Math is multi-cultural, analytical, timeless and hands-on. Provide a piece of mathematical concept, hypothesis, law, paradox, rule or theorem to prove this statement.

To convert the given infix expression a+bc/2 - (ac - 3/b) into postfix notation, we will use a stack to store and manage operators. Here's the step-by-step process:

1. Start scanning the expression from left to right.
2. If an operand (a, b, c, 2, or 3) is encountered, append it to the output.
3. If an operator (+, -, *, or /) is encountered, push it onto the stack if it's empty or if the operator at the top of the stack has a lower precedence. Otherwise, pop operators from the stack and append them to the output until the stack is empty or the operator at the top of the stack has a lower precedence. Then, push the current operator onto the stack.
4. If an open parenthesis '(' is encountered, push it onto the stack.
5. If a close parenthesis ')' is encountered, pop operators from the stack and append them to the output until an open parenthesis '(' is encountered. Pop the open parenthesis but do not append it to the output.
6. After scanning the entire expression, if there are still operators in the stack, pop them and append them to the output.

Applying these rules, we get the following postfix expression:

a b c * 2 / + a c * 3 b / - -

Here's the evolution of the stack during each step:

1. Push '+'
2. Push '*', pop '+' (higher precedence), push '+'
3. Push '/'
4. Pop '*', pop '/', push '-'
5. Push '*', pop '-' (higher precedence), push '-'
6. Push '/'
7. Pop '*', pop '/', pop '+', pop '-'

The resulting postfix expression is: a b c * 2 / + a c * 3 b / - -

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Answer:

The one farthest to the right, graph A.

Step-by-step explanation:

Answer: 4000

Step-by-step explanation: 4280 rounded (down) to the nearest 1000 is 4000.

Answer:

23000

Step-by-step explanation:

Answer:

4x-6

Step-by-step explanation:

2(2x) - 2(3)

4x-6

The upward unit normal to the surface 7cosθ = 10−13 at (9, θ, 0) is (-7√3/13, 0, 2√3/13).

To find the upward unit normal to the given surface, we need to determine the gradient vector of the surface at the specified point. The gradient vector represents the direction of the steepest ascent on the surface.

First, we rewrite the equation of the surface as cosθ = (10−13)/7. Taking the derivative of both sides with respect to θ, we get -sinθ = 0. Rearranging, we have sinθ = 0, which implies θ = 0 or π.

Since we are interested in the point (9, θ, 0), we consider the case when θ = 0. Plugging this value into the equation, we have cos(0) = (10−13)/7, which simplifies to cos(0) = -3/7.

The gradient vector at the point (9, 0, 0) is (-7√3/13, 0, 2√3/13). This vector represents the direction of the upward unit normal to the surface at that point.

Therefore, the upward unit normal to the surface 7cosθ = 10−13 at (9, θ, 0) is (-7√3/13, 0, 2√3/13).

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Answer:

No statements are included in the question.  Several observations are noted.

Step-by-step explanation:

y = 6x + 2

y = 6x + 1

y=mx+b is the equation for a straight line, where m is the slope and b the y-intercept.  

Observations

1.  These are both straight lines.

2.  The slopes are both the same:  +6.  The lines are parallel.

3.  Since they are parallel, they will never intersect (within the solar system)

4.  The second line is one unit lower than the first:  it's y-intercept is +1, comapared to +2 for the first.

5.  Since they do not intercept, there is no solution for this system of equations.

These will likely match some of the statements.

Expressions 2(-3)(7), -2(27 ÷ 9), and (4 - 10) - (8 ÷ (-2)) all have negative values.

The expressions that have negative values are:

1. 2(-3)(7)
2. -2(27 ÷ 9)
3. (4 - 10) - (8 ÷ (-2))

Let's break down each expression to understand why they have negative values.

1. 2(-3)(7):

  - First, we multiply -3 and 7, which gives us -21.
  - Then, we multiply 2 and -21, which gives us -42.
  - Therefore, the expression 2(-3)(7) has a negative value of -42.

2. -2(27 ÷ 9):

  - We start by calculating 27 ÷ 9, which equals 3.
  - Then, we multiply -2 and 3, which gives us -6.
  - Hence, the expression -2(27 ÷ 9) has a negative value of -6.

3. (4 - 10) - (8 ÷ (-2)):

  - Inside the parentheses, we have 4 - 10, which equals -6.
  - Next, we have 8 ÷ (-2), which equals -4.
  - Finally, we subtract -4 from -6, which gives us -6 - (-4) = -6 + 4 = -2.
  - Thus, the expression (4 - 10) - (8 ÷ (-2)) has a negative value of -2.

To summarize, the expressions 2(-3)(7), -2(27 ÷ 9), and (4 - 10) - (8 ÷ (-2)) all have negative values.

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Answer:

The answer to the question provided is possibly 2.

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2\)

Answer:

v = 12

Step-by-step explanation:

to solve this equation you must first multiply 4 to both sides

9 * 4 = 3/4v * 4

36 = 3v

now divide 3 to both sides

36 / 3 = 3v / 3

12 = v

flip it

v = 12

that is your answer

Answer:

They are similar because the smaller right triangle has simply been dialted. All of the angles remain the same which is how you know they are similar.

Step-by-step -

Both the shape and angles are the same on both triangles.

Answer:

(a) The best answer for residuals plot (a) is:

A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

A fanned pattern in the residuals plot suggests that the linear model is not appropriate because the variability of the residuals increases as the values of the explanatory variable increases. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.

(b) The best answer for residuals plot (b) is:

B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear.

A curved pattern in the residuals plot suggests that the linear model is not appropriate because the relationship between the variables is not linear. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.

Answer:

3 necklaces

Step-by-step explanation:

$40.50-$30.00=$10.50   Subtract her total money and cost of dress

$10.50-$3.50=$6.00  subtract each necklace price from remaining money

$6.00-$3.50=$3.50 keep subtracting price of necklace

$3.50-$3.50=$0  that was 3 necklaces

Answer:

a = -10

r = 4/5

Step-by-step explanation:

formula

nth term = ar^n

a1 -a2 = 2

a(1-r)= 2

(1-r) = 2/a

a/(1-r) = 50

a = 50(1-r)

replace the value of (1-r) with 2/a

a = 50(2/a)

a = 100/a

a^2 = 100

a = \(\sqrt{100}\)

a = ± 10

a(1-r)= 2

10(1-r) = 2

1-r = 2/10

1 - r = 1/5

1 + 1/5 = r

r = 4/5

10*4/5 = 8

10 , 8 , 32/5......

since it states that the second term exceeds by two... this means that the second term has to be greater than the first

Hence:

a = -10

meaning the sequence becomes:

-10 , -8 , -32/5

a = -10

r = 4/5

In the given trapezoid, The expression for b in terms of A and a is b = (2A - ah)/h.

In a trapezoid, the bases are the parallel sides, and the height is the perpendicular distance between the bases. The formula to calculate the area of a trapezoid is A = (a + b)/2 * h, where A represents the area, a and b are the lengths of the bases, and h is the height. The question asks us to express b in terms of A and a.

To do that, we can rearrange the formula for the area to solve for b. Multiply both sides of the formula by 2 and divide by h to isolate (a + b):

2A = (a + b) * h.

Next, we distribute the h to both terms on the right side:

2A = ah + bh.

Now, subtract ah from both sides:

2A - ah = bh.

Finally, divide both sides by h to solve for b:

b = (2A - ah)/h.

In a trapezoid, the area is calculated using the formula A = (a + b)/2 * h, where A represents the area, a and b are the lengths of the bases, and h is the height. To express b in terms of A and a, we can rearrange the formula by isolating b. By multiplying both sides of the equation by 2 and dividing by h, we obtain 2A = (a + b) * h. Next, we distribute the h to both terms on the right side to get 2A = ah + bh. We then subtract ah from both sides to yield 2A - ah = bh. Finally, dividing both sides by h allows us to solve for b, resulting in the expression b = (2A - ah)/h.

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We know that 6x(-7) is -42 and we also know that 6+(-7) is -1.

So we can write

\(x^2+6x-7x-42\)

\(x(x+6)-7(x+6)\)

\((x-7)(x+6)\)

So our solutions are \(x=7,-6\)

let age of 6th person is x

sum of x = 14+24+24+20+24+x

= 106 + x

N = 6

mean = 21

now,

\(mean = \frac{sum \: of \: x }{n} \\ 21 = \frac{106 + x}{6} \)

\(126 = 106 + x\)

\(x = 20\)

Answer:

A, y = x

Step-by-step explanation:

Slope is equal to one

Y-intercept is origin

Answer:

A.) Y=X

Step-by-step explanation:

It intercepts with origin

The number 8 is the initial amount of gallon of gas in the car before the trip started.

Linear equation are equation in which the highest power of the variable is equals to 1.

Therefore, the equation for Michael driving on a long road trip is as follows:

where

g = number of gallons

h = time in hours

The representation of 8 is as follows;

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The double integral of 5x cos y over the region D bounded by y = 0, y = x², and x = 7 can be evaluated as follows:

∬D 5x cos y dA = ∫₀⁷ ∫₀ˣ² 5x cos y dy dx

To evaluate the double integral ∬D 5x cos y dA, we first need to set up the limits of integration for the variables x and y based on the given bounds.

The region D is bounded by y = 0, y = x², and x = 7. This means that y ranges from 0 to x², and x ranges from 0 to 7.

Therefore, the double integral can be written as:

∬D 5x cos y dA = ∫₀⁷ ∫₀ˣ² 5x cos y dy dx

.

To evaluate this integral, we first integrate with respect to y from 0 to x², and then integrate the resulting expression with respect to x from 0 to 7.

Performing the integration will yield the final numerical value of the double integral.

Note: The solution provided above sets up the integral for evaluation, but the actual calculation of the integral involves further mathematical operations.

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Answer:-12x

Step-by-step explanation:

just trust me on this

Answer:

The answer is B.

Step-by-step explanation:

Let us first set up an equation.

(3x - 7) + (2x + 3) = 90

5x - 4 = 90

5x = 94

x = 18.8

Hope this helps!

Please mark as brainliest.

Answer:

D  m<A = 49.4 deg

Step-by-step explanation:

Since the lines are perpendicular, the sum of the measures of angles A and B is 90 deg.

m<A + m<B = 90

3x - 7 + 2x + 3 = 90

5x - 4 = 90

5x = 94

x = 18.8

m<A = 3x - 7 = 3(18.8) - 7 = 56.4 - 7 = 49.4

Answer: D  m<A = 49.4 deg

The probability that X is greater than 145.28 is approximately 0.0465.

Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Answer:

1, 5, 25

Step-by-step explanation:

1x25=25

5x5=25

The probability that the sample average falls outside the 3-sigma control limits of the X-bar chart is 0.27%.

The 3-sigma control limits are calculated using the standard deviation of the process. If the process is in control, then 99.73% of the sample averages will fall within the 3-sigma control limits. The remaining 0.27% of the sample averages will fall outside the control limits.

In this case, the sample size is 4, which is smaller than the sample size of 9 that was used to construct the control chart. This means that the control limits for the sample of size 4 will be narrower than the control limits for the sample of size 9.

As a result, the probability that the sample average falls outside the control limits will be higher for the sample of size 4.

Specifically, the probability that the sample average falls outside the 3-sigma control limits for a sample of size 4 is 0.27%. This means that there is a 0.27% chance that the new employee will observe a sample average that falls outside the control limits, even if the process is in control.

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The change in momentum is 22120Ns

The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. This applied force can increase or decrease the momentum or even change the object's direction.

Therefore the change in momentum = Final momentum - initial momentum

i.e mv -mu

where m is the mass

v is the final velocity

u is the initial velocity

The change of momentum is also called impulse. impulse is the product of the force and the time in applying it.

Change in momentum = force × time

= 2800× 7.90

= 22120 Ns

Therefore the change in momentum of the car is 22120Ns

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The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of "P-Value."

A null hypothesis is a sort of statistical hypothesis which asserts that there is no statistical significance in a particular set of observations.

Using sample data, hypothesis testing is performed to determine the believability of a theory. It really is expressed as H0 and is also known to simply as "null."

Some key features regarding null hypothesis are-

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Answer:

\(-\frac{3}{2}\)

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Answer:

Step-by-step explanation:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. y=6 is a straight line perpendicular to the y-axis at point (0,6) , which means that the range is a set of one value {6} .

Given question:

To find the value of y, we will follow the steps below

Step 1: make y the subject of the formula

Step 2: substitute the value of x=-2 into the expression above

Step 3: Divide both sides by 7

Thus, the value of y is: