Answer:
$28
Step-by-step explanation:
S = Shirt N = Shoes
N = S + 17
N is equal to 45
45 = S + 17
S = 28
What is the distance from -5 to 0?
0, because 151=0
O 5, because 1-51=5
O5, because 1-51=-5
O-5, because 1-51 = -5
7 of 23 QUESTIONS
SUBMIT
Answer:
distance between -5 to 0 = 5 units
The total height of the cubes stacked on top of each other is 2f + 3g^2.
The cubes have a combined volume that is the same as a rectangular prism of the same height. What is the area of the base of the rectangular prism? (Recall: V = Bh)
A: 2f + 3g^2
B: 8f^3 + 27g
C: 2f - 6fg^2 + 3g^2
D: 4f^2 - 6fg + 9g^4
(And pls be fast)
The area of the base of the rectangular prism will be D. 4f² - 6fg + 9g⁴.
How to illustrate the information?it should be noted that from the information given, the cubes have a combined volume that is the same as a rectangular prism of the same height.
The total height of the cubes stacked on top of each other is 2f + 3g²
Therefore, the area will be:
= (2f)² - 2(3fg) + (3g²)²
= 4f² - 6fg + 9g⁴
Therefore, the area of the base of the rectangular prism will be 4f² - 6fg + 9g⁴.
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Evaluate this question (2/5^3)
Answer:
The answer will be 18/125 and the decimal form is 0.064Step-by-step explanation:
After the bank cashed a check Maureen wrote for $60, her balance was Negative 14 dollars. The equation b + (negative 60) = negative 14 can be used to represent this situation, where b is Maureen’s balance, in dollars, before the check was cashed. Maureen attempted to solve the equation using the steps below.
Maureen should have added 60 to both sides.
is the answer ^^
Answer:
She had$46
Step-by-step explanation:
b+(-60)=-14
add 60 on both sides
b=46
Somehow my answer got deleted so I had to answer this again.
A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects 10 cans at random, measures their contents, and computes a 95% confidence interval for the true mean volume. For one particular hour, the 95% confidence interval is 11.97 ounces to 12.05 ounces. Does the confidence interval provide convincing evidence that the true mean volume is different than 12 ounces? Explain your answer.
Group of answer choices
A. Even though this confidence interval includes 12 ounces, this might not occur again in different samples. There is not enough evidence to make a conclusion regarding the true mean volume.
B. We are 95% confident that the interval from 11.97 to 12.05 contains the true mean volume of diet cola in cans from this factory. Because 12 is not the center of this interval we have convincing evidence that the true mean volume is different from 12 ounces.
C. Because 12 is one of the plausible values in the 95% confidence interval, there is not convincing evidence that the true mean volume is different from 12 ounces.
D. Because the 95% confidence interval contains values other than 12, there is convincing evidence that the true mean volume is different from 12 ounces.
E. We are 95% confident that the interval from 11.97 to 12.05 contains the true mean volume of diet cola in cans from this factory. Because we are not 100% certain, there is evidence that the true mean volume is different from 12 ounces.
Since 12 ounces is part of the confidence interval, the interval does not provide convincing evidence that the true mean volume is different than 12 ounces.
So, The correct option is (B)
What is the hypothesis tested?It is being tested if the true mean volume is different of 12 ounces, hence:
If the confidence interval contains 12 ounces, it provides convincing evidence that the true mean volume is 12 ounces.
If the confidence interval does not contain 12 ounces, it provides convincing evidence that the true mean volume is not 12 ounces.
It is given that for 95%, the true mean volume is
(11.97 ounces, 12.05ounces)
It means that volume 12 ounces true mean volume is likely.
It implies that there is no evidence that true mean is different than 12 ounces.
Therefore, The correct option is (B).
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Each day, the United States Customs Service has historically intercepted about $28 Million in contraband goods being smuggled into the country with a standard deviation of $16 Million per day. On 64 randomly chosen days in 2002, the U.S. Customs Service intercepted an average of $30.3 Million in contraband goods. Does the sample indicate (at a 5% level of significance), that the Customs Commission should be concerned that smuggling has increased above its historic level?
Show all work I will give like
The sample data does not provide sufficient evidence to conclude that smuggling has increased above its historic level at a 5% level of significance.
To determine if the sample indicates a significant increase in smuggling above the historic level, we can perform a hypothesis test.
- Historic mean: μ = $28 Million
- Standard deviation: σ = $16 Million
- Sample size: n = 64
- Sample mean: \(\bar{x}\) = $30.3 Million
- Significance level: α = 0.05
We can set up the following hypotheses:
Null hypothesis (H0): The average smuggling level has not increased, μ ≤ $28 Million
Alternative hypothesis (Ha): The average smuggling level has increased, μ > $28 Million
To test the hypothesis, we can use a one-sample t-test. Since the population standard deviation is unknown, we use the t-distribution.
The test statistic for a one-sample t-test is calculated as:
t = (\(\bar{x}\) - μ) / (σ / √(n))
Calculating the test statistic:
t = ($30.3 - $28) / ($16 / sqrt(64))
t = $2.3 / ($16 / 8)
t = $2.3 / $2
t = 1.15
Next, we need to find the critical value corresponding to the significance level α = 0.05 and degrees of freedom (df) = n - 1 = 63. We can use the t-distribution table or R to find this value. For simplicity, let's assume a one-tailed test.
In R, you can use the following code to find the critical value:
```R
critical_value <- qt(0.95, df = 63)
critical_value
```
The critical value for a one-tailed test with α = 0.05 and df = 63 is approximately 1.67.
Finally, we compare the test statistic to the critical value to make a decision. If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Since the test statistic (1.15) is less than the critical value (1.67), we fail to reject the null hypothesis. This suggests that the sample data does not provide sufficient evidence to conclude that smuggling has increased above its historic level at a 5% level of significance.
Note: It's important to consider that this analysis assumes the sample is representative and random, and that the conditions for using the t-distribution are met.
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The coordinates (1, 1), (1, 3), (3, 3), and (x, y) form a square when graphed on a coordinate plane. Which ordered pair would be the fourth vertex of the square? A (3, 1) B (1,3) C (3,5) D (3, 0
)
Answer:
3,1
....................................
30
yldpri the linear relationship.
3. The pool is filled every 90 days. What is the least
amount of water that must be added to the pool to
fill it after 90 days?
32
Volume of Wate
24
18
12
Answer:
what does 30 yldpri the linear relationship have do with it
Step-by-step explanation:
what is 1-1/3 pls help me
Answer:
2/3
Step-by-step explanation:
1-1/3 is the same that 3/3 - 1/3
3/3 - 1/3 = 2/3
Evaluating line integrals Use the given potential function o of the gradient field F and the curve C to evaluate the line integral F.dr in two ways 34. p(x, y, z) =xy+xz+yz; C: r(t)= (t, 2t, 3t), for 0
To evaluate the line integral F.dr using the given potential function o of the gradient field F and the curve C, we can use two methods: the first is to directly evaluate the integral using the parameterization of the curve and the second is to use the Fundamental Theorem of Calculus for Line Integrals.
In this case, we have the potential function o(x, y, z) = xy + xz + yz and the curve C given by r(t) = (t, 2t, 3t) for t between 0 and 1. Using the first method, we can substitute the parameterization of the curve into the integral F.dr and evaluate it directly. We have:
F.dr = (xy + xz + yz)(dx/dt, dy/dt, dz/dt)dt
= (2t^2 + 3t^2 + 6t^2)(1, 2, 3)dt
= (11t^2)(1, 2, 3)dt
Integrating this from 0 to 1, we get:
F.dr = ∫_0^1 (11t^2)(1, 2, 3)dt = (11/2, 11, 33/2)
Using the second method, we can apply the Fundamental Theorem of Calculus for Line Integrals, which states that the line integral of a conservative field along a curve C depends only on the endpoints of C and the values of a potential function at these endpoints. Since we have a gradient field F, it is conservative, and we can find the potential function o by integrating the components of F. We have:
Fx = y + z
Fy = x + z
Fz = x + y
Integrating the first component with respect to x, we get:
o(x, y, z) = ∫ (y + z)dx = xy + xz + h(y, z)
Taking the partial derivative of this expression with respect to y, we get:
∂o/∂y = x + ∂h/∂y = x + z
Comparing this with the second component of F, we get:
x + z = x + z
Therefore, h(y, z) = yz, and we have:
o(x, y, z) = xy + xz + yz
Using the potential function, we can evaluate the line integral F.dr by computing the difference of the potential function at the endpoints of the curve. We have:
F.dr = o(r(1)) - o(r(0))
= o(1, 2, 3) - o(0, 0, 0)
= (2 + 3 + 6) - (0 + 0 + 0)
= 11
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VĂ ROG AJUTOR URGENT DAU COROANĂ VĂ IMPLOR
Cercul cel mai mare are raza a unitati (imagine atasată). Cercurile cele mai mici au raza de c unitati. Celelalte doua (medii) au raza de b unitati. Stiind ca toate cercurile sunt tangente, demonstrati ca a : b : c = 6 : 3 : 2.
Stiu ca trebuie sa folosesc Pitagora si sa arat ca a=3c. Dar in rest m-am blocat si e super importanta problema. Va multumesc FOARTE mult. Puteti efectiv doar sa mi dati hints pentru ca de abia mi-am facut contul si am doar 25 de puncte. V-as fi dat 100.
mathematic that is not math
An ant starts at (0, 0), and only makes moves of length 1 in the positive x directions or the positive y direction. How many paths are there from the ant that end at (3, 3) but never pass through (2, 3)
Answer:
The number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.
Step-by-step explanation:
The possible pathways are as follows:
(0, 0) → (1, 0) → (2, 0) → (3, 0) → (3, 1) → (3, 2) → (3, 3)
(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (3, 2) → (3, 3)
(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2) → (3, 2) → (3, 3)
(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (3, 2) → (3, 3)
Thus, the number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.
Owen draws the cube shown. Pat draws a cube with a side length that is 3 units
greater than the side length of Owen’s cube. Carly draws a cube with a side
length that is 1/2 the side length of Pat’s cube.
Determine whether each expression represents the volume, in cubic inches, of Carly's Cube.
The expression represents the volume, in cubic inches, of Carly's Cube is 125 cubic inches.
What is the volume of the cube?Owens cube:
Volume of a cube = side³
= 7 in³
= 343 cubic inches
Pat's cube:
side = 7in + 3in
= 10 in
Volume of a cube = side³
= 10in³
= 1000 cubic inches
Carly's cube:
side length= 1/2 of 10in
= 1/2 × 10
= 5in
Volume of Carly's cube = side³
= 5in³
= 125 cubic inches
Therefore, the volume of Carly's cube I given by 125 cubic inches.
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Please solve in EXCEL using an excel formula such as =npv
ou're buying a house that costs 300,000 with a down payment of \( 25 \% \) in cash and a 30 year mortgage for the rest at \( 2.75 \% \). What are your onthly principal + interest payments?
To calculate the monthly principal + interest payments for a house with a down payment and a mortgage using an Excel formula, you can use the PMT function. Here's how:
Calculate the loan amount by subtracting the down payment from the house cost. In this case, the down payment is 25% of $300,000, so it would be $75,000.
Loan Amount = $300,000 - $75,000 = $225,000
Determine the monthly interest rate by dividing the annual interest rate by 12. In this case, the annual interest rate is 2.75%, so the monthly interest rate would be 2.75% / 12 = 0.00229.
Determine the loan term in months. Since it's a 30-year mortgage, the loan term would be 30 * 12 = 360 months.
Use the PMT function in Excel to calculate the monthly principal + interest payment.
Monthly Payment = -PMT(0.00229, 360, 225000)
The negative sign is used because the payment is an outgoing cash flow.
By using this formula in Excel, you can find the monthly principal + interest payments for your mortgage. Remember to adjust the interest rate, loan amount, and loan term if they differ from the example provided.
To calculate the monthly principal + interest payments using an Excel formula, you can use the PMT function by inputting the appropriate parameters: the monthly interest rate, loan term in months, and loan amount.
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If you continue to subtract 6, what is the last number in the sequence before you get to 0? Explain how you got this answer.
Answer:
6
Step-by-step explanation:
If x represents the last number, to get zero you must subtract 6 from it:
x - 6 = 0
x = 6 . . . . . . add 6 (undo the subtraction)
The last number before zero is 6.
Answer number 10 please. Thank you.
7+2+3 and 3+2+2 are the same?
Associative Property of Addition
HOW DOES YOUR ACCOUNT GET DELETED OVER NOTHING!?!?!?! I FREAKING LOST EVERYTHING OVER SOMETHING I DIDN'T EVEN DO WHAT THE ACTUAL FAWQ!!!
Answer:
when the imposter is sus
what is the equation for a cosecant function with vertical asymptotes found at such that n is an integer?
The equation for a cosecant function with vertical asymptotes found at x = nπ such that n is an integer is `y = csc(x - nπ)`.
The cosecant function is the reciprocal of the sine function. The cosecant of a particular angle in a right triangle is the ratio of the hypotenuse to the side opposite the angle.
The cosecant function is written as follows: `csc(x) = 1/sin(x)`
Asymptotes are straight lines or curves that a graph approaches but never touches.
As a result, the graph of a curve gets closer and closer to the asymptote as it moves further away from the origin, but it never touches it.
For a function to have vertical asymptotes at `x = nπ`, the denominator of the function should equal zero. In the cosecant function, the denominator is equal to `sin(x - nπ)`.
Therefore, the vertical asymptotes are where `sin(x - nπ) = 0`.
The general form of the cosecant function is `y = A csc(B(x - C)) + D`.
The constants A, B, C, and D are used to alter the form of the graph of the cosecant function.
They can be used to alter the amplitude, period, phase shift, and vertical displacement of the graph, respectively.
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How do you identify ordered pairs that are solutions to the inequalities?
Options B, C and D will satisfy the given inequality by putting the values in the given inequality.
let's first try to understand what are inequalities.
An inequality in algebra is a mathematical statement that employs the inequality symbol to show how two expressions relate to one another. The phrases on either side of an inequality symbol are not equal. The phrase on the left should be larger or smaller than the expression on the right, or vice versa, according to this symbol. Relationships between two algebraic expressions that are represented by inequality symbols are referred to as literal inequalities.
If the symbols ">,"< ">=," "<=," are used to connect two real numbers or algebraic expressions, that relationship is referred to as an inequality.
We put Given values in inequality and then see whether inequality is true or not.
Inequality is 3x+y < = 6
first x = 4 y =3
3x+y <= 6
3*4 + 3 <= 6
15 <= 6 this is not true because 15 is greater than 6.
second x = -2 y =4
3x+y <= 6
3*-2 + 4 <= 6
-2 <= 6 this is true because -2 is less than 6.
third x = -5, y =-3
3x+y <= 6
3*-5 + -3 <= 6
-15 <= 6 this is true because -15 is less than 6.
fourth x = 3, y = -3
3x+y <= 6
3*3 - 3 <= 6
6 <= 6 this is true because 6 is equal to 6.
Given Question is incomplete Complete the Question here:
How do you determine ordered pairs are part of the solution set of inequalities ex: #3x+y<=6#
for A(4,3), B(-2,4), C(-5,-3), D(3,-3)?
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Show the family of conics with the same focus
x^2/a^2+C + y^2/b^2+C = 1
is its own orthogonal family of curves.
The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.
To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.
First, we take the derivative of the equation with respect to x:
2x/a^2 = -2y/b^2 * dy/dx
Simplifying, we get:
dy/dx = -b^2*x/a^2*y
Now, we set this equal to -1/b^2:
-b^2*x/a^2*y = -1/b^2
Cross-multiplying and simplifying, we get:
x/a^2*y = 1/b^2
Finally, we can rearrange this equation to get:
y = b^2*x/a^2
This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.
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in how many ways can 2 red lights, 4 yellow lights, 5 blue lights, 1 green light and 2 pink lights be arranged on a string of lights?
Therefore, the total number of ways the lights can be arranged on the string is: 14! / (2! * 4! * 5! * 2!).
To find the number of ways the lights can be arranged on a string, we need to calculate the total number of permutations.
The total number of lights is 2 red lights + 4 yellow lights + 5 blue lights + 1 green light + 2 pink lights = 14 lights.
Since all the lights are distinct, we can arrange them in 14! (factorial) ways. However, since there are repetitions of certain colors, we need to account for that.
The red lights are identical, so we divide by 2! (the number of permutations of the red lights among themselves).
The yellow lights are identical, so we divide by 4! (the number of permutations of the yellow lights among themselves).
The blue lights are identical, so we divide by 5! (the number of permutations of the blue lights among themselves).
The pink lights are identical, so we divide by 2! (the number of permutations of the pink lights among themselves).
Therefore, the total number of ways the lights can be arranged on the string is:
14! / (2! * 4! * 5! * 2!)
You can calculate this expression to find the specific number of arrangements.
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Can someone help me ASAP? It’s due today
The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
How to Identify Independent Events?Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
This is because each event does not depend on another one of the events being described.
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36 inch board is to be cut into three pieces so that the second piece is three times as long as the first piece and the third piece is five times as long as the first piece if X represents the length of the first piece find the length of all three pieces
Answer: the first one would be four then that times 3 would be 12 which is 2 and then 4 times 5 is 20 which would be the third then you could add to check and you would get 36
Step-by-step explanation:
Hope this helped
if something's not clear, write a comment I'll help
the given equation represents a volume x, in gallons, of a 10% saltwater solution that will be mixed with a volume y, in gallons, of a 20% saltwater solution to produce an 18% saltwater solution. what volume, in gallons, of the 20% saltwater solution will be needed if 50 gallons of the 10% saltwater solution is use
In order to get a total combination of 250 gallons with an 18% salt concentration, 200 gallons of a 20% saltwater solution and 50 gallons of a 10% saltwater solution must be combined.
What is the volume formula?A basic formula for volumes is length, breadth, and height, as opposed to length, width, and height for the surface of a rectangle. It doesn't matter how you reference to the various dimensions; you could, for instance, use "depth" instead of "height" without the calculation changing.
The issue provides the equation shown below:
0.1x + 0.2y = 0.18(x + y)
Where 0.18 is the final mixture's salt content and x and y are the volumes of 10% and 20% saltwater solutions, respectively, in gallons.
Given with x = 50 gallons, we can solve for x by substituting the following into the equation:
0.1(50) + 0.2y = 0.18(50 + y)
By condensing and figuring out y, we get at:
5 + 0.2y = 9 + 0.18y
0.02y = 4
y = 200
Therefore, 200 gallons of the 20% saltwater solution will be needed to mix with 50 gallons of the 10% saltwater solution to produce a final mixture of 250 gallons at 18% concentration of salt.
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DeMario has two ltimes and four quarters. Pratima has five dimes and two quarters. They have $2.20 altogether. Write an expression or equation that matches this situation.
Answer:
8 x2.20 = Answer
Step-by-step explanation:
Answer:
7d+6q=2.20
Step-by-step explanation:
Circle A has center of (2, 3) and a radius of 5, and circle B has a center of (1, 4) and a radius of 10. What steps will help show that circle A is similar to circle B?
Dilate circle A by a scale factor of 2.
Translate circle A using the rule (x + 1, y − 1).
Rotate circle A 180° about the center.
Reflect circle A over the y-axis.
Answer:
A
Step-by-step explanation:
To show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have two circles:
Circle A has a center of (2, 3) and a radius of 5
Circle B has a center of (1, 4) and a radius of 10
The standard circle's equation can be written as:
(x - h)² + (y - k)² = r²
The equation for circle A:
(x - 2)² + (y - 3)² = 5²
The equation for circle B:
(x - 1)² + (y - 4)² = 10²
To show that circle A is similar to circle B:
It is required to perform the geometric transformation:
Dilate circle A by a scale factor of 2.
The radius of circle A is 5 units and after dilation by a scale factor of 2, the radius of the circle becomes 10 which is the radius of circle B.
Thus, to show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.
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An experiment will be conducted in which 20 pepper plants are randomly assigned to two groups. The plants in group 1 will receive the current fertilizer, fertilizer a, and the plants in group 2 will receive a new fertilizer, fertilizer b. All other growing conditions, including amount of sunlight and water, will be kept the same for the two groups. The growth of the pepper plants will be compared for the two groups. What are the experimental units in this experiment?.
Answer: E. The 20 plants in the two groups
Step-by-step explanation: experimental units are individuals on which the experiment is being performed. In this case the pepper plants are being used to test the effectiveness of the new fertilizer.
Menaha traveled 86km 520m by train and 11km 480m by car What ditance did he travel in all?
In total, Menaha traveled 97km 1000m (97.1km).
What is distance?Distance is a numerical measurement of how far apart two objects, points, or places are in space. Distance can be measured in linear units such as meters, kilometers, feet, miles, etc. It can also be measured in angular units such as degrees or radians.
Distance can also refer to the space between two points in time, such as the time between two events. Distance can be used to measure physical distance, time, or even emotional distance.
To calculate this, the two distances must be added together.
The train distance is =86km 520m (86.52km)
and the car distance is =11km 480m (11.48km).
When added together, =86km 520m+11km 480m = 97.52km.
However, since the distances are measured in km and m,
it is necessary to convert the measurements into a single unit of measurement.
To do this, the measurements must be converted into metres.
The train distance is 86,520 metres
And the car distance is 11,480 metres.
When added together,
the total distance is 97,000 metres (97km).
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Algorithm Mistery (A[0. . n-1, 0. .n-1]) Input: an n X n array A of integer numbers Output: a boolean value 1 . for
(i=0; i< n-1; it+) 2 . for (j=itl; j < n; j+ +) 3 . if (A [i, j] != A[j, i]) 4 . return false; e 5 . return true;Note: when giving the big-Oh , give the tightest upper bound possible. For example, if you can prove that f(n) is O(n) and that f(n) is O(n2), choose the tighter upper bound, ie f(n) is O(n). a)Give a big-Oh for T(n) the worst-case running time of this algorithm for an input matrix of size n x n. Explain how you obtained this worst case.
b)Give a big-Oh for B(n) the best-case running time of this algorithm for an input matrix of size n x n. Explain the type of inputs (sample inputs) that will give this best case.
a) The worst-case running time of this algorithm is O(n^2).
b) The best-case running time of this algorithm is Ω(n).
a) In the worst case, the algorithm iterates through two nested loops. The outer loop iterates from i=0 to n-1, and the inner loop iterates from j=it+1 to n. This results in a time complexity of O(n^2), as the algorithm examines each pair of elements in the upper triangular part of the matrix.
To obtain this worst case, we consider a scenario where every element in the upper triangular part is different from its corresponding element in the lower triangular part. This forces the algorithm to iterate through all pairs of elements in the upper triangular part, resulting in a quadratic time complexity.
b) In the best case, the algorithm returns early without having to check all pairs of elements in the matrix. This occurs when every element in the upper triangular part is the same as its corresponding element in the lower triangular part. In this case, the algorithm only needs to iterate through a few pairs of elements before returning true.
For example, a symmetric matrix where all elements are the same or a matrix where the upper triangular part is a mirror image of the lower triangular part would result in the best case. This would allow the algorithm to terminate early after checking a small number of pairs of elements.
a) The worst-case running time of the algorithm is O(n^2), indicating a quadratic time complexity.
b) The best-case running time of the algorithm is Ω(n), indicating a linear lower bound.
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