Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form an = a1 ⋅ rn−1. explain how you arrived at your answer.

Answers

Answer 1

The rule of the geometric sequence is [tex]a* r^{n-1} [/tex]
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio

Given: the fourth term (a4) = 121.5 and the common ratio = 3 and n = 4

∴ [tex]121.5 = a* 3^{4-1} [/tex]
∴ a = 121.5/3³ = 121.5/27 = 4.5

So, The formula for this sequence will be [tex]4.5 * 3^{n-1} [/tex]

Answer 2

Answer:

First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.

Related Questions

Claire says the area of a square with a side length of 100 centimeters is greater than the area of a square with a side length of 1 meter. Is she correct? Explain

Answers

To answer Claire's question we need to convert both dimensions into same units.
100 cm=1 m
this implies that both squares are the same hence their areas will be the same. Thus we conclude that Claire was wrong, neither of the area of the squares is greater than the other one.

What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?

Answers

Here's the equation for one year:
0.06(6500) + 6500
But because it is 25 years:
25(0.06(6500)) + 6500
1.5(6500) + 6500
We can make it simpler:
2.5(6500)
The total amount is $16350

To calculate the total amount and interest earned on $6,500 at 6% simple interest for 25 years, you use the formula I = P × r × t, which gives you interest (I) of $9,750. Adding the interest to the principal, the total amount after 25 years is $16,250.

To calculate the total amount and the interest earned on $6,500 at a simple interest rate of 6% for 25 years, we can use the simple interest formula:

I = P × r × t

Where:

I is the interestP is the principal amount ($6,500)r is the annual interest rate (6%, or 0.06)t is the time in years (25)

Using this formula:

I = $6,500 × 0.06 × 25

I = $9,750

The total amount after 25 years will be the principal plus the interest:

Total Amount = P + I

Total Amount = $6,500 + $9,750

Total Amount = $16,250

The interest earned on the investment after 25 years is $9,750.

The two lines, P and Q, are graphed below: Line P is drawn by joining ordered pairs negative 8,15 and 6, negative 12. Line Q is drawn by joining ordered pairs 4,16 and negative 9,10 Determine the solution and the reasoning that justifies the solution to the systems of equations

Answers

Answer:

[tex]\text{Solution: }\left(-\dfrac{2654}{435},\dfrac{1644}{145}\right)[/tex]

Step-by-step explanation:

Line P is drawn by joining ordered pairs (-8,15) and (6,-12)

Using two point formula of line. Find equation of line P

[tex]\dfrac{y-15}{x-(-8)}=\dfrac{-12-15}{6-(-8)}[/tex]

[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{6+8)}[/tex]

[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{14}[/tex]

[tex]y=\dfrac{-27}{14}(x+8)+15[/tex]

[tex]y=\dfrac{-27}{14}x+\dfrac{-27}{14}\times 8 + 15[/tex]

[tex]y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]

[tex]\text{Equation of line P:}y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]

Line Q is drawn by joining ordered pairs (4,16) and (-9,10)

Using two point formula of line. Find equation of line Q

[tex]\dfrac{y-16}{x-4}=\dfrac{10-16}{-9-4}[/tex]

[tex]\dfrac{y-16}{x-4}=\dfrac{-6}{-13}[/tex]

[tex]\dfrac{y-16}{x-4}=\dfrac{6}{13}[/tex]

[tex]y=\dfrac{6}{13}(x-4)+16[/tex]

[tex]y=\dfrac{6}{13}x-\dfrac{6}{13}\times 4 + 16[/tex]

[tex]y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]

[tex]\text{Equation of line Q:}y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]

Using graphing find solution of system of equation.

We draw the line on graph and see the intersection point.

Please see the attachment of the line.

Answer:

(−2, 4), because it is the point of intersection of the two graphs

Step-by-step explanation:

BECAUSE

Factor x2 – 8x + 15.
Which pair of numbers has a product of ac and a sum of b?

Answers

-5 and -3 are your numbers.

which statement most accurately explains why x^5/x^2 is equal to x^3?

Answers

[tex]\bf \cfrac{x^5}{x^2}\implies \cfrac{x^{3+2}}{x^2}\implies \cfrac{x^3\underline{x^2}}{\underline{x^2}}\implies x^3[/tex]

The answer you are looking for would be C.

When you divide varibles with exponents, you subtract the exponents. Since there are no numbers in front of the x, we can assume there is only 1 x. 1x/1x = 1x. Since the top has the largest exponent, you'd subtract the bottom exponent to the top, leaving a power of 3. Thus meaning, the answer of x^3 is explained in C.

I hope this helps!

1. In the figure, m DE = 106 degrees and m BC = 62 degrees. The diagram is not to scale.

What is m< A?

A) 44 degrees

B) 22 degrees

C) 75 degrees

D) 85 degrees

2. In the figure, m AB = 45 degrees and m CD = 23 degrees. The diagram is not drawn to scale.

What is the value of x?

A) 34 degrees

B) 56.5 degrees

C) 22 degrees

D)68 degrees

Can someone please check my work and tell me if I'm correct or not and explain.

Answers

For question 1, the formula for that is m1= 1/2(a-b). 106 being A and 62 being B. You should get m1=.5*(106-62) which equals B.22

The measure of the missing angles in both instances is; m∠A = 22 degrees and x = 34 degrees

How to find the angles in the triangle?

1) For question 1, the formula for the missing angle from triangle is;

m∠A = ¹/₂(∠DE - ∠BC).

Thus;

m∠A = ¹/₂(106 - 62).

m∠A = 44/2

m∠A = 22 degrees

2) To get the missing angle, we will use the formula;

x = ¹/₂(AB + CD)

This is because the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

x = ¹/₂(45 + 23)

x = 34 degrees

Read more about angles in a triangle at; https://brainly.com/question/12621139

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How to find an area of a circumbscribed hexagon using the diameter?

Answers

The formula for the area of a circumscribed hexagon = 1/2 * 6 * a * r where a = side length and r = radius of the circle ( = 1/2 the diameter) so in terms of the diameter and side length its 1/2 * 1/2 * 6 *d * a = 1.5 ad.

You can calculate the value of a by using trigonometry You consider one of the 6 isosceles triangles that make up the hexagon. The vertex angle of these triangles = 60 degrees so:-

tan 30 = 1/2 a / r = 1/2 a / 1/2 d = a/d

a = d tan 30 = sqrt3 d / 3

Substituting for a :-

So the required formula for the area of the hexagon = 1.5 ad

= 1.5 * sqrt3 d * d / 3 = 1/2 sqrt3 d^2 Answer

Is Part A correct? And can someone please help me with part B? (Highlighted)

Answers

Part A. Your model is as good as any. It is hard to tell if the label needs to include the descriptor (length = 12 ft, for example). Certainly your model is sufficient for Part B.

Part B. The total area is the sum of the areas of each of the 6 faces of the box. Opposite faces are the same area, so you have
A = 2(LW +WD +LD) = 2(LW +D(L +W))
Subsituting the given dimensions, you get
A = 2((12 ft)(6 ft) +(3 ft)(12 ft +6 ft))
A = 2(72 ft² +(3 ft)(18 ft))
A = 2(72 ft² +54 ft²) = 252 ft²

The least amount of paper required to cover the box is 252 ft².

A tree's root is 9 feet below ground and spans a radius of 6 feet. If the total length of the tree from root tip to top is 23 feet, what is the tree's elevation above ground?
a. 14 feet
b. 17 feet
c. 26 feet
d. 32 feet

Answers

Hello!

You know the tree goes 9 feet underground and the tree is 23 feet tall from root to top

You can subtract how far the tree goes underground by the length of the tree to get the answer

23 - 9 = 14

The answer is A) 14 feet

Hope this helps!

The measure of arc QS is (4x – 18)°.

What is the value of x?

40.5
49.5
94.5
180

ANSWER IS 49.5

Answers

Answer:

Option B. 49.5 degrees

Step-by-step explanation:

Given that arc QS measures 4x-18

Arc QS is a semicircle and hence subtended angle by semicircle at the centre is 180 degrees.

Use this to find the value of x

4x-18 = 180 degrees

Add 18 to both sides

4x=198

Divide by 4

x =198/4 =49.5

So answer is option B

49.5 degrees

Answer:

49.5

Step-by-step explanation:

Find the geometric mean of 125 and 5.

Answers

The geometric mean would have to be 25.

Write an equation of the graph:

y = |x| translated two units downward

Answers

Y = |x| - 2. Nothing too complicated for this transformation

y = |x| - 1 is the answer

ur mom

Compute the sales tax on the following transactions. An article retails for $37.50. The city sales tax is 6%, and the federal excise tax is 8%. How much does the article cost altogether?

Answers

First you must find the rate of both taxes. Since its 8% and 6%, you must add them both together, then divide them by 100.

14/100 = .14

Then for both rates you must add 1 because it is a tax increase.

1 + .14 = 1.14

Finally times 37.50 with 1.14

37.50(1.14) = 42.75

$42.75 is the answer.

Answer:

The article will cost altogether:

$ 42.75

Step-by-step explanation:

It is given that:

The retail price of the article is: $ 37.50.

Also, the article will hold a city tax of 6% and a federal excise tax of 8%.

Hence, the total percent tax on article is: 6+8=14%

This means that the cost price of the article is:

Retail Price of article+14% of retail price.

= 37.50+14% of 37.50

= 37.50+0.14×37.50

= 37.50+5.25

= 42.75

Hence, the article will cost: $ 42.75

I am struggling with Parts B and D of this calculus question. I think that Parts A and C are OK. I wonder if Parts B and D require the graph that I drew for Part A?

Answers

For part B, you are correct as far as you've gone. There is no algebraic solution to your equation. A graphing calculator or Newton's Method iteration can get you to a solution fairly quickly.
a ≈ 1.114157141

For part C, you need to consider your answer. For a=0, the equation is that of a straight line, so there is no inflection point at x=1. For cos(a)=0, there are an infinite number of possible values of [tex]a[/tex] that will put a point of inflection at x=1. As you have noted, a=π/2 is only one of them in the range 0 < a < 4.

For part D, again you have stopped part way to the answer. Consider what values of [tex]a[/tex] will make [tex]a \sin(ax)[/tex] strictly greater than 1. There aren't any. The sine function always crosses zero. This part of the question has no solution.

Elijah is going to spin a spinner 180 times. mc008-1.jpg He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?

Answers

Answer:

its C on Edge

Answer:c

Step-by-step explanation:

the distance between bay town and oak glen is 175 miles. if the equation y=-x+175 represents the distance left to travel to oak glen, what does the domain represent? what is the domain?

a) time left to reach oak glen; x>0
b) distance left to reach oak glen; x>0
c) time it takes to travel oak glen; x>0
d) distance traveled since leaving bay town; x>0

Answers

The domain is
the distance traveled since leaving bay town; x>0.

The set of input values is distance traveled and it will make the 175 miles decreaxse.

The correct option is D, distance traveled since leaving bay town; x>0.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

Given that the distance between bay town and oak glen is 175 miles. If the equation y=-x+175 represents the distance left to travel to oak glen.

Since the distance left to travel to oak glen can be 0 this will be when you reach Oak glen, while the minimum will be when the journey is just started and you haven't travelled even a single mile.

Therefore, the domain of the function is from 0 to 175, and the domain represents the distance traveled since leaving the bay town.

Hence, the correct option is D, distance traveled since leaving bay town; x>0.

Learn more about Domain and Range here:

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a man made lake is stocked with 10,000 fish. This population is expected to decline by an annual rate of 15%. Predict the fish population 5 years after the lake is stocked

Answers

I got 2,500 left after 5 years.
10,000*15% = 1,500 or you could do 10,000*.15 = 1,500

That is a loss of 1,500 fish per year.
If you want to think of this as a proportion then you would do
Year/fish lost

1/1,500 = 5/x
X=5*1,500
X=7,500

The population of the fish after 5 years equals
10,000-7,500 = 2,500
So your answer is 2,500 fish are left

The population will be approximately 4,437 fish after 5 years.

To predict the fish population 5 years after the lake is stocked,

We can use the formula for exponential decay:

[tex]\[ P = P_0 \times (1 - r)^t \][/tex]

Where:

P is the final population[tex]$ P_0 $[/tex] is the initial populationr is the annual rate of decline (expressed as a decimal)t is the number of years

Given:

[tex]\( P_0[/tex] = 10,000 (initial population)r = 0.15 (annual rate of decline, expressed as 15% or 0.15)t = 5 (number of years)

Substituting the values into the formula:

[tex]\[ P = 10,000 \times (1 - 0.15)^5 \][/tex]

[tex]\[ P = 10,000 \times (0.85)^5 \][/tex]

Calculating:

P ≈ 10,000 × 0.443705

P ≈ 4437.05

So, the fish population 5 years after the lake is stocked is approximately 4437 fish.

The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7. if in the last game he made 77 assists, how many standard deviations is that from the mean? 1.36 standard deviations below the mean 2.71 standard deviations above the mean 1.36 standard deviations above the mean 2.71 standard deviations below the mean

Answers

Given that mean=58
standard deviation=7
thus
77 is (77-58)=18 away from 58
This will be:
19/7=2.71

standard deviations from the mean.

Answer: 2.71 standard deviations above the mean

Answer:

(B)

Step-by-step explanation:

It is given that The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7.

Also, in the last game he made 77 assists, therefore

[tex]77-58=19[/tex] assists away from the mean.

Thus, To get the number of standard deviation that 77 is from the mean, we get the z-score which is given as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substituting the given values, we get

[tex]z=\frac{77-58}{7}[/tex]

[tex]z=\frac{19}{7}[/tex]

[tex]z=2.71[/tex]

Thus, there are 2.71 standard deviations above the mean.

Hence, option B is correct.

A test consists of 10
a. True
b. False questions. to pass the test a student must answer at least 9 questions correctly. if a student guesses on each question, what is the probability that the student will pass the test?

Answers

the answer will be 1/2^9

Frank owns 300 acres of land. If he divides the land into 1/2 acre plots, how many plots will he have?

Answers

If there are 300 acres, each split in half, than the number of plots will be twice that: 600. Frank has 600 plots of land.

your answer would be 150 acre plots
hope that helps

The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)

Answers

For this case we have the following equations that represent the position of the rocket:
x (t) = 3t
y (t) = 4t ^ 2 + 1
Substituting t = 10 in both equations we have:
x (10) = 3 (10) = 30
y (10) = 4 (10) ^ 2 + 1 = 400 + 1 = 401
Therefore, the position of the rocket is:
(x, y) = (30, 401)
Answer:
the ship after 10 seconds is at:
C.) (30,401)

The answer is C. (30,401) I already checked.

Graph BCD with vertices.

Answers

first you need to plot the coordinates given first (along the corridor, up the stairs if you forget which order the directions come in) then join them together.

when you've drawn that, draw on the line x=1

to draw that go to the x axis and go along one, then flip the triangle as though it were in a mirror (use a real mirror if it helps you visualize)

Please help me with this

Answers

Number of Art 2 students who entered digital pieces = 24
%( Art 2 students who entered digital pieces)=(24/300)*100%=8%
Number of all entries that were painted by Art 1 students = 34
%( painted by Art 1 students)=(34/300)*100%≈11.3%
%( clay pieces by Art 3 students)= (20/300)*100%=6.7%

From least to greatest,
6.7% - clay pieces by Art 3 students
8%- Art 2 students who entered digital piece
11.3%-painted by Art 1 students

Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? _____ millimeters

Answers

The standard deviation, of a set of 20 data, is 6.

Given:
set of 20 data
variance of 36

Find the standard deviation from the mean.

The formula for the standard deviation is the square root of the variance.

Standard deviation = √36

Standard deviation = 6

Two rafts are traveling In opposite directions on a straight river. The raft going with the current is traveling at a speed of 12 mph. The raft going against the current is traveling at a speed of 70 miles per hour. Both rafts travel the river for two hours. Which equation represents the situation? Assume the raft traveling with the current travels X miles in the raft traveling against the current travels y miles.

A. 12/x - 7/y = 1/2
B. 12x + 7y = 2
C. x/12 - y/7 = 2
D. x/12 + y/7 = 4
E. 12x + 7y = 4

Answers

Time =(distance)/speed
Time taken by the raft going with the current to travel x miles is:
12/x hours
Time taken by the raft going against the wind is:
7/y
Total time taken for both raft is 4 hours thus:
12/x+7/y=4
hence the answer is:
D. x/12 + y/7 = 4

The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2-foot border of the floor visible on all sides. What should the length (the longer side) of the rug be?

Answers

if the area is 168& the length is 2 feet more so length is 14& width is 12 (14*12= 168), the rug is 8feet in total less from all sides so it gives an area on 160. To come out with length& width knowing the length should be less than 14, so it could be either (10*16, 8*20)

You play darts with a friend. The board is a circle with a 6-inch radius. The “Bull’s Eye” is a smaller circle in the center of the board with an 0.25-inch radius. You throw darts (small metal arrows) at the board. At the end of six weeks, she has thrown 500 darts. She hit the board every time and hit the Bull’s Eye 1 time If you throw 500 darts, how many times should you expect to hit the Bull’s Eye by random chance? Compare this result to your friend’s result. Is she a skilled player for hitting the bull’s eye or is the result of hers expected?

Answers

The area of the board = πr² = 36 π square inches
Area of the Bull's eyes = πr² = 0.0625 π square inches

If a dart is thrown at random, the probability that it will hit the bull's eye can be calculated as:

Area of Bulls's Eyes divided by Area of Complete Board

So, probability of hitting the bulls'e eye = 1/576 = 0.001736

The friend hit Bull's eye once in a 500 throws. So the probability of hitting the Bull's eyes will be = 1/500 = 0.002

If we compare the two probabilities, they are close to each other. So we can conclude that the friend is not a skilled player and she hit the bull's eye just by chance.

Assume that the starting point of a path in such a grid is labeled the origin ≡ (0,0). the destination is the point (m,n). in other words, there are (n+1) streets in the x direction and and (m+1) streets in the y direction; and any portion of of any of these streets can be used to reach the destination. find the total number of distinct paths; assuming that all streets are available.

Answers

(m+1)*(n+1)
if there is a direct street from (0,0) to (m,n) : (m+1)*(n+1)+1

Trey's mom planted an 18 feet by 20 feet garden in his back yard. this new garden reduced the area of trey's backyard by 24%. which answer choice best represents the total area of the back yard

Answers

Ok so the answer should be 1500 square feet

The garden area is given by:

[tex] A = (18) * (20)

A = 360
[/tex]

We are looking for the backyard area now.

For this, we make the following rule of three:

360 ---------------------> 24%

x -------------------------> 100%

From here, we must clear the value of x.

We have then:

[tex] x = (100/24) * (360)

x = 1500 ft ^ 2
[/tex]

Answer:

The total area of the back yard is:

[tex] x = 1500 ft ^ 2 [/tex]

The greatest common factor of 24and 36 is the least common multiple of a pair of numbers.which two number could they be ? Pls make sure to explain this specifically!!
A.3 and 6
B.4 and 6
C.8 and 9
D.8 and 12

Answers

4, and 6. Because 4 is a common factor of 24, and it is also the least factor. Same thing with 36. Remember: 4 x 6 = 24 and 6 x 6 = 36. Hope this helps!

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Psychological research that requires subjects to participate in an experiment without the person giving his or her consent would be viewed by the american psychological society as: If AD=2/3 AB , the ratio of the length BC of to the length of DE is . Complete the analogy benefit :advantage :: gradual: A father is giving his child a 30-inch long softball bat for her birthday.He has a rectangular box that has the dimensions of 5 inches by 6 inches by 25 inches. Will the bat fit in the box ? Explain Peter is working for an hourly wage of 12$ if he worked for 20 hours last week what is his gross pay Scientists discovered fossil evidence of mesohippus, an ancestor of the modern horse. Mesohippus lived in North America about 40 million years ago. Mesohippus was about two feet tall, ran on hooves with three toes, and had large, grinding teeth. It is believed that these early horses lived in the thick forests. What may have helped horses change over the last 40 million years? (05.07 mc) mandy needs to paint all the faces and the base of a model pyramid she made for her history project. the dimensions of the pyramid are shown here. what is the total surface area of the pyramid? a square pyramid is shown. the side of the square is 10 inches. the height of the triangular faces is 9 inches. Which planetary model allows a scientist to predict the exact positions of the planets in the night sky over many years?A) The planets' orbits are circles in a geocentric modelB) The planets' orbits are circles in a heliocentric modelC) The planets' orbits are ellipses in a geocentric modelD) The planets' orbits are ellipses in a heliocentric model In a '20% off' sale, a coat was 220. Work out the original price. the charter of the United Nations was adopted A) immediately following the last session of the League of Nations B) in the year after world war 11 endedC) after the Cold War began D) at the beginning of world war 11 Read the text and answer the following question. In ancient literature, the genre which most closely approximates the novel is the epic. Works such as Homers Iliad and Odyssey as well as Virgils Aeneid, though poetry, are long narratives centered around certain key events and characters with heroic or cowardly actions that determine, not only their own fates, but also those of the nations which they led. The novel carries this tradition on, but in a reduced scope. The novel is much more localized, centering on characters in local settings, whose actions affect themselves and perhaps a few members of their local community. What is the main idea in the text? Epic poems are greater in scope than novels. Epic poetry was a precursor to the novel. Epic poetry is poetry; novels are prose. A batch of cookies requires 3/8 cup of butter. Butter can be purchased in boxes, each containing 4 sticks, with 1 stick equivalent to 1/2 cup of butter. If Monica is to bake 15 batches of cookies, which of the following is the best estimate for the total number of boxes of butter she needs to buy? A saving account pays 3.6% per annum simple interest Heidi puts 400 into the account, how much will she have in the account after 5 years? A plane can fly 300 miles in the same time as it takes a car to go 150 miles. if the car travels 90 mph slower than the plane, find the speed of the plane. when is periodic data useful? give examples to support your answer please a season ticket for bolton f.c. this season cost 410 it is to go up by 34% next season how.much will a season ticket cost next season? For the oxidationreduction reaction equation 2na+s na2s indicate how many electrons are transferred in the formation of one formula unit of product. NEED HELP ASAP!!! Susan makes $5 per hour babysitting and $7 per hour as a life guard. Her goal is to make at least $140. which of the following represents three possible solutions to the problem? what does it mean if the quotient times the divisor does not equal the dividend? What should you do? Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing.Use a two-way table to organize the information and answer the following question:Approximately what percentage of students signed up for neither canoeing nor trekking? 72% 40% 54% 98%