The t-statistic or t-ratio is used to test the statistical significance overall regression model used to test the statistical significance of each β i used to test to see if an additional variable which has not been observed should be included in the regression model is close to zero when the regression model is statistically significant none of the above
The correct statement is:
The t-statistic or t-ratio is used to test the statistical significance of each β_i in a regression model.
The t-statistic is calculated by dividing the difference between the sample mean and the hypothesized population mean by the standard error of the sample mean.
The formula for the t-statistic is as follows:
t = (sample mean - hypothesized population mean) / (standard error of the sample mean)
The t-statistic or t-ratio is used to test the statistical significance of each β_i (regression coefficient) in a regression model. It measures the ratio of the estimated coefficient to its standard error and is used to determine if the coefficient is significantly different from zero.
Learn more about t-statistic or t-ratio:
https://brainly.com/question/30466889
#SPJ11
which factors will influence the margin of error when the population standard deviation is unknown? check all that apply.
We need to know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.
Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.
Therefore the margin of error is influenced by confidence level and sample size.
Learn more about margin of error here:
https://brainly.com/question/10218601
#SPJ4
What is the value of the missing angle?
a ) 50
b ) 69
c ) 61
d ) 60
Answer:
a it has to equal 180
I need this to be 20 letters long so I'm doing dis
Answer:
A is the right answer
Step-by-step explanation:
A triangles angles equal 180° like if you add up all the ablngles no matter what size of the shape. So to find the answer you add the angles you know so in this case 61+69 which equals 130 so then you subtract 180 with 130 to get you 180. And if you want to make sure you are right you can add up all the angles which is 69+61+50=180
Hope this helps :)
Angle 4 and 6 are _____ angles
Answer:
opposite side interior angles
Step-by-step explanation:
NEED HELP ASAP
With Question b) in photo
Answer:
a. 25
b. 3 seconds
c. 70 metres
d. 6.742 seconds
e. 6 seconds
Step-by-step explanation:
a. when x=0, all that is left in the equation is 25
b. this is a parabola, so it hits a max at x=3
c. y value when x=3
d. substitue y for 0 and solve for x
e. plug in 25 for y and solve for x
Carol flips a fair coin. The coin lands on heads 5 times in a row. Enter the probability that the next toss will land on tails
The probability of the next toss landing on tails is the same as the probability of the coin landing on heads, which is 0.5 or 50%.
The result of each coin toss is independent of the previous tosses. The fact that the coin landed on heads five times in a row does not affect the probability of the next toss landing on tails. Each time the coin is flipped, there is a 50-50 chance of it landing on either heads or tails, assuming a fair coin. Therefore, the probability of the next toss landing on tails is the same as the probability of the coin landing on heads, which is 0.5 or 50%.
Learn more about probability here
https://brainly.com/question/13604758
#SPJ11
5. HELP FAST If each person paid an equal amount, who would save the most money? Explain your reasoning using at least two complete sentences
Person A would save the most money because they had a coupon that was worth more than their portion of the purchase price.
To determine who would save the most money if each person paid an equal amount, we need to calculate how much each person paid and then compare the amounts saved by each person. For instance, let's consider an example with four people who want to split the cost of a $60 purchase equally. Each person would pay $60 / 4 = $15.
If person A has a $20 coupon, then they would save $20, and their net cost would be $15 - $20 = -$5. Person B has a $15 coupon, so they would save $15, and their net cost would be $15 - $15 = $0. Person C has a $10 coupon, so they would save $10, and their net cost would be $15 - $10 = $5. Person D has a $5 coupon, so they would save $5, and their net cost would be $15 - $5 = $10.
You can learn more about coupons at: brainly.com/question/31727353
#SPJ11
in general, a change in what causes a movement along a curve in the models we have studied? a change in what causes a shift in the curve?
In general, a change in the price of the product causes a movement along the demand curve; and a change in production cost and related factors causes a shift in the supply curve.
What is demand curve?The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis of the graph, and the quantity demanded on the horizontal axis.
What is supply curve?The supply curve is a graphic representation of the relationship between product price and quantity of product which a seller is willing and able to supply. Product price is measured on the vertical axis of the graph, and the quantity of product supplied on the horizontal axis.
Learn more about supply demand curve at: https://brainly.com/question/1915798
#SPJ4
Please help, this was due yesterday. Ill give brainliest :) the red numbers (in order from top to bottom, left to right) are 112, 116, 234, 166, 400.
Fwam and his children went into a bakery and will buy cupcakes and brownies. Each cupcake costs $4.50 and each brownie costs $1.75. Fwam has a total of $50 to spend on cupcakes and brownies. Write an inequality that would represent the possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b.
The number of cupcakes and brownies Fwam could have purchased is 1.75b + 4.50c ≤50.
What is inequality?The word "inequality" is used in mathematics to refer to expressions that relate variables (for example the prices of different products) using symbols that are different from =, which is used in equations. Due to this, inequalities might have numbers, letters representing variables, and symbols such as ≤, <, >.
How to write the inequality in this situation?1. List the variables
b = cupcakes
c = brownies
4.50 = price of the cupcakes
1.75 = price of the brownies
50 = total money
2. Relate the variables
1.75b + 4.50c ≤50
Each product should be multiplied by its price
The total money can be equal to or less than 50 (≤)
The products should be added
Learn more about inequality in: https://brainly.com/question/20383699
#SPJ1
Mary made costumes for the annual school play. She used rolls of blue fabric. If each roll had of fabric, what is the total length of the fabric she used? Write your answer in yards.
Use the table of conversion facts as necessary, and do not round your answer.
Answer:
It is not specified in the question how many rolls of fabric Mary used, so we can't calculate the total length of the fabric she used.
Sixth grade mathematics
Answer:
Step-by-step explanation:
318÷8=39 3/4 for number 6
From a group of 5 math majors and 4 computer science majors a committee consisting of 3 math majors and 2 computer science majors is to be formed. One math major and one computer science major refuse to serve together. If the committee is randomly selected, what's the probability they wind up on the committee together?
The probability that the one math major and one computer science major who refuse to serve together wind up on the committee together is 3/7.
The probability that the one math major and one computer science major who refuse to serve together wind up on the committee together, we can consider two cases:
Case 1: The math major who refuses to serve is selected.
In this case, we need to select 3 math majors from the remaining 4 math majors and 2 computer science majors from the 4 computer science majors who are willing to serve together. The probability of this case can be calculated as:
P(case 1) = (4 choose 3) × (4 choose 2) / (9 choose 5)
Case 2: The computer science major who refuses to serve is selected.
In this case, we need to select 3 math majors from the 5 math majors who are willing to serve together and 2 computer science majors from the remaining 3 computer science majors. The probability of this case can be calculated as:
P(case 2) = (5 choose 3) × (3 choose 2) / (9 choose 5)
To find the overall probability, we need to sum up the probabilities of both cases:
P = P(case 1) + P(case 2)
Calculating the probabilities:
P(case 1) = (4 choose 3) × (4 choose 2) / (9 choose 5) = (4 × 6) / 126 = 24 / 126 = 4 / 21
P(case 2) = (5 choose 3) × (3 choose 2) / (9 choose 5) = (10 × 3) / 126 = 30 / 126 = 5 / 21
P = P(case 1) + P(case 2) = 4/21 + 5/21 = 9/21 = 3/7
To know more about probability click here :
https://brainly.com/question/10185463
#SPJ4
Which of the following surveys have quantitative data? Select all correct answers. Select all that apply: A 2013 CDC survey on youth fitness asked students which sports they enjoy the most. Possible answers included baseball, golf, and gymnastics. A 2015 Gallup survey about free expression on campus asked students which news sources they follow. A 2015 CDC Survey on family growth asked women how many times they have been pregnant. Question Which of the following is continuous data? Select all correct answers. Select all that apply: The 2015 CDC family growth survey also asked women how many cigarettes they smoked per day. A survey management company, measured how much time each participant takes to complete a survey. An environmental researcher measured the average length of the fish in a certain lake. A librarian counted the number of books returned in a day.
An environmental researcher measured the average length of the fish in a certain lake.
The following surveys have quantitative data:
A 2015 CDC Survey on family growth asked women how many times they have been pregnant.
A survey management company measured how much time each participant takes to complete a survey.
An environmental researcher measured the average length of the fish in a certain lake.
A librarian counted the number of books returned in a day.
The continuous data may take any numerical value over a range, like 1.25, 3.33, 8.99, etc. Continuous data is a common type of data in statistics and math. The following is the list of continuous data from the given options: The 2015 CDC family growth survey asked women how many cigarettes they smoked per day. A survey management company measured how much time each participant takes to complete a survey.
An environmental researcher measured the average length of the fish in a certain lake.
To know more about environmental visit:
brainly.com/question/21976584
#SPJ11
the answer has to be as a fraction
Answer:
49/100
Step-by-step explanation:
So you can find the area of shaded area by finding the area of the circle inside the entire circle that has a diameter of 3 cm and 4 cm and then find the area of the most inner circle which only has a diameter of 4 cm and then subtract these 2. After that you want to find the area of the entire circle and then divide the area of the shaded area by the entire circle. The formula for the area of a circle is given as: \(\pi r^2\)
Area of the two "inner" circles of a diameter of 4 and 3 cm. This gives you an entire diameter of 7 cm with a radius of 3.5. The area of this circle is \(\pi(3.5)^2\) which is \(12.25\pi\).
The area of the most inner circle only has a diameter only 4 cm. The radius is 2, thus the area of this circle is \(\pi (2)^2\) which is \(4\pi\). Now subtract this from the 12.25 pi to find the area of the shaded area. This gives you the equation: \(12.25\pi-4\pi\) which equals \(8.25\pi\).
Now to find the area of the entire circle you add up all the "diameters" which gives you 4 cm + 3 cm + 3 cm = 10 cm. So the radius is 5. This gives you the equation: \(\pi(5)^2\) which is equal to \(25\pi\).
Now to find the fraction of circle that is shaded we divide the area of the shaded area and the area of the entire circle. This gives you the equation: \(\frac{12.25\pi}{25\pi}\) but since it wants it as a fraction, I'm assuming it wants integers in the decimal and numerator place. So we can represent 12.25 as 12 + 1/4. And then convert the 12 into 1/4ths by multiplying by 4 and then adding that to the numerator. This makes the fraction \(\frac{49}{4}=12.25\). So now all we have to is divide the two values: \(\frac{\frac{49}{4}}{\frac{25}{1}}\). If you're wondering where the pi's when you can just cancel them out since they're both in the numerator and denominator. Now all we have to do is keep the 49/4, change the operator to multiplication, and flip the 25/1 to 1/25. This gives you the equation: \(\frac{49}{4} * \frac{1}{25}\) which becomes \(\frac{49}{100}\) which is the answer
Need a some help with explanation. Thank you
Answer:
C. (1, 3)
Step-by-step explanation:
The x-coordinate of a point is the measure of the horizontal distance a point is to the right of the y-axis. When the point is translated 4 units to the left, its x-coordinate is reduced by 4: x ⇒ x-4.
The y-coordinate of a point is the measure of the vertical distance a point is above the x-axis. When the point is translated 2 units up, its y-coordinate is increased by 2: y ⇒ y+2.
__
translated pointsThe translation 4 units left and 2 units up can be summarized by ...
(x, y) ⇒ (x -4, y +2)
Then the translated vertices are ...
Q(1, 3) ⇒ Q'(1 -4, 3 +2) = Q'(-3, 5)
R(5, 1) ⇒ R'(5 -4, 1 +2) = R'(1, 3) . . . . . . . matches choice C
S(3, 5) ⇒ S'(3 -4, 5 +2) = S'(-1, 7)
Of the points listed, the point (1, 3) matches a translated vertex.
how to determine if an integral is convergent or divergent
A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.
B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.
A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.
Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.
Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.
B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.
Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.
for such more question on convergence
https://brainly.com/question/23558817
#SPJ8
What type of argument is this? "All cubes are square. A dice is a cube. Therefore, a dice must be square."
The argument presented is an example of a fallacy known as affirming the consequent, which incorrectly assumes that if the consequent of a conditional statement is true, then the antecedent must also be true. It fails to consider other possibilities and overlooks the fact that not all square shapes are cubes.
The argument presented is an example of a fallacy known as affirming the consequent, which is a formal logical fallacy. This fallacy occurs when one assumes that if the consequent (the "then" part) of a conditional statement is true, then the antecedent (the "if" part) must also be true.
In this case, the argument incorrectly assumes that because all cubes are square (if cube, then square) and a dice is a cube, then the dice must be square. However, this reasoning is flawed. While it is true that all cubes are square, not all square shapes are cubes. Therefore, even though a dice is a cube, it does not necessarily mean that it must be square.
The argument fails to consider other possibilities, such as the fact that cubes can have other shapes besides squares, like rectangular cubes. This logical error highlights the importance of careful reasoning and avoiding fallacies when making arguments.
To know more about argument refer here:
https://brainly.com/question/2645376#
#SPJ11
Use Lagrange multipliers to find the points on the given cone that are closest to the following point.
z^2 = x^2 + y^2; (14, 8, 0)
x,y,z=(smaller z-value)
x,y,z=(larger z-value)
x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)
x,y,z=(larger z-value)=(56/3, 32/3, -16/3)
These are the points on the cone that are closest to the point (14, 8, 0).
What is a point?In a two-dimensional space, a point is defined by two coordinates, typically denoted by (x, y), where x represents the horizontal position, and y represents the vertical position. In a three-dimensional space, a point is defined by three coordinates, typically denoted by (x, y, z), where x, y, and z represent the horizontal, vertical, and depth positions, respectively.
According to question:We want to minimize the distance between the point (14, 8, 0) and the surface of the cone defined by the equation z² = x² + y², subject to the constraint that we stay on the surface of the cone.
Let f(x,y,z) = (x-14)² + (y-8)² + z² be the function we want to minimize subject to the constraint g(x,y,z) = z² - x² - y² = 0.
The Lagrange multiplier method involves finding the critical points of the function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z), where λ is the Lagrange multiplier.
So we have:
L(x,y,z,λ) = (x-14)² + (y-8)² + z² - λ(z² - x² - y²)
Taking the partial derivatives with respect to x, y, z, and λ, and setting them equal to zero, we get the following system of equations:
2(x-14) + 2λx = 0
2(y-8) + 2λy = 0
2z - 2λz = 0
z² - x² - y² = 0
The third equation simplifies to z(1-λ) = 0, which gives us two possibilities:
Case 1: z = 0
In this case, the fourth equation becomes -x² - y² = 0, which implies that x = y = 0. But this point does not lie on the surface of the cone, so it is not a valid critical point.
Case 2: λ = 1
In this case, the first two equations become x-14 = -xλ and y-8 = -yλ, which imply that x = -7λ and y = -4λ. Substituting into the fourth equation gives:
z² = x² + y² = 65λ²
To minimize the distance between the point (14, 8, 0) and the surface of the cone, we want to find the value of λ that minimizes the function f(x,y,z) subject to the constraint g(x,y,z) = 0. Substituting x = -7λ, y = -4λ, and z = √(65λ²) into f(x,y,z), we get:
f(λ) = (7λ-14)² + (4λ-8)² + 65λ²
To minimize this function, we take its derivative with respect to λ and set it equal to zero:
f'(λ) = 30λ - 80 = 0
Solving for λ, we get λ = 8/3. Substituting this back into x = -7λ, y = -4λ, and z = √(65λ²), we get:
x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)
x,y,z=(larger z-value)=(56/3, 32/3, -16/3)
These are the points on the cone that are closest to the point (14, 8, 0).
To know more about points visit:
https://brainly.com/question/16907812
#SPJ1
If 5x to the power of 7 times s = 20x to the power of 4, which expression is equivalent to z
The expression that is equivalent to x is ∛4/s
How to determine the equivalent of x?In this question, the mathematical statement of the equation is given as
5x to the power of 7 times s = 20x to the power of 4
When the mathematical statement is represented as an equation, we have the following representation
5x⁷ * s = 20x⁴
Divide both sides by x⁴
So, we have the following representation
5x⁷/x⁴ * s = 20x⁴/x⁴
Evaluate the quotients
This gives
5x³ * s = 20
Divide both sides by 5
x³ * s = 4
So, we have
x³ = 4/s
Take the cube root of both sides
x = ∛4/s
Hence, the solution is x = ∛4/s
Read more about equivalent expressions at
https://brainly.com/question/15775046
#SPJ1
what step cadence is used during the ymca 3-minute step test?
This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm.
The step cadence used during the YMCA 3-minute step test is a set of three stepping cycles per each 20-second period. This means that the participant takes a total of nine steps within each 20-second period. In other words, the participant steps up and down on the platform at a rate of approximately 24 steps per minute. It is important to maintain this consistent step cadence throughout the entire test in order to get an accurate measure of cardiovascular fitness. Overall, the YMCA 3-minute step test is a simple and effective way to assess an individual's aerobic fitness level.
The YMCA 3-minute step test utilizes a specific step cadence to measure an individual's cardiovascular fitness. The answer is that during the test, a cadence of 96 beats per minute (BPM) is used. This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm. Upon completion of the test, the participant's heart rate is measured for a minute to determine their fitness level. The test results can be compared to established norms to gauge overall cardiovascular health and endurance.
To know more about corresponds visit:-
https://brainly.com/question/29912603
#SPJ11
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 300 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11. 3 seats and the sample standard deviation is 4. 3 seats.
Required:
Construct a 92% confidence interval for the population mean number of unoccupied seats per flight
If a large airline wants to estimate its average number of unoccupied seats per flight over the past year Then a 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats.
To construct a confidence interval for the population mean number of unoccupied seats per flight, we will use the following formula CI = X ± z*(σ/√n)
Where:
X = sample mean = 11.3 seats
σ = sample standard deviation = 4.3 seats
n = sample size = 300
z = z-score corresponding to the desired confidence level of 92%, which we can look up in a standard normal distribution table or use a calculator. For a 92% confidence level, the z-score is 1.75.
Plugging in the values, we get:
CI = 11.3 ± 1.75*(4.3/√300)
CI = 11.3 ± 0.966
Therefore, the 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats. This means we can be 92% confident that the true population means a number of unoccupied seats per flight falls within this interval.
To learn more about “confidence interval” refer to the https://brainly.com/question/20309162
#SPJ11
PLZ HELP ASAP!!!! NEED HELP!!!
Answer:
I'm pretty sure the answer is C
A line passes through the points (-5, 2) and (10,-1). Which is the equation of the line?
o y=-3x+1
O y-zx=3
O y = -5x – 23
O y = 5x + 27
HURRY
agility, balance, coordination, speed, reaction time, and power are all components of ___________-related fitness.
Agility, balance, coordination, speed, reaction time, and power are all components of Skill -related fitness.
What is skill-related fitness components ?The skill-related component of physical fitness is specifically related to skills used in sports and is often (but not always) combined with other components of fitness. For example, power is strength at speed. Agility is a combination of strength and balance. The six basic fitness components related to ability are flexibility, balance, coordination (hand-eye or foot-eye), strength, reaction time and speed. If you already meet ACSM guidelines and want to train more for specific fitness-related goals, consider his six fitness components related to ability. The health component of fitness is of universal importance. Performance-related fitness components are better suited to specific athletes. For example, everyone benefits from a daily walk, but someone who walks just to get their heart pumping doesn't need to be fast enough to run a 5-minute mile.
To learn more Skill-related components, refer:
https://brainly.com/question/1566360
#SPJ4
Determine the measure of the interior angle at vertex C. PLEASE HELP ASAP
Answer:
B. 120°
Step-by-step explanation:
Sum of the measures of the interior angle of a polygon with n sides:
(n - 2)180
We have a pentagon, a 5-sided polygon, so n = 5.
We first find the sum of the measures of the angles of any pentagon.
(5 - 2)180 = 3(180) = 540
From the figure, we add the measures of the 5 angles and set the sum equal to 540°.
3x + 4x + 4x + 4x + 3x = 540°
18x = 540°
Divide both sides by 18.
x = 30°
The angle at vertex C measures 4x.
4x = 4 * 30° = 120°
Answer: B. 120°
35
28
=
20
m
i need it done asap the asingmentis do today i dont want to fail math class
Anyone help please I’m wasting my points for no reason
Answer:
Qn1: -37
Qn2: 16
Qn3:-33.6
Step-by-step explanation:
Qn1:
k(4) = -4*4-6 = -16-6 = -22
m(5) = (5^2)-8*5=-15
k(4)+m(5)= -22+ (-15)= -37
Qn2:
m(-2)= 4 -8*(-2)= 20
n(10) = 2 -6 = -4
20+ (-4)=16
Qn3:
n(-100)= -20-6 = -26
k(-8) = -1.6 -6= -7.6
-26+ (-7.6) = -33.6
Names of TV shows taped in New York are an example of which type of data? Answer a. Qualitative b. Statistic c. Quantitative d. Parameter
Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.
It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.
To know more about qualitative data visit :
https://brainly.com/question/29004144
#SPJ11
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 9n3 1 lim an Enhanced Feedback Please try again. You can divide the numerator and denominator by the highest power of n that occurs in the denominator and then use the Limit Laws. One of the Limit Laws you may need is lim--= 0 if r > 0 Need Help? Read It Talk to a Tutor +-2 points SEssCalcET2 8.1.011.MI My Notes Ask Your Teacher
The limit of the given sequence `9n³ + 1` as n approaches infinity is `10`. The given sequence is = 9n³ + 1. We need to determine whether the given sequence converges or diverges. If it converges, then we need to find the limit.
To find whether the sequence converges or diverges, let's take the limit of the given sequence as n approaches infinity, i.e., lim n→∞ an. lim n→∞ an = lim n→∞ (9n³ + 1) = lim n→∞ 9n³ + lim n→∞ 1.
Since `lim n→∞ 9n³` is of the form `∞•∞•∞` (infinity times infinity), we cannot directly find its limit.
To evaluate this limit, we need to divide the numerator and denominator by the highest power of n that occurs in the denominator, which is n³.
lim n→∞ 9n³` `= lim n→∞ 9` (dividing numerator and denominator by n³).
Thus, `lim n→∞ an` `= lim n→∞ 9n³ + lim n→∞ 1` `= lim n→∞ 9 + lim n→∞ 1` (applying limit laws)`= 9 + 1` (since `lim n→∞ 1 = 1`)`= 10`.
Therefore, the given sequence converges to `10`. Hence, the limit of the given sequence `9n³ + 1` as n approaches infinity is `10`.
To know more about limit refer here:
https://brainly.com/question/30115902#
#SPJ11