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
The algebraic expression 6x - 4 can
be written as which of the
following?
The product of six and a number x
decreased by four
x to the sixth power decreased by four
Six times a number x less than four
four less than six
Answer:
Six times a number x less than four less than six
The product of six and a number x decreased by four.
Given that,
The algebraic expression 6x - 4.
Based on the above information, the information is as follows:
Here 6x - 4 should be written like the product of x and the number x should be decreased by four.
Learn more: brainly.com/question/17429689
A class is made up of 2 boys and 12 girls. Half of the girls wear glasses. A student is selected at random from the class. What is the probability that the student is a girl with glasses
pls help i give brainliest and 5 stars
Step-by-step explanation:
Explanation:
The formula for volume of a sphere is:
V=43πr3
Since we know the volume, and have to find the diameter (twice the radius), we need to determine the radius first.
Hence, using the given data:
2304π=43πr3
We can cancel π from each side.
2304=43r3
Multiply both sides by 34.
2304×34=34×43r3
2304×34=34×43r3
2304×34=r3
5762304×34=r3
576×3=r3
To find the cube root, we separate the factors of the number on the left.
3⋅3⋅3⋅4⋅4⋅4=r3
(3⋅4)(3⋅4)(3⋅4)=r3
12×12×12=r3
12=r
Since the radius (r) is 12, the diameter, which is 2r, will be:
2×12=24
^ this week, The sparkling water was 4 for $5 , the regular was $1.69
I need to do this assignment
Answer:
c
Step-by-step explanation:
(3x+1)(x+6)
3x^2+18x+1x+6
You spin the spinner below once. What is the P(getting a number less than 5)?
Answer:
3/4
Step-by-step explanation:
Other than 5 there are 3 other numbers that could be chosen so its 3/4 chances
The required probability of getting a number less than 5 is 3/4
The correct option is (B)
What is Probability?The mathematical possibility of any event is called probability
The probability of impossible event is zero and sure event is one
The probability can be calculated as
Probability = [tex]\frac{favourable}{total}[/tex]
How to find probability?here we have given total event or sample is
S = {2, 3, 4, 5}
n(S) = 4
The required probability of getting a number less than 5
Favorable event E = {2, 3, 4}
n(E) = 3
Therefore the
P(E) = 3/4
Hence the correct option is (B)
This is the conclusion to the answer.
Learn more about probability here-
https://brainly.com/question/25870256
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Which equation illustrates the commutative property of addition?
12 + 6 + 15 = 12 + 15 + 6
12 + 6 + 15 = 12 + (6 + 15)
12 + 6 + 15 = 18 + 15
12 + 6 + 15 = 12 + 6 + 15
Answer:
12 + 6 + 15 = 12 + 15 + 6
Hope this helps :D
The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend. A 3-column table titled Gift-Wrapping Fundraiser has 3 rows. The first column is labeled Plain Gifts Wrapped with entries 10, 25, 16. The second column is labeled Decorative Gifts Wrapped with entries 9, 12, 12. The third column is labeled Total Raised in dollars with entries 47, 86, 68. Which statement describes the amounts the team charged for wrapping gifts? The team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow. The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow. The team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow. The team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.
Answer:
The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.
Step-by-step explanation:
Gift-Wrapping Fundraiser
Plain Gifts Wrapped Decorative Gifts Wrapped Total Raised in dollars
10 9 47
25 12 86
16 12 68
Let's define:
x: $ charged per gift for Plain Gifts Wrapped
y: $ charged per gift for Decorative Gifts Wrapped
From 2nd 3rd row:
25x + 12y = 86
16x + 12y = 68
Subtracting them:
25x + 12y - (16x + 12y) = 86 - 68
9x = 18
x = 18/9 = 2
Replacing x = 2 into the first equation:
25(2) + 12y = 86
12y = 86 - 50
12y = 36
y = 36/12 = 3
Answer:
The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.
Step-by-step explanation:
B on edg
Suppose you want to build a small walkway around your garden so that there is someplace to walk around and work on your vegetables. The garden measures 20‘ x 30‘ and you want to increase the area of the garden to 1000 ft². What is the width of the walkway
1)Approximately 3.3 feet
2) approximately 3.5 feet
3) approximately 3.7 feet
4) approximately3.9 feet
The figure shown represents a structural portion of the Eiffel Tower. Can the triangles be proven congruent? answers: A) Yes, ΔMNO ≅ ΔPON by HL. B) Yes, ΔMNO ≅ ΔPON by SAS. C) Yes, ΔNOM ≅ ΔPON by AAS. D) Yes, ΔONM ≅ ΔPON by SSS.
Answer:
B) Yes, ΔMNO ≅ ΔPON by SAS
Step-by-step explanation:
The Side Angle Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
In this case, side MO is congruent to side NP and side NO is shared by both triangles. The included angle in ΔMNO is ∠O and in ΔPON is ∠N, and they are congruent.
Answer:
Step-by-step explanation:
B) Yes, ΔMNO ≅ ΔPON by SAS
Just did this test.
please help me out here
*image attached
Answer:
Rate of change = change y / change x
Change y = + 1
Change x = + 2
SO the rate of change is 1/2
WHAT IS THE Y VALUE WHEN X IS 9
y = 1 MULTIPLY by 4.5 = 4.5
x = 2 MULTIPLY by 4.5 = 9
Y = 4.5 when x = 9
What is the missing number that will complete the
factorization?
6
8
12
24
Answer:
6
Step-by-step explanation:
6xa is 6a, just like how 2xa is 2a as shown
If an electric circuit is not grounded, it is best to reach out and touch it to
provide the ground.
O A. True
O B. False
681/4 i dont know this
Answer:
170.25
Step-by-step explanation:
It's a bit tricky to do not on plain paper, but here:
Just assume the long division symbol looks right
_1_7_0_.25
4 ) 681
-4
2 8
-2 8
0 1
The remainder is "1", so you'll just have to write that as either a fraction or decimal, whatever is assigned.
Fraction: 170 1/4
Decimal: 170.25
The answer is 170.25
please see the attached picture for full solution
hope it helps
Good luck on your assignment
I need help solving this asap
Answer:
the answer will be A
Step-by-step explanation:
Answer:
Step-by-step explanation:
I will give the brainiest answer
Answer:
The answer is option (B).
Can someone help me please
Answer:
B
Step-by-step explanation:
To find DC
c²=a²+b² (pythagorean theory)
c²=6²+8²
c²=36+64. c²=100. √100. c=10cm
thus D =10.
AD= 15-6=9
To find AC
c²=a²+b²
c²=15²+8²
c²=225+64. c²=289 √289. c=17
AC=17
perimeter is the distance around a figure thus ADC=9+10+17
=36
What is the volume of a rectangular solid with a length of 12, a width of 3, and a height of 4?
Answer:
144
Step-by-step explanation:
L•w•h
12•4•3= 144
What is the product?
(x+3)(2x - 1)
2x²-3
2x²+66
O 2x²+5x-3
2x²+6x-3
What principal will amount to $3000 if invested at 3% interest compounded
semiannually for 10 years?
Please show the work of the problem
Answer: $2227.41
Step-by-step explanation:
A = P(1 + r/n)^nt
PLEASE HELP!
The dot plots show two different random samples of the number of lunches purchased in a month by some students. Which statement is BEST supported by the data?
Answer: i think its b
Step-by-step explanation:
Answer is B
Step-by-step explanation:
A piece of duct measures 48 inches. When pieces are fitted together, 1 72 inches is lost connecting each successive length of duct. On the job 7 and 12 pieces of ducting are used. What, in inches is the total length of the finished duct?
Answer:
A piece of duct measures 48 inches.
In each connection, we lost 1.72 inches (it also could be 1/2 inches, but i will go with the other option)
Then:
If we have 7 pieces of duct connected we have 5 connections (the ones in the extremes are not connected between them)
So here we have 7 times 48 inches for the pieces, minus 5 times 1.72 inches for the connections, the length is:
L = 7*48in - 5*1.72in = 327.4 inches.
for the 12 pieces duct, we have 12 pieces and 10 connections, so the length is:
L = 12*48in - 10*1.72in = 558.8 in
Now, if we want to make only one duct with those two, then we must add their lengths, but if we connect them, we also need to subtract the 1.72in of the new connection:
L = 558.8 in + 327.4 in - 1.72in = 884.48 in
Which inequalities have the solution set graphed on the number line? Check all that apply.
x Greater-than-or-equal-to -1.5
x Less-than-or-equal-to -1.5
-1.5 Less-than-or-equal-to x
-1.5 Greater-than-or-equal-to x
x Less-than-or-equal-to -2.5
x Greater-than-or-equal-to -2.5
-2.5 Greater-than-or-equal-to x
PLZ HELP QUICKLY I DONT HAVE MUCH TIME WILL GIVE BRAINLIEST
Answer:
This graph represents x is less than or equal to -1.5
Step-by-step explanation:
When the graph faces the direction on the left that represents “less than”, similarly when the graph faces the right directions, that represents “greater than”.
Based on what is given, the graph is “less than”
Closed dot means “equal to”
open dot is just greater or less
Combine all of this and we can safely pick that this graph represents -1.5 less than or equal to 1.5
Answer:
ITS B AND D
CAN I PLEASE GET BRAINLIEST IM TRYING TO RANK UP
Step-by-step explanation:
Help me please!! Anyone
Answer:
180-88
92
Step-by-step explanation:
x=92
Answer:
I think its 92
Step-by-step explanation:
Supplementary angles always add up to 180
This is the question about circle in geometry.
Answer:
A cicle centered in the origin has equation.
[tex]x^2+y^2=r^2\\4^2+1^2=r^2\\r=\sqrt{17}\\ \\\sqrt{5}^2+\sqrt{2}^2\neq \sqrt{17}^2\\ 7\neq 17[/tex]
The point does not lies on the circle
Pls help me to solve this
Answer:
see below
Step-by-step explanation:
19-3 will be greater
We are multiplying 1/2 *(19-3) which is multiplying by a number less than 1 it will be less than 1
18-3 = 16
1/2 * (19-3)
Using PEMDAS
We do parentheses first
1/2 ( 16)
Then multiply
8
vvggggggfgfffgggtttt
Answer:
B
Step-by-step explanation:
The farmer plants 195 rows of beets and has 25 beet plants left over
Answer:
The farmer plants 195 rows of beets and has 25 beet plants left over. The R next to 195 means " remainder" so had acquired an answer which was 195 with a remainder of 25. In conclusion, The farmer plants 195 rows of beets and has 25 beet plants left over.
Step-by-step explanation:
You are a male who has a high school diploma. You plan to attend collage and earn a bachelors degree. When you graduate from college you get a job paying $40,780/yr. how much less areyou earning per year than median?
Answer: I think it’s 20,390
Step-by-step explanation:
Answer: 11,272
Step-by-step explanation: there are 52 weeks in a year multiply that by median wage, which is 1001. Then minus 40,780.
What is the value of x?
6
8
010
O 12
Answer:
8
Step-by-step explanation:
The sum of the internal angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5, hence
sum = 180° × 3 = 540°
Each exterior angle plus interior angle = 180°
Subtract each exterior angle from 180 for corresponding interior angle.
180 - 59 = 121, 180 - 77 = 103, 180 - 66 = 114, 180 - 62 = 118
Sum the 4 interior angles and subtract from 540 for 5 th interior angle
5 th = 540° - (121 + 103 + 114 + 118)° = 540° - 456° = 84°
The 5 th interior angle and 12x sum to 180 ( same reason as above )
Hence
12x + 84 = 180 ( subtract 84 from both sides )
12x = 96 ( divide both sides by 12 )
x = 8
please mark me brainliest :)
95 points!
The scatter plot shows the relationship betweeen the number of hours students spend watching television and the numer of hours they spend with family each week.
What is the y-intercept of the line of best fit and what does it represent?
11.5 hours; the number of hours students spend with family in a week when they do not watch television
9.2 hours; the number of hours students watch television in a week when they do not spend time with family
9.2 hours; the number of hours students spend with family in a week when they do not watch television
11.5 hours; the number of hours students watch television in a week when they do not spend time with family
9.2 hours; the number of hours students watch television in a week when they do not spend time with family
Step-by-step explanation:
We are given,
The x-axis represents the time spent with family and the y-axis represents the time spent on watching television.
Now, y-intercept is the point where the scatter plot crosses y-axis.
From the scatter plot and and according to the options, the data point is located at x= 0 and y= 9.2.
That is, the y-intercept represents that students watched television for 9.2 hours when they do not spend time with their family.
