In Exercises determine which of the two acute angles has the given trigonometric ratio. (See Example ) The cosine of the angle is In Exercises determine which of the two acute angles has the given trigonometric ratio.
(See Example )
The cosine of the angle is

The body style of an automobile (sedan, coupe, wagon, etc.) is an example of a discrete nominal variable. The correct option is A.

A discrete nominal variable is a categorical variable where the categories are distinct and have no inherent order or numerical value associated with them. In the case of the body style of an automobile, the different categories (sedan, coupe, wagon, etc.) are distinct and do not have a specific order or numerical value. Each body style is simply a distinct category without any inherent ranking or measurement. Therefore, the correct option is A. Discrete nominal.

""

Continuous variable 6. The body style of an automobile (sedan, coupe, wagon, etc.) is an example of a

A. Discrete nominal

B. Discrete ordinal

C. Continuous interval

D. Continuous ratio

""

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Epics are characterized by their grand scope, often encompassing heroic journeys, vast settings, and larger-than-life characters. In the plot of an epic, we typically see a central hero embarking on a quest that requires overcoming significant challenges, which in turn highlight the hero's extraordinary qualities.

This journey often involves a mix of external conflicts, such as battles or confrontations with powerful forces, as well as internal struggles, such as moral dilemmas or personal growth.
The setting of an epic is expansive, usually spanning across multiple geographical locations and sometimes even extending into the supernatural realm. This vastness serves to emphasize the enormity of the hero's task and the significance of their achievements.
Characters in epics are often archetypal, with clear distinctions between good and evil, and possessing traits that embody ideal qualities of their respective societies. The hero is typically virtuous, brave, and resourceful, while the antagonist represents opposing forces that challenge the hero's journey. Additionally, supporting characters often aid the hero or provide guidance, further emphasizing the theme of camaraderie or the importance of mentorship.
Themes in epics often revolve around universal human experiences, such as the struggle between good and evil, the importance of loyalty and honor, or the consequences of hubris. These themes resonate across cultures and time periods, ensuring that epics continue to be relevant and appreciated by audiences today.

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Answer:

sqrt(29)

Step-by-step explanation:

distance = sqrt√(  (x2 - x1)^ + (y2 - y1)^2  )

x1 = 6

x2 = 8

y1 = -8

y2 = -3

distance = sqrt(  ( 8 - 6)^2 + (-3 - -8)^2  )

distance = sqrt( 2^2 + 5^2)

distance = sqrt(29)

Answer:

29

Step-by-step explanation:

29

Answer:

it is a statistical measure of the relationship between two variables that indicates the extent to which the variables change together in the same or opposite direction. Correlation does not imply causation, meaning that a correlation between two variables does not necessarily mean that one variable causes the other.

Based on this definition, the correct answer is b. Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between two variables when both variables increase or decrease together. This statement captures the idea that correlation can be positive or negative, and that it reflects a linear relationship between two variables.

Step-by-step explanation:

a is wrong because it only describes positive correlation, not negative correlation.

c is wrong because it confuses correlation with consistency. Correlation does not require that higher values of X always go with higher or lower values of Y, only that they tend to do so on average.

d and f are wrong because they assume causation from correlation, which is a logical fallacy.

e is wrong because it contradicts itself. It says that increasing values of X go with increasing values of Y, which is positive correlation, but then it says that a correlation exists when both variables decrease together, which is negative correlation.

If X is correlated with Y, it implies a predictive statistical relationship between X and Y. This correlation can be positive or negative implying respective increase or decrease in values of both variables. But, this correlation doesn't prove causation.

If X is correlated with Y, it indicates a statistical relationship between the two variables, X and Y. This relationship can be positive or negative. If it is a positive correlation, as X increases, Y will also increase and similarly, as X decreases, Y will also decrease. Contrarily, in a negative correlation, as X increases, Y decreases and vice versa. However, it is important to understand that correlation does not imply causation. That is, if X and Y are correlated, it does not necessarily mean that changes in X cause changes in Y or vice versa. It only means that they move in a predictable manner relative to each other.

