What is the pascal’s theory?

Answer:

-8 or 8

Step-by-step explanation:

We are given the absolute equation:

\(\displaystyle \large{4|x|=32}\)

First, divide both sides by 4 which leaves \(\displaystyle \large{|x|=8}\)

Absolute Value Definition

\(\displaystyle \large{|x|=\begin{cases} x \ \ \ (x\geq 0)\\ -x \ \ \ (x<0) \end{cases}}\)

So from |x| = 8, break into two intervals/conditions.

(1) when x ≥ 0

x = 8

(2) when x < 0

-x = 8

x = -8

From (1) and (2), the solution to 4|x| = 32 is 8 or -8

If the volume of a cylinder stays the same while the radius changes, the height of the cylinder must change inversely with the radius.

We have,

If the volume of a cylinder stays the same while the radius changes, the height of the cylinder must change inversely with the radius.

This means,

If the radius increases, the height must decrease to compensate and keep the volume constant.

If the radius decreases, the height must increase to compensate and maintain the same volume.

This relationship is due to the formula for the volume of a cylinder, which involves both the radius and the height.

By adjusting one variable (radius) while keeping the volume constant, the other variable (height) must change accordingly to maintain the balance.

Thus,

If the volume of a cylinder stays the same while the radius changes, the height of the cylinder must change inversely with the radius.

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Answer:

27/2

Step-by-step explanation:

Hope this helps! Also dont add comments to get gems like bruh ;-;

Answer: 27/2

Step-by-step explanation:

\(9\cdot \:1=x\frac{2}{3}\)

\(x\frac{2}{3}=9\cdot \:1\)

\(x\frac{2}{3}=9\)

\(3x\frac{2}{3}=9\cdot \:3\)

2x= 27

x= 27/2

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Therefore, the slope of the line passing through the points (0, 3) and (2, 6) is 3/2.

In mathematics, the slope refers to the measure of steepness or inclination of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those points. In other words, the slope of a line is the change in y divided by the change in x between any two points on that line. The slope can be positive, negative, or zero, and it determines the direction and the steepness of the line. The slope is an important concept in algebra, geometry, and calculus, and it is used to describe many real-world phenomena, such as the velocity of an object, the rate of change of a function, and the growth or decline of a population.

Here,

To find the slope of the line passing through the points (0, 3) and (2, 6), we can use the formula:

slope = (change in y) / (change in x)

So, we have:

slope = (6 - 3) / (2 - 0)

slope = 3 / 2

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The expression is equivalent to the value of the nth term in the pattern is aₙ = 5n - 1. Then the correct option is A.

Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first 5 terms of a number pattern are shown below.

4, 9, 14, 19, 24

The first term of the sequence is 4 and the common difference between the terms is given as,

d = 9 - 4

d = 5

The expression is equivalent to the value of the nth term in the pattern and will be

aₙ = 4 + (n - 1) x 5

aₙ = 4 + 5n - 5

aₙ = 5n - 1

The expression is equivalent to the value of the nth term in the pattern is aₙ = 5n - 1. Then the correct option is A.

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Answer:

The radius of Cylinder A measures 7 feet.

The radius of Cylinder B measures 2.8 feet.

Step-by-step explanation:

The radius of Cylinder A measures 7 feet.

because the radious is half of the diameter and 14 is the diameter

The radius of Cylinder B measures 2.8 feet.

Answer:

Cylinder A's radius is 7 because the radius is diameter divided by 2.

Cylinder B's radius is 2.8 because the height of Cylinder A is 5 times bigger than Cylinder B's height.

Step-by-step explanation:

Answer:

Step-by-step explanation:

we should divide it by 3 to get a perfect square .and the square root of the perfect square is 49

\(\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\begin{gathered} \begin{array}{c|c} \underline{\sf{3}}& {\sf{ \underline{ \pink{7203} \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \underline{\sf{7}}&{\sf{ \underline{2401 \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{7}}&{\sf{ \underline{343 \: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{7}}&{\sf{ \underline{49\: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{7}}&{\sf{ \underline{7 \: \: \: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{}}&{\sf{ 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \end{array}\end{gathered}\end{gathered}\)

\(\qquad\)\(\purple{ \bf\longrightarrow 7203 = 3 \times 7 \times 7 \times 7 \times 7} \)

____________________________________________

Given :

P(-9, -4), Q(-7, -1), R(-2, 5), S(-6, -1).

To Find :

The slope of line PQ.

Solution :

We know , slope is given by :

\(m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{-9-(-7)}{-4-(-1)}\\\\m=\dfrac{2}{3}\)

Therefore, the slope of line PQ is 2/3.

Hence, this is the required solution.

Answer:

The answer is below

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by the formula:

\(z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mean,\ \sigma=standard\ deviation.\\\\For \ a\ sample\ size(n):\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }\)

Therefore given that μ = $85900, σ = $11000, n = 35.

For x > 70000:

\(z=\frac{x-\mu}{\sigma/\sqrt{n} } =\frac{70000-85900}{11000/\sqrt{35} } =-8.55\\\)

For x < 100000

\(z=\frac{x-\mu}{\sigma/\sqrt{n} } =\frac{100000-85900}{11000/\sqrt{35} } =7.58\)

From the normal distribution table, P(70000< x < 100000) = P(-8.55 < z < 7.58) = P(z < 7.58) - P(z < -8.55) = 1 - 0 = 1 = 100%

Answer:

Answer is C...........................

Step-by-step explanation:

Answer:

C.) y = -2x

Step-by-step explanation:

To solve for y, u gotta divide both sides by -2 to get y by itself. When u do that, u get -2x.

Answer:

∠ 1 = 62° , ∠ 2 = 118°

Step-by-step explanation:

the angles are a linear pair and sum to 180° , so

2x + x + 87 = 180

3x + 87 = 180 ( subtract 87 from both sides )

3x = 93 ( divide both sides by 3 )

x = 31

then

∠ 1 = 2x = 2 × 31 = 62°

∠ 2 = x + 87 = 31 + 87 = 118°

The correct expansion of (3x – 2)(2\(x^2\) + 5) is 3x • 2\(x^2\) + 3x • 5 + (–2) • 2\(x^2\) + (–2) • 5. Thus, option A is the right answer to the given question.

To expand an expression of multiplication of two variables to two variables is done as follows:

1. We take the first term of the first expression which in this case is 3x

2. We multiply it by the first term of the second expression. In this case, we get 3x • 2\(x^2\).

3. Subsequently we multiply the first term with further terms and add them. In the given case, the expression we get is 3x • 2\(x^2\) + 3x • 5

4. Then we take the second term of the first expression and repeat the above steps and add it to the existing equation.

We get x • 2\(x^2\) + 3x • 5 + (–2) • 2\(x^2\) + (–2) • 5 as the answer.

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Answer:

The statement that is FALSE is b) "The area is 26ft²".

Answer:

-1

Step-by-step explanation:

We have 2 letters, x and y. what letter is in all of them? none of them. that means the HCF can't contain a letter. let's take away the letters, we have 12, -4, 15, -5. Since -5 is a prime number. the answer is -1

The Hamming distance metric is the best metric for describing how far apart two binary vectors of the same length are. The reason for this is that the Hamming distance is a measure of the difference between two strings of the same length.

Its value is the number of positions in which two corresponding symbols differ.To compute the Hamming distance, two binary strings of the same length are compared by comparing their corresponding symbols at each position and counting the number of positions at which they differ.

The Hamming distance is used in error-correcting codes, cryptography, and other applications. Therefore, the Hamming distance metric is the best for this particular question.

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Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

90.24 divided by 6.3

Step-by-step explanation:

For reaching to the answer, we have to test each of the options given

The first option says that the divisor and dividend is 90.24 and dividend is 6.3

Now if we rounded it

So it would be 90 and 6

So, the quotient is

= 90 ÷ 6

= 15

Hence, the first option is correct

i.e. 90.24 divided by 6.3

And, all the other options are wrong

Answer:

NR = 12

Step-by-step explanation:

Given that both trjangles are similar, therefore, it follows that their corresponding side lengths would be proportional to each other. Thus:

\( \frac{40}{8} = \frac{60}{2x - 2} \)

\( 5 = \frac{60}{2x - 2} \)

Cross multiply

\( 5(2x - 2) = 60 \)

\( 10x - 10 = 60 \)

\( 10x = 60 + 10 \) (addition property of equality)

\( 10x = 70 \)

Divide both sides by 10

x = 7

✔️NR = 2x - 2

Plug in the value of x

NR = 2(7) - 2 = 14 - 2

NR = 12

Most data is likely to be skewed following a particular trait because when considering real life data, it is likely that it may concentrate on one end of the values on the real line as there is high uncertainty that exists with real life.

There is very little confidence that the population would behave in expected ways.

The skewed distribution implies the distribution that is not symmetrical. If a distribution is skewed it can be skewed to the left i.e. mean lies to the left of the center or skewed to the right i.e. mean lies to the right of the center of the distribution.

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Given that the parent function, y = x², has a leading coefficient of 1, the

following are the comparisons of the equations with the parent functions;

\(\begin{array}{|c|cc|}Steeper \, than \, y = x^2&&Less \, Steep \ than \, y = x^2 \\y = 2 \cdot x^2&&y = \frac{1}{2} \cdot x^2 \\y = \left(2 \cdot x \right)^2&&y = \left(\frac{1}{2} \cdot x \right)^2 \end{array}\right]\)

The parent function is y = x²

The leading coefficient of the parent function = 1

The steepness of a quadratic equation is given by the value of the

leading coefficient.

When the leading coefficient is larger than 1, we have;

The function is steeper than y = x²

When the leading coefficient is a fraction larger than 0 but lesser than 1, we have;

The function is less steep than y = x²

Which gives;

\(\begin{array}{|c|cc|}Steeper \, than \, y = x^2&&Less \, Steep \ than \, y = x^2 \\y = 2 \cdot x^2&&y = \frac{1}{2} \cdot x^2 \\y = \left(2 \cdot x \right)^2&&y = \left(\frac{1}{2} \cdot x \right)^2 \end{array}\right]\)

The function y = -x² is inverted has the same steepness as y = x², but will not be used.

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The nth derivative of y = sin(x)cos(x) is dⁿy/dxⁿ = (-1)^(n+1) * n! * sin(x)cos(x)

To find the nth derivative of y = sin(x)cos(x), we can use the product rule and the chain rule repeatedly. Let's go through the process step by step.

The given function is y = sin(x)cos(x).

First, let's find the first derivative (n = 1):

dy/dx = (cos(x)cos(x)) + (sin(x)(-sin(x)))

= cos^2(x) - sin^2(x)

Now, let's find the second derivative (n = 2):

d²y/dx² = d/dx[cos^2(x) - sin^2(x)]

= d/dx[cos^2(x)] - d/dx[sin^2(x)]

To find the derivative of cos^2(x), we can apply the chain rule:

d/dx[cos^2(x)] = 2cos(x)(-sin(x)) = -2sin(x)cos(x)

To find the derivative of sin^2(x), we can again apply the chain rule:

d/dx[sin^2(x)] = 2sin(x)cos(x)

Substituting these results back into the second derivative expression:

d²y/dx² = -2sin(x)cos(x) - 2sin(x)cos(x)

= -4sin(x)cos(x)

We can continue this process to find higher-order derivatives by differentiating the expression obtained for the (n-1)th derivative.

In summary, the nth derivative of y = sin(x)cos(x) is given by:

dⁿy/dxⁿ = (-1)^(n+1) * n! * sin(x)cos(x)

Note that the alternating signs (-1)^(n+1) arise due to the repeated application of the product rule.

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Answer:

The answer is D

Step-by-step explanation:

Because we don't know whether the molecules are a solid, liquid or a gas

We don't know which element the molecules are part of

And we don't know which sugar it is/phosphate.

Hope that helps?

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

There are 4²⁴ possible ways to complete the multiple-choice test consisting of 24 questions, with each question having four possible answers.

We have 24 questions with each having 4 possible outcomes. If we had a question, then we would have 4 ways of answering question 1 and for each of the four answers in question 1, we would have four ways of answering question 2. So, we have 4² ways of answering the questions.

Like this, we have 24 questions. There are four ways to choose an answer to each question. By counting principle, we multiply the number of choices at each step and then we have -

= 4×4×4×4...= 4²⁴ ways to complete the test

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Answer

Your saviour has come!

The answer is A

Step-by-step explanation:

The conclusion that regular exercise leads to weight loss, based solely on the results of a survey, may have several potential flaws.

It is important to consider potential issues with the conclusion drawn from the survey results. First, the survey itself may suffer from limitations such as sampling bias or self-reporting biases. The sample of participants in the survey may not be representative of the general population, leading to inaccurate or skewed results. Additionally, relying on self-reported data about exercise and weight loss introduces the possibility of response bias or inaccuracies in reporting.

Other factors, such as dietary habits, genetics, or underlying health conditions, could contribute to weight loss alongside exercise. Without controlling for these factors or conducting a more rigorous study design, it is challenging to establish a direct causal relationship between regular exercise and weight loss.

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Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Answer:

\(\sf\longmapsto \: 550\)

Step-by-step explanation:

\(\sf\longmapsto \: 50 \times 11\)

\(\sf\longmapsto \: 550\)

Answer:

\(\sf 550\)

Step-by-step explanation:

\(10 \times 5 = 50 \\ \)

\(50 \times 11 = 550\)

Answer:

x = 5

Step-by-step explanation:

\(\frac{x-2}{x+1}\) = \(\frac{1}{2}\) ( cross- multiply )

2(x - 2) = x + 1 ← distribute parenthesis on left side by 2

2x - 4 = x + 1 ( subtract x from both sides )

x - 4 = 1 ( add 4 to both sides )

x = 5