in δqrs, s = 5.1 cm, q = 2.9 cm and ∠r=135°. find ∠s, to the nearest 10th of a degree.

The straight-line distance between the points (5,7) and (1,11) can be calculated by using the distance formula, which is as follows:distance formula: `sqrt((x2 - x1)^2 + (y2 - y1)^2)`where `(x1, y1)` and `(x2, y2)` are the coordinates of the two points.

Substituting the given values, we get:d = `sqrt((1 - 5)^2 + (11 - 7)^2)`d = `sqrt((-4)^2 + 4^2)`d = `sqrt(16 + 16)`d = `sqrt(32)`d = 4sqrt(2)≈ 5.65Therefore, the straight line (Euclidean) distance between the points (5,7) and (1,11) is approximately 5.65 units.

Distance is a scalar quantity that represents the shortest distance between two points. The distance formula is a mathematical formula that computes the straight-line distance between two points in a two-dimensional plane. It is derived from the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of its other two sides.

The formula for distance is as follows: distance formula: `sqrt((x2 - x1)^2 + (y2 - y1)^2)`where `(x1, y1)` and `(x2, y2)` are the coordinates of the two points.In the given problem, we have to find the straight-line distance between the points (5,7) and (1,11).

Substituting the given values, we get:d = `sqrt((1 - 5)^2 + (11 - 7)^2)`d = `sqrt((-4)^2 + 4^2)`d = `sqrt(16 + 16)`d = `sqrt(32)`d = 4sqrt(2)≈ 5.65Therefore, the straight line (Euclidean) distance between the points (5,7) and (1,11) is approximately 5.65 units. Thus, the correct option is B.

The straight-line distance between the points (5,7) and (1,11) is approximately 5.65 units.

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Answer:

true

Step-by-step explanation:

Answer:

It is still - 5 cause it was rotated ao the original position so H does not change but T and D chane

Answer: 1  gallon

Step-by-step explanation:

Answer:

The domain of the graph is all real numbers less than or equal to 0.

Hope this helps! :D

Answer:

x = 26

Step-by-step explanation:

1 / 3 (x - 2) = 1 / 5 (x + 4) + 2

1/3x - 2/3 = 1/5x + 4/5 + 2

1/3x - 1/5x = 4/5 + 2/3 + 2

(5x - 3x)/15 = (12 + 10 + 30) / 15

2x / 15 = 52 / 15

2x = 52

x = 52 / 2

x = 26

Answer:

x=26

Step-by-step explanation:

Find the surface area of a Cuboid of length, breadth, and height equal to 12 cm, 8 cm and 5 cm respectively.

\( \bullet \) Length (l) of a Cuboid is 12 cm.

\( \bullet \) Breadth (b) of a Cuboid is 8 cm.

\( \bullet \) Height (h) of a Cuboid is 5 cm.

The surface area of a Cuboid.

We know,

Formula of surface area of a Cuboid is 2(lb + bh + lh) sq units.

So, Surface area of a Cuboid = 2(12×8 + 8×5 + 12×5) sq cm.

= 2(96 + 40 + 60) sq cm.

= 2 × 196

= 392 sq cm

Concept: "Logos" has had a significant impact on Western thought. Importance: its recognition of the interplay between rational thought and empirical observation Acknowledgement: role of language and discourse in shaping our understanding of the world.

Topic: The concept of "Logos" in Greek philosophy and its significance in modern scientific fields.

The concept of "Logos" is central to Greek philosophy and has been interpreted in various ways throughout history. In its most basic sense, "Logos" refers to rational thought, speech, and language. It is often associated with the divine or the cosmic principle that governs the universe, as well as human reasoning and discourse.

The significance of "Logos" can be seen in its influence on modern scientific fields, including biology, psychology, and technology, among others. The term "biology," for example, comes from the Greek words "bios" (life) and "logos" (word or reason), reflecting the idea that the study of life requires both empirical observation and rational analysis.

Similarly, the field of psychology, which deals with the workings of the human mind and behavior, derives its name from the Greek word "psyche," meaning "soul," and "logos," meaning "reason." This reflects the idea that the study of the mind and behavior requires both empirical research and theoretical analysis.

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Translation: The Greek word "logos" is typically interpreted as the pinnacle of Western rationalist civilization, having been established by the first schools of classical philosophy. In reality, he is responsible for the names of many scientific fields, including biology, philology, psychology, technology, and others. Since it requires both mind and action, internal and external, the mental notion and pronouncing the word, the concept of "logos" does not have such an abstract meaning. Topic:____________________________________________________ Principal Concept:

The solution to the system of equations is:

x = -131 and y = -63.5

To solve this system of equations, we can use the method of elimination, which involves adding or subtracting the equations in order to eliminate one of the variables.

To eliminate y, we can multiply the first equation by 2 and the second equation by 4, which gives:

2x - 8y = 246 (multiplying the first equation by 2)

4x - 8y = -16 (multiplying the second equation by 4)

We can now subtract the second equation from the first:

2x - 4x - 8y + 8y = 246 - (-16)

Simplifying, we get:

-2x = 262

Dividing both sides by -2, we get:

x = -131

Now that we know x, we can substitute this value into one of the original equations to find y. Let's use the first equation:

x - 4y = 123

Substituting x = -131, we get:

-131 - 4y = 123

Adding 131 to both sides, we get:

-4y = 254

Dividing both sides by -4, we get:

y = -63.5

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Answer: 3:5

Step-by-step explanation:

total students: 12+18=30

ratio: 18 girls :30 students total

simplify: 18/6 : 30/6= 3:5

The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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Answer:

Option C it is sure

,

A

trust me looooooooooll

The time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d). So the answer is d. 40 minutes

Let's set up the equation based on the given information:

1/24 is the rate at which Sean and Colleen work together (clearing the yard in 24 minutes).

Let's denote the time it takes Colleen to clear the yard alone as c minutes. According to the given information, it would take Sean 20 minutes longer than Colleen to clear the yard alone, so Sean's time is (c + 20) minutes.

To set up the equation, we can combine their individual rates of work:

1/c is Colleen's rate of work (clearing the yard in c minutes).

1/(c + 20) is Sean's rate of work (clearing the yard in c + 20 minutes).

Given that their combined rate is 1/24, we can set up the equation:

1/c + 1/(c + 20) = 1/24

To solve this equation and find the value of c, we can multiply both sides by the common denominator of 24c(c + 20):

24(c + 20) + 24c = c(c + 20)

Simplifying and rearranging the equation:

24c + 480 + 24c = c^2 + 20c

48c + 480 = c^2 + 20c

Rearranging the terms and setting the equation equal to zero:

c^2 - 28c - 480 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. By factoring, we find:

(c - 40)(c + 12) = 0

This gives two possible values for c: c = 40 or c = -12.

Since time cannot be negative, we discard the solution c = -12.

Therefore, the time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d).So the answer is d. 40 minutes.

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Answer:

Step-by-step explanation:

Formula (Normal Area Trapezoid)

A = (b1 + b2 ) * h / 2

Formula (Trapezoid Modified for the question)

b1 + b2 is given as 90

Area = 90*h / 2

Givens

b1 + b2 = 90

Area = 1170

h = ?

Solution

Area = 90 * h / 2               Substitute  the givens into the formula

1170 = 90 * h/ 2                 Divide by 2 on the right.

1170 = 45 * h                      Divide both sides by   45

1170 / 45 = 45 * h/45

Answer: h = 45 inches.

The quadrilateral with vertices (0, 0), (0, 4), (8, 4) and (8,0) makes the rectangle.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

The given points are,

(0, 0), (0, 4), (8, 4) and (8,0).

To determine the section for the quadrilateral,

Find distance between points.

