match the code on the left with the precondition p(x,y) and postcondition q(x,y) on the right that verifies its correctness.
Answers
p(x,y): x > 0 ∧ y > 0; q(x,y): x² + y² = z², The code has a precondition that x and y must be greater than zero. The postcondition verifies the correctness of the code by ensuring that the sum of the squares of x and y is equal to the square of z, adhering to the Pythagorean theorem for a right-angled triangle.
Determine the precondition?The code in option C has a precondition p(x,y): x > 0 ∧ y > 0, which means that both x and y should be greater than zero. The postcondition q(x,y): x² + y² = z² verifies the correctness of the code.
After executing the code, it ensures that the sum of the squares of x and y is equal to the square of z. This condition is consistent with the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (z) is equal to the sum of the squares of the other two sides (x and y).
By checking that the postcondition holds true, we can confirm that the code correctly calculates the square of the hypotenuse in a right-angled triangle, given the lengths of the other two sides.
Therefore, the code requires x and y to be positive. The postcondition checks if the sum of the squares of x and y is equal to the square of z, aligning with the Pythagorean theorem for a right-angled triangle.
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Related Questions
describe the apparent relationship between the two variables under consideration. choose the correct choice below. a. test score remains constant as the number of study hours increases. b. test score tends to decrease as the number of study hours increases. c. test score tends to increase as the number of study hours increases. d. there is no apparent relationship between study hours and test score.
Answers
Based on the given information, the question is asking about the apparent relationship between two variables: study hours and test score. The correct answer is c.
Test score tends to increase as the number of study hours increases. This suggests a positive correlation between the two variables, meaning that as one variable (study hours) increases, the other variable (test score) also tends to increase.
The apparent relationship between the two variables under consideration, which are study hours and test score, can be described as follows:
Your answer: c. Test score tends to increase as the number of study hours increases.
This is because, generally, the more time a person spends studying, the better their understanding of the material, which often leads to a higher test score.
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does anything in the plot of the semimajor axis versus the period change when the eccentricity is changed?
Answers
Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.
What is eccentricity?In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.
Here,
In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.
As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.
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9. Jack sells furniture for homes. Jacks is paid an 8.3% commission on all sales. Last month, Jack sold $42,513 worth of furniture. What was his commission?
Answers
Jack sells furniture for homes. Jacks is paid an 8.3% commission on all sales. Last month, Jack sold $42,513 worth of furniture. What was his commission?
we know that
8.3%=8.3/100=0.083
so
Multiply $42,513 by 0.083 to obtain his commission
$42,513*(0.083)=$3,528,58
therefore
the answer is
$3,528,58The equation g equals three fifths times m represents the proportional relationship of the number of gallons of water (g) used by a washing machine over a certain period of time, in minutes (m). Create a written description for the equation. For each minute the washing machine runs, it uses five thirds gallons of water. For each minute the washing machine runs, it uses three fifths of a gallon of water. For each gallon of water the washing machine uses, it runs for three fifths of a minute. For each gallon of water the washing machine uses, it runs for 8 minutes.
Answers
The description of the proportional relationship in the context of this problem is given as follows:
For each minute the washing machine runs, it uses five thirds gallons of water.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with intercept of zero, meaning that the output variable y is obtained as the multiplication of the input variable x and the constant of proportionality k, as follows:
y = kx.
In this problem, the relationship is given by the equation presented as follows:
g = 3/5m
The variables are given as follows:
Input m: number of minutes.Output g: number of gallons of water.The constant is of:
3/5.
Meaning that three fifths gallons of water are used each minute.
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The size of the overall population is __________ in determining the reliability of a poll.
Answers
The size of the overall population is not important in determining the reliability of a poll.
What is the purpose of the overall population in a poll?The overall population that a poll is based on does not have anything significant to do with the poll itself which means that it is not important in determining reliability.
This is because the poll uses a sample of the population and not the population itself.
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Chart Rodrigo's total utility for lattes and the marginal utility for the same using information
from the table.
Quantity
Utility
0
14
2
3
4
on ANO
22
28
32
35
5
1)
40
30
Units of Total Utility
20
10
0
1
2
3
4
N
5
Number of Lattés
2)
)
20
15
Units of Total Utility per Latte
10
5
0
1
2
3
4 5
Number of Lattés
Answers
The marginal utility is the extra satisfaction derived from the consumption of a product.
How to illustrate the marginal utility?Your information isn't well written. Therefore, an overview of utility will be given. The total utility is the total amount of satisfaction that a consumer derives from a product.
The marginal utility simply means the extra satisfaction that's gotten from a product when an additional unit is consumed.
The formula for marginal utility will be:
= Total utility difference/Quantity of goods difference
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2) Which of the following represents an equation of a line parallel to one whose equation is 2y + 8x = 18?
A) y = -4x + 3
B) y = 4x+ 7
C) y = 8x + 2
D) y = -8x + 9
Answers
2y + 8x = 18
Make it slope in form: y = mx + b
Divide the equation by 2
y + 4x = 9
Now subtract 4x
Y = -4x + 9
The slope is -4
Which equation also has same slope?
Solution: A
Answer:
A
-by-step explanation:
i have that exact question
I have multiple questions:
1: 2/3÷4/5
2: 2 1/9÷2/3
3: 3/5÷1 1/4
Answers
Answer:
1: 5/6
2: 3 1/6
3: 12/25
hope this helps!!
p.s
comment if wrong
What is the solution of the proportion fraction numerator x minus 1 over denominator 2 end fraction equals fraction numerator x minus 4 over denominator 5 end fraction
Answers
The Solution of the given expression is -3/2
Fractions:In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or segment taken from a whole, which can be any number, a certain amount, or an object.
In fractions, the upper portion is called Numerator and the lower portion is called the Denominator.
Here given that
fraction numerator x minus 1 over denominator 2 end fraction equals fraction numerator x minus 4 over denominator 5 end fraction
The above fraction can be written Mathematically as given below
=> \([\frac{x-1}{2}] = [\frac{x-4}{5} ]\)
The given expression can be solved as given below
=> \([\frac{x-1}{2}] = [\frac{x-4}{5} ]\)
=> \(5(x-1) = 2(x-4)\)
=> \(5x- 5 = 2x - 8\)
=> \(5x- 3x = - 8 + 5\)
=> \(2x = - 3\)
=> \(x = -\frac{3}{2}\)
Therefore,
The Solution of the given expression is -3/2
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Consider a set of strings defined recursively as follows:
Base case: λ ∈ S
Recursive rules: if x ∈ S and y ∈ S then,
axb ∈ S (Rule 1)
bxa ∈ S (Rule 2)
xy ∈ S (Rule 3)
Prove that every string in S contains the same number of a's and b's.
Note that your proof does not necessarily imply that every string that has the same number of a's and b's is in S.
pls give full solution and explanation
Answers
The set of strings defined recursively consists of the empty string and any string obtained by adding a single 'a' or 'b' to the beginning or end of a string already in the set. This set is infinite and can be generated using mathematical induction.
The set of strings can be defined recursively as follows:
1. The empty string is in the set.
2. For any string s in the set, the strings obtained by adding a single 'a' or 'b' to the beginning or end of s are also in the set.
For example, starting with the empty string, we can add 'a' or 'b' to create the strings 'a' and 'b'. Then, we can add 'a' or 'b' to the beginning or end of these strings to create 'aa', 'ab', 'ba', and 'bb'. Continuing in this way, we can generate an infinite set of strings.
To prove that a string is in the set, we can use mathematical induction. First, we show that the empty string is in the set. Then, we assume that a string s is in the set and show that any string obtained by adding a single 'a' or 'b' to the beginning or end of s is also in the set. By repeating this process, we can show that any string in the set can be generated using the above rules.
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Integrated circuits from a certain factory pass quality test with probability ,8,p=,8. The outcomes of tests are mutually independent. Use The CTL to estimate the probability of finding at most of 50 acceptable circuits in a batch of 60 .
Answers
The estimated probability of finding at most 50 acceptable circuits in a batch of 60 is approximately 0.6591.
What is the estimated probability of obtaining no more than 50 acceptable circuits in a batch of 60, given a pass probability of 0.8 and independent outcomes?To estimate the probability of finding at most 50 acceptable circuits in a batch of 60 from a certain factory, where the probability of passing the quality test is (p = 0.8) and the outcomes of the tests are mutually independent, we can use the Central Limit Theorem (CLT).
The CLT states that for a large enough sample size, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.
Let's denote (X) as the number of acceptable circuits in a batch of 60. Since each circuit passes the test with a probability of 0.8, we can model (X) as a binomial random variable with parameters (n = 60) and (p = 0.8).
To estimate the probability of finding at most 50 acceptable circuits, we can calculate the cumulative probability using the normal approximation to the binomial distribution.
Since the sample size is large \((\(n = 60\))\), we can approximate the distribution of (X) as a normal distribution with mean \(\(\mu = np = 60 \times 0.8 = 48\)\) and standard deviation \(\(\sigma = \sqrt{np(1-p)}\) = \(\sqrt{60 \times 0.8 \times 0.2} \approx 4.90\).\)
Now, we want to find the probability of\(\(P(X \leq 50)\)\). We can standardize the value using the z-score:
\(\[P(X \leq 50) = P\left(\frac{X - \mu}{\sigma} \leq \frac{50 - 48}{4.90}\right) = P(Z \leq 0.41)\]\)
Using the standard normal distribution table or calculator, we can find that \(\(P(Z \leq 0.41) \approx 0.6591\).\)
Therefore, the estimated probability of finding at most 50 acceptable circuits in a batch of 60 is approximately 0.6591.
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Find the circumference of the circle in terms of π .
Answers
Answer:
Circumference of circle = π x Diameter of circle
Step-by-step explanation:
If you know the diameter or radius of a circle, you can work out the circumference. To begin with, remember that pi is an irrational number written with the symbol π. π is roughly equal to 3.14. The formula for working out the circumference of a circle is: Circumference of circle = π x Diameter of circle
the measure of the larger angle is 12 less than 3 times the measure of the smaller angle
Answers
Answer:
Let x be the measure of the smaller angle. Then the measure of the larger angle is 3x - 12.
We can write this as an equation:
larger angle = 3 * smaller angle - 12 or 3x - 12 = larger angle.
Alternatively, we can write it as:
smaller angle + larger angle = 180 (since they form a straight line)
Substituting larger angle with 3x - 12, we get:
x + 3x - 12 = 180
Simplifying:
4x - 12 = 180
4x = 192
x = 48
Therefore, the measure of the smaller angle is 48 degrees, and the measure of the larger angle is 3(48) - 12 = 132 degrees.
The measure of the larger angle is 12 less than 3 times the measure of the smaller angle x = 48
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’ meaning “corner.”
Angles can mean is an acute angle.
Let smaller angle = x
Larger angle = 3x - 12
x & (3x - 12) are supplementary
So, x + 3x - 12 = 180°
4x - 12 = 180
4x = 180 +12
4x = 192
x = 192/4
⇒ x = 48°
Hence, the measure of the larger angle is 12 less than 3 times the measure of the smaller angle x = 48
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emma advertises a reward for the return of her lost dog. frank, who does not know of the reward, finds and returns the dog. frank cannot recover the reward because he
Answers
Frank cannot recover the reward because he was unaware of the reward being offered by Emma.
In order to claim the reward, one typically needs to have knowledge of the reward prior to finding and returning the lost item or fulfilling the specified condition. Since Frank was unaware of the reward, he would not have had the opportunity to intentionally seek the dog with the expectation of receiving the reward. As a result, Emma is not obligated to provide the reward to Frank in this situation.
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help me pleaseeeeeeeeeeeee
Answers
Answer:
Step-by-step explanation:
1. Since we know that Lila wants to use 1 cup of pretzels, we can multiply 1/2 x 1/2, which is 1.
2. Now that we multiplied 1/2 by 1/2, we have to multiply 1 1/4 by 1/2.
So 5/4 x 1/2 is 5/8.
3. Lila will need 5/8 cups of raisins.
What type of number is -1−1minus, 1? Choose all answers that apply: Choose all answers that apply: (Choice A) A Whole number (Choice B) B Integer (Choice C, Checked) C Rational (Choice D) D Irrational
Answers
Answer:
B and C
Step-by-step explanation:
I think that you mean -1 -1. That would equal -2
-2 is an integer and a rational number.
An integer are the whole numbers 0,1,2,3 and so on and their opposites, -1, -2, -3 ,-4 and so on
Rational number is when you can write a number as an integer over and integer. You can write -2 as -2/1
Answer: a,b,c
I did it in the test
Double the product of eight and a number
Answers
Answer:
Oh ok
Step-by-step explanation:
An expression is defined as a set of numbers, variables, and mathematical operations. The given statement "Double the product of eight and a number" in the form of an expression can be written as 16x.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let the unknown number be represented by x.
The product means multiplication, therefore, we need to double or multiply the product or multiplication of eight and x.
Thus, The given statement in the form of an expression can be written as,
2(8 × x)
= 2(8x)
= 16x
Hence, the given statement "Double the product of eight and a number" in the form of an expression can be written as 16x.
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Wyatt is hiking a trail that is 11/12 mile long.After hiking 1/4 mile he stops for water he continues hiking for another 1/6 mile and stops to rest how much farther must he hike to finish the trail
Answers
Answer:
the answer in the simplest form is 1/2 miles and if it's not in its simplest form is 6 /12 .hope it helps.
(b) Expand and simplify (2r + 5)(x-6)(3x + 3)
Answers
Answer: Answers below
Step-by-step explanation:
The step by step answer is below, enjoy.
if the tangent line to y = f ( x ) at ( 6 , 2 ) passes through the point ( 0 , 1 ) , find f ( 6 ) and f ' ( 6 ) .
Answers
if the tangent line to y = f ( x ) at ( 6 , 2 ) passes through the point ( 0 , 1 ) , then f(6) = 2 and f'(6) = 1/6.
To find f(6), we can use the fact that the tangent line to y = f(x) at (6, 2) passes through the point (0, 1). The equation of a line can be written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Since the line passes through (6, 2) and (0, 1), we can substitute these values into the equation to get:
2 - 1 = m(6 - 0)
1 = 6m
Solving for m, we find m = 1/6.
Since the slope of the tangent line is equal to the derivative of f(x) at x = 6, we have f'(6) = 1/6.
Now, to find f(6), we can integrate f'(x) with respect to x:
f(x) = ∫(f'(x))dx = ∫(1/6)dx = (1/6)x + C
To find the value of C, we can substitute the point (6, 2) into the equation:
2 = (1/6)(6) + C
2 = 1 + C
C = 1
Therefore, f(x) = (1/6)x + 1.
Substituting x = 6 into the equation, we get:
f(6) = (1/6)(6) + 1 = 2.
So, f(6) = 2 and f'(6) = 1/6.
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Find the length of the variable X
Answers
Answer:
D
Step-by-step explanation:
the two triangles are similar so the proportion of similarity is equal to 3/12=1/4=>x/x+12=1/4=>4x=x+12=>x=4
yeah ok thanks I love u .
Answers
Answer:
\( \frac{9}{10} \)
Step-by-step explanation:
flip 8/9and then multiply by 4/5
Write the following percentages as a fraction in simplest form
Answers
hope this helped
how to work out 109 divided by 200?
Answers
Answer:
0.545 your welcome :D
Step-by-step explanation:
109÷200
Answer: 0.545
I just searched it up...... ya welcome homie
Step-by-step explanation:
search it "109 divided by 200" you'll get ur answer
Tom bought a bag full of coal. After one week the bag was 2|3 full. During the next week he used of the remaining coal What fraction was left in the bag?
Answers
Answer:
None
Step-by-step explanation:
When he first bought the coal, it was full. After one week, he used 1/3, leaving the bag 2/3 full. If he used the remaining coal in the bag, that means he used all of the coal - all two thirds of it.
The fraction of coal left in the bag was zero or none since Tom used the remaining coal.
What is the reasoning?The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.
The reasoning is a tricky but interesting problem in mathematics that requires relations of variables to solve.
As per the given,
After one week the bag was 2|3 full
Now remaining coal = 1 -2/3 = 1/3 part
Now, Tom used this remaining amount.
So, 1/3 - 1/3 = 0 part.
Hence "The fraction of coal left in the bag was zero or none since Tom used the remaining coal".
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Jenna bought some rope for a project. The rope cost $3.50 per meter. She bought 432 centimeters of ropehow much did jenn pay for the rope
Answers
Answer:
1 meter= 100 cm
432cm/100=4.32 cm
$3.50*4.32=$15.12
the total cost is: $15.12
Step-by-step explanation:
Answer:
15.12
Step-by-step explanation:
7 teams participated in a hip-hop dance competition the table shows the average number of hours each team for each week in the school did you received the competition which scatter plot represents the data in the table
Answers
Answer:
Step-by-step explanation:
The answer is D
what is 1% of 30 answer
Answers
Step-by-step explanation:
100/30= 0.3
because,
1/100= 0.01
0.01*100= 1%
Hope this helped!
Answer:
0.3
Step-by-step explanation:
To get this divide 1 by 30 :) hope this helps!
if the original quantity is 12 and the new quantity is 15, what is the percentage increase? The percent increase is___
Answers
Explanation:
15-12/12 * 100 = 25
Answer:
25%
Step-by-step explanation:
increase = 15-12 = 3
percentage increase = 3/12 × 100 = 25%
Given GH with G(-8, 8) and H(7,2), if point P divides GH one- third of the way from G to H, find the coordinates of P.
Answers
Answer:
P (-3 , 6)
Step-by-step explanation:
p (x,y), G (x₁,y₁), H(x₂,y₂) : GP:PH = 1:2 a=1, b=2
x = (bx₁ + ax₂) / (a+b) = (2x-8 + 1x7) / (2+1) = -9/3 = -3
x = (by₁ + ay₂) / (a+b) = (2x8 + 1x2) / (2+1) = 18/3 = 6
P (-3 , 6)
The coordinates of P is (-3 , 6).
It is required to find the coordinates of P.
What is co-ordinate geometry?Coordinate geometry is defined as the study of geometry using the coordinate points. Coordinate geometry is required to provide a link between algebra and geometry through the use of line and curve graphs
Given:
p (x,y), G (x₁,y₁), H(x₂,y₂) :
GP:PH = 1:2
a=1, b=2
x = (bx₁ + ax₂) / (a+b)
= (2x-8 + 1x7) / (2+1)
= -9/3
= -3
x = (by₁ + ay₂) / (a+b)
= (2x8 + 1x2) / (2+1)
= 18/3
= 6
∴P (-3 , 6)
Therefore, the coordinates of P is (-3 , 6).
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