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A ruler is 12 inches long. What is the length of this ruler in centimeters? Round to the nearest hundredth.

Answer:

D

Step-by-step explanation:

the area of the triangle is 20. using the base of the rectangle [5] and the height of the triangle[8]. I did the same for the rectangle and got the area of  40 for the rectangle

I hope this helped :)

The conversions are :

a) 2.8 km =  2800 m.

b) 27.55 dm =   2.755 m.

c) 27.9 hm =   2790 m.

d) 275 dam =   2750 m.

By multiplying the value by 1000 will help us to change kilometers (km) to meters (m). In order to change decimeters into meters, it is necessary to divide the figure by 10.

To convert, Note that:

a) 2.8 km to m:

= 2.8 x 1000 m

= 2800 m

b) 27.55 dm to m:

= 27.55 ÷ 10 m

= 2.755 m

c) 27.9 hm to m:

= 27.9 x 100 m

= 2790 m

d) 275 dam to m:

= 275 x 10 m

= 2750 m

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Convert the following to meter

2,8km

27,55dm

27,9hm

275dam

The integration of cos(x) ln(sin(x)) dx is sin(x) ln(sin(x)) - sin(x) + C.

To integrate the function cos(x) ln(sin(x)) dx, you can use integration by parts, which is given by the formula ∫u dv = uv - ∫v du.

Choose u and dv.
Let u = ln(sin(x)) and dv = cos(x) dx.

Compute du and v.
To find du, differentiate u with respect to x: du = (1/sin(x)) * cos(x) dx = cot(x) dx.
To find v, integrate dv with respect to x: v = ∫cos(x) dx = sin(x).

Apply the integration by parts formula.
∫cos(x) ln(sin(x)) dx = uv - ∫v du = sin(x) ln(sin(x)) - ∫sin(x) cot(x) dx.

Simplify the remaining integral.
Since cot(x) = cos(x) / sin(x), the remaining integral becomes:
∫sin(x) (cos(x) / sin(x)) dx = ∫cos(x) dx.

Integrate the remaining integral.
∫cos(x) dx = sin(x) + C.

Combine the results.
The final answer is sin(x) ln(sin(x)) - sin(x) + C.

So, the integration of cos(x) ln(sin(x)) dx is sin(x) ln(sin(x)) - sin(x) + C.

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Answer: 3x-6xy-4y

Step-by-step explanation: So, it’s been a few years since I’ve been in high school, but if I remember correctly...it should break down as such...

A good method to breaking this down is to use parentheses to break up the equation.

Example: (2x)(-4xy)(+5x)(-2xy)(-4x)(-4y)

Keep in mind we are only using the parentheses as a breaker and not as multiplication as it can be seen.

So, start with the singular ‘x’ variants. (2x) (+5x) (-4x). 2x+5x is 7x. 7x-4x is 3x. Now, move onto ‘xy’ variant. (-4xy) and (-2xy). As these are both negative, they add together to make an even lower number...being -6xy. Onto the final step taking the singular ‘y’ variant. There’s only 1 ‘y’ variant so it just stays -4y.

In the end, you end up with 3x-6xy-4y. :) Hope this helps. If you have any more questions, let me know!

Answer:

a) c

b) 62

Step-by-step explanation:

He is correct because the Median weight is 56 grams.

Option C is the correct answer.

The range of weights of Felipe's tomatoes is 62.

The interquartile range of weights of Felipe's tomatoes is 44 grams.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

From the box plot,

Median = 56 grams

Now,

The statement that Felipe describe is correct because the median weight of 56 grams.

The range of the weights of the tomatoes.

= Highest value - Lowest value

= 78 - 16

= 62

The interquartile range of weights of Felipe's tomatoes.

= Upper quartile - Lower quartile

= 72 - 28

= 44 grams

Thus,

Median weight = 56 grams.

Range = 62

Interquartile range = 44 grams.

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The horizontal distance from the tower to the fire is 7 feet

The term "angle of depression" describes the angle created by a horizontal line and the line of sight from the observer's eye to a location below their horizontal line of sight. It is often calculated by descending from the horizontal line.

The angle of depression is a term that is frequently used in discussions of observations or measurements involving objects that are below the observer's location in geometry and trigonometry.

We know that;

Tan 3 = x/140

x = 140 Tan 3

x = 7 feet

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Answer:it would be y=2x+3

Step-by-step explanation:

If you find the slope of 2 over and 1 up it is a positive slope of 2 and then the slope is always _x so it’s 2x + the y intercept which is 3 and the y intercept is just the cordon are where x=0

Answer:

240 yards lost, if I understand the question correctly.

Step-by-step explanation:

If I read this correctly the team lost 85 yards lost in 8 plays.  Then they tripled their loss on the next 17.  3 x 85 = 255 yards lost in the last 17 plays.

Total yards lost was (85 + 255) = 240 yards in 22 plays.

The correlation coefficients and security returns provided suggest a relationship between security 1 and security 2.

The given information includes security returns and correlation coefficients between different securities. Based on the data, it is evident that there is a relationship between security 1 and security 2. The correlation coefficient P12 is -1, indicating a perfect negative correlation between the two securities. This means that when security 1's returns increase, security 2's returns decrease, and vice versa.

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The volume of the triangular prism is 308 in³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, Alfred made a container shaped like a triangular prism,

Given are the dimensions, 14 in., 4 in. and 11 in.

Volume of a triangular prism = BxHxL/2

= 14x4x11/2 = 616/2 = 308 in³

Hence, The volume of the triangular prism is 308 in³

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Answer:

5.024 × 10^8 tons /day

Step-by-step explanation:

This question has to deal with conversion

We are told in the question that:

On average, water flows over a particular water fall at a rate of 2.05 x 10^5 cubic feet per second.

Water flow rate = 2.05 × 10^5 ft³/s

From the question,

One cubic foot of water weighs 62.4 lb.

1 ft³ = 62.4 lb

1 ton = 2200 lb

We are to calculate the flow rate in tons per day

Hence,

1 ft³ = 62.4 lb

2.05 × 10^5 ft³ =

Cross Multiply

2.05 × 10^5 × 62.4

= 12792000lb

Hence the water flow rate = 12792000lb/s

From the question,

2200 lb = 1 ton

12792000 Ib =

Cross Multiply

12792000lb × 1 ton/2200 lb

= 5814.5454545 tons

Hence the water flow rate = 5814.5454545 tons/second

We want the flow rate to be in tons/day

1 ton / second = 86400 tons / day

5814.5454545 tons/second = x tons/ day

Cross Multiply

x = 5814.5454545 tons/second × 86400 tons /day/ 1 ton / second

= 502376727.27 tons/day

= 5.0237672727 × 10^8 tons/day

Approximately ≈ 5.024 × 10^8 tons /day

Therefore, the rate of water flow in tons of water per day is 5.024 × 10^8 tons of water /day

the simplified expression is:

\(1 / ( y^{24} * x^{18 })\)

To simplify the expression:

\(( y^4 / x^{(-3)} )^{(-6)}\)

We can use the property of negative exponents, which states that x^(-n) is equal to \(1 / x^n\).

First, let's apply this property to the denominator:

\(x^{(-3)} = 1 / x^3\)

Now, we can rewrite the expression as:

\(( y^4 / (1 / x^3) )^{(-6)}\)

To simplify further, we can apply the rule of dividing fractions, which states that \((a / b)^n\) is equal to \((a^n / b^n)\):

\(( y^4 * x^3 )^{(-6)}\)

To simplify even more, we can apply the power rule, which states that \((a^m)^n\) is equal to a^(m*n):

\(y^{(4*{(-6)})} * x^{(3*{(-6)})}\)

Simplifying the exponents, we have:

\(y^{(-24)} * x^{(-18)}\)

Finally, using the property of negative exponents, we can rewrite the expression with positive exponents:

\(1 / ( y^{24} * x^{18} )\)

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The result in (a) is not true if we replace "=" with "~."

In deterministic logic, the statement "A implies B" is equivalent to the statement "not B implies not A," known as the contrapositive. In probability, we might interpret "A implies B" as P(B|A) = 1.

Let A and B be any events in a probability space. If P(B|A) = 1, then P(AC|BC) = 1. This is because if P(B|A) = 1, then P(AC|BC) = P(AC∩BC)/P(BC) = P(AC)/P(BC) = 1.

If we replace the "=" with "~" in the statement "P(B|A) = 1," then the result in (a) is not true. For example, let A and B be independent events. Then P(B|A) = P(B) and P(AC|BC) = P(AC). If P(B) is very close to 1, then P(AC) can be very close to 0, even though P(B|A) is very close to 1. This shows that the result in (a) is not true if we replace "=" with "~."

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As a result, 315 pupils attended the school play.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The first equation in the system is given by the total number of attendees:

c + a = 330

The second equation is given by the number of children being 21 times the number of adults:

c = 21a

We can use substitution to find the value of a and then find the value of c. Substituting the second equation into the first equation, we get:

21a + a = 330

Combining the two terms on the left-hand side, we have:

22a = 330

Dividing both sides by 22, we have:

a = 15

So there were 15 adults in attendance at the school play. To find the number of children, we can use the second equation:

c = 21a = 21 * 15 = 315

So there were 315 children in attendance at the school play.

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Answer:

y - 3 = 2/3(x - 5)

Step-by-step explanation:

Formula:

y - y1 = m(x - x1)

It doesn't apply to this problem but keep in mind that two negatives make a positive so instead of writing, for example, y - (-5), you can just write y +5.

Makes it a lot cleaner and easier to work with.

Hope this helps you :)

Answer:

2/8 which simplifies to 0.111111

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

∠ a and 150° are a linear pair and sum to 180° , then

∠ a + 150° = 180° ( subtract 150° from both sides )

∠ a = 30°

the sum of the 3 angles in a triangle = 180° , then

∠ b + ∠ a + 60° = 180° , that is

∠ b + 30° + 60° = 180°

∠ b + 90° = 180° ( subtract 90° from both sides )

∠ b = 90°

The speed of the sports car is 65 miles per hour.

Given that a sports car travels 650 miles in the same length of time a compact car travels 500 miles. If the sports car is traveling 15 miles per hour faster than the compact car, we need to find out the speed of the sports car.

Speed of the compact car can be represented as x miles per hour.Speed of the sports car is 15 miles per hour more than the compact car.

Hence, speed of the sports car can be represented as (x + 15) miles per hour.

Both cars travel for the same length of time, t.We know the formula for speed, distance and time is s = d / tWhere,s is speed, d is distance, and t is time.

The speed of the compact car is x miles per hour and the distance traveled is 500 miles, then the time taken by the compact car is calculated as t = d / s, which is t = 500/x hours.

On the other hand, the speed of the sports car is (x + 15) miles per hour and the distance traveled is 650 miles, then the time taken by the sports car is calculated as t = d / s, which is t = 650/(x + 15) hours.

We can write these two equations as below:500/x = 650/(x + 15)

Cross-multiply to get 500(x + 15) = 650x

Simplifying the above equation gives x = 50

Therefore, the speed of the compact car is 50 miles per hour and the speed of the sports car is (50 + 15) = 65 miles per hour.

:The speed of the sports car is 65 miles per hour.

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Given the function f(x)=sin(2πx), with x = 0.3, f(x) = 0.951057. The objective is to approximate the value of f(0.2) using the first two terms in the Taylor series and Vx=0.1.

We know that the Taylor series for a function f(x) can be written as:f(x)=f(a)+f′(a)(x−a)+f′′(a)2(x−a)2+…+f(n)(a)n!(x−a)n+…The first two terms of the Taylor series are given by:f(x)=f(a)+f′(a)(x−a)The first derivative of f(x) is given by:f′(x)=2πcos(2πx)On substituting x = a = 0.1, we get:f′(0.1) = 2πcos(2π * 0.1) = 5.03118603447The value of f(x) at a=0.1 is given by:f(0.1) = sin(2π * 0.1) = 0.587785252292With a=0.1, the first two terms of the Taylor series become:f(x)=0.587785252292+5.03118603447(x−0.1) = 0.587785252292+0.503118603447x−0.503118603447×0.1Using x=0.2 and substituting the values of a and f(a) in the equation above, we get:f(0.2)=0.587785252292+0.503118603447*0.2−0.503118603447×0.1=0.712261After approximating the value of f(0.2) using the first two terms in the Taylor series,

we can conclude that the value of f(0.2) = 0.712261 with a = 0.1, with an error of approximately 0.012796.

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Answer:

D

Step-by-step explanation:

Teachers favor logo A by a vote of 14 to 11 while students heavily favor logo b with a vote of 86 to 14.

Logo A is more popular with teachers, but logo B is more popular

with students so option (D) will be correct.

A frequency table is a list of objects with the frequency of each item shown in the table.

The quantity of times that an event or value occurs is its frequency.

A frequency table is a table in which we have some data and their frequency.

Given,

Number of students = 100

Out of 100 students 86 preferred logo B.

Number of teachers = 25

Out of 25 teachers, 14 teachers preferred logo A.

Hence Logo A is more popular with teachers, but logo B is more popular with students.

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In order to solve the system of equations, let's equate both values of y and solve for x using the quadratic formula:

Now, let's calculate the values of y for each value of x:

Therefore the solutions are (1, 7) and (5/2, 10).

Correct option: second one.

Answer:

Step-by-step explanation:

Let the two whole numbers be 5x and 2x then

by the question

5x - 2x = 33

3x = 33

x = 33/3

x = 11

Therefore the numbers are

hope it helps:)

The matrix structure combines vertical and horizontal lines of authority, forming a matrix shape in the organization chart.

The matrix structure is a type of organizational structure where both vertical and horizontal lines of authority are present. It involves superimposing product departmentalization on top of functional departmentalization. In this structure, employees are grouped based on their specialized functions, such as marketing, finance, or operations, while also being assigned to specific project teams or product lines.

In a matrix organization, authority flows both vertically and horizontally. Employees report to both a functional manager, who oversees their specialized function, and a project manager or product manager, who is responsible for the specific project or product line they are working on. This creates a dual reporting relationship, as individuals have multiple superiors simultaneously. The matrix structure is often implemented in organizations where there is a need for flexibility, collaboration, and resource sharing across different functions. It allows for efficient coordination and utilization of expertise from different functional areas. However, the matrix structure can also bring challenges such as role confusion, power struggles, and complex communication channels.

Overall, the matrix structure offers a balance between functional specialization and project-focused teamwork, allowing organizations to adapt to dynamic environments and effectively manage complex projects or product lines.

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The percentage of the coin are​ quarter would be 88%.

Since the denominator of percentages is 100, they are effectively fractions. percentage is a relative value that denotes hundredths of any amount. One percent, denoted by the symbol 1%, is equal to one hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified.

In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.

"Out of 100" is what "percentage" means. When describing parts of a whole in mathematics, percentages are employed along with fractions and decimals. The full is divided into one hundred equal portions for the purpose of computing percentages.

To determine, multiply the fraction 44/50 by 100 to convert it to a percentage.

(44/50) × 100 = 88%.

Therefore, the percentage of the coin are​ quarter would be 88%.

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Answer:

\( \huge \boxed{x = 8}\)

Step-by-step explanation:

f(x) = 70 + 11x

To find the value of x when f(x) =158 , equate f(x) to 158

We have

\(70 + 11x = 158 \\ 11x = 158 - 70 \\ 11x = 88\)

Divide both sides by 11

\( \frac{11x}{11} = \frac{88}{11} \\ \)

We have the final answer as

Hope this helps you

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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Answer:

its b

Step-by-step explanation:

just did it on edge

Graph C represents a sequence that converges because the values approach 2.

Convergent definition in mathematics is a property (displayed by certain innumerable series and functions) of approaching a limit more and more explicitly as an argument (variable) of the function increases or decreases or as the number of terms of the series gets increased.

According to the given problem,

Graph 1, Graph 2 and Graph 4 are diverging graphs. We are assuming this because the a divergent sequence doesn't have a limit. Thus, this sequence converges to 0. In many cases, however, a sequence diverges that is, it fails to approach any real number.

Graph 3 has a limit and converges as it approaches 2.

Hence, we can conclude that Graph 3 converges because the values approach 2.

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To find the number with a given z-score, The number with a z-score of -0.8 is approximately 9.8.

\(\( z = \frac{{x - \mu}}{{\sigma}} \)\)

Where:

- \(\( z \)\) is the z-score,

-\(\( x \)\) is the number we want to find,

- \(\( \mu \)\) is the population mean, and

-\(\( \sigma \)\) is the standard deviation.

In this case, we are given:

-\(\( \mu = 13 \)\)

- \(\( \sigma = 4 \)\)

-\(\( z = -0.8 \)\)

Let's substitute these values into the formula and solve for \( x \):

\(\( -0.8 = \frac{{x - 13}}{{4}} \)\)

Multiply both sides by 4 to eliminate the fraction:

\(\( -3.2 = x - 13 \)\)

Add 13 to both sides:

\(\( x = -3.2 + 13 = 9.8 \)\)

Therefore, the number with a z-score of -0.8 is approximately 9.8.

Please note that the provided answer choices are not applicable to this question.

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Answer: variability between means increases relative to the variability within groups

Step-by-step explanation:

The formula to calculate F-ratio : variance between groups divided by variance within groups

Here, F-ratio \(\propto\) is proportional to variance between groups but inversely proportional to variance within groups .

So, F-ratio increases when variability between means increases relative to the variability within groups.