What is partial sum limit?.

Work done when a 100 lb rock is lifted to height of 3 ft is 9652.215 ft-lb.

What is meant by work done?

The work done on an object is equal to the force applied to it multiplied by the distance over which the force is applied. In this case, the force applied is the weight of the rock, which is equal to the force of gravity acting on it.

The weight of an object is given by the formula:

W = mg

Where m is the mass of the object (in this case, 100 lb) and g is the acceleration due to gravity (approximately 9.8 m/s^2 or 32.17405 ft/s^2).

So the weight of the rock is:

W = (100 lb)(32.17405 ft/s^2) = 3,217.405 ft-lb

The work done on the rock is equal to the force applied (its weight) multiplied by the distance it is lifted (3 ft), so the work done is:

Work = (3,217.405 ft-lb) x (3 ft) = 9652.215 ft-lb

Therefore, the work done when a 100 lb rock is lifted to a height of 3 ft is 9652.215 ft-lb.

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The numerical value of the slope and its meaning include the following: C. 312; velocity increases at rate of 312 kilometers per minute as the time increases.

Mathematically, the slope-intercept form of a line can be modeled by using this equation:

y = mx + c

Where:

Based on the information provided above, a function which represents the speed of a spaceship that is been launched from the station is given by:

v(t) = 5,924 + 312t

where:

By comparison, we can logically deduce that the slope is equal to 312 and it represents the rate of change of velocity with respect to time.

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The distributive property states that for any real numbers a, b and c, the following is true:

a(b + c) = ab + ac

To use the distributive property to write an expression that is equivalent to 6 - 9x, we can factor out the -9x from the second term:

6 - 9x = 6 - 9x + 0 - 0x = 6 - 9x + (-9x) = 6 + (-9x)

Therefore, using the distributive property, we can write an expression that is equivalent to 6 - 9x as:

6 + (-9x)

Answer:

-3 ( 3x - 2 )

Step-by-step explanation:

- 9x + 6

Using algebraic expressions, cost before finance charges is $2019.63 and $1669.63.

Algebraic Expressions: Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can be solved using algebraic expressions. Monomial, binomial, and polynomial expressions are the three different categories of algebraic expressions. Additionally, Boolean algebra is essential to algebraic expressions.

In the basics of algebraic expressions, the letters x, y, and z stand in for an unknown value. Variables are the names given to these letters. Both variables and constants can be present in an algebraic expression. They combine to create the algebraic expression.

Let x = cost of desktop computer;

then x - 350 = cost of laptop computer

converting % to decimals, 7% = 0.07 and 9.5% = 0.095

Then, 0.07x + (x - 350)0.095 = $305

0.07x + 0.095x - 33.24 = $300

0.165x = $333.24

x = $2019.63

then x - 350 = $1669.63

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Answer:

If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.

But if you multiply or divide both sides of an inequality by a negative number, the inequality is no longer true.

Step-by-step explanation:

Answer:

The multiplication property of inequality states that if one side of the inequality is multiplied or divided by a positive number, we can multiply and divide the other side of the inequality by the same number without changing or disturbing the direction sign of the inequality.

Step-by-step explanation:

The corresponding point on the unit circle for the angle θ = 5pi/3  is given by: (0,5, -0.866).

What is the unit circle?

Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.

What is area of circle ?

The area of circle can be defined as the product of pi and square of radius of a given circle.

In this problem, we have that θ = 5pi/3 , hence:

cos θ = 0.5

sin θ = -0.866

Thus the point is (0,5, -0.866).

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From the given angles of the triangle, it was possible to find the angle x=29°.

Triangles are geometric figures with three (3) sides. They present different classifications regarding their sides or angles.

Like a classification for angles, it is possible to cite, a right triangle. A triangle is classified as a right triangle when it presents one of your angles equal to 90º.

For another side, an equilateral triangle whose classification is associated with the sides. An equilateral triangle presents the three  equal sides.

Regardless of its classification, the sum of the a triangle's angles will always be 180°.

The question gives two angles: 50° and 101°. And, it asks the value of angle x.

Therefore,

50+101+x=180

x+151=180

x=180-151

x=29°

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The solution of the expression is 216(cd)³.

