substitution 4x+y=-5 -2x-8y= -20
Answers
Answer:
35 over 6 an 10 over 3
Step-by-step explanation:
Related Questions
8) Which term is defined as a professional that is responsible for the overall financial health of an organization or business?
Question 8 options:
financial analyst
financial planner
chief financial officer
financial accountant
Answers
The professional which is responsible for the organization's overall financial health is (c) chief financial officer.
The "Chief-Financial-Officer" (CFO) is a senior executive in an organization who is responsible for overseeing the financial activities of the company.
The CFO reports to board of directors and is responsible for managing the company's financial actions, including financial planning, budgeting, accounting, and reporting.
The CFO's main responsibility is to ensure the overall financial-health of the company, which involves developing and implementing financial strategies.
The CFO is also responsible for managing the company's cash flow and working capital.
Therefore, the correct option is (c).
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The given question is incomplete, the complete question is
Which term is defined as a professional that is responsible for the overall financial health of an organization or business?
(a) financial analyst
(b) financial planner
(c) chief financial officer
(d) financial accountant
the number of research papers in dr. carey's area of expertise has been increasing by 3% every year. given that 34,176 research papers were published this year, how many will be published 2 years from now?
Answers
If the number of research papers in Dr. Carey's area of expertise is increasing by 3% every year and 34,176 research papers were published this year, then approximately 35,168 research papers will be published two years from now.
To calculate the number of research papers that will be published two years from now, we need to apply the 3% annual increase for two consecutive years to the initial count of 34,176 papers.
First, we calculate the increase for the first year:
Increase = 34,176 * 3% = 34,176 * 0.03 = 1,025.28 (approximately)
Next, we add this increase to the initial count to get the count after one year:
Count after one year = 34,176 + 1,025.28 = 35,201.28 (approximately)
Now, we calculate the increase for the second year based on the count after one year:
Increase = 35,201.28 * 3% = 35,201.28 * 0.03 = 1,056.04 (approximately)
Finally, we add this increase to the count after one year to get the count after two years:
Count after two years = 35,201.28 + 1,056.04 = 36,257.32 (approximately)
Therefore, approximately 36,257 research papers will be published two years from now.
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For the following set of data, find the percentage of data within 2
population standard deviations of the mean, to the nearest percent.
58, 77, 31, 54, 58, 54, 56, 58, 56
Answers
Answer:
58,+77,+31,+54+,58+,54+,46+,58+,56/9
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
The data set is given below.
58, 77, 31, 54, 58, 54, 56, 58, 56.
Then the mean of the data set will be
Mean = (58 + 77 + 31 + 54 + 58 + 54 + 56 + 58 + 56) / 9
Mean = 502 / 9
Mean = 55.78
Then the standard deviation will be
\(\rm SD = \sqrt{\dfrac{(58 - 55.78)^2+(77-55.78)^2 + ..... + (56-55.78)^2 }{9}}\\\\SD = \sqrt { \dfrac{1085.5}{9}}\\\)
On further solving we have
SD = 10.98
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
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Analyze the definition below and complete the instructions that follow.
A calf is a young cow.
Identify the p and q statements from the given definition.
A.
p: A cow is young ↔ q: A cow is not a calf
B.
p: A young cow is a calf ↔ q: A calf is a cow
C.
p: A cow is a young calf ↔ q: A calf is a young cow
D.
p: A cow is a calf ↔ q: A cow is young
Answers
Answer: B
Step-by-step explanation:
Assuming we mean biconditional statements. A biconditional must always be true. B is the only answer choice were both p and q are true. A young cow is a calf, and calfs are cows. Hope this helps!
, 80 POINTS Find k so that P(k,0) is equidistant from points A(1,2) and B(2,5).
ANSWER IN NEXT 20 MIN
Answers
Answer:
P(1.5, 3.5)
Step-by-step explanation:
We need to find the average of the x and y coordinates. We do this by adding the two values, then dividing by two:
P(x1 + x2/ 2, y1 + y2/2) = P(1 + 2/ 2, 2 + 5/ 2) = P(3/2, 7/2) = P(1.5, 3.5)
These are our coordinates!
Dholakpur Beverage (DB) 25 Marks After learning some tricks from Prof. Dhoomketoo, Mr. Dholu and Mr. Bholu decided to utilize their skills by purchasing a small juice making factory in Dholakpur and named it Dholakpur Beverage (DB). Their purchase included the equipment needed to produce the juice from the grapes. Preparing juice for the final packaging requires the following 4 - step process. First, the farmers transport the grapes to DB and store them in storage containers (capacity is sufficient). Then the grapes enter the crushing machine, which crushes the grapes into a form that includes liquid, skins, seeds and stems. From the crusher, the juice substance moves to the filtration machine immediately, where the skins, seeds, and stems are separated from the liquid. The grape juice then proceeds to the concentration step. It is not desirable to store the juice being processed either after crushing or before concentration stage as it losses its freshness forever i.e. juice being processed cannot be stored between crushing and filtration and hence move immediately to filtration after crushing. Same applies between filtration and concertation. Once these 4 steps of the preparation process are completed, the juice is placed in a very large storage tank and stored in a temperature-controlled environment for further packaging. On a typical day, farmers supply grapes equivalent to 60 gallons of juice per hour. The farmers begin picking grapes at 5:00 am and finish by 1:00 pm. At the end of each hour, the farmers bring their yield to the DB to store in containers until the grapes are sent to the first processing step, the crushing machine. Therefore, actual time of juice processing start at 6 a.m. and continue till 2 p.m. equal to 8 hours shift. The crushing machine can process 50 gallons of juice per hour. The filtration machine can separate the liquid from the solids at a rate of 60 gallons of juice per hour. However, after every 3 hours of operations, the filter in the filtration machine requires cleaning. This cleaning takes one hour to complete. Finally, the concentration step can process 75 gallons of juice per hour. The processed juice is immediately transferred from one process to another till it reaches to a large storage tank. Dholu and Bholu need two workers in the DB in 4 - steps when the grapes are being produced - one worker at the crushing machine and one worker at the filtration machine. Either Dholu or Bholu checks the final quality of the processed juice, since this step requires the skills of a "juice master". The workers are paid Rs. 25 per hour for the first 8 hours, then receive overtime pay of Rs. 35 per hour for every additional hour per day. All grapes received must be processed within 24 hours, or the grapes spoil. While answering the following questions ignore lunch and tea breaks and also assume that the filter is clean at the start of each day and Dholu and Bholu do not pay themselves as they directly share the profit.
a. Draw process flow diagram for DB operation. (4 marks)
b. If all processes work independent of each other, what is the daily capacity of the crushing, filtration and concentration per day (6 am to 2 pm - 8 hour shift)? (2 marks)
c. How many gallons of juice can be processed per day (6 am to 2 pm - 8 hours shift) considering entire DB’s operation from crushing through concentration? What is the labor cost per gallon for the juice processed in 8 hour shift? (5 marks)
d. Is it possible to process all grapes supplied by farmers in 8 hour shift? If not how many hours of overtime is required to process all the grapes supplied. Round up the fractional number of OT hours while answering. What is overtime labor cost per gallon for the juice processed during overtime? (4 marks)
e. Raju suggested to add buffer storage either after crushing or filtration process to improve the capacity of the plant. This storage works as temporary buffer and make sure that juice will not lose it freshness for two hours when it moves from one step to another. Does it make sense? Yes or No? If yes, where would you place the buffer storage? What is the minimal capacity of buffer storage? What would be revised capacity of DB in 8 hour shift? (6 marks
f. Generally, juice produced and stored in large storage tank on a given day are packed or tined next day. Only 360 gallons (1 gallon = 4 liters) of juice are generally sold in packets while remaining are sold in tins. The packaging station can fill juice in 500 ml and 1500 ml size packet. It can fill 6 packets of 500 ml per minute and 4 packets of 1500 ml per minute. Recent sales records indicate that the distribution of sales by package size is: 60% and 40% for 500 ml and 1500 ml respectively per day. DB decide to produce the given proportion of packets every day from 360 gallons. How many hours are required to produce all the packets? How many number of each type of packets will be produced each day? (4 marks)
Answers
For the number of packets produced each day, we multiply the filling rate by the number of minutes required to fill the packets.
a. The process flow diagram for DB operation can be represented as follows:
Grapes from farmers --> Storage containers --> Crushing machine --> Filtration machine --> Concentration step --> Large storage tank
b. The daily capacity of each process is as follows:
- Crushing: 50 gallons/hour x 8 hours = 400 gallons/day
- Filtration: 60 gallons/hour x 8 hours = 480 gallons/day
- Concentration: 75 gallons/hour x 8 hours = 600 gallons/day
c. To calculate the total gallons of juice processed per day, we need to consider the lowest capacity among the processes, which is 400 gallons/day for crushing. Therefore, the total gallons of juice processed per day is 400 gallons. The labor cost per gallon for the juice processed in an 8-hour shift is calculated as the total labor cost divided by the total gallons of juice processed. The labor cost for an 8-hour shift is 8 hours x Rs. 25 per hour = Rs. 200. Therefore, the labor cost per gallon is Rs. 200/400 gallons = Rs. 0.50 per gallon.
d. The total gallons of juice supplied by the farmers is 60 gallons/hour x 8 hours = 480 gallons. Since the daily capacity of the concentration step is 600 gallons, it is possible to process all the grapes within the 8-hour shift without requiring overtime. Therefore, no overtime is required, and the overtime labor cost per gallon is not applicable.
e. Adding buffer storage after the filtration process makes sense as it allows for better capacity utilization of the plant. The buffer storage can be placed after the filtration machine. The minimal capacity of the buffer storage should be able to hold the juice for a maximum of 2 hours of processing time, which is 60 gallons/hour x 2 hours = 120 gallons. With the buffer storage in place, the revised capacity of DB in an 8-hour shift would be 480 gallons + 120 gallons = 600 gallons.
f. To calculate the number of hours required to produce all the packets, we need to divide the total volume of juice (360 gallons) by the filling rate of the packaging station. For the 500 ml packets, the filling rate is 6 packets/minute, which is equivalent to 6 packets/60 minutes = 0.1 packets/minute. Therefore, the number of minutes required to fill the 500 ml packets is 360 gallons / (0.1 packets/minute) = 3600 minutes. Similarly, for the 1500 ml packets, the filling rate is 4 packets/minute, so the number of minutes required to fill the 1500 ml packets is 360 gallons / (0.067 packets/minute) = 5357 minutes.
To calculate the number of packets produced each day, we multiply the filling rate by the number of minutes required to fill the packets. For the 500 ml packets, the number of packets produced is 6 packets/minute x 3600 minutes = 21,600 packets/day. For the 1500 ml packets, the number of packets produced is 4 packets/minute x 5357 minutes = 21,428 packets/day.
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Scores on IQ tests are normally distributed, with a mean of 100 and a standard deviation of 15. What is the score such that 10 percent of people taking the test achieve a higher score
Answers
Answer:
103.75 score
Step-by-step explanation:
10 % scored higher than the mean?
50% is the mean % so we need to look for the z score corresponding to 60 % from z-score table this is z-score of .25
.25 standard deviations (which is 15) above 100 =
.25 * 15 + 100 = 103.75 score
what is 3 and 1/6 as an improper fraction
Answers
Answer:
Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer
Expressions equivalent to 16x+12
Answers
Answer:
-4/3 or -1 1/3
Step-by-step explanation:
16x+12=0
16x=-12
x=16/-12
before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ? group of answer choices population variance 1 equals population variance 2 population variance 1 differs from population variance 2 population variance 1 is less than population variance 2 population variance 1 exceeds population variance 2
Answers
The correct option is B, The null hypothesis to test if the population variances differ is population variance 1 differs from population variance 2.
Variance is calculated as the average of the squared differences of each data point from the mean. In other words, variance measures how far the data points are from their average value. A high variance indicates that the data points are spread out over a wider range, while a low variance indicates that the data points are clustered more tightly around the mean.
Variance is an important concept in statistical analysis because it helps to assess the reliability of data and to make inferences about the population from a sample. It is also used in many areas of research, such as finance, economics, and engineering, to measure the risk or uncertainty associated with a set of data. Variance is closely related to other statistical measures such as standard deviation, covariance, and correlation, and is often used in conjunction with these measures to gain a deeper understanding of the data.
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Complete Question:-
Before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ?
a. population variance 1 equals population variance 2
b. population variance 1 differs from population variance 2
c. population variance 1 is less than population variance 2
d. population variance 1 exceeds population variance 2
An economics graduate student in the united states earns an $18,000 stipend per year. the u.s. sees significant inflation. how might the student react?
Answers
The reaction of the graduate student on inflation is that a cost-of-living increase to her stipend.
What is inflation?Inflation is the pace of expansion in costs over a given time-frame. Inflation is regularly a wide measure, like the general expansion in costs or the expansion in the typical cost for many everyday items in a country.
According to question:Inflation is term which states there is an expansion in the cost level for any labor and products.
In the unique situation, a set of experiences graduate living in the US got a payment of 18,000 dollar. However, there is a critical expansion that US economy endures. In this way the expense of products and the administrations accessible to individuals increments quickly. Individuals presently need to spend more on everything. Accordingly the alumni understudy requirements to request the typical cost for most everyday items to be remembered for the payment as need might arise to spend more on living.
Thus, graduate student argue on the a cost-of-living increase to her stipend.
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The time complexity for the the closest pair of points problem (in the text) using divide-and-conquer is __________. Group of answer choices O(log(n)) O(2^n) O(n*n) O(n) O(n log(n))
Answers
The time complexity for the closest pair of points problem using divide-and-conquer is O(n log(n)).
In the divide-and-conquer algorithm for finding the closest pair of points, the main time-consuming step is the divide step, where the points are recursively divided into smaller subsets. This step has a time complexity of O(log(n)).
After the division, the conquer step involves combining the results from the subproblems and finding the closest pair of points among them. This step has a time complexity of O(n) since it requires comparing each point in one subset with the points in the other subset.
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Solve the equation for the individual variable.
P= W/t, for t
A.) t = P/W
B.) t = P - W
C.) t = W/P
D.) t = PW
Answers
Answer:
C.) t = W/P
Step-by-step explanation:
P=W/t
t x P= t x W/t
Pt=W
Pt/P=W/P
t=W/P
what is 2+2+4+6×6×2+3+5
Answers
Answer:
88
Step-by-step explanation:
Use BODMASbrackets of division , multiplication , addition and subtraction
2+2+4+6*6*2+3+5
start with the multiplication
6*6*2 = 72
now do the addition
2+2+4+72+3+5 =88
Which expression is equivalent to (7-8) (78)?
А
49-5
B
49-11
C
7-5
D 7-11
Answers
-78
Step-by-step explanation:
(7-8)(78)
(-1)(78)=-78
Suppose that the objective function coefficient for product C increases by $8. What impact will this have on the current values of the optimal solution
Answers
When the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change.
What is an objective function?An objective function simply means the function whose value is to be either maximized or minimized over the alternatives.
In this case, when the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change. The change is due to the varied objectives.
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add the quotient of 9 and 7 to d
Answers
Answer:
9 ÷ 7 + d.
Step-by-step explanation:
When constructing a perpendicular bisector why must the compass opening be greater than 1/2.
Answers
It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.
What is perpendicular bisector?A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.
Now, consider an example;
When you wish to build a perpendicular line on a line segment, like line AB, you do the following;
Set the compass on a radius more than half the length of the line AB.Using A as your center, draw an arc above and below line AB.With the same radius and B as our center, draw additional arcs on top or below line AB to join a first arcs on the both side of the line.Join the two arc intersections to cut line AB at M.A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.
