\(\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}\)
Find max, min, sup and inf
Answers
The maximum value of the sequence is \(1/6\), the minimum value is 0, the supremum is \(1/2\), and the infimum is 1/6.
The given sequence is: \({1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}\)
To find the maximum and minimum values of the sequence, we can start by taking the first few terms and looking for patterns:When \(n = 1,\) the sequence evaluates to: \(1/2 + (-1)^1 / 2 * 2 = 0\)
When \(n = 2,\) the sequence evaluates to: \(1/4 + (-1)^2 / 3 * 2 = 1/6\)
When \(n = 3,\) the sequence evaluates to: \(1/8 + (-1)^3 / 4 * 2 = 7/96\)
When \(n = 4,\) the sequence evaluates to: \(1/16 + (-1)^4 / 5 * 2 = 17/240\)
It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.
Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.
The maximum value occurs at n = 2, where it evaluates to 1/6.
To find the supremum and infimum of the sequence, we can start by considering the upper and lower bounds of each term separately.The term \(1/(2 ^ n)\) has a lower bound of 0 and an upper bound of 1.
The term \(((- 1) ^ n)/(n + 1) / n * N\) has a lower bound of \(-1/4\) and an upper bound of \(1/4\).
Therefore, the supremum of the sequence occurs when \(n = 1\), where the sequence evaluates to \(1/2\).
The infimum of the sequence occurs when \(n = 2\), where the sequence evaluates to \(1/6.\)
In summary, the maximum value of the sequence is \(1/6\), the minimum value is 0, the supremum is \(1/2\), and the infimum is \(1/6.\)
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Related Questions
A bag contains five Snickers bars, nine Milky Way bars, two Crunch bars,
and twelve Twix bars. If Jack randomly selects a candy bar, eats it, then
randomly selects another, find the probability that both candy bars were
Milky Way.
Answers
Answer:
about a 9.5 percent chance of both being a milky way
Step-by-step explanation:
Probability that both candy bars were milky way is \(\frac{2}{21}\)
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur
Given,
Number of snickers bars = 5
Number of Milky way bars =9
Number of crunch bars = 2
Number of Twix bars = 12
Total number of Candy bars = 5+9+2+12 =28
If Jack randomly selects a candy bar, eats it, then randomly selects another
Probability = Number of favorable outcome / Number of total outcome
Probability of taking Milky way bar in first pick = \(\frac{9}{28}\)
So Total number of candy bars and number of Milky way bar are decreased by 1.
Probability of taking Milky way bar in second pick = \(\frac{8}{27}\)
Probability that both candy bars were milky way = \((\frac{9}{28}).(\frac{8}{27})=\frac{2}{21}\)
Hence, Probability that both candy bars were milky way is \(\frac{2}{21}\)
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Translate this phrase into an algebraic jahauahahshshshshshshshshshshhs
Answers
Answer:
Step-by-step explanation:
Jdshdcjecjjwdjwddhwedhwedwedwehwdhw?
i think?
Simplify.
2x-4
²-8+12
O
O
O
-6
x+6
x-6
-
x-2
²-82+12
Answers
The simplified value of (2x - 4)² is 4x² - 16x + 16.
First, let us understand the algebraic identities;
Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.
Some of the identities are:
(a + b)² = a² + 2ab + b²(a - b)² = a² - 2ab + b², etc.We are given (2x - 4)².
Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.
So, a = 2x and b = 4.
Put it into the identity, we will get;
Therefore,
(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16
Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.
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Explain in your own words:
What is a linear function?
Answers
) Find the gradient of a line joining the points 1) (1,-1) and (4,9) 2) (5,1)and(2-2) 2) Find the x and y intercepts for the equation 3y = 2x-2
Answers
The gradient of the line joining the points (1,-1) and (4,9) is 10/3, while the gradient of the line joining (5,1) and (2,-2) is 1. The x-intercept of the equation 3y = 2x - 2 is 1, and the y-intercept is -2/3. These calculations follow the formula for gradient and the methods for finding intercepts in linear equations.
1) To find the gradient of a line joining two points, you can use the formula: gradient = (change in y)/(change in x).
Given the points (1,-1) and (4,9), the change in y is 9 - (-1) = 10 and the change in x is 4 - 1 = 3.
Therefore, the gradient of the line joining these points is 10/3.
2) Similarly, to find the gradient of a line joining two points (5,1) and (2,-2), we can use the same formula. The change in y is -2 - 1 = -3 and the change in x is 2 - 5 = -3.
Therefore, the gradient of the line joining these points is -3/-3 = 1.
3) To find the x-intercept, we set y to 0 and solve for x.
Given the equation 3y = 2x - 2, if we substitute y with 0, we have 3(0) = 2x - 2, which simplifies to 0 = 2x - 2.
To solve for x, we can add 2 to both sides: 0 + 2 = 2x - 2 + 2, which gives us 2 = 2x.
Dividing both sides by 2, we get x = 1.
Therefore, the x-intercept of the equation 3y = 2x - 2 is 1.
To find the y-intercept, we set x to 0 and solve for y.
Using the same equation, if we substitute x with 0, we have 3y = 2(0) - 2, which simplifies to 3y = -2.
To solve for y, we can divide both sides by 3: (3y)/3 = (-2)/3, which gives us y = -2/3.
Therefore, the y-intercept of the equation 3y = 2x - 2 is -2/3.
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A closet in the shape of a rectangular prism is 2 feet deep, 5 feet wide, and 7 feet tall. What is the volume of the closet in cubic feet?
Answers
Answer:
70 cm
Step-by-step explanation:
Answer:
70 cubic feet
Step-by-step explanation:
First step is to multiply the 2 feet deep by th 5 feet wide. which is also written as:
2*5=10
Next multiply 10 by the 7 feet tall. You can write this like:
10*7=70
70 cubic feet is the answer
Multiply 25 by the difference of 34.78 and 12.99.
Answers
1. (x - 2) + (3x + 8)
Answers
Answer:
4x+6
Step-by-step explanation:
(x-2) + (3x + 8)
combine like terms
4x + 6
Hope this helps!!!
Answer:
4x+6
Step-by-step explanation:
Find the vertex of the function y = ∣x−|1/2|∣ + 6.(1/2, 6)(1/2, -6)(-1/2, 6)(-1/2, -6)
Answers
The given function is:
\(y=|x-|\frac{1}{2}||+6\)The vertex is given by the x-number that makes the argument inside the absolute value symbol equal to 0, so:
\(\begin{gathered} x-\frac{1}{2}=0 \\ \\ x=\frac{1}{2} \end{gathered}\)Now, the y-coordinate of the vertex can be found by replacing x=1/2 and solving it as follows:
\(\begin{gathered} y=|\frac{1}{2}-|\frac{1}{2}||+6 \\ \\ y=|0|+6 \\ \\ y=6 \end{gathered}\)The vertex is located at (1/2,6)
She borrows $25.63 from her sister to help pay for the dress. Then Jenny earns $16.33 helping her dad organize his home office. If she gives all the earnings to her sister, Jenny will still owe her sister $
.
Answers
she still owes 9.3$
answer : 9.30$
Step-by-Step-
25.63-16.33=9.30
Jenny still owns $9.30 dollars to her sister.
Hope this helps :)
I need help with this Regression question!
Answers
A quadratic model for the data is y = -0.0076x² + 0.6915x + 14.711.
The fuel economy at 80 mph is 21.39.
How to determine the linear regression equation and correlation coefficient?In this scenario, the speed (x) would be plotted on the x-axis of the scatter plot while the fuel economy (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the speed (x) and fuel economy (y), a quadratic model for the line of best fit is given by:
y = -0.0076x² + 0.6915x + 14.711
When the speed (x) = 80 mph, the fuel economy (y) is given by;
y = -0.0076(80)² + 0.6915(80) + 14.711
y = 21.39
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Open Response A weather forecast calls for a 60% chance of rain today and a 60% chance of rain tomorrow. The table shows the results of 10 simulated trials, where "R" represents rain and "N" represents no rain.
Answers
Therefore , the solution of the given problem of probability comes out to be this equals 0.60, or 60%.
What is probability?Estimating the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as statistical inference. Chance can be represented by any number between 0 and 1, in which 1 usually represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.
Here,
The likelihood of RR is 0.6 x 0.6, which equals 0.36 (or 36%).
Similar to RN, NR, and NN, each of which has a chance of 0.6 * 0.4 = 0.24 (or 24%).
This knowledge allows us to respond to a variety of queries. For instance:
The likelihood of rain today is equal to the product of the probabilities of RR and RN, which is 0.36 + 0.24 (or 60%) in chance.
The likelihood of rain tomorrow is equal to the product of the RR and NR odds, which equals 0.36 + 0.24 = 0.60 (or 60%).
The chance of RR, which is 0.36 (or 36%), is the likelihood that it will rain today and tomorrow.
The chance of RR, RN, or NR, which is 0.36 + 0.24 + 0.24 = 0.84 (or 84%), is the likelihood that it will rain today, tomorrow, or both days.
P(rain tomorrow | no rain today) = P(NR) / [P(NR) + P(NN)] = 0.24 / (0.24 + 0.16); this equals 0.60, or 60%.
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There are 40 students in a class. 4 of them are absent, then find the
percent of present students.
Please help by writing down the steps as well.
Answers
Answer:
90%
Step-by-step explanation:
present students:40-4=36
36/40*100
=90%
Answer:
90% are present
Step-by-step explanation:
40-4=36
36 are present
36/40 = x/100
36x100=3600
3600/40=90
answer: 90/100 = 90%
Loans Bill took out two loans that totaled $15,000. One
of the loans charges 12% per year, and the other charges
10% per year. If the total interest charged in the first year
is $1,600, how much was each loan?
Answers
Let, money in loan with 12% interest is x.
So, money in loan with 10% interest is 15000-x.
Now , sum of interest :
\(\dfrac{12x}{100}+\dfrac{10(15000-x)}{100}=1600\\\\12x+150000-10x=160000\\\\2x=10000\\\\x=5000\)
Therefore, money on 12% interest is $5000 and 10% interest is $10000.
Hence, this is the required solution.
What is the solution set for the following inequality?
5(2x – 1) ≥ 3x + 7 + x
Answers
Step-by-step explanation:
-52x + 3 = 7
-52x + 3 = 7
-3 -3
-52x = 4
/52 /52
-x = 1/13
/-1 /-1
x = -1/13
Hopefully this helps you! :)
A quiz had 20 questions. Andre scored 16 of them correctly. What was
Andre's percent score? *
Answers
Answer:
80%
Step-by-step explanation:
16 divided by 20
Two sisters start in the same place and walk in opposite directions. The
older sister walks to the right 4 yards and the younger sister walks
6 yards to the left. How far and in what direction does their dog need to run to go from the younger to the older sisters?
Answers
Answer:
10 yards
Step-by-step explanation:
6+4=10
Answer:
10 yards hope this helps
Help asap!!! (DIFFERENT THAN ALL THE OTHERS!!!) brainliest if correct
Each soccer player has one yellow, one blue, and one white jersey. For the last game of the season, each player could choose which jersey they wanted to wear. The table below shows the percentage of players that wore each color jersey.
Jersey Color Percentage of Players
Yellow 0.45
Blue 0.25
White 0.30
Compare the probabilities of a randomly selected player wearing a certain jersey color and interpret the likelihood. Choose the statement that is true.
The player will be more likely to wear a blue jersey than a yellow jersey because P(Blue) > P(Yellow).
The player will be more likely to wear a white jersey than a yellow jersey because P(White) > P(Yellow).
The player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue).
The player will be equally likely to wear a yellow jersey or a white jersey because P(Yellow) = P(White).
Answers
Answer:
The player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue).
Which of the following can divide into 756 with no remainder?
Select all that are correct. (Chapter 4)
Select
4
2
9
25
5
8
10
3
6
Answers
Answer:
4, 2, 9, 3, 6
Step-by-step explanation:
756/4= 189
756/2= 378
756/9= 84
756/25= 30.24
756/5= 151.2
756/8= 94.5
756/10= 75.6
756/3= 252
756/6= 126
Find the value of x for the following
Answers
Answer:
x = 13
Step-by-step explanation:
2(x + 18) and (3x + 79) are a linear pair and sum to 180° , that is
2(x + 18) + 3x + 79 = 180
2x + 36 + 3x + 79 = 180
5x + 115 = 180 ( subtract 115 from both sides )
5x = 65 ( divide both sides by 5 )
x = 13
Answer:
x = 13
Step-by-step explanation:
Given angles are,
→ 3x + 79°
→ 2(x + 18)° = 2x + 36°
Now we have to,
→ Find the required value of x.
We know that,
→ Sum of all angles in a line is 180°.
Forming the equation,
→ (3x + 79°) + (2x + 36°) = 180°
Then the value of x will be,
→ (3x + 79°) + (2x + 36°) = 180°
→ 3x + 79° + 2x + 36° = 180°
→ (3x + 2x) + (79 + 36)° = 180°
→ 5x + 115° = 180°
→ 5x = 180° - 115°
→ 5x = 65
→ x = 65/5
→ [ x = 13 ]
Hence, the value of x is 13.
Which choice is the correct graph of Ix <3?
A +
-6
B++
-6
C
-6
DH
-4
-5
-5
-6 -5
F++
-6
EH
-6
-4
-3
-4
-3
-3
3
-4
-5
-2
-2 -1
OA. Graph A
OB. Graph B
C. Graph C
-3 -2 -1
-2 -1
-20
-2
-3
0
0 1
0
0
-1 0
1
1
1
1
2
2
2
2
2
2
3
3
e
4
3 4
4 5
01
3
4
3
3 4
5
5
5
5
6
6
6
6
6
5
4
6
Answers
Answer:
2347 elevated in the cube
Step-by-step explanation:
nashe
Can somebody walk me through this please!
Answers
Answer:
x = 5, y = -6, z = -2
Step-by-step explanation:
Given the following systems of linear equations:
Equation 1: x = y + 11
Equation 2: x + 2y - 4z = 1
Equation 3: 2x = 10
In order to use the substitution method, choose one of the given equation where the variable has a coefficient of 1. We could use Equation 1 and substitute its value into Equation 3:
Step 1:Use Equation 1: x = y + 11 substitute into Equation 3 to solve for y:
2x = 10
2(y + 11) = 10
Distribute 2 into the parenthesis:
2y + 22 = 10
2y + 22 - 22 = 10 - 22
2y = -12
\(\frac{2y}{2} = \frac{-12}{2}\)
y = -6
Step 2:Substitute the value of y = -6 into Equation 1:
x = y + 11
x = -6 + 11
x = 5
Step 3:Substitute the values of x = 5 and y = -6 into Equation 2 to solve for z:
x + 2y - 4z = 1
5 + 2(-6) - 4z = 1
5 - 12 - 4z = 1
-7 - 4z = 1
Add 7 to both sides:
-7 + 7 - 4z = 1 + 7
-4z = 8
Divide both sides by -4 to solve for z:
\(\frac{-4z}{-4} = \frac{8}{-4}\)
z = -2
Verify whether the values for x, y, and z satisfy the three equations in the given linear system:
x = 5, y = -6, z = -2
Equation 1: x = y + 11
5 = -6 + 11
5 = 5 (True statement)
Equation 2: x + 2y - 4z = 1
5 + 2(-6) - 4(-2) = 1
5 - 12 + 8 = 1
13 - 12 = 1
1 = 1 (True statement)
Equation 3: 2x = 10
2(5) = 10
10 = 10 (True statement).
Therefore, x = 5, y = -6, z = -2 satisfy all the equations within the given system.
Please find missing side length!
Answers
Answer:
\(4\sqrt{3}\)
Step-by-step explanation:
64 - 16 = 48
49 = 16 x 3
ur finding side length a
a = c^2 - b^2
a = 8^2 - 4^2
a = 64 - 16
a = 48
48 squared is 6.93
rounded is 7
A rectangle has an area of 99 square in. What is the length of the long side?
Answers
Answer:
The longer length is either 99, 33 or 11 inches
Step-by-step explanation:
Given
\(Area = 99\)
Required
The length of the longer side
Area of a rectangle is:
\(Area = Length * Width\)
List out all possible products that give 99 [Assume the dimension are whole numbers]
\(Length * Width = 99 * 1 = 99\)
\(Length * Width = 33 * 3 = 99\)
\(Length * Width = 11 * 9 = 99\)
List out the longer factors
\(L = \{99, 33, 11\}\)
Hence, the longer length is either 99, 33 or 11 inches
What is the simplified form of the following expression
Answers
An angle bisector of a triangle divides the opposite side of the triangle into segments 8 cm and 2 cm long. A second side of the triangle is 4.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter.
Answers
Bisector angle
Then apply relation
8/2 = L3 / L2
L2 = 4.9
then
8/2= 4 = L3/ 4.9
So, L3 = 4•4.9 = 19.6 cm
Also
8/2= 4= 4.9/L2
So ,L2= 4.9/4 = 1.2 cm
Then, answer is OPTION D) 19.6 cm, 1.2 cm
p-chart is to be constructed to monitor the fraction non-conforming for a process. 20 samples of 100 items were collected when the process was known to be in control. There were 100 total nonconforming items identified. a. (10 pts) Construct a p-chart from this data (use L-3)
Answers
p chart from this data are attached below.
Describe about p chart?
A p-chart is an attributes control chart that is used with data collected in varying size subgroups. Because the size of the subgroup varies, it displays a proportion of nonconforming items rather than the actual count. P-charts depict how the process evolves over time.P bar = total detective / total sampled
P bar = \(\frac{20}{100}\)
= \(\frac{1}{5}\)
UCL = P bar + L . \(\sqrt{\frac{p bar q bar}{n} }\)
= \(\frac{1}{5}\) + 3 * \(\sqrt{\frac{1}{5} *\frac{4}{5} * \frac{1}{100} }\)
= (\(\frac{1}{5} + \frac{3 * 2}{50}\))
= (0.20 + 0.12)
UCL = 0.32
CL = P bar = 0.20
LCL = P bar - L . \(\sqrt{\frac{p bar q bar}{n} }\)
= (\(\frac{1}{5} - \frac{3 * 2}{50}\))
= (0.20 - 0.12)
LCL = 0.08
Therefore, UCL = 0.32, CL = 0.20, LCL = 0.08
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What is the value of x? 63, 42, 50
Answers
Answer:
Step-by-step explanation:
Which function is increasing and has a domain of (1, ∞)?
Answers
The functiοn is increasing and has a dοmain οf (1, ∞) is οptiοn D f(x) = lοg (x - 1) + 1.
What is ratiοnal functiοn?Every equatiοn with οne οr mοre ratiοnal expressiοns is said tο be ratiοnal. A fractiοn whοse numeratοr and denοminatοr are pοlynοmials is knοwn as a ratiοnal expressiοn. A ratiο οf twο pοlynοmials is, in οther wοrds, a ratiοnal expressiοn.
The LCD (Least Cοmmοn Denοminatοr) οf the fractiοns, eliminatiοn οf the denοminatοrs, and simplificatiοn οf the resultant equatiοn are methοds fοr sοlving ratiοnal equatiοns. Sοlving the resultant equatiοn—which can require factοring, simplificatiοn, οr the use οf οther algebraic strategies—will prοvide the answers tο a ratiοnal equatiοn.
Fοr the given functiοn:
Optiοn A:
f(x) = -lοg(x - 1) + 2
Here, lοg is negative, hence fοr increasing value οf x f(x) will decrease.
Optiοn B:
f(x) = -lοg(x - 2) + 1
Here, lοg is negative, hence fοr increasing value οf x f(x) will decrease.
Optiοn C:
f(x) = lοg(x - 2) + 1
Here, (x - 2) > =
x > 2
The dοmain dοes nοt satisfy.
Optiοn D:
f(x) = lοg (x - 1) + 1
Here, (x - 1) > 0
x > 1 tο infinity.
Hence, the functiοn is increasing and has a dοmain οf (1, ∞) is οptiοn D f(x) = lοg (x - 1) + 1.
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The complete function is:
select all the ways you can describe the given polygon
Answers
Answer:
Isoceles and obtuse
Step-by-step explanation: