[tex]\huge\textbf{TheStarryNights }[/tex]Hi There!
Solve the Inequality:
2x-1≤x+5
Move all the variables (in this case, x's) to the left, using the opposite operation:
2x-x-1≤5
Move -1 to the left:
2x-x≤5+1
Combine like terms:
x≤6 (Answer)
Hope it helps & enjoy your day![tex]\huge\textbf{TheStarryNights}[/tex]
What is the limit of the infinite series?
∞∑n=1 (3n^5 / 6n^6 + 1)
Answer:
The limit of the infinite series is equal to zero.
The nth term test is inconclusive ∵ the limit is equal to 0.
By the Comparison Test, this sum diverges.
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Series Comparison Tests
nth Term TestDirect Comparison Test (DCT)Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \sum^{\infty}_{n = 1} \frac{3n^5}{6n^6 + 1}[/tex]
Step 2: Find Convergence
[Series] Define: [tex]\displaystyle a_n = \frac{3n^5}{6n^6 + 1}[/tex][Series] Set up [nth Term Test]: [tex]\displaystyle \sum^{\infty}_{n = 1} \frac{3n^5}{6n^6 + 1} \rightarrow \lim_{n \to \infty} \frac{3n^5}{6n^6 + 1}[/tex][nth Term Test] Evaluate limit [Limit Rule - VDS]: [tex]\displaystyle \lim_{n \to \infty} \frac{3n^5}{6n^6 + 1} = 0[/tex][nth Term Test] Determine Conclusiveness: [tex]\displaystyle 0 ,\ \sum^{\infty}_{n = 1} \frac{3n^5}{6n^6 + 1} \ \text{can't be concluded that it converges}[/tex]Therefore, the nth term test is inconclusive and another test must be done.
Step 3: Find Convergence Pt. 2
[DCT] Condition 1 [Define comparing series]: [tex]\displaystyle \frac{1}{2} \sum^{\infty}_{n = 1} \frac{1}{n}[/tex][DCT] Condition 1 [Test convergence of comparing series]: [tex]\displaystyle p = 1 ,\ \frac{1}{2} \sum^{\infty}_{n = 1} \frac{1}{n} \ \text{divergent by p-series (harmonic series)}[/tex]∴ since the comparison series is divergent, then our original series is also divergent according to the Direct Comparison Test.
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Learn more about limits: https://brainly.com/question/26091024
Learn more about Taylor Series: https://brainly.com/question/23558817
Topic: AP Calculus BC (Calculus I + II)
Unit: Taylor Series
Answer:
zero
Step-by-step explanation:
L’Hospital’s rule states that for two functions f(x) and g(x), if either:
[tex]\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} g(x)=0, \textsf{or}[/tex]
[tex]\ \lim_{x \to \infty} f(x)=\pm \infty \ \textsf{and} \ \lim_{x \to \infty} g(x)\pm \infty[/tex]
[tex]\textsf{Then provided that} \ \lim_{x \to \infty} \dfrac{f(x)}{g(x)} \textsf{ exists, }\lim_{x \to \infty} \dfrac{f(x)}{g(x)}=\lim_{x \to \infty} \dfrac{f'(x)}{g'(x)}[/tex]
[tex]\lim_{n \to \infty} \dfrac{3n^5}{6n^6+1} \rightarrow \dfrac{\infty}{\infty}[/tex]
[tex]\textsf{Let } f(n)=3n^5 \textsf{ and let } g(n)=6n^6+1[/tex]
[tex]\implies f^{'}(n)=15n^4 \textsf{ and } g^{'} (n)=36n^5[/tex]
By L’Hopital’s rule:
[tex]\lim_{n \to \infty} \dfrac{3n^5}{6n^6+1}=\lim_{n \to \infty} \dfrac{15n^4}{36n^5}= \lim_{n \to \infty} \dfrac{5}{12n}=0[/tex]
what is the formula of a square
Answer:
a=s2
Step-by-step explanation:
s is the length of the side of the square.
Mr. Neil is painting his coffee table. The mixture that he adds to the paint is made of 5/6
The Chicago Bulls make a three-point shot in basketball.
A snowmobile priced at $2,800 is on sale for 20% off. What is the SALES price of this snowmobile?
Answer:
SALES price of this snowmobile is $2,240
Step-by-step explanation:
percentage:value of sales:
20% of 2,80020/100 × 2,80056,000 /100$560price after discount:
$2,800 - $560$2,240write the equation if this line below
Check whether 20, 18, 40 and 36 are in proportion .
Answer:
Yes, they are in proportion
Step-by-step explanation:
20:18 and 40:36
20×36 and 18×5
720=720✓
Find the perimeter of the composite figure
Victoria was given the expression -3x+x^2-8+4x-3x^2-2 and asked to simplify it. how can she simplify the expression?
A. -2x^2+x-10
B. 2x^2-x+10
C. -4x^2-7x-6
D. 4x^2+7x+6
Answer:
A.
Step-by-step explanation:
Organize the terms and you have this:
(-3x^2+x^2)+(4x-3x)+(-8-2)
The equal terms, i.e the terms with the same exponent (the ones that are in parentheses) are reduce:
(-3x^2+x^2)=-2x^2
(4x-3x)=x
(-8-2)=-10
Then
-2x^2+x-10
Find the area of a rectangle with side lengths 3/5 inch and 5/6 inch
Answer:
15/30 0r 1/2
Step-by-step explanation:
You multiply the fractions
A cookie recipe make 24 cookies. Jaio made 11 less than double the recipe. How many cookies did she make
Answer:
he made 37 cookies
Step-by-step explanation:
24+24=48
48-11=37
p.s your welcome
What is the answer for ( c )
Answer: 37
Step-by-step explanation:
In the example below, check all the answers that are TERMS.
8x + 7 - y
y
8x
+
7
Answer: 8x, 7,
Step-by-step explanation: Terms are separated with an addition or subtraction sign.The terms for 8x + 7 - y are:8x, 7, - yHope this helps!
i need the answer to the below question
Answer:
69.15%
Step-by-step explanation:
You want the probability of a race time being less than 348 minutes if times are normally distributed with mean 319 minutes, and standard deviation 58 minutes.
ProbabilityThe probability is found using the suggested resources. It will be ...
P(X<348) ≈ 0.6915
As a percentage, that is ...
0.6915 × 100% = 69.15%
The percentage of times shorter than 348 minutes is about 69.15%.
__
Additional comment
The corresponding Z-score is (348-319)/58 = 0.500. Your table should give you the above value directly for that Z-score. No interpolation will be necessary.
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Select the equation that describes the situation
Han's house is 450 meters from the school. Lin’s house is 135 meters closer to school. How far is Lin’s house from school?
Which shows the correct solution of the equation 1/2 a + 2/3 b, when ? b=30
Answer:
The answer is 1/2a + 20
Step-by-step explanation:
Given;1/2a + 2/3bb = 30Now, Substitute value of b
1/2a + 2/3b
1/2a + 2/3(30)
1/2a + 2 × 10
1/2a + 20 = a/2 + 20 = (a + 40) ÷ 2
Thus, The answer is 1/2a + 20
-TheUnknownScientist 72
What is the equation of the line that passes through the point (6,2) and has a slope of 1/3?
Answer:
[tex]y=\frac{1}{3}x[/tex]
*View attached graph*
Step-by-step explanation:
Point-slope: [tex]y-y_1=m(x-x_1)[/tex]
m = slope ([tex]\frac{1}{3}[/tex])
point (6,2)
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-2=\frac{1}{3}(x-6)[/tex]
[tex]y-2=\frac{1}{3}x-2[/tex]
[tex]+2[/tex] [tex]+2[/tex]
[tex]y=\frac{1}{3}x[/tex]
Hope this helps!
Solve the measurement conversion problem.
12inches = 1 foot. Convert 3 feet 4 inches to inches, then multiply by 4. Convert back to feet to find your answer.
lake Each canoe is 3 feet 4 inches long. How long would 4 canoes in a row be ?
A) 12 feet 15 inches
B) 12 feet 4 inches
C) 48 inches
D) 13 feet 4 inches
tom training for a marathon he currently can run 12 miles in 3 hours. how long will it take tom to run 20 miles?
Answer:
5 hours
Step-by-step explanation:
because every hour she runs 4 miles so in 3 hours she will run 12 miles.
so 20 she would run 5 miles.
4 miles=1 hour
8 miles=2 hours
12 miles=3 hours
16 miles=4 hours
20 miles=5 hours.
Hope this helps have a great day:)
Answer:
Tom will take 5 hours
Step-by-step explanation:
Unit Rate
Tom runs 12 miles in 3 hours. We can calculate two different unit rates:
12 miles / 3 hours = 4 miles/hour
3 hours / 12 miles = 0.25 hours/mile
The first rate measures how many miles Tom runs per hour. The second rate measures how long it takes to Tom to run one mile.
We are asked to find the time needed for Tom to run 20 miles, thus the second rate will be useful:
0.25 hours/mile * 20 miles = 5 hours
To run 20 miles, Tom will take 5 hours
6 x (2+ 15) divided by 3=
By the order of operation, we first do the operation in parentheses
( 6 * (2 + 15) ) /3 = (6* 17)/3 = 102 / 3
Then we do the division
Answer = 102 / 3 = 34
Hope that helps!
There are 6 members of the student council and there are 10 chairs in their meeting room. If all 6 members
attend a meeting, how many different seating arrangements are possible?
The number of different seating arrangements is an illustration of permutation
There are 151200 different seating arrangements
How to determine the number of sitting arrangementsThe number of seats (n) is given as:
n = 10
The number of people (r) is given as:
r = 6
So, the number of seating arrangements is:
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
This gives
[tex]^{10}P_6 = \frac{10!}{(10 - 6)!}[/tex]
Simplify
[tex]^{10}P_6 = \frac{10!}{4!}[/tex]
Evaluate the quotient
[tex]^{10}P_6 = 151200[/tex]
Hence, there are 151200 different seating arrangements
Read more about permutation at:
https://brainly.com/question/12468032
Find the product:
(i) (5 – 2x) (3 + x)
[tex] \: [/tex]
[tex] \large\red{ \longrightarrow} \pmb{ \sf{(5 – 2x) (3 + x)}}[/tex]
[tex] \: [/tex]
[tex] \mapsto \: \: \: \sf{5(3 + x) – 2x(3 + x)}[/tex]
[tex] \: [/tex]
[tex] \mapsto \: \: \: \sf{(5 × 3) + (5 × x) – (2x × 3) – (2x × x)}[/tex]
[tex] \: [/tex]
[tex]\leadsto \: \: \: \sf{ 15 + 5x – 6x – 2x ^{2} }[/tex]
[tex] \: [/tex]
hope it helps!! :)
Find the equation of the line that passes through (2,-1) and is parallel to y = 4 − 2 x . Leave your answer in the form y = m x + c
Answer:
y = -2x + 3
Step-by-step explanation:
The slope intercept equation of a straight line is [tex]y=mx+b[/tex],
where m is the slope and b is the y-intercept.
Therefore, the slope of [tex]y=4-2x[/tex] is -2.
If a line is parallel to another line, they have the same slope.
Therefore, the slope (m) of the new line is also -2.
Using the point-slope form of a linear equation, where m = -2 and
[tex](x_1,y_1)[/tex] is a point on the line (2, -1):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y+1=-2(x-2)[/tex]
[tex]\implies y=-2x+3[/tex]
Weights of American adults are normally distributed with a mean of 180 pounds and a standard deviation of 8 pounds. What is the probability that a randomly selected individual will be between 185 and 190 pounds?
Answer:
There is 16.2% probability that a randomly selected individual will be between 185 and 190 pounds
Step-by-step explanation:
Z score
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ) / σ
where μ is the mean, x = raw score and σ is the standard deviation.
Given μ = 180, σ = 8.
For x = 185:
z = (185 - 180)/8 = 0.625
For x = 190:
z = (190 - 180)/8 = 1.25
P(185 < x < 190) = P(0.625 < z < 1.25) = P(z < 1.25) - P(z < 0.625) = 0.8944 - 0.7324 = 16.2%
There is 16.2% probability that a randomly selected individual will be between 185 and 190 pounds
Please help me with this math question!
Answer:
25/9% or approximately 2.78
Step-by-step explanation:
We have 6 sides on the die so we can get 6 numbers. We can do 6x6 to find the total amount of possible numbers she can get. 6x6 is 36. There is only one way she can get a 4 and a 6. Now we can say that she has a 1/36 chance to win the bet. But we have to find the percent so we can multiply it by hundred and we get 25/9%.
PLEASE HELP ILL MARK AS BRAIN LEIST!
Answer:
a. square
b. square
c. The shapes are the same because they are in the same form and are similar. They are different because they have different dimensions.
Help me please I beg
Answer:
19y+21
Step-by-step explanation:
[tex] = 3y + 3y + 7y + 6y + 15 + 6 \\ = 6y + 6y + 7y + 15 + 6 \\ = 12y + 7y + 21 \\ = 19y + 21[/tex]
Determine the option that is the least expensive for buying a car.
A.paying $21,000 cash
B.making a $5,000 down payment for a $20,000 installment loan with an APR of 4% over 36 months
C.making a $10,000 down payment for a $20,000 installment loan with APR of 2% over 48 months
D.making no payment for a $20,000 installment loan with APR of 1% over 60 months
Answer:
C
Step-by-step explanation:
Just because I think that's the one ^^
Which decimal has least value 0.0093 0.6 0.017
The table shows the amount of money that Memphis saved in his savings account after different amounts of time
Number of Amount
Months Saved
4 $50
8 $100
18 $225
1.what is the constant of proportionality?
(please make sure to show the work)
2. How much money did Memphis save after one month?
GIVEING BRAINLY AND WORTH 50!!! POINTS!!
Answer:
Part 1.) Is in the screenshot.
Part 2.) One month would give him 12.5
For every 1 month saved Memphis has 12.5
50÷2=25
4÷2=2
25÷2=12.5
2÷2=1
Step-by-step explanation:
Hope this helped.
A brainliest is always appreciated.
#1
Slope:-
[tex]\\ \rm\rightarrowtail m=\dfrac{100-50}{8-4}=\dfrac{50}{4}=25/2[/tex]
#2.
Equation:-
[tex]\\ \rm\rightarrowtail y-50=25/2(x-4)[/tex]
[tex]\\ \rm\rightarrowtail 2y=25x[/tex]
So
put x=1[tex]\\ \rm\rightarrowtail 2y=25[/tex]
[tex]\\ \rm\rightarrowtail y=12.5[/tex]
