What is the meaning of commutative property?

The box dimensions with the least surface area are length and width x = 8 feet, and height h = 4 feet.

To find the dimensions of the box with a square base and no top that has a volume of 256 cubic feet and the least (minimum) surface area, we can follow these steps:
Define the variables
Let x be the length and width of the square base, and let h be the height of the box.
Write the volume equation
The volume of the box is given by the product of its length, width, and height: V = x * x * h = x^2 * h.
Since the volume is 256 cubic feet, we have x^2 * h = 256.
Write the surface area equation
The surface area of the box (without the top) is given by the sum of the areas of its sides: S = x^2 + 4 * x * h.
Solve for h from the volume equation
From the volume equation x^2 * h = 256, we can solve for h in terms of x: h = 256 / x^2.
Substitute h into the surface area equation
Substitute the expression for h into the surface area equation: S = x^2 + 4 * x * (256 / x^2).
Simplify the surface area equation
Simplify the surface area equation by canceling out terms: S = x^2 + 1024 / x.
Minimize the surface area
To minimize the surface area, take the derivative of S with respect to x and set it equal to zero:
dS/dx = 2 * x - 1024 / x^2 = 0.
Solve for x
To solve for x, multiply both sides by x^2 and rearrange the equation:
2 * x^3 = 1024.
Now, divide by 2 and take the cube root to find x:
x = (512)^(1/3) = 8 feet.
Find h
Using the value of x, find the height h:
h = 256 / x^2 = 256 / 64 = 4 feet.

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Any expression that can be simplified to a ratio of two integers is a rational number.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. Therefore, any expression that can be simplified to a ratio of two integers is a rational number.

Expressions that represent rational numbers include:

1. 5/7 - This is a ratio of two integers (5 and 7) and can be simplified to a fraction.

2. -3/4 - This is a negative ratio of two integers (3 and 4) and can be simplified to a fraction.

3. 0.25 - This is a decimal, but it can be written as 1/4, which is a raio of two integers.

4. -6/8 - This is a negative ratio of two integers (6 and 8) and can be simplified to a fraction.

5. 1/2 + 1/3 - This is the sum of two ratios of integers (1/2 and 1/3), which can be combined and simplified to a fraction.

6. (2x + 3)/(x - 4) - This expression can be simplified to a ratio of two polynomials, but it still represents a rational number because polynomials are just combinations of integers.

In general, any expression that involves only arithmetic operations (+, -, x, ÷) with rational numbers or polynomials will represent a rational number.

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7.051 can be written as the fraction 7051/1000.

To express 7.051 as a fraction in the form of p/q, we need to identify the decimal places and convert them to the corresponding fractional parts.

Since 7.051 has three decimal places, we multiply it by 1000 to move the decimal point three places to the right, which gives us 7051.

Now, the numerator (p) of the fraction will be 7051, and the denominator (q) will be the corresponding power of 10, which is 1000.

Therefore, 7.051 can be expressed as 7051/1000.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

In this case, the GCD of 7051 and 1000 is 1, so the fraction is already in its simplest form.

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Answer:

Step-by-step explanation:

(2x^2-11)(x^2+2)

2x^4-7x^2-22

The correct order of the steps in the scientific method is: observation, hypothesis, experiment, result, and conclusion

The correct order of the steps in the scientific method is as follows:

e. Observation - Start by making observations or gathering information about a particular phenomenon or problem. This involves carefully observing and noting relevant details and patterns.

b. Hypothesis - Based on the observations, formulate a hypothesis, which is a proposed explanation or prediction that can be tested through experimentation.

c. Experiment - Design and conduct experiments or investigations to test the hypothesis. This step involves carefully controlling variables, collecting data, and performing measurements.

a. Result - Collect and analyze the data obtained from the experiments or investigations. This analysis helps determine if the results support or reject the hypothesis.

d. Conclusion - Draw a conclusion based on the analysis of the data. Evaluate whether the results support the hypothesis and discuss the implications and significance of the findings. The conclusion may also involve suggesting further research or revisions to the hypothesis.

The scientific method is a systematic approach used in scientific inquiry to investigate and understand the natural world. It allows researchers to gather evidence, test hypotheses, and draw reliable conclusions based on empirical data.

