m ∠M=74° and  m ∠N=41°. Find the length of l, to the nearest 10th of an inch.

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Answer: 424.3

Step-by-step explanation: n ΔLMN, m = 450 inches, m∠M=74° and

m∠N=41°. Find the length of l, to the nearest 10th of an inch.

A.A.S.→Law of Sines

Plug in. Opposite sides go together. 450 sin, 65 sin 74 ≈ 424.2742 ≈ 424.3

l=

sin74

450sin65

​

≈424.2742≈424.3

Tayjen's kite flew 5,860 centimeters in the air then Tayjen's kite flew 10.6 meters higher than Sara's kite.

What is BODMAS?

BODMAS is an acronym used to remember the order of operations in arithmetic. The acronym stands for:

B - Brackets (or Parentheses)

O - Orders (exponents and roots)

DM - Division and Multiplication (performed left to right)

AS - Addition and Subtraction (performed left to right)

BODMAS provides a set of rules that dictate the order in which mathematical operations should be performed in an expression that contains multiple operations. It is important to follow the order of operations to ensure that the expression is evaluated correctly and consistently. For example, in the expression 5 + 3 x 2, if we follow the BODMAS rule, we first perform the multiplication (3 x 2) and then the addition (5 + 6), giving us the answer of 11. If we were to perform the addition first, we would get a different answer (5 + 3 = 8, and 8 x 2 = 16), which would be incorrect.

To compare the height of Sara's kite, which is measured in meters, with the height of Tayjen's kite, which is measured in centimeters, we need to convert Tayjen's kite's height to meters.

To do that, we divide the height of Tayjen's kite by 100, since there are 100 centimeters in a meter:

5,860 centimeters ÷ 100 = 58.6 meters

Now we can compare the heights of the two kites:

58.6 meters - 48 meters = 10.6 meters

Therefore, Tayjen's kite flew 10.6 meters higher than Sara's kite.

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