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What is the solution for x in the inequality 4−2x>8
Answers
Answer:
X<-2
Step-by-step explanation:
Answer:
x<-2
Step-by-step explanation:
1. Write equation
4-2x>8
2. Combine like terms
-2x>4
3. Divide(and switch ineqaulity sign because the coefficent is negative)
-2x<4
x<-2
What is 25 times 1/6
Don’t ask me why it’s for my cousin
Answers
Jennifer has recently interviewed for two different jobs. She feels there is a 0.340 probability of being offered the first job and a 0.600 probability of being offered the second job. Assume that the two job offers are statistically independent. a. What is the probability that Jennifer will be offered both jobs? Do not round intermediate calculations. Round your answer to three decimal places. Probability = b. What is the probability that Jennifer will be offered neither of those two jobs? Do not round intermediate calculations. Round your answer to three decimal places. Probability = c. What is the probability that Jennifer will be offered at least one of the two jobs? Do not round intermediate calculations. Round your answer to three decimal places. Probability = d. What is the probability that Jennifer will be offered the first job but not the second job? Do not round intermediate calculations. Round your answer to three decimal places. Probability= e. What is the probability the Jennifer will not be offered the first job but will be offered the second job? Do not round intermediate calculations. Round your answer to three decimal places. Probability =
Answers
The probability offered both jobs is 0.204,offered neither of the two jobs is 0.060,at least one job is 0.976,offered the first job not the second job is 0.136,offered the first job but will be offered the second job is 0.204.
To find the probability that Jennifer will be offered both jobs, we multiply the probabilities of being offered each job since the two job offers are independent. Therefore, 0.340 * 0.600 = 0.204.
The probability that Jennifer will be offered neither of the two jobs is calculated by subtracting the probability of being offered at least one job from 1. Since being offered at least one job is the complement of being offered neither, the probability is 1 - 0.976 = 0.024.
The probability that Jennifer will be offered at least one of the two jobs is found by summing the probabilities of being offered each job and subtracting the probability of being offered neither. Therefore, 0.340 + 0.600 - 0.024 = 0.976.
The probability that Jennifer will be offered the first job but not the second job is obtained by subtracting the probability of being offered both jobs from the probability of being offered the first job. Thus, 0.340 - 0.204 = 0.136.
The probability that Jennifer will not be offered the first job but will be offered the second job is equal to the probability of being offered the second job but not both jobs. Since the two job offers are independent, this probability is the same as the probability of being offered both jobs, which is 0.204.
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Find the common difference or common ratio of the sequence -8.2,-8.4,-8.6,....?
A. r = -0.2
B. r = 0.2
C. d = -0.2
D. d = 0.2
Answers
Rationalize the radical:
9√6
6√9
9
54√6
9√6
6
Answers
The rationalized form of 9√6 is simply 9.
To rationalize the radical expression 9√6, we can simplify it by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √6 is also √6.
Let's perform the rationalization step by step:
9√6 * (√6 / √6)
Multiplying the numerators and denominators, we get:
(9 * √6 * √6) / (√6 * √6)
Simplifying further, we have:
(9 * √36) / 6
Since the square root of 36 is 6, we can substitute the value:
(9 * 6) / 6
Canceling out the common factor of 6 in the numerator and denominator, we obtain:
9
Therefore, the rationalized form of 9√6 is simply 9.
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What is the y-intercept of the function?
Select one:
(.25, 0)
(-2,0)
O (1,0)
(0, - 1)
Answers
Answer:
D
Step-by-step explanation:
none of the others make sense my guy
Answer:
the y-intercept is (0,-1)
Step-by-step explanation:
the y-intercept is the point in which the line passes through the y axis
I need this answered please
Answers
Danika live 5 block from her chool. If he walk to and from chool 5 day each week how many block doe he walk in one week?
Answers
Danika walks 50 blocks in one week.
Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.
As per the data given,
We have,
Danika lives at 5 blocks from her school.
As Danika walks 5 blocks to and from school, making her round trip
So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.
As Danika walks to and from school 5 days a week,
Hence, she walks 10 blocks * 5 days = 50 blocks in one week.
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a triangular window can only have an area of 120 square feet and the architect wants the base to be 4 feet more than twice the height. find the base and height of the window.
Answers
the base of the triangular window is 24 feet and the height is 10 feet.
Let's denote the height of the triangular window as h feet. According to the given information, the area of the window is 120 square feet.
The formula to calculate the area of a triangle is:
Area = (1/2) × base × height
In this case, we can write the equation as:
120 = (1/2) × base × h
Now, we are also given that the base of the window is 4 feet more than twice the height. So we can express the base as:
base = 2h + 4
Substituting this expression for the base into the area equation, we have:
120 = (1/2) × (2h + 4) × h
Now we can solve this equation for the height.
Multiplying both sides of the equation by 2 to remove the fraction:
240 = (2h + 4) × h
Expanding the right-hand side:
240 = 2h² + 4h
Rearranging the equation and setting it equal to zero:
2h² + 4h - 240 = 0
Now we can solve this quadratic equation. Factoring out a 2:
2(h² + 2h - 120) = 0
Factoring the quadratic expression inside the parentheses:
2(h + 12)(h - 10) = 0
Setting each factor equal to zero:
h + 12 = 0 or h - 10 = 0
Solving these equations, we get:
h = -12 or h = 10
Since height cannot be negative in this context, we discard the negative value. Therefore, the height of the triangular window is h = 10 feet.
Substituting the height value back into the expression for the base:
base = 2h + 4
= 2(10) + 4
= 20 + 4
= 24
Therefore, the base of the triangular window is 24 feet and the height is 10 feet.
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the probability of winning a certain game is 0.5. the player wins a prize if he/she wins at least 70 percent of the games in a series of n if the possible choices of n are 10, 20, and 100, which value of n should the player choose in order to have the best probability of winning a prize?
Answers
Using the Binomial probability distribution , the player should choose n= 10 , in order to have the best probability of winning a prize.
We have given that,
the probability of winning a game by the player
= 0.5
let X be number of games won by player .
A player got a prize when he wins 70% of games in a series of n .
we should find out value n such that he wins a prize.
For this we can use, binomial Probability distribution,
a) n = 10
X~Bin(10 ; 0.5)
P(X>7) = ¹⁰C₇(0.5)¹⁰+ -----+ ¹⁰C₁₀ (0.5)¹⁰
= 0.1718
b) n = 20
X~Bin(20 ; 0.5)
P(X> 14 ) = ²⁰C₁₄ (0.5)²⁰ + -----+ ²⁰C₂₀ (0.5)²⁰
= 0.05766
c) n = 100
X~Bin(100 ; 0.5)
P(X> 70 ) = ¹⁰⁰C₇₀(0.5)¹⁰⁰ + ---- +¹⁰⁰C₁₀₀(0.5)¹⁰⁰
= 0.00005
Hence, the player should choose n= 10 in order to maximize the probability of winning prize.
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Please helppp from edge :)
Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?
0.1n + 0.05(n – 175) = 13.30
0.1n + 0.05(175 – n) = 13.30
0.1(n – 175) + 0.05 = 13.30
0.1(175 – n) + 0.05n = 13.30
Answers
Answer:
0.1(175 – n) + 0.05n = 13.30
Step-by-step explanation:
0.1(175 – n) is solving for the amount of dimes, which is achieved by subtracting nickles fromt eh 175 which leaves us with the dimes.
+ 0.05n is the acutal value of the nickles themselves.
If this helps mark me brainliest
Let number of nickels be n
The equation is
\(\\ \sf\longmapsto 0.1n+0.05(175-n)=13.30\)
Why?
First we set n by putting 0.1n Then we subtract it from total i.e 175 .Are 90 degrees (clockwise) and -270 degrees (counter clockwise) coterminal? WHY or why not?
Answers
Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.
What are coterminal angles ?Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.
To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:
-270 + 360 = 90
Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).
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