The total number of books that we had in out bookcase when we were 11 years old was 2,187 books.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is [tex]a[/tex]
and the term by which we multiply the previous term to get the next term is [tex]r[/tex]
Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
(till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
What is the sum of terms of a geometric sequence?Lets suppose its initial term is [tex]a[/tex] , multiplication factor is [tex]r[/tex]
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
For this case the initial number of books (2) is multiplied by 3 each year.
So we got:
a = 2,
r = 3
Since a = 2 was for age 5, and if we take age 5 at 1st position, then age 11 is at the 7th position.
The number of books we read at each age is a geometric sequence with initial term 2 and multiplication factor 3.
The sum of its term(which would make it geometric series) will give the total number of books we will have.
Since age 11 is at 7th position, so n = 7
Thus, the total number of books we had in the bookcase when we were 11 years old is:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}\\\\S_7 = \dfrac{2((3)^7-1)}{3-1} = 2187[/tex]
We could've derived it without formula as:
Age 5: 2 booksAge 6: [tex]2 \times 3[/tex] booksAge 7: [tex]2 \times 3^2[/tex] booksAge 8: [tex]2 \times 3^3[/tex] booksAge 9: [tex]2 \times 3^4[/tex] booksAge 10: [tex]2 \times 3^5[/tex] booksAge 11: [tex]2 \times 3^6[/tex] booksTheir sum is 2187.
Thus, the number of books that we had in out bookcase when we were 11 years old was 2187 books.
Learn more about sum of terms of geometric sequence here:
brainly.com/question/1607203
For f(x)= 4x+1 and g(x) = x^2 -5, find (f g)(x).
O A. 4x2 -19
O B. 4x3 + x2 - 4x -6
O C. 4x3 + x2 - 20x-5
O D. 4x3 + x2 - 5x -5
Answer:
The answer is option c.
4x³ + x² - 20x - 5
Answer:
C
Step-by-step explanation:
The midpoint of the coordinates (7,9) and (12,11) is ______.
A. (9.5, 10)
B. (13, 12)
C. (19, 20)
D. none of the above
Answer:
The answer is option a.
Step-by-step explanation:
=(7+12/2 , 9+11/2)
=(19/2, 20/2)
= ( 9.5 , 10)
Hope this helps.
PLATO USERS!
Select the correct answer from each drop-down menu.
cos(420°) =
sin(450°) =
Answer:
see below
Step-by-step explanation:
cos(420°) = cos 60 = 1/2
sin(450°) = sin 90 = 1
Answer:
See below in bold.
Step-by-step explanation:
cos (420) = cos (420 - 360)
= cos 60
= 1/2.
sin 450 = sin(450-360)
= sin 90
= 1.
The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will 3:4. Find their present ages..................pls help me
Answer: 8:11
Step-by-step explanation:
5 and 3 is Hari's ages.
5+3=8 (Now Hari is 8 ages)
7 and 4 is Harry's ages.
7+4=11 (Now Harry is 11 ages)
Ratio is 8:11
Answer:
Harry is 11 and Hari is 8
Step-by-step explanation:
5:7+3:4=8 and 11
help me VERY FAST !!!!!!!!
Answer:
A
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x , y ) → (- y, x ) , thus
X(1, - 1 ) → X'(1, 1 )
Y(3, 4 ) → Y'(- 4, 3 )
Z(5, - 1 ) → Z'(1, 5 ) → A
Answer:
A
Step-by-step explanation:
X(1, - 1 ) → X'(1, 1 )
Y(3, 4 ) → Y'(- 4, 3 )
Z(5, - 1 ) → Z'(1, 5 ) → A
Since we know U is the midpoint, we can say TU equals BLANK? Substituting in our values for each we get BLANK? =12x - 1
Answer:
x = 3
Length of each segment = 3
Step-by-step explanation:
Since point U is the midpoint of the line segment TV, that means both the parts of the segment UV and TU will be equal in measure.
m(TU) = m(VU)
(8x + 11) = (12x - 1)
By further solving this,
8x + 11 + 1 = 12x - 1 + 1
8x + 12 = 12x
8x + 12 - 8x = 12x - 8x
12 = 4x
x = [tex]\frac{12}{4}[/tex]
x = 3
(12x - 1) = 12×3 - 1
= 35
And the length of each segment will be 35 units.
If f(x) and g(x) are inverse functions of each other, what is the graph of f(g(x))?
Answer:
y = x
Step-by-step explanation:
The graph of f(g(x)) is the straight line y = x.
PLEASE HELP! WILL MARK BRAINLIEST!!
A bag has 4 red marbles, 12 blue marbles and 6 yellow marbles. What is the probability of picking a yellow marble, replacing it, and then picking a blue marble?
1/18
18/121
55/22
22/131
In a bag of marbles, you have 4 green, 3 yellow, 5 blue, and 8 red marbles. What is the probability of picking a blue marble from the bag?
3/20
1/5
1/10
1/4
Answer:
18/121
1/4
(not 100% sure)
select the correct answer. witch is the correct simplified form of the expression
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
-1/3 -1/2 = -5/6
1/2-1/4 = 1/4
The negative makes the reciprocal
x^1/4/y^5/6
Solve: 2 ln 3 = ln(x - 4) x = 9 x = 10 x = 13
Solve: 2 ln 3 = ln(x - 4)
a)x = 9
b)x = 10
c)x = 13
Answer:
x = 13
Step-by-step explanation:
To solve the problem above, we will follow the steps below;
2 ln 3 = ln(x - 4)
[using logarithm rule aInb = Inbᵃ]
so also our equation becomes
In 3² = In (x-4)
The In at the left-hand side of the equation will cancel-out the In at the right-hand side of the equation
Our equation becomes;
3² = x- 4
9 = x-4
add 4 to both-side of the equation in other to make x subject of the equation
9 + 4 = x-4 + 4
13 = x
x = 13
Answer:
C on Edge x = 13 x =
-4 and x = 4
the solution is x = 4
Step-by-step explanation:
I just did the assignment on edge.
HELP WILL GIVE BRAINLIEST!!!!
How many 1/2 cups are in 3/4 cups?
Answer:
1 1/2 or 1.5
Step-by-step explanation:
think: half of 4 is 2 so 1 half cup would make it to 2/4
than half of that is 1/4 which is 1/2 of 1/2 a cup
adding that to 2/4 makes it 3/4 so therefore... (Peep the answer)
Find the zeros of the function f(x) = x^3 + 2x^2 -25x - 50 = 0
Answer:
x = -2, x= -5 , x= +5
Step-by-step explanation:
x^3 + 2x^2 -25x - 50 = 0
Factor by grouping
x^3 + 2x^2 -25x - 50 = 0
x^2(x+2) -25( x+2) = 0
(x+2) ( x^2 -25) =0
Using the zero product property
x+2 =0 x^2 -25 =0
x=-2 x^2 = 25
x= -2 Taking the square root of each side
x = ±5
helpppp plleaassseee
Answer:
the answer is 1/2
explanation:
the answer is 1/2 because 3 is in the middle of 1 through 6 so it would be 1/2
Which number produces an irrational number when multiplied by 0.4?
Answer:
B unless it isnt
Step-by-step explanation:
B- some long decimal
(It’s pi. I hate pi.)
what’s the best answer ?????
Answer:
zero
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The line is horizontal and parallel to the x- axis
Since the x- axis has a slope of zero then the line has a slope of zero.
Find x.
A)7
B)7"2
C)"(14)
Answer:
x = 7
Step-by-step explanation:
Since this is a right triangle, we can use a trig function
tan theta = opposite/ adjacent
tan 45 = 7/x
Multiply each side by x
x tan 45 = 7
Divide each side by tan 45
x = 7/ tan 45
x = 7
Answer:
7
Step-by-step explanation:
It is a 45 45 90 triangle
meaning that the side lenghts will be x, x, x root 2
the hypotenuse will be x root 2, so that means that the side length will be 7
Which is the equation of a line that has a slope of One-half and passes through point (2, –3)?
Answer:
y=0.5x-4
Step-by-step explanation:
y+3=0.5(x-2)
y+3=0.5x-1
y=0.5x-4
HELP NOW
3600 dollars is placed in an account with an annual interest of 9% How much will be in the account after 25 years to the nearest cent !!
Answer:
A = $ 31,043.09
A = P + I where
P (principal) = $ 3,600.00
I (interest) = $ 27,443.09
Step-by-step explanation:
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Tristan is working two summer jobs, making $7 per hour babysitting and $19 per hour lifeguarding. Tristan must earn at least $210 this week. Write an inequality that would represent the possible values for the number of hours babysitting, bb, and the number of hours lifeguarding, ll, that Tristan can work in a given week.
Answer: 7bb +19 ll ≥210
Step-by-step explanation:
Hi, to answer this question we have to write an inequality:
The product of the number of hours he works babysitting (bb) and the amount he earns per hour (7); plus The product of the number of hours he works lifeguarding (ll) and the amount he earns per hour 19; must be higher or equal to the amount he must earn this week (210)
Mathematically speaking:
7 bb + 19 ll ≥210
The diameter of a circle is 20m. Find its area in terms of pie(urgent)
Answer:
100 pie m^2
[tex]solution \\ diameter = 20 \: m \\ radius = \frac{20}{2} = 10 \: m \\ area \: = \pi \: {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: = \pi \times {10}^{2} \\ \: \: \: \: \: \: \: \: \: \: = \pi \times 100 \\ \: \: \: \: \: = 100\pi \: {m}^{2} \\ hope \: it \: helps....[/tex]
Answer:
[tex]= 100\pi {m}^{2} \\ [/tex]
Step-by-step explanation:
[tex]d = 2r \\ 20 =2 r \\ \frac{20}{2} = \frac{2r}{2} \\ r = 10[/tex]
[tex]area = \pi {r}^{2} \\ = \pi \times 10 \times 10 \\ = 100\pi {m}^{2} [/tex]
hope this helps
What is the measure of the obtuse angle?
Answer:
The measure of and obtuse angle is 180°
Step-by-step explanation:
obtuse angles are more than 90°but less than 180°
Marcus has 2 blue pens, 3 red pens, and a green pen in his backpack. He will pick a pen, give it to a friend, and pick another pen. What is the probability that he picks 2 green pens?
Answer:
There is a zero percent chance of him giving his friends two green pens.
Step-by-step explanation:
He only has One pen.
A toy store marks down every toy by 15% in June. How much does a toy cost during June?
Answer:
since the toy is marked down 15%,
you do p*.85
to find the remaining cost
Step-by-step explanation:
I don't know how to find the value of x in the isosceles triangle.
Answer:
x=4
Step-by-step explanation:
split the triangle into two and you will get another smaller triangle as shown in what I have drawn
so notice that there's a right angle?? this means that this is a right angle triangle and you can use Pythagoras theorem to solve it
so by Pythagoras theorem, 5^2= 3^2 + x^2
then you can solve for x
Half the sum of a number and 5
CAN SOMEONE PLEASE HELP ME OUT PLEASE I WOULD APPRECIATE IT VERY MUCH
Answer:Decreasing
Step-by-step explanation:
Focus only on the 8-10 interval for x. Note that for x=8 , y=1, for x=9, y=0 and for x=10, y=-1. Y is obviously decreasing for [tex]8<x<10[/tex] .
What is the vale of of???
Answer:
B
Step-by-step explanation:
Because ∠EDF and ∠BDC are vertical angles, ∠D = 9x. Since ∠ABD and ∠BDC are supplementary, our answer is 2x + 105° + 9x = 180° or B.
Answer:
B
Step-by-step explanation:
∠ BDC = 9x ( vertical angles )
∠ ABD and ∠ BDC are supplementary , thus
∠ ABD + ∠ BDC = 180 , substitute values
2x + 105 + 9x = 180 → B
Find the slope of a line that crosses through (-5,-2) and (9,3)
5 / 14
if you graph the two points, just count the units and put them in a simplified fraction (rise (up or down) divided by run (side to side))
help help help helphelp h;i
Answer:
2
Step-by-step explanation:
It's 2 because the numbers go up by 2 each time the mean is identified meaning that the mean of each is 4.
Answer:
I got 2
Step-by-step explanation:
Which expression is equivalent to 121 - x^2
Answer:
(11-x)x(11+x)
Step-by-step explanation:
