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An explanation of an event that is based on repeated observations and experiments is a scientific theory

A thorough, well-researched explanation of a natural occurrence constitutes a scientific theory.

We frequently use the word "theory" to refer to a hypothesis or informed guess in common speech, but in science, a theory is an explanation that is the result of a substantial and repeated investigation. The purpose of theories is to explain a broad concept; they are not intended to establish facts

Some of the most well-known and complicated events are explained by scientific theories. The theories of relativity, evolution, and gravity are a handful of the most well-known scientific concepts.

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Answer:

Step-by-step explanation:

Total amount of money earned is x.

Answer:

Solution given

tax = 4.5%

Amount of tax = $46

Let total amount of money earned is x.

we have

4.5% of x = $46

x×4.5/100 = 46

x×0.045 =46

x = 46/0.045

x= 1022.22

So Racheal earn $ 1022.22.

Jamal need to invest $35838.77 in an account.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

As given Jamal wants to save $54,000 for a down payment on a home with 8.2% APR, compounding daily for 5 years.

The compound interest formula is,

\(A = P(1+\frac{r}{n})^n^t\)

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Here, A = $54000, r = 8.2% = 0.082, t = 5, n = 365

Plug the values in the above formula,

\(54000 = P(1+\frac{0.082}{365} )^(^3^6^5^)^(^5^)\\54000 = P(1.0002246575)^1^8^2^5\\54000= P(1.5067483068)\\P = \frac{54000}{1.5067483068} \\P = 35,838.766\\P = 35838.77\)

Hence, Jamal need to invest $35838.77 in an account.

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The dimensions that will minimize the total cost of material for the crate are a square base with side length approximately 37.43 ft and a height of approximately 20.86 ft.

Let's assume that the side length of the square base is x ft and the height of the crate is h ft.

The volume of the crate is given as 27648 ft³, so we have the equation:

x² h = 27648

The cost of the material for the top and sides is $2 per square foot, and the cost of the material for the bottom is $6 per square foot.

The surface area of the crate is given by the equation:

Surface area = x² + 4xh

We want to minimize the surface area while maintaining the given volume.

Surface area = x² + 4x(27648 / x²)

= x² + 110592 / x

By taking the derivative of the surface area equation with respect to x and setting it equal to zero:

d(surface area) / dx = 2x - 110592 / x²

0 = 2x - 110592 / x²

To solve this equation, we can multiply both sides by x² to eliminate the denominator:

0 = 2x³ - 110592

2x³ = 110592

x³ = 55296

x ≈ 37.43

Now,

x² * h = 27648

(37.43)² * h = 27648

h ≈ 20.86

Therefore, the dimensions that will minimize the total cost of material for the crate are a square base with a side length of approximately 37.43 ft and a height of approximately 20.86 ft.

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We are given two equations, one of which has an isolated variable \(x\).

That screams to me that substitution would be a prefered strategy here, compared to elimination, although both work.

That means we'll be substituting our value of \(x\), which is given as \(-y+3\), into the first equation, \(15x+31y=-3\).

\(15x+31y=-3\)

\(x=-y+3\)

\(15(-y+3)+31y=-3\)

\(-15y+45+31y=-3\)

\(16y=-48\)

\(y=-3\)

With this value, we can plug it back into either of the two equations to solve for \(x\), I'll be substituting it back into the second equation, since it's easier.

\(x=-y+3\)

\(y=-3\)

\(x=-(-3)+3\)

\(x=6\)

So our solution is \((6,-3)\), and to check we can plug it back into the first equation.

\(15x+31y=-3\)

\(15(6)+31(-3)=-3\)

\(90-93=-3\)

Which is true, so our solution is correct.

Hope this helps!

Answer:

Step-by-step explanation:

\(\begin{cases} 15x+31y=-3 \\\\ x=-y+3 \ \ | \times 15\end{cases} \Leftrightarrow \ominus\begin{cases} 15x+31y=-3 \\\\ 15x=-15y+45 \ \ \end{cases} \Leftrightarrow \\\\\\ 15x-15x+31y=-3-(-15y)-45 \\\\ 31y=15y-48 \\\\ 31y-15y=-48 \\\\ 16y=-48 \ \ |\div 16 \\\\ y=-3 \ \ ; \ \ x=-y+3=3+3=6 \\\\\)

\(\huge \boldsymbol{\mathfrak {Unswer}}: x=6 \ \ ; \ \ y=-3\)

The difference quotient for the function f(x) = 69x + 2 is a constant value of 69. This means that the average rate of change of the function over any interval is always 69.

To evaluate and simplify the difference quotient for the function f(x) = 69x + 2, we first need to understand what the difference quotient represents. The difference quotient is a mathematical expression that measures the average rate of change of a function over a given interval. It is defined as:

[f(x + h) - f(x)] / h,

where h represents a small change in the x-values.

Let's proceed with calculating the difference quotient for the given function:

[f(x + h) - f(x)] / h

= [(69(x + h) + 2) - (69x + 2)] / h

= [69x + 69h + 2 - 69x - 2] / h

= (69h) / h

= 69.

To simplify the expression, we used the distributive property to expand the function f(x + h). Then, we simplified the numerator by combining like terms. The constant terms 2 and -2 canceled each other out. The h term in the numerator can be factored out, which allows us to cancel it out with the h term in the denominator. Finally, we are left with the simplified expression of 69.

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The second number between 40 and 50 is 45.

What is the greatest common factor?

In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y.

We have,

The greatest common factor of 18 and another number is 9.

The second number is between 40 and 50.

The prime factorization of 18 is 2 x 3 x 3 = 18.

The prime factorization of 27 is 3 x 3 x 3 = 27.

The prime factorization of 45 is 5 x 3 x 3 = 45.

The occurrences of common prime factors of 18, 27, and 45 are 3 and 3.

So the greatest common factor of 18, 27, and 45 is 3 x 3 = 9.

Hence, the second number between 40 and 50 is 45.

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Rounding to the nearest tenth, the area of the sector is approximately 3.4 square meters.

The area of a sector of a circle can be found using the formula:
Area = (θ/2π) * πr²
where θ is the central angle and r is the radius of the circle.
In this case, the radius is given as 3.2 m and the central angle is 2π/3.
Substituting these values into the formula, we get:
Area = (2π/3 * 1/2π) * π(3.2)²
Simplifying further, we have:
Area = (1/3) * 3.2²
Calculating the value, we get:
Area ≈ 3.4133 square meters
Rounding to the nearest tenth, the area of the sector is approximately 3.4 square meters.

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Answer:

D)\(x = \frac{8}{3} \: or \: x = - \frac{5}{2} \)

Step-by-step explanation:

\(6 {x}^{2} - x - 40 = 0 \\ 6 {x}^{2} - 16x + 15x - 40 = 0 \\ 2x(3x - 8) + 5(3x - 8) = 0 \\ (3x - 8)(2x + 5) = 0 \\( 3x - 8)(2x + 5) = 0 \\ 3x - 8 = 0 \: \: \: \: or \: \: \: 2x + 5 = 0 \\ x = \frac{8}{3} \: \: \: or \: \: \: x = - \frac{5}{2} \)

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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The standard matrix of a linear transformation T can be found by using the formula A = [T(e1) T(e2) ... T(en)], where A is the standard matrix, e1, e2, ..., en are the columns of the identity matrix, and T(e1), T(e2), ..., T(en) are the images of the identity matrix columns under the transformation T.

1. For the first transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(3,1,3,1) (-5,2,0,0)] = [[3 -5] [1 2] [3 0] [1 0]]. Therefore, the standard matrix of T is [[3 -5] [1 2] [3 0] [1 0]].

2. For the second transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2) T(e3)] = [(1,3) (4,-7) (-5,4)] = [[1 4 -5] [3 -7 4]]. Therefore, the standard matrix of T is [[1 4 -5] [3 -7 4]].

3. For the third transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)], where cos(31/2) and sin(31/2) are the cosine and sine of 31/2 radians, respectively. Therefore, the standard matrix of T is [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)].

4. For the fourth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)], where cos(-1/4) and sin(-1/4) are the cosine and sine of -1/4 radians, respectively. Therefore, the standard matrix of T is [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)].

5. For the fifth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (2,1)] = [[1 2] [0 1]]. Therefore, the standard matrix of T is [[1 2] [0 1]].

6. For the sixth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (3,1)] = [[1 3] [0 1]]. Therefore, the standard matrix of T is [[1 3] [0 1]].

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Step-by-step explanation:

isosceles triangle (|>) this but right side up

Discrete-data is a category of quantitative information that has countable or finite values.

This indicates that there are no intermediate values between the precise numerical values that can be used to convey the data; only those values can be used. The number of siblings a person has, the number of pets a home has, and the number of individuals in a room are all examples of discrete data.

Numerous statistical methods, such as measures of central tendency like the mean, median, and mode, as well as measures of dispersion like range and standard deviation, can be used to analyse discrete data. Additionally, discrete data can be displayed graphically using tools like bar charts and frequency histograms.

A discrete data set is the number of stories in a skyscraper in Manhattan. A continuous data set, on the other hand, can be divided into ever-smaller pieces and can take on any value within a range. Therefore (b), "A discrete data set because the possible values can be counted."

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Answer: Shows us the pictures of the subsets.

Step-by-step explanation:

Answer:

34418

Step-by-step explanation:

Answer:

The answer is:

34418

The lower specification limit (LSL) for the plastic liner is 3.9 mm (rounded to three decimal places).

To calculate the upper specification limit (USL) for the plastic liner, we know that it lies about 5 standard deviations (σ) from the centerline or mean thickness. The process has a mean thickness of 4.0 mm and a standard deviation (σ) of 0.02 mm.

So, the USL can be calculated as follows:

USL = Mean + (5 * σ)

= 4.0 mm + (5 * 0.02 mm)

= 4.0 mm + 0.1 mm

= 4.1 mm

Therefore, the upper specification limit (USL) for the plastic liner in this highway project is 4.1 mm (rounded to three decimal places).

Similarly, the lower specification limit (LSL) can be calculated by subtracting 5 standard deviations from the mean thickness:

LSL = Mean - (5 * σ)

= 4.0 mm - (5 * 0.02 mm)

= 4.0 mm - 0.1 mm

= 3.9 mm

Therefore, the lower specification limit (LSL) for the plastic liner is 3.9 mm (rounded to three decimal places).

It's worth noting that the given information also mentions the process capability index (Cpk), which is a measure of how well the process meets the specifications. In this case, the Cpk is calculated as (USL - Mean) / (3 * σ), and it is determined to be 1.667 (rounded to three decimal places).

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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:

1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.

So, the answer is B. 5 line pairs per millimeter.

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Answer:

4 1/3

Step-by-step explanation:

1 1/15 + 1 3/5 + 1 2/3=

1 1/15 + 1 9/15 = 1 10/15 =

3 20/15 =

4 5/15 = 4 1/3

Answer:279,723

Step-by-step explanation: 124,417+118,214+37,092=279,723

Answer:

12

Step-by-step explanation:

Answer:

(8-28i)/53

hope it helps!

Step-by-step explanation:

Answer:

1.8c+32=f

Step-by-step explanation:

The difference between the number of heads and the number of tails in 100 coin tosses follows the distribution of a box (i, ii, iii, iv, v). The expected value for the difference can be calculated, as well as the standard error.

(a) The difference "number of heads − number of tails" in 100 coin tosses follows the distribution of Box (ii). The box represents the sum of 100 draws, which corresponds to the number of times the coin lands on heads or tails. Each box represents a different distribution, and in this case, Box (ii) accurately models the difference.

(b) To find the expected value for the difference, we need to consider that the coin has an equal probability of landing on heads or tails. In 100 tosses, the expected value is half of the total tosses, which is 50. So, the expected value for the difference between the number of heads and the number of tails is 50.

(c) The standard error for the difference can be calculated as the square root of the variance. In this case, since the coin tosses are independent and have the same probability, the variance is equal to the number of tosses divided by 4. Therefore, the standard error is the square root of 100 divided by 4, which is 5.

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Answer:

x = 2 and y = 1

Step-by-step explanation:

Given equations are :

2x-y=3 ...(1)

3x+y=7 ...(2)

Add equation (1) and (2) as follows :

2x-y + 3x+y = 3 + 7

2x + 3x = 10

5x = 10

x = 2

Put the value of x in equation (1)

2(2)-y=3

4-y = 3

y = 4-3

y = 1

Hence, the solution of the given equations are (2,1).

Answer:

Not!

Volume = m/d

Step-by-step explanation:

It is just Volume = m/d

where

m is the mass of the ice cube and

d is the density of water.

In the second state, where the ice has melted, it turns into water of volume....

Volume = m/d! exactly the same volume as it displaced before.

Answer:

x = 5

Step-by-step explanation:

4x + 3 = 23 ( subtract 3 from both sides )

4x = 20 ( divide both sides by 4 )

x = 5

Step-by-step explanation:

By subtracting 3 from both sides, we get

By dividing both sides with 4, we get