Answers
Using geometric sequence concepts, it is found that the one which results in a sum of -69,905 is:
D. [tex]\sum_{k = 0}^{9} -\frac{1}{5}(4)^k[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.As a sum, it can be represented by:
[tex]\sum_{k = 0}^{n - 1} a_1(q)^k[/tex]
In which [tex]a_1[/tex] is the first term.The result of the sum is:
[tex]S = \frac{a_1(1 - q^n)}{1 - q}[/tex]
Item A:
For this sequence, we have that:
[tex]a_1 = \frac{1}{4} = 0.25, n = 8, q = -5[/tex]
Hence, the sum is:
[tex]S = \frac{0.25(1 - (-5)^8)}{4} = -24414[/tex]
Item B:
For this sequence, we have that:
[tex]a_1 = -\frac{1}{4} = -0.25, n = 12, q = 5[/tex]
Hence, the sum is:
[tex]S = \frac{-0.25(1 - (5)^12)}{-4} = -15258789[/tex]
Item C:
For this sequence, we have that:
[tex]a_1 = \frac{1}{5} = 0.2, n = 11, q = -4[/tex]
Hence, the sum is:
[tex]S = \frac{0.2(1 - (-4)^11)}{3} = 279620.3[/tex]
Item D:
For this sequence, we have that:
[tex]a_1 = -\frac{1}{5} = -0.2, n = 10, q = 4[/tex]
Hence, the sum is:
[tex]S = \frac{-0.2(1 - (4)^10)}{-3} = -69905[/tex]
Hence option D is correct.
You can learn more about geometric sequence concepts at https://brainly.com/question/11847927
Related Questions
What is the slope of the line? 4x-1=3y+5
Answers
Answer:x7
Step-by-step explanation:
Answer:
The slope would be 4/3, found from the equation: y=4/3x-2
Step-by-step explanation:
4x-1=3y+5
Subtract the 5
4x-6=3y
Divide the 3
y=4/3x-2
which line contains both points P (-2, 3) and Q (-1, 2) ?
Answers
Answer: A is the answer
Step-by-step explanation: because nun of the other make sense
What is the solution for x in 5x - 2 + 2x = 7x - 2?
Answers
I hope this helps :)
Find the distance between the two points rounding to the nearest tenth (if necessary).
(−2,2) and (−8,−6)
Answers
Explanation: you use the distance equations
Which in this case is the one in the picture.
The function 56 – 4y = –5x can be used to determine the total amount of money in a coin jar, y, after money isadded for x days. What is the rate of change in dollars with respect to the number of days?
Answers
Answer:
$1.25 dollars per day added to the coin jar
Step-by-step explanation:
the given equation is: 56 – 4y = –5x
we can rewrite it:
4y = 56 + 5x
y = (56 + 5x) / 4
y = 14 + ⁵/₄x
the slope of the equation is ⁵/₄, which gives us how much money is added into the coin jar every day. We can write ⁵/₄ as 1.25 or $1.25 dollars per day added to the coin jar
The fuel for a chain saw is a mix of oil and gasoline. The label says to mix 3 ounces of oil with 5 gallons of gasoline. How much oil would you use if you had 120 gallons of gasoline?
Answers
Answer:
120 gallons of gasoline needs 180 ounces of oil
Step-by-step explanation:
Since the label for the chain saw reads to mix 3 ounces of oil with 5 gallons of gasoline, it means we have a ratio of 3 ounces of oil to 5 gallons of gasoline. That is
3 ounces of oil = 5 gallons of gasoline
Using the the unity method, by dividing both sides by 5,
3/5 ounces of oil = 1 gallon of gasoline.
So, for 120 gallons of gasoline, we have
120 × 1gallon of gasoline = 120 × 3/5 ounces of oil
So, 120 gallons of gasoline = 60 × 3 ounces of oil
So, 120 gallons of gasoline = 180 ounces of oil
So, 120 gallons of gasoline needs 180 ounces of oil
Answer:
Try 15,360 gallons or it could be 15,360 oz. one of those I hope it helps a bit. I did 128 times 120 gl. witch gave me 15,360.
Step-by-step explanation:
Dave's optometrist used medicine to dilate his eyes. Before dilation, his pupils had a diameter of 2.1 millimeters. After dilation, his pupils had a diameter of 6.3 millimeters. What was the scale factor of the dilation?
Answers
Answer:
Step-by-step explanation:
6.3 divided by 2.1 equals 3.
3 is the scale factor
Answer:
2
Step-by-step explanation:
I just took the quiz
Determine if segments AB and CD are parallel, perpendicular, or neither. AB formed by A(3,8) and B(-6,5) CD formed by C(-6,7) and D(-3,8)
Answers
Answer:
They are parallel
Step-by-step explanation:
(3,8)(-6,5): do sloe formula (y1-y2 over x2-x1)
AB: 1/3 slope (Full formula y=1/3x+7)
(-6,7)(-3,8) ---> 8-7 over -3-(-6) = 1/3
CD: 1/3 slope (Full formula y=1/3x +9)
They have the same slope so they are parallel
Solve and graph the compound inequality:
5C + 3 < 28 and -4C – 2 14
Answers
5 C + 3 < 28 a - 4 C - 214
a>9c +31
------------
28. 4
C >28a-21
------
9
Answer:
c < 5 or c <= -4
Step-by-step explanation:
apek
At a movie theater, the size of popcorn bags decreased 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold?
Answers
Answer:
12?
Step-by-step explanation:
since this is a percent deal I would a simple trick
x/15 = 20/100
15 x 20 = 300
divide 300 by 100
that equals 3
15 - 3 = 12
Answer
12?
Step-by-step explanation:
since this is a percent deal I would a simple trick
x/15 = 20/100
15 x 20 = 300
divide 300 by 100
that equals 3
15 - 3 = 12
Which of the following inequalities matches the graph?
answers:
x < 2
y > 2
y < 2
x > 2
Answers
Answer:
None of them but for the actual question on the picture it is x < -3
Step-by-step explanation:
Write an equation that represents the function. (linear equations)
Answers
Answer:
y = 2x + 2
Step-by-step explanation:
First solve for the slope using [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]\frac{8-2}{3-0}[/tex] = 2
Plug the slope into the slope intercept form equation y = mx + b
y = 2x + b
To solve for b, plug in any (x, y) point on the table.
2 = 2(0) + b
2 = b
Now you can plug the b value into your equation.
y = 2x + 2
Emily wants to buy new boots that cost $68. The sales tax rate in her city is 5%. What is the total cost for the boots?
Answers
Which number is equal to 17.75?
F. 1.775
G. 17.075
H. 17.750
I. 1.7750
Answers
H. 17.750
When a zero is on the end of the decimal, you can drop it making 17.750=17.75
Choose yes or no weather the expression are equivalent
2(8f-5) and 10f-10
Answers
Step-by-step explanation:
I think the answer is no
Answer:
no
Step-by-step explanation:
once distributed, 2(8f-5) becomes 16f-10 which is not equivalent to 10f-10
(2x + 3y) + (4x - 3y) = 11+(-5)
Which of the following is equivalent to the equation above?
A. 6x=10
B. 6x=16
C. 6x+6y=6
D. 6x+6y=16
Answers
Answer:
The correct option should have been [tex]6x=6[/tex].
Step-by-step explanation:
Given the expression
[tex]\left(2x\:+\:3y\right)\:+\:\left(4x\:-\:3y\right)\:=\:11+\left(-5\right)[/tex]
solving the expression
[tex]\left(2x\:+\:3y\right)\:+\:\left(4x\:-\:3y\right)\:=\:11+\left(-5\right)[/tex]
Remove parentheses: (a) = a
[tex]2x+3y+4x-3y=11-5[/tex]
Group like terms
[tex]3y-3y+2x+4x=11-5[/tex]
Add similar elements
[tex]6x=6[/tex]
It is clear that not a single given option is [tex]6x=6[/tex]. It means no option is correct. It seems you mistyped the correct options.
The correct option should have been [tex]6x=6[/tex].
Annabelle went rock climbing. The below graph is a model of her climbing as
time passes.
Answer the following questions about the graph:
a. What are the labels on each axis?
b. What is happening for the first 5 minutes of Annabelle's climbing session?
What is your reason for saying that?
c. When was Annabelle climbing fastest? How do you know?
d. What is happening from 5 to 7 minutes? What is your reason for saying
that?
Answers
please help; i’m confused
Answers
Answer:
The values of k that make the given equation having imaginary roots are:
k < -18, or (-∞,-18).
Step-by-step explanation:
Nature of the Roots of a Quadratic Equation
The standard representation of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The expression:
[tex]d=b^2-4ac[/tex]
Is called the discriminant. The discriminant determines the nature of the roots of a quadratic equation as follows:
If d=0, there is only one real root.
if d>0, there are two different real roots
if d<0, there are two different imaginary (complex) roots
We are given the equation:
[tex]-2x^2+12x+k=0[/tex]
Comparing with the standard quadratic equation, we have:
a=-2, b=12, c=k
Calculating the discriminant:
[tex]d=12^2-4(-2)k[/tex]
[tex]d=144+8k[/tex]
If the equation has imaginary roots, then d<0, thus:
144 + 8k < 0
Subtracting 144:
8k < -144
Dividing by 8:
k < -18
The values of k that make the given equation having imaginary roots are: k < -18, or (-∞,-18).
HELP ASAP GIVING BRAINLIEST
Solve for x in the diagram below
Answers
Answer:
Step-by-step explanation:
60=x+45
x=15
I JUST NEED 4 PLS!!!!!!
IM REDOING THIS SO THERE IS WRITING ON THE PAPER!!
I WILL MARK BRAINLIEST!
Answers
Answer:
C
Step-by-step explanation:
When doing 4 divided by 2 you get 2. Looking at the sign it is saying 3 is greater than the number we solve for. Since we solved and got 2 we can double check and ask is 3 greater than 2? Yes it is so that would make the statement correct.
Hope this Helps :)
The volume of a fish tank is given by the function V(x)=(x+7)(x-4)(x+3). Write a function describing a fish tank that has the same height but is longer in length by 3 units and wider by 2 units.
Answers
Answer:
V(x)=(x+9) * (x-4) * (x+6)
Step-by-step explanation:
A fish tank is normally in the shape of a rectangular prism. The volume of a rectangular prism can be calculated using the following formula
V = w * h * l
where w represents the width, h represents the heigh, l represents the length, and V represents the volume of the rectangular prism/fish tank. Therefore, we can use the function provided in the question and simply add 3 units to the length and 2 units to the width in order for it to work for our new fish tank.
V(x)=(x+9) * (x-4) * (x+6)
Can y’all help me solve this two step equation?
1=x/3-5
Answers
Answer:
18
Step-by-step explanation:
Teacher asked us the question
Answer:1/2 i think
Step-by-step explanation:
im going to self destruct lol
Answers
Answer:
noooooooooooo dont:(
Step-by-step explanation:
(40, 3,000) and (60, 4,000)
find the slope of the line that passes through
Answers
Answer:
slope of the line is 50
Step-by-step explanation:
The slope of a line (gradient) is determined by the rise/run so
(y2 - y1) / (x2 - x1)
We simply substitute in our coordinates and solve. So:
(4000 - 3000) / (60 - 40)
= 1000 / 20
= 100/2 = 50
Gradient is 50
Q1. An airplane flies with a constant speed of 600 miles per hour. How far can it travel in 3 1/2 hours?
Q2. A minibus drives with a constant speed of 68 km/h. How long will it take to travel a distance of 102 kilometers?
pls fast I need the answers for these I swear I'll make you the brainliest.
Answers
Answer:
Q1. 1050 miles
Q2. 1h 30m
Step-by-step explanation:
Q1. 1h = 300 miles
3[tex]\frac{1}{2}[/tex]h = 3.5 × 300 miles
= 1050 miles
Q2. 68km = 1h
102km = [tex]\frac{102}{68}[/tex] × 1h
= 1.5h
= 1h 30m
help me plzzzzzzzzzzzzzz
Answers
every five years in march, the populations of a certain town is recorded. In 1995, the town had a populations of 4,500 people. From 1995 to 2000, the population increased by 15%. From 2000 to 2005, the population decreased by 4%. What was the town's population in 2005.
Answers
Answer:
population= 4968
Step-by-step explanation:
15/100= 0.15
1+0.15= 1.15
1.15 x 4500= 5175
4/100= 0.04
1-0.04= 0.96
0.96 x 5175= 4968
3•3^-1
Show work plz!
Answers
Answer:
1
Step-by-step explanation:
Firstly we need to do the exponent,3^-1, which equals 1/3.
Now, we multiply 3 with 1/3.
3•1/3 =1
The map of a biking trail is drawn on a coordinate grid. The trail starts at P(−5, 4) and goes to Q(2, 4). It goes from Q to R(2, −2) and then to S(7, −2). What is the total length (in units) of the biking trail? WILL GIVE BRAINLIEST NEED ASAP WILL ALSO GIVE 5 STARS AND THANKS!!!!!!!!!! SOMEONE PLZ HELP I NEED THIS!!!!!!!!!!!!!!!!!!!!!!!!!
12
18
16
14
Answers
Answer:
18 units
Step-by-step explanation:
PQ= 7 units
QR = 6 units
RS = 5 units
its really not that hard..
will mark brainliest answer!! 50 points!! pls help!!
Ben shared his post with 2 friends. Each of them share the post with 3 friends a day.
a) write an exponential equation to show the growth of Ben’s social media post
Carter shares his post with 10 friends who each share the post with 2 friends a day
b) write an exponential function to show the growth of Carter’s social media post
Answers
Answer:
1. Ben
Let the number of days be x.
Let the total no. of shares be y
[tex]No.\ of\ shares\ on\ Day\ 0=2\\No.\ of\ shares\ on\ Day\ 1\ = 2*3\\No.\ of\ Shares\ on\ Day\ 2\ =\ 2*3*3\\No.\ of\ Shares\ on\ Day\ 3\ = 2*3*3*3\\No.\ of\ Shares\ on\ Day\ x\ =2*3^x\\As\ Total\ no.\ of\ shares\ = y\\y=2*3^x[/tex]
2. Carter
Let the no. of days be x
Let the total no. of shares be y
[tex]No.\ of\ shares\ on\ Day\ 0=10\\No.\ of\ shares\ on\ Day\ 1\ = 10*2\\No.\ of\ Shares\ on\ Day\ 2\ =\ 10*2*2\\No.\ of\ Shares\ on\ Day\ 3\ = 10*2*2*2\\No.\ of\ Shares\ on\ Day\ x\ =10*2^x\\f(y)=10*2^x[/tex]