What is unique about Pythagorean triples?

Answer:

$75

Step-by-step explanation:

3/4 -tuition

4/4-3/4=1/4 1/3×1/4=1/12 -books

1/12+1/4=1/3 1-1/3= 2/3 -left which is equal to $50

2/=$50

1=

1×3/2×$50= $75

The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Rita the mentor has two independent exercise designs that she offers her clients: Plan An and Plan B. Every client does it is possible that either (not both). On Friday there were 5 clients who arranged A and 3 who arranged B. On Saturday there were 2 clients who arranged A and 6 who arranged B. Rita prepared her Friday clients for a sum of 10 hours and her Saturday clients for a sum of 10 hours.

The length of each Plan A workout is given as,

Rate = (5 + 2) / 10

Rate = 7 / 10

Rate = 0.70 per hour

The length of each Plan B workout is given as,

Rate = (3 + 6) / 10

Rate = 9 / 10

Rate = 0.90 per hour

The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.

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(a)The percentage error is 0.123%.

(b)The percentage error is 0.049%.

Find the equation of the tangent line at the point (0,f(0)),

⇒ f(x)  = exp(x/500)
⇒ f'(x) = 1/500 exp(x/500)

⇒ f(0) = exp(0/500)

          = 1

So the equation of the tangent line at x = 0 is,

⇒ y = f(0) + f'(0)(x - 0) y

      = 1 + 1/500x y

      = x/500 + 1

Find the equation of the tangent line at the point (100,f(100)),

⇒ f(x)  = exp(x/500)

⇒ f'(x) = 1/500 exp(x/500)

⇒ f(100) = exp(100/500)

             = exp(1/5)

So the equation of the tangent line at x = 100 is,

⇒ y = f(100) + f'(100) (x - 100)

⇒ y = e^(1/5) - (1/500)(x - 100)

⇒ y = -x/500 + exp(1/5) + 1

Now we can use these two equations to approximate the function f(x) for 0 < x < 100.

For example, when x = 25

⇒ y = x/500 + 1

⇒ y = 25/500 + 1

⇒ y = 1.05

And the actual value of f(25) is,

⇒ f(25) = exp(25/500)

⇒ f(25) = exp(1/20)

⇒ f(25) ≈ 1.0513

So the percentage error is,

⇒ |1.05 - 1.0513| / 1.0513 x 100% ≈ 0.123%

We can repeat the process for x = 50 and find that the percentage error is 0.049%.

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The average rate of change from x = -2 to x = 0 of the function f(x) = 3x² - 2x + 5 is -8.

The average rate of change from -2 to 0 is;

f(0) - f(-2) / 0 - (-2)

Given the quadratic equation in question;

f(x) = 3x² - 2x + 5

Plug in the values;

[ ( 3(0)² - 2(0) + 5 ) - ( 3(-2)² - 2(-2) + 5  ) ]/ 0 - (-2)

[ ( 0 - 0 + 5 ) - ( 12 + 4 + 5  ) ]/ 0 - (-2)

[  5 - 21 ] / 0 - (-2)

[  -16 ] / 2

-16/2

-8

Therefore, the average rate of change is -8.

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Therefore , the solution of the given problem of input and output comes out to be methods for Fixing an Input-Output Table begin with the very first input.

The function generates an output value by using an input value, such as x = 3, as an example. If you substitute 3 for the number x in the equation y = x + 5 y = x + 5, you get y = 3 + 5 = 8 y = 3 + 5 = 8. So, y = 8.

Here,

The output value is as follows.

Both the value of the final goods and services produced and the value added at each stage of production can be used to calculate total output.

An input-output table's governing principle is the mathematical operation or operations that are applied to the input to yield the desired output. The rule can be very basic, like adding 1, or quite complex, like squaring the amount and taking 17 out.

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The probability that the sum of the numbers on the dice facing up add up to 3 is 1/18 and VAR(A)= 1

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

A 6-sided dice has numbers 1, 2, 3, 4, 5, 6 at each of the 6 sides.

The event of rolling two fair 6-sided dice, which the numbers on the dice facing up add up to 3, is by having (1, 2) or (2, 1).

probability = desired outcome / total outcomes

probability = 2 / (6 x 6)

probability = 2 / 36

probability = 1/18

VAR(A)= 1

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The smaller side of the triangle from missing sides is 63cm.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

According to Pythagorean theorem,

H^2=P^2+B^2

Where H=hypotenuse, B=base, P=Perpendicular

Given base=16

let perpendicular=x then hypotenuse=x+2 as  The lengths of the other two sides are consecutive odd integers

Therefore, (x+2)^2=x^2+16^2

x^2+4+4x=256+x^2

x=63 and x+2=65

Hence,

          The smaller side of the triangle from missing sides is 63cm.

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Step-by-step explanation:

8/2 = 48/b

4=48/b

b=48/4

b=12

Answer:

Step-by-step explanation:

8/2 = 48/b

b = 48×2/8

b = 12

C(x) = 16x – 63, where x is the number of thousands of bottles, gives the cost of producing bottled spring water.

The formula R(x) = - x2 + 326x – 7463 calculates the total amount (revenue) from the sale of these bottles.

Bottles sold will yield the highest profit.

Profit maximization

Profit after selling 245 thousand bottles

C(x) = 16x – 63

R(x) = – x² + 326x – 7463.

Revenue – Cost = Profit

P(x) = R(x) – C (x)

= – x² + 326x – 7463 – (16x – 63) (16x – 63)

= – x² + 310x – 7400

Choice c)

Profit = x2 minus 310x minus 7400

P(x) = – x² + 310x – 7400

P’(x) = -2x + 310

P’(x) = 0 => -2x + 310 = 0 => x = 155

P’’(x) = - 2 < 0

As a result, profit is greatest at x = 155.

The highest profit will be generated if 155 bottles are sold.

Alternative b)

Profit maximization at x = 155

P(x) = – x² + 310x – 7400

= -(155)² + 310(155) – 7400

= Rs 16625

The highest possible profit is Rs 16625.

Alternative b)

Profit after selling 245 thousand bottles

X = 245

−(245)2 + 310(245) – 7400 = profit

= 8525

Alternative (a) Rs 8525

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Answer:

[tex]5 \leqslant 20 - 1.3x < 10[/tex]

Answer:

C and D

Step-by-step explanation:

3x + 1 and 1 + 3x are the phrase for 'Thrice a number more than 1.

they can simplify to get the same answer.

After 3 years, Beth's investment will be worth $1,281.216.

What is percentage ?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used.

The formula to calculate the future value of an investment is:

FV = PV * (1 + r/n)^(nt)

where:

PV = present value = $1,000

r = annual interest rate = 8.25%

n = number of compounding periods per year = 12 (monthly)

t = number of years = 3

FV = $1,000 * (1 + 0.0825/12)^(12 * 3)

Plugging in the values and using a calculator, we get:

FV = $1,000 * (1 + 0.0825/12)^(12 * 3) = $1,000 * (1.006866)^36 = $1,000 * 1.281216 = $1,281.216

So after 3 years, Beth's investment will be worth $1,281.216.

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Answer:

52

Step-by-step explanation:

Using the exterior angle theorem, [tex]112+x=164 \implies x=52[/tex]

The area of the cylinder is 3, 399. 74 square centimeters

The formula for calculating the area of  a cylinder is expressed with the equation;

A = 2πrh + 2πr²

Given that the parameters are;

From the information given, we have that;

Radius, r = 13.4 centimeters

Height, h = 27 centimeters

Now, subsitute the values, we get;

Area = 2× 3.14 × 13. 4× 27 + 2× 3.14 × (13.4)²

expand the bracket

Area = 2272. 104 + 1127.64

Add the values

Area = 3, 399. 74 square centimeters

Hence, the value is 3, 399. 74 square centimeters

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Answer:

[tex]\frac{1}{4y^9}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]\frac{a^m}{a^n}[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex]

[tex]\frac{y^{-3} }{4y^{6} }[/tex]

= [tex]\frac{1}{4}[/tex] × [tex]\frac{y^{-3} }{y^6}[/tex]

= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6-(-3))} }[/tex]

= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6+3)} }[/tex]

= [tex]\frac{1}{4y^9}[/tex]

Answer:

x = -6

Step-by-step explanation:

x/15 + 3/15 = -1/5

x/15 + 1/5 = -1/5

x/15 = -2/5

x = -6

Let's check

-6/15 + 3/15 = -1/5

-3/15 = -1/5

-1/5 = -1/5

So, x = -6 is the correct answer.

a. The percentage of GMAT scores is 647 or higher approximately 15.9%

b. The percentage of GMAT scores that are 747 or higher (to 1 decimal) is approximately 2.3%.

c. The percentage of GMAT scores between 447 and 547 is approximately 84.1%.

d. The percentage of GMAT scores between 347 and 647 (to 1 decimal) is approximately 98.0%.

a. The GMAT score of 647 is 100 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 647-547/100 = 1.

Using a standard normal table, we can find that the percentage of GMAT scores that are 647 or higher is approximately 15.9%.

b. The GMAT score of 747 is 200 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 747-547/100 = 2.

Using a standard normal table, we can find that the percentage of GMAT scores that are 747 or higher is approximately 2.3%.

c. The GMAT scores between 447 and 547 are 100 points below and 100 points above the average score of 547, respectively.

Using the standard deviation of 100, we can calculate the standard score (z-score) as (447-547)/100 = -1 and (547-547)/100 = 0.

Using a standard normal table, we can find that the percentage of GMAT scores that are between -1 and 0 is approximately 84.1%.

d. The GMAT scores between 347 and 647 are 200 points below and 100 points above the average score of 547, respectively.

Using the standard deviation of 100, we can calculate the standard score (z-score) as (347-547)/100 = -2 and (647-547)/100 = 1.

Using a standard normal table, we can find that the percentage of GMAT scores that are between -2 and 1 is approximately 98.0%.

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The complete question is -

The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100.

a. What percentage of GMAT scores are 647 or higher?

b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?

c. What percentage of GMAT scores are between 447 and 547 ?

d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?

Answer

percentage= 100

a. 10% of 70

10/100 × 70 = 7

b. 10% of 110

10/100 × 110 = 11

c. 25% of 160

25/100× 160 = 40

d.25% of 48

25/100 × 48 = 12

e. 50% of 90

50/100 × 90 = 45

f. 50% of 350

50/ 100 × 350 = 175

g.75% of 300

75/100 × 300 = 225

h. 75% of 48

75/100 × 48 = 36

A non-fruitful function which makes a turtle draw an equilateral triangle is given in the explanation.

Here is an example of a non-fruitful function in Python that takes a turtle object and a size as arguments and makes the turtle draw an equilateral triangle:

import turtle

def draw_triangle(some_turtle, some_size):

   for i in range(3):

       some_turtle.forward(some_size)

       some_turtle.left(120)

# Create a turtle object

t = turtle.Turtle()

# Call function to draw an equilateral triangle of size 100

draw_triangle(t, 100)

# Hide turtle and exit the turtle window

turtle.done()

This function makes the turtle move forward by some_size units and turn left by 120 degrees three times, resulting in a triangle with three equal sides and three 60-degree angles.

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Answer:

If you have one x2-block and 2n x-blocks, you need to add (2n)^2 1-blocks to form a square. The dimensions of the square will be (x2-block + 2n x-blocks) x (x2-block + 2n x-blocks) = (2n+2) x (2n+2) = (2n + 2)^2.

Answer: The initial amount (a) in the exponential function is 5, and the decay factor (b) is 0.5.

Step-by-step explanation: :D

The graph shows that f is not continuous at x=-4 and x=4. This is because the graph does not have a continuous line at those points.

A graph is a visual representation of data that uses dots, lines, or bars to show how different elements of a set of data are related. Graphs are typically used to show patterns or trends in data over time, or to compare different sets of data. Graphs can also be used to show the relationships between different variables.

At x=-4, there is a large gap between the left side and the right side of the graph. At x=4, the graph has a sharp corner, which shows that the graph is not continuous.

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Answer:

Second choice : -3, 11, -45, 179

Step-by-step explanation:

First term: a₁ =  - 3

Second term a₂ = -4a₁ -1 = (-4)(-3) - 1 = 12 - 1 = 11

There are only two options with 11 as the third term, Options 2 and 4 look the same but the fourth option has curly braces around the numbers making it a set rather than a sequence

If you wanted to be sure and compute the third term to see if it matches

a₃ = -4a₂ - 1 = -4(11)- 1 = -44 - 1 = -45

Answer:

$29

Step-by-step explanation:

Since the gifts are matching, the cost of each gift be equal, say $x
Now, Total cash - cash leftover = cost of both gifts
which is, 75 - 17 = 2x
or $58 = 2x
Thus, x would be 58/2 = $29
Or each gift would cost $29

The total sound level at the point is 100 dB (10 dB x 10 speakers).

The formula for calculating the sound level emitted by each speaker is 10 * log (100 / 10) = 10 dB. This means that each speaker emits a sound level of 10 dB.

To calculate this, we first need to understand the principle of the logarithmic addition of sound levels. The logarithmic addition of sound levels states that when two sound waves with different amplitudes overlap, the resulting amplitude is the sum of the logarithms of the individual amplitudes.

For example, let's say we have two sound waves with amplitudes of 10 dB and 20 dB. The resulting amplitude will be 10 * log (10 + 20) = 10 * log (30) = 10 dB + 20 dB = 30 dB.

Therefore, in our example, the 10 speakers each emit a sound level of 10 dB. This means that when all 10 speakers play simultaneously, the total sound level at the point is 100 dB (10 dB x 10 speakers).

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The business records related amounts in their respective accounts known as ledger accounts.

All such accounts are assembled in a book or collection called the

ledger.

All the accounts, including assets, liabilities, equity, revenues, and expenses, that are required to adequately portray a company's financial operations are included in the General Ledger.

Financial statements like the balance sheet, income statement, and cash flow statement are created from the accounts in the general ledger and offer an overview of the company's financial situation.

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well, we know there are 60 minutes in 1 degree, so 24' is 24/60 = 0.4°, so 61°24' is really 61.4°,  now, we also know that there are 180° in π radians, so

[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 61.4&x \end{array}\implies \cfrac{180}{61.4}~~ = ~~\cfrac{\pi }{x} \\\\\\ 180x=61.4\pi \implies x=\cfrac{61.4\pi }{180}\implies x=\cfrac{307\pi }{900}\implies x\approx 1.07~radians[/tex]

The scale factor of the dilation of the given object is 4.

The scale factor of dilation:

The scale factor of the dilation of an object is determined by taking the ratio of image length to the corresponding object length.

Dilation is the process of resizing or transforming an object. The transformation that makes the objects smaller or larger with the help of the given scale factor.

The basic formula to find the scale factor of a dilated is:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

[tex]SD=\frac{32cm^2}{4cm^2}[/tex]

SD=4

Thus, the scale factor of the dilation of the given object is 4.

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