10) Using Limit Comparison Test (LCT), the following series
+00
M:
-1 + 2n5
n6 + 1
n=1
Answers
Compare to the divergent series,
[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]
Then by the limit comparison test, the given series also diverges, since the limit
[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{2n^5-1}{n^6+1}}{\frac1n} = \lim_{n\to\infty}\frac{2n^6-n}{n^6+1}=\lim_{n\to\infty}\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2[/tex]
is positive and finite.
Related Questions
Students and adults purchased tickets for a recent school play. All tickets were sold at
the ticket booth (discounts of any type) were not allowed.
Student tickets cost $8 each, and adult tickets cost $10 each. A total of $1,760 was
collected. 200 tickets were sold.
b. Solve the system you create to find the exact number of student tickets sold and
adult tickets sold.
Answers
Answer:
120 student and 80 adult tickets
Step-by-step explanation:
8x + 10y = 1760
x + y = 200
you toss six coins at the same time. how many possible outcomes are there?
64
36
12
6
Answers
Answer:
64 outcomes
Step-by-step explanation:
Let the number of coins be n.Let the number of outcomes per coin be X.Given the following data;
Number of coins = 6
Number of outcomes for a single coin = 2
A single coin comprises of a head (H) and a tail (T), thus, the number of outcomes for a single coin is two (2).
To find how many possible outcomes we would have from tossing six coins at the same time, we would use the following formula;
[tex] Number \; of \; outcomes = X^{n} [/tex]
Substituting the values, we have;
Number of outcomes = 2⁶
2⁶ = 2 * 2 * 2 * 2 * 2 * 2
2⁶ = 64
Number of outcomes = 64
Therefore, the number of outcomes for a single coin tossed at the same time is equal to sixty four (64). It would have a total of 32 heads (H) and a total of 32 tails (T).
Two functions are shown in the table below f(x) equals -X squared plus 4X +12 And G(x)
equals X +2
Answers
Answer:
[tex]x = -2; x = 5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = -x^2 + 4x + 12[/tex]
[tex]g(x) = x +2[/tex]
Required
For what value of x is: [tex]f(x) = g(x)[/tex]
[tex]f(x) = g(x)[/tex] implies that
[tex]-x^2 + 4x + 12 = x + 2[/tex]
Collect like terms
[tex]-x^2 + 4x -x + 12 -2 = 0[/tex]
[tex]-x^2 + 3x + 10 = 0[/tex]
Expand
[tex]-x^2 + 5x-2x + 10 = 0[/tex]
Factorize
[tex]-x(x - 5)-2(x - 5) = 0[/tex]
Factor out x - 5
[tex](-x - 2)(x - 5) = 0[/tex]
Solve for x
[tex]-x - 2 = 0; x - 5 = 0[/tex]
So:
[tex]x = -2; x = 5[/tex]
Find the slope in each line
Answers
please answer ASAP (math)
Answers
Answer: Undefined
Step-by-step explanation:
Replace x with -5
Choose all of the symbols that make the following sentence true.
4 ^0 ___ 5 ^-1
=
<
≥
≤
≠
>
Answers
Answer:
≠ and >
Step-by-step explanation:
_________________
QUESTION 14 · 1 POINT
Translate the English phrase into an algebraic expression: 6x less than 81xsquared
Answers
Answer:
Step-by-step explanation:
81x² - 6x
Answer:
81x² - 6x
Step-by-step explanation:
81x² - 6x
My rule is: y = 1/3x + 11/15
Find y, if x=1
Find y, if x=6
Answers
Answer: if x=1 , then y= 48/45
If x=6 then y= 42/15
Explaination
If x=1
Replacing value of x in the equation
y= 1/3*1 + 11/15
y= 48/45
If x= 6
Replacing value of x
y= 1/3*x + 11/15
= 42/15
Maddy has a bag of 36 marbles. The probability of picking green is 1 in 2, the probability of picking red is 1 in 3, and the probability of picking blue is 1 in 9. The only other color in the bag is black. Find the probability of Maddy picking a black marble.
Answers
Answer: 1 in 18
This is the same as writing the fraction 1/18
==============================================================
Explanation:
Since she has 36 marbles total, and the probability of picking green is 1 in 2, this means (1/2)*36 = 18 marbles are green.
Then she also has (1/3)*36 = 12 red marbles and (1/9)*36 = 4 blue marbles.
So far, that accounts for 18+12+4 = 34 marbles in all. That leaves 36-4 = 2 marbles left over that must be black, as it's the only color left.
From that, the probability of choosing a black marble is 2/36 = 1/18.
There's a 1 in 18 chance of Maddy picking a black marble.
1/18 = 0.0556 = 5.56% approximately
Which of the following is a characteristic of a plane
Answers
Answer:
I think you meant to add a list of answers but didn't so here's the characteristics of a plane: Flat, two dimensional, extends infinitely, and is assembled about multiple points and lines.
Step-by-step explanation:
Answer:
If you are taking the FLVS test it is "Two endpoints"
Step-by-step explanation:
Just took the test
hope it helps :)
Which is the graph of an even monomial function?
Answers
Answer:
The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.
Keith is looking at a cliff. He determines that the angle of elevation to the top is 70° from where he is at. 70m away from Keith, Alan estimates the angle between the base of the cliff, himself, and Keith to be 29° while Keith estimates the angle between the base of the cliff, himself, and Alan to be 48°. What is the height, h, of the cliff to the nearest tenth of a metre?
1) 78.8m
2) 83.9m
3) 89.0m
4) 95.7m
This question completely baffled me on my homework, I still haven't done it because I don't even know how to approach it (Since it's a 3D problem)
Please help me out
Also, this homework is due in an hour so I'm starting to sweat
Answers
9514 1404 393
Answer:
4) 95.7 m
Step-by-step explanation:
The angle at the cliff base between Alan and Keith is ...
B = 180° -29° -48° = 103°
The law of sines will tell you the distance KB from Keith to the cliff base is
KB/sin(A) = KA/sin(B)
KB = KA×sin(A)/sin(B) = (70 m)sin(29°)/sin(103°) ≈ 34.82935 m
The height of the cliff is found from the tangent relation ...
Tan = Opposite/Adjacent
tan(70°) = height/(34.83 m)
height = (34.83 m)tan(70°) = 95.693 m
The height of the cliff is about 95.7 m.
_____
Additional comment
These problems can usually be resolved into two 2-D problems. Here, we can work out the distance we need from Keith to the cliff by considering only the ground plan of the site. Then we can work out the height of the cliff only considering the vertical plane containing Keith and the base of the cliff.
The attachment shows the ground plan triangle KAB.
Please help me please please I really need help please please
A moving company charges $30 plus $0.15 per mile to rent a moving van. Another company charges $15 plus $0.20 per mile to rent the same van. For how many miles will the cost be the same for the two companies? Write and solve an equation.
Answers
10 = .05x
200= x
200 miles
Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.
Answers
Answer:
x=3 and x=-2 is the root of given eq
Answer:
Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.?
x = –2 or x = 3 is the answer
Step-by-step explanation:
An item costs S430 before tax, and the sales tax is $17.20.
Find the sales tax rate. Write your answer as a percentage.
Answers
Answer:
Step-by-step explanation:
430
x4%
_________
$17.20+ $430= $447.20
PLEASE HELP ASAP PLSSSSS !!!
Answers
Answer:
133 answer ---------------------------------------- helpful answer
Tamara uses a coupon to save 20% off her purchase at the bookstore. The original cost of Tamara's purchase is d dollars.
Which expressions represent the cost, in dollars, of Tamara's purchase after using the coupon? Choose all that apply.
Answers
Answer:
The equation would be d - (d×0.2)
ACTIVITY 1 Directions: Interpret these circle graphs
A. The pie graph below shows what a normal human body is made of.
Questions:
1. As shown in the graph,what composes the human body?
2. Which makes up the greatest part of the human body? the least?
Answers
Step-by-step explanation:
1) it is composed of 20% of fat, 17% of bone, 50% of muscle and 13% others(minerals)
2) muscle makes up the greatest part and the minerals makes up the least.
hope it heals u.
make me brain list Pls.
please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
9514 1404 393
Answer:
the correct answer is marked
Step-by-step explanation:
The circle with center (h, k) and radius r has equation ...
(x -h)² +(y-k)² = r²
For the given center, that is ...
(x -1)² +(y +1)² = r²
The value of r² can be found by using the given point for x and y, and seeing what value of r² makes the equation true.
(5 -1)² +(7 +1)² = 4² +8² = 16 +64 = 80
So, r² = 80 makes the equation true, and that equation is ...
(x -1)² +(y +1)² = 80
Evaluate the function.
f(x) = 2x2
Find f(-3)
Can anybody answer this?
Answers
Answer:
18
Step-by-step explanation:
f(x) = 2x^2
Let x = -3
f(-3) = 2 * (-3)^2
Exponents first
f(-3)=2 *9
f(3) = 18
Answer:
f ( - 3 ) = 18
Step-by-step explanation:
f ( x ) = 2x²
Find f ( - 3)
let , x = - 3
lf ( - 3 ) = 2 ( -3 )²
f ( - 3 ) = 2 × ( - 3 )²
Evaluate the power
f ( -3) = 2 × 9
multiply the numbers
f ( - 3 ) = 18
m(x) = x2 + 4x
n(x) = x
(mn)(x) =
x2 + 4x(x)
(x2 +4x)(x)
Answers
Answer:
Answer:
1. B. (x^2 + 4x)(x)
2. A. (x^3+4x^2)
3. 9
4. 0
5. 1
Step-by-step explanation:
if jane give £2 pounds to charlotte they will have equal amount of money. instead
charlotte give £4 to jane the ratio of jane's money to charlotte will be 2:1. how much
do jane and charlotte each have to start with
Answers
Let j = amount Jane has and c = amount Charlotte has
j - 2 = c + 2 if Jane gives Charlotte 2 pounds
j + 4 = 2(c - 4) if Charlotte gives Jane 4 pounds
j + 4 = 2c - 8
Subtract equation 1 from equation 3
6 = c - 10
c = 16
j = c + 4 = 20
Are the triangles congruent? Why or why not?
Answers
Answer:
ffffffssssssssssssssssscv
Step-by-step explanation:
using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation 10.0y-4.55x=581. where x is the number of years after 2000 what is projected population in 2026?
Answers
Answer:
The projected population in 2026 is of 699.3 million.
Step-by-step explanation:
Population:
The population, in x years after 2000, is given by the follwing equation:
[tex]y - 4.55x = 581[/tex]
That is:
[tex]y(x) = 4.55x + 581[/tex]
What is projected population in 2026?
2026 - 2000 = 26, so this is y(26).
[tex]y(26) = 4.55(26) + 581 = 699.3[/tex]
The projected population in 2026 is of 699.3 million.
the product of 2 numbers, p and q, decreased by 3 times their sum. (as an algebraic expression)
Answers
Answer:
3 - (p*q) im not sure lol
Step-by-step explanation:
What is the value of X
A. x=20
B. x=15
C. x=10
D. x=5
Answers
This is because (x+5) + (7x-5) + x = 180
Simplify the given expression and enter in numerical form.6+5
Answers
Answer:
6+5=11
Step-by-step explanation:
6 is added to 5
i am sorry if i am wrong
Meg makes a dot plot for the data 9, 9, 4, 5, 5, 3,
4,5, 3, 8, 8, 5. Where does a gap occur?
Answers
The gap consists of the values 6 and 7.
Check out the dot plot below to see what I mean. We have one cluster on the left from 3 to 5. Then another cluster on the right from 8 to 9.
Answer:
The gap is present around 6 & 7
Step-by-step explanation:
Since there is no evidence of dots above 6 & 7, there must have been a freeze in data around then, called a gap.
Jake wants to surprise his parents with a small anniversary party at their favorite restaurant.
It will cost $35.75 per person for dinner, including tip and tax.
His budget for the party is $600.
What is the maximum number of people Jake can have at the party without exceeding his budget?
Answers
Answer:
16 people
Step-by-step explanation:
35.75 times 16 is 572, times 17 is 607.75, he only has 600 and he cant have a fraction of a person, so he can have 16 people
x/35.75=600/35.75
x=16.78
He can invite 16 people without exceeding his budget.
5x + 7y = 42 I need to find the x−and y−intercepts.
Answers
Answer:
Y intercept = (0;6)
X intercept = (42/5;0)
