Answer:
The LCM of two numbers is the least common multiple. You want to find the least possible number that is divisible by the two numbers. So, you can list the factors of the two numbers. If there are factors that are repeated, put the repeated factors to the side. With the remaining factors, multiply the factors by each other and the repeated factors.
For example, let's try to find the least common multiple between 10 and 15.
Factors of 10: 2 * 5
Factors of 15: 3 * 5
The repeated factor is 5.
2 and 3 are left over. 2 * 3 = 6. 6 * 5 = 30. So, that is the least common multiple.
The GCF of two numbers is the greatest common factor. You want to find the greatest factor that is included in both numbers. So, again, you can list the factors of the two numbers and find the greatest factor that is repeated between the two numbers.
For example, let's try to find the greatest common factor between 30 and 45.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
Between the two numbers, shared factors are 1, 3, 5, and 15. So, the greatest common factor is 15.
Hope this helps!
Among cases of heart pacemaker malfunctions, were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in different pacemakers randomly selected from this batch of and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Complete question is;
Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Answer:
P(All three are not caused by firmware) = 83.84%
Probability that the entire batch will be accepted = 0.8384
Step-by-step explanation:
We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.
Thus,
Cases not caused by firmware = 8834 - 504 = 8330
So, probability of the first case not being affected by firmware is;
P(first case not caused by firmware) = 8330/8834
Also,
Probability of second case not being affected by firmware is given as;
P(second case not caused by firmware|first case not affected by firmware) = 8329/8833
Similarly,
Probability of third case not being affected by firmware is given as;
P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832
Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.
Thus, we will make use of the general multiplication rule which is;
P(A & B) = P(B) × P(A|B)
Thus;
P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)
Plugging in the relevant values, we have;
P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)
P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%
The value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2, find the value of y when x = 3 and z = 336. I will rate you brainliest
Answer:
18
Step-by-step explanation:
Given that:
y∞ xz
y=kxz. Where k is constant
When z=196 and x= 2 then y= 7
7=(196)(2)k
7=392k
k=1/56
There fore y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
if value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2 then the value of y when x = 3 and z = 336 is 18.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Value of y varies jointly with x and z.
y ∞ xz
y=kxz.
Where k is constant
When z=196 and x= 2 then y= 7
Let us find the value of k
7=(196)(2)k
7=392k
Divide both sides by 7
k=1/56
y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
Hence, the value of y when x = 3 and z = 336 is 18.
To learn more on Ratios click:
https://brainly.com/question/13419413
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Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
Kristin is building a pattern using triangles. The table shows the number of triangles in the first 4 terms of the pattern.
Term Number (7)
1 2 3 4
Number of Triangles (t) 1 3 5 7
Which formula describes the number of triangles in the nth term of the pattern?
O A n=1+2
O B. n=1+3
Oc. n = 21-1
OD n = 2t + 3
Answer:
[tex]\bold{n =2t-1}[/tex]
Step-by-step explanation:
Given table is:
[tex]\begin{center}\begin{tabular}{ c c}Term Number (t) & Number of triangles (n) \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\\end{tabular}\end{center}[/tex]
i.e. when term number, t = 1, number of triangles (n) = 1
when term number, t = 2, number of triangles (n) = 3
when term number, t = 3, number of triangles (n) = 5
when term number, t = 4, number of triangles (n) = 7
If we closely look at the pattern, number of triangles (n) in each row are 1 lesser than twice of term number (t).
i.e. for [tex]t=1, n = 2\times 1 -1=1[/tex]
[tex]t=2, n = 2\times 2 -1=3[/tex]
[tex]t=3, n = 2\times 3 -1=5[/tex]
[tex]t=4, n = 2\times 4 -1=7[/tex]
Therefore, the number of triangles in the nth term will be given as:
[tex]\bold{n =2t-1}[/tex]
Answer:
an = 2t -1
Step-by-step explanation:
We are adding 2 each time
1+2 =3
3+2 = 5
5+2 = 7
an is the nth term in the sequence and t is the number of triangle
an =1+ 2(t-1)
Distribute
an = 1 +2t -2
an = 2t -1
Lila is camping with her family. She wants to hike to the lake, go fishing, and hike back before 6:05 P.M. It will take 1 hour and 10 minutes to hike to the lake and 1 hour and 50 minutes to hike back. Lila wants to fish for 3 hours and 10 minutes. What is the latest time Lila can start the hike to the lake?
Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 p.m (6: 04 p.m.)
Explanation:
To solve this question, the first step is to calculate how much time does hiking to the lake, go fishing, and go back takes in total. This can be calculated by adding the time of the three activities. This means 1 hour 10 minutes + 3 hours 10 minutes + 1 hour 50 minutes which is equal to 6 hours 10 minutes. The detailed process is shown below.
Add the hours: 1 + 3 + 1 = 5
Add the minutes: 10+50 +10 = 70
Also, because the total of minutes is above 60 (each hour has 60 minutes) it is necessary to subtract 60 minutes and add 1 hour.
5 hours + 1 hour and 70 minutes - 60 minutes = 6 hours and 10 minutes
Now, to solve the question subtract the time of the activities to the time Lila needs to complete all the activities.
6: 05 p.m. - 6 hours and 10 minutes = 11: 55 a.m
You can get this result by substracting first the hours and then the minutes
6: 05 p.m. - 6 hours = 12: 05 p.m.
12: 05 - 10 minutes = 11: 55 a.m.
According to this, Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 a.m because if she starts at 11: 54 a.m. she will be back at 6:04, which is a minute before 6:05 p.m.
A point (x,y) is a distance of 6 units from the x-axis. It is a distance of 5 units from the point (8,3). It is a distance [tex]\sqrt{n}[/tex] from the origin. Given that x<8, what is n?
Answer: n = 52
Step-by-step explanation:
when we have two vectors (x,y) and (a,b) the distance between the vectors is:
D = √( (x - a)^2 + (y - b)^2)
now, we know that:
1) the distance between (x, y ) and the x-axis is 6 units.
The nearest point to (x, y) in the x-axis is the point (x, 0) so we have:
D = 6 = √( (x - x)^2 + (y - 0)^2) = √y^2
so y can be 6 or -6.
So we know that y = 6, and now we can write our point as (x, +-6)
2) The distance between our point and (8, 3) is 5 units:
D = √( (x - 8)^2 + (y - 3)^2) = 5.
And we know that the distance from the origin, (n, n) is:
D = √n = √(x^2 + y^2}
n = x^2 + y^2
Now, we should start with:
√( (x - 8)^2 + (y - 3)^2) = 5
first suppose that y = -6, then:
√( (x - 8)^2 + (-6 - 3)^2) = √( (x - 8)^2 + (-9)^2) = 5.
√( (x - 8)^2 + 81) = 5.
Then we must have that:
and we know that √25 = 5
so (x-8)^2 + 81 = 25
this can never happen, so we can discard y = -6
Now the second case, if y = 6,
√( (x - 8)^2 + (6 - 3)^2) = 5.
√( (x - 8)^2 + (3)^2) = 5.
√( (x - 8)^2 + 9) = 5.
here:
(x - 8)^2 + 9 = 25
(x - 8)^2 = 16
(x - 8) = √16 = +-4
So again we have two cases:
if x - 8 = 4, then:
x = 4 + 8 = 12
but we must have x < 8, so this can be discarded.
now, if x - 8 = -4 then:
x = -4 + 8 = 4, this is an acceptable answer, then our point is (4, 6)
And we have:
n = 4^2 + 6^2 = 16 + 36 = 52
(-2×3)+(3×2) how do we solve it
Answer:
0
Step-by-step explanation:
- 2×3= - 6
2×3=6
-6+6=0
Answer:
0
Step-by-step explanation:
first
(-2x3)+(3x2)
-6+6=0
What does the tape measure say Measurement # 2 is?
Answer:
Measure number 2 of the tape is for the pinus
Step-by-step explanation:
To measure, kindly place pinus next to ruler and pinus will be in line with measurement #2
Call and ask for pinus step by step
Answer:
7 and one sixteenths of an inch.
around 2.232 to the nearest hundredth
[tex]2.232\approx2.32[/tex]
Tessa’s employee benefits include family health care coverage. She contributes 18% of the cost. Tessa gets paid biweekly and $108.00 is taken out of each paycheck for family health care coverage. How much does her employer contribute annually for the family coverage? Clearly show your work.
The answer is $12792
Explanation:
It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:
1. Write the values you know and use x to represent the value you need to find
108 = 18
x = 82
3. Cross multiply
x 18 = 8856
4. Find the value of x by solving this simple equation
x = 8856 ÷ 18
x = 492 - Amount the employer pays every two weeks for Tessa's family coverage
Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.
1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks
52 ÷ 2 = 26
2. Finally, multiply the money paid by the employer every two weeks by 26
26 weeks x $492 = $12792- This is the total the employer pays annually
Jeff is playing a racing game. The game awards him an initial of virtual money. In addition, he gets of virtual money for each race he wins. In the end, he calculates average earnings of for each race he won. If represents the number of races he won, which equation can be used to find the number of wins? A. B. C. D.
A box is filled with 8 blue cards, 6 red cards, and 6 yellow cards. A card is chosen at a random from the box. What is the probability that the card is not red ? Write your answer as a fraction.
Answer:
14/20 or .7 or 70%
Step-by-step explanation:
Total Number of cards: 20
Number of Red cards: 6
The leftover cards: 20 -6 = 14
The probability of not getting a red = 14/20
14/20 as a decimal = 14/20 = 70/100 = .7
14/20 as a percent = 14/20 = 70/100 = 70%
What is the difference between a consistent and inconsistent system of equations?
Answer:
A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.
Answer: see below
Step-by-step explanation:
Consider the standard form of a linear equation in Slope-Intercept form:
y = mx + b where
m is the slopeb is the y-interceptA CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.
This results in the lines crossing so they have at least one solution.
An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.
This results in parallel lines so they have no solutions.
State the correct polar coordinate for the graph shown.
It is not the option selected.
One way to write this polar coordinate is to say (2.5, pi/2) meaning we move 2.5 units away from the origin toward the pi/2 direction
pi/2 radians = 90 degrees
An alternative is to write (-2.5, 3pi/2) which is where we aim at the 3pi/2 direction (270 degrees) and walk backward while still facing directly south, and we'll arrive at the same location.
In a regression class, a student suggested the following: If extremely influential outlying cases are detected in a data set, simply discard these cases from the data set. Provide your comments as the validity of this statement.
Answer:
Discarding the influential outlying cases when detected is also known as flagging outliers in a data set, and this is because outliers do not follow the rest of the dataset's pattern. if this outliers are not discarded they would have a negative effect on any model attached to the dataset
Step-by-step explanation:
In a regression class ; If extremely influential outlying cases are detected in a Data set, discarding this influential outlying cases is the right way to go about it
Discarding the influential outlying cases when detected is also known as flagging outliers in a data set, and this is because outliers do not follow the rest of the dataset's pattern. if this outliers are not discarded they would have a negative effect on any model attached to the dataset
If 75% of a number 60, what is the number?
Answer:
80
Step-by-step explanation:
75 60
------ = ------
100 x
100 x 60 = 6000
75x = 6000
x = 80
Tanθ - cosecθ secθ (1-2 cos²θ) = cotθ
Answer:
I thinksomething is wrong.
I'm getting another proving it's-tan thita.
I hope this is the one you are searching for..
The data set {3, 7, 5, 4, 1} consists of the lengths, in minutes, of a sample of speeches at an awards banquet. Use a formula to find the standard deviation of the sample, and label it with the correct variable.
Answer:
Standard deviation = 2.2360679774998
Step-by-step explanation:
We are asked to find the Standard deviation of a samples of speeches as an awards.
The formula for sample standard deviation is given as:
√[(x - μ)²/N - 1 ]
Step 1
We find the mean (μ)
The mean of the sample =>
= Sum of term/ Number of terms
= (3 + 7 + 5 + 4 + 1)/5
= 20/5
= 4
Step 2
Find the Standard deviation of the sample
√[(x - μ)²/N - 1 ]
N = number of samples or terms = 5
= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]
= √ (1 ² + 3² + -1² + 0² + -3²/4)
= √( 1 + 9 + 1 + 0 + 9/4)
= √20/5 - 1
= √5
= 2.2360679774998
The standard deviation of the sample = 2.2360679774998
Take thus quote, and embed (introduce) it into a complete sentence: "TV plots
and characters tended to be simple" The author is Ostergaard.
An honest die is rolled. If the roll comes out even (2, 4, or 6), you will win $1; if the roll comes out odd (1,3, or 5), you will lose $1, Suppose that in one evening you play this game n=2500 times in a row.
(a) Estimate the probability that by the end of the evening you will not have lost any money.
(b) Estimate the probability that the number of "even rolls" (roll a 2, 4, or 6) will fall between 1250 and 1300.
(c) Estimate the probability that you will win $100 or more.
Answer:
(a) 50%
(b) 47.5%
(c) 2.5%
Step-by-step explanation:
According to the honest coin principle, if the random variable X denotes the number of heads in n tosses of an honest coin (n ≥ 30), then X has an approximately normal distribution with mean, [tex]\mu=\frac{n}{2}[/tex] and standard deviation, [tex]\sigma=\frac{\sqrt{n}}{2}[/tex].
Here the number of tosses is, n = 2500.
Since n is too large, i.e. n = 2500 > 30, the random variable X follows a normal distribution.
The mean and standard deviation are:
[tex]\mu=\frac{n}{2}=\frac{2500}{2}=1250\\\\\sigma=\frac{\sqrt{n}}{2}=\frac{\sqrt{2500}}{2}=25[/tex]
(a)
To not lose any money the even rolls has to be 1250 or more.
Since, μ = 1250 it implies that the 50th percentile is also 1250.
Thus, the probability that by the end of the evening you will not have lost any money is 50%.
(b)
If the number of "even rolls" is 1250, it implies that the percentile of 1250 is 50th.
Then for number of "even rolls" as 1300,
1300 = 1250 + 2 × 25
= μ + 2σ
Then P (μ + 2σ) for a normally distributed data is 0.975.
⇒ 1300 is at the 97.5th percentile.
Then the area between 1250 and 1300 is:
Area = 97.5% - 50%
= 47.5%
Thus, the probability that the number of "even rolls" will fall between 1250 and 1300 is 47.5%.
(c)
To win $100 or more the number of even rolls has to at least 1300.
From part (b) we now 1300 is the 97.5th percentile.
Then the probability that you will win $100 or more is:
P (Win $100 or more) = 100% - 97.5%
= 2.5%.
Thus, the probability that you will win $100 or more is 2.5%.
Complete the table for the given rule.
Rule: y = 6x – 4
х. Y
1
3
10
Answer:
a y = 2
b.y = 14
c. y =56
Step-by-step explanation:
a .6 (1)- 4=2
y=2
b. 6 (3)- 4
=18-4
y=14
c. 6 (10) - 4
= 60 - 4 =56
If there are 25 students in a class - 11 are guys and 14 are girls what is the probability that one of the students on the class is a guy?
Answer:
0.44
Step-by-step explanation:
11/25 = 0.44 = 44%
Answer:
11/25
Step-by-step explanation:
since there are 25 students, there will be 25 choices, and the 25 will be the denominator
and there are 11 guys so there will be 11 choices of guys and the 11 will go on top
What is the first step in mathematical induction?
Answer:
Show that the statement is true for n=1
Step-by-step explanation:
Hey,
Show that the statement is true for n=1
You can check my other answer there which explains a little bit more the ideas.
https://brainly.com/question/17162256
thank you
Question:
A school's band members raised money by selling magazine subscriptions and shirts. Their profit from selling shirts was per shirt minus a one-time set-up fee. Their profit from selling magazine subscriptions was per subscription. They made exactly the same profit from shirts as they did from magazines. They also sold the same number of shirts as magazine subscriptions. How many shirts did they sell?
Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
The gasoline gauge on a van initially read ⅛ full. When 15 gallons of gasoline were added to the tank, the gauge then read ¾ full. How many more gallons would be needed to fill the tank?
Answer:
Question 1: 40 shirts and 40 magizines
Question 2: $4.4
Question 3: 6 gallons
Answer:
hello
Step-by-step explanation:
Tina's age is 4 years less than 3 times her niece's age. If her niece's age is x years, which of the following expressions best shows Tina's age? x − 4 4x − 3 3x − 4 4 − 3x
Answer:
3x - 4
Step-by-step explanation:
As Tina's age is 3 into x ( 3 x x= 3x)but 4years less (-4)
Therefore Tina's age is 3x - 4
Answer:
3x - 4
Step-by-step explanation:
Use these representations: niece's age: x
We triple x and then subract 4 years from the result, obtaining:
Tina's age: 3x - 4
Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
Find the first six partial sums S1, S2, S3, S4, S5, S6 of the sequence whose nth term is given. 1 2 , 1 22 , 1 23 , 1 24 , . .
Answer:
the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Step-by-step explanation:
The term of the sequence are given as : [tex]\dfrac{1}{2}[/tex], [tex]\dfrac{1}{2^2}[/tex], [tex]\dfrac{1}{2^3}[/tex], [tex]\dfrac{1}{2^4 }[/tex] , . . .
The nth term for this sequence is , [tex]\mathtt{a_n =( \dfrac{1}{2})^n}[/tex]
The nth partial sum of the sequence for [tex]\mathtt{a_1,a_2,a_3.... a_n}[/tex] is [tex]\mathtt{S_n}[/tex]
where;
[tex]\mathtt{S_n = a_1 +a_2+a_3+ ...+a_n}[/tex]
The first partial sum is: [tex]\mathtt{S_1= a_1}[/tex]
[tex]\mathtt{S_1= (\dfrac{1}{2})^1}[/tex]
[tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
Therefore, the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
The second partial sum is: [tex]\mathtt{S_2= a_1+a_2}[/tex]
[tex]\mathtt{S_2= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2}[/tex]
[tex]\mathtt{S_2= \dfrac{1}{2} + \dfrac{1}{4}}[/tex]
[tex]\mathtt{S_2= \dfrac{2+1}{4} }[/tex]
[tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
Therefore, the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
The third partial sum is : [tex]\mathtt{S_3= a_1+a_2+a_3}[/tex]
[tex]\mathtt{S_3= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3 }[/tex]
[tex]\mathtt{S_3= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}}[/tex]
[tex]\mathtt{S_3= \dfrac{4+2+1}{8}}[/tex]
[tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
Therefore, the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
The fourth partial sum : [tex]\mathtt{S_4= a_1+a_2+a_3+a_4}[/tex]
[tex]\mathtt{S_4= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 }[/tex]
[tex]\mathtt{S_4= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}}[/tex]
[tex]\mathtt{S_4= \dfrac{8+4+2+1}{16}}[/tex]
[tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
Therefore, the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
The fifth partial sum : [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5}[/tex]
[tex]\mathtt{S_5= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 }[/tex]
[tex]\mathtt{S_5= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}}[/tex]
[tex]\mathtt{S_5= \dfrac{16+8+4+2+1}{32}}[/tex]
[tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
Therefore, the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
The sixth partial sum: [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5+a_6}[/tex]
[tex]\mathtt{S_6= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 +(\dfrac{1}{2})^6 }[/tex]
[tex]\mathtt{S_6= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64} }[/tex]
[tex]\mathtt{S_6= \dfrac{32+16+8+4+2+1}{64}}[/tex]
[tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Therefore, the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
The length of a rectangle is three times its width. If the perimeter of the rectangle is 160 cm, what are the dimensions of this rectangle?
Answer:
The dimensions or Area of the rectangle is 1200cm².
Using the power series methods solve the 1st order Lane-Emden Equation:
xy = 2y + xy = 0
You may only use a power series solution to find both linearly independent functions. This means you may not use Abel’s theorem, variation of parameters or reduction of order.
Answer:
Step-by-step explanation:
xy = 2y + xy = 0
Hence, 2y + xy = 0 ---------(1)
Differentiating equation (1) n times by Leibnitz theorem, gives:
2y(n) + xy(n) + ny(n - 1) = 0
Let x = 0: 2y(n) + ny(n - 1) = 0
2y(n) = -ny(n - 1)
∴ y(n) = -ny(n - 1)/2 for n ≥ 1
For n = 1: y = 0
For n = 2: y(1) = -y
For n = 3: -3y(2)/2
For n = 4: -2y(3)
Sebastian studies from 3:15 - 4:45 p.m his sister,Sara studies from 4:30 -6:15 p.m who studies longer and by how,much?
Answer:
Sara studies longer by 15 minutes.
Step-by-step explanation:
Let's calculate how long Sebastian studies for. From 3:15 - 4:15, there is 1 hour and from 4:15 to 4:45, there are 30 minutes so Sebastian studies for 1 hour and 30 minutes. Now, let's calculate how long Sara studies for. From 4:30 - 5:30, there is 1 hour, from 5:30 - 6:00, there are 30 minutes and from 6:00 - 6:15, there are 15 minutes so Sara studies for 1 hour 45 minutes. This means that Sara studies longer by 45 - 30 = 15 minutes.