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Answer:

C or the triangles

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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Answer:

sorry i got to

Step-by-step explanation:

According to the statement Donald is using Stratified sampling to collects data from the sample.

The correct option is A.

A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.

The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.

When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.

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I understand that the question you are looking for is:

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

a. Systematic sampling

b. Convenience sampling

c. Stratified sampling

d. Cluster sampling

Answer:

x = -4

Step-by-step explanation:

3x - 2(3x - 2) = 16

3x - 6x + 4 = 16

-3x + 4 - 4 = 16 - 4

-3x = 12

(-3x)/(-1/3) = 12/(-1/3)

x = -4

Answer:

\({ \tt{3x - 2(3x - 2) = 16}} \\ { \tt{3x - 6x + 4 = 16}} \\ { \tt{ - 3x = 12}} \\ { \tt{x = - 4}}\)

Checking solution....!

\({ \tt{ 3x - 2(3x - 2) = 16}} \\ { \tt{3( - 4) - 2(3 \times - 4 - 2) = 16}} \\ { \tt{ - 12 + 28 = 16}} \\ { \tt{16 = 16}}\)

Since L.H.S = R.H.S, the solution is consistent

a) If the true rate of rejection is 10%, then the probability that the production will be suspended based on a sample of 15 bearings is 10%.

b)  The assumptions made in part a are that the sample of 15 bearings is representative of the population of bearings produced, and that each bearing is independent of the others.

To ensure that the production process is producing quality products, samples of 15 bearings are taken periodically and carefully inspected. If more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended for necessary adjustments.

a) If the true rate of rejection is 10%, what is the probability that the production will be suspended based on a sample of 15 bearings? To answer this question, we need to use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials. In this case, the number of trials is 15, and the probability of success (i.e., a bearing not meeting the required specifications) is 10%.

b) The assumptions allow us to use the binomial distribution to calculate the probability of having a certain number of bearings fail to meet the required specifications in a sample of 15. Additionally, we assume that the true rate of rejection is 10%, which may not always be the case.

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John will need 1728 4x4-inch shingles to cover the rectangular roof.

To calculate the number of 4x4-inch shingles needed to cover a roof measuring 12x16 feet, we need to convert the measurements to the same units.

Given that 1 foot is equal to 12 inches, we can convert the roof measurements as follows:

Length of the roof in inches: 12 feet × 12 inches/foot = 144 inches

Width of the roof in inches: 16 feet  12 inches/foot = 192 inches

Now, we can calculate the number of 4x4-inch shingles needed to cover the roof.

The area of one 4x4-inch shingle is 4 inches × 4 inches = 16 square inches.

To find the total number of shingles needed, we divide the total area of the roof by the area of one shingle:

Total number of shingles = (Length of the roof × Width of the roof) / Area of one shingle

Total number of shingles = (144 inches × 192 inches) / 16 square inches

Total number of shingles = 1728 shingles

Therefore, John will need 1728 4x4-inch shingles to cover the roof.

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Answer: I think

Step-by-step explanation:

The numbers greater than 1 and less than 0 cannot be a probability of any event.

Properties of probability. In words, this means that probability of an even must be a number between 0 and 1 (inclusive).

Input:

{F(x) = 3 x + 1, 1/f = x - 1/3 f(2)}

Result:

{F(x) = 3 x + 1, 1/f = x - f(2)/3}

Alternate forms:

{3 x + 1 = F(x), 3 x = f(2) + 3/f}

{F(x) = 3 x + 1, f(2) = 3 x - 3/f}

{F(x) = 3 x + 1, 1/f = 1/3 (3 x - f(2))}

Alternate form assuming f and x are positive:

{3 x + 1 = F(x), 3 f x = f(2) f + 3}

Answer:

3/4 = A

Step-by-step explanation:

-8+Ax(-8) - (-6)= -8 - 8A + 6

-3 + (-8)/2x4 = -3 -1= -4

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

-8 -8A + 6= -2(-4)

-8 + 8 +6=8A

6/8=A

3/4 = A

As describes in geometry the area of the rectangle = 288cm

what is geometry ?

The area of mathematics known as geometry is concerned with the characteristics of the surrounding space as well as the shapes of individual objects and their spatial relationships.

solution

radius of semicircle = 12

diameter will be = 24 and this is the length of rectangle s given in the question

area of the rectangle  = l*b

                                     = 24*12

area of the rectangle = 288cm

Hence the area of the rectangle = 288cm

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(a) The regular expression for the language L1 is ((a|b)(a|b))(a|b)*((a|b)(a|b))$^R$ Explanation: For a string to be in L1, it should have two characters of either a or b followed by any number of characters of a or b followed by two characters of either a or b in reverse order.

(b) The regular expression for the language L2 is (ab|ba)?((a|b)(ab|ba)?)*(a|b)?

For a string to be in L2, it should either have no consecutive a's and b's or it should have an a or b at the start and/or end, and in between, it should have a character followed by an ab or ba followed by an optional character.

(c) The regular expression for the language L3 is ((bb|a(bb)*a)(a|b)*)*|b(bb)*b(a|b)* Explanation: For a string to be in L3, it should either have n number of bb, where n is divisible by 3, or it should have bb at the start followed by any number of a's or b's, or it should have bb at the end preceded by any number of a's or b's.  In summary, we have provided the regular expressions for the given languages on the alphabet {a,b}.

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Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x  =  − 9 /25

Decimal Form:

x  =  − 0.36

I hope this helps! Have a great day!

Answer:

Y= -x-3

Step-by-step explanation:

17.7 gallons of gas would she require to travel 413 miles at this rate when Jenny used 9 gallons of gas to travel 210 miles.

Given that,

Jenny used 9 gallons of gas to travel 210 miles.

We have to find how many gallons of gas would she require to travel 413 miles at this rate.

We know that,

Jenny used 9 gallons of gas to travel 210 miles.

Then

Rate = 210 miles/9 gallons

= 23.3 miles/gallon.

So,

Nicole can achieve a fuel efficiency of 23.3 miles per gallon.

He has a 413-mile drive ahead of him.

So,

413/23.3 = 17.7 gallons needed.

Therefore, 17.7 gallons of gas would she require to travel 413 miles at this rate when Jenny used 9 gallons of gas to travel 210 miles.

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Answer:

45 degrees times StartFraction pi Over 180 degrees EndFraction

Answer:

Step-by-step explanation:

Initial value is x, current value is $13600, price reduction by 15%.

The figure is composed of 1 rectangle and 2 triangles.

Area 1: rectangle

Area of a rectangle:Length x width

Length : 6

width : 4

A1 = 6 x 4 = 24 ft2

Area 2: triangle

Area of a triangle: 1/2 x base x height

Base = (9-6)/2 = 1.5

heigth = 4

A2 = A3 = 1/2 x 1.5 x 4 = 3 ft2

Finally, add all the areas:

Area of the figure: A1 + A2 + A3 = 24 + 3 + 3 = 30ft2

Answer:

12

Step-by-step explanation:

\(\frac{1}{3}\) × 24 = 24 ÷ 3 = 8 ← stars studied from one week

24 - 8 = 16 left to study

\(\frac{1}{4}\) × 16 = 4 ← number studied in second week

number studied over the 2 weeks = 8 + 4 = 12

number left to study = 24 - 12 = 12

Answer:

Cos, a abreviation of cosine is used in trigonometry, and it represents the ratio of the hyptenuse and the adjacent side of a right triangle (a triangle with a right/90 degree angle). The formula for evaluating cosine/cos is the length of the adjacent side of the triangle divided by length of the hypotenuse of the triangle. To be clear, the hypotenuse is the side of the triangle the 90 degrees is facing, and the adjacent side is the side across the hypotenuse.

Step-by-step explanation:

Answer:

A trigonometric function that for an acute angle is the ratio between the leg adjacent to the angle when it is considered part of a right triangle and the hypotenuse.

What is cos law?

The cos law or cosine law defines the relationship between the sides and the angles of the triangle. This law is also known as the law of cosine or cosine rule. According to this law,

c2 = a2 + b2 − 2ab cos α

Where a, b and c are the sides of the triangle.

900Answer:900

Step-by-step explanation: