The Maclaurin series expansion for sin x is sin x = x - x^3/3! + x^5/5! - x^7/7! + ... Starting with the simplest version, sin x = x, add terms one at a time to estimate sin(π/3). After each new term is added, compute the true and approximate percent relative errors. Use your pocket calculator to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures.

Answer:

Impossible not likely to happen

On solving the provided query we have Therefore, assuming that order equation counts, there are 20,736 different ways to arrange 12 different books on four shelves.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Using the permutation formula with repetition, we can determine how many different ways there are to arrange 12 books on 4 shelves.

\(n^r\)

where r is the number of empty spaces to be filled (in this example, 4 shelves) and n is the number of options to select from (12 distinct books in this case).

\(12^4 = 20,736\)

Therefore, assuming that order counts, there are 20,736 different ways to arrange 12 different books on four shelves.

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Answer:  

5 and 11/50  

Step-by-step explanation:

5.22 = 261/50 = 5 and 11/50

Answer:

The solution to the equation (x-13)<18 is that x can be equal to the numbers 0-17 (NOT including negative numbers)

Answer:

$250

Step-by-step explanation:

Total parts:

2+3+9 = 14

500/14 = 250/7

2×250/7 : 3×250/7 : 9×250/7

500/7 : 750/7 : 2250/7

The largest share is 2250/7, the smallest share is 500/7.

Find the difference.

2250/7 - 500/7 = 250

Answer:

$250

Step-by-step explanation:

2x+3x+9x= $500

9x-2x= 7x=?

14x= $500

7x= $500/2= $250

The toy company should use \(\frac{1}{36}\) as the scale factor. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often referred to as "arithmetic operations", are thought to be capable of fully explaining all real numbers. The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

We are given that a monster truck wheel has an area of 324 square inches and a toy company wants to create a scaled copy of the monster truck with a wheel area of 9 square inches.

So, by using the division operation, we get

324 ÷ 9 = 36

This means that the monster truck wheel is 36 times bigger that what the toy company wants to create.

Hence, the toy company should use \(\frac{1}{36}\) as the scale factor.

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The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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Using the area of rectangle, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

In the given question we have to find the dimensions of the rectangle with maximum area.

Given Semicircle Radius is 5.

As we know that standard equation of circle is \(x^2+y^2=a^2\)

a=5, so the equation is \(x^2+y^2=(5)^2\)

\(x^2+y^2=25\)

Therefore, Half circle y=\(\sqrt{25-x^2}\)

Area of Rectangle(A) =xy

Because Half of the rectangle is lies in first quadrant and half lies in second quadrant

Therefore,

Area of Rectangle(A) = 2xy

Now putting the value of y

Area(A) = 2x\(\sqrt{25-x^2}\)

Here we need to maximize the area of Rectangle, so find derivative and set equal to zero.

A'= \(\frac{d}{dx}(2x\sqrt{25-x^2})\)

A'= 2\([x\frac{d}{dx}\sqrt{25-x^2}+\sqrt{25-x^2}\frac{d}{dx}x]\)

A'= 2\([x\cdot\frac{-x}{\sqrt{25-x^2}}+\sqrt{25-x^2}\cdot1]\)

A'= 2\([\frac{-x^2}{\sqrt{25-x^2}}+\sqrt{25-x^2}]\)

A'= 2\((\frac{-x^2+25-x^2}{\sqrt{25-x^2}})\)

A'= 2\((\frac{25-2x^2}{\sqrt{25-x^2}})\)

For critical Number A' = 0

2\((\frac{25-2x^2}{\sqrt{25-x^2}})\) = 0

25-2x^2 = 0

2x^2=25

x^2=25/2

x=±√25/2

x=±5/√2

Therefore,

Base of the Rectangle = 2x

Base of the Rectangle = 2×5/√2

Base of the Rectangle = 5√2

and

height of rectangle = \(\sqrt{25-x^2}\)

height of rectangle = \(\sqrt{25-(5/\sqrt{2})^2}\)

height of rectangle = \(\sqrt{25-(25/2)}\)

height of rectangle = √(50-25)/2

height of rectangle = √25/2

height of rectangle = 5/√2

Hence, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

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Answer:

7.5 feet per second

Step-by-step explanation:

Answer:

I believe it is 7.5 feet per second

Step-by-step explanation:

Do 225 divided by 30

Answer:

median = 3 pieces

Step-by-step explanation:

The median is the middle value of the data arranged in ascending order. If there is not an exact middle value then the median is the average of the values either side of the middle.

Given the number of pieces then

2   2   4   4 ← pieces of cheese in ascending order

       ↑ middle is between 2 and 4, thus

median = \(\frac{2+4}{2}\) = \(\frac{6}{2}\) = 3

In order to calculate the length of the missing side, since we have a right triangle, we can use the Pythagorean Theorem.

So we have:

Rounding to the nearest tenth, the length is 7.5, so the correct option is the third one.

Answer:

The time can not be negative. Thus, the domain of the given graph function must have the interval [0, ∞].

In other words, t ≥ 0.

Step-by-step explanation:

We know that the domain of a function is the set of input or argument values for which the function is real and is defined.

Given that the graph is showing the height of a thrown ball x seconds after it is thrown.

We must check that the time can not be negative. Thus, the domain of the given graph function must have the interval [0, ∞].

In other words, t ≥ 0.

Answer:

more free points

Step-by-step explanation:

The following statements "In any comparison, the two values compared can be either variables or constants" is True.

In any comparison, the two values compared can be either variables or constants. Variables are values that can change, while constants are fixed values. Comparisons can involve any combination of these (e.g., variable-variable, variable-constant, or constant-constant).

In computer programming, variables and constants are two fundamental concepts used to store and manipulate data.

A variable is a named storage location in computer memory that holds a value of a certain data type, such as a number, a string of characters, or a Boolean value (true/false). The value stored in a variable can change during program execution, hence the name "variable". Variables are typically used to store data that may change frequently, such as user input, intermediate results of calculations, or data read from a file.

For example, in a program that calculates the area of a circle, the radius of the circle would be stored in a variable. If the user changes the value of the radius, the value stored in the variable would also change accordingly.

A constant, on the other hand, is a value that remains the same throughout the program execution. It is also a named storage location in memory, but unlike a variable, the value stored in a constant cannot be changed after it has been defined. Constants are typically used to store data that does not change, such as mathematical constants (e.g., pi), physical constants, or configuration settings.

For example, in the same program that calculates the area of a circle, the value of pi would be stored in a constant. The value of pi would not change during program execution, and hence it would be defined as a constant.

In summary, variables and constants are two important concepts in programming used to store and manipulate data. Variables are used to store data that may change during program execution, while constants are used to store data that remains constant throughout the program.

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Axioms serve as the starting point of other mathematical statements. These statements, which are derived from axioms, are called theorems. A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives.

The flywheel you described is a uniformly thick disk with a radius of 1.88 m and a mass of 60.1 kg. It spins counterclockwise at a rate of 207 rpm (revolutions per minute).

The flywheel in the form of a uniformly thick disk with a radius of 1.88 m has a mass of 60.1 kg and spins counterclockwise at 207 rpm. Since the flywheel is a disk, its moment of inertia can be calculated using the formula I = (1/2)mr^2, where m is the mass of the disk and r is its radius. Using this formula, we can calculate that the moment of inertia of the flywheel is approximately 433.92 kg*m^2. Additionally, since the flywheel spins counterclockwise, it is rotating in the opposite direction of the clockwise motion.

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Jada can buy approx. 4 bags of chips if each bag costs $0.99 and she also buys a bottle of soda.

Given, Jada has $6. She goes to the store and buys one bottle of soda for $1.20.

Each bag of chips cost $0.99

We have to find the number of chips bags she can buy,

as, she has $6 from which she spent $1.20 for a bottle of soda.

now she left with,

= 6 - 1.20

= $ 4.8

Now, as each chips bag is of $0.99

so, the number of chips bags she can buy are

= 4.8/0.99

= 4.84

So, she can buy approx. 4 bags of chips.

Hence, she can buy approx. 4 bags of chips if each bag costs $0.99 and she also buys a bottle of soda.

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Answer:

What technology devices do you use everyday?

Step-by-step explanation:

Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.

Answer:

What technology devices do you use everyday?

Step-by-step explanation:

Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.

Answer: (-2, 1)

Step-by-step explanation:

The 1st value in a pair is x, the 2nd is y.

▪︎ (-2, 1)

1 = 2(-2)+5

1 = -4+5

1 = 1 ✅

▪︎ (-1, 4)

4 = 2(-1)+5

4 = -2 + 5

4 = 3❌

▪︎ (1, 6)

6 = 2*1+5

6 = 2 + 5

6 = 7❌

▪︎ (3, 10)

10 = 2*3+5

10 = 6 + 5

10 = 11❌

The quadrature formula for the natural cubic spline with evenly spaced knots becomes I = 2h(y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3(k0 + k1 + k2 + ⋯ + kn-1 + kn), where h is the distance between the knots and ki = yi''.

To show that if y = f(x) is approximated by a natural cubic spline with evenly spaced knots, the quadrature formula becomes I = 2h(y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3(k0 + 2k1 + k2 + ⋯ + 2kn-1 + kn), where h is the distance between the knots and ki = yi''.

The natural cubic spline interpolates the function f(x) using piecewise cubic polynomials between each pair of adjacent knots. Let's denote the spline functions as Si(x) for i = 0 to n-1, where Si(x) is defined on the interval [xi, xi+1].

The composite trapezoidal rule is used to approximate the integral of f(x) over each interval [xi, xi+1]. It is given by the formula:

Ti = h/2 * (yi + yi+1)

where Ti represents the approximation of the integral over the interval [xi, xi+1].

Summing up the trapezoidal approximations over all intervals, we get:

I = T0 + T1 + T2 + ⋯ + Tn-1

 = (h/2) * (y0 + y1) + (h/2) * (y1 + y2) + ⋯ + (h/2) * (yn-1 + yn)

 = h/2 * (y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn)

Now, let's consider the correction term for curvature. The curvature term measures the second derivative of the spline functions at each knot. Using the notation ki = yi'', we have:

C = (2/4)h^3 * (k0 + k1 + k2 + ⋯ + kn-1 + kn)

Adding the curvature correction term to the trapezoidal approximation, we obtain the final quadrature formula:

I = h/2 * (y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3 * (k0 + k1 + k2 + ⋯ + kn-1 + kn)

This formula represents the integration approximation using the natural cubic spline with evenly spaced knots. The first part corresponds to the composite trapezoidal rule, and the second part provides a correction for the curvature of the spline.

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Answer:

Channel 9 conducting this interview would be an example of a convenience sample.

Step-by-step explanation:

Convenience sampling is a kind of non-probability sampling (i.e. all items does not have an equivalent chance of being selected), which does not comprises of random collection of items.

Convenience sampling is where we take in items which are easy to reach.

For instance, gathering information on customer satisfaction by interviewing 6 randomly selected customers from a local store is an illustration of convenience sampling.

In this case Channel 9 selected a very easily available sample. Since, the elderly viewers are usually retired and can be reached easily either at home or on the phone, the sampling method used is convenience sample.

Answer:

1

14

The answer is one over fourteen because there are 8 white eggs (remember the 10 brown eggs), and half of them (the white ones) are cracked, so four. And, if you randomly grab an egg, there is 1/14 of a chance you could grab a cracked, white, egg.

The Kruskal-wallis one-way ANOVA compares the overall difference between two or more independent samples. So, the correct option is option a. kruskal-wallis one-way ANOVA

The answer is option A, the Kruskal-Wallis one-way ANOVA compares the overall difference between two or more independent samples.

The Sign test and Wilcoxon rank test are non-parametric tests used for comparing paired samples, while the Mann-Whitney U test is used for comparing two independent samples.

This test is used to compare the overall difference between two or more independent samples when the assumptions of a regular one-way ANOVA are not met.

The Kruskal-Wallis test is applicable when the data violate the assumptions of normality and/or equal variances required by parametric ANOVA tests.

Instead of comparing means, it compares the ranks of the data values within each group to assess if there are significant differences between the groups.

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The z-score of apple price of $7.99/lb is 0.66

Probability is a measure of the possibility of an event occurring.

The likelihood could range from 0 to 1, where 0 indicates an impossibility and 1 indicates a certainty.

Every event in a sample space has an overall probability of one.

The probability that the apple price is less than or equal to $7.99 / lb can be calculated using the normal distribution method

                                   P(x ≤ 5.99)

The standard form of the given random sample can be found using the formula,

                               Z = (X - μ) / σ

where Z is the standard score

          X is the random sample

          μ is the mean

          σ is the standard deviation.

For x =7.99,

                  Z = (7.99 - 5.99) / 2.99

                      = 2 / 2.99

                  Z  = 0.66

Therefore, by standardizing the random sample, we get

              P(x ≤ 5.99) = P( z ≤ 0.66)

By using the z-table, we get the value of z

            P(z ≤ 0.66) = 0.7454

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Approximately 8.89 gallons of lemonade is needed to make 20 gallons of the special lemonade punch is the answer.

To find out how many gallons of lemonade is needed for 20 gallons of the special lemonade punch, it's essential to use the ratio that the secret recipe calls for, which is 2 gallons of lemonade for every 3 gallons of strawberry soda.

As the total amount of lemonade punch needed is 20 gallons, we can calculate the amount of strawberry soda required by breaking down 20 gallons into the ratio of 2 gallons of lemonade for every 3 gallons of strawberry soda.

This can be done using cross-multiplication as shown below: 2/3 = x/20 (where x is the amount of strawberry soda needed)Cross-multiplying, we get: 3x = 40x = 40/3 gallons of strawberry soda (approx. 13.33 gallons)

Now, using the same ratio, we can find out the amount of lemonade needed.2/3 = y/13.33 (where y is the amount of lemonade needed)

Cross-multiplying, we get:3y = 26.66y = 26.66/3 gallons of lemonade (approx. 8.89 gallons)

Therefore, approximately 8.89 gallons of lemonade is needed to make 20 gallons of the special lemonade punch.

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Answer:

36² metres

Step-by-step explanation:

I'm assuming you mean 6 metre wide/long floor. Area is L*W so 6*6

The inequality:

Basically tells us that the solutions will be the numbers strictly greater than 5, so:

Therefore, the solutions are:

8, 10, 6

There are 720 possible horse combinations for the first 3 places in the race.

To solve this problem, let us break this down one by one.

There are 10 possible horses that could win in first place.

Therefore, this means that for each of these possibilities, there are now 9 horses that could come in second.

So there are 10 x 9 possible combinations for the first 2 places.

10 x 9 = 90.

And for each of those combinations, there are also 8 possible horses that could come in the third place. So

10 x 9 x 8 = 720

There are 720 possible horse combinations for the first 3 places in the race.

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The hypotenuse and base has a length of option(d) √3; 2

Define Trigonometric functions

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The trigonometric ratio of sin(A) = perpendicular / hypotenuse

Let, hypotenuse = h

so, sin(30) = s / h

we know, sin(30) = 1/2

1/2 = s/h

h = 2s

Now, calculate base in terms of s by Pythagoras theorem

4s² = s² - b²

3s² = b²

b = √3 s

In the angle 30-60-90 we have the ratio,

s, √3 s, 2s

Now, the hypotenuse and base is  2s and √3 s

Therefore, we can say that the hypotenuse and base has a length of option(d) i.e, √3; 2

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Answer:

Step-by-step explanation:

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