The mathematical expression combines 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 denote the logical syntax's operation order and other properties.

Given that the exponential expression is (6cd⁻¹)⁻³. The expression will be simplified as below,

E = (6cd⁻¹)⁻³.

Use the property of the exponents to multiply the powers and now solve.

E= (6cd³)

E = 6³ x (cd³)

E = 216(cd³)

Therefore, the simplified value of the expression is 216(cd)³.

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The number 3 is a special number that carries a lot of meaning in various cultures and religions.

Number is a mathematical concept that is used to count, measure, or label. It is used to quantify or quantify objects, events, or ideas. In mathematics, numbers can be classified as either rational or irrational. Rational numbers include integers, fractions, and decimals, while irrational numbers include pi and square root. Numbers are also used to represent data and can be used to represent a variety of objects and concepts including digits, dates, and time.

It is often seen as the number of unity and harmony, as it is comprised of three individual parts. In Christianity, the number 3 is associated with the Holy Trinity. In Hinduism, Buddha, and other Eastern religions, the number 3 is associated with the three qualities: action, knowledge, and devotion.

In mathematics, 3 is a prime number, meaning that it cannot be divided by any other number except itself and 1. It is also an odd number, and the third number in the Fibonacci sequence.

The number 3 is a powerful number and is often associated with creativity and luck. It is also seen as a number of growth and expansion. In literature, 3 is often used as a symbol of completeness and wholeness.

The number 3 is also associated with balance and harmony. It is seen as the number of perfection and balance between opposites. It is seen as the number of the divine and is often used in spiritual practices.

The number 3 is often used in art and design. Its three distinct parts make it a perfect number for creating a pleasing and attractive composition.

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The number 3 is a special number that carries a lot of meaning in various cultures and religions.

Number is a mathematical concept that is used to count, measure, or label. It is used to quantify or quantify objects, events, or ideas. In mathematics, numbers can be classified as either rational or irrational. Rational numbers include integers, fractions, and decimals, while irrational numbers include pi and square root. Numbers are also used to represent data and can be used to represent a variety of objects and concepts including digits, dates, and time.

It is often seen as the number of unity and harmony, as it is comprised of three individual parts. In Christianity, the number 3 is associated with the Holy Trinity. In Hinduism, Buddha, and other Eastern religions, the number 3 is associated with the three qualities: action, knowledge, and devotion.

In mathematics, 3 is a prime number, meaning that it cannot be divided by any other number except itself and 1. It is also an odd number, and the third number in the Fibonacci sequence.

The number 3 is a powerful number and is often associated with creativity and luck. It is also seen as a number of growth and expansion. In literature, 3 is often used as a symbol of completeness and wholeness.

The number 3 is also associated with balance and harmony. It is seen as the number of perfection and balance between opposites. It is seen as the number of the divine and is often used in spiritual practices.

The number 3 is often used in art and design. Its three distinct parts make it a perfect number for creating a pleasing and attractive composition.

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The complete question is-

Please explain there are 9 thirds in in 3 ones​.

The value of x from the given figure is 16 units.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given figure,

Using Pythagoras theorem to ΔBDC

Now, BC²=8²+4²

BC=√80

In ΔABD,

AB²=BD²+AD²

AB²=8²+x² ------(I)

In ΔABC

AC²=AB²+BC²

(x+4)²=AB²+80

AB²=(x+4)²-80 ------(II)

From equation (I) and (II), we have

64+x²=x²+8x+16-80

8x=128

x=16

Therefore, the value of x from the given figure is 16 units.

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Answer:

129,156

Step-by-step explanation:

The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.

The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is not a special type of triangle. It is a general right triangle because it has one right angle (90 degrees) and two acute angles (29 degrees and 61 degrees).

This triangle is not a 30-60-90 triangle because it does not have the specific angle measurements of 30-60-90 degrees. Similarly, it's not a 45-45-90 triangle because the angles don't match the specific angles of 45-45-90 degrees. There are no specific ratios between the sides of this triangle.

In general, right triangles are triangles that have one right angle (90 degrees), and the other two angles can take any value between 0 and 90 degrees. The sides of a right triangle have a relationship known as the Pythagorean Theorem. This theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Therefore, In short, the triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.

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1. 288 tons of oats can be stored in the silo.

2. 432 tons of barley can be stored in the silo.

3. 540 tons of wheat can be stored in the silo.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A storage silo for grain can house 18,000 bushels of grain.

1. One bushel of oats weighs 32 pounds which is equal to 32/2000 tons.

= 0.016 tons.

Therefore, The number of tons of oats that can be stored is,

= 0.016×18000.

= 288 tons.

2. One bushel of barley weighs 48 pounds or 48/2000 = 0.024 tons.

Therefore, The number of tons of barley that can be stored is,

= 0.024×18000.

= 432 tons.

3. One bushel of wheat weighs 60 pounds or 60/2000 tons = 0.03 tons.

Therefore, The number of tons of wheat that can be stored is,

= 0.03×18000.

= 540 tons.

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Answer:

7.3

Step-by-step explanation:

The equation for Garage A can be expressed as A = 12 + 4t, and the equation for Garage B as B = 7 + 5t.

A = 12 + 4t

B = 7 + 5t

12 + 4t = 7 + 5t

4t - 5t = 7 - 12

-t = -5

t = 5 hours

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Answer:

-----------------------------

Let the first term be a.

The common ratio is r = 2 and the sum of the first 6 terms is S₆ = 7.

Use the sum of first n terms formula:

Substitute and solve for a:

If 10 people share 3 brownies equally, each person will get the same amount. To find out how much each person will get, you can divide the total number of brownies by the number of people.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

3 brownies / 10 people = 0.3 brownies per person

So, each person will get 0.3 of a brownie. Since a brownie is a solid object, it is not possible for each person to get 0.3 of a brownie, It would be best to cut the brownies into 10 equal pieces.

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The graph of the equation 4x+6y=48 is given below.

And the intercepts are (0, 8) and (12, 0).

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given:

A football team has an away game, and the bus breaks down.

The coaches decide to drive the players to the game in cars and vans.

Four players can ride in each car.

Six players can ride in each van.

There are 48 players on the team.

The equation 4x+6y=48 models this situation, where x is the number of cars and y is the number of vans.

And the graph with in intercepts is given in the attached image.

Therefore, (0, 8) and (12, 0) are the intercepts.

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The complete question:

A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation 4x+6y=48 models this situation, where x is the number of cars and y is the number of vans.

Graph the equation.

Interpret the intercepts.

There are several ways to find the length of the third side of an acute triangle, depending on the information given about the triangle and the sides. Some common methods include:

Using the Pythagorean theorem: If you have a right triangle, you can use the Pythagorean theorem to find the length of the third side. The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the Law of Cosines: If you know the lengths of two sides and the measure of the angle between them, you can use the law of cosines to find the length of the third side.

Using the Law of Sines: If you know the lengths of two sides and the measure of the angle opposite one of them, you can use the law of sines to find the length of the third side.

It's important to note that you need to know at least 2 sides and an angle or the side opposite to the right angle (if the triangle is a right triangle) in order to find the length of the third side.

Answer:

the answer to get x = 116 and y=54

Step-by-step explanation:

Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 2) ← 2 ordered pairs from the table

m = [tex]\frac{2-(-1)}{3-0}[/tex] = [tex]\frac{2+1}{3}[/tex] = [tex]\frac{3}{3}[/tex] = 1

No, these statements are not needed to prove that ABCD is a parallelogram.

A parallelogram is a type of four-sided geometric shape with two pairs of opposite sides that are parallel. Each side of the parallelogram is a line segment, and all four of the interior angles are equal. The opposite sides of a parallelogram are also equal in length. Parallelograms can be found in a variety of applications, including engineering, architecture, and other fields. The most common types of parallelograms are squares, rectangles, and rhombuses.

A parallelogram is defined as a four-sided shape with opposite sides that are equal in length and with opposite angles that are equal in measure.
To prove that ABCD is a parallelogram, it is necessary to show that two of its sides are parallel and that its opposite sides are equal in length.
The statements provided do not show any of these properties, and so are not needed to prove that ABCD is a parallelogram.

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To depict the curve, we will make use of the idea of slope and intercept in linear equations.

A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.

When y = 2x - 4 is put into comparison with the generic form, we get

The curve has a slope of 2 and a y-intercept of -4.

To assist us plot the graph, let's take two points along the line y = 2x – 4.

The line y = 2x - 4 passes through since its y-intercept is equal to -4. (0, -4)

In the formula y = 2x - 4, replace y with 0.

0 = 2x - 4

2x = 4

x = 2

the line therefore goes through (2, 0).

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Full Question = Which graph represents the function y = 2x - 4?

In the expression (ax⁶)^(1/n) = 7x³ the values of a and n are

The expression (ax⁶)^(1/n) = 7x³is simplified as follows

Information from the problem

(ax⁶)^(1/n) = 7x³

to make x⁶ to be equal to x³ we use the powers

6 * y = 3

y = 1/2

hence n = 2

substituting n = 2 and solving

(ax⁶)^(1/2) = 7x³

√(a) x³ = 7x³

dividing both sides by x³

√a = 7

squaring both sides of the equation wil result to

√a = 7

(√a)² = 7²

a = 7²

a= 49

We can therefore say that a = 49 and n = 2

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A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A data set must (when graphed) follow a bell-shaped, symmetrical curve that is centered around the mean in order to be regarded as having a normal distribution. Additionally, it must follow the empirical rule that shows the proportion of the data set that lies within (plus or minus) 1, 2, and 3 standard deviations of the mean.

Using the inverse standard normal calculator, we can determine the height at which 70% of 5-year-olds are below it, yielding a z-score of 0.84162. Using the formula x = mean + (z-score * standard deviation), this z-score can be used to determine the corresponding x value, which in this case would be

36 + (0.84162*10) = 42.4 inches.

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We were able to recognize the following two sentences because parallelism involves the repetition of grammatical structures in a sentence or text.

Today, 25 years ago, America underwent a change of heart and a change of direction.

She is currently working on a project to find low-cost strategies to minimize pollution and share them with smaller businesses with businesses situated near three Ohio rivers.

Describe parallelism.

The repetition of the same grammatical structure is known as parallelism. It can be used as a rhetorical device or just as a method of disseminating data more effectively. In a text, parallelism helps prevent ambiguity and confusion.

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Answer:

C) 1/2

Step-by-step explanation:

We know that 3/8 cup of brown sugar and 1/3 cup of white sugar are mixed together to make the sugar mixture.

From this sugar mixture, 1/4 cup is set aside for the crumb topping.

To find out how much sugar mixture is used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.

We can start by converting the mixed unit of measurement (brown sugar in cups and white sugar in cups) to a single unit of measurement (cups)

3/8 cup of brown sugar + 1/3 cup of white sugar = (3/8)+(1/3) = 5/12 cup + 4/12 cup = 9/12 cup.

1/4 cup is set aside for the crumb topping.

So, the remaining sugar mixture used to make the cake is 9/12 cup - 1/4 cup = (9/12) - (1/4) = (9-3)/12 = 6/12 cup = 0.5 cup

Answer:

Step-by-step explanation:

b:c= 3:6

Answer:

Step-by-step explanation:

We know that:
a : b = 1 : 2 (or a = (1/b)*b)
b : c = 3 : 4 (or b = (3/4)*c)

So, we can substitute the value of b from the second equation into the first equation to get the ratio of a : c:

a = (1/b)*b = (1/((3/4)c))((3/4)c) = (4/3)(1/c)*c = (4/3)*1 = 4/3

So, the ratio of a : c is 4 : 3.

Alternatively, we can use the cross-multiplication method to find the ratio.

a : b = 1 : 2, and b : c = 3 : 4

so a4 = b3, and b4 = c3

so a4 = c3

so a:c = 3:4

In this way also we got the ratio of a:c as 3:4

The inverse of the expression +9 is -9.

Expression in math is defined as  any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

Here we have the expression +9 and we need to find the inverse for it.

As we all know that the term inverse in math is known as a function or operation which reverses the order or operation of another function or operation

Based on the definition, the given expression is written as,

=> +9

Now, the inverse of the expression is written as in the negative form such that,

=> -9

Therefore, the resulting value is -9.

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