A new dam being built has the shape of a trapezoid.
The length of the base at the bottom of the dam is 2 times the height.
The length of the base at the top of the dam is 1/5 times the height
minus 30 feet.

a. Write an expression to find the area of the trapezoidal cross
section of the dam.

b. If the height of the dam is 180 feet, find the area
of this cross section.

Answer: 18x+24

Step-by-step explanation:

Parallel lines are lines that are always the same distance apart and will never intersect. Intersecting lines are lines that cross or meet at a point. Perpendicular lines are lines that intersect at a right angle (90 degrees).

To determine if lines are parallel, you can look at their slopes. If two lines have the same slope, they are parallel. For example, the lines y = 2x + 3 and y = 2x - 5 are parallel because they both have a slope of 2.

To determine if lines are intersecting, you can look at their slopes and y-intercepts. If two lines have different slopes, they will intersect at some point. For example, the lines y = 2x + 3 and y = -x + 7 are intersecting because they have different slopes (2 and -1, respectively).

To determine if lines are perpendicular, you can look at their slopes. If the product of the slopes of two lines is -1, they are perpendicular. For example, the lines y = 2x + 3 and y = -0.5x + 7 are perpendicular because the product of their slopes (2 and -0.5) is -1.

I hope this helps! Let me know if you have any further questions.

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The number of the ways to seat the jury members around a circular table for deliberations are 5040.

A permutation is a word that describes the number of ways things can be ordered or arranged.

Given that, we need to find that how many ways are there to seat the jury members around a circular table for deliberations,

We know that,

There are (n-1)! ways to seat n people at a circular table,

Since, there are no number of people is given, let us assume that there are 8 members,

Therefore,

The number of ways to seat the jury members around a table =

(8-1)! = 7!

= 5040

Hence, the number of the ways to seat the jury members around a circular table for deliberations are 5040.

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The value of 12.5 kg into lbs can be converted by multiplying kilogram by 2.204622  so the answer is 27.55 pounds.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

Pounds = kilograms × 2.20462262184878

= 12.5 x 2.20462262184878

= 27.55 pounds or lbs.

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The range of the number of miles Maria jogged is 1 to 7.99

C. 1 to 7.99

What is the histogram?

A histogram is a graph used to represent the frequency distribution of a few data Set of one variable.

Let's recall that for calculating the range of a data set, we have to find out the lowest and the highest values of the data set.

As we can see in the graph below, the lowest value in the histogram is 1 and the highest is 7.99, therefore the correct answer is:

Hence, the range of the number of miles Maria jogged is 1 to 7.99

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Answer:

It would be zero

Step-by-step explanation:

The length of the shadow casted by the building is 31.06 meters. The solution has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is a discipline of mathematics that deals with the study of sides, angles, and relationships in triangles.

We are given that at a certain time of day, the angle of elevation of the sun is 44 degrees. The height of the building is given as 30 meters.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan 44° = 30/x

⇒0.9657 = 30/x

⇒x = 31.06

Hence, the length of the shadow casted by the building is 31.06 meters.

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1800

200 is the hundreds place value
2000 is the value to its left
2000-200 is 1800

False. The Six Sigma DMAIC approach is best suited for number of problems and issues that require a systematic approach and have measurable results. It should not be employed for all problems as some may require a different approach.

The Six Sigma DMAIC (Define, Measure, Analyze, Improve, Control) approach is a systematic process that is used to identify and eliminate defects in processes, products, or services. This approach is best suited for problems and issues that have a structured approach, measurable results, and an opportunity for improvement. However, it should not be employed for all problems as some may require a different approach such as root-cause analysis or process mapping. Additionally, some number of problems may require creative solutions that cannot be addressed using the DMAIC approach. In these cases, alternative approaches such as brainstorming or design thinking should be employed.

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The percentages of executives receiving bonuses are given as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for the percentage of executives receiving bonuses in t years after 1998 is given as follows:

B(t) = 4.816(1.338)^t.

2002 is 2002 - 1998 = 4 years after 1998, hence the percentage is given as follows:

B(4) = 4.816(1.338)^4 = 15.44%.

The percentage for 2003 is then given as follows:

B(5) = 4.816(1.338)^5 = 20.65%.

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The formula for calculating the z-score is z = (x-μ)/σ.

where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula suggests, the Z-score is simply the raw score minus the population mean divided by the population standard deviation.

A positive Z-score indicates that the raw score is higher than the average. For example, a z-score of +1 is one standard deviation above the mean.

A negative z-score indicates that the raw score is below average. For example, a Z-score of -2 is two standard deviations below the mean.

Another way to interpret z-scores is to create a standard normal distribution (also known as the z-score distribution or probability distribution).

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The closure of set a) includes the boundary, unit circle, and origin; the closure of set b) includes the boundary, line segments, origin, and closed disk; the closure of set c) includes the boundary and origin; the closure of set d) includes the boundary, imaginary axis, origin, and closed half-plane to the right of the imaginary axis.

a) The closure of the set {-pi < arg(z) < pi, z ≠ 0} includes all points on the boundary of this region. This boundary consists of the real axis (where arg(z) = 0), the imaginary axis (where arg(z) = ±pi/2), and the unit circle centered at the origin (where |z| = 1). The closure of the set also includes the point at the origin, since this is a limit point of the set.

b) The closure of the set {|Re(z)| < |z| ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the unit circle centered at the origin (where |z| = 1/2) and the line segments connecting this circle to the x-axis (where |z| = |Re(z)|). The closure of the set also includes the origin and the points on the closed disk centered at the origin with radius 1/2.

c) The closure of the set {Re(1/z) ≤ 1/2} includes all points on the boundary of this region. This boundary consists of the line Re(z) = 1/2 (where the imaginary part of z can take on any value) and the point at the origin, since this is a limit point of the set.

d) The closure of the set {Re(z^2) > 0} includes all points on the boundary of this region. This boundary consists of the imaginary axis (where Re(z^2) = 0) and the rays emanating from the origin at angles ±π/4 (where Re(z^2) is positive). The closure of the set also includes the origin and the points on the closed half-plane to the right of the imaginary axis.

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The area of the shaded region that is the segment of the circle is equal to 4.6 ft² to the nearest tenth.

To calculate the area of a segment of a circle, you need to know the radius of the circle, the central angle of the segment (in radians or degrees), and possibly the height of the segment (the distance from the chord of the segment to the center of the circle).

The formula for the area of a segment of a circle is:

A = θ/360° × πr² - 1/2 × r² × sinθ

where A is the area of the segment, r is the radius of the circle, and θ is the central angle of the segment in degrees.

From the question;

the central angle = 90°

radius r = 4ft

Area of the segment = 90°/360° × π4² - 1/2 × 4² × sin90°

Area of the segment = 1/4 × π × 4 × 4 - 1/2 × 4 × 4 × 1 {sin90° = 1}

Area of the segment = 4π × 8

Area of the segment = 4.5714

Therefore, the exact area of the shaded region that is the segment of the circle is equal to 4.6 ft² to the nearest tenth

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A partial fraction calculator is a tool used to decompose a rational function into simpler fractions, known as partial fractions.

A partial fraction calculator is a tool used to decompose a rational function into simpler fractions. It is commonly used in algebra and calculus to simplify complex expressions and solve equations. The partial fraction calculator takes a rational function as input and breaks it down into simpler fractions that can be more easily integrated or manipulated. This process involves finding the partial fraction decomposition of the rational function by factoring the denominator into linear and quadratic factors and then solving for the coefficients of the partial fractions. This calculator can be useful for students, engineers, and anyone working with complex algebraic expressions.

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The answer is A: x = 22√3 / 2 and y = 11. We can simplify x by multiplying both the numerator and denominator by 2 to get x = 22√3.

A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed where the two shorter sides of the triangle meet. The side opposite to the right angle is called the hypotenuse, while the other two sides are called the legs.

The Pythagorean theorem is a fundamental relationship that applies to right-angle triangles. It states that the sum of the squares of the two shorter sides (legs) of a right-angle triangle is equal to the square of the hypotenuse. In other words, a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right-angle triangles are commonly used in mathematics, physics, engineering, and many other fields. They can be used to solve problems related to distances, heights, and angles, and are a fundamental building block in many geometric constructions.

The special properties of right-angle triangles also make them useful in practical applications, such as in construction, where they can be used to measure angles and distances accurately, and in navigation, where they can be used to calculate distances between two points using trigonometric functions.

In triangle ABC, we know that angle BAC is 30 degrees, and angle ABC is a right angle. Therefore, angle ACB is 60 degrees (since the angles in a triangle add up to 180 degrees).

We can use the sine and cosine ratios to find the values of x and y. Using the definition of sine and cosine:

sin(30) = opposite / hypotenuse

cos(30) = adjacent / hypotenuse

In this case, AB is the adjacent side to angle BAC, and AC is the hypotenuse. Therefore:

cos(30) = AB / AC

Substituting the given values, we get:

cos(30) = x / y

Solving for x, we get:

x = y cos(30)

Plugging in y = 11, we get:

x = 11 cos(30)

Using a calculator, we can find that cos(30) = √3 / 2, so:

x = 11 × √3 / 2

x = 11√3 / 2

Therefore, the answer is A: x = 22√3 / 2 and y = 11. We can simplify x by multiplying both the numerator and denominator by 2 to get x = 22√3.

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11/21 as a decimal rounded to the nearest tenth is 0.5. Below, you will learn how to solve the problem.

To convert the fraction 11/21 to a decimal rounded to the nearest tenth, we can follow these steps:

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The approach used to test if the function is even or odd is as follows: if it is an even function, it will be symmetrical around the y-axis: f(x)=f (-x). Odd functions are also symmetric about the x- and y-axes: f(x)=-f (-x).

When its input is changed to its negative, the output of an even function remains intact.

An odd function is one whose output changes sign when its parameter is made negative.

We may plot a function and examine its graph to determine if it is even or odd. The function is an even function if the graph is symmetrical around the origin (x=0, y=0). The function is an odd function if the graph is symmetrical around the y-axis (x=0).

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The bucket of fish are the sea otters fed each day is 2 buckets or 3/2 bucket(in fractions).

What is fraction?
A fraction is a mathematical expression that represents a part of a whole. It is written as a number (the numerator) over another number (the denominator), separated by a horizontal line. The denominator indicates the number of equal parts into which the whole is divided, while the numerator indicates how many of those parts are being considered.

Explanation:

The sea otters are fed 1/4 as much fish as the dolphins, which means they are fed:

(1/4) x 6 = 6/4 = 3/2 buckets of fish each day.

However, we cannot have half a bucket of fish, so we need to round this up to the nearest whole number. Therefore, the sea otters are fed:

2 buckets of fish each day.

So the answer is: 2 buckets.

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Therefore, the solutions to the simultaneous equation are (x, y) = ((5 + √(21))/2, (5 - √(21))/2) and (x, y) = ((5 - √(21))/2, (5 + √(21))/2).

To solve the simultaneous equation 1÷x + 1÷y = 5, 1÷y - 1÷x = 1, we can use the substitution method. Here are the steps to solve the equation:
1. Rearrange the first equation to get 1÷y = 5 - 1÷x
2. Substitute this into the second equation to get 1÷(5 - 1÷x) - 1÷x = 1
3. Multiply both sides by x(5 - 1÷x) to get x - (5 - 1÷x) = x(5 - 1÷x)
4. Simplify and rearrange to get x² - 5x + 1 = 0
5. Use the quadratic formula to solve for x: x = (-(-5) ± √((-5)² - 4(1)(1)))÷(2(1)) = (5 ± √(21))/2
6. Substitute the values of x back into the first equation to find the corresponding values of y: y = 1÷(5 - 1÷((5 + √(21))/2)) = (5 - √(21))/2 and y = 1÷(5 - 1÷((5 - √(21))/2)) = (5 + √(21))/2

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In the United States, a bushel is legally defined as 2,150.42 cubic inches or approximately 35.24 liters. The weight of a bushel depends on the density of the item being measured.

For example, a bushel of wheat weighs approximately 60 pounds, a bushel of soybeans weighs approximately 60 pounds, and a bushel of apples weighs approximately 42 pounds.

A bushel is a unit of measurement used to quantify dry goods such as grains, fruits, and vegetables. The exact weight of a bushel can differ depending on the item being measured.

It is worth noting that the bushel is not a universal measurement, and other countries may use various standards for measuring dry goods.

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Answer:

Area is approximately 113.1

So the answer is: the first arc should pass through point B (not A). All other elements in the diagram appear to be correct.

The elements or members of a set are the parts that make it up. To divide the components of a set, commas and two curly (idle) braces are typically employed. Capital letters are always used to print the set's name. The set "A" in this context consists of the letters v, w, x, y, and z.

Based on the given diagram and instructions, it appears that the error in the construction is that the first arc is centered at point C instead of point A. The correct procedure for constructing a line parallel to line AB and passing through point P is as follows:

1.Draw a line AB and mark point P not on line AB.

2.From point P, draw an arc that intersects line AB at points D and E.

3.Draw another arc, centered at point D, with the same radius as the first arc. This arc should intersect the first arc at point F.

4.Draw a line through point P and point F. This line is parallel to line AB and passes through point P.

So the answer is: the first arc should pass through point B (not A). All other elements in the diagram appear to be correct.

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The third arc should be drawn centred at F.

What is an arc?

In geometry, an arc is a curved segment of a circle or any curved line. It is a part of a curve that is bounded by two distinct endpoints and is characterized by its length, its curvature, and its central angle.

Constructing a parallel line to line AB and passing through point P.

To find:

The error occurred in the construction.

The procedure is,

The first arc must be drawn centred at C.

The second must be drawn centred at P.

Finally, the third arc must be drawn centred at F.

But here, the third arc is drawn centred at D. This is wrong.

The correct step is that the third arc must be centred at F.

Hence, The third arc should be drawn centred at F.

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Answer:

Step-by-step explanation:

Answer:

so the bike is 7. car is 8 walk is 9 bus is 12 so in total it will be 36 pupils to travel to school

From the given information provided, the approximate volume of the cone is 94.24777 cubic inches.

The volume of a cone can be calculated using the formula V = (1/3) × π × r² × h, where "r" is the radius of the base of the cone, "h" is the height of the cone, and "π" is the mathematical constant approximately equal to 3.14159.

Radius r= 3 inches

Height h= 10 inches

π = 3.14159

Using the formula for the volume of a cone, V = (1/3) × π × r² × h, we can substitute the given values to calculate the volume of the cone:

V = (1/3) × 3.14159 × 3² × 10

V ≈ 94.24777 cubic inches

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Answer:

Step-by-step explanation:

To find what the ratio would be, we need to know what to multiply 5 & 3 by so that when we add them, we get 80. Let's assume the number we multiply by is x:

5x + 3x = 80

8x = 80

x = 80 / 8

x = 10

Now, we multiply 5 by 10 and 3 by 10

= 50:30

Your ratio would be 50:30

Double check: 50 + 30 = 80

The method to convert milimeter to kilometre will be the formula - quantity in milimeter divided by 10⁶.

We know that mm represents milimeter and km represents kilometres. Now, relating the two quantities as follows -

1 kilometre is equal to 10⁶ milimeter

So, converting milimeter to kilometres using the above mentioned relation.

10⁶ milimeter is 1 kilometre

So, 1 milimeter in kilometre will be = 1/10⁶ kilometres

Now, convert the 5000 milimeter to kilometres for practice.

So, the formula will be -

Distance from milimeter to kilometre = 1/10⁶ kilometres

The required distance is = 5000 /10⁶

Performing division on Right Hand Side of the equation

The required distance = 0.005 kilometres

Hence, 5000 milimeter will be 0.005 kilometre.

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The number 713.49 is already written in standard form.

Standard form, also known as standard notation or scientific notation, is a way of writing numbers using digits and decimal places. In standard form, a number is written with one digit to the left of the decimal point and the remaining digits to the right of the decimal point.

For example, the number 7,134.9 would be written in standard form as 7,134.9. The number 713.49 is already written in this format, so there is no need to convert it to standard form.

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To become a forensic pathologist, you must first complete an undergraduate degree in medicine, biology, chemistry, or a similar discipline, with electives in forensic science, psychology, or a related field.

what is a forensic pathologist?

The forensic pathologist is a pathologist who specialises in the examination of people who die suddenly, unexpectedly, or brutally. A forensic pathologist specialises in establishing the cause and manner of death.

Autopsies are performed to determine the presence or absence of disease, injury, or poisoning; to evaluate historical and law-enforcement investigative information pertaining to determine the cause of death; to gather medical evidence, such as trace evidence and secretions; to document sexual assault; and to recreate how a person was injured.

Now,

To become a forensic pathologist, you must first complete an undergraduate degree in medicine, biology, chemistry, or a similar discipline, with electives in forensic science, psychology, or a related field.

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45 is 5 times as many as 9 and is 9 times as many as 5.

We have the following statement -

45 is x times as many as 9 and is y times as many as 5

We have to find x and y.

A number 'n' is 'a' times as many as 'b'. Then n equals to ?

n will be equal to -

n = ab

According to the question -

45 is x times as many as 9 and is y times as many as 5. Using the method shown above we can write two equations -

45 =  x 9     ---(1)

and

45 = y x 5     ---(2)

Now -

Solving both, we get -

x = 5 and y = 9

Hence, 45 is 5 times as many as 9 and is 9 times as many as 5.

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