Given:
The explicit function is:
[tex]f(n)=1000\left(\dfrac{1}{4}\right)^{n-1}[/tex]
To find:
[tex]f(1)=?,r=?[/tex] and first 5 terms.
Solution:
The explicit formula a geometric sequence is:
[tex]f(n)=ar^{n-1}[/tex] ...(i)
Where, a is the first term and r is the common ratio.
We have,
[tex]f(n)=1000\left(\dfrac{1}{4}\right)^{n-1}[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1000[/tex]
[tex]f(1)=1000[/tex]
And,
[tex]r=\dfrac{1}{4}[/tex]
For [tex]n=1[/tex],
[tex]f(1)=1000\left(\dfrac{1}{4}\right)^{1-1}[/tex]
[tex]f(1)=1000\left(\dfrac{1}{4}\right)^{0}[/tex]
[tex]f(1)=1000(1)[/tex]
[tex]f(1)=1000[/tex]
For [tex]n=2[/tex],
[tex]f(2)=1000\left(\dfrac{1}{4}\right)^{2-1}[/tex]
[tex]f(2)=1000\left(\dfrac{1}{4}\right)^{1}[/tex]
[tex]f(2)=1000\times \dfrac{1}{4}[/tex]
[tex]f(2)=250[/tex]
Similarly, substituting [tex]n=3,4,5[/tex], we get
[tex]f(3)=62.5[/tex]
[tex]f(4)=15.625[/tex]
[tex]f(5)=3.90625[/tex]
Therefore, [tex]f(1)=1000,r=\dfrac{1}{4}[/tex] and the first five terms are [tex]1000,250,62.5,15.625,3.90625[/tex].
Given:
The explicit function is:
To find:
and first 5 terms.
Solution:
The explicit formula a geometric sequence is:
...(i)
Where, a is the first term and r is the common ratio.
We have,
...(ii)
On comparing (i) and (ii), we get
And,
For ,
For ,
Similarly, substituting , we get
Therefore, and the first five terms are .
find the midpoint and distance between (5,1) and (-15,11)
Answer:
look i think is -5.005 I don't really know but I hope you get it right. Have a good day
*IS MY ANSWER CORRECT?!? IF NOT PLEASE TELL ME THE CORRECT ONE.*
[[ READ ATTACHMENTS ]]
Answer:
As I analysed it for me yes it is
How to solve linear equation
You can use elimination and substitution method
EXAMPLE :
Given :
2x + y = 5
3x - 5y = 1
2x + y = 5 (× -5)
3x - 5y = 1
__________
-10x - 5y = - 25
3x - 5y = 1
____________ _ (elimination)
-13x = - 26
x = - 26/-13
x = 2
Substitution x = 2 to 2x + y = 5 :
2x + y = 5
2(2) + y = 5
4 + y = 5
y = 5 - 4
y = 1
simplify the expression 6(a-4+2b)
Answer:
6a + 12b - 24
Step-by-step explanation:
Will mark brainliest, plss help
Answer
C and A
Step-by-step explanation:
Select the circumstance when the expression (a <= b and a >= b) is true. a = −1, b = −2 a = 1, b = 1 a = 1, b = 2 a = 2, b = 1
Answer:
b = 1 a = 1
or
b = 2 a = 2
Step-by-step explanation:
scribe
de exponente.
1- 2 x 2 x 2 x 2 =
2-3x3-
3-2/x 4 X 4 X 4 x 4 =
A 5x5 =
Answer:
1 - 2 exponent 4
2 - 3 exponent 2
A - 5 exponent 2
I don't understand 3
Step-by-step explanation:
10 and 4/5 as a decimal
Answer:
5.4
Step-by-step explanation:
Multiply 10x5 and add 4 to get 54/10. Divided 54 by 10 and get 5.4 as your decimal answer!
In a collection of nickels, dimes, andquarters the value of the collection is$12.85. If the number of nickels is 6 lessthan twice the number of dimes and thenumber of quarters is 5 more than twicethe number of dimes, how many quartersare there?
please help thank you
Answer:
[tex]x - 2 = 0 \\ x = 2 \\ p(2) = 0 \\ {2}^{4} - d {2}^{3} + 8 \times {2}^{2} - 14 \times 2 + 16 = 0 \\ 16 - 8d + 32 - 28 + 16 =0 \\ 8d = 36 \\ d = 36 \div 8 = 4.5[/tex]
enjoy it
The curve above the graph of a sinusoidal function. It goes through the points (-11,0) and (3,0). Find a sinusoidal function that matches the given graph.if needed you can enter pi=3.1416… as pi in your answer otherwise use at least 3 decimal digits.
F(x)=
Considering the zeros, the graph for the sinusoidal function is:
[tex]F(x) = \sin{\frac{\pi}{7}(x-3)}[/tex]
The zeros given for the function are: [tex]x = -11, x = 3[/tex].For practicality, we are going to define a sine function, which has a zero at x = 0, so we use shifting.The sine function is given by:
[tex]F(x) = A\sin{Bx}[/tex]
In which:
The amplitude is A.The period is [tex]T = \frac{2\pi}{B}[/tex].In this problem:
We suppose an amplitude of 1, thus [tex]A = 1[/tex].The difference between the zeros is 14, so we use a period of 14, thus [tex]T = 14[/tex], and:[tex]\frac{2\pi}{B} = 14[/tex]
[tex]B = \frac{2\pi}{14}[/tex]
[tex]B = \frac{\pi}{7}[/tex]
Thus:
[tex]F(x) = \sin{\frac{\pi}{7}x}[/tex]
Like this, the zeros are at [tex]x = -14[/tex] and [tex]x = 0[/tex]. We want it at [tex]x = -11, x = 3[/tex], thus, we shift the function 3 units to the right, that is, the function is:
[tex]F(x) = \sin{\frac{\pi}{7}(x-3)}[/tex]
The graph is sketched at the end of this answer, and has the desired behavior, which are points (-11,0) and (3,0).
A similar problem is given at https://brainly.com/question/22136310
Enter the number in scientific notation. 33,254 = x10
Answer:
33254=3.3254*10^4
Step-by-step explanation:
You use the hint
11x-6=60 please give details
Answer:
6
Step-by-step explanation:
11(6)-6=60
11 x 6 = 66
66-6 = 60
Therefore, x=6
6. Carla runs 3 miles in 30 minutes.
Find the number of miles Carla runs each minute. Show your work using mathematics.
Find the number of minutes Carla runs for each mile. Show your work using mathematics.
Answer:
Carla ran 0.1 miles per minute.
Step-by-step explanation:
To solve this, we need to use the distance formula.
The formula is d=rt, where d is the distance traveled, r is the rate in which the distance is traveled, and t is the amount of time it took to go that distance. So lets plug it all in.
d=rt
3=(r)(30)
Now, we need to do the inverse of multiplying 30 to both sides, which would be the same as dividing by 30 on both sides.
3/30=(r)(30/30)
0.1=r
The rate is 0.1. Carla ran 0.1 miles per minute.
if 1/3 of taffy cost $2.10 how much is one pound of taffy?
Answer:
$6.30
Step-by-step explanation:
since 1/3 is considered 1/3 of a pound, you can multiply 2.10 by 3.
2.10 x 3 = 6.30
Answer:
$6.30
Step-by-step explanation:
3 × 2.10 = 6.30
You know you got the question right if you divide 6.30 by 3 because it's 1/3
Question Progress
Homework Progress
10/47
Find the nth term of this quadratic sequence
4, 7, 12, 19, 28,...
Answer:
4 7 12. 19 28 then and is 39
Marsha has $400 in a savings account. The interest rate is 5% per year and is not compounded. How much will she have in total in 1 year?
The total amount in the account after 1 year will be $420
Based on the information given, the following can be deduced:
Principal = $400
Interest rate = 5%
Time = 1 year
Therefore, the simple Interest will be:
= PRT/100
= ($400 × 5 × 1)/100
= $2000/100
= $20
Therefore, the amount will then be:
= Principal + Interest
= $400 + $20
= $420
Therefore, the total amount is $420
Read related link on:
https://brainly.com/question/24989563
6-3(x+2)>15 solving inequalities
Answer: x < - 5
Step-by-step explanation:
6-3(x+2) > 15 [substract six from both sides]
-3(x+2) > 15 - 6 [divide both sides by -3; flip greater than sign to less than]
x + 2 < - 3 [subtract two from both sides]
x < - 5
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
Jeanette earn $33 in 8 hours. At the rate, how much would she earn in 5 hours?
Answer:
If you made $33 in 8 hours, then you should divide 8 into 33 to see how much you make per hour. 8÷33= (explaining how to get answer) can 8 go into 3? No. put a zero on top of the first three. Now can 8 go into 33? yes, 4 times, 4×8= 32, so we have 1 left over. add 2 decimals to the number so that it is $33.00, (still that same number just with zeros on the end). So far the answer is $04.??. How many times can 8 go into 10? 1 time with 2 left over, so write the one on top of the .0! Now with 2 left over we have to see how many times 8 can go into 20, 8×2= 16 16+8=24, so it can only go in 2 times without going over 20. Now that we have rounded it up to 2 decimals we don't have to keep going and your answer is
$4.12 times that by 5 and you will get the final answer.
4.12
× 5
20.60
Hope I explained I okay!
Step-by-step explanation:
Answer:
about 20.63
Step-by-step explanation:
Sebastian was driving down a road and after 4 hours he had traveled 98 miles. At this
speed, how many hours would it take Sebastian to thrive 245 miles?
Fill out the table of equivalent ratios until you have found the value of x.
Answer:
4 hours = 98miles
x hours = 245miles
4Hours × 245miles
-----------------------
98miles
= 10hours
=
Write the equation of the line that passes through the points (9,3)(9,3) and (-7,-7)
Answer:
y=5/8x-21/8
Step-by-step explanation:
Do 10-13 and make my life easier please answer it please
#10
[tex]\\ \sf\longmapsto 8^1=8[/tex]
#11
[tex]\\ \sf\longmapsto 1^8=1[/tex]
#12
[tex]\\ \sf\longmapsto (-5)^3=-125[/tex]
#13
[tex]\\ \sf\longmapsto (-5)^4=625[/tex]
Answer:
Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)
Equating (1) and (2)
6n+5=a+(n−1)d
6n+5=a+nd−d ..... (3)
Equating n terms:6n=nd
d=6 ...... (4)
Substituting (4) in (3)
6n+5=a+6n−6
5=a−6
a=11 ..... (5)
Now
Sn=2n(2a+(n−1)d)
Sn=2n(a+Tn) ....... (6)
Substituting (1) and (5) in (6)
Sn=2n(11+6n+5)
Sn=2n(16+6n)
Sn=n(8+3n)
What dilation happened below
Answer:
Dilation of 3
Step-by-step explanation:
In a river, a trout passed beneath a woman who was swimming at 1,800 centimeters per minute. The trout swam 8,000centimeters directly upstream at a constant velocity. It swam that distance in 0.8minutes. What was the trout's velocity?
Write your answer as a whole number.
centimeters per minute upstream
Answer:
It would approximately be 3.73 m/h
Step-by-step explanation:
0.8 mins is 48 seconds
I then divided 8000 by 48 seconds to see how many cm it traveled per second.
It traveled 166.666666667 cm per second
I then converted cm to feet
so it was 5.468066491699474 feet per second
I then converted feet to miles, so it was 0.0010356186537309611598 miles per second.
Then I multiplied it by 60 so it was 0.06213711922 miles per minute.
Finally I multiplied it by 60 again to make it 3.72822715343 miles per hour.
I rounded it to the nearest hundredth making it 3.73 m/h
f(x) = 3(2)x What is f(4)?
A. 24
B. 12
C. 4
D. 48
Answer:
a.
Step-by-step explanation:
x=4
3(2)=6
6(4)=24
24 is your answer!
represent the following situations using quadratic equation in standard form
1. If the square of a number is added to 8 times the number, the result is 100
2. Mr. Apoloan wants to lay out a rectangular playground with an area of 30 square feet. The desired length will be 7 times the width
1. If the square of a number is added to 8 times the number, the result is 100.
Let x be the number.
Equation: x² + 8x - 100 = 0
2. Mr. Apoloan wants to lay out a rectangular playground which will contain 30 square feet. The desired length will be 7 times the width.
Area: 30ft²
Length: 7w
Width: w
Area of a rectangle: LW
(7w)w = 30ft²
Equation: 7w² - 30 = 0
how to order 4,\pi ,8 from least to greatest
Answer:
pi, 4, 8
Step-by-step explanation:
A college student has $240 to use for laundry money. Each time he does laundry, he spends $7.50. Which equation represents the amount of money, M, he has after he has done laundry “x” times?
A) M= 7.50x - 240
B) M= 240 - 7.50x
C) M= 7.50 - 240x
D) M= 240x - 7.50
Answer:
B
Step-by-step explanation:
x = the number of times he does laundry.
Let's say he does the laundry 5 times then x = 5.
Each time costs $7,50.
If you want to know how much money he has spent after 5 times, you have to calculate 5 times $7,50. 7,5 times 5 = 37.5.
M stands for how much money he still has left from the 240 dollars.
If you apply the formula it would be 'M = 240 - 7.50x (7.50 times 5) = 240 - 37.5 = 202.5'
Therefore, the correct answer is B (M = 240 - 7.50x).
I need help!! it is very confusing.
PLZ HELP!!
Tim explained a function in words and Paul wrote an equation.
Tim
The amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it.
Paul
y−1,400=56(x+26)
Whose function has the smaller y-intercept?
Tim’s with a y-intercept of $2,700
Paul’s with a y-intercept of $2,856
Paul’s with a y-intercept of $2,800
Tim’s with a y-intercept of $2,780
Answer:
Tim's with a y-intercept of $2,780
Step-by-step explanation:
To find Paul's y-intercept, solve the equation y-1400=56(x+26) for y. Then use the standard format for a linear equation y=mx+b to determine the y-intercept which would be b.
Step 1. Get y by itself by adding 1,400 to both sides.
y-1400 + 1400 = y
56(x+26) + 1400 = 56(x+26) + 1400
New equation y = 56(x+26) + 1400
Step 2. Distribute 56(x+26)
56(x+26) = 56 * x + 56 * 26 = 56x + 1456
New equation y = 56x + 1456 + 1400
Step 3. Simplify.
y = 56x + 2856
Paul's y-intercept would be 2856 because when y=0 x=2856
To Find Tim's y-intercept, subtract 225 * 8 from 4580.
225 * 8 = 1800
4580 - 1800 = 2780
Answer:D or answer 4 or 2,780 dollars.
Step-by-step explanation:
test