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Part A: JoAnn's team collects 3m magazines.

Part B: The number of magazines (m) = 218 magazines.

Part A: To represent the total number of magazines JoAnn's team has collected, we can set up an equation. We know that JoAnn's team collected 3 times as many magazines as Clarissa's team. Therefore, we can set up the equation 3m = 654, where m represents the number of magazines that Clarissa's team collected. Part B: To solve the equation, we can divide both sides by 3. This gives us m = 218. This means that the number of magazines (m) Clarissa's team collected is 218 magazines.  In conclusion, Clarissa's team collected 218 magazines, and JoAnn's team collected 3 times as many magazines, which is 654 magazines.

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Answer:

Hi! The answer to your question is \(\frac{3}{4}\)

Step-by-step explanation:

This equation is in y=mx+b or -b which is Slope Intercept form for Graphing basically y is the y intercept and b means slope, you don't have to do anything extra to find the slope when its in Slope Intercept Form all you have to do is look for usually its a fraction but it can also be a number but all you have to look for is the number that comes before b in the equation! If this has helped you please say that this has helped, if it hasn't please tell me what confuses you and i can quickly clear up that confusion! Have a nice day!

The terminal-point P(x, y) on the unit circle for "t = 7π/6' is (-√3/2 , -1/2), and the labelled graph of "y = 3+cos(x)" is shown below.

We have to find the terminal-point for t = 7π/6.,

The angle is given to be 7π/6, which means in degree it's measure is 210 degrees, and since the circle is unit circle ,So, radius = 1

The value of x and y, for terminal-point can be calculated as:

x = r × cos(θ)  = 1 × cos(210°) = -√3/2,

y = r × sin(θ) = 1 × sin(210°) = -1/2,

So, the required terminal point will be = (-√3/2 , -1/2).

To sketch graph of function "y = 3+cos x",

We substitute the values, and plot them,

For x = -2π, we get y = 4, the point is (-2π, 4);

For x = -π, we get y = 2, the point is (-π, 2);

For x = 0, we get y = 4, the point is (0, 4);

For x = π, we get y = 2, the point is (π, 2);

For x = 2π, we get y = 4, the point is (2π, 4);

Therefore, the graph of these points is sketched below.

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The given question is incomplete, the complete question is

Find the terminal point P(x, y) on the unit circle determined by the given value of t. (Remember to show work to justify your answer.) t = 7π/6.

Sketch the graph of y = 3+cos x. Remember to label your axes carefully (with numbers) and to show the five points accurately.

Answer:

5 bracelets

Step-by-step explanation:

take the 200 - 120

now take the 80 thats left over and divide that by 15

that will equal 5.33 so you go by the whole number she can make a total og 5 bracelets

hope this helped

Answer:

5

Step-by-step explanation:

Therefore, the volume of the paper cone to the nearest tenth is 418.7 inches cubed.

The volume of the paper cone that Gretchen made to hold a gift for a friend is given by;V= (1/3)πr²hWhere;r = radius of the paper coneh = height of the paper coneπ = 3.14

Given that;Height of the paper cone (h) = 16 inches Radius of the paper cone (r) = 5 inchesWe are to find the volume (V) of the paper cone to the nearest tenth of an inch.

To obtain the volume of the paper cone, we can substitute the values of r and h in the formula above to obtain;

\(V= (1/3)\pir^2hV\)= \((\frac{1}{3} ) \times 3.14\times5^2 \times16V = (\frac{1}{3} ) \times 3.14\times25\times16V = (\frac{1}{3}) \times 1256V=418.7\)

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The true about the numbers Sara added is that one of the numbers is even and the other number is odd

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

Count of numbers added = 2

The sum of the numbers = odd number

Represent the two numbers using x and y

So, we have the following representation

Sum = x + y

Substitute the known values in the above equation, so, we have the following representation

x + y = odd number

As a general rule of addition, we have:

Odd number + Odd number = Even number

Even number + Even number = Even number

Even number + Odd number = Odd number

Odd number + Even number = Odd number

Using the above as a guide, we have the following:

x = Odd number and y = Even number

Or

y = Odd number and x = Even number

Hence, the true statement is that one of the numbers is odd

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The equation of the line shown in the graph, from (–2,2) to (–3,–1) is y = -5/4x – 7/4.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

To solve for the equation of the line, we can use the point-slope formula, y – y1 = m(x – x1), where m is the slope of the line and (x1, y1) is a point on the line. In this case, the point (x1, y1) is (–2,2) and the slope of the line is m = (–1 – 2)/(–3 – (–2)) = –3/–1 = 3. Therefore, the equation of the line is y – 2 = 3(x – (–2)).

Simplifying, we get y = 3x + 2. To put the equation in the slope-intercept form, y = mx + b, we can rewrite the equation as y = 3x + 2 = 3x + 2 – 2 = 3x – 2 + 2 = 3x – 2, which is the equation of the line, y = –5/4x – 7/4.

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The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This line is a horizontal line, which means that all points on the line have the same y-coordinate.

To verify this equation, we can use the two points given on the graph: (-2,-3) and (3,-3). Using the slope-intercept form of a line, we can plug in the points to determine the equation of the line.

The slope-intercept form is y = mx + b, where m is the slope, x is the x-coordinate, and b is the y-intercept. The slope is calculated by finding the change in y over the change in x. In this case, both points have the same y-coordinate, so the slope is 0. Therefore, the equation of the line is y = 0x + b.

Plugging in the coordinates of one of the points, (-2,-3), we get -3 = 0x + b. By solving for b, we get b = -3. Substituting b into the equation, we get y = 0x - 3. This is the equation of the line shown in the graph.

In conclusion, the equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This equation was verified by using the slope-intercept form of a line and plugging in the two points given on the graph.

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Answer:

A

Step-by-step explanation:

According to the given question.

Total number of shirts, n = 12

Number of shirts to be selected, r = 3

As we know, the total number of ways of selection of r objects from n objects at a time without replacement is given by

C(n, r) = n!/r!(n - r)!

Answer:

the answers D

Step-by-step explanation:

i took the quiz

Answer:

King Leopold became the monarch of Belgium in 1865

Answer:

i believe number 1 is 18 and number 2 is 9.

Step-by-step explanation:

if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.

Christina's initial monthly cell phone bill is $50 and it increases at a rate of 0.02 dollars per month.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (60 - 50)/(500 - 0)

Slope (m) = 10/500

Slope (m) = 0.02

At data point (0, 50), a linear equation in slope-intercept form for this line can be calculated as follows:

y = mx + c

y = 0.02x + 50

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A) -4n-36

You multiply -4 by n, which is -4n, and -4 by 9, which is -36

Answer: The sales tax on the meal is 6%, and the family leaves a 20% tip. What is the total cost of the meal? Please answer with whole number or decimal. Linda C. answered • 01/05/15. We can do this problem a few different ways.

Step-by-step explanation:

Answer:

Jaycee walked \(2.5\) miles farther.

Step-by-step explanation:

Given

Jaycee walked 14.5 miles in 3 hours at a constant rate.

Step 1 of 1

From given graph \($(1,4)$\), \($(2,8)$\) is a two points.

Then the equation of the line are \($y=4 x$\)

This imply at \($x=3\) ;

\(y=12$\)

Therefore, James walked \(12\)miles in \(3\) hours.

Jaycee walked \($14.5$\) miles in \(3\) hours.

Jaycee walked farther and that is \($(14.5-12)$\)mile

\(=2.5\)miles

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Answer:

use -9 to multiply the first equation

use -4 to multiply the second equation.

Step-by-step explanation:

5x-4y=28.....eqn (1)×-9

3x-9y=30....eqn(2)×-4

-45x+36y=-252

-(-12x+36y=-120)

therefore, -33x÷33 =-132÷-33

x=4.

substitute (x=4) in any of the equation. I'm just going to use eqn 1.

