1 Design your own real-world scenario in which the solution requires the Pythagorean Theorem. Use complete sentences to describe the scenario.2 Model your real-world scenario with an equation and a sketch.3 In two or more complete sentences, explain the steps necessary to solve for the missing value in your real-world scenario. Include the solution in your explanation.

Cornell's class took 2 field trips last year. This is determined by setting up and solving the equation based on the given information.

To solve this problem, we need to set up an equation. Given in the problem that Cornell's class took one more than three times as many field trips as last year's class, we can represent this as 3x + 1 = y, where x is the number of field trips last year and y is the number of field trips this year. We know that y is 7 so we can substitute this into our equation getting 3x + 1 = 7.

To find x, you would subtract 1 from both sides of the equation giving 3x = 7 - 1, which simplifies to 3x = 6. Finally, dividing both sides of the equation by 3 gives us x = 2, so Cornell's class took 2 field trips last year.

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The amount of money that Helen would have left after all these expenses is  $460.

In order to determine the amount that would be left, determine the money value of the expenses, add the expenses together and subtract it from the earnings.

Amount left = 1840 - 1380 = $460

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To have $400,000 for retirement in 25 years with an annual interest rate of 6% compounded annually, Thurston must invest $93,171.77 today.

Thurston must calculate how much he needs to invest today to have $400,000 when he is 80 years old, given that he is currently 55 years old and the investment will yield 6% interest compounded annually. To find this amount, we use the formula for the present value of a lump sum, which takes into account the future value desired, the interest rate, and the number of compounding periods. The formula is:

PV = FV / (1+r)n

Where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years until retirement.

In Thurston's case:

Plugging these values into the formula gives us:

PV = $400,000 / (1+0.06)25

PV = $400,000 / (1.06)25

PV = $400,000 / 4.29187072

PV = $93,171.77 (rounded to two decimal places)

Thus, Thurston must invest $93,171.77 today to retire with $400,000 in 25 years at an annual interest rate of 6% compounded annually.

Answer:

60

Step-by-step explanation:

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem!

At a factory, a mechanic earns $17.25 an hour

[tex]\texttt{ Mechanic's Wage } = \$17.25[/tex]

The president of the company earns 6 2/3 times as much for each hour the mechanic works

[tex]\texttt{ President's Wage } = 6\frac{2}{3} \times \texttt{ Mechanic's Wage }[/tex]

[tex]\texttt{ President's Wage } = 6\frac{2}{3} \times \$17.25[/tex]

[tex]\texttt{ President's Wage } = \$115[/tex]

The janitor at the same company earns 3/5 much as the mechanic

[tex]\texttt{ Janitor's Wage } = \frac{3}{5} \times \texttt{ Mechanic's Wage }[/tex]

[tex]\texttt{ President's Wage } = \frac{3}{5} \times \$17.25[/tex]

[tex]\texttt{ President's Wage } = \$10.35[/tex]

Total all three people employees' wages for one hour of work

[tex]\texttt{ Total Wages } = \$17.25 + \$115 + \$10.35[/tex]

[tex]\texttt{ Total Wages } = \boxed{\$142.60}[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Order Of Operations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent

Total money earned by Juan = 3w-6

Now Juan saved 1/3 of the money.

So money Juan spent will be 2/3 of what he earned.

Money Juan spent :

[tex] \frac{2}{3} (3w-6) [/tex]

Simplifying we get :

2w-4

Emma wrote the expression as 2(3w-6) which is not equal to 2w-4.

So we can say that the expression found by Emma was incorrect .

the answer is 11 :))

Answer:

The original graph will shift 6 units down.

Step-by-step explanation:

Given : If the equation y = x + 4 is changed to y = x - 2.

To find : How will the graph of the equation change.

Solution : We have given

Original graph equation : y =  x + 4.

Transformed equation : y = x -2.

y =  x + 4 →→ y = x - 2.

If we subtract the 6 from 4 it become - 2

We can see x + 4 -6 = x -2 .

So , y = x +4 -6  →→ y = x - 2.

By the transformation rule : f(x) →→  f(x) - k it mean graph shifted down by k units.

Then the original graph will shift 6 units down.

Therefore, The original graph will shift 6 units down.

The value of the surface area of this cube is,

⇒ 1536 feet²

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

Given that;

One side of a cube = 16 feet

We know that;

the surface area of this cube is,

⇒ 6 × (side)²

Here, Side = 16 feet

Thus, The value of the surface area of this cube is,

⇒ 6 × (side)²

⇒ 6 × (16)²

⇒ 6 × 256

⇒ 1536 feet²

Thus, The value of the surface area of this cube is,

⇒ 1536 feet²

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The capacity of the gas tank is 20 gallons

.To determine the capacity of the gas tank, we can set up a proportion based on the information given. We know that the tank is 40% full and contains 8 gallons of gas. Let's denote the total capacity of the tank as C gallons.Since 40% of the tank's capacity is equal to the 8 gallons of gas currently in the tank, we can write the following equation: [tex]\[ 0.40 \times C = 8 \[/tex]. To find the total capacity C, we divide both sides of the equation by [tex]0.40:\[ C = \frac{8}{0.40} \[ C = 20 \].[/tex]  Therefore, the capacity of the gas tank is 20 gallons. This means that when the tank is completely full, it can hold 20 gallons of gas.

To calculate the remaining amount of grain in a silo discharging at a constant rate, we subtract the total amount discharged (rate times time) from the initial amount. This can be expressed as 'G = I - 3.5s' where 'G' is the amount of grain left after 's' seconds, 'I' is the initial amount, and '3.5' is the discharge rate in ft3/s.

If the silo empties at a constant rate, it can be modeled with linear equations. In this case, the rate of grain being emptied from the silo is 3.5 units of grain every second. Please note that to find the amount of grain left after a certain amount of time, we need to know the initial amount of grain in the silo, let's call it 'I'.

For your problem the general mathematical expression would be: total amount of grain left = initial amount of grain (I) - (rate × time),

If we denote the amount of grain left after 's' seconds as 'G', we can write the equation as: G = I - 3.5s

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Answer:

1/3 :)

Step-by-step explanation:

if you do the math it eqals 2/6 but if you simplify it its 1/3 i did this test and got 100% ur welcome

Answer:

ummm, ohhh i just realized that i entered in the wrong question and i was so confused lol

Step-by-step explanation:

To find the sum, add each amount together, starting from the ones place and carrying over any excess to the next place value. The total sum is $256.15.

To find the sum of the amounts of money, you will add each amount together. $10.15 + $31.60 + $34.75 + $40 + $69.25 + $54.75. Starting with the ones digit, you have 5 + 0 + 5 + 0 + 5 + 5 = 20. Write down 0 and carry over the 2 to the tens place. Next, add the tens place digits, which gives you 1 + 6 + 7 + 0 + 2 + 4 = 20. Write down 0 again and carry over the 2 to the hundreds place. Finally, add the numbers in the hundreds place, which equals 0 + 3 + 3 + 0 + 6 + 5 + 5 = 22. Write down 2 and add it to the sum. The total sum of the amounts of money is $256.15.

The sum of $10.15, $31.60, $34.75, $40.00, $69.25, and $54.75 is calculated by adding each value together, which results in a total of $242.50.

To calculate the sum of the amounts of money $10.15, $31.60, $34.75, $40, $69.25, and $54.75, you simply need to add each of these values together. Adding money involves lining up the decimal points and adding each column from right to left, just as with regular addition. Here's how you do it step by step:

Next, add the numbers in the rightmost column (the cent column), carry over if necessary, then move to the next column to the left (the dollar column), and do the same:

Add both totals together:

Therefore, the sum of the amounts of money is $242.50.

Answer: The answer is 9.647*10^7

Step-by-step explanation: in scientific notation or in standard form the expression can be written as.

9.647*10^7

This was achieved by counting one decimal place after the first digit and multiplying the the whole number by 10 raised to the power of the number counted from the write to the decimal point

The number 96,470,000 in scientific notation is written as 9.647 × 10⁷.

Given is a number we need to write it into scientific notation,

In scientific notation, a number is expressed as a product of two parts: a coefficient and a power of 10. The coefficient is a number between 1 and 10, and the power of 10 indicates the number of places the decimal point needs to be moved to obtain the original number.

To convert 96,470,000 to scientific notation, we start by moving the decimal point to the left until we have a coefficient between 1 and 10. In this case, we need to move the decimal point 7 places to the left, which gives us 9.647.

The next step is to determine the power of 10. Since we moved the decimal point 7 places to the left, the power of 10 is 7.

Therefore, we can express 96,470,000 in scientific notation as 9.647 × 10⁷.

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Answer:

-16t² + 24t = 0

-8t(2t - 3) = 0

t = 1.5 seconds

The tennis ball returns to the ground in 1.5 seconds.

The tennis ball returns to the ground after [tex]\(\frac{3}{2}\)[/tex] seconds.

To find when the tennis ball returns to the ground, you need to determine when the height y is equal to zero. In the given function [tex]y = -16t^2 + 24t\)[/tex], set y equal to zero and solve for t:

[tex]\[ -16t^2 + 24t = 0 \][/tex]

Factor out 8t from both terms:

[tex]\[ 8t(-2t + 3) = 0 \][/tex]

Now, set each factor equal to zero:

1. 8t = 0: This gives t = 0.

2. -2t + 3 = 0: Solve for t.

[tex]\[ -2t = -3 \][/tex]

Divide both sides by -2:

[tex]\[ t = \frac{3}{2} \][/tex]

So, the two solutions are t = 0 and [tex]\(t = \frac{3}{2}\)[/tex]. However, \(t = 0\) corresponds to the initial bounce, and we are interested in the time it takes for the ball to return to the ground after the first bounce.

Therefore, the tennis ball returns to the ground after [tex]\(\frac{3}{2}\)[/tex] seconds.

The answer is 68

Hope I could help you!

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To find the angle supplementary to <COB, we must look for an angle that adds up to 180 degrees with <COB. Assuming <COD is adjacent and forms a straight line with <COB, option 2. COD would be the supplementary angle.

The subject of this question is Mathematics, and it requires an understanding of angle relationships, particularly supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees.

Based on the given theorems and proofs, we must assume that the angles are situated such that finding the angle supplementary to <COB involves identifying an angle that, when combined with <COB, equals 180 degrees.

Given the options provided:

The correct answer to find the angle supplementary to <COB is 2. COD, assuming that <COB and <COD are adjacent angles forming a straight line.