A certain mass of sugar can be divided into equal heaps. Each heap contains either 27g, 45g, 30g, or 20g. Find the smallest mass of sugar for which is possible

The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer:

4, 6, and 475

Step-by-step explanation:

See attached image.

The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

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Answer:

To make only 12% profit, the discount should be increased to 16%

Step-by-step explanation:

The given information are;

The percentage discount on goods = 10%

The profit made from the sale of the watch = 20%

The amount the watch was sold = Rs.10,710

The percentage VAT included = 13%

Let the recommended selling price of the watch = X

Therefore, we have;

The price after 10% discount = 0.9×X

Which gives;

The amount the watch was sold = Price after 10% discount + Price after 10% discount ×VAT

The amount the watch was sold = 0.9×X + 0.9×X×13% = 0.9×X + 0.9×X×0.13

Rs.10,710 = 0.9×X + 0.9×X×0.13 = 1.017×X

X = Rs.10,170/1.017 = Rs. 10,000

The recommended selling price of the watch = Rs. 10,000

The profit was 20% of selling price which gives;

Profit = Selling price - Cost price = Rs. 9,000  - Rs. X = 0.2 × Rs. X

9000 - X = 0.2×X

9000 = X + 0.2×X  = 1.2×X

X = 9000/1.2 = Rs. 7,500

To make only 12% profit, we have;

12% of Rs. 7,500 = 0.12 × Rs.7,500 = Rs. 900

Selling price = Cost price + Profit = Rs. 7,500 + Rs. 900 = Rs. 8,400

Percentage discount from Rs.10,000 to get Rs. 8,400 is given as follows;

Percentage discount = Y%

Therefore;

Y = (10,000 - 8,400)/10000 × 100 = 0.16 × 100 = 16%

Y = 16%

Therefore, to make only 12% profit, the discount should be increased to 16%.

Therefore, the maximum capacity of the cylindrical water tank is approximately 58904.52 cubic meters when rounded to the nearest hundredth.

To find the maximum capacity of the cylindrical water tank, we need to calculate its volume. The volume of a cylinder can be determined using the formula:

Volume = π * radius^2 * height

Given that the tank has a diameter of 50 meters, the radius would be half of that, which is 25 meters. The height of the tank is 30 meters.

Plugging these values into the formula:

Volume = π * (25)^2 * 30

Calculating the volume:

Volume ≈ 3.14159 * 25^2 * 30

Volume ≈ 3.14159 * 625 * 30

Volume ≈ 3.14159 * 18750

Volume ≈ 58904.52

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The probability that Melinda will be able to make an integer between 10 and 20 (inclusive) is 1/6.

The probability that Melinda will be able to make an integer between 10 and 20 (inclusive) with the two numbers she rolls can be calculated by determining the number of favorable outcomes and dividing it by the total number of possible outcomes.

To find the number of favorable outcomes, we need to identify the combinations of two numbers that will result in a two-digit number between 10 and 20. We can list these combinations as follows:

11, 12, 13, 14, 15, 16

Notice that we only have six favorable outcomes.

Now, let's determine the total number of possible outcomes when rolling two six-sided dice. Each die has six possible outcomes (1, 2, 3, 4, 5, 6), so the total number of outcomes is 6 multiplied by 6, which equals 36.

To calculate the probability, we divide the number of favorable outcomes (6) by the total number of possible outcomes (36):

Probability = Favorable outcomes / Total outcomes
Probability = 6 / 36
Probability = 1 / 6

Therefore, the probability that Melinda will be able to make an integer between 10 and 20 (inclusive) is 1/6.

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The correct answer is A. True

A linear equation represents a line in the xy-plane. In the form of y = mx + b, where m is the slope and b is the y-intercept, a linear equation defines a straight line relationship between x and y. Each x value corresponds to a unique y value on the line.

By plotting the points that satisfy the equation, a line can be formed. The slope determines the steepness or direction of the line, while the y-intercept represents the point where the line intersects the y-axis.

Therefore, a linear equation does determine a line in the xy-plane.

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True. A linear equation determines a line in the xy-plane.

A linear equation is an equation that describes a straight line in the xy-plane. It is an equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. The slope-intercept form of a linear equation is commonly used to graph lines.

The equation y = mx + b shows that for every value of x, there is a corresponding value of y that lies on the line. The slope, m, determines the steepness of the line, while the y-intercept, b, represents the point where the line crosses the y-axis.

Therefore, it is true that a linear equation determines a line in the xy-plane.

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13 is the inequality so that it represents the whole-number values.

What is Triangle Inequality Theorem?

Triangle inequality, in Euclidean figure, theorem that the sum of any two sides of a triangle is lesser than or equal to the third side; in symbols, a b ≥ c. In substance, the theorem states that the shortest distance between two points is a straight line.

the Triangle Inequality Theorem, which states that

the sum of the lengths of two sides of a triangle must always be greater than the length of the third side

      a = c + b

         = 7 + 6

         = 13

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The rate of falling temperature is 5 1/3 degrees per hour.

What do you mean by the rate of temperature?

