Answers
9514 1404 393
Answer:
3(4/3)^2543
Step-by-step explanation:
Using logarithms base 2, we have ...
[tex](a_n)^{\log{a_n}}=(a_{n+1})^{\log{a_{n-1}}}\\\\(\log{a_n})(\log{a_n}) = (\log{a_{n-1}})(\log{a_{n+1}}) \\\\ \dfrac{\log{a_{n+1}}}{\log{a_{n}}}=\dfrac{\log{a_n}}{\log{a_{n-1}}}=\dots\dfrac{\log_2{16}}{\log_2{8}}=\dfrac{4}{3}[/tex]
That is, the ratio of each term to the previous is a constant equal to 4/3. This is the definition of a geometric sequence. This sequence has first term 3 and common ratio 4/3, so the general term is ...
[tex]\log_2 a_n=3\left(\dfrac{4}{3}\right)^{n-1}[/tex]
and the 2544th term is ...
[tex]\boxed{\log_2{a_{2544}}=3\left(\dfrac{4}{3}\right)^{2543}}[/tex]
Related Questions
The graph of linear function k passes through the points (-3, 0) and (1, 8). Which statement must be true?
A. The x-Intercept of the graph of k is 8.
B. The slope of the graph of k is 2.
C. The graph of k passes through (-1, -8).
D. The zero of k is 3.
Fr someone help me
Answers
Answer:
B. The slope of the graph of k is 2.Step-by-step explanation:
Find the equation of the line.The slope is:
m = (8 - 0)/(1 + 3) = 2The y-intercept is:
0 = -3*2 + bb = 6The line is:
y = 2x + 6Now lets look at the answer optionsA. The x-Intercept of the graph of k is 8.
The x- intercept is -3, FalseB. The slope of the graph of k is 2.
m = 2, TrueC. The graph of k passes through (-1, -8).
-8 = 2(-1) + 6-8 = 4, FalseD. The zero of k is 3.
x = 0 ⇒ y = 0+ 6 = 6, FalseThe slope of the graph of k is 2.
The correct statement is B.
Given that the graph of linear function k passes through the points (-3, 0) and (1, 8).
We need to check which option is correct.
To determine the correct statement, let's first find the equation of the linear function k using the given points (-3, 0) and (1, 8).
The slope of a linear function is given by:
slope = (change in y) / (change in x)
Using the points (-3, 0) and (1, 8):
slope = (8 - 0) / (1 - (-3))
slope = 8 / 4
slope = 2
So, the slope of the graph of k is 2.
Now we can write the equation of the linear function using the slope-intercept form: y = mx + b, where m is the slope, and b is the y-intercept.
Using the point (1, 8):
8 = 2 × 1 + b
8 = 2 + b
b = 8 - 2
b = 6
Now, the equation of the linear function k is:
y = 2x + 6
Now, let's evaluate the given statements:
A. The x-Intercept of the graph of k is 8.
To find the x-intercept, we set y = 0 and solve for x:
0 = 2x + 6
2x = -6
x = -3
The x-intercept is -3, not 8. So statement A is false.
B. The slope of the graph of k is 2.
We already found earlier that the slope of k is 2. So statement B is true.
C. The graph of k passes through (-1, -8).
Let's check if (-1, -8) satisfies the equation of k:
-8 = 2 × (-1) + 6
-8 = -2 + 6
-8 = 4
The equation is not satisfied, so statement C is false.
D. The zero of k is 3.
To find the zero of k (the x-value where y = 0), we set y = 0 and solve for x:
0 = 2x + 6
2x = -6
x = -3
The zero of k is -3, not 3. So statement D is false.
In conclusion:
Statement A is false.
Statement B is true.
Statement C is false.
Statement D is false.
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A total of 176 valves were used for 8 cars as
they were being assembled. The same number
of valves were used for each car. How many
valves were used for each car?
Answers
BECAUSE IF YOU DIVIDE 176 TO 8 THE ANSWER WILL BE 22.
176÷8=22
HOPE IT HELPS YOU
Kenya picked 18 flowers from her garden. If 3/5 of flowers in her garden remain unpicked, how many flowers are still in her garden?
Answers
Answer:
I think it's 27
Step-by-step explanation:
because if she picked 2/5 of the flowers if u divide 18 by 2 u get 9 so that's 1/5 I think and then if u times that by 3 u get 27 and like that's the 3/5
An athlete drinks 448 ounces of water in 7 days. If the athlete drinks the same amount of water each day, how many ounces does the athlete drink in 1 day?
Answers
Answer:
64 ounces
Step-by-step explanation:
Divide the total number of ounces by the number of days.
448 / 7 = 64 ounces
Which of the following comparisons is NOT true?
A 5,125.5 > 5,125.081
B 617.07 > 617.058
C 15.88 < 15.98
DC 14,109 > 14,21
Answers
Answer:
.
Step-by-step explanation:
Answer:
D.) is not true, though you didn't finish the whole number we can see that 14,109 is not greater than 14,21(0)... I hope this helped.
Iv'e been stuck on this question pls help
Answers
What is the solution to the equation?
-6x - 3 = 21
Answers
Answer:
x = -4
Step-by-step explanation:
−6 − 3 = 21
−6 − 3 + 3 = 21 + 3
= −4
The solution to the equation -6x - 3 = 21 is x = -4.
We must separate the variable x on one side of the equation in order to determine the answer to the equation -6x - 3 = 21.
Here's how to accomplish that:
Step 1: Add 3 to both sides of the equation to start moving the constant term (in this example, -3), which is the first step:
-6x - 3 + 3 = 21 + 3
To put it simply, we have:
-6x = 24
Step 2: Subtract -6 from both sides of the equation to find the value of x:
(-6x) / -6 = 24 / -6
This can be written as x = -4.
Consequently, x = -4 is the answer.
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if Devaughn is 13 years older than Sydney. and The sum of their ages is 67 what is sydney's age
Answers
Answer:
27
Step-by-step explanation:
Sydney's age = x
x + 13 = Sydney's age
67 - 13 = 54
54 divided by 2 = 27
If <1 and <2 are complementary angles, and m<1 = 74", find m<2
what’s the answer?
Answers
Answer:
m<2=16
Step-by-step explanation:
A team of explorers on an expedition was interrupted by bad weather on 20% of the days. If the weather was bad for 45 days, what was the total number of days the team was on its mission?
Answers
Answer:
a total of 9 days
Step-by-step explanation:
20% of 45 is 9
answer
=9days
step by step explanation
20% is always over 100,so you are to do 20 over a hundred of 45 days....since 45 can't divide 100 do 20
[tex] \times [/tex]
45 divide by one hundred and the final answer will be 9
Given the function g ( x ) = x 2 + 10 x + 20 g(x)=x 2 +10x+20, determine the average rate of change of the function over the interval − 9 ≤ x ≤ − 3 −9≤x≤−3.
Answers
Step-by-step explanation:
the average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
so,
(g(-3) - g(-9)) / (-3 - -9)
g(-3) = (-3)² + 10×-3 + 20 = 9 - 30 + 20 = -1
g(-9) = (-9)² + 10×-9 + 20 = 81 - 90 + 20 = 11
-3 - -9 = -3 + 9 = 6
(-1 - 11) / 6
-12/6 = -2
the average change rate in this interval is -2 (or fully -2/1).
How much time is between 9:25am then return home at 7 :10pm
Answers
Answer: the answer is 9 hours 45 minutes
Do you know what 0.009 x 75 is if you do can you help me
Answers
Answer:
.0675
Step-by-step explanation:
Please help me asap with explanation please
Answers
Answer:
[tex] \sqrt{5 \times 5 \times 2 \times {x}^{2} \times {y}^{2} \times y} = \\ 5xy \sqrt{2 \times y} [/tex]
You and a friend are discussing how many sections you completed so far in algebra one you tell your friend I finish three times as many sections as you your friend replies you’ve only finished four more sections and I have how many sections have you and your friend completed
Answers
Answer:
4
Step-by-step explanation:
There are a total of 6 sections that have been completed by him and his friend.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the section be finished by one is y, and finished by his friend be x.
According to 1st condition,
y = 3x - - - - - (1)
According to the second condition,
y = 4 + x
From equation 1
3x = 4 + x
2x = 4
x = 2
Now,
y = 3x
y = 3 * 2
y = 6
Thus, there are a total of 6 sections that have been completed by him and his friend.
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Cadence has cups of strawberries. She needs cup of strawberries to make a batch of tarts. How many batches can she make?
Answers
Answer:
How many cups does she have and how many does she need to make a batch? I do not think this questions is complete
Step-by-step explanation:
Subtract and write your answer as a mixed number 9 4/5 - 7 1/2
Answers
5. The volume of a cube is 125 cubic centimeters. How many centimeters long iseach edge of the cube?5 centimeters11 centimeters15 centimeters42 centimeters
Answers
Answer: 5 cm
Step-by-step explanation:
A cube means all sides have an equal length. therefore you need to find what number times itself 3 times will equal 125
to do this you can also do the cube root(∛) of 125 which will give you 5 cm
to verify your answer, simply do 5 x 5 x 5 which is 125
5x+3x-6=6x+12 what is the answer
Answers
Answer:
x=9
Step-by-step explanation:
1. Combine like terms
2. Add 6 to both sides
3. Simplify
are flies called flies because they fly- well if that's the case why aren't all other bugs that fly called fly's to that's not fair what if they want to be called by an amazing talent that they have to, smh- dragonfly's and flies get special treatment in the name game and it ait fair
( i was dared to post sum du.mb so yeah um )
Answers
Answer:
Fly is any of a large number of insects characterized by the use of only one pair of wings for flight and the reduction of the second pair of wings used for balance. The term fly is commonly used for almost any small flying insect
Step-by-step explanation
i just searched it up
Ronald wanted an allowance. his father gave him a choice of getting it on a weekly or on a daily basis. He said he would either pay him $1.25 a week or pay him in the following manner for a week: On Monday he would give him $0.01; On Tuesday $0.02; On Wednesday $0.04 and on through Sunday. What would you tell Ronald to do so he can get more allowance?
Answers
Step-by-step explanation:
Well the addition of ($0.01+$0.02+$0.04) would be $0.07
And he since he can get $1.25 a week if he chose the weekly option
Since $1.25>$0.07
I would tell Ronald to choose the weekly option for getting more allowance.
you are playing a card game. if you pull an ace you win $26, if you pull the king of hearts you win $204, if you pull a jack or queen you win $13, all other pulls you lose. what price should you be charged to make this a fair game?
A. $5
B. $7
C. $8
D. $6
Answers
Specify?
Answer:
The answer is 8$- Took the test
Step-by-step explanation:
divide 3x^3 -2x^2 -61x -20 by x-5
Answers
7. Conser the following graph of an absolute value function
Port A: Define the domain
Port : Define the range.
Part C. Where is the graph increasing
(-4,1, -2,3)
Part D: Where is the graph decreasing
Part E: EIdentify any relative maximums.
Part F: Identify any relative minimums.
Answers
Answer:
Step-by-step explanation:
guys pls help me!!!!!!!
Answers
Your answer would be 154*. Reason being, if there are two parallel lines and a line running through them, you will only have 2 types of angles. The labeled 154* tells us that the angle to its right would be 26 degrees. Making line m = to 180 degrees at that angle. Then if you did the same thing with line t, you would get angle x to be equal to 154 degrees.
It is complicated like that, or as simple as just taking the 154 and saying that x has the same angle. Due to the fact that both angles are adjacent, they are the same.
WHat is the square root of 76?
Answers
Answer:
It is 8.72 if it needs to be rounded up. If not, it is 8.71779788708
Step-by-step explanation:
Which two numbers have a negative sum?
Answers
Answer:
C
Step-by-step explanation:
convert the fractions to decimals
somebody please help I hate geometry
Answers
Answer:
70
-----
20
Step-by-step explanation:
mark me as brilliant
Solve for the value of y
Answers
8y=32
y=4
We could simply establish the following formula to solve for y:
m < 60° + m < (8y — 2)° = 90°
60° + 8y — 2 = 90°
58° + 8y = 90°
Subtract 58° from both sides
58° — 58° + 8y = 90° — 58°
8y = 32°
Divide both sides by 8:
8y/8 = 32°/8
y = 4
Therefore, the value of y = 4°
Double check whether we derived with the correct answer:
m < 60° + m < (8y — 2)° = 90°
m < 60° + m < 8 (4)— 2° = 90°
m < 60° + m < 32 ° — 2° = 90°
m < 60° + m < 30° = 90°
m < 90° = 90° (True statement). Thus, we have the correct value for y.
Please mark my answers as the Brainliest if you find my explanations helpful :)
What is the slope of the line x = -2?
Answers
Answer:
Since x=−2 is a vertical line, there is no y-intercept and the slope is undefined.
Step-by-step explanation: