I assume you're supposed to find the limit as n approaches infinity, not x.
You have
[tex]\displaystyle \lim_{n\to\infty}\frac{4^n-5.3^n+1}{2.4^n+2} = \lim_{n\to\infty}\frac{\left(\dfrac4{5.3}\right)^n-\left(\dfrac{5.3}{5.3}\right)^n+\dfrac1{5.3^n}}{\left(\dfrac{2.4}{5.3}\right)^n+\dfrac2{5.3^n}} \\\\ = \lim_{n\to\infty}\frac{\left(\dfrac4{5.3}\right)^n-1+\dfrac1{5.3^n}}{\left(\dfrac{2.4}{5.3}\right)^n+\dfrac2{5.3^n}}[/tex]
For |x| < 1, we have lim |x|ⁿ = 0 as n goes to infinity. Then each exponential term converges to 0, which leaves us with -1/0. This means the limit is negative infinity.
On the other hand, perhaps you meant to write
[tex]\displaystyle \lim_{n\to\infty}\frac{4^n-5\times3^n+1}{2\times4^n+2}[/tex]
The same algebraic manipulation gives us
[tex]\displaystyle\lim_{n\to\infty}\frac{\left(\dfrac44\right)^n-5\left(\dfrac34\right)^n+\dfrac1{4^n}}{2\left(\dfrac44\right)^n+\dfrac2{4^n}} = \lim_{n\to\infty}\frac{1-5\left(\dfrac34\right)^n+\dfrac1{4^n}}{2+\dfrac2{4^n}}[/tex]
Again the exponential terms converge to 0, but this time we're left with the limit 1/2.
Explain how to know when to use mean, median, or mode as a measure of
central tendency. For each measure, give an example of a situation where the
center should be used.
Answer:
Step-by-step explanation:
Mean
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Median
Arrange your numbers in numerical order.
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2.
Mode
To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.
Kristen and Stephen share some money on the ratio 3:2 Kristen receives $72. How much will Stephen receive
Answer:
$48
Step-by-step explanation:
A ratio of 3:2 could be $3 and $2, or any multiple of 3 and 2 such as $6 and $4. Kristen corresponds to $3 and receives $72.
$72/$3 = x/$2
3x = 2 * $72
3x = $144
x = $48
Answer: $48
Answer:
$48
Step-by-step explanation:
Since we are given the ratio 3:2 we can use that with the given number to find our missing amount
first, we divide 72 by 3 to find what 1/3 will be 72/3 = 24
Then, we multiply by 2 to find our missing amount 24 * 2 = 48
Write the y-intercept of the line
Answer: -2. Bc if you look on the graph of the y axis you'll see its located at -2.
Hope this helps :)
Step-by-step explanation:
Tom wants to borrow $16,578 for a car. The bank is going to charge him 12% interest annually, compounded monthly. If his car payment is $345.00 a month. How much will he owe at the end of 4 months? (Take this one month at a time. Determine the interest for the month; add it to the principal. Then subtract the payment, and that is your new principal for the next month.)
Answer:
Step-by-step explanation:
Principal, P = $16,578
Interest rate, r = 12% = 0.12
Monthly interest rate = annual interest rate / 12
= 12%/12
= 1%
= 0.01
Time, t = 1 year
Number of period, n = 12
Car payment per month = $345.00
Month 1:
A = P(1 + r/n)^nt
A = 16,578(1 + 0.01/12)^(12)(1)
A = 16,578(1 + 0.000833333)^(12)
= 16578(1.000833333)^12
= 16578(1.0100459608871)
A = $16,744.54
Principal after month 1 repayment = $16,744.54 - $345
= $16,399.54
Month 2:
A = P(1 + r/n)^nt
= $16,399.54(1 + 0.01/12)^(12)(1)
= 16,399.54(1 + 0.000833333)^(12)
= 16,399.54(1.000833333)^12
= 16399.54(1.0100459608871)
= 16,564.289137406431934
= $16,564.29
Principal after month 2 repayment = $16,564.29 - $345
= $16,219.29
Month 3:
A = P(1 + r/n)^nt
= $16,219.29(1 + 0.01/12)^(12)(1)
= 16,219.29(1 + 0.000833333)^(12)
= 16,219.29(1.000833333)^12
= 16219.29(1.0100459608871)
= 16382.228352956532159
= $16,382.23
Principal after month 3 repayment = $16,382.23 - $345
= $16,037.23
Month 4:
A = P(1 + r/n)^nt
= $16,037.23(1 + 0.01/12)^(12)(1)
= 16,037.23(1 + 0.000833333)^(12)
= 16,037.23(1.000833333)^12
= 16037.23(1.0100459608871)
= 16198.339385317426733
= $16,198.34
Principal after month 4 repayment = $16,198.34 - $345
= $15,853.34
Currently, Mike is 8 years more than twice Tom's age. In 3 years from now,
Mike's age
will be three times Tom's age. What are their current ages?
Answer:
The current age of Mike is 12 years old while that of Tom is 2 years old.
Step-by-step explanation:
Let the current age of Mike be m years old and that of Tom be t years old.
Currently
m= 2t +8
3 years from now
Tom's age= t +3
Mike's age
= m +3
= 2t +8 +3
= 2t +11
Given that in three years, Mike's age is 3 times Tom's age,
2t +11= 3(t +3)
Expand:
2t +11= 3t +9
3t -2t= 11 -9
t= 2
Current age of Mike
= 2t +8
= 2(2) +8
= 4 +8
= 12
A cone has a volume of 150 cm cubed and a base with an area of 12 cm square. What is the height of the cone?
(I'm asking this again :') No one answered it.)
P.S Its 30 Points now
SO PLEASE HELPPP tyyyy :)
Answer:
37.5cm
Step-by-step explanation:
V=1/3Bh
150=1/3 12h
150=4h
37.5=h
Bella has joined a new gym in town. The cost of membership is $25 per month. The after-hours policy at the gym allows her to work out late at night for an extra fee of $4 per visit. If Bella's first monthly bill totaled $53, which equation can be used to determine how many times Bella worked out after hours?
Answer:
So, we get
$25+4n = $53 is the required equation.
Therefore, $25+4n = $53 equation can be used to determine how many times Bella worked out after hours.
Step-by-step explanation:
The total monthly bill of the gym = $53
The cost of membership of a month = $25
Let 'n' be extra the number of hours Bella worked on.
The cost for working on extra hours = $4
So, we have to determine the equation, Bella worked out after hours.
We will determine the equation by:
(Monthly cost of membership) + ( cost for extra hours number of hours extra worked on ) = Total monthly bill received
HELP ASAP 2 and 3!! please :)
Answer:
2. D. division property of equality
3. B. transitive
Step-by-step explanation:
2. well, we divide both sides by the same factor 3.
3. the same reason as for 4. we are using that if A = B, and B = 30, then A =30 in both lines.
find the difference between of the greatest and smallest 5 digit number
Answer:
Step-by-step explanation:
The largest 5-digit number is 99999 and the smallest 5-digit number is 10000. If it was mentioned that the largest unique 5-digit number then it would have been 98765 and the smallest 5-digit number would have been 10234.
Hope this answer helps you :)
Have a great day
Mark brainliest
What is the remainder when (x^3 + 1) is divided by (x^2 – x + 1)?
O x +1
Ο x
O 2
Ο 0
Answer:
The answer is 0 .... solution is X+1 the REMAINDER IS 0
Step-by-step explanation:
The remainder when (x³ + 1) is divided by (x² - x + 1) is 0.
The correct option is D.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
We can use polynomial long division to find the remainder of (x³ + 1) divided by (x² - x + 1):
x + 1
-------------
x² - x + 1 | x³ + 0x² + 0x + 1
- (x³ - x² + x)
---------------
x² - x + 1
- (x² - x + 1)
-------------
0
Therefore, the remainder when (x³ + 1) is divided by (x² - x + 1) is 0.
To learn more about Polynomials;
brainly.com/question/11536910
#SPJ7
HELP! (25 points) i think i might know the answer
Answer:
[tex]\sqrt{7}[/tex]
Step-by-step explanation:
I need answers asappppp plz
Answer:
Step-by-step explanation:
10 million= ___ million
Answer:
10
Step-by-step explanation:
Add. State the sum in simplest form.
6/5x + 7/3y
Answer:
6x/5 + 7y/3
Step-by-step explanation:
Answer:
3.53xy
Step-by-step explanation:
I’m probably wrong but give it a try I think
plzzz helppp will mark brainlest stpps plzz if possible
Answer:
c.
Step-by-step explanation:
Law of sines
[tex]\frac{Sin A}{a}[/tex] = [tex]\frac{Sin B}{b}[/tex]
A and B are angles.
a and b are sides opposite corresponding angles.
Which of the following expressions can be used to find x? Solve for x. Round to the nearest hundredth. A tan 28 = x32 ; x=17.01∘ B sin 28 = x32 ; x=15.02∘ C tan 28 = 32x ; x=60.18∘ D tan x= 2832; x=41.19∘
Answer:
B
Step-by-step explanation:
1) solve the following system of Equations by graphing. Label the solution and all intercepts.
Please show me how u did it and graphed it ;-;
Answer:
Um. There is no equation?
Step-by-step explanation:
2x^2-3x+2=x√(3x^2-2)
Which system is equivalent to y=-2x^2 y=x-2
a) y=-2y^2 x=y-2
b) y=-2y^2+2 x=y+2
c) y=-2y^2-8y-8 x=y+2
d) y=-2y^2+8y-8 x=y-2
Answer:
answer C
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y&=&-2x^2\\y&=&x-2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2(y-2)^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2y^2-8y-8\\\end{array}\right.\\\\[/tex]
At a homecoming pep rally, one student will win free tickets to the homecoming dance. There are 2,400 students attending the pep rally. The student council wants to pull the winning student’s name from a container with the school’s mascot on it. Unfortunately, the container only holds 600 names.
Which method can the student council use to ensure each student has a fair chance of winning?
A.
Randomly assign the 2,400 students to four equal groups. Select a group at random and put all the names from that group in the container. Randomly select the winner from the container.
B.
Put the names of the first 600 students who arrive at the pep rally in the bag. Randomly select the winner from the container.
C.
Select a section of the bleachers and only put the names of students sitting in that section in the container. Randomly select the winner from the container.
D.
Select a grade and only put the names of students from that grade in the container. Randomly select the winner from the container.
Answer:
A
Step-by-step explanation:
Answer A. Logically speaking there is no fair chance unless they use all the names but we can rule out C by the higher chance of students crowding, B is less likely as selecting winners from students who arrive first would be nearly the same as who bought their tickets first. D, selecting a grade excludes (estimating) around 1500 students or more from being included. A is the only logical answer left and by dividing them randomly you give everyone a full chance.
Factor x4 – 81. Question 20 options: A) (x2 + 3)(x2 – 3) B) (x2 – 9)(x + 3)(x – 3) C) (x2 + 9)(x + 3)(x – 3) D) (x + 3)2(x – 3)2
Answer:
C is correct
Step-by-step explanation:
A square minus a square can always be factored into the square root of the 1st term plus and minus the square root of the 2nd term. So
x**4 - 81 = (x**2 + 9)(x**2 -9) = (x**2 + 9) (x + 3)(x - 3)
The graph of a quadratic function
displays output values that approach
negative infinity. What do you know
about the leading coefficient of this
function?
A
The leading coefficient is negative.
B
The leading coefficient is positive.
Answer:
A
The leading coefficient is negative.
Step-by-step explanation:
Quadratic equation:
A quadratic equation has the following format:
[tex]y = ax^2 + bx + c[/tex]
The leading coefficient is a.
a negative:
The graph of the function is concave down, that is, it displays values that approach negative infinity.
a positive:
The graph of the function is concave up, that is, it displays values that approach up infinity.
In this question:
Displays values that approach negative infinity, so the leading coefficient is negative, and the correct answer is given by option A.
Answer:
B it's positive.. I went with negative because that's what it said, but it was wrong!
Step-by-step explanation:
If Sunil earns $3672 per month, what is his annual salary?
Answer:
$44064
Step-by-step explanation:
Sunil earns $3672 every month. To find out his annual salary, we will need to multiply this monthly salary by the number of months in a year; 12.
3672 * 12 = $44064
DIVISON METHOD OF 527,646,1105
Answer:
17 is the answer
Step-by-step explanation:
Someone plz help me and show the work 10 points!
Answer:
78°
Step-by-step explanation:
you have to add it up and then divide after multiply
Help me pls‼️‼️‼️❤️❤️
Answer:
= 50%
Step-by-step explanation:
There is one point, random number = 1
There are two circles, sample space = 2
[tex]{ \tt{probability = \frac{1}{2} }} \\ { \tt{percentage = \frac{1}{2} \times 100\% }} \\ = 50\%[/tex]
Answer:
25%
Step-by-step explanation:
1. Find the area of both Circles: [tex]A = \pi r^{2}[/tex] [tex]A = \pi 2^{2}[/tex] = [tex]4\pi[/tex] [tex]A = \pi 1^{2} = \pi[/tex]
2. [tex]\frac{\pi }{4\pi }[/tex] to find the percentage
3. 0.25 = 25%
Given JIH~ LMN. what is the value of LN?
Answer:
7 units
Step-by-step explanation:
In similar triangles, corresponding sides are same ratio.
[tex]\frac{LN}{JH}=\frac{LM}{JI}\\\\\frac{LN}{14}=\frac{5}{10}\\\\LN=\frac{5}{10}*14\\\\LN=7[/tex]
Y= 3x+6; (4,7) in slop intercept form
What we are given:
*equation
* intercepts (4,7)
All we have to do is plug in what we know:
Y= 3x + 6
x=4 and y= 7
NEW EQUATION:
7= 3(4) + 6
7= 12+6
7= 18
then divide 18 by 7
18/7= 2.5
Find the missing side of the right triangle
Work Shown:
a^2 + b^2 = c^2
x^2 + 10^2 = 15^2
x^2 + 100 = 225
x^2 = 225 - 100
x^2 = 125
x = sqrt( 125 )
Which graphs show functions with direct variation? select three options.
Answer:
the daily graphs
Step-by-step explanation:
the news paper
Answer:
B C E
Step-by-step explanation:
