A geometric sequence is given by the recursive rule $a_1=\frac{2}{3},\ a_n=3a_{n-1}$ . Give an explicit rule for the nth term of the sequence $b_1,\ b_2,\ b_3,\ \dots\ ,$ given that $b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots$ .
Answer:
[tex]b_n = \frac{2}{27} (9^n)[/tex]
Step-by-step explanation:
Given
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Required
An explicit rule for [tex]b_1,\ b_2,\ b_3,\ \dots[/tex]
Where [tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
We have:
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Calculate a2
[tex]a_2 = 3a_{2-1}[/tex]
[tex]a_2 = 3a_1[/tex]
[tex]a_2 = 3 * \frac{2}{3}[/tex]
[tex]a_2 = 2[/tex]
Calculate a3
[tex]a_3 = 3a_{3-1}[/tex]
[tex]a_3 = 3a_2[/tex]
[tex]a_3 = 3 *2[/tex]
[tex]a_3 = 6[/tex]
Calculate a4
[tex]a_4 = 3a_{4-1}[/tex]
[tex]a_4 = 3a_3[/tex]
[tex]a_4 = 3*6[/tex]
[tex]a_4 = 18[/tex]
Calculate a5
[tex]a_5 = 3a_{5-1}[/tex]
[tex]a_5 = 3a_4[/tex]
[tex]a_5 = 3*18[/tex]
[tex]a_5 = 54[/tex]
So:
[tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
[tex]a_1=\frac{2}{3}[/tex] [tex]a_3 = 6[/tex] [tex]a_5 = 54[/tex]
The above sequence form a geometric sequence.
Calculate common ratio (r)
[tex]r = \frac{b_3}{b_2}[/tex]
[tex]r = \frac{a_5}{a_3}[/tex]
[tex]r = \frac{54}{6}[/tex]
[tex]r = 9[/tex]
So, the explicit formula is:
[tex]b_n = b_1 * r^{n-1[/tex]
[tex]b_1=a_1[/tex], so:
[tex]b_n = a_1 * r^{n-1[/tex]
[tex]a_1=\frac{2}{3}[/tex], so:
[tex]b_n = \frac{2}{3} * 9^{n-1[/tex]
Split:
[tex]b_n = \frac{2}{3} * \frac{9^n}{9}[/tex]
[tex]b_n = \frac{2}{3*9} (9^n)[/tex]
[tex]b_n = \frac{2}{27} (9^n)[/tex]
The explicit rule is: [tex]b_n = \frac{2}{27} (9^n)[/tex]
hii pls help i’ll give brainliest
Answer:
Disagree, Disagree, Agree
Step-by-step explanation:
Hope this helps! BTW I am in 6th grade doing 8th grade math so trust me if u want.
Which are examples of statistical questions?
Question 11
Question 2
Question 3
Question 4
Questions
What is Mikki's favorite time to go to sleep?
What time does each student go to sleep?
What time does Malia wake-up in the morning?
What time does each student wake-up?
O questions 1 and 2
O questions 1 and 3
questions 2 and 4
questions 2 and 3
I don't really understand this
Can someone help me with this one problem!!!!
Answer: No
Step-by-step explanation: No because y is not the same as x.
The largest three-digit multiple of 6 ?
Answer:
Step-by-step explanation:
100 is the smallest three-digit number. 999 is the highest three-digit number. 102 is the smallest three-digit number divisible by six. 996 is the largest three-digit number divisible by six.
Answer:
744Step-by-step explanation:
The largest 3-digit multiple of 6 that uses digits 4 and 4.
The multiple of 6 is an even number which is divisible by 3.
Numbers are only divisible by 3 if the sum of the digits is divisible by 3.
We have 4 + 4 = 8 and the largest digit to add is 7.
744 is the largest possible number.Proof:
744/6 = 124only need this one please....
its timed
please solve!!!!!!!!!
2(14y-3y+28x+12.2-5y-17.5)
then which one is it equavilint to?
A. 84x-167-5.3
B. 28x-6y-10.6
C. 42x-8y-5.3
D. 84x-16y-5.3
help please its timed 20 points
Answer:
56x+12y-10.6
Step-by-step explanation:
The multiple choice answer is B.
Answer:
Step-by-step explanation:
2(14y-3y+28x+12.2-5y-17.5) = 2(14y - 3y - 5y + 28x + 12.2 - 17.5)
= 2( 6y + 28x - 5.3)
= 2*6y + 28x* 2 - 5.3*2
= 12y + 56x - 10.6
When an equation in one variable is solved using a system of equations, the solution is always the
of each intersection.
Answer:
When an equation in one variable is solved using a system of equations, the solution is always the x-coordinate of each intersection.
Step-by-step explanation:
Answer:
1st part: X Coordinate
2nd part: A and C
Step-by-step explanation:
The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?
150
300
450
600
y=360
Step-by-step explanation:
y goes up by 30 everytime and would start at 30 if X =1, so X x 30= y. 12 x 30= 360=y
Answer:
300 or B
Step-by-step explanation: give the other person brainliest
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 70(0.96)
Answer:
it is a decay, it's value drops by 4%
Step-by-step explanation:
0.96 is less than 1 so it is a decay function.
1-0.96 = 0.04 so it drops at the rate of 4%
can u guys give me kobe faimley fun facts PLZZ
Answer:
His father spent eight seasons playing in the NBA and an additional eight years playing professional basketball
Step-by-step explanation:
The table below displays the enrollment of freshmen taking Algebra 1. Geometry, or Algebra 2.
The total number of girls enrolled is equal to the number of boys.
There are twice as many boys enrolled in Algebra 1 as boys enrolled in Geometry.
Based on this information, complete the two-way table below.
Answer:
for the boys it is 92 then 58 and the total is 150 an then 68 for the girls then for the total it is 100
The missing values in the two-way table is shown in the table in the image attached below.
What is a Two-way Table?A two-way table can be described as a table that displays the frequencies of two categorical variables, in such a way that, one category is represented by columns and the other by rows.
Given the information, the missing values in the two-way table would be:
Total number of boys enrolled = 150
Boys that enrolled in Algebra 1 = 2(46) = 92
Boys that enrolled in Algebra 2 = 150 - 92 - 46 = 12
Girls that enrolled in Algebra 1 = 150 - 54 - 28 = 68
Total for boys and girls that enrolled in Geometry = 46 + 54 = 100.
Therefore, the missing values in the two-way table is shown in the table in the image attached below.
Learn more about two-way table on:
https://brainly.com/question/20744563
Carl Lock took out a simple interest loan at 12.75% interest for 12 months. His previous balance is $942.36.
What is his final payment if the loan is paid off with the next payment?
Answer:I believe it is $955.11
Step-by-step explanation:
Divide the interest by 12 (number of months) which comes to about $1.07 (rounded) multiply that by 12 which give you with how much the total interest is, add it by the total and boom
Joaquin walked exactly 3 _ 4 of a mile. According to the line plot, what is the difference between the distance Joaquin walked and the least distance any of the other students walked to school?
Answer:
The difference is [tex]\frac{3}{8}[/tex] mile
Step-by-step explanation:
The question is incomplete, as the line plot is not attached.
I will answer this question with the attached line plot.
From the question:
[tex]Joaquin = \frac{3}{4}[/tex]
From the attached line plot:
[tex]Least = \frac{3}{8}[/tex]
The difference (D) is:
[tex]D = Joaquin - Least[/tex]
[tex]D = \frac{3}{4} - \frac{3}{8}[/tex]
Take LCM
[tex]D = \frac{6 - 3}{8}[/tex]
[tex]D = \frac{3}{8}[/tex]
Hence: The difference is [tex]\frac{3}{8}[/tex] mile
please answer asap!!!!
first answer will get brainliest
Answer:
The answer is C
Step-by-step explanation:
Answer: )D
Step-by-step explanation:
Find the value of x .
Answer:
98
Step-by-step explanation:
x+30+52=180
x+82=180
x=180-82
x=98
Franco earns $8 per hour at his after-school job. Last week, he received a paycheck of more than $168. If he worked for h hours that week, find all the inequalities that represent this situation.
a.) 8 x h > 168
b.) 8 > 22 x h
c.) 8 x h < 168
d.) h > 21
e.) h < 21
Answer: A and D
Step-by-step explanation:
if he earns $8 an hour and he got $168 and h= the hours then
h=8 x 21 = 168
Answer:
The other person is correct.
Step-by-step explanation:
what is 80% of 25 help me
what is the 30th term In the sequence 10,7,4,1-3,...
determine the term to term rule
Answer:
7
Step-by-step explanation:
ok so it 7 but 10 is out so is 3
Find the sum of the measures of the interior angles of a convex 45-gon.
Answer: 7740
Step-by-step explanation: take 180(n-45) and n represents the sides
The sum of the measures of the interior angles of a convex 45-gon.
is 7740.
What is a cube?It is a polygon having six faces.
The volume of a cube is a side³.
We have,
Polygon with side = 45
Sum of interior angles of any polygon = (n - 2) x 180 ______(1)
Now,
n = 45
So,
Substituting n in (1)
(n - 2) x 180
= (45 - 2) x 180
= 43 x 180
= 7740
Thus,
The sum of the measure of the interior angles is 7740.
Learn more about cubes here:
https://brainly.com/question/11168779
#SPJ2
!!!OMGG I NEED HELP QUESTION AT THE BOTTOM!!!!
Answer:
C I think
Step-by-step explanation:
A.75
B.80
C.95
D.110
Answer:
D. 110
Step-by-step explanation:
CDHK ≅ MPTS
So: D = P
P = 110°
D = 110°
Is 1/10 closer to 0 or 1/2 ?
Answer:
its much closer to 0
Step-by-step explanation:
1/2 is more 5/10 and 0 is 0/10
0 is one away from one and 5 is 4 away
Which of the following equations has infinitely many real solutions?
A. 2(x - 7) = 2x + 14
B. 2(x - 7) = 2x – 14
C. 2x + 1 = 2x - 1
D. 2x + 1 = x - 1
Answer:
B - 2(x -7) = 2x - 14
Step-by-step explanation:
If you expand this equation, you get 2x-14 = 2x-14. This means that the equation will be true for any x, and has infinitely many solutions
Hopefully this helps! Let me know if you have any questions
Mr. Hoosier has gathered all these data about his finances.
Salary $159,000
Taxable interest $5600
Municipal Bond interest $15,000
Total Itemized deductions $9500
The personal exemption is $4700. The standardized deduction for a single filer is 5000.
Answer:
1. His tax is $37,490.
2. His average effective tax rate is 22%
3. His average tax rate is 24.93%
4. His marginal tax rate is 35%.
5. His tax liability will fall by $170
6. His tax liability will fall by $500.
Step-by-step explanation:
Note: This question is not complete. See the attached pdf file for the complete question.
The explanation of the answer is now given as follows:
1. What is his tax?
Note: See the attached excel for Mr. Hoosier's Tax Computation Based on the Tax Table in the question.
From the attached excel file, the Net tax is $37,490 which is his tax.
Therefore, his tax is $37,490.
2. His average effective tax rate
His average effective tax rate = Tax / (Taxable income + Tax exempt income) = Tax / (Taxable income +Municipal Bond interest) = $37,490 / ($150,400 + $20,000) = 0.2200, or 22%
3. His average tax rate
Average tax rate = Tax / Taxable Income = $37,490 / $150,400 = 24.93%
4. His marginal tax rate
His marginal tax rate is 35% as in the tax computation used based on the tax table.
5. Assume he discovers that he is eligible for a 500 tax deduction. How much does his tax liability fall with that addition?
Taxable income = 150400 - 500 = $149,900
Based on the tax table in the question, we have:
Tax = 8850 + (149900 - 55000) * 30% = $37,320
Reduction in tax liability = $37,490 - $37,320 =$170
Therefore, his tax liability will fall by $170
6. Now he discovers that he is eligible for a $500 tax credit. How much does his tax liability fall due to this credit?
The purpose of the tax credit is to make tax liability reduced dollar by dollar.
Therefore, if he discovers that he is eligible for a $500 tax credit, his tax liability will fall by $500.
I need help I would appreciate it if u would help me with this problem :)
Answer:
The answer is letter A.
Step-by-step explanation:
The amount that each company charges per hour on the pool is known, however the amount of hours they will be working is not, and is needed to distinguish which company is cheaper. Therefore, the number of hours is substitued by x and it is right next to the amount they charge for each hour. To find what each company charges, you must sum up what they charge and what they charge per hour, times the hours they will have to work on it( which is unknown and by x).
Mrs. Williams has 7 gallon of juice left in a bottle. She pours an equal amount of
juice into 5 glasses to empty the bottle. Which model represents the fractional
amount of the gallon of juice in each glass?
20
LLLL
Answer:
1/20 of a gallon
Step-by-step explanation:
If she divides 1/4 into 5 glasses, the answer would be 0.05, or 1/20 gallons.
what is 30 = –5d – 5
Answer:
-7
Step-by-step explanation:
30=-5d-5
-5d=30+5
-5d=35
d=35/-5
d=-7
help pls, fast to, thx
Answer:
∠b = 64°
Step-by-step explanation:
We know that a complete rotation is 360°, so:
∠b + 57° + 239° = 360°
∠b = 360° - 57° - 239°
∠b = 64°
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help i only need number 3
very urgent need help asap