Is Paul's Online Math Notes a good enough source for self-teaching calculus 3 and ODE?

3/5 = 0,6, it is 0.6 × 100 = 60%

Therefore, 3/5 is expressed as 60% in terms of percentage.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.

According to the Question:

To convert a fraction to a decimal, it's always best to look at the denominator first. If the denominator only has prime factors of 2 and 5, you can easily pick a number multiplied by the denominator and convert it to a denominator that is a power of 10, and the result is the final prime number. If you have prime factors other than 2 and 5, converting to decimal takes longer and can result in infinite but repeating decimals.

In this case, the denominator is 5, so you can easily convert to decimal by multiplying the denominator and numerator by 2.

(3 × 20) / (5 × 20) = 60/100

Now,

To convert a fraction to a percentage, simply multiply by 100 and put a % sign next to the result.

As 3/5 = 0,6, it is 0.6 × 100 = 60%

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The standard deviation lies in the range of 0 to 1. The numerical value of standard deviation can never be negative.

The standard deviation is a measure of amount of variation or dispersion of a set of values. When we compare two unequal observations, the result is always greater than zero i.e., always positive.

Standard deviation is the square root of the variance of the observations and the root always gives values either positive or zero, it can never be negative.

Therefore, the numerical value of the standard deviation can be positive. The value of standard deviation is always greater or equal to zero.

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Answer:

10 packs

Step-by-step explanation:

Allie wants to give each of her classmates 3 pencils, so she needs a total of 3 pencils * 26 classmates = 78 pencils.

The pencils come in packs of 8, so she needs 78 pencils / 8 pencils per pack = 9.75 packs of pencils.

Since you can't buy a fraction of a pack, Allie needs to buy 10 packs of pencils.

Answer:

If the cost price (CP) is 380 and the gain percentage is 25%, we can use the following formula to find the selling price (SP):

SP = CP + (gain percentage/100) * CP

Substituting the given values, we get:

SP = 380 + (25/100) * 380

SP = 380 + 95

SP = 475

Therefore, the selling price is 475.

Step-by-step explanation:

The value of f(3/4) is 5/4.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a function.

f(x) = 2x - 1/4

We have to find the value of the function when the input value x = 3/4.

For that, substitute 3/4 in place of x.

f(3/4) = (2 × 3/4) - 1/4

         = 6/4 - 1/4

         = 5/4

Hence the value of the function is 5/4.

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Answer:

622.03

Step-by-step explanation:

A rigid motion maps each part of a figure to an Rotation.

What is rotation ?

In physics, rotation refers to the movement of an object around an axis or a fixed point. When an object rotates, every point on the object moves in a circle around the axis of rotation, and the object typically completes one full rotation or revolution after it has moved a full 360 degrees around the axis.

The study of rotation in physics is important in many fields, including mechanics, electromagnetism, and quantum mechanics. Rotational motion is characterized by several key parameters, including the angle of rotation, the angular velocity (how fast the object is rotating), and the angular acceleration (how quickly the angular velocity is changing).

In addition, rotational motion is subject to a number of physical laws and principles, such as Newton's laws of motion, which describe the relationship between the forces acting on a rotating object and its resulting motion. Other principles, such as the conservation of angular momentum, relate to the conservation of the rotational energy of a system as it undergoes rotational motion.

Therefore, a rigid motion maps each part of a figure to an Rotation.

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The length of the rectangular prism is 20.35

The diagonal of the base is calculated using Pythagoras theorem. This is a side that will use to find the length of the box.

The diagonal A - B given as 2 feet = 24 inches is the hypotenuse while solving for the length of the prism

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 9² + 9²

x² = 81 + 81

x = √162

x = 12.728

The length of the rectangular prism is solved as follows

let y be the required distance

24² = y² + 12.728²

y² = 24² - 12.728²

y = √413.998

y = 20.35 in

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The value of the expression is -8. Option A

It is important to note that algebraic expressions are expressions that are made up of variables, terms, coefficients, constant and factors.

From the information given, we have that;

3x-6= 5x - 2

collect like terms

3x - 5x = -2 +6

subtract the like terms

-2x = 4

Make 'x' subject

x = -2

Substitute the value in the equation

2x - 4

2(-2) - 4

expand bracket

-8

Hence, the value is -8

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The horizontal distance between Ryan and the dolphin is  57.87 feet.

The airplane is 10735.96 feet away from the control tower

The angle of depression from the top of the lighthouse to the boat is 0 degrees.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Using trigonometry, we can find the horizontal distance x:

tan(15) = x / 228

x = 228 tan(15)

x = 57.87 feet

Therefore, the horizontal distance between Ryan and the dolphin is  57.87 feet.

2. Using trigonometry, we can find the horizontal distance between the airplane and the control tower:

tan(56) = x / 7450

x = 7450tan(56)

x = 10735.96 feet

Therefore, the airplane is approximately 10735.96 feet away from the control tower

3. We want to find the angle of depression from the top of the lighthouse to the boat. Since the lighthouse is 275 feet above the water, we can use trigonometry to find the height of the lighthouse above the boat:

tan(90) = 275 / x

x = 275 / tan(90)

x = undefined

Therefore, the angle of depression from the top of the lighthouse to the boat is 0 degrees.

Hence,  the horizontal distance between Ryan and the dolphin is approximately 57.87 feet.

the airplane is approximately 10735.96 feet away from the control tower

the angle of depression from the top of the lighthouse to the boat is 0 degrees.

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Answer: 2.3716 <-------- This is the Code

Step-by-step explanation:

1.4 x 2.5 = 3.5

2.2 x 2.5 = 5.5

1.4 x 0.2 = 0.28

2.2 x 0.2 = 0.44

3.5 x 0.28 = 0.98

5.5 x 0.44 = 2.42

Then:

X         1.4           2.2

2.5      3.5          5.5

          - x -          - x -    

0.2      0.28        0.44

           - = -           - = -

        0.98  x    2.42 = 2.3716 <-------- This is the Code

To represent the data, the display used is histogram.

A frequency distribution shows how often each different value in a set of data occurs. A histogram is the most commonly used graph to show frequency distributions. Histograms visualize quantitative data or numerical data, whereas bar charts display categorical variables.

Given,

Data of 24 students eating vegetables in the frequency table.

The data is quantitative.

Histograms are visual displays of frequencies using columns plotted on a graph. The Y-axis (vertical axis) generally represents the frequency count, while the X-axis (horizontal axis) generally represents the variable being measured.

Hence, Histogram will be used to represent the data.

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Answer:

This is Non-terminating

decimal: 0.777

Step-by-step explanation:

One must evaluate the function as the independent variable gets closer to the point from the provided side.

So in order to determine the limit of a function at a point from one side, one must evaluate the function as the independent variable gets closer to the point from the provided side. Take the subsequent function, for instance: scss. Copy the code f(x) = (x2 - 4) /. (x - 2)

You can evaluate the function for x values that are getting closer to 2 but always greater than 2 in order to determine the limit of this function as x approaches 2 from the positive side (i.e., as x goes closer and closer to 2 from values greater than 2). The function can be evaluated, for instance, at x = 2.1, x = 2.01, x = 2.001, and so forth. The function values will approach the target value as x approaches 2, which is 2. In order to determine the limit of this function as x approaches 2 from the positive side (i.e., as x goes closer and closer to 2 from values greater than 2). The function can be evaluated, for instance, at x = 2.1, x = 2.01, x = 2.001, and so forth.

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Answer:

Step-by-step explanation:

Answer: 25 inches

Step-by-step explanation:

The equation for area of a rectangle is Length x Width, since we have the width which is 20 in., we can multiply it by a variable and set it equal to 500.

20(b)=500

divide both sides by 20

b=25

The  triangle is rotated 90° counterclockwise about the origin shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

we have to rotate 90° counterclockwise about the origin.

as, the rule for 90° counterclockwise about the origin is (x, y) becomes

(-y, x).

As, the coordinates after rotation are :

(-8, 3)---> (-3, -8)

(-2, 8)---> (-8, -2)

(-5, 7) -----> (-7, -5)

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1.The beginning balance should be $4,000

2.The amount to be adjusted is $2554

3.The ending balance of the account after the adjustment $2554

4. Office Supplies Account is $14846

"Information available from the question"

The Office Supplies account started the year with a $4,000 debit balance

The company purchased supplies for $13,400,

The inventory of supplies available at the end of the year totaled $2,554.

Now, According to the question:

1. The beginning balance should be $4,000

2.The adjusted amount is

Opening balance = 4000

Add: New purchases = 13400

Balance after Purchase = 17400

Less: Year end balance = 2554

3. The ending balance is $2,554

4. The adjusting journal entry is

Dr. Supplies Expense Account is 14846

Adjustment in the year = Cr. 14846 (subtracted from the balance)

Office Supplies Account is 14846

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H0: mean=1.45

H1: mean< 1.45

=-3.175

The result is significant at p < .01.

Reject Null Hypothesis

the mean level of exhaust emitted for this model reduces emissions

A)

Null hypothesis:

H0: mean=1.45

Alternative hypothesis:

H1: mean< 1.45

b)

estimate - the value we hypothesize standard error test statıstıc - t-statisticS

[tex]\begin{gathered}\text { test statistic }=\frac{\text { estimate }-\text { value we hypothesize }}{\text { standard error }} \\\text { t-statistic }=\frac{\bar{x}-\mu_o}{s / \sqrt{n}}\end{gathered}[/tex]

t=1.21-1.45/0.4/sqrt(28)

=-3.175

c)

t=-3.175

df=28-1=27

alpha=0.01

The P-Value is .001863.

The result is significant at p < .01.

d)

p=0.001

< alpha of 0.01

Reject Null Hypothesis

e)

there is sufficient evidence

the mean level of exhaust emitted for this model reduces emissions

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The length of the side AB in triangle ABC is 6.58 units.

What are trigonometric ratios in terms of a right-angle triangle?

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjacent/hypotenuse and

tan = opposite/adjacent.

From the given figure we can conclude that we have length of the adjacent

with an angle of 20° and we have been asked to find the hypotenuse.

We know cos = adjacent/hypotenuse.

∴ cos20° = adjacent/7.

0.937 = adjacent/7.

adjacent = 7*0.937.

adjacent = 6.58.

Hence , the length of the side AB in triangle ABC is 6.58 units.

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Answer:

3,293 yards are more than a mile

Step-by-step explanation:

1 mile is 1,760 yards. Thereby, we know that 3,293 is more than 1,760.

Answer: 3,293 yards is more than a mile since a mile is 1,760 yards

Step-by-step explanation:

2 miles are 3,520 yards which can further prove that 1 mile is way less the 3,293 yards

Hope this helped

Answer: (0,6), (1,5), (2,4), (3,3)

Step-by-step explanation:

I don't think I can add a picture but I can give you points and you can just draw a line through all of them

(0,6), (1,5), (2,4), (3,3)

If you want to, you can use a graphing calculator and just put the equation in. If you don't have an actual graphing calculator, I recommend using desmos online graphing calculator because it works really well.

The correct ranking of the spheres according to the magnitude of the electric field they produce at point P (greatest first) is: 1 > 2 > 3. The answer is option C.

Since all three spheres have the same charge Q and radius, the magnitude of the electric field at point P due to each sphere is proportional to 1/d^2, where d is the distance between the center of the sphere and point P. Therefore, the sphere closest to point P will produce the greatest electric field at that point.