5x-4y=28

5(4)-4y=28

20-4y=28

-4y =28-20

-4y÷-4 = 8÷-4

y=-2

so, x=4, y=-2

Note: for proof of answers substitute the answers for x and y and see if you have the same result...e.g

5(4)-4(-2)=28.

Answer:

The first equation should be multiplied by 9 and the second equation by −4.

Step-by-step explanation:

Answer: -3/2

Step-by-step explanation:

There are two methods to find the slope

METHOD 1. Rise/Run

Rise: the y-axis value

Run: the x-axis value

In the graph, rise/run=3/2

The line is going down, so it should be negative

-3/2

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

2 Tetrahedrons combined create an Octahedron.

Step-by-step explanation:

Despite the lack of information.

The Plato Polyhedrons are Tetahedron, Cube (Hexaedron), Dodecahedron, Octahedron and Icosahedron. They are regular ones, made up by regular plane figures.

An Octahedron can be built by combining two pyramids. Each Tetrahedron is made up by 4 equilateral triangle.

The rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station is approximately 322.8 miles per hour.

Ware required to find the rate at which the distance from the plane to the station is increasing.

Let's use the Pythagorean theorem to find PR:PR² = QR² + PQ²

Where,

PQ = speed of the plane * time

To find time,Let t be the time taken by the plane to travel from Q to P. Then, the time taken by the plane to travel from R to Q is also t.

Distance = Speed × Time

Therefore

,QR = 500t

PR² = QR² + PQ²

PR² = (500t)² + 1²

Differentiate both sides of the above equation w.r.t time t, we get:

2PR * dPR/dt = 2(500t)(500) + 2(1)(dPQ/dt)

Rearrange the above equation to find dPR/dt:

dPR/dt = [(500t)(500) + PQ(dPQ/dt)] / PR

Substitute PQ = 500t and PR = √(500t)² + 1²), we get:

dPR/dt = [(500t)(500) + 500t(dPQ/dt)] / √(500t)² + 1²)

We know that PQ = 500t, therefore,

dPQ/dt = 500

So,dPR/dt = [(500t)(500) + 500t(500)] / √(500t)² + 1²)

Putting t = 2, we get:

dPR/dt = [(500 × 2)(500) + (500)(500)] / √(500 × 2)² + 1²)

dPR/dt = 322.8

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Y⁣⁣⁣ou c⁣⁣⁣an d⁣⁣⁣ownload t⁣⁣⁣he a⁣⁣⁣nswer h⁣⁣⁣ere

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In 1927 charles lindberg had his first solo flight across the atlantic ocean, then the he fly each hour 107.76 miles/hour.

Based on the given conditions,

In 1927 charles lindberg had his first solo flight across the atlantic ocean.

He flew 3610 miles in 33.5 hours

So,

We can write,

To find out the unit rate, divide the total distance by the total time

Then,

33.5 hours = 3610 miles

1 hour = x miles

Cross Multiply

33.5 hours × x miles = 3610 miles × 1 hour

x miles = 3610 miles × 1 hour/33.5 hours

x miles = 107.76119403 miles

Approximately = 107.76 miles per hour

Therefore,

In 1927 charles lindberg had his first solo flight across the atlantic ocean, then the he fly each hour 107.76 miles/hour.

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Answer:

15

Step-by-step explanation:

divide the perimeter by two and minus 1

Answer: 15ft

Step-by-step explanation:

Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!

What type of survey was used during the data collection process? .This question is important because it helps the researcher understand the methodology employed

This can impact the data's accuracy and relevance for their specific research needs. Additionally, knowing the survey type can help assess any potential biases or limitations in the collected data.

A marketing researcher should ask questions such as: who collected the data, what methodology was used in the data collection process, what sources were used to obtain the data, what was the sample size and composition, how recent is the data, and how was the data analyzed and presented.

It is important to determine the credibility and accuracy of the data sources and the survey methodology used in order to establish the reliability of the secondary data in the international arena. The cost of the data should not be the primary concern when evaluating the reliability of the data sources.

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The area under the curve over [2,5] is 24.

Given function is f(x) = 2xIntervals [2, 5] is given and it is to be divided into subintervals.

Let us consider n subintervals. Therefore, width of each subinterval would be:

$$
\Delta x=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}
$$Here, we are using right-hand end point. Therefore, the right-hand end points would be:$${ c }_{ k }=a+k\Delta x=2+k\cdot\frac{3}{n}=2+\frac{3k}{n}$$$$
\begin{aligned}
\therefore R &= \sum _{ k=1 }^{ n }{ f\left( { c }_{ k } \right) \Delta x } \\&=\sum _{ k=1 }^{ n }{ f\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ 2\cdot\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ \frac{12}{n}\cdot\left( 2+\frac{3k}{n} \right) }\\&=\sum _{ k=1 }^{ n }{ \frac{24}{n}+\frac{36k}{n^{ 2 }} }\\&=\frac{24}{n}\sum _{ k=1 }^{ n }{ 1 } +\frac{36}{n^{ 2 }}\sum _{ k=1 }^{ n }{ k } \\&= \frac{24n}{n}+\frac{36}{n^{ 2 }}\cdot\frac{n\left( n+1 \right)}{2}\\&= 24 + \frac{18\left( n+1 \right)}{n}
\end{aligned}
$$Take limit as n → ∞, so that $$
\begin{aligned}
A&=\lim _{ n\rightarrow \infty  }{ R } \\&= \lim _{ n\rightarrow \infty  }{ 24 + \frac{18\left( n+1 \right)}{n} } \\&= \boxed{24}
\end{aligned}
$$

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Given function f(x) = 2x. The interval is [2,5]. The number of subintervals, n is 3.

Therefore, the area under the curve over [2,5] is 21.

From the given data, we can see that the width of the interval is:

Δx = (5 - 2) / n

= 3/n

The endpoints of the subintervals are:

[2, 2 + Δx], [2 + Δx, 2 + 2Δx], [2 + 2Δx, 5]

Thus, the right endpoints of the subintervals are: 2 + Δx, 2 + 2Δx, 5

The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, we have to find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. The width of each subinterval is:

Δx = (5 - 2) / n

= 3/n

Therefore,

Δx = 3/3

= 1

So, the subintervals are: [2, 3], [3, 4], [4, 5]

The right endpoints are:3, 4, 5. The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, Δx is 1, f(x) is 2x

∴ f(c1) = 2(3)

= 6,

f(c2) = 2(4)

= 8, and

f(c3) = 2(5)

= 10

∴ S = f(c1)Δx + f(c2)Δx + f(c3)Δx

= 6(1) + 8(1) + 10(1)

= 6 + 8 + 10

= 24

Therefore, the Riemann sum is 24.

To calculate the area under the curve over [2, 5], we take the limit of the Riemann sum as n → ∞.

∴ Area = ∫2^5f(x)dx

= ∫2^52xdx

= [x^2]2^5

= 25 - 4

= 21

Therefore, the area under the curve over [2,5] is 21.

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The time length of the warranty should be approximately 1.515 times the mean life of the timepiece. To calculate the time length of warranty so that only 1.9% of the the quartz timepieces will be replaced before warranty expires, we use the formula: P(X ≤ x) = 0.019 Where P(X ≤ x) is the probability of failure before the warranty expires.

Let X be the number of months after purchase before a timepiece fails, and let m be the mean life of a timepiece. Then, the standard deviation of the life of a timepiece is σ = 0.25m (given). Also, the probability that a timepiece fails before the warranty expires is 0.019, which means that the probability of success is 1 - 0.019 = 0.981.

Using the standard normal table, we can find the Z-score such that the area to the left of Z is 0.981. From the table, we find that Z ≈ 2.06 (rounded to two decimal places).Therefore, Z = (x - m) / σ implies

x = σZ + m

≈ 0.515m + m

= 1.515m (since σ = 0.25m and Z = 2.06).

Thus, the time length of the warranty should be approximately 1.515 times the mean life of the timepiece.

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