Prove the following theorem (Euclid's Proposition I.28) and its converse.
ℎ. ′ ,, ℎ ℎ ,ℎ ′

Answer: wheres the page/diagram

Step-by-step explanation:

Answer:

si y = a 55 es 5.7

Step-by-step explanation:

la otra es 3.9

Answer:

Step-by-step explanation:

Claro que sí. El ingreso neto es el ingreso que queda después de restar los impuestos y otros gastos del ingreso bruto. La fórmula del ingreso neto es:

Ingreso neto = Ingreso bruto – Impuestos – Comisiones – Intereses – Créditos – Otros Gastos

En tu caso, el ingreso bruto es $105500 y los impuestos son $26982 por el impuesto sobre la renta y $2110 por el impuesto de Medicare. No sé si tienes otros gastos que debas restar, pero si no los tienes, entonces el ingreso neto sería:

Ingreso neto = $105500 - $26982 - $2110 Ingreso neto = $77408

Espero que te haya servido de ayuda.

Area of the first triangle is 582.86 square units

Area of the second triangle is 694 square units

The formula for area of a triangle is solved by

= 1/2 * b * h

For the first figure, we solve for h first using trigonometry

tan 68 = 48 / h

h = 48 / tan 68

h = 19.39

The other side of the base is solved using tan 58

tan 58 = 43.22 / b

b = 43.22 / tan 58

b = 12.12

base of the triangle = 48 + 12.12 = 60.12

Area of the first triangle = 0.5 * 60.12 * 19.39 = 582.86 square units

22. Solving for h

cos 64 = h / 50

h = 50 * cos 64 = 21.92

the other part of the base

sin 64 = b / 50

b1 = 50 * sin 64 = 44.94

tan 50 = h / b2 = 21.92 / b2

b2 = 21.90 / tan 50 = 18.38

base = b1 + b2 = 44.94 + 18.38 = 63.32

Area of the second triangle = 0.5 * 21.92 * 63.32 = 693.99 square units

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Answer:

IT IS B hope this helped

Step-by-step explanation:

The standard deviation of the data set is 1.03.

What is the standard deviation?

The standard deviation is a measure of the amount of variation or dispersion of a set of data values. It measures how spread out the data is from the mean or average value.

To find the standard deviation, we first need to find the mean of the data set:

Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 7.4

Next, we calculate the deviations from the mean for each data point:

| x - mean | (x - mean)²

0.2           0.04

1.5           2.25

4.7           22.09

4.2           17.64

1.6           2.56

2.8           7.84

To find the variance, we add up the (x - mean)² values and divide by the number of data points:

Variance = (0.04 + 2.25 + 22.09 + 17.64 + 2.56 + 7.84) / 6 = 6.36/6 = 1.06

Finally, we take the square root of the variance to get the standard deviation:

Standard deviation = √(1.06) = 1.03 (rounded to two decimal places)

Therefore, the standard deviation of the data set is 1.03.

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Answer:

a = 4.5 , b = 7.5

Step-by-step explanation:

using Pythagoras' identity in the two right triangle

outer right triangle

b² + 10² = (8 + a)² = 64 + 16a + a²  → (1)

inner right triangle

a² + 6² = b² → (2)

substitute b² = a² + 6² = a² + 36 into (1)

a² + 36 + 100 = 64 + 16a + a² ( subtract a² from both sides )

136 = 64 + 16a ( subtract 64 from both sides )

72 = 16a ( divide both sides by 16 )

4.5 = a

----------------------------------------

substitute a = 4.5 into (2)

4.5² + 6² = b² , that is

20.25 + 36 = b²

56.25 = b² ( take square root of both sides )

[tex]\sqrt{56.25}[/tex] = b , then

b = 7.5

Answer: 22 sophomores were surveyed

Step-by-step explanation:

Step-by-step explanation:

hope it will help you , and give some clue to do typical qno..

Answer:

x = 30 cm
Perimeter = 72 cm

Step-by-step explanation:

By Pythagoras theorem,

x² = 18² + 24²

x² = 324 + 576

x² = 900

x² = 30²

x = 30 cm

Perimeter of a triangle is just the sum of its sides,

Perimeter = 18 + 24 + 30

Perimeter = 72 cm

Answer:

30cm, 72cm

Step-by-step explanation:

c²=a²+b²

x²=18²+24²=900

x=√900

x=30cm

p=a+b+c

p=18+24+30

p=72cm

Answer:

4.85423

Step-by-step explanation:

D equals C/PI

Where D=Diameter and C=Circumference and PI=PI(3.14)

Answer:

74 kilometers per hour.

Step-by-step explanation:

Let's call the speed of the faster car "x" (in kilometers per hour). Then, according to the problem, the speed of the slower car is "x - 12" (in kilometers per hour).

The two cars are traveling towards each other, so the distance between them decreases at a rate equal to the sum of their speeds. In other words, the relative speed between the two cars is:

x + (x - 12) = 2x - 12

According to the problem, they meet after 2 hours of travel, so the total distance they cover is:

distance = speed × time

For the faster car, the distance it covers is:

distance = x × 2

For the slower car, the distance it covers is:

distance = (x - 12) × 2

Since they are both traveling towards each other, the sum of the distances covered by both cars should be equal to the total distance between them at the start of the trip (320 kilometers):

x × 2 + (x - 12) × 2 = 320

Simplifying this equation:

2x + 2x - 24 = 320

4x = 344

x = 86

Therefore, the speed of the faster car is 86 kilometers per hour.

To find the speed of the slower car, we can use the expression we found earlier:

x - 12 = 86 - 12 = 74

Therefore, the speed of the slower car is 74 kilometers per hour.

The sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.

Sample space refers to the set of all possible outcomes of a random experiment or a probability event. In the context of your card example, the sample space is the set of all possible cards that could be chosen from the labeled set.

In this case, the sample space would be {E, X, P, R, S, I, O, N}, as these are the possible outcomes when selecting one card from the set.

Therefore the sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.

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Answer: the answer is two :)

Step-by-step explanation:

4x=5+3

4x=8

x= 8/4

x=2

The bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.

We can start by drawing a diagram to represent the positions of the four towns. Let A be the origin of the coordinate system, B be located 30 km due east of A, C be located 30 km due north of A, and D be located 45 km due south of A. The diagram would look like this:

       C (30 km)

         |

         |

         |

A (0,0)---+---B (30 km)

         |

         |

         |

         |

        D (45 km)

To calculate the bearing of D to B, we need to determine the angle that DB makes with the north-south axis (i.e., the y-axis) in a clockwise direction.

First, we can use the Pythagorean theorem to find the distance between B and D:

BD² = AB² + AD²

BD² = 30² + 45²

BD² = 2025

BD = √2025

BD = 45 km

Next, we can use trigonometry to find the angle that DB makes with the north-south axis. Let θ be the angle we are looking for. Then:

tan θ = (opposite / adjacent) = (AB / AD) = (30 / 45) = 2/3

Taking the arctangent of both sides, we get:

θ = tan⁻¹(2/3) ≈ 33.7°

Therefore, the bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.

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Answer: Bob 3 Hours Jack 2 Hours

Step-by-step explanation:

The unit of labor required to produce one unit of output for the two countries are 2 and 1/3.

The world automobiles-to-rice relative supply curve slopes upward, indicating that as the world price ratio of rice to automobiles rises, so will the relative supply of automobiles to rice.

To draw the world automobiles-to-rice relative supply curve, calculate the relative supply of automobiles to rice for each country. The relative supply is the ratio of the quantity of automobiles produced to the quantity of rice produced, multiplied by the ratio of the world price of rice to the world price of automobiles. Express this mathematically as:

Relative supply of automobiles to rice = (QA/RA)/(QR/RR) x (PR/PA)

where QA and RA are the quantities of automobiles and rice produced by a country, QR and RR are the quantities of rice produced by a country, and PR and PA are the world prices of rice and automobiles, respectively.

Using the unit labor requirements given in the table, calculate the relative supply of automobiles to rice for China and India as follows:

Relative supply of automobiles to rice for China = (1/4)/(1/2) x (2/1) = 2

Relative supply of automobiles to rice for India = (1/12)/(1/2) x (2/1) = 1/3

We can then plot these points on a graph, where the x-axis represents the relative supply of automobiles to rice and the y-axis represents the world price ratio of rice to automobiles. Assume that the world price ratio of rice to automobiles is initially set at 1, which means that the price of rice is equal to the price of automobiles. We can then draw a line connecting the two points, which represents the world automobiles-to-rice relative supply curve.

The kink point of the relative supply curve occurs when the relative supply of automobiles to rice is equal to 2, which is the point where China switches from being a net exporter of automobiles to a net importer of automobiles. At this point, the world price ratio of rice to automobiles increases, which means that the price of rice increases relative to the price of automobiles. As a result, China reduces its production of automobiles and increases its production of rice, which reduces its relative supply of automobiles to rice.

The second segment of the relative supply curve occurs when the relative supply of automobiles to rice is less than 1/3, which is the point where India switches from being a net exporter of automobiles to a net importer of automobiles. At this point, the world price ratio of rice to automobiles decreases, which means that the price of automobiles increases relative to the price of rice. As a result, India reduces its production of rice and increases its production of automobiles, which increases its relative supply of automobiles to rice.

The world automobiles-to-rice relative supply curve is upward sloping, which means that as the world price ratio of rice to automobiles increases, the relative supply of automobiles to rice also increases. This reflects the fact that countries specialize in the production of goods for which they have a comparative advantage, and trade with other countries to obtain goods for which they do not have a comparative advantage.

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Step-by-step explanation:

To solve the system of equations:

2y = -2x + 6 ----(1)

x - 5y = -15 ----(2)

We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.

Multiplying equation (1) by -5, we get:

-10y = 10x - 30 ----(3)

Adding equations (2) and (3), we get:

-15y = -45

Dividing by -15 on both sides, we get:

y = 3

Substituting y = 3 in equation (2), we get:

x - 5(3) = -15

x - 15 = -15

Adding 15 on both sides, we get:

x = 0

Therefore, the solution of the system of equations is (x, y) = (0, 3).

To solve the system of equations:

5x + y = 2 ----(1)

20x + 3y = -4 ----(2)

We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.

Multiplying equation (1) by -3, we get:

-15x - 3y = -6 ----(3)

Adding equations (2) and (3), we get:

5x = -10

Dividing by 5 on both sides, we get:

x = -2

Substituting x = -2 in equation (1), we get:

5(-2) + y = 2

-10 + y = 2

Adding 10 on both sides, we get:

y = 12

Therefore, the solution of the system of equations is (x, y) = (-2, 12).

Answer:

1)   (0, 3)

2)  (-2, 12)

Step-by-step explanation:

1)

2y = -2x + 6     →    y = -x + 3

x - 5y = -15

Substitute the simplified first equation into the second equation and solve for x.

x - 5( -x + 3 ) = -15

x + 5x - 15 = -15

6x = 0

x = 0

Substitute into first equation to get y.

y = -(0) + 3

y = 3

The solution to the system is the coordinate (0, 3).

2)

5x + y = 2

20x + 3y = -4

Solve the first equation for y.

y = -5x + 2

Substitute this into the second equation and solve for x.

20x + 3 ( -5x + 2 ) = -4

20x - 15x + 6 = -4

5x = -10

x = -2

Substitute this value on the first equation to get y.

y = -5( -2 ) + 2

y = 10 + 2

y = 12

The solution to the system is the coordinate (-2, 12).

The mass of substance left after 6 days is 9 g

The mass of substance left, N is given by

N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time

Also, λ = 0.693/t' where t' = half-life of iodine = 8 days

So, λ = 0.693/t'

λ = 0.693/8

λ = 0.086625/day

Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 6 days,

N = N₀exp(-λt)

N = 16 gexp(-0.086625/day × 7 days)

N = 16 gexp(-0.606375)

N = 16 g × 0.5453

N = 8.72 g

N = 8.72 → 9 g

So, the mass of substance left after 7 days is 9 g

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we need to invest  $1,410.91 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.

The rate of interest is the percentage amount charged by a lender or financial institution for borrowing money or the percentage amount paid to an investor or saver for lending money. It represents the cost of borrowing or the return on investment over a period of time.

To calculate the monthly investment required, we can use the formula for future value of an annuity, which is:

FV = PMT x ((1 + r)ⁿ⁻¹) / r

where:

FV is the future value of the annuity

PMT is the monthly payment or investment

r is the monthly interest rate

n is the total number of periods (months)

In this case, we want to save $600,000 in 25 years, which is equivalent to 300 monthly payments (25 years x 12 months/year). The monthly interest rate is 8% / 12 = 0.00667.

Plugging in the values, we get:

$600,000 = PMT x ((1 + 0.00667)³⁰⁰⁻¹) / 0.00667

Solving for PMT, we get:

PMT = $600,000 x 0.00667 / ((1 + 0.00667)³⁰⁰⁻¹)

= $1,410.91 (rounded to the nearest cent)

Therefore, we need to invest approximately $1,410.91 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.

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answer

82

steps

put data in numerical order

55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83

there are 20 numbers = 20

85 is the percentile = p

percentile rank formula

PR = (p/100) * (n + 1)

PR = (85/100) * (20 + 1) = 17.85

round up 17.85 to 18

it's the 18th number which is

82

chatgpt

(a) For every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited. (b) for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.

