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 deposit required to accumulate $7700 after investing 3 years in an account that pays an APR of 5% compounded quarterly. How much is earned in interest?
Answer:
The deposit required is $6633.62 and the interest earned is $366.38
Step-by-step explanation:
Compound interest occurs when the interest earned is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It's given the final amount A=$7700 after t=3 years of investment in an account that pays an APR of r=5%=0.05. Since the interests compound quarterly and there are 4 quarters in a year, then n=4.
To find the principal P, we solve the previous equation for P as follows:
[tex]{\displaystyle P=A\left(1+{\frac {r}{n}}\right)^{-nt}}[/tex]
Substituting:
[tex]{\displaystyle P=7700\left(1+{\frac {0.05}{4}}\right)^{-4\cdot 3}}[/tex]
[tex]{\displaystyle P=7700\left(1+0.0125}\right)^{-12}}[/tex]
P=$6633.62
The interest earned is:
I = A - P = $7700 - $6633.62 = $366.38
The deposit required is $6633.62 and the interest earned is $366.38
What is the area of the right triangle shown below?
1.5
2.5
Answer:
Hello! The answer is 1.5
The area of the given right-angle triangle will be 1.5 unit².
What is a triangle?
A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
Given the tringle with,
Base =1.5 unit
Hypotaneous = 2.5 unit
By Pythagoras theorem
Perpendicular² = (Hypo² - Base²)
Perpendicular² = 2.5² - 1.5²
Perpendicular = 2 units.
Now the area of the right-angle triangle is
⇒ (1/2) × base × height.
Area = (1/2) × 1.5 × 2 ⇒ 1.5 unit²
Hence the area of the given triangle will be 1.5 unit².
For more information about triangle
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Harry earns$12 20 per hour Monday to Friday if he works on a Sunday he owns 1.75 times hourly rate how much will Harry earn if he works for 8 hours on a Sunday
Answer:
he will make 170.80 that day
Step-by-step explanation:
12.20*1.75*8
Answer:
good question................
PLEASE ANSWER ASAP Find the slope of the line
Answer:
4
Step-by-step explanation:
Slope is [tex]\frac{rise}{run}[/tex]. Or, in other words the distance it travels in the y direction divided by the distance it travels in the x direction. Each time the y variable increments +4 and the x variable increments +1. Which means the line rises 4 units every time it runs 1 unit.
Slope=[tex]\frac{rise}{run}=\frac{4}{1}=4[/tex]
Express 8e^i16pie in rectangular, polar and trignometric form?
Euler's formula immediately gives
[tex]8e^{i\cdot16\pi}=8\cos(16\pi)+8i\sin(16\pi)=8[/tex]
and the equation above lists, from left to right, the polar, trigonometric, and rectangular forms.
What is the equation of the line that passes through the points (3,6) and (-4,-8)
Hi
You have two points A ( X;Y) and B ( X ; Y)
slope is : ( Yb -Ya) / (Xb -Xa )
( -8 - 6 ) / ( -4 - 3) = -14 /-7 = 2
slope is 2
now : we have : 2 ( 3) +... = 6
6 +0 = 6
equation of line is : y = 2x
A company that makes hair-care products had 4,000 people try a new shampoo. Of the 4,000 people, 24 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
The answer is 0.7%
Hope this helped!
Answer:
0.6%
Step-by-step explanation:
Percentage = 24/4000 *100
=0.6%
Mr. Chavez has assets of $250,000 and liabilities of $18,000. He decides to finance the entire amount of the purchase of a car valued at $26,000. Which of the following is true? a. Mr. Chavez increased his assets. b. Mr. Chavez increased his net worth. c. Mr. Chavez increased both his assets and net worth. d. Mr. Chavez did not increase his assets or his net worth. Please select the best answer from the choices provided A B C D
Answer:
C.
Step-by-step explanation:
Answer: C. Mr Chavez increased both his assets and net worth
Step-by-step explanation: edgenu 2021
what is the 50th term of the sequence that begins -4,2,8,14,...?
A. 290
B. 294
C. 296
D. 300
Answer:
B
Step-by-step explanation:
I am learning this now and I used the equation I'm learning and I got 294.
Answer:
d
Step-by-step explanation:
d because 50th term is 300....50×6=300 thats the answerFind slope or line grab
Answer:
Step-by-step explanation:
divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
Find three consecutive odd integers such that the sum of the first and the third is 34,
HURRY PLEASE
Answer:
15,17,19
Step-by-step explanation:
assume the first number is X which means the third number will be X+4 so X+ X+4=34
solve for X which will be 15
thus the numbers are 15,17 and 19
please help me ig :/
Answer:
either A&C of B&C
Step-by-step explanation:
why i think that is because perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°). and both A&C of B&C are (90°).
Francesca obtains a loan of $18.965.00. The loan has a simple interest rate of 3%. How much interest will Francesca owe at the end of the first year?
Answer:
$568.95
Step-by-step explanation:
Given parameters:
Value of loan = $18965
Interest rate = 3%
Time = 1year
Unknown:
Interest = ?
Solution:
The interest on a particular amount is given as:
I = [tex]\frac{PRT}{100}[/tex]
I is the interest
P is the principal
R is the rate
T is the time
I = [tex]\frac{18965 x 3 x 1}{100}[/tex] = $568.95
40 percent of the people in the club are new this year if there are 12 be people how many people are in the club
Answer:
The answer is 30
Step-by-step explanation:
12 ÷ 40% = 30
Given m||n, find the value of x.
x=21
Step-by-step explanation:
• 8x - 7 = 9x - 28
(group like terms)
• 8x - 9x = -28 + 7
• -1x = - 21
(negative cancels out)
• x = 21
Find the zeros of f(x) =x^3+2x^2-3x
Answer: 0, 1, -3
Step-by-step explanation:
f(x) = x^3 +2x^2 -3x
f(x) = x(x^2 +2x-3)
f(x) = x(x-1)(x+3)
to find zeroes, plug into f(x) and solve for each value of x. doing this gives 0, 1, and -3
The solution to -3(2 - 5x) = 3x + 12 is
1. -2.25
2. -1.625
3. 1.5
4. 3
Answer:
1.5
Step-by-step explanation:
i am not certain but this is how I got it
First distribute which gives you the -3 with 2 I switched them around so I did -3(-5x+2) and you will get 15x-6
Then the opposite of subtraction is addition so you add 6 to both sides so you add six to 12 and to 6 leaving you with 15x=3x+18 you then will subtract 3x from 15x and 3 leaving you with 12x=18 the divide the numbers
After you divide you get 3/2 then put it has a decimal and you get 1.5
Can someone help me please?
Answer:
the first one and the last three
Step-by-step explanation:
that should be it.
PLEASE NEED HELP URGENTLY!
Raul tried to find the midpoint between 5 & 3i and 12 + 7i. Check his work below.
Sum=(5+(-3))+(12+7)i
=2+19i
so the midpoint is 1+ 19over2 i
What mistake did Raul make?
AHe subtracted the values instead of adding them.
BHe did not add the corresponding parts of the complex numbers.
CHe found the sum instead of the average because he forgot to divide by two.
DHe added the numbers in the wrong order.
Answer:
B.He did not add the corresponding parts of the complex numbers.
Step-by-step explanation:
A mid point is a point that is of equal distance to two reference points.
Given: Find the midpoint of 5+(-3)i and 12+7i.
These expressions have two parts: the value and complex number parts.
Thus the addition ought to have been;
(5+(-3i)) + (12+7i) = (5 - 3i) + (12 + 7i)
= (5 + 12) + (-3i + 7i)
= 17 + 4i
The midpoint can be determined as:
[tex]\frac{(17 +4i)}{2}[/tex]
Thus it can be observed that Raul did not add the corresponding parts of the complex numbers.
Answer:
bbbbbbbbb
Step-by-step explanation:
I need help on this question
Answer:
B. 63 degrees
Step-by-step explanation:
Its the same angle as the one above it.
I hope this helps :)
Have a nice day!
Answer:
B
Step-by-step explanation:
If lines AB and CD are parallel, then angle h is equal to 63 degrees
What value of b will cause the system to have an
infinite number of solutions?
6
y = 6x-b
+3x+12y=-3
-3x + y = -3
b =
Answer: b=6
Step-by-step explanation:
I hope this helps on edge
To make the system have an infinite number of solutions, the value of b can be any real number.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
For the system to have an infinite number of solutions, the two equations must be dependent, which means that one of the equations can be obtained by a linear combination of the other two equations.
So,
Let's rearrange the given equations into the slope-intercept form:
y = 6x - b _____(1)
3x + 12y = -3 ______(2)
-3x + y = -3 ______(3)
From equation (3),
y = 3x - 3 _______(4)
Now,
We can see that equation (1) is a multiple of equation (4) with a slope of 6/3 = 2.
Specifically, equation (1) can be obtained by multiplying equation (4) by 2 and then subtracting b from both sides.
So,
2(3x - 3) - b = 6x - b
Simplifying this expression.
6x - b = 6x - b
Since this equation is true for any value of x and b, we have an infinite number of solutions.
Therefore,
To make the system have an infinite number of solutions, the value of b can be any real number.
Learn more about solutions of equations here:
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Devra soled the
inequality, and she says that x= -10 is a solution
Lavan says that a negative value of r does not make
sense in the context of the problem. He says that
x=1 is a solution Who is correct? Explain
Answer:
What’s the problem? If you could attach the problem we can help u out!
Step-by-step explanation:
helppp me please i’m going to fail
What compound inequality describes the graph shown below?
Mrs. Alonza ordered 4 x 10³ markers for her store. How many markers did she order?
the question is the picture
Identify the critical t. An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t value t∗t∗ for the given sample size and confidence level. Round critical t values to 3 decimal places.Sample size, n Confidence level Degree of Freedom Critical value, t∗t∗5 90 13 95 22 98 15 99
Answer and Step-by-step explanation: The critical value for a desired confidence level is the distance where you must go above and below the center of distribution to obtain an area of the desired level.
Each sample has a different degree of freedom and critical value.
To determine critical value:
1) Calculate degree of freedom: df = n - 1
2) Subtract the level per 100%;
3) Divide the result by 2 tails;
4) Use calculator or table to find the critical value t*;
For n = 5 Level = 90%:
df = 4
t = [tex]\frac{1-0.9}{2}[/tex] = 0.05
Using t-table:
t* = 2.132
n = 13 Level = 95%:
df = 12
t = [tex]\frac{1-0.95}{2}[/tex] = 0.025
Then:
t* = 2.160
n = 22 Level = 98%
df = 21
t = [tex]\frac{1-0.98}{2}[/tex] = 0.01
t* = 2.819
n = 15 Level = 99%
df = 14
t = [tex]\frac{1-0.99}{2}[/tex] = 0.005
t* = 2.977
The critical values and degree of freedom are:
sample size level df critical value
5 90% 4 2.132
13 95% 12 2.160
22 98% 21 2.819
15 99% 14 2.977
In the square pyramid shown below, the diagonal length FC = 16√2 centimeters and the height of the pyramid is 7 centimeters. Find the slant height AD of the pyramid, to the nearest tenth. Show your work with reasoning for each step.
Answer:
Don't have
Step-by-step explanation:
In the square pyramid shown below, the diagonal length FC = 16√2 centimeters and the height of thid, to the nearest tenth. Show your work with reasoning for each step. stepstep
Justin played video games for the following amount of time this past week 42 mins, 35 mins, 28 mins, 55 mins, and 57 mins what was the median amount of time justin played video games this past week
Answer:
42 minutes
Step-by-step explanation:
Put all numbers in order then cross out a number from each side until you reach the middle.
28, 35, 42, 55, 57
/ 35, 42, 55 /
/ / 42 / /
Answer:
3 hours and 37 minutes
Step-by-step explanation:
42+35+28+55+57=217
217/60=3.61666.....
217-60-60-60=37
If the ratio of the sides of two similar prisms is 4:1. Is the ratio of the volume of the prisms the same? (4:1)
Answer:
The ratio of their volumes is not the same 4:1, but [tex](4:1)^3[/tex] = 64:1.
Step-by-step explanation:
Measurements in Similar Figures
In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the other corresponding lengths can also be expressed as a:b.
In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the areas can be expressed as (a:b)^2 and the ratio of the volumes can be expressed as (a:b)^3.
We are given the ratio of the sides of two similar prisms as 4:1. The ratio of their volumes is not the same 4:1, but [tex]\mathbf{(4:1)^3}[/tex] = 64:1.