When we calculate the probability of multiple events occurring, we use the concept of conditional probability.
Conditional probability is the probability of one event occurring given that another event has already occurred. In this case, the first event is flipping a heads, and the second event is rolling less than a 6 on a 66-sided die.
To find the probability of both events occurring, we multiply the individual probabilities:
P(heads and roll less than 6) = P(heads) * P(roll less than 6 | heads)
Here, P(heads) is the probability of flipping a heads, which is 1/2 for a fair coin. P(roll less than 6 | heads) is the probability of rolling less than a 6 given that we have already flipped a heads, which is 5/66 for a fair 66-sided die.
So:
P(heads and roll less than 6) = 1/2 * 5/66
P(heads and roll less than 6) = 5/132
So, the probability of flipping a heads and rolling less than a 6 on a fair 66-sided die is 5/132.
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We multiply the individual probabilities in order to determine the likelihood that both occurrences will occur:
P(heads and roll under 6) equals P(heads) Times P(roll under 6 | heads).
So:
P(heads and roll less than 6) is equal to 1/2 * 5/66.
P(heads, roll less than 6), equals 5/132
Therefore, the likelihood of getting a number less than a 6 on a fair 66-sided die is 5/132.
What is 65 Inches in Feet?
When 65 inches are converted to feet, the result is 5.41667 feet.
How do I convert an inch to a foot?To convert 65 inches to feet, divide 65 by 12.We can calculate 65 inches equals 5.41667 feet using a calculator or long division. As a result, 65 inches is equivalent to 5.41667 feet. It is important to note that inches and feet are both length units, so converting between the two involves moving the decimal point in the number two places to the left or right, depending on which unit you are converting to.Divide the number of inches by 12 to convert to feet, because a foot is 12 inches long. Similarly, multiply the number of feet by the number of inches.As a result, 65 inches equals 5.41667 feet, and you can convert inches to feet by dividing the number of inches by 12.To learn more about inches refer to :
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Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give a counterexample.
(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4
(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist.
(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2.
(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.
lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4, If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist, If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2, If lim t→0 h(t) does not exist, then h(0) cannot exist all these Limits statement are False
What do you mean by limits?A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.
lim x -> c f(x) = L
(a) False.
According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.
(b) False.
According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.
In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.
(c) False.
A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.
Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.
(d) False.
The absence of a limit does not imply the existence of the function's value at that time.
In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.
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All these given Limit statement are False.
(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4
(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist
(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2
(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.
What do you mean by limits?A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.
lim x -> c f(x) = L
(a) False.
According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.
(b) False.
According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.
In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.
(c) False.
A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.
Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.
(d) False.
The absence of a limit does not imply the existence of the function's value at that time.
In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.
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how many ways are there to split a dozen people into 3 teams, where each team has 4 people?
By using permutations and combinations, We can arrange 12 people into 3 teams of 4 in 5775 different ways.
Here, we will use the concept of permutations and combinations to solve the question.
We have to arrange 12 people into 3 teams of 4.
We know that ⁿCr = n! / [(n - r)! × r!]
No. of ways to select the first 4 people in the first group = ¹²C₄
= 12! / [(12 - 4)! × 4!]
= 12! / [(8! × 4!)]
= 495
No. of ways to select 4 people from the remaining 8 for the second group = ⁸C₄ = 8! / [(8 - 4)! × 4!] = 8! / [(4! × 4!)] = 70
No. of ways to select 4 people from 4 for the third group = ⁴C₄ = 4! / [(4 - 4)!] × 4!] = 4! / [(0! ×4!)] = 1
Total no. of ways to select people for group = (495 x 70 x 1) / 3! = 34650 /6 = 5775
Hence, we can split 12 people into 3 teams of 4 in 5775 different ways.
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You roll a 6-sided die two times. What is the probability of rolling a number less than 4 and then rolling a number greater than 3? Write your answer as a percentage%.
Answer:
Step-by-step explanation:
3/6
Which of the following statements is TRUE about the value of a college degree?
O A high school graduate can expect to earn about the same as a college graduate
• Every college graduate can expect to have a starting salary over $60,000 right after college
• A college graduate can expect to earn, on average, more than a high school graduate over a career
• A college graduate typically earns less than someone with a high school diploma for the first 10 years
Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.
what is proportionality ?Links are regarded to as appropriate when they typically have the same ratio. For instance, the trees in an estate and or the number of peaches in a harvest in apples depend on the average number of apples provided by each tree. A linear correlation between two numbers as well as variables is referred to as being proportional in mathematics. When the primary quantity doubles, the other amount also does so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two components are proportional, it suggests that if one rises, the other climbs as well, and their correlation is continuous at all values. The diameter and circumference of such a circle are used as an example.
given
The true statement is
starting salary = $60,000
average = $60,000 / 3
= $ 20,000
Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.
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Ainsley works for the owners of a bookstore. Her starting salary is $24,500, and she gets a 3% raise each year.
a. Write an equation in function notation to represent Ainsley's salary as a function of the number of years she has been working at the bookstore.
b. What will Ainsley's salary be when she begins her fourth year working at the bookstore? Show your work.
Thanks for helping me : )
Answer:
y = $24,500 * (1 + 0.03x)
Step-by-step explanation:
Please find the attachment for detail
Sahara's dog has a mass of 25 kilograms. What is the mass of the dog in grams?
Answer:
25,000g
Step-by-step explanation:
multiply the mass value by 1000
25 x 1000 = 25,000g
Solve by graphing
4x - 4y = 22
y = -5.5
The system of equations has a unique solution. The solution is (0,-5.5).
What is the system of equations?
A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables.
The system of equations is
4x - 4y = 22 ....(i)
y = -5.5 ...(ii)
Putting x = 0 in 4x - 4y = 22:
4 × 0 - 4y = 22
- 4y = 22
y = -5.5
Putting x = 1 in 4x - 4y = 22:
4 × 1 - 4y = 22
- 4y = 18
y = -4.5
The points on equation (i) are (0,-5.5) and (1, -4.5).
The points on the line y = -5.5 are (-3,-5.5), (2,-5.5).
Plot the points and join them.
The intersection point is the solution of the system of equations.
The solution is x = 0 and y = -5.5
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Tara’s dog weighs 9.25 pounds. Jenna’s dog weighs times as much as Tara’s dog. How much does Jenna’s dog weigh?
A 12.75 pounds12.75 pounds
B 32.375 pounds32.375 pounds
C 27.5 pounds27.5 pounds
D 27.125 pounds
The weight of Jenna's dog is 32.375 pounds
How much does Jenna’s dog weigh?From the question, we have the following parameters that can be used in our computation:
Tara = 9.25 pounds
Also, we have
Jenna = 3.5 * Tara's dog
Substitute the known values in the above equation, so, we have the following representation
So, we have
Jenna = 3.5 * 9.25 pounds
Evaluate
Jenna = 32.375 pounds
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Lines mm and nn are parallel. The equation of line mm is y=3x+3y=3x+3. What is the equation of line nn?.
Answer:
y = 3x + c
Step-by-step explanation:
c - any number which is not 3
Tanisha is a waitress at a restaurant. Each day she works, Tanisha will make a guaranteed wage of $40, however the additional amount that Tanisha earns from tips depends on the number of tables she waits on that day. From past experience, Tanisha noticed that she will get about $14 in tips for each table she waits on. How much would Tanisha expect to earn in a day on which she waits on 10 tables? How much would Tanisha expect to make in a day when waiting on
�
t tables?
The total amount earned by Tanisha will be $180.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Tanisha is a waitress at a restaurant. Each day she works, Tanisha will make a guaranteed wage of $40, however, the additional amount that Tanisha earns from tips depends on the number of tables she waits on that day. From past experience, Tanisha noticed that she will get about $14 in tips for each table she waits on.
The amount of money earned by Tanisha in 10 days will be:-
Amount = Fixed Wage + Tip
Amount = 40 + ( 10 x 14 )
Amount = 40 + 140
Amount = $180
Hence, Tanisha will have earned $180 in total.
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a sample of n = 9 scores has a variance of s2 = 18. if the scores were a population, what value would be obtained for the population variance?
Value 02 = 16 represents the population variance.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It can mean "identify how much something is worth" like a reward valued at $200 or it can indicate "hold something in high esteem" like "I value our friendship."The occurrence of two complete sets of tens gives the number 24 its place value of two.To learn more about value, refer to:
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72% it goes down by 20% what is the original price of the jacket
Answer:
4x/5
Step-by-step explanation:
the price of the jacket before goes down = x
20/100*x = x/5
the original price of the jacket= x-(x/5) = 4x/5
Can you find the area of the triangle by forming a parallelogram
Yes, we can find the area of the triangle by forming a parallelogram.
The area of a triangle is equal to half the area of a parallelogram.
The conditions are given below.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The area of the triangle can be calculated by forming a parallelogram under the conditions:
1)
If the triangle and the parallelogram are on the same base.
2)
If the triangle and the parallelogram are between the same parallels.
Then,
The area of the triangle is equal to half the area of a parallelogram.
Thus,
The area of the triangle is equal to half the area of a parallelogram.
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Research On effects of poor scale Interpration in maths
The effects of poor scale interpretation in maths are discussed below.
What are the effects of poor scale Interpretation in maths?Poor scale interpretation in mathematics can have significant effects on various areas of life and work that require the use of mathematical concepts and skills. Some of the consequences of poor scale interpretation are:
1. Inaccurate Results: Poor interpretation of scales on graphs, charts, and other mathematical representations can lead to incorrect conclusions and decisions based on the resulting data.
2. Miscommunication: Poor scale interpretation can result in misinterpretation of information and lead to miscommunication between individuals and groups.
3. Ineffective Problem Solving: Poor scale interpretation can hinder the ability to solve mathematical problems effectively, resulting in incorrect solutions and wasted time and resources.
4. Limited Career Opportunities: Poor scale interpretation skills can limit career opportunities in fields that require mathematical proficiency, such as engineering, finance, and technology.
5. Low Confidence and Motivation: Poor scale interpretation skills can lead to frustration and low confidence in mathematics, causing students and individuals to lose interest in the subject.
To avoid the negative effects of poor scale interpretation, it is important to receive proper mathematical education and training, and to continually practice and improve one's mathematical skills. Additionally, seeking help and guidance from teachers and mentors can be beneficial in improving one's scale interpretation skills.
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Find the indicated measure.
Using the inscribed angle theorem:
7. m<A = 79°
8. m<B = 90°
9. m(BC) = 152°
What is the Inscribed Angle Theorem?The Inscribed Angle Theorem states that if two chords of a circle intersect, the measure of the inscribed angle formed by the two chords is equal to half the measure of the central angle that subtends the same arc as the inscribed angle.
Applying the inscribed angle theorem, we have:
7. m<A = 1/2(158)
m<A = 79°
8. m<B = 1/2(180)
m<B = 90°
9. m(BC) = 2(76)
m(BC) = 152°
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In 2015, the per capita consumption of bottled water in the United States was reported to be 36.2 gallons. Assume that the per capita consumption of bottled water in the U.S. is approximately normally-distributed with a standard deviation of 10 gallons.
Find the Z-score of someone who consumed 26.2 gallons of water. Using the Empirical Rule, what is the approximate probability that someone in the United States consumed less than 26.2 gallons of water, what is the approximate probability that someone in the United States consumed between 26.2 and 36.2 gallons of water, and what is the approximate probability that someone in the United States consumed between 26.2 and 46.2 gallons of water?
The required probabilities = 0.16
The required probabilities = 0.68
What is z-score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a particular data collection.
As given that,
μ = 36.2
σ = 10
As per empirical Rule:
μ± σ = 36.2 ±10 = 26.2, 46.2 = 68%
μ± 2σ = 36.2 ±20 = 16.2, 56.2 = 95%
μ ± 3σ = 36.2 ±30 = 6.2, 66.2 = 99.7%
less than 26.2:
13.5% + 2.35% + 0.15% = 0.16
between 26.2 and 36.2:
68% = 0.68
The required probabilities = 0.16
The required probabilities = 0.68
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Solve for xxx. Enter the solutions from least to greatest.Round to two decimal places. (x + 7)^2 - 11 = 0
The value of x in the equation (x + 7)² - 11 = 0 are x = -7 + √11 and x = -7 - √11
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The variable to be solved is x . Variables are numbers represented by letters in an equation.]
Therefore,
(x + 7)² - 11 = 0
(x + 7)(x + 7) - 11 = 0
x² + 7x + 7x + 49 - 11 = 0
x² + 14x + 38 = 0
Therefore, let's factorise the quadratic equation as follows:
x² + 14x + 38 = 0
Using the quadratic formula,
[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
Hence,
a = 1
b = 14
c = 38
Therefore,
x = -7 + √11 and x = -7 - √11
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PLEASE HELP ME WITH THESE QUESTIONS IM SO DESPERATE
WILL GIVE BRAINLIEST
Answer:
11.55m², 181.12mm²,11ft,
Step-by-step explanation:
Simplify the expression.
and multiply A=1/2bh
A charitable organization in Oxford i hoting a black tie benefit for charity and the organization member hope to bring in at leat $1,200 tandard ticket are available for 21 each wherea vip ticket are offered for 43 a piece
To reach the goal of $1,200, the organization needs to sell at least 28 standard tickets (1,200 / 42 = 28.57) or 28 VIP tickets (1,200 / 43 = 27.91). They can also combine the sales of standard and VIP tickets to reach the goal.
The charitable organization is hosting a black-tie benefit event and aims to raise at least $1,200 through ticket sales.
The standard tickets are priced at $21 each, while the VIP tickets are priced at $43 each.
To reach the goal of $1,200, the organization needs to sell a minimum of 28 standard tickets ($1,200 / $21 = 57.14).
However, if they only sell VIP tickets, they will need to sell at least 28 VIP tickets ($1,200 / $43 = 27.91).
Finally, they can also achieve their goal by selling a combination of standard and VIP tickets.
For example, they can sell 20 standard tickets and 8 VIP tickets, which would result in a total of 20 * $21 + 8 * $43 = $840 + $344 = $1,184, reaching their goal of $1,200.
In conclusion, the charitable organization has multiple options to reach their goal of $1,200 through ticket sales for their black-tie benefit event.
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greatest common factor for 90 and 80
Answer:
10
Step-by-step explanation:
The GCF of 80 and 90 is 10.
Water flows at a speed of 20 cm/s along a rectangular channel into a lake. The width of the channel is 15 cm, the depth of the water is 2.5 cm. Calculate the amount of water that flows from the channel into the lake in 1 hour. Give your answer in litres.
Answer is 2.7 million liters/hour
What is speed?
Speed tells us how fast something or someone is travelling.
The flow rate of water can be calculated as the cross-sectional area of the channel multiplied by the speed of the water.
The cross-sectional area of the channel can be calculated as width x depth = 15 cm x 2.5 cm = 37.5 cm^2
The flow rate of water can be calculated as 37.5 cm^2 x 20 cm/s = 750 cm^3/s
To convert this to liters, we need to multiply by 1000 to convert cubic centimeters to cubic centimeters:
750 cm^3/s x (1000 cm^3/L) = 750 L/s
Finally, to find the amount of water that flows into the lake in 1 hour, we need to multiply the flow rate by the number of seconds in an hour:
750 L/s x (3600 s/hr) = 2700000 L/hr = 2.7 million liters/hour.
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Simplify 3/7 =7^1/3.
The cube root of a cube of the number is the same number for any number. Thus, option A is the answer.
In the given question,
[tex]\sqrt[3]{7} = 7^{1/3} \\[/tex]
We have to prove L.H.S = R.H.S
Let's take R.H.S
= [tex]7^{1/3}\\[/tex]
Taking a cube for this,
[tex]= (7^{1/3} )^{3}[/tex]
We can separate this into three terms.
[tex]= 7^{1/3} . 7^{1/3} . 7^{1/3}[/tex]
We know that [tex]x^{n}. x^{m} = x^{n+m}[/tex]
Then,
[tex]= 7^{1/3 + 1/3 +1/3} \\= 7^{3/3}\\ = 7[/tex]
From L.H.S
We have to take cube root,
[tex](\sqrt[3]{7})^{3} \\= 7[/tex]
Hence, L.H.S = R.H.S, and it is verified.
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Using the formula f (n) = 35 - 5n, starting with n = 1. Find the 5th term in the sequence.
For the given the formula f (n) = 35 - 5n, the 5th term of the sequence is f(5) = 10.
A sequences is an ordered sets of integers (usually called ad "terms"), such as 1, 5, 9. Some sequences follow a specific pattern that can be exploited to indefinitely expand them. For example, 4, 9, 14 follows the pattern "add 5," and we can now proceed with the sequence. Formulas that tell us how to discover any term in a series can be found in sequences.
The formula of the sequence in this case is:
f(n) = 35 - 5n.
Then
n = 1 --> f(1) = 35 - 5(1) = 30
The 5th term means we substitute n = 5 into the formula.
n = 5 --> f(5) = 35 - 5(5) = 35 - 25 = 10
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Use the distributive property to write an expression that is equivalent to 5(- 2x - 3)
Answer: -10x - 15
Step-by-step explanation:
The distributive property is used when you multiply a number over an addition or subtraction problem.
5 x (-2x - 3)
Step 1
Take 5 and multiply it by -2x
5 x -2x = -10x
Step 2
Take 5 and multiply it by - 3
5 x - 3 = -15
Step 3
Put the entire problem together.
5 x (-2x - 3) = -10x - 15
. use implicit function theorem to verify whether the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation
Yes, the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation.
To verify this we can use Implicit Function Theorem. According to the theorem, if a relation f(x,y) = c is given, then if the partial derivative of f(x,y) concerning y is nonzero at the point (x0,y0), there is a unique function y = g(x) such that f(x,g(x)) = c.
In this case, the partial derivative of f(x,y) concerning y is -2 sin(x-y). At the point (x0,y0), this derivative is nonzero, so there exists a unique function y = g(x) such that f(x,g(x)) = c. This implies that the given relation does indeed define an implicit solution of the differential equation.
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An iterative formula is shown below.
Xn+1 = 3/4xn-1
Work out the values of x2, x3 and x4, starting
with x1 = 2.
Give your answers to 2 d.p.
The value for the following order of the given iterative formula of xₙ + 1 = 3/4 xₙ₋₁ are:
x₂ = 0.5x₃ = - 0.63x₄ = - 1.47Iterative formula is used to process a repeating procedure to produce a series of results
We have an iterative formula of:
xₙ + 1 = 3/4 xₙ₋₁
We know that:
x₁ = 2
Hence:
x₂ + 1 = 3/4 x₁
x₂ + 1 = 3/4 (2)
x₂ + 1 = 3/2
x₂ = 1/2 = 0.5
x₃ + 1 = 3/4 x₂
x₃ + 1 = 3/4 (1/2)
x₃ + 1 = 3/8
x₃ = -5/8 = - 0.63
x₄ + 1 = 3/4 x₃
x₄ + 1 = 3/4 (-5/8)
x₄ + 1 = -15/32
x₄ = - 47/32 = -1.47
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Please help !,,,!,!,,!,,,meeee long division step by step
15 POINTS! WILL MARK BRAINLIEST
If f(x) and g(x) are inverse functions, use the information shown to find g(x)
f(2x - 10) = x + 1
f(-10) = 1
f(-12) = 0
f(2x - 12) = x
Answer Choices:
g(x) = -12
g(x) = 2x - 10
g(x) = -10
g(x) = 2x - 12
The function g(x) is defined as follows:
g(x) = 2x - 12.
How to obtain the inverse function?The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:
The fact that the variables are exchanged means that the functions are symmetric over the line y = x.
As the lines are symmetric over the line y = x, these following statements regarding the composition of a function with it's inverse is given as follows:
f(g(x)) = x.g(f(x)) = x.We have that f(2x - 12) = x, hence the function g(x) is defined as follows:
g(x) = 2x - 12.
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A rectangular garden has a walkway around it. The area of the garden is 6(5.5x+2.5). The combined area of the garden and the walkway is 6.5(8x+6). Find the area of the walkway around the garden as the sum of two terms.
The area of the walkway around the garden as the sum of two terms is
19x + 24.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The area of the garden is 6 (5.5x + 2.5).
The combined area of the garden and the walkway is 6.5 (8x + 6).
Now,
The area of the walkway around the garden.
= Combined area - Area of the garden
= 6.5(8x + 6) - 6(5.5x + 2.5)
= 52x + 39 - 33x - 15
= 19x + 24
Thus,
The area of the walkway around the garden is 19x + 24.
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