Here is a list of numbers. 6 7 2 4 6 6 9 5 3 3 find the mean and median
Answers
Mean= 5.1 (Sum of all the terms/number of terms)
( 6 + 7 + 2 + 4 + 6 + 6 + 9 + 5 + 3 + 3 ) ÷ 10 = 5.1
Median= 5.5 (The middle term when you order them from lowest to highest)
2 3 3 4 5 6 6 6 7 9
Step-by-step explanation: The mean of a data set is equal tot he sum of the set of numbers divided by however many numbers are in the set.
So to find the mean of the data set shown here,
let's begin by adding the numbers.
So we have 6 + 7 + 2 + 4 + 6 + 6 + 9 + 5 + 3 + 3.
Adding the numbers, we get 51.
Now, 51 will be divided by the number
of numbers in the set which is 10.
So 51 divided by 10 gives us 5.1.
So the mean of the data set is 5.1.
Now, the median is the middle number in the data set
when the data set is written from least to greatest.
So let's write our data set from least to greatest.
So we have 2, 3, 3, 4, 5, 6, 6, 6, 7, 9.
Notice that there are two numbers in the middle, 5 and 6.
In this situation, add the numbers and divide by 2.
So 5 + 6 is 11 and 11 divided by 2 is 5.5.
So the median is 5.5.
Related Questions
Solve the following systems of equations using Gaussian Elimination. 2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Find the inner product of two vectors A = (2, -3,0) and B = = (-1,0,5)
Answers
The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).
Solving the given system of equations using Gaussian elimination:
2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Matrix form of the system is
[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13
Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1
Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4
Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5
Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5
Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6
The solution is (x,y,z) = (6,-5,5)
Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).
The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by
A·B = |A||B|cosθ
Given,A = (2, -3,0) and B = (-1,0,5)
Magnitude of A is |A| = √(2²+(-3)²+0²) = √13
Magnitude of B is |B| = √((-1)²+0²+5²) = √26
Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2
Cosine of the angle between A and B is
cosθ = A·B / (|A||B|)
cosθ = -2 / (√13×√26)
cosθ = -2 / √(13×26)
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A local fast food restaurant takes in $9000 in a 4 hour period, where the amount taken in varies directly with the number of hours the restaurant is open. Use the
direct variation formula to estimate how many hours it would take the restaurant to earn $25,000. Round your answer to the nearest tenth (one decimal place)..
Answers
As per the direct variation formula, it take 11 hours : 6 minutes : 36 seconds to earn $25,000 for the restaurant.
Direct variation:
Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.
Direct variation equation: y = kx
Given,
A local fast food restaurant takes in $9000 in a 4 hours period. Write a direct variation equation for the relationship income and number of hours.
Here we need to estimate how many hours it would take the restaurant to earn $25,000.
a) Let us consider income (I) directly varies to number of hours (h) where k is the constant of variation.
I = kh ⇒ Direct variation equation
Solve for k:
9,000 = (k)(4)
k = 9,000/4
k = 2,250
b) When income (I) = 25,000, find the number of hours:
I = kh
25,000 = (2,250) (h)
h = 25,000/2,250
h = 11.11
It will take approximately 11 hours : 6 minutes : 36 seconds for the restaurant to earn $25,000.
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in an effort to remember the quadratic formula, justice writes the equation 50 times. she is using a technique known as
Answers
Justice is using a technique known as chunking.
Short-term memory can function more effectively thanks to chunking, however the quantity of chunks that can be stored efficiently declines as chunk size grows.
Large pieces of information may be divided into smaller bits and then grouped together using relevant information or attributes before being stored in order to improve retention of that information in the short term memory. To establish relational information or similarity between the information to be stored in order to improve retention and recall in the short term memory, information must be broken down before being regrouped. However, as chunk size grows, so does the efficiency of information chunking.
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Katie wants to collect over 100100100 seashells. She already has 343434 seashells in her collection. Each day, she finds 121212 more seashells on the beach. Katie can use fractions of days to find seashells.
Answers
Answer:
Step-by-step explanation:
Lucy recently asked the servers at her restaurant to only give straws to customers who request them. she thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. she randomly selects 100 customers and finds that 43 of them ask for a straw. to determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. lucy is testing the hypotheses: h0: p = 50% and ha: p < 50%, where p = the true proportion of customers who will ask for a straw. based on the results of the simulation, what is the estimate of the p-value of the test? a. 0.0333 b. 0.05 c. 0.0733
d. 0.11
Answers
Answer:
Because the P-value of 0.0733 > , Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.
A runner is 7/8 miles away from the finish line. If she can travel 3/8 miles per minute, how long will it take her to finish the race?
Answers
The time that runner takes to finish the race is 2.133 minutes.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The speed of the runner is given as 3/8 miles per minute.
The remaining distance to be travelled is 7/8 miles.
Then, the time taken by the runner is the ratio of distance to be travelled to the speed. It can be written as follows,
Time taken by runner = (7/8)/(3/8)
= 7/3
= 2.133
Hence,the time taken by the runner to finish the race is 2.133 minute.
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-13, -11 -9,- 7,
What are the next three terms of the arithmetic sequence?
Answers
Answer:
-5, -3, -1, 1
Step-by-step explanation:
Write sin t in terms of cos t using the Pythagorean Identity for:
Answers
The solution to sin(t) is sin(t) = -√[1 - cos²(t)]
How to determine the solution to sin(t)From the question, we have the following parameters that can be used in our computation:
The angle t is the quadrant IV
This means that
sin²(t) + cos²(t) = 1
Subtract cos²(t) from both sides of the equation
So, we have the following representation
sin²(t) = 1 - cos²(t)
Take the square root of both sides
sin(t) = ±√[1 - cos²(t)]
sin(t) is negative in quadrant IV
So, we have
sin(t) = -√[1 - cos²(t)]
Hence, the solution is sin(t) = -√[1 - cos²(t)]
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Which numbers are irrational numbers?
Select each correct answer.
Answers
Answer
Well pi is an irrational number because it can't be simplified into a fraction. And from what I can see neither can the sqaure root of 10/49. So I believe it would be both of them. But if there is only one answer than i'm not sure sorry. But it also says each so maybe there is more than one answer.
Step-by-step explanation:
Calculating the Number of Periods [LO4] You expect to receive $39,000 at graduation in two years. You plan on investing it at 10 percent until you have $174,000. How long will you wait from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Period years
Answers
You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.
To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:
FV = PV * \((1 + r)^n\)
Where:
FV is the future value
PV is the present value (initial investment)
r is the interest rate per period
n is the number of periods
In this case:
PV = $39,000
FV = $174,000
r = 10% per year
Let's calculate the number of periods (years):
FV = PV * \((1 + r)^n\)
174,000 = 39,000 * \((1 + 0.10)^n\)
Divide both sides by 39,000:
4.4615 = \((1.10)^n\)
Take the logarithm of both sides to solve for n:
log(4.4615) = n * log(1.10)
n ≈ log(4.4615) / log(1.10)
n ≈ 2.1270 / 0.0414
n ≈ 51.33 (rounded to two decimal places)
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sat scores in one state is normally distributed with a mean of 1403 and a standard deviation of 200. Suppose we randomly pick 32 SAT scores from that state. a) Find the probability that one of the scores in the sample is greater than 1484. P(X > 1484) = b) Find the probability that the average of the scores for the sample of 48 scores is greater than 1484 P(X > 1484) = Round each answer to at least 4 decimal places.
Answers
The probability that one of the scores in the sample is less than 1484 is 0.2437 .
a)Given that mean u = 1403
standard deviation σ = 200
sample size n = 32
P(x>1484) = P(X-u/σ > 1484-1403/200)
= P (z > 0.405)
P(x>1484) = 0.2437 .
hence the probability that one score is greater than 1484 is 0.405 .
b) Now we have to find the average of the scores of 48 samples.
P(x>1484)
= P(x-μ/ σ/√n> 1484-1403 /200/√48)
= P(z>2.805.)
Now we will use the normal distribution table to calculate the p value to be 0.002516.
p-value = 0.0025
Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.
They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.
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……………………………………………………………………………
Answers
Answer:
ITS 64 degrees
Step-by-step explanation:
Answer:
116
Step-by-step explanation:
hope this helps:)..........
When you flatten a spherical meatball into a hamburger do you increase its volume or surface area?
Answers
when you flatten a spherical meatball into a hamburger, you increase its surface area while keeping the volume constant.
A sphere is a three-dimensional shape that has a curved surface. When you flatten a spherical meatball into a hamburger, you are essentially reshaping it into a flat, disk-like form. By doing so, you increase the area that is in contact with the cooking surface, such as a pan or grill. This larger surface area allows for more even cooking and browning.
However, the total amount of meat remains the same when you flatten the meatball. The volume of an object refers to the amount of space it occupies, and since the meatball is being flattened without adding or removing any meat, the volume remains constant. In other words, the flattened hamburger will have a larger surface area but the same amount of meat as the original spherical meatball.
So, when you flatten a spherical meatball into a hamburger, you increase its surface area while keeping the volume constant.
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When you flatten a spherical meatball into a hamburger, you decrease its volume and increase its surface area.
When a spherical meatball is flattened into a hamburger, its shape changes from a sphere to a flat disk. This transformation affects both the volume and surface area of the meatball.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. The surface area of a sphere is given by the formula A = 4πr^2.
On the other hand, the volume of a disk (or a circle) is given by the formula V = πr^2, where r is the radius of the disk. The surface area of a disk is given by the formula A = 2πr.
When the meatball is flattened, its radius decreases, resulting in a smaller volume. The volume of the flattened meatball is less than the volume of the original spherical meatball.
However, the surface area of the flattened meatball increases. The surface area of the flattened meatball is greater than the surface area of the original spherical meatball.
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Can any kind soul help me ASAP!
Answers
Answer:
the answer is B
x = 1
Step-by-step explanation:
the symmetry is in the middle of the curve like a mirror and the equation of the mirror or symmetry line is x=1
in a recent survey, what reason was given by nearly half of the respondents when asked what their reason was for changing jobs?
Answers
According to a recent survey, nearly half of the respondents cited better pay as their primary reason for changing jobs.
The survey was conducted on a national level and the results indicate that a majority of people are looking to increase their earnings by switching jobs.
Other reasons are:
The increasing cost of living and the desire to make ends meet. Opportunities to increase their skill set and gain experience in a new industry were other major factors that pushed them to seek a new job. Better working conditions were also cited as a primary reason by some survey respondents. This included working hours, location, job security, and organizational culture. To pursue a career path more aligned with their passions and interests. Move to a new location and a job change presented the perfect opportunity to do so.In conclusion, the survey clearly showed that the main reason for job changes among respondents was better pay. However, various other factors also play a role in an individual's decision to switch jobs, such as working conditions, career paths, and location.
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all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
Answers
The answer to the given question after considering the two options is true under the condition all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
Probability is also known as the estimation of possible changes of a particular event taking place. Furthermore, it is important while dealing with calculations in the branch of science and mathematics. It is useful in eliminating the total changes of systematic errors, which are hampering the research population.
Some examples of probability
The probability on the event of rolling a 4 with a die is 1/6.
The probability of getting a tails while tossing a coin is 1/2.
The probability of getting one joker from a deck of cards is 1/51.
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The complete question is
All probabilities can be expressed as decimal values ranging from 0.00 to 1.00. True or False
Yes, it is true that all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
This is because probabilities represent the likelihood of an event occurring, and the probability of an event can range from impossible (0.00) to certain (1.00). Therefore, probabilities are expressed as decimal values between these two extremes.
Hi! Yes, all probabilities can be expressed as decimal values ranging from 0.00 to 1.00. A probability of 0.00 represents an impossible event, while a probability of 1.00 represents a certain event. Values between these two extremes indicate varying levels of likelihood for the event to occur.
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what is the measure of angle OAC
Answers
Answer:
60
Step-by-step explanation:
A lecture class has 30 full-time students and 20 part-time students. A random sample of 10 students is drawn. UseRcommands to answer the following questions: (a) What is the probability that exactly 6 of the students will be full-time? (b) What is the probability that at most 8 of the students will be full-time? (c) Use the binomial approximation that exactly 6 of the students will be full-time, wherep=30/50=0.6. How does this compare to your answer in part a? Is it appropriate to use the binomial approximation in this scenario?
Answers
It's important to remember that using the binomial approximation assumes a large population size, which may not be the case here.
To answer your questions, we will use R commands to calculate the probabilities.
(a) To find the probability that exactly 6 of the students will be full-time, we can use the "dhyper" function in R. The parameters are x = 6, m = 30 (number of full-time students), n = 20 (number of part-time students), and k = 10 (sample size).
R command:
```R
dhyper(x = 6, m = 30, n = 20, k = 10)
```
(b) To find the probability that at most 8 of the students will be full-time, we can use the "phyper" function in R, which calculates the cumulative probability. We need to calculate P(X ≤ 8).
R command:
```R
phyper(q = 8, m = 30, n = 20, k = 10)
```
(c) To use the binomial approximation, we can use the "dbinom" function in R with p = 0.6 (probability of full-time student) and n = 10 (sample size). We want to calculate P(X = 6).
R command:
```R
dbinom(x = 6, size = 10, prob = 0.6)
```
Compare this result with the answer in part (a). If the difference is relatively small, it's appropriate to use the binomial approximation in this scenario.
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What is the perimeter of a circle with a diameter of 7.8 yds
Use pi as 3.14
Answers
The circumference of the circle is approximately 24.492 yards.
what is circumference ?
Circumference is the distance around the edge of a circle or any other closed curve. It is the perimeter of a circle and is often denoted by the symbol "C". The circumference is a key measurement when working with circles, as it can help us calculate the radius, diameter, and area of the circle.
The formula for the circumference of a circle is:
C = 2πr
where "C" is the circumference, "π" (pi) is a mathematical constant approximately equal to 3.14, and "r" is the radius of the circle.
A circle does not have a perimeter as it is a two-dimensional shape. However, it has a circumference, which is the distance around the circle.
To find the circumference of a circle with a diameter of 7.8 yards and using π as 3.14, we can use the formula:
Circumference = π × Diameter
Circumference = 3.14 × 7.8 yards
Circumference = 24.492 yards (rounded to three decimal places)
Therefore, the circumference of the circle is approximately 24.492 yards.
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I really don't understand how to do this, can I please get some help?
thank youu
Answers
We have to plug in given things that are the volume and radius.
So, the equation would look like:
2- 54 x (pie) = (pie) x 3^2 x h
We can turn (pie) into 3.14=
3- 54 x 3.14 = 3.14 x (3^2=9) x h
simplify the 3.14’s
you’re left with:
4- 54= 9h
divide by 9 on each side
5- h=6
there you go! the height is 6!
Which values are solutions to the inequality below? Check all that apply.
√x <10
A. 100
B. 25
C. -100
D. 105
E. 36
F. 9
Answers
Answer:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v
Step-by-step explanation:
its E and A
Answer:
The solutions to the inequality are B, E, and F: 25, 36, and 9.
Step-by-step explanation:
The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:
√x < 10
x < 10^2 = 100
So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:
A. 100 (not a solution)
B. 25 (solution)
C. -100 (not a solution)
D. 105 (not a solution)
E. 36 (solution)
F. 9 (solution)
in a binomial experiment, the number of successes can never exceed the number of trials. (True or False)
Answers
Answer: True
Step-by-step explanation:
Write a linear function f with f(-4) = 2 and f (6) = -3.
Answers
Explanation: Use the slope formula and slope-intercept form y = mx + b to find the equation.
Answer:
Step-by-step explanation:
we have 2 pts (-4,2) and (6,-3)
slope = \(\dfrac{-3-2}{6-(-4)}=\dfrac{-5}{10}=-\dfrac{1}{2}\)
so: \(y=-\dfrac{1}{2}+b\)
plug in any point:
\(-3=-\dfrac{1}{2} * 6 +b\)
\(b=0\)
so, \(y=-\dfrac{1}{2} x\)
5 – 6x = 8x + 17 and simplify \(\frac{-6}{7}\)
Answers
Answer:
x = -6/7
Step-by-step explanation:
5 – 6x = 8x + 17
-5 - 5 Subtract 5 from both sides
-6x = 8x + 12
-8x - 8x Subtract 8x from both sides
-14x = 12 Divide both sides by -14
x = -12/14 Simplify
x = -6/7
class 10question - If the sum of 5 numbers is 175 and the product of second and third term is 1125. find the answer
pls give it fast will mark brainliest
Answers
If the sum of 5 numbers is 175 and the product of second and third term is 1125, and then the five numbers are 20, 45, 25, 30, and 55.
Let's solve the problem step by step.
Let the five numbers be a, b, c, d, and e.
According to the given information, we have two equations:
a + b + c + d + e = 175 (Equation 1)
b * c = 1125 (Equation 2)
We need to find the values of a, b, c, d, and e that satisfy both equations.
From Equation 2, we know that b * c = 1125. To find the values of b and c, we need to find the factors of 1125.
The factors of 1125 are: 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125.
Since the product of b and c is 1125, we can assign b = 45 and c = 25.
Substituting the values of b and c into Equation 1, we have:
a + 45 + 25 + d + e = 175
a + d + e = 175 - 45 - 25
a + d + e = 105 (Equation 3)
Now we have two equations:
a + d + e = 105 (Equation 3)
b * c = 1125 (Equation 2)
We need to find the values of a, b, c, d, and e that satisfy both equations.
We can choose any values for a, d, and e as long as their sum is 105. For example, let's assign a = 20, d = 30, and e = 55.
Substituting these values into Equation 3, we have:
20 + 30 + 55 = 105
Therefore, the five numbers are a = 20, b = 45, c = 25, d = 30, and e = 55.
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Jack's train arrived at the station at 8:30 in the evening. The train ride was 2 hours and 10 minutes
What time did Jack's family leave? Move numbers to the clock to show the time.
Answers
Answer:
The answer is 10:40 pm
Step-by-step explanation:
Because if its 8:30 than add 2 hours its 10:30 than add 10 minutes and you get 10:40
Find the 8th term of the geometric sequence 10, -40, 160, ..
Answers
Answer:
kkkk74
Step-by-step explanation:
please help me with this problem
Answers
Step-by-step explanation:
\(12^{9} / 12 ^{3} =\)
When dividing exponential expressions with similar bases (in the problem, the base is 12), calculate the difference (this means subtract) between their exponents and keep the base:
so:
9 - 3 = 6
so the answer is : \(12^{6}\)
in how many ways can you move the token if in addition you're also allowed to move the token diagonally (in one move you can also move it to the adjacent right up square).
Answers
The token has eight possible moves: four cardinal directions (up, down, left, right) and four diagonal directions (left-up, right-up, left-down, right-down).
If we consider a token positioned on an arbitrary square of a grid, and we are allowed to move the token diagonally to the adjacent right-up square, we can determine the number of possible moves.
Let's assume the token is on a square in a grid, and let's label the directions as follows:
```
1 2 3
4 T 5
6 7 8
```
where T represents the token, and the numbers 1-8 represent the possible directions the token can move.
In this scenario, the token can move in the following ways:
1. Move left (direction 4)
2. Move right (direction 5)
3. Move up (direction 2)
4. Move down (direction 7)
5. Move diagonally left-up (direction 1)
6. Move diagonally right-up (direction 3)
7. Move diagonally left-down (direction 6)
8. Move diagonally right-down (direction 8)
Therefore, the token has eight possible moves: four cardinal directions (up, down, left, right) and four diagonal directions (left-up, right-up, left-down, right-down).
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HELP ASAP PLS 20 POINTS WILL GIVE BRAINLIEST
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the equation of
y=x3
with the given transformations?
vertical stretch by a factor of 3, horizontal shift 4 units to the right, vertical shift 3 units down
Answers
Answer:
The parent function is y = x³.
After a vertical stretch by a factor of 3, obtain
y = 3x³
After a horizontal shift 4 unit to the right, obtain
y = 3(x - 4)³
After a vertical shift 3 units down, obtain
y = 3(x - 4)³ - 3
Answer: y = 3(x - 4)³ - 3
y = 3(x - 4)³ - 3 is the equation of y=x³ with the given transformations
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
The given equation is y=x³
A translation of a graph is its rigid movement, vertically or horizontally.
From given we have,
There is a vertical stretch of 3 units, hence the function is multiplied by 3.
There is a horizontal shift of 4 units to the right, hence x -> x - 4.
There is a vertical shift of 3 units down, hence 3 is subtracted from the function.
The required equation is given by y = 3(x - 4)³ - 3.
Hence y = 3(x - 4)³ - 3 is the equation of y=x³ with the given transformations
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