Assuming that the three spheres are arranged in a straight line with sphere 1 being the closest to point P and sphere 3 being the farthest, we can rank the spheres according to the magnitude of the electric field they produce at point P as follows:

Sphere 1 produces the greatest electric field at point P since it is the closest to it.

Sphere 2 produces the second greatest electric field at point P since it is farther away from point P than sphere 1 but closer than sphere 3.

Sphere 3 produces the smallest electric field at point P since it is the farthest from it.

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Answer: You can make 5/3 * (1/1) = 5 servings with a cup of macaroni.

And, with 5 servings, you can make 5 * (3/1) = 15 1/3 servings of pasta salad.

Step-by-step explanation:

The 4-2-1 rule is a guideline used to help determine the amount of water an individual needs to drink each day.

The rule states that an individual should drink 4 liters of water for every 50 pounds of body weight, 2 liters of water for every 50 pounds of body weight if they are exercising, and 1 liter of water for every 50 pounds of body weight if they are in a hot or dry environment.

To calculate how much water you need to drink using the 4-2-1 rule, simply follow these steps:

1. Determine your body weight in pounds.
2. Divide your body weight by 50 to get the number of 50-pound increments in your weight.
3. Multiply the number of 50-pound increments by 4 to get the amount of water you need to drink if you are not exercising or in a hot or dry environment.
4. Multiply the number of 50-pound increments by 2 to get the amount of water you need to drink if you are exercising.
5. Multiply the number of 50-pound increments by 1 to get the amount of water you need to drink if you are in a hot or dry environment.
6. Add the amounts from steps 3, 4, and 5 together to get the total amount of water you need to drink each day.

For example, if you weigh 150 pounds, you would need to drink 4 liters of water for every 50 pounds of body weight (150 / 50 = 3), 2 liters of water for every 50 pounds of body weight if you are exercising (3 x 2 = 6), and 1 liter of water for every 50 pounds of body weight if you are in a hot or dry environment (3 x 1 = 3). Therefore, you would need to drink a total of 13 liters of water each day (4 + 6 + 3 = 13).

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A medium-sized orange contains 68 calories. Which is one-fifth the number of calories in a slice of cheese pizza.

If one slice of cheese pizza contains 340 calories, and a medium-size orange has one-fifth that number of calories, we can find the number of calories in a medium-size orange by dividing 340 by 5. Calories in a medium-sized orange = [tex]\frac{340}{5}[/tex] calories = 68 calories. The division is an arithmetic operation used to find out how many times one number is contained within another number. The result of a division operation is called the quotient.

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Answer:

47% for rolling a blue and 33% for rolling a red

Step-by-step explanation:

The both answers are- How much does it take to fill the cylinder? and How much is needed to completely fill the cylinder?

The cylindrical, which is routinely a two half solid, is one of the most basic curved geometric patterns. In simple geometry, it is known as a pyramid with a ring as its basis. The term "cyl" is also used to refer to a continuously curved surface in a broad range of contemporary areas of mathematics and geometry. A "cylinder" is a four structure made up of sloping surfaces with circle tops and bases. A canister is a muti solid figure with three grounds that have two identical circles connected at its height, which is defined by the separation of the structures from the centre. Examples of canisters are chilled drinks cans and toilet tissue wicks.

given

All four statements stats about cylinders .

How much does it take to cover the cylinder? and How much does it take to fill the cylinder? are both not showing volume or capacity of cylinder.

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Option a is correct- The length of MC is 16mm.

The equilateral triangle has its three sides with the same length.

So if the perimeter is 96 mm, we have,

perimeter = 3 * side

3 * side = 96

side = 32mm

The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation,

height = (side * root(3))/2

height = 16root(3)

Using the Pythagoras' theorem in the triangle ACM, we have,

side^2 = MC^2 +height ^2

1024 = MC^2 + 768

MC^2 = 256

MC = 16mm

so, The length of MC is 16mm.

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Answer:

b

Step-by-step explanation:

Use the Avogadro constant of 6.02 x 10^23