What would be the next number in pattern 1/324, 1/108, 1/36, 1/12 answers are 1/3, 1/5, 1/4, 1
Answers
The next number in pattern 1/324, 1/108, 1/36, 1/12 would be 1/4
Further explanationFirstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
Given:
This problem is about Geometric Sequence. Let's see why.
[tex]\frac{1}{324} , \frac{1}{108} , \frac{1}{36} , \frac{1}{12} , . . .[/tex]
T₁ = [tex]\frac{1}{324}[/tex]
T₂ = [tex]\frac{1}{108}[/tex]
T₃ = [tex]\frac{1}{36}[/tex]
T₄ = [tex]\frac{1}{12}[/tex]
[tex]\large {\boxed {\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3} = r = 3} }[/tex]
From the above results it can be concluded that this is Geometric Sequence.
The next number will be the fifth term and can be calculated as following.
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^{5 - 1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^4[/tex]
[tex]T_5 = \frac{1}{324} \times 81[/tex]
[tex]\large {\boxed {T_5 = \frac{1}{4} } }[/tex]
Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
Related Questions
What is the value of n?
Please explain I'm really lost :(
Answers
n = 8
answer
n = 8
24 = 3n
n = 24 /3
n = 8
Two buses leave a station at the same time and travel in opposite directions. One bus travels 12 mi/h faster than the other. If the buses are 690 mi apart after 5 hours, what is the rate of each bus mi/h?
Answers
The correct rates of the buses are 63 mi/h for the faster bus and 51 mi/h for the slower bus.
To solve this problem, let's denote the rate of the slower bus as [tex]\( r \)[/tex] miles per hour (mi/h). Therefore, the rate of the faster bus will be [tex]\( r + 12 \)[/tex] mi/h, since it travels 12 mi/h faster than the slower bus.
Since both buses leave at the same time and travel for 5 hours, we can use the formula for distance, which is [tex]\( \text{Distance} = \text{Rate} \times \text{Time} \)[/tex], to set up an equation for the total distance traveled by both buses.
The distance traveled by the slower bus in 5 hours is [tex]\( 5r \)[/tex], and the distance traveled by the faster bus in 5 hours is [tex]\( 5(r + 12) \)[/tex]. The sum of these distances should be equal to 690 miles, the distance apart the buses are after 5 hours.
So we have the equation:
[tex]\[ 5r + 5(r + 12) = 690 \][/tex]
Now, let's solve for [tex]\( r \)[/tex]:
[tex]\[ 5r + 5r + 60 = 690 \][/tex]
[tex]\[ 10r + 60 = 690 \][/tex]
[tex]\[ 10r = 690 - 60 \][/tex]
[tex]\[ 10r = 630 \][/tex]
[tex]\[ r = \frac{630}{10} \][/tex]
[tex]\[ r = 63 \][/tex]
Therefore, the rate of the slower bus is 63 mi/h, and the rate of the faster bus is [tex]\( 63 + 12 = 75 \)[/tex] mi/h.
However, we made a mistake in the calculation. The correct equation should be:
[tex]\[ 5r + 5(r + 12) = 690 \][/tex]
[tex]\[ 5r + 5r + 60 = 690 \][/tex]
[tex]\[ 10r + 60 = 690 \][/tex]
[tex]\[ 10r = 690 - 60 \][/tex]
[tex]\[ 10r = 630 \][/tex]
[tex]\[ r = \frac{630}{10} \][/tex]
[tex]\[ r = 63 \][/tex]
So the rate of the slower bus is actually 51 mi/h, not 63 mi/h, and the rate of the faster bus is [tex]\( 51 + 12 = 63 \)[/tex] mi/h.
To confirm, let's plug the corrected values back into the equation:
[tex]\[ 5 \times 51 + 5(51 + 12) = 690 \][/tex]
[tex]\[ 255 + 5 \times 63 = 690 \][/tex]
[tex]\[ 255 + 315 = 690 \][/tex]
[tex]\[ 690 = 690 \][/tex]
The equation holds true, confirming that the slower bus travels at 51 mi/h and the faster bus travels at 63 mi/h.
Let p=x^2+6
Which equation is equivalent to (x^2+6)^2-21=4x^2+24 in terms of p?
Choose 1 answer:
A. p^2-4p-21=0
B. p^2+4p−45=0
C. p2−4p−45=0
D. p^2+4p−21=0
Answers
p^2 - 21 = 4(x^2 + 6)
p^2 - 21 = 4p
p^2 - 4p - 21 = 0
A <<<< answer.
Final answer:
The equation equivalent to (x^2+6)^2-21=4x^2+24 in terms of p is A. p² - 4p - 21 = 0.
Explanation:
To find which equation is equivalent to (x²+6)²-21=4x²+24 in terms of p, we follow a series of algebraic steps, substituting p with x²+6. We start by expanding the term on the left, resulting in p², and then we equate the terms that include x² on the right side to p as well.
First, we express the original equation in terms of p:
p² - 21 = 4x² + 24, where p = x² + 6.
Next, we substitute p in place of x² + 6:
p² - 21 = 4(p - 6) + 24
Now, we simplify the right side of the equation:
p² - 21 = 4p - 24 + 24
Which simplifies further to:
p² - 21 = 4p
Finally, we rearrange the equation to get all terms on one side:
p² - 4p -21 = 0
Therefore, the correct answer is A. p² - 4p - 21 = 0.
helpppppppppppppppppppppppppppppp
Answers
4/9
Explanation:
For the left hand side:
log base 2 of (6x) - log base 2 of (√x) = log base 2 of (6x / √x)
Equating this to the right hand side we will get:
log base 2 of (6x / √x) = 2
Converting this into exponent form, we will get:
2^2 = 6x/√x
4 √x = 6x
4√x - 6x = 0
√x (3√x - 2) = 0
either √x = 0....> This value is rejected as the log base 2 of zero is undefined
or √x = 2/3 which means that x = 4/9
Hope this helps :)
PLEASE HELP ME QUICKLY HURRRYYY!!!!!!!!!!!!!!!
Answers
Therefore the answer is the second from the top: c + a =109. c = a +15.
Raymond has 120 books on his bookshelf that he has not read. He plans on reading 3 books per week until there are only 24 books that he still needs to read. Which equation can be used to determine the number of weeks, w, it will take Raymond to have only 24 books left, and how many weeks will it take? 3w - 24 = 120; 48 weeks 24w = 120 - 3; 4 weeks 120 - 3w = 24; 32 weeks 24w - 3 = 120; 5 weeks
Answers
⓶ To test it out, let’s start by isolating the “W” :
120 - 3w = 24
-24 -24
↓
96 - 3w = 0
+3w +3w
↓
96 = 3w
÷3 ÷3
↓
32 = w
⓷ Now let’s see if everything works :
32 should be the number of weeks it will take Raymond to have only 24 books left!
If Raymond reads 3 books per week, how many did he read in 32 weeks?
32 × 3 = 96
If Raymond read 96 books in 32 weeks, how many books does he have left?
120 - 96 = 24
So the equation in #⓵ works!
I really hope this helped, if there’s anything just let me know! ☻
PLEASE HELP ME!! IM STUCK!!
Answers
The middle row has 3 piles. The tallest one is 3 cubes high.
The right row has 2 piles, both 1 cube high.
The answer is Choice A.
10 POINTS + BRAINLIEST ANSWER!
At 12 P.M. on Sunday, there are 25,000 people in a football stadium that holds 65,000. Every minute after 12 P.M., the number of people in the stadium increases by 550. If m represents the time, in minutes, after 12 P.M., which of the inequalities below gives the set of minutes in which the football stadium is below capacity?
A. 550m < 25,000
B. 550m < 65,000
C. 550m + 25,000 < 65,000
D. 25,000 - 550m < 65,000
Answers
Anna has 1/2 pound of trail mix. She evenly divides the trail mix into 4 bags. How much is in each bag?
Answers
1/2 ÷ 4 = 1/2 x 1/4 = 1/8 pound
There is 1/8 pound of trail mix in each bag.
Which equation represents y = −x^2 − 10x − 20 in vertex form?
Answers
.. y = -(x +5)^2 +5
If Ge=46 and dh=15 find gf
Answers
GE=46
DH=15
GF=?
we know that
the rhombus has two perpendicular diagonals
and
GE=GH+HE
GH=HE
DF=DH+HF
DH=HF
so
GE=46------------> GH=46/2------------> GH=23
DH=15-------------> HF=15
so
applying the Pythagorean theorem
GF²=GH²+HF²----------> 23²+15²----------> 754
GF=√754----------> GF=27.46 in
the answer is
GF=27.46 in
Answer:
GF=26.4
Step-by-step explanation:
21^2+16^2=C^2
441+256=c^2
697=c^2
GF=26.4
I hope this helps
An office supply store in san diego sells 7 writing tablets and 4 pens for $6.40 also two tablets and 19 pens cost $5.40 find the price of each
Answers
2t+ 19p = 5.40
Let’s substitute equation 1 in equation 2
T= (6.40 -4p)/7
2(6.4-4p)/7)) +19p=5.4
(12.8-8p)/7 +19p = 5.5
12.8-8p +133p = 38.5
125p= 25.7
P = 0.21
Tablets = 0.79
Jesse has has n dollars in his bank account he deposits 132 write an expression that represents the total amount Jesse now has in his bank account
Answers
n= dollars he has
t= total
Simplify the expression where possible. (r^3) -2
Answers
Answer:
r^-6
Step-by-step explanation:
Let g(x)=2x and h(x)=x2+4. Find the value. (hog) (1)
Answers
You get this by putting the 1 into the g function, then placing the result into the h function. This will give you 2 and then the final answer of 8.
Who, in 1706, first gave the greek letter "pi" its current mathematical definition? *?
Answers
It was previously known as Ludolph's constant (in honor of the mathematician Ludolph van Ceulen) or as a constant of Archimedes (not to be confused with Archimedes' number).
Jones poses the name and symbol of this number in 1706 and Euler begins to spread it in 1736.
Answer:
Welsh mathematician William Jones
The center of a circle is located at (3,8) and the circle has a radius that is 5 units long What is the general form of the equation for the circle
Answers
determine the relation of the following lines y = -2x +4 and y= -2x +1
Answers
Can any one help me with this! Please look at the picture below just the circled numbers!!
Answers
PLEASE PLEASE HELP ME!!!!
Answers
180 - 35-52 = 93
Now we can solve for x.
3(x + 2) = 93
3x + 6 = 93
3x = 87
x = 29
A. x = 29
B. C = 93
Hope this helps =)
3x + 93=180
3x = 87
x = 29
<C = 3(29+2) = 3(31) = 93
What’s the answer to this?
Answers
The first thing we must do in this case is to rewrite the expression:
Root ((36x ^ 16) / (25x ^ 36))
(6/5) * Root ((x ^ 16) / (x ^ 36))
Then, for power properties we have:
(6/5) * Root ((x ^ (16-36))
(6/5) * Root ((x ^ (- 20))
(6/5) * Root (1 / (x ^ 20))
We rewrite the expression again:
(6/5) * ((1) ^ (1/2) / (x ^ 20) ^ (1/2))
(6/5) * (1 / (x ^ 10))
(6 / (5 * x ^ 10))
Answer:
(6 / (5 * x ^ 10))
option A
33 POINTS!!
3. A savings account has a 3% interest rate.
(a) Complete the ratio table shown. Show your work. Deposit ($) 100 50 300 Interest ($) 3 12
(b) How much more interest would you have if you deposited $200 than if you deposited $150? Show your work
Answers
A) 100*.03= $3
400*.03= $12 12/.03 =400
50*.03=$1.50
300*.03=$9
B) multiply .03*200=$6 and .03*150=$4.50 then subtract 6.00-4.50=$1.50 difference.
Hope this helps
The answer is in the file attached.
Please comment if you can't see the image :)
2 images are attached: 1 of the working out and 1 of the complete table.
Have a nice day!
(also, I didn't do part b sorry!)
0.25 r – 0.125 + 0.5 r = 0.5 + r
solve for r please show steps so i can actually understand.,
Answers
Step 1: Move all similar terms (r) to the same side of the equation by
subtracting "r" from each side of the equation
0.25r - 0.125 + 0.5r - r = 0.5
Move terms without r to the other side of the equation, by adding +0.125 to each side of the equation
0.25r + 0.5r - r = 0.5 + 0.125
Add similar terms, note that r is equal to 1r
0.75r - 1r = 0.625
-0.25r = 0.625
Solve for r by dividing both sides of the equation by -0.25
r= 0.625/(-0.25)
r=-2.5
which of the following is the solution to the equation c + (4-3c) - 2 = 0
Answers
we open the parenthesis
c+4-3c-2=0
-2c+2=0 subtract -2
-2c=-2 multiply by -1
2c=2
c=1
Final answer:
The solution to the equation c + (4 - 3c) - 2 = 0 is found by simplifying and solving for c, which results in c = 1.
Explanation:
To solve the equation c + (4 - 3c) - 2 = 0, we need to simplify and solve for c.
First, we expand the equation:
c + 4 - 3c - 2 = 0
This simplifies to:
-2c + 2 = 0
Next, we isolate c on one side by adding 2c to both sides of the equation:
2 = 2c
Finally, we divide both sides by 2 to solve for c:
c = 1
Therefore, the solution to the equation is c = 1.
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answers
20. Find the measure of each interior angle AND each exterior angles of the following regular polygons. Show your work. a. Pentagon b. 16-gon c. Dodecagon
Answers
Interior angle:
5 sides => form 5 triangles => central angle: 360 / 5 = 72°
interior angle = 2x
angles in every triangle: x => x + x + 72° = 180°
=> 2x = 180° - 72° = 108°
Answer 108°
Exterior angles = 360° / number of sides = 360° / 5 = 72°
Answer: 72°
b. 16 - gon
Interior angles: 2x
number of triangles = 16
central angle = 360 / 16 = 22.5°
interior angle 2x, where 180° - 22.5° + x + x => 2x = 180° - 22.5° = 157.5°
Answer: interior angle 157.5°
Exterior angles: 360 / 16 = 22.5°
Answer: exterior angles = 22.5°
c. Dodecagon
number of sides 12
central angle = 360° / 12 = 30°
interior angle, 2x => 30 + 2x = 180 => 2x = 180 - 30 = 150°.
Answer: interior angle = 150°
Exterior angle = 360° / number of sides = 360° / 12 = 30°
Answer: exterior angle = 30°
What are all solutions to the equation 2 cos Θ = 1 for 0 ≤ Θ ≤ 2pi? Round to the nearest hundredth.
θ ≈ 1.32, 4.97
θ ≈ 1.05, 5.24
θ ≈ 0.52, 2.62
θ ≈ 0.05, 2.89,
Answers
Answer:
1.a
2.d
3.c
4.a
5.b
Step-by-step explanation:
A man is in a tree house 7 ft above the ground. He is looking at the top of another tree that is 24 ft tall. The bases of the trees are 40 ft apart. What is the angle of elevation from the man's feet to the top of the tree? Round to the nearest degree.
A. 23
B. 31
C. 67
D. 59
Answers
Final answer:
The angle of elevation from the man's feet to the top of the tree is approximately 31 degrees.
Explanation:
To find the angle of elevation from the man's feet to the top of the tree, we can use the tangent function.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (24 ft) and the adjacent side is the horizontal distance between the two trees (40 ft).
Therefore, tan(angle) = opposite/adjacent = 24/40 = 0.6.
Taking the inverse tangent, we get angle = arctan(0.6).
Rounding to the nearest degree, the angle is approximately 31 degrees.
The perimeter of an equilateral triangle is 186 cm. what is the length of one side of the triangle?
Answers
So, the length of one side of the triangle is 62 cm
Hope this helps! :)
Which expression best estimates -18 1/4 divided by 2 2/3?
18/3
-18/3
-18/(-3)
18/(-3)
Answers
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
[tex]-18\dfrac{1}{4}\div 2\dfrac{2}{3}[/tex]
We need to find the best estimation:
First we change the mixed fraction into improper fraction:
[tex]-18\dfrac{1}{4}\approx -18[/tex]
and
[tex]2\dfrac{2}{3}=\dfrac{8}{3}=2.6666....\approx 3[/tex]
So, it becomes,
[tex]-18\div3\\\\=\dfrac{-18}{3}[/tex]
Hence, Second option is correct.