Prove the Converse of the Pythagorean Theorem

The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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The Correct answer is  D) Most students read more often than they draw.as the median of the "read" plot is lower than the median of the "draw" plot.

Based on the box plots, we can see that:

The median for the "read" data is around 8 days per month, and the interquartile range (IQR) is between 4 and 12 days.

The median for the "draw" data is around 12 days per month, and the IQR is between 8 and 16 days.

So, we can conclude that:

A) Most students read less than 12 days a month. This is true, since the median for the "read" data is below 12 days per month, and the box plot shows that most of the data is concentrated in the lower half of the range.

B) Most students draw at least 12 days a month. This is not true, since the median for the "draw" data is around 12 days per month, and the box plot shows that there is a considerable amount of data below that median.

C) Most students draw more often than they read. This is not true, since the median for the "read" data is lower than the median for the "draw" data.

D) Most students read more often than they draw. This is true, since the median for the "read" data is lower than the median for the "draw" data, and the box plot shows that most of the "read" data is concentrated in the lower half of the range, while most of the "draw" data is concentrated in the upper half of the range.

The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.

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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.

The probability of rolling an even number on a single die is 1/2, or 50%. This can be calculated by considering the possible outcomes of rolling the die.

There are six possible outcomes, and three of these are even numbers (2, 4, and 6). Therefore, there is a 3/6, or 1/2, chance of rolling an even number. In terms of probability, this can be expressed as a fraction, percentage, or decimal. As a fraction, the probability of rolling an even number on a single die is 3/6, or 1/2. As a percentage, the probability of rolling an even number on a single die is 50%. As a decimal, the probability of rolling an even number on a single die is 0.5. No matter how it is expressed, the probability of rolling an even number on a single die is 1/2, or 50%. This can be easily remembered by considering that there are six possible outcomes, and three of them are even numbers.

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A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

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The quadratic equation in the given graph can be written in the vertex-form as:

y = -2(x - 1)² + 4

We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

in the graph we can see that the vertex is (1, 4), replacing that we will get:

y = a*(x - 1)² + 4

In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:

2 = a*(0 - 1)² + 4

2 = a + 4

-2 = a

Then the quadratic is:

y = -2(x - 1)² + 4

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Answer:

3. 216 cm^3

4a. A = 5 ft, B = 4 ft.

4b. 88 ft^3

Step-by-step explanation:

3. Separate into two rectangular prisms:

Volume of first one: 4cm*2cm*3cm = 24cm^3

Volume of second one: 4cm*12cm*4cm = 192cm^3

Add them together: 24 + 192 = 216cm^3

4a.

Length A = 8-3 = 5ft.

Width B = 8-4 = 4ft.

4b. Separate into two rectangular prisms:

Volume of first one: 2ft*3ft*4ft = 24ft^3

Volume of second one: 8ft*4ft*2ft = 64ft^3

Add them together: 24 + 64 = 88ft^3

29 + 14 = 44 by decomposing numbers to add and make a new 10.

Decomposition of numbers involves breaking a number down into its constituent parts or smaller numbers that add up to the original number. This can be done in different ways depending on the purpose and context of the problem.

For example, one common way of decomposing a number is by place value. In this case, the number is broken down into its digits, which represent different powers of ten. For instance, the number 562 can be decomposed into 500 + 60 + 2.

Another way of decomposing numbers is by factoring. In this case, the number is expressed as a product of its factors. For example, the number 12 can be decomposed as 2 x 2 x 3.

Decomposing numbers is a useful skill in many areas of mathematics, including arithmetic, algebra, and geometry. It is often used to simplify problems, make computations easier, and facilitate further analysis.

To decompose 29 to make a new 10, we can break it into 9 and 20. Then, to decompose 14 to make a new 10, we can break it into 6 and 8.

So, we have:

29 + 14 = (9 + 20) + (6 + 8)

Now, we can regroup the numbers to make a new 10:

= (9 + 1) + (20 + 6) + 8

= 10 + 26 + 8

= 44

Therefore, 29 + 14 = 44 by decomposing numbers to add and make a new 10.

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Answer: yes correct i love math

Step-by-step explanation:

The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.

Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:

BSA = √(H x M) / 3600

We can rearrange the equation to solve for M:

M = (BSA^2 x 3600) / H

Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:

M = (2.0^2 x 3600) / 165

M = (4 x 3600) / 165

M = 87.27 kg

The above question is in response to the full question as seen in the image;

A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less

than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?

