1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Keith_Richards [23]
3 years ago
15

The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to mode

l the same sequence?
Mathematics
1 answer:
astraxan [27]3 years ago
7 0

Answer:

The explicit formula is Tn = 18[(2/3)^(n-1)]

Where n is the term we are looking for

Step-by-step explanation:

Here, we want to get an explicit formula to model the equation

Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12

F(3) = 2/3 * f(2) = 2/3 * 12 = 8

F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3

F(5) = 2/3 * 16/3 = 32/9

Thus, seeing how the equations are progressing, we can definitely see a pattern.

That is Tn = (2/3)^(n-1)(18)

You might be interested in
A bakery made 26 cherry pies, using 115 cherries for each pie. They threw away 36 cherries that were bad. If they used all the c
Artemon [7]

The bakery start with 2954 cherry

<em><u>Solution:</u></em>

Given that,

A bakery made 26 cherry pies, using 115 cherries for each pie

So they used 115 cherry for each pie

26 cherry pies, 115 cherry per pie

Therefore,

Number of cherries used = 26 x 115 = 2990 cherries used

They threw away 36 cherries that were bad

36 cherry were bad

2990 - 36 = 2954

Thus they start with 2954 cherries

7 0
3 years ago
Hannah invested $4000 in a savings account that that earned 2% interest compounded quarterly. she determined that if she does no
Svetach [21]

Answer:

Her account balance after 3 years is $4,246.71

Step-by-step explanation:

In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations

Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.

Mathematically, the amount A earned on a compound interest is calculated as

A = P(1+r/n)^{nt}

where A is the account balance after the number of years which is what we want to know

P is the initial amount invested which is $4000

r is the interest rate which is 2%(2/100 = 0.02) according to the question

n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)

t is the number of years which is 3

We plug the values into the question;

A = 4000(1 + 0.02/4)^(3)(4)

A = 4000(1+0.005)^12

A = 4000(1.005)^12

A = $4,246.71

P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations

5 0
3 years ago
PLEASE HELP FAST ILL MARK YOU BRAINLYEST
Alborosie

Answer:

look at explanation (I go down the first column of scenarios and then move on to the right column)

Step-by-step explanation:

1) The first one will be same as original because the decrease and increase are the same, and happen right after each other so you get the same amount

2) Second one you get greater than original. You're doubling the initial value, and then decreasing by a smaller percentage, so you still get greater than your initial value

3) Third you get greater than original. You're adding 50% of the initial value, and decreasing by 33.5% of the new value, which will still give you more than the original

4) Fourth, you get greater than original. You're adding 60% of the initial value, and then decreasing by 40% of the new value, which will still give you greater than the initial value

5) Fifth you get less than the original. You're decreasing by 75%, and then adding 50% of the new value, which still gives you less than the initial value

4 0
3 years ago
Y= 4x-9 <br> and y=x-3 <br><br><br> Also using transitive property
Andreyy89
Y = 4x - 9 and y = x-3 so the two right sides (4x-9 and x-3) must be equal

4x-9 = x-3

Let's solve for x

4x-9 = x-3
4x-9+9 = x-3+9 ... add 9 to both sides
4x = x+6
4x-x = x+6-x ... subtract x from both sides
3x = 6
3x/3 = 6/3 ... divide both sides by 3
x = 2

If x = 2, then y is...
y = 4*x - 9 = 4*2-9 = 8-9 = -1
which can also be found by 
y = x-3 = 2-3 = -1

So overall x = 2 and y = -1

We have the ordered pair (x,y) = (2,-1)
4 0
3 years ago
H E L P PLZZZ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Kitty [74]

Answer:

138

Step-by-step explanation:

just plug in the numbers:

4*6^2 - 36/6

use pemdas

4*36 - 6 = 144-6 = 138

7 0
2 years ago
Read 2 more answers
Other questions:
  • Find the average (mean) of the following test scores.
    5·1 answer
  • What is the value of x, given that PQ||BC?
    7·1 answer
  • The solution set for |2x - 1| = 15 is {8} {-8, 8} {-7, 8}
    14·2 answers
  • Need helppppp asappppppp
    11·1 answer
  • Please help me find the missing measurement!
    14·2 answers
  • 4. 12 ___ -15 = 27<br> 5. -18 ___ -¾ = 24
    15·2 answers
  • What is this answer to the picture i put below
    15·1 answer
  • Rewrite (3x + 2)(x - 3) in standard form
    12·1 answer
  • Which of the following is not considered a buying incentive?
    13·1 answer
  • In a country there are 48 000 people in the defence services. They work in the army, navy and air force in the ratio : 2.3. How
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!