(a) To calculate the odds that a taxpayer will be audited, we need to divide the probability of being audited by the probability of not being audited. The probability of being audited is given as 1.5 percent or 0.015. The probability of not being audited is the complement of the probability of being audited, which is 1 - 0.015 = 0.985. Therefore, the odds that a taxpayer will be audited are:

0.015/0.985 = 0.0152284264

To convert this to odds notation, we divide the probability of being audited by the probability of not being audited:

0.015/0.985 = 0.0152284264 = 0.0152 (rounded to four decimal places)

This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited.

(b) The odds against a taxpayer being audited is the ratio of the probability of not being audited to the probability of being audited. We have already calculated the probability of not being audited to be 0.985, and the probability of being audited to be 0.015. Therefore, the odds against a taxpayer being audited are:

0.985/0.015 = 65.66666667

To convert this to odds notation, we divide the probability of not being audited by the probability of being audited:

0.985/0.015 = 65.66666667 = 66 (rounded to the nearest whole number)

This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.

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The function notation  formula is given as g(x) = f(x/2)

Function notation is a way of representing a mathematical function using symbols and variables. It is a shorthand way of writing the rule or formula for a function, which specifies how the input values (usually denoted by x) are transformed into output values (usually denoted by y or f(x)).

In function notation, a function is typically represented by a letter (usually f, g, or h) followed by parentheses that enclose the input value or variable, such as f(x), g(t), or h(y). This notation indicates that the function takes an input value (x, t, or y) and produces a corresponding output value (f(x), g(t), or h(y)).

Assuming we want to horizontally stretch the graph of f(x) by a factor of 2 to obtain the graph of g(x), the function notation for g(x) can be written as:

g(x) = f(x/2)

In other words, we plug in x/2 instead of x in the formula for f(x) to get the corresponding value of g(x) that is horizontally stretched by a factor of 2. This is because when we substitute x/2 in f(x), it effectively multiplies the input (x) by 2, which horizontally stretches the graph by a factor of 2.

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Step-by-step explanation:

3/4  bag / months   *   10 month =  30/ 4 bags = 7  1/2 bags

The equation of the new line which is parallel to the given line of equation y= 4/3x+4 is found to be: y + 7  = 4/3(x - 3).

The amount by which a line is inclined towards the horizontal axis is known as its slope. The slope can also provide a measure of a line's steepness and is helpful in assessing if two lines remain parallel or perpendicular.

Standard equation of line:

y = mx + c

m is the slope and c is the y intercept.

equation of a line: y = 4/3x + 4

On comparing both equation:

m = 4/3 and c is 4

Now, we know that : slopes of parallel lines are equal.

m = 4/3 and passing point is given as:  (3,-7).

Using the point slope form:

y - y1 = m(x - x1)

y - (-7) = 4/3(x - 3)

y + 7  = 4/3(x - 3)

Thus, the equation of the new line which is parallel to the given line of equation  y= 4/3x+4 is found to be: y + 7  = 4/3(x - 3).

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The solution to the expression 7 + (one-fifth x 18 – 3) using the order of operations is 7.6 .

The order of operations is:

Perform any calculations inside parentheses first.

Exponents (ie powers and square roots, etc.)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

To solve the expression 7 + (one-fifth x 18 – 3), we need to apply the order of operations, which is a set of rules that determines the sequence in which we perform mathematical operations.

Using the order of operations simplifies the expression as follows:  

Calculate what's inside the parentheses:

one-fifth x 18 – 3 = (1/5) x 18 – 3

= 3.6 - 3

= 0.6

Add 7 to the result:

7 + 0.6 = 7.6

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Answer:

0.1 gallons per second or 6 gallons per minute

Step-by-step explanation:

Unit rate =measurement/time

Measurement=

42

gallons

Time=

7

42/7=6

Or if you want in seconds, change the mins to seconds. There are 60 seconds in a minute

7

×

60

=

420

seconds

Unit rate =

42

420

=

0.1

gallons per second

Answer: It is 144 but add pi symbol

Step-by-step explanation:

In conclusion the exact volume of the cone is 144π cubic inches.

How to solve and what does volume mean?

The radius of the circular base is half the diameter, which is 12/2 = 6 inches.

The volume of a cone can be found using the formula V = (1/3)πr²2h, where r is the radius and h is the height.

Substituting the given values, we get:

V = (1/3)π(6²2)(12)

V = (1/3)π(36)(12)

V = (1/3)(432π)

V = 144π

Therefore, the exact volume of the cone is 144π cubic inches.

Volume is a measure of the amount of space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be determined by measuring its dimensions, such as length, width, and height, and applying the appropriate formula for the shape of the object.

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