Graph each function and identify its domain, range, intercepts, asymptotes, and holes.
Thank you! :)
Answers
Answer:
Domain: real numbers except {-4, -3, 0}Range: real numbers except {2}Intercepts: (-1, 0); no y-intercept (see Holes)Asymptotes: horizontal, y = 2; vertical, x = -3Holes: (-4, 6), (0, 2/3)Step-by-step explanation:
You want the domain, range, intercepts, asymptotes, and holes of the rational function f(x) = (2x³ +10x² +8x)/(x³ +7x² +12).
SimplifiedThe given function can be simplified by cancelling common factors from numerator and denominator. These cancelled factors show where the holes are in the graph.
[tex]f(x)=\dfrac{2x^3+10x^2+8x}{x^3+7x^2+12}=\dfrac{2x(x+4)(x+1)}{(x(x+4)(x+3)}=2\left(\dfrac{x+1}{x+3}\right)\quad x\notin\{-4,-3,0\}[/tex]
DomainThe function is defined for all real numbers except those where the denominator is zero: {-4, -3, 0}.
RangeThe function can produce every output value except the value of the horizontal asymptote: y = 2. The range is all real numbers except 2.
InterceptsThe x-intercept is found where the numerator of the simplified function is zero: x = -1
The y-intercept is the function value at x=0. The function is undefined there, so the y-intercept does not exist. (The limit as x approaches zero is y = 2/3.)
AsymptotesThe function has a horizontal asymptote at the y-value corresponding to the ratio of the highest-degree terms of the numerator and denominator: y = 2.
The vertical asymptote is at the uncanceled denominator zero, x = -3.
HolesThe holes are where a numerator and denominator factor cancel. The y-value at the hole is the limit of the function value as x approaches the hole location. This is the value of the simplified function.
The holes are (-4, 6) and (0, 2/3).
Related Questions
3,635 nearest thousand
Answers
Answer:
4000
Step-by-step explanation:
If we were to take the number 3,635 and round it to the nearest thousand, we can do it like this.
Start with 5. (Ones place)
3,635
5 is rounded to 10.
Now work on the number 4. (Tenths place)
3,640
4 is rounded to 0.
And now we can do the number 6. (Hundreds place)
3600
6 is rounded to 10.
If we look at the number now, it is
4000
3.635 rounded to the nearest thousand is 4000.
if a person is making the minimum salary for a construction worker, they are making more than what percentage of teachers?
Answers
If a person is making a minimum salary for a construction worker, in that case, they will make more than 75% of the teachers.
A salary is a form of periodic fee from a corporation to a worker, which can be laid out in an employment contract. it is contrasted with piece wages, in which every task, hour, or other unit is paid one after the other, in place of on a periodic foundation. From the factor of view of going for walks in a commercial enterprise, revenue can also be considered as the fee of obtaining and keeping human sources for jogging operations and is then termed personnel fee or salary cost. Payroll accounts are used in accounting to record.
Salary is a hard and fast amount of cash or compensation paid to a worker via an enterprise in return for work executed. salary is generally paid in fixed durations, for example, monthly bills of 1-twelfth of the annual salary.
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The table shows the proportional relationship between the price for a certain number of buckets of golf balls at a driving range.
Buckets 3 5 7
Price (dollars) 28. 50 47. 50 66. 50
Determine the constant of proportionality.
9. 5
10. 5
18. 25
28. 5
Answers
The constant of proportionality is 9.5.
The correct option is (a)
Given,
In the question:
The proportional relationship between the price for a certain number of buckets of golf balls at a driving range.
Buckets 3 5 7
Price (dollars) 28. 50 47. 50 66. 50
To determine the constant of proportionality.
Now, According to the question:
We know that:
Proportional relationship equation:
y = kx, where k-constant of proportionality
In the given table, number of buckets represent input values (x) and the price represents output values (y).
We have for the first column:
x = 3, y = 28.50
Find the value of k by plugging in the values of x and y:
28.50 = 3k
k = 28.50/3
k = 9.5
The options are:
a) 9. 5
b) 10. 5
c) 18. 25
d) 28. 5
Hence, The constant of proportionality is 9.5.
So, The correct option is (a).
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Azlyn had $25. She went to lunch and spent $15 what percentage of her money did Azlyn spend on lunch
Answers
Answer: 60%
Step-by-step explanation:
15 divided by 25 = 0.6
0.6 x 100 = 60%
:)
a frog starts at location a and wants to get to location b that is 500 meters away. starting at a, it sits at a given spot on the path from a to b for a time that is exponen- tially distributed with parameter 1 (minute). after that, it jumps 1 meter towards b, sits in the new spot for an exponentially distributed time, etc. all the times are independent. what is the probability (approximately) that it will get to b within 7 hours?
Answers
The probability that it will get to b within 7 hours is approximately 0.014.
Probability:
In math, the favorable way of happening the event is known as probability.
Given,
A frog starts at location a and wants to get to location b that is 500 meters away. starting at a, it sits at a given spot on the path from a to b for a time that is exponentially distributed with parameter 1 (minute). after that, it jumps 1 meter towards b, sits in the new spot for an exponentially distributed time, etc. all the times are independent.
Here we need to find the the probability (approximately) that it will get to b within 7 hours.
While we looking at the given question we have identified that,
starting point = a
ending point = b ( 500 meters)
Time take for one jump = 1 minute
Distance covered in one jump = 1 meter.
Here they also said that the time is independent but the distance remains constant.
So, the probability that it will get to b within 7 hours is calculated as,
=> 7/500
=> 0.014
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diego brought a box of 120 colored pencils to school. he gave 14 pencils to marcus and 32 pencils to anna. how many pencils did diego have left
Answers
Diego will have 74 pencils remaining after giving 14 pencils to Marcus and 32 pencils to Anna.
The question is about simple Subtraction. First, we know that the total number of colored pencils in the box is 120. Following is the step-by-step explanation for this question.
Let suppose,
Total Colored pencils = x = 120
Pencils given to Marcus = y = 14
Pencils are given to Anna = z = 34.
And, Total Pencil Remaining = R =?
We can show the given information in the equation as given below:
R = x - y - z
By putting the value in the above equation:
R = 120 - 14 -34
R = 74.
So, after giving the 14 and 32 pencils to Marcus and Anna, respectively. Marcus would remain with 74 Pencils.
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how do i do Write the prime factorization of 6. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answers
Answer:
2*3
Step-by-step explanation:
divide by smallest number possible
6/2=3
3/3=1
2*3=6
so 2*3
The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 59.1. O b. 7.688. O C. 7.018. O d. 49.25.
Answers
The point estimate of the population standard deviation is 5.91 (Option A)
Standard deviation refers to the spread of a data distribution and measures the distance between each data point and the mean. The sample standard deviation (s) is a point estimate of the population standard deviation σ.
The mean of the population ẋ = sum of all values/ total number of values = 97/6 ≈ 16
The point estimate of the population standard deviation S =√(∑(xi - ẋ)^2/n-1)
∑(xi - µ)^2 = (9 – 16)^2 + (13– 16)^2 + (15– 16)^2 + (15– 16)^2 + (21– 16)^2 + (24– 16)^2 = 79 + 9 + 1 + 1 + 25 + 64 = 179
s = √(179/5) = 5.98
Note: The question is incomplete. The complete question probably is: The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 5.91. O b. 7.688. O C. 7.018. O d. 4.925.
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a 28 year old man plays 165 for a one year life insurance policy with coverage of 140000 if the probability that he will live through the year is 0.9994 what is his expected value for the insurance polixy
Answers
The insurance policy's anticipated value is -$81 for the one year life insurance policy.
Explain the term insurance policy?Term insurance is a form of life insurance policy which offers protection for a certain "term" of years, or a set amount of time.A deceased person will be paid if the insured passes away while the term insurance is still in effect and the insurance is active.Consider the various factors and the man's potential benifits.
-$165 because he already paid that sum.
The beneficiary could earn as a potential profit.
140000-165 = $139835
The probability of surviving is 0.9994.
The likelihood of not living is 0.0006.
The expected value is given by;
E(v) = (-165)(0.9994) + (139835)(0.0006)
E(v) = -164.901 + 83.901
E(v) = -81.
Thus, the insurance policy's anticipated value is -$81.
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what is the probability of these events when we randomly select a permutation of {1, 2, 3, 4}? a) 1 precedes 4. b) 4 precedes 1. c) 4 precedes 1 and 4 precedes 2. d) 4 precedes 1, 4 precedes 2, and 4 precedes 3. e) 4 precedes 3 and 2 precedes 1.
Answers
The probability that these events when we randomly select a permutation is 24, 1/2, 1/2, 1/3, 1/4, 1/4
What is a probability simple definition?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
What is the probability formula?P(A) = n(A)/n (S)
The probability of an event "A" is P(A). The number of successful outcomes is n(A). The total number of events in the sample space is denoted by n(S).
1) From the set we can select 4*3*2*1=24 permutations.
2) There are six permutations that begin with 1, three that begin with 2, three that begin with 3, and no permutations that begin with 4 when 1 comes before 4. So, P1 ={ 6+3+3+0}/{24} = 1/2
3) No permutations begin with 1, three permutations begin with 2, three permutations begin with 3, and six permutations begin with 4, where 4 comes before 1. P2=1/2
4) There are no permutations that begin with 1, no permutations that begin with 2, no permutations that begin with 2, no permutations that begin with 3, and six permutations that begin with 4, where 4 comes before both 1 and 2. Therefore, P 3 = 1/3
5) No permutations begin with 1, no permutations begin with 2, no permutations begin with 3, and there are six permutations that begin with 4, where 4 comes before 1, 2, and 3. So, P4= 1/4
6) There are no combinations that begin with 1, three combinations that begin with 2, no combinations that begin with 3, and three combinations that begin with 4, where 4 comes before 3 and 2 comes before 1. So, P5= 1/4
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Aaron separates 11 carrot sticks equally among 3 bags.
Drag carrots to show how many carrots will be in each bag and how many carrots will be left over.
Answers
Answer:
there will be 3 carrots in each bag and you will have 2 carrots left over
Step-by-step explanation:
hope this helps
A book sold 32,100 copies in its first month of release. Suppose this represents 8.2% of the number of copies sold to date. How many copies have
been sold to date?
Round your answer to the nearest whole number.
Answers
Answer:
2,632 copies
Step-by-step explanation:
32100× 0.082= 2632.2
About 2,632
The interior angles formed by the sides of a hexagon have measures that sum to 720°.
What is the measure of angle F?
Enter your answer in the box.
m∠F=
Answers
Answer:
Step-by-step explanation:
(x-60)+(x-20)+(x-40)+130+120+110=720
3X -120 + 360=720
3x +240= 720
3x= 720-240
3x=480
x= 480/3 = 160
x=160
angle F = (x-20)
angle F = 160-20=140
angle F = 140
ohnny is a sophomore in college and has a 1.5 cumulative grade point average (gpa). johnny's cumulative gpa will fall even further next semester if he performs worse than (i) his cumulative gpa. (ii) he ever performed before. (iii) he did last semester.
Answers
The value of the solution is B i.e., his cumulative gpa (i), he ever performed before (ii)
What do you mean by statistics?The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.
What are types of statistics?The two types of statistics are: Descriptive and inferential.
With the alternatives available, Johnny can only do worse if his performance falls short of both his lifetime GPA and his previous best performance. It's possible that the last scenario, in which Johnny performed worse than last semester, won't necessarily have an impact on his GPA. A cumulative GPA represents Johnny's overall GPA since he first began attending school. Considering that his most recent semester may have been one of his best and had a solid outcome, earning a result somewhat below that of his previous semester may not necessarily result in a drop in his cumulative GPA. Therefore, choice B is right.
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Suppose that 14 inches of wire costs 84 cents.
At the same rate, how much (in cents) will 37
inches of wire cost?
Answers
Answer: 222 cents
Step-by-step explanation: 84/14 = 6 This is the unit rate.
6 x 37 = 222
Please help me with this 2 problems
Answers
[9] Answer: x = 4
Step-by-step explanation:
Both of these problems use triangle's exterior angles. We will set up an equation and solve. The two opposite angles are equal to opposite exterior angle. After writing our equation, we will solve and isolate the variable using inverse operations.
17x + 1 + 18x + 3 = 144
35x + 4 = 144
35x = 140
x = 4
[10] Answer: x = 3
Step-by-step explanation:
Both of these problems use triangle's exterior angles. We will set up an equation and solve. The two opposite angles are equal to opposite exterior angle. After writing our equation, we will solve and isolate the variable using inverse operations.
20x + 23x + 1 = 130
43x + 1 = 130
43x = 129
x = 3
The second is x = 3
Caculate the simple interest earned on $5000 at 5% for 3.5 years
Answers
Answer:
56.0
Step-by-step explanation:
when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes,: group of answer choices the variance of both of the original populations must be known (as opposed to estimated) the scores from both samples are combined to form a single sample, and the estimated variance is figured in the usual way, but using this combined sample the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants the variance of at least one of the original populations must be known (as opposed to estimated), but the other can be estimated from sample scores
Answers
The estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.
What is population variance?
Each data point's distance from the population mean is quantified by the population variance, which is a measure of dispersion. The average of the squares of the deviations from the data's mean value is known as population variance.
Hence, when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes, the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.
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Write an inequality and use substitution to solve the following problem:
Janet plans on mowing lawns for 12 weeks in the summer. Her goal for the summer is to earn more than $500. Which of the following rates of weekly earning would allow her to reach her goal?
Answers
The rates of weekly earning would allow her to reach her goal will be 12x > 500.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Janet anticipates cutting yards for quite a long time in the late spring. Her objective for the late spring is to acquire more than $500.
Let 'x' be the weekly rate. Then the inequality is written as,
12x > 500
The rates of weekly earning would allow her to reach her goal will be 12x > 500.
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I don’t understand this question , it’s so confusing
Answers
the second row is 18+12=30
The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5), and (6, 4).
Find the length of the sides of the rectangle and its perimeter.
Answers
Check the picture below.
the length of a rectanglar photograph is 7 inches more than the width. if the are is 78 inches squared, what are the dimensions of the photograph
Answers
The dimensions of the photograph are found as 13 in and 6 in.
Explain the term rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides.Let length = x.
So, width = x - 7
Area = length x width
A = x (x -7)
and A = 78 inches squared.
Thus,
78 = x (x -7)
On solving.
x² - 7x - 78 = 0
Find the factors of the quadratic equation,
x² - 7x - 78 = 0
(x - 13)(x + 6) = 0
Thus,
x = 13 and x = -6 but (x > 0)
Thus, when x = 13 in,
Width = x + 7
Width = 13 - 7
Width = 6 in
Thus, the dimensions of the photograph are found as 13 in and 6 in.
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Enter an equation of the line (in slope-intercept form) that passes through the point (20, −7) and is perpendicular to the line y = −5x + 9. Express any numeric values as integers or simplified fractions.
Answers
Answer:
y = 1/5x -11
Step-by-step explanation:
You want the slope-intercept equation of the line perpendicular to y=-5x+9 that goes through the point (20, -7).
Slope-intercept formThe slope-intercept form of the equation for a line is ...
y = mx +b . . . . . . . . where m is the slope and b is the y-intercept
This can be solved to find the y-intercept from a point on the line:
b = y -mx
Comparing this form to the given equation, you see the given line has a slope of m = -5.
Perpendicular lineThe perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line:
slope = -1/(-5) = 1/5
Y-interceptThe y-intercept of the desired line can be found using the equation for b above. The y-intercept of the line with slope 1/5 through point (x, y) = (20, -7) is ...
b = y -mx = (-7) -1/5(20) = -7 -4
b = -11
Now, we have the slope and intercept of the desired line, so we can write its equation:
y = 1/5x -11
a multiple regression model has . select one: a. more than one dependent variable b. only one independent variable c. at least two dependent variables d. more than one independent variable
Answers
The multiple regression model represented by y = a₀ + a₁x + a₂x + ... has one independent variable.
Explanation:
Simple or linear regression model represents one dependent and one independent variable.Multiple regression model represents one dependent and more than one independent variable.Simple regression model represent by y = mx + b , here y is dependent variable where as 'x' independent variable.Multiple regression model represented by y = a₀ + a₁x + a₂x + ... Multiple regression model is expanded form of linear regression model where more than one independent variables are included.Therefore, the multiple regression model has more than one independent variable that is option d.
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If 6s=24, does 6s÷6=24÷6?
Answers
Answer:
i need points
Step-by-step explanation:
Therefore it is equal to 6s/6 = 24/6, as you are dividing 6 on both sides.
How to solve 3(1+p)=-5(p+1)
Answers
Step-by-step explanation:
3(1+p)=-5(p+1)
here is your answer
I hope this helpful for u
to make sure that a few unusual responses don’t skew results or lead to inaccurate judgements, a data analyst focuses on what element of the data collection?
Answers
The component of the data that a data analyst is most interested in is sample size.
Given,
To prevent results from being skewed or causing incorrect conclusions, we must identify the data element on which the data analyst should concentrate;
The data analyst;
A data analyst looks at data to uncover useful consumer insights and possible applications for the knowledge. They also tell the management of the business as well as other stakeholders of this information.
Although it is advisable for data analysts to have a foundational knowledge of statistics and mathematics, many of their responsibilities can still be carried out without it. However, knowledge in statistics, linear algebra, and calculus is often required for data analysts.
Here,
A data analyst's primary interest in the data is sample size
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the gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. a simple random sample of 81 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. construct a 95% confidence interval for the mean gas mileage for this car model.
Answers
The 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.
The confidence interval for a statistical data is written as-
(x+ zr/√n, x- zr/√n)
Here, we are given that-
Mean ⇒ x = 27.5 mi/gallon.
Standard deviation ⇒ r = 4 mi/gallon
Number of samples ⇒ n = 49
and Confidence interval = 95%
z-score at 95% confidence level = 2.17
Substituting the values we have;
= [27.5 - 2.17(4.0) /(√49), 27.5 + 2.17(4.0) /(√49)]
= (27.5 - 8.68 / 7, 27.5 + 8.68 / 7)
= (27.5 - 1.24, 27.5 + 1.24)
= ( 26.26, 28.74)
Therefore, the 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.
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The question is attached on the image below. Help is needed urgently please help!
Answers
The intersection point is (2,5).
A coordinate pair is defined (x, y)
The x-coordinate is 2, the y-coordinate is 5.
x = 2
y = 5
need help working this problem
Find the missing angle values
Answers
a) ∠a = 35
b) ∠b = 40
c) ∠c = 35
d) ∠d = 70
e) When we add all the angles together we get an angle of 360°.
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Given, ∠b = 40
∠d = 70
∠1 = ∠ a
∠2 = ∠c
∠1 = ∠2
So, ∠1 =∠2 = ∠a = ∠c
70 + 40 + ∠a + ∠2 = 180
110 + 2∠a = 180
2∠a = 180 - 110
∠a = 70/2
∠a = 35
∠1 =∠2 = ∠a = ∠c = 35
When we add all the angles together we get an angle of 360°
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