The equation for BSA is BSA = √(H x M)/3600

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The value of the variable x for the similar triangles is equal to 25

The triangles BDR and QDC are similar, this implies that the length DC of the smaller triangle is similar to the length DR of the larger triangle

and the length DQ of the smaller triangle is similar to the length DB of the larger triangle

so;

x/(15 + x) = 40/64

64x = 40(15 + x) {cross multiplication}

64x = 600 + 40x

64x - 40x = 600 {subtract 40x from both sides}

24x = 600

x = 600/24

x = 25

Therefore, the value of the variable x for the similar triangles is equal to 25

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The calculated value of the force of the resistance is 15.62 N

We can use Newton's Second Law of Motion to solve this problem. The formula is:

F = m*a

where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, the brick is falling through water, so there are two forces acting on it:

The net force is the difference between these two forces:

F_net = F_gravity - F_resistance

The weight of the object is:

F_gravity = m*g

So, we have

F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N

Now we can use the formula for net force to find the force of water resistance:

F_net = F_gravity - F_resistance

F_resistance = F_gravity - F_net

F_resistance = 19.62 N - m*a

This gives

F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N

Therefore, the force of water resistance is 15.62 N.

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Answer:

The product of two numbers is 21.

Step-by-step explanation:

If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21.

Answer:

147

Step-by-step explanation:

A= h^b b=21*14= 147

Answer: no they wouldn't be similar

Step-by-step explanation: if x=60 if triangle 1 then the third angle would be (180-(58+60)) =180-118=62
if we decide to calculate the third angle in triangle 2 we will have 180-(50+58) = 180-108=72

therefore not all angles in 1 are similar to angles in 2 so the triangles aren't similar

Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc

The algebraic expression is: [tex]6x - 9[/tex].

To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.

An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.

For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.

Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.

Therefore, The algebraic expression is: [tex]6x - 9[/tex]

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The resulting number is 12/5

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it

So, performing the operations,

15/16+15/16×3/5

= 15/16(1+3/5)

= 15/16(8/5)

= 120/80

= 3/2

Now,

3/2+3/2×3/5

= 3/2(1+3/5)

= 3/2(8/5)

= 24/10

= 12/5

Hence, the resulting number is 12/5

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Option A correctly describes the area of the graph of the function.

How is an area of the graph calculated?

The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.

It is the integration of the function polynomial of the possible values of x that the function curve lies in.

Here the function equation is : [tex]f(x) = ( 25 - x^{2} )[/tex]

From the figure, we can see that the value of x varies from -5 to 5.

Initial x-value of integration = minimum value of x

                                          = -5

Final x-value of integration = maximum value of x

                                          = 5

Thus, the area of the graph can be correctly calculated as. :

               [tex]Area = \int\limits^{maxX}_ {minX} \, f(x)dx[/tex]

               [tex]Area = \int\limits^5_ {-5} \, (25-x^{2} )dx[/tex]

Hence, Option A correctly calculates the area of the graph given.

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Try going to the store and they should be surprisingly cheap.

Answer: here it is.

Step-by-step explanation:

Answer:

Step-by-step explanation: 1. is Yes 2 is no 3. is all 4 is Y and 50 5 is yes and -1

The  X, Y, and Z values ​​are 84, 90, and 90, respectively. To answer this question, we need to understand the meaning of the words "median", "mean" and "range".

Median is the middle number of a set of numbers - it is the number in the middle when the numbers are ordered from smallest to largest.

Since the median is 90, this means that Y (the mean number) is 90. Since the average is 92, this means that the sum of the three numbers is 276 (92 x 3). The interval is 6, which means that the difference between the largest number and the smallest number is 6.

To solve for X and Z, we can use the equation X Y Z = 276. We know that Y is 90, so we can plug 90 into Y:

X 90 Z = 276

Then we can  subtract 90 from both sides to find the value of X and Z:

X Z = 186

Since the range of the three numbers is 6, this means that X and Z must be 6 plus. The only two numbers that differ by six and add up to 186 are 84 and 90.

Therefore the  X, Y, and Z values ​​are 84, 90, and 90, respectively.

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Answer:

First, we need to find the radius of the base of the cone. We can see from the grid that the diameter is 8 units, so the radius is 4 units (or 4 feet).

Next, we can use the formula for the volume of a cone to find the height:

V = (1/3)πr^2h

Substituting the given volume and radius, and using 3.14 for π, we get:

200.96 = (1/3) x 3.14 x 4^2 x h

Simplifying and solving for h, we get:

h = 200.96 / (1/3 x 3.14 x 4^2)

h = 200.96 / 53.02

h ≈ 3.79 feet (rounded to two decimal places)

To construct the cone vertically on the grid with respect to the center of the base, we can draw a circle with radius 4 units (or 4 feet) centered at the point (4,4) on the grid. Then, we can draw a line from the center of the circle (point (4,4)) up to a point above the circle that is 3.79 units (or 3.79 feet) away from the center. This line represents the height of the cone. Finally, we can connect the endpoint of the line to the points where the circle intersects the grid to complete the cone.

The expressions can be written as  :a. log5.625 ≈ 0.75.

                                                             b. log6.4 + log6.12 ≈ 1.67.

                                                             c. log3.9^{4} ≈ 2.47.

What is logarithm function?

A logarithm function is a mathematical function that determines the power to which a fixed number, called the base, must be raised to produce a given value and The logarithm function is the inverse of the exponential function. The most commonly used base for logarithmic functions is 10 (log base 10), but other bases such as 2 (log base 2) and the natural logarithm base e (ln) are also used.

a. Since there is no base specified, we assume the base to be 10 by default. Therefore, we can write:

log5.625 = log(5625/1000)

Using the property log(a/b) = log(a) - log(b), we can simplify this expression to:

log5.625 = log(5625) - log(1000)

Using the change of base formula, we can convert the logs to a common base, such as 2 or e:

log5.625 = log(5625)/log(10) - log(1000)/log(10)

Evaluating the logs using a calculator or by simplifying, we get:

log5.625 ≈ 0.75

Therefore, log5.625 ≈ 0.75.

b. Using the property log(a) + log(b) = log(ab), we can simplify the expression:

log6.4 + log6.12 = log(6.4 × 6.12)

Using the change of base formula, we can convert this to a common base:

log6.4 + log6.12 = log(6.4 × 6.12)/log(10)

Evaluating the log using a calculator or by multiplying 6.4 and 6.12 and simplifying, we get:

log6.4 + log6.12 ≈ 1.67

Therefore, log6.4 + log6.12 ≈ 1.67.

c. Using the property log(a^{n}) = n log(a), we can simplify the expression:

log3.9^{4} = 4 log3.9

Using the change of base formula, we can convert this to a common base:

log3.9^{4} = 4 log(3.9)/log(10)

Evaluating the log using a calculator or by simplifying, we get:

log3.9^{4} ≈ 2.47

Therefore, log3.9^{4} ≈ 2.47.

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Answer:

"Undefined slope"

Step-by-step explanation:

The line is vertical on the graph.

Every point on the line has the same x-coordinate.

If the line crosses the x-axis where x=-7, then the

x-coordinate of every point on the line is -7, and the

equation of the line is

                                     x = -7 .

The probability that John's drive to work will take between 36 and 40 minutes is 0.3413.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.

Using the normal distribution, the probability of John's drive taking between 36 and 40 minutes can be calculated using the standard normal distribution table. The formula for calculating the probability is: P(x<X<y) = P(y) - P(x).

For the given problem, the lower boundary is 36 minutes and the upper boundary is 40 minutes. Using the standard normal distribution table, the probability of John's drive taking between 36 and 40 minutes can be calculated by subtracting the probability of 36 minutes from the probability of 40 minutes. This gives us a probability of 0.3413.

Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3413.

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The probability that John's drive to work will take between 36 and 40 minutes is 0.3829.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.

The probability that John's drive to work will take between 36 and 40 minutes can be calculated using a normal distribution table. The mean of the distribution is µ = 38 minutes, and the standard deviation is σ = 5 minutes.

To calculate the probability, we need to convert the given range (36 minutes to 40 minutes) into standard normal scores. This is done by subtracting the mean (µ = 38 minutes) from the lower bound (36 minutes) and then dividing by the standard deviation (σ = 5 minutes). The result is a standard normal score of -0.4. The same calculation is carried out for the upper bound (40 minutes) and the result is a standard normal score of 0.4.

Using a normal distribution table, we can then determine the probability that John's drive to work will take between 36 and 40 minutes. This probability is equal to the area under the normal curve between the two standard normal scores of -0.4 and 0.4. The result is a probability of 0.3829.

Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3829.

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Step-by-step explanation:

To find the percentage that $4250 represents of $6500, we can use the following formula:

percentage = (part / whole) x 100%

where "part" is $4250 and "whole" is $6500.

Substituting these values into the formula, we get:

percentage = (4250 / 6500) x 100%

percentage = 0.6538 x 100%

percentage = 65.38%

Therefore, $4250 represents 65.38% of $6500.

Answer: It is approximately 65%

Step-by-step explanation: Divide $4,250 by $6,500 and your answer without rounding is 65.3846%

Answer:

The given equation is 3 + 7x + 11 + 10x = y.

Simplifying the equation, we get:

y = 17x + 14

Comparing with the standard linear equation y = mx + b, we can see that:

m = 17

b = 14

Therefore, m = 17 and b = 14.

It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

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

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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