Answer:
See explanation
Step-by-step explanation:
Solving (a):
[tex]a_n = 6a_{n-1}[/tex] where [tex]a_0 = 2[/tex]
n = 1
[tex]a_n = 6a_{n-1}[/tex]
[tex]a_1 = 6a_{1-1}[/tex]
[tex]a_1 = 6a_{0}[/tex]
Substitute 2 for [tex]a_0[/tex]
[tex]a_1= 6 * 2[/tex]
[tex]a_1= 12[/tex]
n = 2
[tex]a_n = 6a_{n-1}[/tex]
[tex]a_2 = 6a_{2-1}[/tex]
[tex]a_2 = 6a_{1}[/tex]
Substitute 12 for [tex]a_1[/tex]
[tex]a_2= 6 * 12[/tex]
[tex]a_2= 72[/tex]
n = 3
[tex]a_n = 6a_{n-1}[/tex]
[tex]a_3 = 6a_{3-1}[/tex]
[tex]a_3 = 6a_2[/tex]
Substitute 72 for [tex]a_2[/tex]
[tex]a_3= 6 * 72[/tex]
[tex]a_3= 432[/tex]
n = 4
[tex]a_n = 6a_{n-1}[/tex]
[tex]a_4 = 6a_{4-1}[/tex]
[tex]a_4 = 6a_{3}[/tex]
Substitute 432 for [tex]a_3[/tex]
[tex]a_4 = 6 * 432[/tex]
[tex]a_4 = 2592[/tex]
n = 5
[tex]a_n = 6a_{n-1}[/tex]
[tex]a_5 = 6a_{5-1}[/tex]
[tex]a_5 = 6a_4[/tex]
Substitute 2592 for [tex]a_4[/tex]
[tex]a_5 = 6 * 2592[/tex]
[tex]a_5 = 15552[/tex]
n = 6
[tex]a_n = 6a_{n-1}[/tex]
[tex]a_6 = 6a_{6-1}[/tex]
[tex]a_6 = 6a_{5}[/tex]
Substitute 15552 for [tex]a_5[/tex]
[tex]a_6 = 6 * 15552[/tex]
[tex]a_6 = 93312[/tex]
[tex]a_1= 12[/tex] [tex]a_2= 72[/tex] [tex]a_3= 432[/tex] [tex]a_4 = 2592[/tex] [tex]a_5 = 15552[/tex] [tex]a_6 = 93312[/tex]
Solving (b):
[tex]a_n = a^2_{n - 1[/tex] where [tex]a_1 = 2[/tex]
We have
[tex]a_1 = 2[/tex] which serves as the first term
n =2
[tex]a_n = a^2_{n - 1[/tex]
[tex]a_2 = a^2_{2-1}[/tex]
[tex]a_2 = a^2_{1}[/tex]
Substitute 2 for [tex]a_1[/tex]
[tex]a_2 = 2^2[/tex]
[tex]a_2 = 4[/tex]
n = 3
[tex]a_3 = a^2_{3-1}[/tex]
[tex]a_3 = a^2_{2}[/tex]
[tex]a_3 = 4^2[/tex]
[tex]a_3 = 16[/tex]
n = 4
[tex]a_4 = a^2_{4-1}[/tex]
[tex]a_4 = a^2_3[/tex]
[tex]a_4 = 16^2[/tex]
[tex]a_4 = 256[/tex]
n =5
[tex]a_5 = a^2_{5-1[/tex]
[tex]a_5 = a^2_4[/tex]
[tex]a_5 = 256^2[/tex]
[tex]a_5 = 65536[/tex]
n = 6
[tex]a_6 = a^2_{6-1[/tex]
[tex]a_6 = a^2_{5[/tex]
[tex]a_6 = 65536^2[/tex]
[tex]a_6 = 4294967296[/tex]
[tex]a_1 = 2[/tex] [tex]a_2 = 4[/tex] [tex]a_3 = 16[/tex] [tex]a_4 = 256[/tex] [tex]a_5 = 65536[/tex] [tex]a_6 = 4294967296[/tex]
Solving (c):
[tex]a_n=a_{n-1}+3a_{n-2};[/tex] [tex]a_0=1[/tex] ; ; [tex]a_1=2[/tex]
[tex]a_1=2[/tex] ---- First term
n = 2
[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes
[tex]a_2=a_{2-1}+3a_{2-2}[/tex]
[tex]a_2=a_1+3a_0[/tex]
Substitute values for a1 and a0
[tex]a_2=2+3 * 1[/tex]
[tex]a_2=2+3[/tex]
[tex]a_2=5[/tex]
n = 3
[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes
[tex]a_3=a_{3-1}+3a_{3-2}[/tex]
[tex]a_3=a_{2}+3a_{1}[/tex]
[tex]a_3=5+3 * 2[/tex]
[tex]a_3=5+6[/tex]
[tex]a_3=11[/tex]
n = 4
[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes
[tex]a_4=a_{4-1}+3a_{4-2}[/tex]
[tex]a_4=a_{3}+3a_{2}[/tex]
[tex]a_4=11+3 * 5[/tex]
[tex]a_4=11+15[/tex]
[tex]a_4=26[/tex]
n = 5
[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes
[tex]a_5=a_{5-1}+3a_{5-2};[/tex]
[tex]a_5=a_{4}+3a_3[/tex]
[tex]a_5=26+3 * 11[/tex]
[tex]a_5=26+33[/tex]
[tex]a_5=59[/tex]
n = 6
[tex]a_n=a_{n-1}+3a_{n-2};[/tex] becomes
[tex]a_6=a_{6-1}+3a_{6-2}[/tex]
[tex]a_6=a_{5}+3a_4[/tex]
[tex]a_6=59+3*26[/tex]
[tex]a_6=59+78[/tex]
[tex]a_6=137[/tex]
[tex]a_1=2[/tex] [tex]a_2=5[/tex] [tex]a_3=11[/tex] [tex]a_4=26[/tex] [tex]a_5=59[/tex] [tex]a_6=137[/tex]
Solving (d):
[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex]; [tex]a_0=1[/tex]; [tex]a_1=1[/tex]
[tex]a_1=1[/tex] --- First term
n = 2
[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes
[tex]a_2=2 * a_{2-1}+2^2a_{2-2}[/tex]
[tex]a_2=2 * a_1+4*a_0[/tex]
[tex]a_2=2 * 1+4*1[/tex]
[tex]a_2=2 +4[/tex]
[tex]a_2=6[/tex]
n = 3
[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes
[tex]a_3=3 * a_{3-1}+3^2 * a_{3-2}[/tex]
[tex]a_3=3 * a_{2}+9 * a_{1}[/tex]
[tex]a_3=3 * 6+9 * 1[/tex]
[tex]a_3=18+9[/tex]
[tex]a_3=27[/tex]
n = 4
[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes
[tex]a_4=4*a_{4-1}+4^2*a_{4-2}[/tex]
[tex]a_4=4*a_{3}+16*a_{2}[/tex]
[tex]a_4=4*27+16*6[/tex]
[tex]a_4=204[/tex]
n = 5
[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes
[tex]a_5=5 * a_{5-1}+5^2 * a_{5-2}[/tex]
[tex]a_5=5 * a_{4}+25 * a_{3}[/tex]
[tex]a_5=5 * 204+25 *27[/tex]
[tex]a_5=1695[/tex]
n = 6
[tex]a_n=na_{n-1}+n^2a_{n-2}[/tex] becomes
[tex]a_6=6 * a_{6-1}+6^2*a_{6-2}[/tex]
[tex]a_6=6 * a_{5}+36*a_{4}[/tex]
[tex]a_6=6 * 1695+36*204[/tex]
[tex]a_6=17514[/tex]
[tex]a_1=1[/tex] [tex]a_2=6[/tex] [tex]a_3=27[/tex] [tex]a_4=204[/tex] [tex]a_5=1695[/tex] [tex]a_6=17514[/tex]
Solving (e):
[tex]a_n= a_{n-1}+a_{n-3};\ a_0=1; a_1=2; a_2=0[/tex]
First term: [tex]a_1=2[/tex]
Second Term: [tex]a_2=0[/tex]
n = 3
[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes
[tex]a_3= a_{3-1}+a_{3-3}[/tex]
[tex]a_3= a_{2}+a_0[/tex]
[tex]a_3= 0+1[/tex]
[tex]a_3= 1[/tex]
n = 4
[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes
[tex]a_4= a_{4-1}+a_{4-3}[/tex]
[tex]a_4= a_{3}+a_{1}[/tex]
[tex]a_4= 1+2[/tex]
[tex]a_4=3[/tex]
n = 5
[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes
[tex]a_5= a_{5-1}+a_{5-3}[/tex]
[tex]a_5= a_{4}+a_{2}[/tex]
[tex]a_5= 3 + 0[/tex]
[tex]a_5= 3[/tex]
n = 6
[tex]a_n= a_{n-1}+a_{n-3}[/tex] becomes
[tex]a_6= a_{6-1}+a_{6-3}[/tex]
[tex]a_6= a_{5}+a_{3}[/tex]
[tex]a_6= 3 + 1[/tex]
[tex]a_6= 4[/tex]
[tex]a_1=2[/tex] [tex]a_2=0[/tex] [tex]a_3= 1[/tex] [tex]a_4=3[/tex] [tex]a_5= 3[/tex] [tex]a_6= 4[/tex]
find the measure of 0. (to the nearest tenth).
A) 36.9
B) 38.7
C) 51.3
D) 53.1
Answer:
B) 38.7
Step-by-step explanation:
Answer:
A) 36.9
Step-by-step explanation:
took the test :)
15x + 10 - 6 PLEASE HELP ME SOLVE THIS PLEASE SHOW WORK TO? THANK YOU
Brittany is selling car magnets she purchases them for 7.50 each and marks up the price by 30% how much planning to charge
Answer:
0.25
Step-by-step explanation:
i hope this helps! :]
4+ (-1 2/3) what’s the answer
Answer:
2 1/3
Step-by-step explanation:
What percentage of the eggs hatched?
Answer:
Is there supposed to be a picture or what??
Step-by-step explanation:
how to find a inequality
Which equations has a solution of X=1.5
Find the 3 ×3 matrix that produces the described composite 2D transformation below, using homogeneous coordinates. Translate by ( −6, 3), and then scale the x-coordinate by 0.3 and the y-coordinate by 1.3.
Answer:
「0.8 0 -2
0 1.2 3
0 0 1 」
Step-by-step explanation:
The [tex]3\times 3[/tex] matrix will be "[tex]\left[\begin{array}{ccc}0.3&0&-1.8\\0&1.3&3.9\\0&0&1\end{array}\right][/tex]".
According to the question,
The [tex]3\times 3[/tex] with homogenous coordinates is:
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
Translation from (0, 0) to (a, b) will be:
[tex]T = \left[\begin{array}{ccc}1&0&a\\0&1&b\\0&0&1\end{array}\right][/tex]
Here,
a = -6b = 4Translation by (-5,4)
[tex]T = \left[\begin{array}{ccc}1&0&-6\\0&1&3\\0&0&1\end{array}\right][/tex]
Now,
Let's find the scaling matrix 5.Scale the x-coordinated by "0.3" and y-coordinates by "1.3".i.e.,
[tex]S = \left[\begin{array}{ccc}0.3&0&0\\0&1.3&0\\0&0&1\end{array}\right][/tex]
then,
The [tex]3\times 3[/tex] matrix will be:
→ [tex]A = ST[/tex]
[tex]= \left[\begin{array}{ccc}0.3&0&0\\0&1.3&0\\0&0&1\end{array}\right] \ \left[\begin{array}{ccc}1&0&-6\\0&1&3\\0&0&1\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}0.3&0&-0.3\times 6\\0&1.3&1.3\times 3\\0&0&1\times 1\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}0.3&0&-1.8\\0&1.3&3.9\\0&0&1\end{array}\right][/tex]
Thus the above answer is correct.
Learn more about Matrix here:
https://brainly.com/question/9035564
Solve this system for m and b 342=23m+b 147=10m+b
Answer:
b = − 3
m = 5 ( 39 + 2 m ) /23
Use the following information for the questionThe average travel time to work for a person living in kokomo is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time follows a normal distribution. Approximately what percentage of people living in Flint have a travel time to work that is less than 12.5 minutes?A) 15% B) 25% C) 75% D) None of these.
Answer:
16%
Step-by-step explanation:
We solve using z score formula
= z = (x-μ)/σ, where
x is the raw score = 12.5 minutes
μ is the population mean = 17 minutes
σ is the population standard deviation = 4.5 minutes
z = 12.5 - 17/4.5
z = -1
Probability value from Z-Table:
P(x<12.5) = 0.15866
Converting to percentage
= 0.15866 × 100
= 15.866%
Approximately , the percentage of people living in Flint have a travel time to work that is less than 12.5 minutes is 16%
find the inverse of the function y equals x squared minus 12
Answer:
Step-by-step explanation:
y=x^2-12
The inverse is
√x+12, -√x+12
DUE IN A HOUR!!!!!!!!!!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
y=1/4x+7/4
Step-by-step explanation:
-25.63+ -30.59 ??? Can someone let me know what this equals?
Answer:
= -56.22
Step-by-step explanation:
have a great day
pls mark as brainliest!
hope this helped!
Answer:
-56.22
just calculated it (:
On his most recent math test, Jeremy answered 48 questions correct out of 80 total questions. Which statement can be made about Jeremy's math test?
Answer:
Jeremy has gotten more than half of the test's questions correctly.
Step-by-step explanation:
To get half of the questions correctly, Jeremy needed at least 40, and Jeremy got more than 40, meaning he got more than half.
Aarti posted a comment on her blog. Each day the number of responses to her comment was 125% of the number she
received on the previous day. If there were 64 responses the first day, how many were there on the fourth day?
O 100
112
оооо
125
132
Mark this and return
Save and Exit
Next
Submit
Answer:
125
Step-by-step explanation:
Answer:
125
Step-by-step explanation:
What is the median for 6.74
Answer:
sorry i needed the points for school
Step-by-step explanation:
Answer:
Median normally is the middle figure in a set of numbers. not totally sure.
Please help I’m stuck on this question
Answer:
A. this is a vector, so you need a bar on top (ie not D)
Step-by-step explanation:
70 feet in 2 rolls as a unit rate
Answer:
What is the question?...
Answer: 35
Step-by-step explanation:
How much sparkling water would you need to make 100 quarts of sparkling grape juice? (Recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quarts of grape juice)
Answer:
66.6666
Step-by-step explanation
This is the answer because I found it up here and I got the answer right.
to convert measurements in the metric system you can move the decimal point left or right why does this work?
Answer:
C
Step-by-step explanation:
i took the assignment
Does the three in 3.0 mean
Answer:
the 3 is in the tenths place, so it represents 3.
Step-by-step explanation:
<3
True or false the sum of two negative numbers is always negative explain why or why not this is true or false
Answer:
true
Step-by-step explanation:
Let's say you have -7 dollars in your bank account, and then you go and spend 5 more, which is -5, now you have -12 bucks in your account
Answer:
true!
Step-by-step explanation:
if you add negative numbers together, it will have to be negative because you are not adding positive numbers. same thing with positive numbers, if you add two positive numbers together, the sum will be a bigger positive number!
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
105 is on the graph
Answer:
Probability =0.8854 (Approx)
Step-by-step explanation:
Given:
Mean μ = 100
Standard deviation σ = 15
Computation:
Z at 70
Z = (70-100)/15
Z at 70 = -2
Z at 120
Z = (120-100)/15
Z at 100 = 1.33
Probability = φ(1.33) - φ(-2.0)
Probability = 0.9082-0.0228
Probability = 0.8854 (Approx)
Student can eat 1/8 of a pizza. If there are 24 students in David's class how many pizzas does David need
Answer: 7 boxes of pizza
Step-by-step explanation:
8x3=24
Answer:
David needs 3 pizzas.
Step-by-step explanation:
This is grammatically incorrect, but based on the information provided, I would infer that each student eats *only* 1/8 of a pizza. You would need 3 pizzas, as 3 x 8 =24.
Determine if the following vectors are orthogonal, parallel, or neither.
<2,5> and <-4, 10 >
Answer:
the are parallel to eachother
5(x+2) - 3 = 2x + 7 + 3x *
One Solution
No Solution
Infinitely Many Solutions
5x + 27x - 10 = 8(4x +10)
One Solution
No Solution
Infinitely Many Solutions
what is the slope of the line
Answer:
y-mx+b
Step-by-step explanation:
What's the recursive rule for the arithmetic sequence described in the following list? Use the rule to find the eighth term of the sequence.
5, 9, 13, 17, 21
Answer:
33
Step-by-step explanation:
T8 = A + (8 - 1) d
T8 = 5 + 7d
T8 = 5 + 7(4)
T8 = 5 + 28
T8 = 33
note : d is the common difference gotten from T2 - T1
Answer:
33
Step by step explanation:
Eight term of the sequence = a + 7d
where:
a= first term
d= common difference
first term = 5
common difference = 4
= 5 + 7(4)
= 5 + 28
= 33
A 30 foot cable is being cut into pieces that are 7 1/2 feet long
Answer:
Cool
Step-by-step explanation:
Do you mean a 30 foot cable is being cut into pieces that are 7 1/2 feet long, how many pieces is it cut into?
Answer:
goodluck
Step-by-step explanation:
what is n in a hexagon
Answer:
For a hexagon, n=6.
Step-by-step explanation:
Answer:
n = 6
Step-by-step explanation:
A hexagon has 6 sides