Answer: The radius of convergence of the series Σ(-1)ⁿ xⁿ 3ⁿ ln(n) with n=2 is 3.
To find the radius of convergence of the series Σ(-1)ⁿ xⁿ 3ⁿ ln(n) from n=2 to infinity, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges absolutely, and the radius of convergence r is the reciprocal of the limit. If the limit is greater than 1, then the series diverges, and if the limit is equal to 1, the test is inconclusive.
So, applying the ratio test to our series, we have:
|(-1)(ⁿ+¹+¹) x(ⁿ+¹) 3(ⁿ+¹) ln(n+1)| / |(-1)ⁿ xⁿ 3ⁿ ln(n)|
= |x|/3 * ln(ⁿ+¹)/ln(n)
As n approaches infinity, the limit of this expression is:
lim n->inf |x|/3 * ln(n+1)/ln(n) = |x|/3 * 1 = |x|/3
So the series converges absolutely if |x|/3 < 1, or equivalently, if |x| < 3. Therefore, the radius of convergence is r = 3.
Learn more about radius of convergence : https://brainly.com/question/17019250
#SPJ11
A football field is 160 feet wide and 360 feet in length. what is the distance around the field?
Answer:
Step-by-step explanation:
Distance around = 2*160 + 2*360
= 320 + 720
= 1080 feet.
The distance around the field is 1040 feet.
It is required to find the distance around the field.
What is rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that:
A football field is 160 feet wide and 360 feet in length.
A football field is in the shape of rectangle.
So, we know that ,
Perimeter of rectangle= 2(length +breadth)
Distance around
= 2(160 + 360)
=2(520)
= 1040 feet.
Hence, the distance around the field is 1040 feet.
Learn more about rectangle here:
https://brainly.com/question/28040873
#SPJ2
A palindrome is a number that reads the same forward and backward. a palindrome will be designated good if the first half of the number is strictly increasing. (example: 123321 is good, and so is 454 or 16961, but 1224221 or 324423 are not good). how many 5-digit good palindromes are there?
The total number of 5 digit palindrome that we have is 900.
What is a palindrome?This is the term that is used to refer to a number or a word phrase that is the same way when it is written from the front and from the back.
Examples of palindrome numbers are
10101 10201 10301 10401Read more on palindrome here:
https://brainly.com/question/14076732
#SPJ1
What is the probability of on-time arrival in class given that the subject is biology?
The probability of on- time arrival in class given that the subject is biology is 82.4%.
Given the following table relating to subject on tie assignment submission and on time arrival in class.
Subject On time submission On time arrival
Physics 89.7% 82.3%
Maths 88.2% 88.7%
Chemistry 89.4% 83.1%
Biology 90.1% 82.4%
Total 88.5% 84.7%
We have to find the probability of on time arrival in class given that the subject is biology.
We have been given the corresponding percentages and percentages in itself shows some quantity. Percentage is the ratio of total favourable outcome to total outcome.
From the table the probability of on time arrival in class given that the subject is biology is 82.4%
Hence the probability of on- time arrival in class given that the subject is biology is 82.4%.
Learn more about probability at https://brainly.com/question/24756209
#SPJ4
Question is incomplete as it should includes the following table:
Subject On time submission On time arrival
Physics 89.7% 82.3%
Maths 88.2% 88.7%
Chemistry 89.4% 83.1%
Biology 90.1% 82.4%
Total 88.5% 84.7%
Answer:
82.4%.
Step-by-step explanation:
given that the midpoints of pq is (-3,1) and q (7,5), obtain the co-ordinates of p
The coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).
The midpoint of AB, given any points A (x₁, y₁) and B(x₂, y₂) is given as point M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).
In the question, we are given that the midpoint of PQ is (-3, 1) and point Q is (7, 5).
We are asked to find the coordinates of point P.
We assume the coordinates of point P as (x, y).
Thus, the midpoint of PQ = ({(x + 7)/2}, {(y + 5)/2}),
that is, (-3, 1) = ({(x + 7)/2}, {(y + 5)/2}).
Thus, we can show that:
(x + 7)/2 = -3,
or, x + 7 = -6,
or, x = -6 - 7 = -13.
(y + 5)/2 = 1,
or, y + 5 = 2,
or, y = 2 - 5 = -3.
Thus, the coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).
Learn more about midpoints at
https://brainly.com/question/4521677
#SPJ4
If there are n ants once a month how many will there be a month la
Answer: 3n ants
Step-by-step explanation:
If there are n ants one month, and the ants triple every month, then next month there will be 3n ants.
We can multiply 3 by n to show it tripling.
To test this, 3(10,000) = 30,000 and 3(270,000) = 810,000, which corresponds to what you've filled out in the table.
PLEASE HELP!!!! A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
a. Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
b. Are these independent or dependent events?
c. Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
d. Find the probability of drawing two blue marbles if the first marble is not replaced. Explain your reasoning.
The answers are as follows:
a. There are 6 ways of tossing a coin and then drawing a marble from the bag. (Tree diagram is shown in the diagram below) The probability is 1/12.
b. These are independent events since tossing a coin does not affect the drawing of marble from the bag.
c. From the tree diagram, the probability of tossing a head and drawing a red marble is 1/6(since they are independent events).
d. The probability of drawing two blue marbles if the first marble is not replaced is 1/5(since they are dependent events).
What are compound events in probability?Two or more events that occur simultaneously or one after the other are said to be compound events. They are calculated by multiplying the probability of the first event by the probability of the second event.Calculation:It is given that a bag contains,
Number of white marbles(W) = 1
Number of Blue marbles (B) = 3
Number of Red marbles (R) = 2
Thus, there are 6 marbles in the bag. So, the sample space for drawing a marble = 6
a. Finding all the possible outcomes using a tree diagram:
The possible outcomes from the tree diagram are
(H, W), (H, B), (H, R), (T, W), (T, B), and (T, R)
The probability of tossing head or tail = 1/2
The probability of drawing a marble from the bag = 1/6
So, the compound probability = (1/2)(1/6) = (1/12)
The sample space for this is 12.
b. Independent or dependent events:
These are independent events since the tossing of a coin does not affect the drawing of marble from the bag.
c. Finding the probability of tossing a head and drawing a red marble:
The probability of tossing a head = 1/2
The probability of drawing a red marble = 2/6 = 1/2
Since they are independent events,
The required probability = (1/2)(1/2) = 1/4
d. Finding the probability of drawing two blue marbles if the first marble is not replaced:
The probability of drawing a blue marble from the bag(1st attempt) = 3/6
The probability of drawing another blue marble from the bag (2nd attempt) = 2/5 (From the leftover marbles after the first attempt)
Since they are dependent events, the probability of the 2nd event is calculated only after the first event is calculated.
So, the required probability = (3/6)(2/5) = 1/5
Thus, all the probabilities are calculated.
Learn more about compound probabilities here:
https://brainly.com/question/4471151
#SPJ1
Which is the population standard deviation of the data set: 8, 9, 10, 11, 12?
a. 10.123
1.414
b.
2.654
Please select the best answer from the choices provided
A
C.
d. 10
B
The population standard deviation of the data set is 1.414.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
How is standard deviation calculated?Determine the mean of the observationDetermine the difference between each value and the mean and then square the resultDetermine the mean of the sum of the squared differences and then find the square root of the mean:Mean = (8 + 9 + 10 + 11 + 12) / 5 = 10
Sum of squared differences: (8 - 10)² + (9 - 10)² + (10 - 10)² + (11 - 10)² + (12 - 10)² = 10
√10/5 = 1.414
To learn more about standard deviation, please check: https://brainly.com/question/26201837
#SPJ1
Bob rolls a fair six-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a $1$, then he rolls again. In a non-leap year, what is the expected value of the difference between the number of days Bob eats unsweetened cereal and the number of days he eats sweetened cereal
Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.
According to the statement
we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.
and we have to find that the expected value of the difference between the number of days.
So, the total number of days in a year is 365 days.
Chance to get a prime number on a die = 3/6
Chance to get a prime number on a die = 1/2.
and chances to get a composite number = 2/6
chances to get a composite number = 1/3
and chances to get a 1 on a die = 1/6.
Then the expected value =
so, expected value = 365(1/6) + 365(1/3) + 365(1/2)
then after calculating
Expected value = 1+2+1
then the value become is 4
and by this way he eat 171 days sweet cereal and other days he eat unsweetened.
So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.
Learn more about Expected value here https://brainly.com/question/15858152
#SPJ4
x/2 + 11 = 19
solve this equation
Answer:
x/2 = 19-11
x/2 = 8
x = 8×2
x= 16
Answer:
x=16
Step-by-step explanation:
x/2 + 11 = 19
*2 *2 *2 Multiply 2 on both sides to make x stand by itself
x+22 = 38
-22 -22
x=16
Check
Plug in 16 instead of x.
16/2 + 11 = 19
8+11=19
19=19
Hope it helps:)
Suppose you are looking to purchase a new TV. You are placing it in an opening that is 136 cm wide but want to leave at least 2 cm of room on either side of the TV. If the TV screen measures 86 cm high, what is the largest size TVin inches, that you can purchase? TV's are measured based on the diagonal measure. (1inch = 2.54cm) Write your answer as an integer
Answer:
404 inches
Step-by-step explanation:
Since a room of 2cm is to be left of either side of the TV, thus, the permissible required length of the TV is 136-2 = 134cm
Use Pythagoras Theorem,
h² = 134² + 86² = 17956 + 7396 = 25352
h = √25352 = 159.22 ≈ 159cm = 404.41 inches ≈ 404 inches.
Find the fifth term and the nth term of the geometric sequence whose initial term a, and common ratio r are given.
a₁ = 5, r=2
Answer:
a₅ = 80 , [tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]
Step-by-step explanation:
to find a term in the geometric sequence multiply the previous term by r
a₁ = 5
a₂ = a₁ × 2 = 5 × 2 = 10
a₃ = a₂ × 2 = 10 × 2 = 20
a₄ = a₃ × 2 = 20 × 2 = 40
a₅ = a₄ × 2 = 40 × 2 = 80
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
here a₁ = 5 and r = 2 , then
[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]
The function f(x) = 200(0.5)x/50 models the amount in pounds of a particular
radioactive material stored in a concrete vault, where x is the number of years since
the material was put into the vault. Find the amount of radioactive material in the
vault after 140 years. Round to the nearest whole number.
Answer:
29 years
Step-by-step explanation:
Given the function [tex]f(x)= 200(0.5)^{\frac{x}{50} }[/tex], where x stands for the number of years since the material was put into the vault, we can plug 140 into x to find the amount leftover.Another way of doing this is to change the function to [tex]f(x)=200(0.5^{\frac{1}{50} })^{x}[/tex] which are equivalent functions, and then plug 140 into x. This function is helpful if you also needed to find the rate. I'll use the 1st function because the question doesn't ask for the rate[tex]f(x)= 200(0.5)^\frac{140}{50}}[/tex]
From here I'll just use a calculator & get 28.7, or 29 years.
One number is 4 more than another, and their sum is 60.
If x = the larger number and y = the smaller number, then which of the following systems could be used to solve for the value of the smaller number?
The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding
Calculate the value of the numbers:Given that one number is 4 more than another,
⇒x = y + 4 (equation (1))
Their sum is 60,
⇒x + y = 60
y + 4 + y = 60 (From (1))
2y + 4 = 60
2y = 56 ⇒ y = 28
x = y + 4 = 28 + 4 ⇒x = 32
Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.
Learn more about algebraic expressions here:
brainly.com/question/19245500
#SPJ1
HELPPPPPP MATHHHH pleaseee
Answer:
A
Step-by-step explanation:
3.
There was an earthquake in San Francisco April 18, 1906. More recently there was another earthquake in Columbia June 27, 2014. Earthquakes are measured using the associated amplitude on the Richter scale. Let a1 be the amplitude for the San Francisco earthquake and a2 be the amplitude for the Columbian earthquake.
San Francisco earthquake equations is below
Columbia earthquake below (view image)
a. Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below:
a1/a2
Using the properties of logarithms, it is found that the San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.
How to find the ratios of the intensity of earthquakes?As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2, R_1 > R_2[/tex], the ratio of the intensities is given by:
[tex]R = 10^{\frac{R_1}{R_2}}[/tex]
For this problem, the intensities are:
[tex]R_1 = 7.8, R_2 = 5.6[/tex]
Hence the ratio is:
[tex]R = 10^{\frac{7.8}{5.6}} = 24.71[/tex]
The San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.
More can be learned about logarithms at https://brainly.com/question/20719486
#SPJ1
What is the measure of angle ABC
Answer: A
Step-by-step explanation:
[tex]m\angle ABC=59^{\circ}[/tex] by the inscribed angle theorem.
The movement of the progress bar may be uneven because questions can be worth more or less
(including zero) depending on your answer.
What are the exponent and coefficient of the expression 46-³?
The exponent is 3 and the coefficient is -4.
The exponent is -3 and the coefficient is 4.
O
The exponent is -3 and the coefficient is -4.
The exponent is 4 and the coefficient is -3.
f(x)=x^2-x-56=0 what are the zeros in the function?
please help!!!
Answer:
-7, 8.
Step-by-step explanation:
x^2 - x - 56 = 0
Let's see if we can factor this function:
We need 2 numbers whose product is -56 and whose sum is -1 ( which is the coefficient of x).
They are -8 and 7 , so the factors are:
(x - 8)(x + 7) = 0
x - 8 = 0 giving x = 8 and
x + 7 = 0 giving x = -7.
The zeros are -7, 8
Solve for X.
X = [?]
5x - 16 X + 10
[tex] \boxed{ \sf{ \color{purple}\huge Answer :}}[/tex]
[tex] \: \: [/tex]
[tex] \large \tt \purple↪ \: \: \: \: \: 5x - 16 = x + 10 [/tex]
[tex] \: \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \:5x - x = 10 + 16 [/tex]
[tex] \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \: 4x = 26[/tex]
[tex] \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \: x = \cancel\frac{26}{4} [/tex]
[tex] \: \: [/tex]
[tex] \underline{ \boxed{\large \tt \purple↪ \red{ \: \: \: \: x = \frac{13}{2} }}}{ \large✓}[/tex]
[tex] \: \: [/tex]
hope helps ~
find the area of a semicircle with the height of 33 ft in the diameter of 66 ft
Answer:
Step-by-step explanation:
Comment
The radius is 33 feet. The height is really a radius. The diameter consists of 2*r
r = diameter / 2
diameter = 66 feet
r = 66 /2 = 33
So you have 2 ways of finding the radius.
Solution
Area of a full circle = pi r^2
Area of a full circle = pi * 33^2
Area of a full circle = 1089 pi
Area of a semicircle = area of a full circle / 2
Area of a semicircle = 1089 * pi /2
Area of a semicircle = 544.5 * pi
Answer
Exact answer in terms of pi is 544.5 * pi
Approximate answer using 3.14 for pi = 3.14*544.5 = 1709.73
Answer:
Area=
πr2
2
Step-by-step explanation:
3.14159⋅(33)2
2
=1710.5958
A designer is hanging a mirror that is 101 centimeters (cm) wide in a room.
The center of the wall is 190 cm from the right end of the wall. If the designer
hangs the mirror so that the center of the poster is located at the center of the wall,
how far will the left and right edges of the poster be from the right end of the wall?
Answer:
240.5 cm and 139.5 cm, respectively
Step-by-step explanation:
101 cm / 2 = 50.5 cm
The right edge of the mirror is 50.5 cm to the right of the center line.
The right end of the wall is 190 cm from the center line.
190 cm - 50.5 cm = 139.5 cm
139.5 cm + 101 cm = 240.5 cm
240.5 cm and 139.5 cm, respectively
How do I find and construct the geometric mean in this problem?
x would be the side-length of a square that has the same area as a rectangle with width b and length a.
√(a*b) = x
How to find the value of x?Notice that you have two "lengths" which are a and b.
And you want to find x such that:
a/x = x/b
Now, notice that w e can rewrite the above expressions as:
a*b = x*x
This means that x would be the side-length of a square that has the same area as a rectangle with width b and length a.
Now, if you know the values of a and b (you can get these by using a ruler for example)
Then you can replace them in the equation:
a*b = x*x
√(a*b) = x
And find the value of x that meets the given condition.
If you want to learn more about expressions:
https://brainly.com/question/4344214
#SPJ1
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse
Answer:
Step-by-step explanation:
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse
Find the volume of this square
based pyramid.
12 cm
10 cm
10 cm
V = [?] cm³
Answer:
[tex]400m^3[/tex]
Step-by-step explanation:
Use the formula [tex]V=\frac{1}{3}Ah[/tex]
Where h=the height of the pyramid (12cm)
A=the base area of the pyramid, also known as the area of the square (10cm*10cm=100cm)
So, inserting this into the equation:
[tex]V=\frac{1}{3} (100)(12)[/tex]
[tex]V=\frac{1}{3} (1200)[/tex]
[tex]V=400m^3[/tex]
Can someone help me please
Answer:
[tex]y=7x[/tex]
I hope this helps and that you can give a brainliest!
Step-by-step explanation:
If x and y vary directly, that means that y is directly proportional to x. So, the parent function is y = kx.
So, by plugging in the given y=42 when x=6 into this parent function, we get:
42=6k
If we solve for k, we end up with 7.
Now if we plug in the value of k back into the parent function of this scenario, we get:
[tex]y=7x[/tex]
what is the ration that equivalent to 6/7
An equivalent ratio of the given ratio 6/7 is; 12/14
How to find Equivalent Ratios?To find equivalent ratios, we will just multiply the given ratio by any number that is equivalent to 1 such as 2/2, 3/3, 4/4, 5/5 e.t.c
Now, we want to find equivalent ratio of 6/7. Applying the procedure above, we can say that;
Equivalent ratio = (6/7) * (2/2) = 12/14
Thus, an equivalent ratio of 6/7 is; 12/14
Read more about Equivalent Ratios at; https://brainly.com/question/2328454
#SPJ1
In Bayes Theorem, you have some starting information, then you collect some new information so that you can _______ the original probabilities so you now have better information.
In Bayes Theorem, apart from the already starting information, some new information so that you can update or transform the original probabilities so you now have better information.
What is Bayes Theorem?
The Bayes' theorem was named after Thomas Bayes and it is used in probability theory and statistics as one of the fundamental theorems. It estimates the likelihood of an event based on knowledge of circumstances that might be connected to it in the past.
The Formula for Bayes' Theorem
The Bayes' theorem is given as,
P(A|B) = P(A).P(B|A) / P(B)
Here, for two events A and B,
P(A|B) is the probability for likelihood of A when B is true
P(B|A) is probability for likelihood of B when A is true
P(A) is the independent probability of event A
P(B) is the independent probability of event B
Learn more about Bayes' theorem here:
https://brainly.com/question/17010130
#SPJ4
The average of a set of 18 consecutive integers is 22.5.what is the smallest set in the integer
Answer:
(y+17)÷18=22.5
y+17=22.5×18
y+17=405
y=405-17
y=388
You purchase 9.25 gallons of gasoline at $3.15/gallon. You also buy gum ($1.10) and
windshield wiper fluid ($4.97). The state has a food tax of 4% and you give the clerk $30.00
cash. You pay the rest with your debit card. How much is charged to your debit card?
Answer:
$ 5.25 is charged to debit cardStep-by-step explanation:
Add 4% food tax:
1.1*1.04 = 1.14 (rounded)Total amount of purchase is:
9.25*3.15 + 1.14 + 4.97 = 35.25Subtract $30 paid in cash:
35.25 - 30 = 5.25Answer:
$5.25
Step-by-step explanation:
Cost of gasoline
9.25 gallons at $3.15 per gallon:⇒ 9.25 × $3.15 = $29.1375
Cost of gum
$1.10 plus 4% food tax:
⇒ $1.10 × 1.04 = $1.144
Total cost of purchases
Gasoline + gum + Windshield wiper fluid
⇒ $29.1375 + $1.144 + $4.97 = $35.2515 = $35.25 (nearest cent)
If $30.00 was paid by cash and the rest was paid for by debit card:
Debit card charge = $35.25 - $30.00 = $5.25
Dina's mother is four times older than Dina. Dina is 35 years younger than her father. Dina's father was 5 years older than Dina's mother when Dina was born. How old is Dina now?
Answer:
10 years old
Step-by-step explanation:
Let m = mother's age
Let f = father's age
Let d = Dina's age
m = 4d d = f-35 f = m+5
Substitute the middle equation in to the first equation
m = 4(f - 35) Use the distributive property
m = 4f - 140 subtract 4f from both sides
*m -4f = -140
In equation 3 above, subtract m from both sides to get
f = m+5
f - m = 5 rearrange so that the m term is first
*-m + f = 5
Now add the equations together that have *
m -4f = -140
-m + f = 5
-3f = -135 Divide both sides by -3
f = 45 This is the father's age. To find Dina's age, plug 45 into the second equation above:
d = f -35
d = 45 -35
d = 10.
To find the mom's age, use the third equation:
f = m+5
45 = m + 5
40 = m
You can check this by plugging the answers you found and you can see that all three equations are solved.
m = 4d d = f - 35 f = m + 5
40 = 4(10) 10 = 45 - 35 45 = 40 + 5
40 = 40 10 = 10 45 = 45