The distance between two points A(x₁, y₁) and B(x₂, y₂)

Distance

= √(x₂ - x₁)² + (y₂ - y₁)²

The distance between (0, 0) and (0, 4)

= √(0-0)² + (4-0)² = √(0)² + (4)² = √(4)² = 4

The distance between (0, 4) and (8, 4)

= √(8-0)² + (4-4)² = √(8)² + (0)² = √(8)² = 8

The distance between (8, 4) and (8, 0)

= √(8 - 8)² + (0 - (4))² = √(0)² + (4)² = √(4)² = 4

The distance between (8, 0) and (0, 0)

= √(0 - 8)² + (0- 0)² = √(-8)² + (0)² = √(8)² = 8

Since, the opposite sides are equal,

Therefore, the quadrilateral is rectangle.

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A graph that represents the function g(x) = 2/(x − 1) − 3: D. graph D.

In Mathematics, an asymptote is a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a rational function simply refers to the value of x which makes its denominator equal to zero (0).

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a rational function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines;

Therefore, x - 1 ≠ 0;  x ≠ 1, and as such, the vertical asymptote is at x = 1 as depicted by graph D.

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Answer:

I don't know how to answer this

Regarding the multiple-choice problems, I see that you have included three separate problems. To provide the answers within the specified word limit, I will list the correct options for each problem:

Problem 11: The correct answer is **b) Line current equals phase current at the load**. In a balanced three-phase circuit with a Y source and Δ load, the line current is equal to the phase current at the load.

Problem 12: The correct answer is **c) 74.8x−45∘V rms**. Given the specified values for phase voltage, line impedance, and load impedance, the calculation yields a line voltage of 74.8x−45∘V rms.

I hope this clarifies the answers to the given problems. If you have any further questions, please let me know!

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Answer:

To solve the system below by substitution, replace y in the second equation with 7−6x.

==> False

This statement is false. To solve the system by substitution, replace x in the second equation with 7−6x.

==> False.

This statement is false. To solve the system by substitution, replace y in the first equation with 7−6x.

==> False

This statement is false. To solve the system by substitution, replace y in the second equation with 6x−7.

==> True.

From the first equation, 6x-y=7

y= 6x-7

Answer: This statement is false. To solve the system by​ substitution, replace y in the second equation with 6x−7.

The required exact surface area of the cylinder is 2\(\pi\)r(r+h).

To calculate the surface area of the cylinder, the required measurement of the radius (r) of the base of the given cylinder and height (h) of the cylinder.

The  formula to find the lateral surface area of a given cylinder is 2\(\pi\)rh and the formula to find the surface area of  a given cylinder is 2\(\pi\)r(r+h).

Let the radius of the base of the cylinder be f and height of the cylinder be g then the lateral surface of cylinder is 2\(\pi\)fg, the surface area of  a given cylinder is 2\(\pi\)f(f+g).

Hence, the required exact surface area of the cylinder is 2\(\pi\)r(r+h).

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Natalie will receive a weekly salary of $656.61 and a summer salary of $10505.76.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that Natalie earns $15.27 per hour while working as a playground supervisor for 8 weeks throughout the summer. Although she works a 40-hour week, she typically puts in 3 hours of overtime.

For a week = ( 40 + 3 ) x 15.27 = $656.61

For a summer = 4 x 4 = 16 weeks

For a summer = 16 x $656.61 = $10505.76

Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.

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The probability that the average final exam score for a sample of 64 students is between 140 and 150 is approximately 0.2893, or 28.93%.

What is normal distribution?

Normal distribution, also known as Gaussian distribution or bell curve, is a probability distribution that is symmetric and bell-shaped. It is widely used in statistics and probability theory to model a wide range of phenomena observed in nature, society, and various fields of study.

To calculate the probability that the average final exam score for a sample of 64 students is between 140 and 150, we need to use the properties of the normal distribution.

Given:

Mean score (μ) = 149

Standard deviation (σ) = 16

Sample size (n) = 64

Step 1: Find the standard deviation of the sample mean (standard error):

The standard deviation of the sample mean, also known as the standard error, is given by the formula:

Standard error (SE) = σ / √n

SE = 16 / √64 = 16 / 8 = 2

Step 2: Convert the values to z-scores:

To work with the standard normal distribution, we need to convert the values of 140 and 150 to z-scores using the formula:

z = (x - μ) / σ

For 140:

z1 = (140 - 149) / 16 = -9 / 16 ≈ -0.5625

For 150:

z2 = (150 - 149) / 16 = 1 / 16 ≈ 0.0625

Step 3: Find the cumulative probability:

Using the z-scores obtained, we can find the cumulative probability for each z-score using a standard normal distribution table or a statistical software.

P(z1 < Z < z2) = P(-0.5625 < Z < 0.0625)

Consulting a standard normal distribution table or using a statistical software, we find that P(-0.5625 < Z < 0.0625) is approximately 0.2893.

Therefore, the probability that the average final exam score for a sample of 64 students is between 140 and 150 is approximately 0.2893, or 28.93%.

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b) It will take approximately 24.6 years to save $3,000 for your vacation by saving $100 each month with a 3% nominal interest rate compounded monthly.

c) equivalent effective interest rates are:

i. Semi-annually: 5.06%

ii. Quarterly: 5.11%

iii. Daily: 5.13%

iv. Continuously: 5.13%

EXPLANATION:

To calculate the time it will take for you to save $3,000 for your vacation, we can use the future value formula for monthly compounding:

\(Future Value = Principal * (1 + rate/n)^(n*time)\)

Where:

- Principal is the amount you save each month ($100)

- Rate is the nominal interest rate (3% or 0.03)

- n is the number of compounding periods per year (12 for monthly compounding)

- Time is the number of years we want to calculate

We need to solve for time. Let's substitute the given values into the formula:

\($3,000 = $100 * (1 + 0.03/12)^(12*time)Dividing both sides of the equation by $100:30 = (1.0025)^(12*time)\)

Taking the natural logarithm (ln) of both sides:

\(ln(30) = ln((1.0025)^(12*time))Using logarithmic properties (ln(a^b) = b * ln(a)):ln(30) = 12*time * ln(1.0025)\)

Solving for time:

\(time = ln(30) / (12 * ln(1.0025))\)

Using a calculator:

time ≈ 24.6

c)To calculate the equivalent effective interest rate for a nominal rate of 5% compounded at different intervals:

i. Semi-annually:

The effective interest rate for semi-annual compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

For semi-annual compounding:

\(Effective Interest Rate = (1 + (0.05 / 2))^2 - 1\)

Calculating:

Effective Interest Rate ≈ 0.050625 or 5.06%

ii. Quarterly:

The effective interest rate for quarterly compounding is calculated similarly:

\(Effective Interest Rate = (1 + (0.05 / 4))^4 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051136 or 5.11%

iii. Daily:

The effective interest rate for daily compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

Since there are approximately 365 days in a year:

\(Effective Interest Rate = (1 + (0.05 / 365))^365 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051267 or 5.13%

iv. Continuously:

The effective interest rate for continuous compounding is calculated using the formula:

\(Effective Interest Rate = e^(nominal rate) - 1\)

For a nominal rate of 5%:

\(Effective Interest Rate = e^(0.05) - 1\)

Calculating:

Effective Interest Rate ≈ 0.05127 or 5.13%

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Answer:

C.

Step-by-step explanation:

Since the slope is 1 meaning it goes up and over by 1 the GPA would increase by 1 every hour

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

23a + 9b + 9c

Step-by-step explanation:

9a + 6b + 3b + 14a + 9c ( collect like terms )

= (9 + 14)a + (6 + 3)b + 9c

= 23a + 9b + 9c

Answer:

B

Step-by-step explanation:

A line with a positive slope is indicated by

The line sloping up from left to right

This is shown in graph B

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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Answer:

37.5

Step-by-step explanation:

The median age of his friends is 13

From the question, we have the following parameters that can be used in our computation:

Age (years) 11 12 13 14 15 16

Frequency 3 5 4 2 4 2​

The median age is the age at the middle

So, we have

Median position = (20 + 1)/2

Median position = 10.5th

Here, we have

10.5th = 13

Hence, the median age is 13

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