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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

The experimental probability is0.33 or 33% to dock .

The probability calculated without performing any experiments is known as theoretical probability.  It can be characterised as the proportion of favourable results to all other possible outcomes.  No experiment is required to determine the theoretical probability.  As an alternative, we should be aware of the circumstances in order to determine the likelihood that an event will occur.

The actual outcome of an experiment is known as the experimental probability, which may differ from the theoretical probability.

In this instance, the marina 1 is home to 6 boats from Maine and 12 vessels from other states.

Hence,

6/(6+12) = 0.33 or 33%

the chance that the next boat to port comes from Maine.

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Answer:

1/3

Step-by-step explanation:

Answer: 22 sophomores were surveyed

Step-by-step explanation:

Answer:

4.85423

Step-by-step explanation:

D equals C/PI

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

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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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).

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.

Answer:

IT IS B hope this helped

Step-by-step explanation:

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

The result of the matrix multiplication for  F³  is determined as [[1,0],[-2,3]].

Matrix multiplication is a mathematical operation that takes two matrices and produces a new matrix.

Given two matrices A and B, the resulting matrix C is obtained by multiplying the elements of the rows of matrix A with the corresponding elements of the columns of matrix B, and summing the products.

To calculate F³, we need to multiply the matrix F by itself three times:

F² = F * F = [[1,0],[2,-3]] * [[1,0],[2,-3]] = [[11+02,10+0(-3)],[21+(-3)2,20+(-3)(-3)]] = [[1,0],[-4,9]]

F³ = F * F² = [[1,0],[2,-3]] * [[1,0],[-4,9]] = [[11+02,10+09],[21+(-3)(-4),2*0+(-3)*9]] = [[1,0],[-2,3]]

Therefore, F³ = [[1,0],[-2,3]].

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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: the answer is two :)

Step-by-step explanation:

4x=5+3

4x=8

x= 8/4

x=2

After answering the provided question, we can conclude that So the experimental probability that the next freshman will register for earth science is 23/66.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Switching a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a branch of mathematics that studies random events rather than their properties. It is applied in many fields, including statistics, finance, science, and engineering.

There are a total of 77 + 5 + 4 + 46 = 132 freshmen who have registered for a science class. Out of these, 46 have registered for earth science.

P(earth science) = number of freshmen who registered for earth science / total number of freshmen who registered for a science class

P(earth science) = 46 / 132

Simplifying the fraction, we get:

P(earth science) = 23 / 66

So the experimental probability that the next freshman will register for earth science is 23/66.

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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

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 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:

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

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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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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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: wheres the page/diagram

Step-by-step explanation:

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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Step-by-step explanation:

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

Step-by-step explanation:

रामले 3 वर्षको लागि 12% प्रतिवर्ष साधारण ब्याजदरले रु. 50000 लगानी गरेको थियो। यसको आधारमा उनले प्राप्त गरेको ब्याज हो:

Simple Interest (S.I.) = (P × R × T) / 100

यहाँ, P = रु. 50000 हो, R = 12% = 12/100 = 0.12 हो, र T = 3 वर्ष हो।

S.I. = (50000 × 0.12 × 3) / 100 = रु. 18000

त्यसैपछि, श्यामले चक्रीय ब्याजदरले रु. 50000 लगाएर 3 वर्षमा त्यति रकम लिन्छन्। चक्रीय ब्याजदरले ब्याज प्राप्त गर्नको लागि प्रत्येक वर्षको अन्तिम रकममा पूर्ववत ब्याज पनि जोडिन्छ। त्यसको आधारमा उनले प्राप्त गरेको ब्याज हो:

Compound Interest (C.I.) = P × [(1 + R/100)ᵀ - 1]

यहाँ, P = रु. 50000 हो, R = 10% = 10/100 = 0.10 हो, र T = 3 वर्ष हो।

C.I. = 50000 × [(1 + 0.10)³ - 1] = रु. 16532.10

त्यस्तै ब्याजदर र समयको आधारमा रामले पनि रकम लगाएर बराबर ब्याज प्राप्त गर्न चाहनुहुन्छ। यसलाई गणना गर्न प्रयोग गरिएको समान ब्याज तथा समय भएको सिस्टमको नाम "Compound Interest with annual installments" हो। यसक

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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The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.

What is a triangle?

A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.

To start, let's graph the triangle to get a better understanding of the problem:

(0,3)   *

       |\

       | \

       |  \

       |   \

       |    \

(0,0)   *-----*-----> x

        (5,0)

The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.

The area of a semicircle is πr²/2, so the volume of this slice is:

V(x) = π * (3/10 * x)² / 2 * dx

To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:

V = ∫₀₅ π * (3/10 * x)² / 2 dx

V = π/20 * ∫₀₅ x² dx

V = π/20 * [x³/3] from 0 to 5

V = π/20 * (5³/3)

V = π/4 * (25/3)

V = 25π/12

Therefore, the volume of the solid is 25π/12 cubic units.

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The coordinates of the final point after the reflections across the x-axis twice is (6, -4)

Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.

So reflecting (6,-4) across the x-axis gives us the point (6,4).

Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.

So reflecting (6,4) across the x-axis gives us the point (6,-4).

Therefore, the final point after both reflections is (6, -4).

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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: Bob 3 Hours Jack 2 Hours

Step-by-step explanation: