12 4 8 16 3'9' 27' 81' 243 a. yes, b. yes. 2 233 119 C. d. yes. 6 not geometric
Answers
Option A is correct, the sequence is a geometric and common ratio is 2/3.
To determine whether the given sequence is geometric, we need to check if there is a common ratio between consecutive terms.
Let's examine the given sequence:
1/3, 2/9, 4/27, 8/81, 16/243...
To find the ratio between consecutive terms, we can divide each term by its preceding term:
(2/9)/(1/3) = 2/9 × 3/1 = 2/3
(4/27)/(2/9) = 4/27 × 9/2 = 4/6 = 2/3
(8/81)/(4/27) = 8/81 × 27/4 = 2/3
(16/243)/(8/81) = 16/243 × 81/8 = 2/3
As we can see, there is a common ratio of 2/3 between consecutive terms.
Therefore, the given sequence is indeed geometric.
Hence, the sequence is a geometric and common ration is 2/3, Option A is correct.
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Related Questions
The distance around a lake is 8 km. On
a map, this distance around the lake is
represented by a length of 2 cm. The scale
on the map is
Answers
Answer:
1 = 4 or 1 cm : 4 km
Step-by-step explanation:
if 2 cm = 8 km
just divide 2 each side
1 = 4 or 1 cm : 4 km
Scale factor is 4 kilometer in 1 centimeter
Given that;
Distance around a lake = 8 kilometer
Map represent distance = 2 centimeter
Find:
Scale distance of map
Computation:
Scale distance of map = Distance around a lake / Map represent distance
Scale distance of map = 8 / 2
Scale distance of map = 4 km in 1 cm
So,
Scale factor is 4 kilometer in 1 centimeter
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BC has endpoints at B(2, 9) and C(8, 7). Find the midpoint M of BC.
Answers
Answer:
Midpoint, M is (5,8)
Step-by-step explanation:
To find the midpoint, average the x's (add and divide by2) then average the y's.
The x's are the first numbers (2+8)/2 is
10/2 which is 5.
The y's are the second numbers in the parentheses, (9+7)/2 is 16/2 which is 8.
So the x of the midpoint is 5 and the y is 8.
The midpoint is (5,8)
Enter the appropriate value to answer the question or solve the problem.
What is the value of x in the triangle below?
65°
to
75°
Answers
Answer:
x = 40 degrees
Step-by-step explanation:
Triangle angle sum is 180 so 180 = 65 + 75 + x.
180 = 65 + 75 + x
180 = 140 + x
40 = x
If the angle of elevation of P from Q is 38, then the angle of depression of Q from P is:
Answers
Answer:
52°
Step-by-step explanation:
The angle of depression is 90 - angle of elevation
So angle of depression = 90 - 38 = 52°
If lines l, m, and n are parallel,AE is perpendicular to l, AC = 10, CD = 14, andAF = 6, what is the length of DG ? Give your answer as a decimal.
Answers
Using the properties of parallel line and similar triangle we calculate the length of the side DG to be 19.4 units .
In triangle ACF by using the properties of Pythagoras Theorem we can say that
AC² = FA² + CF²
Given:
AC = 10 , FA = 6
∴10² = 6² + CF²
or, CF = 8 units.
Now in triangles ΔACF and triangle ΔADG
CF is parallel to DG , therefore the two triangles are similar.
therefore we can say that using the properties of similar triangle we will use the ratio of the sides to find the given side.
AC/AD=CF/DG
or, 10/24 = 8 / DG
or, DG = 192 /10
or, DG = 19.2 units
Triangles that share the same form but differ in size are said to be similar. All equilateral triangles and squares with equal sides serve as examples of related items.
In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.
Hence the length of the side is 19.2 units.
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You are one of ten people in a swim race. Prizes are awarded to swimmers who finish in first, second, and third places only. Determine the total number of different ways in which the 10 swimmers can achieve 1st, 2nd, or 3rdplace?
Answers
The total number of different ways in which the 10 swimmers can achieve 1st, 2nd, or 3rd place is 720 ways.
Given that:
There are one of ten people in a swimming race. Prizes are awarded to swimmers who finish in first, second, and third places only.
Let's assume that there is A to J swimmers counted as 10 in number.
Then A comes in first, or B comes in first, or ... or J comes in first. So, there are 10 possibilities that any swimmers can come in the first place.
For second place, it can't be the swimmers that arrived first, but it could be any of the remaining 9 swimmers.
For third place, it can't be the first or second swimmers but there are 8 others and one of them will be the third.
Using permutation we can find the total number of different ways in which the 10 swimmers can achieve 1st, 2nd, or 3rd place, because the order of places matters.
The permutation is considered an ordered combination. Objects are arranged from last to first in permutations. The general formula for this is:
P(n, r) = n! /(n-r)!
Therefore, the required number of ways is = 10 possible first swimmers x 9 possible 2nd swimmers x 8 possible third swimmers.
The required number of ways = 10 x 9 x 8 = 720 ways.
Hence, there are 720 ways swimmers can achieve 1st, 2nd, or 3rd place.
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Please help would really appreciate it!
Answers
Answer:
\( r = 6\sqrt{3} \)
Step-by-step explanation:
Area of the shaded section = θ/360*πr²
Area = 15π m²
θ = 360° - 310° = 50°
r = ??
If in the values into the equation and solve for r
15π = 50/360 × π × r²
\( 15 \pi = \frac{5 * \pi * r^2}{36} \)
Multiply both sides by 36
\( 15 \pi * 36 = \frac{5\pi * r^2}{36}*36 \)
\( 540 \pi = 5\pi * r^2\)
Divide both sides by 5π
\( \frac{540 \pi}{5\pi} = \frac{5\pi * r^2}{5\pi} \)
\( 108 = r^2 \)
\( r = \sqrt{108} \)
\( r = \sqrt{36*3} \)
\( r = 6\sqrt{3} \)
A tank in the shape of a hemisphere has a diameter of 16 feet. If the liquid that fills the tank has a density of 93 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
We can do the following steps to solve the exercise:
Step 1: We find the volume of the tank. For this, we use the formula to calculate the volume of a hemisphere.
\(\begin{gathered} V=\frac{2}{3}\cdot\pi\cdot r^3 \\ \text{ Where} \\ V\text{ is the volume} \\ r\text{ is the radius of the sphere} \end{gathered}\)Then, we have:
\(r=\frac{\text{diameter}}{2}=\frac{16ft}{2}=8ft\)\(\begin{gathered} V=\frac{2}{3}\cdot\pi\cdot r^3 \\ V=\frac{2}{3}\cdot\pi\cdot(8ft)^3 \\ V=\frac{2}{3}\cdot\pi\cdot8^3ft^3 \\ V=\frac{2}{3}\cdot\pi\cdot512ft^3 \\ V\approx1072.33ft^3\Rightarrow\text{ The symbol }\approx\text{ is read 'approixmately'} \end{gathered}\)Step 2: We apply the density formula to find the total weight of the liquid in the tank.
\(\text{Density }=\frac{\text{ Mass}}{\text{Volume}}\)We replace the know values into the above formula.
\(\begin{gathered} \text{Density }=\frac{\text{ Mass}}{\text{Volume}} \\ 93\frac{lb}{ft^3}=\frac{\text{ Mass}}{1072.33ft^3} \\ \text{ Multiply by }1072.33ft^3\text{ from both sides} \\ 93\frac{lb}{ft^3}\cdot1072.33ft^3=\frac{\text{ Mass}}{1072.33ft^3}\cdot1072.33ft^3 \\ 93lb\cdot1072.33=\text{ Mass} \\ 93lb\cdot1072.33=\text{ Mass} \\ 99,727lb\approx\text{ Mass} \end{gathered}\)Therefore, the total weight of the liquid in the tank rounded to the nearest full pound is 99,727 pounds.
The sale price of a pair of pants is $24. This sale price is 80% of the original price. What was the original price?.
Answers
Answer:
$30
Step-by-step explanation:
x = original price
0.8x = 24
8x = 240
x = 30
what is the measure of the larger angle in this degree?
Answers
A straight line is equivalent to 180 degrees with that in mind,
(2.4x)+(9.6x)=180
2.4x+9.6x=180
12x=180
12x/12=180/12
x=15
Now to find the measurement of the larger angle,
9.6*15=144
Just in case you need it
180-144=36
Which is your smaller measurement.
Two cards are chosen at random without replacement from a pack of 52 playing cards. If the first card chosen is an Ace, what is the probability the second card chosen is a King?
Answers
Answer:
4/52 or 1/13
Step-by-step explanation:
Answer:
the probabilyy of that will probably be the probability of that question porbably speaking about probability
Is (7,-6) a solution to this system of equations?
y = 1/7x+ 7
X = 7
yes
no
Answers
If you want to get is
Y=mx+b
Y=1/7x+7
Y=1/7*7+7 Since x=7
Y=1+7 Compute 1/7*7
Y=8
The expression above can also be written in the form
So what is A =
Answers
Answer:
what is the expressio
Step-by-step explanation:
What is the image of the point (-6, 2) after a rotation of 180° counterclockwise
about the origin?
Answers
Answer:
\((6,2)\)
Step-by-step explanation:
When rotating 180° about the origin, \((x,y) \longrightarrow (-x, -y)\).
What are the 2  formulas to find the area of a circle
Answers
Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).
What is the area of a circle?The area of a circle is given by the formula A = πr², where r is the radius of the circle.
According to the given information:The area of a circle can be found using either of the following formulas:
\(\pi r^2\), where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.
\(A = (d/2)^2π,\) where d is the diameter of the circle. This formula can also be written as \($A = r^2\pi$\), where r is the radius of the circle and A is the area.
Both formulas are equivalent and can be used interchangeably, depending on the given information about the circle.
Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).
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Question 2
A box contains 22 coloured pencils.
6 pencils are pink, 9 pencils are blue and 7 pencils are yellow.
Write down the ratio pink pencils : not pink pencils.
Give your answer in its simplest form.
Answers
Answer:
3/8 or 3:8
Step-by-step explanation:
pink : not pink
6 : 16
Think of it as a fraction. Simplify it in the same way.
6/16 simplifies to 3/8
So the pink:notpink ratio is 3/8 or 3:8
when simplified it becomes 3:8
need this by today! Pls help! Im desperate! I will give correct anwser brainliest!
Answers
How the grinch stole Christmas- 25%
Rudolph the red nosed reindeer- 37.5%
Frosty the snowman- 6.25%
Need help. This please
Answers
The domain of the quadratic function in this problem is given as follows:
All real values.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
On the graph, the domain of the function is given by the values of x of the function.
A quadratic function has no restrictions on the domain, hence it is defined by all the real values.
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Hot dogs and corndogs were sold at last night's football game. A total of 81 were sold which allowed the concession stand to bring in $201. How many of each were sold?
Answers
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
What is total cost?Total cost is the overall expense incurred for a particular product, service, or project. It includes both fixed and variable costs, such as materials, labor, and overhead. It is often used in business and economic analysis as a measure of the efficiency and profitability of a particular venture. The total cost of a product or service can also be used to set prices and make pricing decisions.
According to question:-
step1
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
step2
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
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you are helping your sister plan her sweet 16. the venue you want to host it at charges $75 for every 3 guest as well as a rental deposit of $200 write an equation to determine the total party cost
Answers
Answer:
y = 25x + 200
Step-by-step explanation:
y = the total cost of the party
x = the number of guests
75/3 = 25
25 is the cost per guest.
Helping in the name of Jesus.
The recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed?
Solve the proportion StartFraction one-fourth over 3 EndFraction = StartFraction p over 9 EndFraction to answer the question. Explain your steps.
Answer:3/4 teaspoons Trust me it is correct
Answers
The number of teaspoons of pepper required for beef is ( 3 / 4).
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes the number of teaspoons required for 9 potatoes will be calculated as below:-
3 potatoes = ( 1 / 4 ) teaspoon
1 potato = ( 1 / 12 ) teaspoon
9 potatoes = 9 / 12 teaspoon
9 potatoes = 3 / 4 teaspoon
Therefore, the number of teaspoons of pepper required for beef is ( 3 / 4).
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so can u help me guys
Answers
Thus, 715,000 = 7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.
Explain about the scientific notations:The number of times that decimal point must be moved to obtain a number between 1 and 10 is the exponent in scientific notation. The decimal point is shifted to the left in order to represent this number in scientific notation.
The main goal of scientific notation is to simplify computations using numbers that are abnormally large or small. With scientific notation, every digit counts because zeros are just no longer used to denote the decimal point.
Given expression:
715,000 __ 7.15 x 10⁵
LHS = 715,000
Take the RHS value :
= 7.15 x 10⁵
This, can be simplifies as:
= 7.15 x 100,000
Now multiply the two values,
= 715,000 (RHS values)
as, LHS = RHS
LHS = 715,000
715,000 (RHS values)
Thus, 715,000 = 7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.
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Divide and express your answer to lowest term
1. 3/4 ÷ 2/5 =
2. 3/8 ÷ 2/12
3. 4/10 ÷ 1/2
4. 6/9 ÷ 8/5
5. 10/12 ÷ 7/8
please answer quick!!!
Answers
Step-by-step explanation:
3/4:2/5=3/4×5/2=15/8
3/8 ÷ 2/12=3/8 ×12/2=36/16=9/4
28. Which unit rate is equivalent to the ratio 12 to 3?
A. 12/1
B. 4/1
C. 9/1
D.3/1
Answers
Answer:
B. 4/1
Step-by-step explanation:
12/3 can be divided by 3.
Therefore 4/1.
If the m/80 degrees then the m/5 =
Answers
Answer:
I don't understand this question, try rephrasing
You can download 15 songs from Spotify for $12. At Itunes, you can download 10 songs for $9. Which Music app has the lower cost per song? How much less is the cost?
Answers
Answer:
ITunes.
Step-by-step explanation:
In iTunes, 1 song is equivalent to $1.11 and on Spotify, 1 song is equivalent to $1.25. So, iTunes has the lowest cost per song by 14 cents.
(but if you want more songs Spotify is better imo)
y = 2x – 15
y = 5x
Can anyone tell me the steps how to solve this and the answer
Answers
Plug in 5x for y
5x = 2x - 15
Subtract 2x
3x = -15
Divide by 3
x = -5, y = -25
Solution: (-5, -25)
please help find the surface area. i will give brainliest
Answers
Answer:
The first one is 145 in^2 and the other is 250 in^2
Step-by-step explanation:
For the first one you have to find the base first so 5*5=25, then you find the area of the other faces and since theres 4 of them dont bother diving them by 2 and just do it twice, so the faces would be 120 in^2 in all add it together and you get 145
For the second one its the same thing but instead of a square base its a triangle so theres only 3 faces. 8*10 = 80/2 =40, 2 of the faces are 140 in all and to find the last one just 14*10=140/2=70 and you add them together and get 250
Find 140 percent of 15.
Answers
Answer:
21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
Firstly, convert this percentage into a decimal. All you have to do is move the decimal point two digits to the left.
Your percentage is currently 140.00. The decimal would be 1.40.
Next, take the given number (15 in this case) and multiply it by the decimal number:
15 * 1.40 = 21.
Hope this helped!
Help! I asked one of the brainly tutors and they got it wrong! Please help!
Answers
Step-by-step explanation:
12x-15-4x+1=-6
12x-4x= -6+15-1
8x= 8
x=1
my answer is 100 % correct