This indicates the sensitivity of the reaction to change in temperature.

Given that;

The temperature fell 4 degrees in 3/4 of an hour.

So, we can set up a proportion to see how much temperature fell in an hour,

\(\frac{4}{3/4} = \frac{x}{1}\)

4 /0.75 = x

x = 5 1/3

Hence, The rate of falling temperature is 5 1/3 degrees per hour.

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Answer:

Coordinate of A: -9

Coordinate of Q: 9

Step-by-step explanation:

1 - 10 = -9

1 + 8 = 9

Answer:

y8x122

Step-by-step explanation:

Simplify this expression.

a. The number of choices possible for each digit of the code is of: 10.

b. The total number of 4-digit passwords that Jess can create is of: 10,000.

c. The number of different ways to create even passwords is of: 5,000.

The Fundamental Counting Theorem states that if there are n independent trials, each with \(n_1, n_2, \cdots, n_n\) possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial, according to the rule presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

Each digit can be between 0 and 9 inclusive, hence the number of outcomes possible for each digit of the password is given as follows:

10.

The password is composed of four digits, hence the total number of passwords possible is of:

N = 10 x 10 x 10 x 10 = 10,000.

Considering that Jess would like an even number, there are only five outcomes possible for the last digit (0, 2, 4, 6 or 8), hence the number of outcomes is of:

N = 10 x 10 x 10 x 5 = 5,000.

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Hey there!

44(4 - 7)(4)

= 44(-3)(4)

= -132(4)

= -528

Therefore, your answer is: -528

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The expression or equation that correctly represents the situation given is y = 2x.

Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:

Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.

Note: This question is incomplete; below I attach the missing information:

Write an equation to represent this relationship:

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We can write the second linearly independent solution y2 as y2 = (C1x +C2) * e^(-x).

The general solution to the given differential equation is the linear combination of y1 and y2: y(x) = C3 * e^(-x) + (C1x + C2) * e^(-x), where C1, C2, and C3 are constants

To find a second linearly independent solution using the method of reduction of order, follow these steps:

1. Since y1 = e^(-x) is a given solution, we assume a second solution y2 = v(x) * e^(-x), where v(x) is an unknown function.
2. Compute the first derivative: y2' = (v'(x) - v(x)) * e^(-x).
3. Compute the second derivative: y2'' = (v''(x) - 2v'(x) + v(x)) * e^(-x).
4. Substitute y2, y2', and y2'' into the differential equation: (v''(x) - 2v'(x) + v(x)) * e^(-x) + 2(v'(x) - v(x)) * e^(-x) + v(x) * e^(-x) = 0.
5. Since e^(-x) is never 0, we can divide the equation by e^(-x) to get: v''(x) - 2v'(x) + v(x) + 2v'(x) - 2v(x) + v(x) = 0.
6. Simplify the equation: v''(x) = 0.
7. Integrate twice to find v(x): v'(x) = C1 and v(x) = C1x + C2, where C1 and C2 are constants.
8. Now, we can write the second linearly independent solution y2 as y2 = (C1x + C2) * e^(-x).

The general solution to the given differential equation is the linear combination of y1 and y2:

y(x) = C3 * e^(-x) + (C1x + C2) * e^(-x), where C1, C2, and C3 are constants.

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Answer:

The value of p is 10

Step-by-step explanation:

Here, we are told that the midpoint of the segment AC is B. What this means is that, applying the midpoint formula on AC would give the coordinates of B.

Mathematically;

(x,y) = {(x1 + x2)/2, (y1 + y2)/2}

(2,3) = (p -6)/2 , (7-1)/2

equating identities;

(p-6)/2 = 2

p-6 = 2 * 2

p-6 = 4

p = 4 + 6

p = 10

The value of p as described in the question is; 10

Since the point B, with coordinates (2,3) is the midpoint of the line segment AC.

Therefore, the x-coordinate of point B (2) is the midpoint of the x-coordinate of point A and C.

The value of p can then be evaluated as follows;

By Cross-product; we have;

The value of p is therefore; 10

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The factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Given

5x³ + 20x³ + 2x +8 is a polynomial.

The factor of the polynomial.

5x³ + 20x³ + 2x +8 is a polynomial.

Take common, we get

5x²(x + 4) + 2(x + 4)

(5x² + 2) (x + 4)

[(x√5)² - (i√2)](x + 4)

(√5x - i√2)(√5x + i√2)(x + 4)

Thus, the factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).

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Answer:

> Option D, or (5x2 + 2) (x + 4), is the correct choice.

Step-by-step explanation:

> This is the only correct answer choice for this equation.

Answer:

  a.  31.4 inches

  b.  314 square inches

Step-by-step explanation:

You want to know the circumference of a pillow with a radius of 5 inches, and the area if the radius doubles.

The formula for the circumference of a circle is ...

  C = 2πr

For a radius of 5 inches, the circumference is about ...

  C ≈ 2(3.14)(5 in) = 31.4 in

Jasmine will need about 31.4 inches of fringe.

The formula for the are of a circle is ...

  A =  πr²

If the 5-in radius is doubled, it becomes 10 in, and the area becomes ...

  A = π(10 in)² = 100π in² ≈ 314 in²

The area of the top of the pillow would be about 314 square inches.

Answer:

he swims 0.9 kilometers each day.

Step-by-step explanation:

Answer:

He swims 0.9km each day.

Step-by-step explanation:

To convert m to km divide by 1000

900/1000 =0.9

Answer:

$11.40 per dozen

Step-by-step explanation:

there are 2 ways to do this. the simpler way to do it is to multiply 2.85 times  4 because you are adding the price of 3 muffins 4 times. another way is to find the unit rate of 1 muffin which is $0.95 per muffin, then multiply that by 12. hope this helps. also brainliest pls:)

Main Answer: A normalized binary number typically consists of three parts:

Supporting Question and Answer:

What is a sign bit in a normalized binary number?

The sign bit is the leftmost bit of a normalized binary number and indicates whether the number is positive or negative .A value of 0 indicates a positive number, while a value of 1 indicates a negative number.

Body of the Solution: A normalized binary number typically consists of  the following three parts:

Final Answer: A normalized binary number typically consists of three parts:

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Answer:

A. 5/2

Step-by-step explanation:

Can't be c or d since those are negative and b would have a much steeper slope rise over run is how you find side the two points connect by going up 5 and over 2

Critics claim that supermarkets tend to put sugary kids' cereals on lower shelves where kids can see them. The question asks if the data from a study support this claim.

To answer this question, we would need to review the data from the study. Unfortunately, you did not provide any information about the study or the data collected. Therefore, without knowing the specifics of the study, it is not possible to determine whether the data supports or refutes the claim made by the critics.

To assess whether supermarkets tend to put sugary kids' cereals on lower shelves, it would be necessary to examine specific research studies or data related to this claim.

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The example of using blocking to emphasize dialogue and emotion is multiple characters grouped into small clumps around the stage. Therefore, the correct option is option 4.

This type of blocking creates a sense of intimacy and intensity as the characters are physically close to each other, emphasizing the emotional content of their dialogue. It also allows for individual characters to have their own space and focus, creating a sense of hierarchy and importance within the scene.

In contrast, the other options do not specifically use blocking to emphasize dialogue and emotion. Finding Nemo swimming closer to the screen during his monologue is simply a camera technique, while Donnie Darko walking during a scene and all of the characters on stage traveling in a clockwise pattern throughout the scene are examples of movement blocking, which may or may not emphasize dialogue and emotion depending on the context.

Therefore, the correct answer is option 4.

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Answer:

Change the value of years to months.

Step-by-step explanation:

Western Beach: f(x) = -2x + 100

Dunes Beach: g(x) = 5x + 20

1 Year = 12 Months

Months will make the width interception more accurate.

Answer:

Instead of years, use a more specific unit such as months or weeks to measure the time.

The measure of the angle PRS is given as follows:

m<PRS = 45º.

As stated in this problem, these following angles are given:

MRQ and and QRN form a ray, hence they are supplementary angles.

For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:

142 + x = 180

x = 180 - 142

x = 38º.

The entire diagram forms an angle of 360º, hence:

142 + 38 + 90 + m<MRS = 360º.

270 + m<MRS = 360º

m<MRS = 90º.

The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:

The diagram is given by the image at the end of the answer.

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The graphs that are not graphs of polynomials are the ones that have a cusp, a break, do not pass the horizontal line test, or are not smooth.

The graph could be that of a polynomial function if it meets the following criteria: it is smooth, continuous, and does not have any cusps or breaks.

Reasons why the other graphs are not polynomial functions:

1. The graph has a cusp: Polynomial functions have smooth curves without any sharp points (cusps).

2. The graph has a break: Polynomial functions are continuous, meaning there should not be any breaks or gaps.

3. The graph does not pass the horizontal line test: This is not a criterion for polynomial functions. The horizontal line test checks if a function is one-to-one, which is unrelated to polynomial functions.

4. The graph is not smooth: Polynomial functions have smooth, continuous curves.

Based on these criteria, only the graph that is smooth and continuous without any cusps or breaks could be the graph of a polynomial function.

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Answer:

The answer is about 4.242 feet

Answer:

Option D

Step-by-step explanation:

Using the surd law :

\(\sqrt{ab} = \sqrt{a}\sqrt{b}\)

We can find the largest square number that goes into 75 :

Let's write the multiples of 75 :

1 , 75

3 , 25

5 , 15

The only square number is 25

So using the law mentioned above we split √75 into :

√25√3

The square root of 25 is 5

Now we have our final answer of 5√3

Hope this helped and have a good day

The simplified form of expression √75 is 5√3.

Option D is the correct answer.

We have,

To simplify √75, we can factor it into its prime factors and then take the square root:

√75 = √(3 * 5 * 5)

= √(3 x 5²)

Take out the perfect square factor from under the square root:

= √3 x √5²

= √3 x 5

= 5√3

Thus,

The simplified form of expression √75 is 5√3 which is option D.

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