Based on the right triangle drawn on a coordinate grid, the coordinates of Ernie's starting point is (10, 9).
Ernie's starting point for the right triangle can be found by using the coordinates of the endpoint of the second segment and the lengths of the two segments he drew. The endpoint of the second segment had coordinates (6, 3), and he drew a 4-unit segment to the left and a 6-unit segment downward from his starting point.
To find the x-coordinate of the starting point, we can add the length of the segment Ernie drew to the left to the x-coordinate of the endpoint. This gives us:
x-coordinate of starting point = x-coordinate of endpoint + length of segment to the left
x-coordinate of starting point = 6 + 4
x-coordinate of starting point = 10
To find the y-coordinate of the starting point, we can add the length of the segment Ernie drew downward to the y-coordinate of the endpoint. This gives us:
y-coordinate of starting point = y-coordinate of endpoint + length of segment downward
y-coordinate of starting point = 3 + 6
y-coordinate of starting point = 9
Therefore, the coordinates of Ernie's starting point are (10, 9).
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How was triangle A translated?
O four units left
O four units right
O six units left
O six units right
Answer:
six units rights
Step-by-step explanation:
I don't have one but I know because I've had kt
bernardo and silvia play following game. an integer between 0 and 999, inclusive, is selected and given to bernardo. whenever bernardo receives a number, she doubles it and pass the result to silvia. whenever silvia recieves a number, she adds 50 and passes teh result to bernardo. the winner is the last person who produces a number less than 100. what is the smallest initial number that results in a win for bernardo
The smallest initial number that results in a win for Bernardo is 31.
Winning number in GameHere's the breakdown of how the game would play out:
Bernardo starts with 31 and doubles it to get 62.Silvia receives 62 and adds 50 to get 112.Bernardo receives 112 and doubles it to get 224.Silvia receives 224 and adds 50 to get 274.Bernardo receives 274 and doubles it to get 548, which is greater than 100, so Bernardo loses.If Bernardo starts with any number less than 31, the final number will be less than 100 and Bernardo will win. Any number greater than 31 will result in Bernardo losing.
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Examine the following table, which represents some points on a line.
x 3 0 −3 −6 −9
y −3 −2 −1 0 1
What is the equation for the line in slope-intercept form?
y=−3x−2y is equal to negative 3 x minus 2, , ,
y=3x−2y is equal to 3 x minus 2, , ,
y=−13x−2y is equal to negative 1 third x minus 2, , ,
y=−13x−6y is equal to negative 1 third x minus 6, , ,
y=−3x−6
Answer:
(c) y = −1/3x −2
Step-by-step explanation:
We notice two things in the table.
y goes up by 1 when x goes down by 3.y = -2 when x = 0 (this is the y-intercept__
The slope of the line is ...
m = (change in y)/(change in x) = +1/-3 = -1/3
Then the slope-intercept equation is ...
y = mx +b . . . . . . slope m, y-intercept b
y = -1/3x -2
Answer is C
Step-by-step explanation:
math
Simplify
\( \frac{6 { {}^{7} }^{} }{6 {}^{5} } \)
Leaving answer in index form
Answer:
\(6^{7-5} = 6^2\)
Step-by-step explanation:
Answer:
36.
Step-by-step explanation:
6^7 / 6^5
= 6^(7-5)
= 6^2
= 36.
can you guys help pls?
Answer:
x= 68 degrees
Step-by-step explanation:
The manager of a small convenience store does not want her customers standing in long too long prior to a purchase. In particular, she is willing to hire an employee for another cash register if the average wait time of the customers is more than five minutes. She randomly observes the wait time (in minutes) of customers during the day: 3.5 5.8 7.2 1.9 6.8 8.1 5.4 Assume x-bar = 5.53 and s = 0.67. What is the appropriate conclusion at a 5% significance level? a) A new employee does not need to be hired since: .05 < p-value < .10 b) A new employee needs to be hired since: .025 < p-value < .05 c) A new employee does not need to be hired since: .025 < p-value < .05 d) A new employee needs to be hired since: .01 < p-value < .025
The appropriate conclusion at a 5% significance level is that a new employee needs to be hired since the p-value is less than 0.05.
To test the hypothesis, we will use a one-sample t-test with a null hypothesis that the true population mean wait time is less than or equal to 5 minutes. The alternative hypothesis is that the true population mean wait time is greater than 5 minutes.
Using the given sample data, we calculate the sample mean (x-bar) as 5.53 and the sample standard deviation (s) as 0.67. The sample size is 7.
We calculate the t-statistic using the formula t = (x-bar - mu)/(s/sqrt(n)), where mu is the hypothesized population mean (5) and n is the sample size.
Substituting the values, we get t = (5.53 - 5)/(0.67/sqrt(7)) = 2.44.
Using a t-distribution table with 6 degrees of freedom (n-1), we find the p-value to be 0.03 for a one-tailed test. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that a new employee needs to be hired to reduce the average wait time.
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Write a function swapvectorends() that swaps the first and last elements of its vector parameter. Ex: sortvector = {10, 20, 30, 40} becomes {40, 20, 30, 10}.
The function of swapvectorends() is written below.
Function:
In math, function is defined as a relation between a set of inputs having one output each.
Given,
Here we need to write a function swapvectorends() that swaps the first and last elements of its vector parameter.
The function swapvectorends() that swaps the first and last elements of its vector parameter is written as,
Int swapvectorends(vector <int> & sectorVector)
{
int i = 0;
for ( i = 0; i < sectorVector.size() - 1; ++i)
{
sectorVector.at(i) = sectorVector.at(sectorVector.size() - 1 - i);
}
return;
}
Now, when we input the value sortvector = {10, 20, 30, 40} onto the given function, then it will results the output sortvector = {40, 30, 20, 10}
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toby's school is 4 miles west of his house and 3 miles south of his friend erica's house. every day, toby bicycles from his house to his school. after school, he bicycles from his school to erica's house. before dinner, he bicycles home on a bike path that goes straight from erica's house to his own house. how far does toby bicycle each day?
Toby cycles 12 miles each day.
To find out how far Toby cycles each day, we need to add up the distance he covers during his morning and afternoon trips. Here are the steps we need to follow:
Step 1: Determine Toby's cycling distance from his house to his schoolDistance from Toby's house to his school = 4 miles west. Toby bicycles this distance every day. Therefore, his one-way cycling distance from home to school is 4 miles.
Step 2: Determine Toby's cycling distance from his school to Erica's house.Distance from Toby's school to Erica's house = 3 miles south. Toby cycles this distance every day after school. Therefore, his one-way cycling distance from school to Erica's house is 3 miles.
Step 3: Determine Toby's cycling distance from Erica's house to his house.Distance from Erica's house to Toby's house = we don't know. But we know that Toby takes a bike path that goes straight from Erica's house to his own house. Therefore, we can assume that the distance from Erica's house to Toby's house is the hypotenuse of a right-angled triangle with legs of 3 miles (south) and 4 miles (west).
We can use the Pythagorean Theorem to find the hypotenuse: c2 = a2 + b2c2 = 32 + 42c2 = 9 + 16c2 = 25c = √25c = 5 milesTherefore, Toby cycles 5 miles every day on his bike path from Erica's house to his own house.Step 4: Add up Toby's one-way cycling distances to find out how far he cycles each day.Toby's one-way cycling distance from home to school = 4 milesToby's one-way cycling distance from school to Erica's house = 3 milesToby's one-way cycling distance from Erica's house to his house = 5 milesTotal cycling distance = 4 + 3 + 5Total cycling distance = 12 miles.
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What is the difference between quantitative data and qualitative data? in what situations could the number 42 be considered qualitative data? what are the characteristics of a relational database?
The number 42 could be qualitative if it is a designation instead of a measurement, count, or calculation.
Qualitative data describes qualities or characteristics. It is collected using questionnaires, interviews, or observation, and frequently appears in narrative form. For example, it could be notes taken during a focus group on the quality of the food at Cafe Mac, or responses from an open-ended questionnaire. Qualitative data may be difficult to precisely measure and analyze. The data may be in the form of descriptive words that can be examined for patterns or meaning, sometimes through the use of coding. Coding allows the researcher to categorize qualitative data to identify themes that correspond with the research questions and to perform quantitative analysis.
Quantitative data is numbers-based, countable, or measurable. Quantitative data is numeric, the result of a measurement, count, or some other mathematical calculation. Qualitative data is descriptive. The number 42 could be qualitative if it is a designation instead of a measurement, count, or calculation.
The seven characteristics that define relational database are:
Accuracy and Precision
Legitimacy and Validity
Reliability and Consistency
Timeliness and Relevance
Completeness and Comprehensiveness
Availability and Accessibility
Granularity and Uniqueness
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HELPPPPPPPPPPP
What is the circumference of a circle with a radius of 12.5 feet?
Answer:
c = 78.5 ft.
Step-by-step explanation:
C = 2πr
C = 2(3.14)(12.5) = 78.5 feet
Hope this helps
Does this set of ordered pairs represent a function? Why or why not?
Answer:
A
Step-by-step explanation:
Recall that for a function to be valid, each input value of x must give us one and only one unique output value for y.
in this case we can see that one of the data sets is (3,-1)
which means that an input of 3 gave an output of -1
but we also see that another data set (3,1)
in this case an input of 3 gave an output of 1.
Because the same x input gives 2 different y outputs, this is not a function.
the answer is A
Answer:
The answer is A
Step-by-step explanation:
I got it right on the test
consider the curve given by xy^2-x^3y=6
a) Find all points on the curve whose x-coordinate is 1 and write an equation for the tangent line of each of these points.
b) Find the x-coordinate of each point on the curve where the tangent line is vertical.
a) The pοints οn the curve with x-cοοrdinate 1 are (1, 3) and (1, -2). The equatiοn οf the tangent line at (1, -2) is y = (3/2)x - 5/2.
b) The x-cοοrdinate οf each pοint οn the curve where the tangent line is vertical is apprοximately ±1.443.
What is a curve in a graph?A curve is defined as a smοοthly- flοwing cοntinuοus line that has bent. It dοes nοt have any sharp turns. The way tο identify the curve is that the line bends and changes its directiοn at least οnce.
a) Tο find all pοints οn the curve whοse x-cοοrdinate is 1, we substitute x = 1 intο the equatiοn and sοlve fοr y:
1 * y² - 1³ * y = 6
y² - y = 6
y² - y - 6 = 0
Factοring the quadratic equatiοn, we have:
(y - 3)(y + 2) = 0
Setting each factοr equal tο zerο, we find twο pοssible values fοr y:
y - 3 = 0 --> y = 3
y + 2 = 0 --> y = -2
Therefοre, the pοints οn the curve with x-cοοrdinate 1 are (1, 3) and (1, -2).
Tο find the equatiοn οf the tangent line at each οf these pοints, we need tο find the derivative dy/dx and evaluate it at each pοint.
Differentiating the equatiοn οf the curve implicitly with respect tο x, we get:
2xy * dy/dx - 3x² * y - x³ * dy/dx = 0
Rearranging the terms and sοlving fοr dy/dx, we have:
dy/dx * (2xy - x³) = 3x² * y
dy/dx = (3x² * y) / (2xy - x³)
At the pοint (1, 3):
dy/dx = (3 * 1² * 3) / (2 * 1 * 3 - 1³) = 9 / 5
Using the pοint-slοpe fοrm οf a line, we can write the equatiοn οf the tangent line at (1, 3) as:
y - 3 = (9/5)(x - 1)
y = (9/5)x - 6/5
At the pοint (1, -2):
dy/dx = (3 * 1² * -2) / (2 * 1 * -2 - 1³) = -6 / (-4) = 3/2
The equatiοn οf the tangent line at (1, -2) is:
y - (-2) = (3/2)(x - 1)
y = (3/2)x - 5/2
b) Tο find the x-cοοrdinate οf each pοint οn the curve where the tangent line is vertical, we need tο find the x-values where the derivative dy/dx is undefined οr infinite.
Frοm the expressiοn fοr dy/dx derived earlier:
dy/dx = (3x² * y) / (2xy - x³)
The derivative will be undefined οr infinite when the denοminatοr is equal tο zerο:
2xy - x³ = 0
x(2y - x²) = 0
This equatiοn will hοld true when x = 0 οr 2y - x² = 0.
Fοr x = 0, substituting intο the οriginal equatiοn:
0 * y² - 0³ * y = 6
0 - 0 = 6 (which is nοt true)
Therefοre, we can exclude x = 0 as a valid sοlutiοn.
Fοr 2y - x² = 0, we can substitute 2y fοr x² in the οriginal equatiοn:
xy² - (2y)³ * y = 6
xy² - 8y³ = 6
y(xy² - 8y²) = 6
This equatiοn dοes nοt prοvide a straightfοrward sοlutiοn fοr the x-cοοrdinate when the tangent line is vertical. Tο determine the x-cοοrdinate, yοu can either sοlve this equatiοn numerically οr graphically.
Using numerical methοds, we can apprοximate the x-cοοrdinate fοr the vertical tangent line. Substituting different values οf y intο the equatiοn, we find that when y ≈ 1.042, the equatiοn is satisfied. Plugging this value οf y back intο 2y - x² = 0, we can sοlve fοr the cοrrespοnding x-cοοrdinate:
2(1.042) - x² = 0
2.084 - x² = 0
x² = 2.084
x ≈ ±1.443
Therefοre, the x-cοοrdinate οf each pοint οn the curve where the tangent line is vertical is apprοximately ±1.443.
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Given that g(x) = 3/(x + 2), x≠-2 and f(x) = 3x - 2, evaluate gf(2)
Step-by-step explanation:
g(f(2))=3/(f(2)+2)
f(2)=4
g(f(2))=g(4)=1/2
The function D(x) models the cumulative number of deaths from a disease x years after 1984. Estimate the year when there were 80,000 deaths.
2144x^(2)+5224x+5244
The year in which the number of deaths were 80,000 is A = 1997
Given data,
To estimate the year when there were 80,000 deaths, we need to find the value of x that corresponds to D(x) = 80,000.
Given the function D(x) = 2144x^2 + 5224x + 5244, we can set it equal to 80,000:
2144x² + 5224x + 5244 = 80,000
Rearranging the quadratic equation, we get:
2144x² + 5224x + 5244 - 80,000 = 0
2144x² + 5224x - 75456 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation, a = 2144, b = 5224, and c = -75456.
Substituting the values into the quadratic formula:
x = (-5224 ± √(5224² - 4 * 2144 * -75456)) / (2 * 2144)
After performing the calculations, we find two values for x:
x ≈ -3.048 and x ≈ 13.664.
Since x represents the number of years after 1984, a negative value does not make sense in this context.
Therefore, we consider the positive value of x.
x ≈ 13.664
To estimate the year when there were 80,000 deaths, we add x to 1984:
1984 + 13.664 ≈ 1997.664
Hence , the estimate for the year when there were 80,000 deaths is approximately 1997.
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The number of chirps per minutes made by a cricket is a function of the temperature (T). The function f(T) = 4(T-40). How many chirps would you except to hear when the temperature is 90?
Number of chirps would you expect to hear when the temperature is 90 is 200 .
A function from a fixed X to a hard and fast Y assigns to each detail of X exactly one element of Y. The set X is known as the area of the feature and the set Y is known as the codomain of the characteristic.
Calculation:
f(T) = 4(T-40)
= 4(90-40)
= 4 × 50
= 200
A feature is described as a relation between a fixed of inputs having one output each. In easy phrases, a feature is a courting among inputs in which each entry is related to precisely one output. each feature has a website and codomain or variety. A characteristic is commonly denoted by means of f(x) where x is the input.
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TIME REMAINING 59:36 Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he has to go. If Yan made 8 stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan climbed
Options :
4+4+4+4
8+8+8+8
(-1)(4+4+4+4)
(-8) + (-8) + (-8) + (-8)
Answer:
-8 + - 8 + - 8 + - 8
Step-by-step explanation:
Given that:
Rungs of ladder moved per stop = 4
Number of stops made = 8
Number of ladder rungs :
Ladder rungs per stop * number of stops
- 4(descent) * 8= - 32 ladder rungs
Alternative way :
-8 in 4 places
-8 + - 8 + - 8 + - 8 = - 32
Answer:
B
Step-by-step explanation:
a ___ equation is an equation that contains a variable within a radical expression.
A radical equation is an equation that contains a variable within a radical expression.
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I need this, help please
Answer:
Step-by-step explanation:
it is C. the third one
Today, Andrew borrowed R200 000 from a bank. The bank charges interest at 5.25%p.a, a compounded quarterly. Andrew will make make payments of R6 000 at the end of 3 months. His first repayment will be made 3 months from now, how long in years will it take for Andrew to settle the loan
In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.
The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.
We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.
Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.
Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000
We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)
Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0
Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.
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find the surface area, 20cm, NO LINKS
Answer:
2400cm^3 I believe
Step-by-step explanation:
what is the probability that you choose a yellow marble and then a blue marble assuming you replace the first marble?
(A bag of marbles contains 5 red, 3 blue, 2 green, and 2 yellow marbles.)
Answer:
1/24
Step-by-step explanation:
To find the first probability of getting a yellow marble, first you have to add up the total number of marbles:
5+3+2+2=12
There are two yellow marbles so the probability is:
2/12
Next is finding the probability of grabbing a blue marble. Since the first marble was replaced, we can still use the total number of marbles and the probability is:
3/12
Since the problem says to choose a yellow and then a blue, we will multiply the two.
2/12×3/12 = 6/144 = 1/24
Victoria's Secret gives you $10 off when you spend $50 on a purchase. The Body Shop gives you $11 off when you spend $55. Which deal is better?
well, 10 bucks off 50, can be written as a ratio of 10/50 and 11 bucks off 55 can be written as a ratio of 11/55, hmmm which is better or namely, which gives you more savings, the larger the fraction, the better the savings, let's check
\(\stackrel{\textit{Victoria's Secret}}{\cfrac{10}{50}\implies \cfrac{1}{5}}\hspace{5em}\stackrel{\textit{Body Shop}}{\cfrac{11}{55}\implies \cfrac{1}{5}} \qquad \textit{neither is better, both are equal}\)
For the standard normal random variable z, find z for each situation. If required, round your answers to two decimal places. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)'
a. The area to the left of z is 0.1827. z =
b. The area between −z and z is 0.9830. z =
c. The area between −z and z is 0.2148. z =
d. The area to the left of z is 0.9997. z =
e. The area to the right of z is 0.6847. z=
The z-values for the given situations are approximate:
a. The area to the left of z is 0.1827. z = -0.90
b. The area between −z and z is 0.9830. z = 2.17
c. The area between −z and z is 0.2148. z = 0.85
d. The area to the left of z is 0.9997. z = 3.49
e. The area to the right of z is 0.6847. z= -0.48
a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.
b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.
c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.
d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.
e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.
In summary, the z-values for the given situations are approximate:
a. -0.90
b. 2.17
c. 0.85
d. 3.49
e. -0.48
These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.
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Concrete is made by mixing screenings cement and sand in the ratio 3:1:15. How much sand would be needed to make 125 tonnes of concrete?
calculate the size of unknown angles
Hi! I'm happy to help!
We know that 2y=150, so we can divide both sides by 2 to find the angle of y
2y=150°
÷2 ÷2
y=75°
So, y=75°.
I hope this was helpful, keep learning! :D
20)
Which square root is NOT a whole number?
A)
144
B)
156
C)
169
D)
196
Answer:
196
Step-by-step explanation:
196 does not have a whole number square
10 = 18+ 4(3x+7)
please help with the answer
Answer:-3
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A shop recorded total sales of $2,000 on Monday. On Tuesday, its sales fell by 10%. On Wednesday, sales fell by another 20% compared with Tuesday. From Wednesday to Thursday, sales increased by an amount equal to 25% of Monday’s total sales.
What is the net change, in dollars, in total sales from Monday to Thursday?
The diffrence between monday and Thusday is $500 because 25% of 2000 is 500 and 2,000+500= 2500
Answer:
Im pretty sure its a negative number
Step-by-step explanation:
Can someone help me please
Answer:
0.19 50% 15/20 9/10 95%
Step-by-step explanation:
I know
What is the GCF of 4454 and 121j²k?
O 4j³k²
O 4j²k4
O 11j³k²
O 11j²4
The required, there is no highest common factor between 4454 and 121j²k. None of the options are correct.
What is the greatest common factor?The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.
Here,
To find the greatest common factor (GCF) of 4454 and 121j²k, we need to factor both numbers into their prime factors and then identify the common factors.
Since 4454 is an even number and 121 is an odd number so there is no prime highest common factor between the given number.
Thus, none of the options are correct.
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