Given N1 = 6 and Nn+1 = 6(Nn - 4) ). Find N3.
Answers
Answer:
48
Step-by-step explanation:
N₁ = 6
N(n+1) = 6*(Nn -4 )
N₍₁₊₁₎= 6* (N₁ - 4)
N₂ = 6 *(6-4) = 6*2
N₂ = 12
N₍₂₊₁₎ = 6*(N₂ - 4)
N₃ = 6*(12 -4) = 6* 8
N₃ = 48
Related Questions
5.6.8 let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e). show that this need not be true if f is continuous but not uniformly continuous.
Proof. (1): To prove {f(xn)} is a Cauchy sequence just need to prove ∀ > 0, ∃N, s.t.,∀n, m > N,
have |f(xn) − f(xm)| < . Since f is uniformly continuous on set E, thus ∀ > 0, ∃δ > 0, s.t.,
∀x, y ∈ E, if |x − y| < δ,then |f(x) − f(y)| < .as {xn} is a Cauchy sequence, then ∃N, s.t.,
∀n, m > N, |xn − xm| < δ, thus |f(xn) − f(xm)| < which proves {f(xn)} is a Cauchy sequence.
(2): for example f(x) = 1
x
, x ∈ (0, 2) which is continuous but not uniformly continuous. {
1
n
} is
a Cauchy sequence, however, {f(xn)} does not converge which proves that it is not a Cauchy
sequence.
Answers
Showing that this need not be true if f is continuous but not uniformly continuous.
Given :
let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).
( 1 )
If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,
then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,
then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.
( 2 )
Let E = {1, 1/2, 1/3, · · } and f(1/n) = 1 is n is odd, f(1/n) = −1 if
n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the
sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.
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Help me and u get 20 points
Answers
Answer: 2 or letter A
Step-by-step explanation:
She is baking 3 cakes and since each cake equals 2/3 You only have to add the 3 2/3's in the problem to get your answer so
2/3 + 2/3 + 2/3 =2
Hope this helps!
Answer:
this is because 2 over 3 times 3is going to give as 2 over 1 and 2 over 1 is approximately 2
Greg bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $300 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 7% per year. The total finance charges for one year were $365. How much did each computer cost before finance charges?Desktop: $Laptop: $
Answers
Greg bought a desktop computer and a laptop computer.
Before finance charges, the laptop cost $300 more than the desktop.
Let Desktop cost be x
Then Laptop cost be x + 300
He paid for the computers using two different financing plans.
For the desktop the interest rate was 9% per year, and for the laptop it was 7% per year.
Interest on desktop = 0.09x
Interest on laptop = 0.07 (x+300)
The total finance charges for one year were $365:
\(\begin{gathered} \text{Interest}+\text{Interest = }Interest \\ 0.09x+0.07(x+300)=365 \\ 0.09x+0.07x+21=365 \\ \text{collect like terms} \\ 0.16x=365-21 \\ 0.16x=344 \\ x=2150 \end{gathered}\)Therefore the cost of the desktop = $2150
and the cost of the laptop = $2150+300 = $2450
Work out the area of this circle.
Give your answer in terms of r and state its units.
TT
6 mm
Answers
=Pi6 to the power of 2
Answer is 113.0 (rounded to the 1 decimal place)
Find the product of the binomial (4x+3) with the trionomial (2x square -5x -3)
Answers
Answer:
The product of given binomial and trinomial is:
\(8x^3-34x^2-27x-9\)
Step-by-step explanation:
A binomial is a polynomial with 2 terms and trinomial is a term with 3 terms.
Given
\((4x+3)\\and\\(2x^2-5x-3)\)
Distributive property can be used to find the result.
Writing mathematically
\((4x+3)(2x^2-5x-3)\\= 4x(2x^2-5x-3)+3(2x^2-5x-3)\\= 8x^3-40x^2-12x+6x^2-15x-9\)
Combining alike terms
\(= 8x^3-40x^2+6x^2-12x-15x-9\\= 8x^2-34x^2-27x-9\)
Hence,
The product of given binomial and trinomial is:
\(8x^3-34x^2-27x-9\)
In which number does the digit 7 represent 10 times the value of the digit 7 in the number 4,275
Answers
So, 7,000 is the number in which the value of the digit 7 is 10 times that of the digit 7 in the number 4,275.
What is significant figures ?
The relevant digits in a number that show the precision or accuracy of a measurement or calculation are known as significant figures, sometimes known as significant digits. The following guidelines can be used to determine a number's number of significant figures: Each significant digit that is not zero.
The number 123.45, for instance, includes five significant digits. Zeros in between digits that are not zero are important. Zeros at the start of a number have no real meaning. The number 0.0023, for instance, has two significant figures.
To solve this problem, we need to identify the value of the digit 7 in the number 4,275 and then discover the number in which the digit 7 represents 10 times this value.
The digit 7 is in the hundreds place in the number 4,275, hence its value is 7 x 100 = 700.
As a digit in the ones place only has its face value, we must discover a number that contains the digit 7 in the thousands, hundreds, or tens places in order to determine the number in which the digit 7 represents 10 times this value.
Consider the number 7,000. The digit 7 is one position to the left of the digit 7 in 4,275, in the thousands place.
When we multiply 7 in 4,275 by 10, we get 10 x 700, which is 7,000. Hence, the value of the digit 7 in the number 7,000 is 10 times more than that of the digit 7 in the number 4,275.
So, 7,000 is the number in which the value of the digit 7 is 10 times that of the digit 7 in the number 4,275.
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In which number does the digit 7 represent 10 times the value of the digit 7 in the number 4,275?
1 year insurance policy covering its equipment was purchased for 6,144. The date purchased was June 14 but it doesn't go into effect until June 16th, How much is paid for that
month?
Year?
Answers
1 year insurance policy covering its equipment was purchased for 6,144. The date purchased was June 14 but it doesn't go into effect until June 16th, the amount paid for the month of June is approximately $252.75, and the amount paid for the entire year is approximately $6,144.
To calculate the amount paid for the month and the year, we need to consider the number of days covered by the insurance policy. Let's break it down step by step:
Step 1: Determine the number of days covered in June.
Since the policy doesn't go into effect until June 16th, there are 15 days remaining in June that will be covered by the insurance policy.
Step 2: Calculate the daily rate.
To find the daily rate, we divide the total cost of the insurance policy by the number of days in a year:
Daily rate = 6,144 / 365
Step 3: Calculate the amount paid for June.
The amount paid for June can be found by multiplying the daily rate by the number of days covered:
Amount paid for June = Daily rate * Number of days covered in June
Step 4: Calculate the amount paid for the year.
To calculate the amount paid for the year, we simply multiply the daily rate by 365 (the total number of days in a year):
Amount paid for the year = Daily rate * 365
Now let's perform the calculations:
Step 2: Daily rate
Daily rate = 6,144 / 365 ≈ 16.85 (rounded to two decimal places)
Step 3: Amount paid for June
Amount paid for June = 16.85 * 15 ≈ 252.75 (rounded to two decimal places)
Step 4: Amount paid for the year
Amount paid for the year = 16.85 * 365 ≈ 6,144 (rounded to two decimal places)
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if the numbers 8 and 12 are increased by 25%and 33 1/3 % respectively,what will be the average increament
Answers
The average increment is 3.
To find the average increment, we need to calculate the total increment and divide it by the number of values.
Let's calculate the increments for 8 and 12:
For 8 increased by 25%:
Increment = 8 * 0.25 = 2
For 12 increased by 33 1/3%:
Increment = 12 * (1/3) = 4
Now, let's find the average increment:
Total increment = Increment for 8 + Increment for 12 = 2 + 4 = 6
Number of values = 2
Average increment = Total increment / Number of values
= 6 / 2
= 3
Therefore, the average increment is 3.
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simplify 3(5a+b)+4(a+2b)
Answers
Answer:
19a + 11b
Step-by-step explanation:
first (3 • (5a + b)) + 4 • (a + 2b) then you do this 3 • (5a + b) + 4 • (a + 2b) then you get this answer 19a + 11b.
Which functions are linear?
y=4/x
y=-4x + 1
y= 5(x – 0.6)
Answers
Answer:
y=-4x + 1
y= 5(x – 0.6)
Step-by-step explanation:
y = -4x + 1 follows the linear equation of y = mx + b.
y = 5(x - 0.6) can be simplified into y = mx + b by distribution,
y = 5x - 3 which follows the linear equation of y = mx + b.
Kylie just accepted a job at a new company where she will make an annual salary of $43000. Kylie was told that for each year she stays with the company, she will be given a salary raise of $5000. How much would Kylie make as a salary after 6 years working for the company? What would be her salary after tt years?
Answers
Answer:5600
Step-by-step explanation:
Because I just did it
What is the next term in the pattern? 1,1,5,17,71,247
Answers
Answer: 1085
Step-by-step explanation:
Which equation choice could represent the graph show below?
Answers
Answer:
A
Step-by-step explanation:
Hopefully this helps
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with grams of a radioactive isotope, how much will be left after 4 half-lives?
Answers
After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:
Amount remaining = Initial amount × (1/2)^(number of half-lives)
In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.
So, the equation becomes:
Amount remaining = Initial amount × (1/2)^4
Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.
Simplifying the equation:
Amount remaining = Initial amount × (1/16)
Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
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Write and solve an equation to find the value of x.
Answers
The value of x for each item is given as follows:
28. x = 5.
29. x = 3.44.
How to obtain the value of x in each item?For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:
16x = 10 x 8
16x = 80
x = 5.
For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:
10(x + 10) = 12(12 + 25)
10x + 100 = 444
10x = 344
x = 3.44.
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is the function f even odd or neither
Answers
Answer:
I think the answer will be odd
Step-by-step explanation:
Consider a fair coin, such that the probability of observing a head or a tail in a random toss is 0.5. Consider an experiment in which the coin is tossed twice and the two outcomes (O1 and O2) are recorded. Obviously, the probability of observing one head and one tails is 0.5 and the probability of observing both heads or both tails is 0.25 each. Consider the following two probabilities: Given the knowledge that there is at least 1 tails, the probability that there is one head observed is pa. If O1 is heads, the probability that O2 is tails is pb Which of the following statements are true: a) pa is 1/2 and pb is 1/2 b) pa is 1/3 and pb is 2/3 c) pa and pb are not equal d) pa is 2/3 and pb is 1/3
Answers
Applying probability concepts, it is found that the correct statements are:
c) pa and pb are not equal d) pa is 2/3 and pb is 1/3-------------------------------------------
A probability is the number of desired outcomes divided by the number of total outcomes.The sample space, that is, the possible outcomes for the coin tosses is given next, considering H for heads and T for tails.
H - H
H - T
T - H
T - T
-------------------------------------------
Considering that there is at least 1 tails, the new sample space is:H - T
T - H
T - T
pa: probability of one head, two outcomes with 1 head out of three, thus, pa = 2/3.pb: probability that the second is tails, so one outcome(T - T) out of three, thus pb = 1/3.-------------------------------------------
The correct statements are:
c) pa and pb are not equal d) pa is 2/3 and pb is 1/3A similar problem is given at https://brainly.com/question/14798120
A student received a standardized score of -.63 on a class assignment. Which statement best describes the student’s score in relation to the rest of the class?
Answers
In a normal distribution, approximately 50% of the scores fall below the mean and 50% fall above the mean. Since the student's score is below the mean, we can say that the student scored lower than the average student in the class.
However, we cannot make any conclusions about how the student's score compares to the rest of the class without knowing more information about the distribution of scores. If the distribution is approximately normal, we can say that the student scored lower than approximately 73% of the class (since .63 standard deviations below the mean corresponds to approximately the 26th percentile of a normal distribution).
Therefore, the best statement we can make about the student's score in relation to the rest of the class is that the student scored lower than the average student in the class and lower than approximately 73% of the class if the distribution is approximately normal.
If you put all of the bean sprouts together end to end what
would be the total length of all the objects?
inches
Answers
Answer:
5.625 = 45/8 = 5 5/8
Step-by-step explanation:
A
-pound bag of Kitty Kibbles is
. An
-pound bag of Feline Flavor is
. Which statement about the unit prices is true?
Feline Flavor has a higher unit price of
/pound.
Kitty Kibbles has a higher unit price of
/pound.
Kitty Kibbles has a higher unit price of
/pound.
Feline Flavor has a higher unit price of
/pound.
Answers
The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.
The correct answer choice is option D.
How to solve unit prices?Cost of 16-pound bag of Kitty Kibbles = $20.80
Unit price of kitty kibbles = Price / number of pounds
= $20.80 / 16
= $1.30 per pound.
Cost of 8-pound bag of Feline flavor = $11.20
Unit price of feline flavor = Price / number of pounds
= $11.20 / 8
= $1.40 per pound
Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.
Complete question:
A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?
A. Feline Flavor has a lower unit price of $1.40/pound.
B. Feline Flavor has a lower unit price of $1.30/pound.
C. Kitty Kibbles has a lower unit price of $1.40/pound.
D. Kitty Kibbles has a lower unit price of $1.30/pound.
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Which expression is equivalent to 1/5×15: 5÷15, 1÷5, 15÷5, 15÷1
Answers
Answer:
the question is not valid with "obj."
Can someone pls tell me how to do this?
Simplify (5y)³
Answers
Answer: 125y³
To rise a product to a power, rise each factor to that power:
(5y)³ = 5³y³ = 125y³
Find a 3rd degree polynomial function with real coefficients satisfying the given condition. 2 and -3 +3i are zeros; leading coefficients is 1
Answers
A 3rd degree polynomial function with real coefficients satisfying the given condition. 2 and -3 +3i are zeros; leading coefficients is 1, is:
f(x) = x³ + 4x² + 6x - 36
What is polynomial function?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.
we have to find third degree polynomial, so, n = 3
Since 2 is its zero ,so, x - 2 is its factor
As complex zeros occur in conjugate pairs .
So,other factors are (x + (3 + 3i)) and (x + (3 - 3i)) ,
Firstly, we find the product of these two factors:
= x² + 6x + 9 - 9i²
= x² +6x +9 - 9(-1)
= (x² +6x + 18)
Now multiply (x² +6x + 18) with (x - 2) we get f(x):
= (x² +6x + 18) (x - 2)
= x³ - 2x² + 6x² - 12x + 18x - 36
= x³ + 4x² + 6x - 36
Correct option: b
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Which pair of expressions represents inverse functions?
4x-3x/4x-2 and x+2/x-2
4x+2/x-3 and 5x+3/4x-2
2x+5 and 2+5x
x+3/4x-2 and 2x+3/4x-1
Answers
Answer:2 hope this helps it was right on my test
Step-by-step explanation: it was right on the test i took
A cube with side length mmm has a volume of 343343343 cubic centimeters. The following equation shows the volume of the cube.
m^3 = 343m
3
=343m, cubed, equals, 343
What is the side length of the cube in centimeters?
Answers
Answer:7cm
Step-by-step explanation:
m^3=343
Take the cube root of both sides
m=7
A container has the shape of an open right circular cone, as shown in the figure above. The container has a radius of 4 feet at the top, and its height is 12 feet. If water flows into the container at a constant rate of 6 cubic feet per minute, how fast is the water level rising when the height of the water is 5 feet?
Answers
If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min
How to find the rate of change?When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.
We are given the dimensions of the tank as;
Radius; r = 4 feet
Height; h = 12 feet.
The water in the tank will also have a conical shape.
By similar triangles, we know that;
r/h = 4/12
r = h/3
Now the volume of the water is;
V = ¹/₃πr²h
Put h/3 for r in this volume equation to get;
V = ¹/₃π(h/3)²h
V = (1/27)πh³
Differentiating with respect to time gives;
dV/dt = (3/27)πh²(dh/dt)
We are given;
dV/dt = 6 cubic feet per minute
h = 5
Thus;
6 = (3/27)π(5²)(dh/dt)
dh/dt = 0.688 ft/min
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What is the slope of the line
Answers
Answer:
3/4
Step-by-step explanation:
There is a dice game at the casino that costs $3 to play. A player rolls two dice. If the player gets a sum of 2 or 12 he or she gets back $ 28 (wins $25). the person gets a 7he or she gets back $5 (wins $2). If the player rolls anything other than a 2, 12 or 7 he or she gets nothing back (loses $3). Find the expected value for the player?
Answers
Answer:
The expected value for the player is -$0.63.
Step-by-step explanation:
The dice game has the following rules:
The game costs $3 to play. A player rolls two dice. If the player gets a sum of 2 or 12 he or she gets back $ 28 (wins $25). If the person gets a 7 he or she gets back $5 (wins $2). If the player rolls anything other than a 2, 12 or 7 he or she gets nothing back (loses $3).The outcomes for a sum of 2 or 12 are: {(1, 1) and (6, 6)}
The probability of a sum of 2 or 12 is: 2/36 = 0.055.
The outcomes for a sum of 7 is: {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)}
The probability of a sum of 7 is: 6/36 = 0.167.
The probability of a sum other than 2, 12 or 7 is: 1 - 8/36 = 0.778
The probability distribution is:
Result X P (X)
Sum 2 or 12 $25 0.055
Sum 7 $2 0.167
Others -$3 0.778
Total 1.000
Compute the expected value as follows:
\(E(X)=\sum x\cdot P(x)\\\\\)
\(=(25\times 0.055)+(2\times 0.167)+(-3\times 0.778)\\\\=1.375+0.334-2.334\\\\=-0.625\\\\\approx -0.63\)
Thus, the expected value for the player is -$0.63.
Volume of a trapezoidal prism
Answers
Answer:
109.59m^3
Step-by-step explanation:
Hope you would understand from the attachment; attachment is a bit blurred at the moment so can't attach it at the moment...not much lightning at my end.
Volume is that of the suppose big pyramid - the suppose small pyramid.
The angle is 45degrees from my calculation.
Volume of big pyramid = (256√2 )/3
Volume of small pyramid= (32√2)/3
256√2 )/3-(32√2)/3= (224√2)/3
The volume of the given trapezoidal prism is 84 m³
What is a trapezoidal prism?A trapezoidal prism is a three-dimensional solid consisting of two identical trapezoidal faces joined together by four rectangular faces.
Given is a trapezoidal prism, we need to find its volume,
So, the volume will be given by = area of the trapezoid x length
= (8+4)x3.5 / 2 x 4
= 84
Hence the volume of the given trapezoidal prism is 84 m³
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How to solve adjacent angles?
Answers
Answer:
D
Step-by-step explanation:
1 + 4x and 57° are corresponding angles and are congruent , so
1 + 4x = 57 ( subtract 1 from both sides )
4x = 56 ( divide both sides by 4 )
x = 14