Find the area of the region bounded by f(x) = x^2 - 4x and g(x) = x -
4
Answers
The area between the curves is:
(62/3) - (3/2) ≈ 5.5 square units.
To find the area of the region bounded by these two curves, we need to find the points where they intersect. Setting the equations equal to each other, we get:
x^2 - 4x = x - 4
Simplifying, we get:
x^2 - 5x + 4 = 0
Factoring, we get:
(x - 1)(x - 4) = 0
So the curves intersect at x = 1 and x = 4.
To find the area between the curves, we need to integrate the difference between f(x) and g(x) with respect to x over the interval [1, 4]. That is:
∫[1,4] [(x^2 - 4x) - (x - 4)] dx
Simplifying, we get:
∫[1,4] (x^2 - 5x + 4) dx
Integrating, we get:
(1/3)x^3 - (5/2)x^2 + 4x | from 1 to 4
Substituting the limits of integration, we get:
(1/3)(4^3) - (5/2)(4^2) + 4(4) - [(1/3)(1^3) - (5/2)(1^2) + 4(1)]
Simplifying, we get:
(64/3) - 22 + 16 - (1/3) + (5/2) - 4
Which simplifies to:
(62/3) - (3/2)
Therefore, the area between the curves is:
(62/3) - (3/2) ≈ 5.5 square units.
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Related Questions
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
S:{10}
S:{3}
S:{2}
S:{0}
Answers
Hence, when \(n=10\) the given inequality is true.
What is the inequality?
An inequality is said to be sharp if it cannot be relaxed and still be valid in general.
Here given that,
Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.
So,
\(2(n + 2) < 5(n-1)\)
When
\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)
Hence, when \(n=10\) the given inequality is true.
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How do I solve x for 2x+8=3x+10
Answers
To solve for x in: \(2x + 8 = 3x + 10\)
Collect like terms
\(→8 - 10 = 3x - 2x \\ - 2 = x\)
Therefore:
\(x = - 2\)
Please solve this for me
Answers
Answer:
Step-by-step explanation:
F
Y=2x^2 + 3x+1
a.Find the x - and y-intercept
b. Where is the line of symmetry of this parábola? Write its equation
c. Find the coordinates of the vertex
Answers
For the parabola y = 2x² + 3x + 1,
a. i. The x-intercepts are x = -1/2 and x = -1
a. ii. The y-intercept is y = 1
b. i. The line of symmetry is at x = -3/4
b. ii. The equation of the line of symmetry is x = -3/4
c. The vertex is at (-3/4, -1/8)
What is a parabola?A parabola is part of a conic section which is a curve.
a. i. Find the x - interceptGiven the parabola y = 2x² + 3x + 1, we find the x- intercept when y = 0.
So, y = 2x² + 3x + 1
2x² + 3x + 1 = 0
2x² + 2x + x + 1 = 0
Factorizing, we have
2x(x + 1) + (x + 1) = 0
(2x + 1)(x + 1) = 0
2x + 1 = 0 or x + 1 = 0
2x = -1 or x = -1
x = -1/2 or x = -1
So, the x-intercepts are x = -1/2 and x = -1
ii Find the y intercept?Given the parabola y = 2x² + 3x + 1, we find the y- intercept when x = 0.
So, y = 2x² + 3x + 1
So, y = 2(0)² + 3(0) + 1
y = 0 + 0 + 1
y = 1
So, the y-intercept is y = 1
b. i. Where is the line of symmetry of this parábola?The line of symmetry passes through the vertex of the parabola where dy/dx = 0.
So, y = 2x² + 3x + 1
dy/dx = d(2x² + 3x + 1)/dx
= d(2x²)/dx + d3x/dx + d1/dx
= 4x + 3 + 0
= 4x + 3
So, when dy/dx = 0,we have
4x + 3 = 0
4x = -3
x = -3/4
So, the line of symmetry is at x = -3/4
ii. Write its equationThe equation of the line of symmetry is x = -3/4
c. Find the coordinates of the vertex?Since the vertex of the parabola is a t x = -3/4, substituting this into the equation, we have
y = 2x² + 3x + 1
y = 2(-3/4)² + 3(-3/4) + 1
y = 2(9/16) - 9/4 + 1
y = 9/8 - 9/4 + 1
y = (9 - 18 + 8)/8
y = (17 - 18)/8
y = -1/8
So, the vertex is at (-3/4, -1/8)
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look at image.................
Answers
Answer:
-1/3
Step-by-step explanation:
When x is 1, y is 5
When x is 4, y is 4
5-4=1
1-4=-3
1/-3=-1/3
Assume we have two events, A and B, that are mutually exclusive. Assume further we knowP(A) = .30 and P(B) = .40.What is P(A ⋂ B)?What is P(A | B)?
Answers
From the given question, we can easily calculate that P(A⋂ B) is equal to 0 and P(A | B) is also equal to 0.
Mutually exclusive events are those events that indicate that two or more events “do not occur” at the same time.
that clearly means that the intersection of their probabilities will be equal to 0
i.e. P(A⋂ B) = 0
and P(A|B) is called "Conditional probability", which means the possibility of an event or outcome happening(A), based on the given probability of a previous event or outcome(B)
and is given by,
P(A|B) = P(A ⋂ B)/P(B)
= 0/0.40
= 0
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You are at the grocery store choosing between bananas and walnuts. You know that the price of walnuts is $2 per pound and the price of bananas is $1 per pound, and your satisfaction from consuming is given by the following utility function: U=W .5
B .5
a. What is your marginal rate of substitution of walnuts for bananas? b. Using the Lagrangian approach, find your optimal consumption bundle. What is your total utility at this level? c. If the price of bananas doubles to $2 per pound, how much income must you have to maintain the same level of utility?
Answers
a. MRS = √(W/B)
b. Optimal bundle and total utility.
c. Adjusted income for constant utility.
a. The marginal rate of substitution (MRS) of walnuts for bananas is the rate at which you are willing to give up walnuts in exchange for one additional pound of bananas while keeping the utility constant. In this case, the MRS is equal to the ratio of the marginal utility of walnuts to the marginal utility of bananas. Since the utility function is U = √(W * B), the MRS can be calculated as MRS = √(W/B).
b. Using the Lagrangian approach, we can set up the following optimization problem: maximize U = √(W * B) subject to the constraint 2W + B = I, where W represents the pounds of walnuts, B represents the pounds of bananas, and I represents income. By solving the Lagrangian equation and the constraint, we can find the optimal consumption bundle and income level.
c. If the price of bananas doubles to $2 per pound, we need to determine the income required to maintain the same level of utility. With the new price, the constraint becomes 2W + 2B = I. By solving the Lagrangian equation again and substituting the new constraint, we can find the income level required to maintain the same level of utility.
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Let F(x,y,z) = (x−z)i+ 0j+xk. Evaluate ∫CF·dr, where C is the half circle of x^2+z^2= 1 (on the xz-plane), beginning at (1,0,0) to (0,0,1) to (−1,0,0).
Answers
Answer:
J+XKEN
Step-by-step explanation:
Determine whether each pair of expressions is equivalent. Explain your reasoning.
Answers
The answer is:
\(\large\textbf{They aren't equivalent.}}\)
In-depth explanation:
To determine the answer to this problem, we will use one of the exponent properties:
\(\sf{x^{-m}=\dfrac{1}{x^m}}\)
And
\(\sf{\dfrac{1}{x^{-m}}=x^m}\)
Now we apply this to the problem.
What is 4⁻³ equal to? Well according to the property, it's equal to:
\(\sf{4^{-3}=\dfrac{1}{4^3}}\)
And this question asks us if 4⁻³ is the same as 1/4⁻3.
Well according to the calculations performed above, they're not equivalent.
When probability sampling is done correctly, there should be no systematic bias. A) true. B) false.
Answers
A) True. Therefore, there should be no systematic bias when probability sampling is done correctly.
When conducting a research study, it is important to ensure that the sample chosen is representative of the population. Probability sampling is a method that aims to achieve this by giving each member of the population an equal chance of being included in the sample.
When this sampling method is done correctly, it minimizes bias and ensures that the sample is truly representative. For example, let's consider a study on the average height of students in a particular school.
If we were to use probability sampling, we would assign a number to each student and then randomly select a certain number of students from that pool. This would give every student an equal chance of being chosen for the sample, eliminating any systematic bias that might arise if we were to select students based on subjective criteria.
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help pleas for 12 points
Answers
Answer:
126 ft²
Step-by-step explanation:
surface area of rectangular prism: 2(LW + HW + WL)
Here Given:
Length: 9 ftWidth: 3 ftHeight:3 ftSurface Area:
2(LW + HW + WL)2(9*3 +3*3 + 9*3)2(27 +9 + 27)2(63)126height= 3 ft
width= 3 ft
length= 9 ft
to find:the surface area of the given prism.
solution:\(s.a = 2(hw + wl + hl )\)
\(s.a = 2(3 \times 9 + 3 \times 9 + 3 \times 3)\)
\(s.a = 126 \: {ft}^{2} \)
therefore, the surface area of the given prism is 126 square feets.
Type the correct answer in the box. Use numerals instead of words.
For this item, if the answer is not a whole number, enter it as a fraction in simplest form using / as the fraction bar.
Isolde is stacking books. The stack of books forms a rectangular prism.
Each book is the same size. Isolde knows the area of the base of one book is 22 1/2 square inches and each book is 3/4 inch thick.
The volume of a stack of 9 books is cubic inches.
Answers
The volume of a stack of 9 books is 1368.75 cubic inches.
Volume of a book stackTo find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.
Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.
Therefore, the volume of the stack of 9 books is:
Volume = Area of base x heightVolume = (202 1/2 square inches) x (6 3/4 inches)Volume = 1368.75 cubic inchesMore on volume of stacked books can be found here: https://brainly.com/question/1058070
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Assume that the college in Offer #1 has a Cost of Attendance of $73,332. Which of the statements below comparing Offer #1 to Offer #2 is TRUE?
College #1 has a lower “cost of attendance” than College #2
Both College #1 and College #2 have the same “net price”
College #1 has a lower “net price” than College #2
College #1 has a higher “net price” than College #2
Answers
Answer:
Both College #1 and College #2 have the same “net price”
This is going by the fact that the equivalent money which happens to remain after all the deductions had been made are same. The gross amount, though quite different happens to be same in the available net amount for same education cost in both college.
Step-by-step explanation:
What are the 4 conditions to be a normal curve?
Answers
Here, we see the four characteristics of a normal distribution. Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal
To pass inspection, a new basketball should bounce back to between 68% and 75% of the starting height. A new ball is dropped from 6 feet and bounces back 4 feet 1 inch. does the ball pass inspection? Explain
To pass inspection, the ball must bounce back to between 68% and 75% of the starting height. written as a decimal, the ball must bounce between a low of __ feet and height of __ feet.
Answers
Answer: Yes, it does. It must bounce of a low of 4.08 feet and a high of 4.5 feet
Step-by-step explanation:
analysts should not worry about the users' perceptions of the new system during acceptance testing. true or false?
Answers
False. Analysts should definitely worry about the users' perceptions of the new system during acceptance testing. Acceptance testing is the final stage of software development where the system is tested by end-users to ensure that it meets the specified requirements and is ready for deployment.
During acceptance testing, analysts need to ensure that users find the system easy to use, efficient, and effective in performing the intended tasks. If the users perceive the system to be difficult to use or inefficient, it can lead to user resistance, decreased productivity, and increased costs. Therefore, analysts need to gather feedback from users during acceptance testing and make necessary adjustments to ensure that the system meets the user's expectations. By doing so, analysts can ensure a successful deployment and adoption of the new system.
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Hiiii someone please help me I'm confused please helppp
If the length of the bases of right triangle GHI are 9 units and 15 units respectively, what is the length of the hypotenuse of GHI?
Answers
Answer:
17.5 units
Step-by-step explanation:
a² + b²= c²
9² + 15² = c²
81 + 225 = c²
c² = 306
c = √306
c = 17.5
There were 1125 books sold last week at Sid's Bookstore. The circle graph below summarizes these books by genre.
The central angle for the Self-Help slice is 80.64. How many of the books sold were Self-Help books?
Answers
Answer:
Number of self-Help books sold = 252 books
Step-by-step explanation:
Total books sold last week = 1,125
Central angle for the Self-Help slice = 80.64°
Total angle in a circle = 360°
How many of the books sold were Self-Help books?
Number of self-Help books sold =
Central angle for the Self-Help slice / Total angle in a circle × total number of books sold
= 80.64° / 360° × 1,125
= 0.224 × 1,125
= 252
Number of self-Help books sold = 252 books
Two numbers, x and y, when added together equal 9 and equal -5 when subtracted.
Answers
Answer:
x=2 and y=7
Step-by-step explanation:
Let x and be the unknown numbers.
By the condition given in the question the first equation is
x+y=9
And the second equation is
x-y=-5
By solving the first and second equations,we get the answer as
x=2 and y=7
geometry - please help me ?
Answers
\(\large\huge\green{\sf{Answer:-}}\)
\( \red {\mathbb{ \underline { \tt By \: ASA\: congruence \: postulate}}}\)
➡in ∆ ORS and ∆OUT
➡ UO = 0S ( given)
➡UOT = SOR ( by vertically opposite angle)
➡OUT= OSR( by alternate angle)
( bcaz UT is parallel to RS
there fore ,
∆ ORS ≅ ∆OUT (by ASA congruence postulate)Answer:
not enough information.
Step-by-step explanation:
none of the others are satisfied.
2x1 + 1x2 = 30. Setting x1 to zero, what is the value of x2?
Answers
Setting x1 to zero in the equation 2x1 + 1x2 = 30 results in the value of x2 being 30.
The given equation is 2x1 + 1x2 = 30, where x1 and x2 represent variables. To find the value of x2 when x1 is set to zero, we substitute x1 with zero in the equation.
By replacing x1 with zero, we have 2(0) + 1x2 = 30. Simplifying further, we get 0 + 1x2 = 30, which simplifies to x2 = 30.
When x1 is set to zero, the equation reduces to a simple linear equation of the form 1x2 = 30. Therefore, the value of x2 in this scenario is 30.
Setting x1 to zero effectively eliminates the contribution of x1 in the equation, allowing us to focus solely on the value of x2. In this case, when x1 is removed from the equation, x2 becomes the sole variable responsible for fulfilling the equation's requirement of equaling 30. Thus, x2 is determined to be 30.
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Andre tried to solve the equation 1/4 (x+12)=2. What was his mistake in solving the equation?
1/4 (x+12)=2
1/4x=-10
x=-40
CHOOSE TWO
A. Andre changed the sign to -10 when it should be +10
B. Andre distributed 1/4 to x but not to 12
C. Andre forgot to subtract 1/4 from each side of the equation
D. Andre tried to subtract 12 from each side
E. Andre forgot to study for his math test
F. Andre solved correctly. No mistakes
Answers
Andre’s first mistake was that he didn’t distribute properly or at all. Instead of using the distributive property to get rid of the parenthesis, he moved the x to the 1/4 and subtracted 12 to the other side
The correct option is D.
Now, According to the question:
Let's know:
What is a BODMAS rule?
BODMAS rule means for the Bracket, Order, Division, Multiplication, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Andre tried to solve the equation 1/4 ( x + 12 ) = 2.
First, open the bracket, then we have
\(\frac{x}{4} +\frac{12}{4}\) = 2
On simplifying, we have
\(\frac{x}{4} + 3\) = 2
Subtract 3 from both sides, we have
x/4 = -1
Multiply the equation by 4, we have
x = -4
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The high temperature on monday was -14 degrees. On Tuesday the high temperature was 24 degrees. Which integer represents the difference in high temperature on these 2 days?
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The integer that represents the difference in high temperature from Monday to Tuesday is 38.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The high temperature on Monday was -14 degrees.
On Tuesday the high temperature was 24 degrees.
The temperature difference between Monday and Tuesday.
= Temperature on Tuesday - Temperature on Monday
= 24 - (-14)
= 24 + 14
= 38
Thus,
The integer that represents the difference in high temperature from Monday to Tuesday is 38.
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A random sample of 75 juniors are asked whether they plan to attend homecoming. of these, 62 juniors said they will attend. what is the margin of error at 90% confidence and its interpretation?
Answers
The interpretation of the margin of error at a 90% confidence level is that we can be 90% confident that the true proportion of juniors who plan to attend homecoming lies within a range of plus or minus 0.093 of the sample proportion.
To calculate the margin of error, we need to use the formula:
Margin of Error =\(Z * (sqrt(p * (1-p) / n))\)
Where:
Z is the z-score corresponding to the desired level of confidence
p is the proportion of juniors who said they will attend homecoming
n is the sample size
In this case, the sample size is 75 and the proportion who said they will attend homecoming is 62/75 = 0.827.
To find the z-score for a 90% confidence level, we can use a z-table or a calculator. The z-score for a 90% confidence level is approximately 1.645.
Now we can plug in the values into the formula:
Margin of Error = \(1.645 * (sqrt(0.827 * (1-0.827) / 75))\)
Calculating this, we find that the margin of error is approximately 0.093.
The interpretation of the margin of error at a 90% confidence level is that we can be 90% confident that the true proportion of juniors who plan to attend homecoming lies within a range of plus or minus 0.093 of the sample proportion.
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A horse gallops around a track 2.5 times in 15 minutes. if the track measures 1.5 miles long, what is the average speed of the horse in miles per hour?
please
Answers
The average speed of the horse is 15 miles per hour.
What is average speed?Average speed is defined as the ratio of the total distance to the total time covered by a body.
To calculate the average speed of the horse, we use the formula below.
Formula:
S = d/t............. Equation 1Where:
S = Average speedd = Total distancet = Total time.From the question,
Given:
d = (2.5×1.5) = 3.75 milest = 15 minutes = 15/60 = 1/4 = 0.25 hours.Substitute these values into equation 1
S = 3.75/0.25S = 15 miles per hoursHence, the average speed of the horse is 15 miles per hour.
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Suppose we are making a 95% confidence interval for the population mean from a sample of size 15. What number of degrees of freedom should we use?.
Answers
The number of degrees of freedom we should use is 14 for makin95% confidence interval.
Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate. It’s not quite the same as the number of items in the sample. In order to get the df for the estimate, you have to subtract 1 from the number of items.
Degree of freedom of sample size of n : n -1
When we don't have any idea about population standard deviation,
and also, the sample size is less than 30 .
We use t-distribution to calculated the statistics.
According to the question,
We are making a 95% confidence interval
The sample is 15 (<30) . So , we have to adjust and use a t-value instead of a Z score in order to account for the smaller sample size and using the sample SD.
Note that the t-value depends on the degrees of freedom (df) as a reflection of sample size. When using the t-distribution to compute a confidence interval, df = n-1.
So , making 95% confidence interval for population mean from sample size 15 , we need degree of freedom of 14
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I'm looking at extreme daily temperature under a histroical scenario and a future scenario and would like to know the relationship between the 99th percentile temperature value, a 100 year return value and the exceedence probability. I know that a 100 year event has an exceedence probability of 1%/year. Does this mean that a 100 year event has a 1% chance of exceeding the historical 99th percentile temperature value?
Answers
No, the fact that a 100-year event has an exceedance probability of 1%/year does not mean that it has a 1% chance of exceeding the historical 99th percentile temperature value.
The 99th percentile temperature value represents a threshold below which 99% of the historical temperature values fall. It is a statistical measure that indicates the temperature value that is exceeded by only 1% of the historical data. It is calculated based on the historical temperature observations.
On the other hand, the exceedance probability refers to the probability of a specific temperature value being exceeded in a given time period. For example, if a 100-year event has an exceedance probability of 1%/year, it means that in any given year, there is a 1% chance of experiencing a temperature value that exceeds the threshold for a 100-year event.
The relationship between the 99th percentile temperature value, a 100-year return value, and the exceedance probability is not direct. The exceedance probability of the 99th percentile temperature value depends on the specific distribution of temperature values and their statistical characteristics. While a 100-year event has an exceedance probability of 1%/year, it does not necessarily imply that it has a 1% chance of exceeding the historical 99th percentile temperature value.
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A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation $4x+6y=48$ models this situation, where $x$ is the number of cars and $y$ is the number of vans
Answers
The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
Given the equation that models the situation expressed as:
4x + 6y = 48
We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.
If there are no cars i.e. at when x = 0
4(0) + 6y = 48
0 + 6y = 48
6y = 48
y = 48/6
y = 8
One of the solution is (0, 8)
If there are 3 cars, i.e. at when x = 0
4(3) + 6y = 48
12 + 6y = 48
6y = 48 - 12
y = 36/6
y = 6
The second solution will be (3, 6)
If there are 6 cars, i.e. at when x = 6
4(6) + 6y = 48
24 + 6y = 48
6y = 48 - 24
y = 24/6
y = 4
The third solution will be (6, 3)
If there are 9 cars, i.e. at when x = 9
4(9) + 6y = 48
36 + 6y = 48
6y = 48 - 36
y = 12/6
y = 2
The fourth solution will be (9, 2)
Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
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Work out the total surface area of this hemisphere which has a radius of 8cm
give your answer to 1 decimal place
Answers
Answer:
603.2 cm^2
Step-by-step explanation:
Surface Area = 1/2 x 4πr^2+πr^2
Surface Area = 1/2 x 4π8^2+π8^2
Surface Area = 603.1857895 cm^2
1 Decimal Place = 603.2 cm^2
Hope this helps.
Consider the following generic C comparison function and its assembly language representation C code: byte compbyte a,byte b)/a in rdi,b in rsi Assembly code cmpb %rsi,%rdi set_inst %a1 ret Your jobs(fill-in blank):now sh given values of a and b g SET instruction and the A.5 points set CI SF OF %al setg 47 23 B.5 points set h SF OF %a setl 23 47 C.5 points ZA SF OF %al set sete 23 23 D.5 points CF ZF SF OF 00%1 set b setne 23 47
Answers
The correct answer is D. setne 23 47. Based on the provided information, I understand that you have a comparison function in C code and its corresponding assembly code. You are asked to fill in the blanks by selecting the appropriate instructions based on the given values of a and b and the status flags SF, OF, ZF, and CF. Let's go through the options:
A. setg 47 23: This option is incorrect because setg is used to set a byte to 1 if the Greater flag (ZF=0 and SF=OF) is set, but the given values of a and b are 47 and 23, respectively, so it does not satisfy the condition for setg to be set.
B. setl 23 47: This option is incorrect because setl is used to set a byte to 1 if the Less flag (SF≠OF) is set, but the given values of a and b are 23 and 47, respectively, so it does not satisfy the condition for setl to be set.
C. sete 23 23: This option is incorrect because sete is used to set a byte to 1 if the Zero flag (ZF=1) is set, but the given values of a and b are 23 and 23, respectively, so it does not satisfy the condition for sete to be set.
D. setne 23 47: This option is correct. setne is used to set a byte to 1 if the Zero flag (ZF=0) is not set, which means the values of a and b are not equal. In this case, the given values of a and b are 23 and 47, respectively, so they are not equal, and setne should be used.
Therefore, the correct answer is D. setne 23 47
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