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2 years ago

-2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3, ... Which formula can be use to describe the sequence?

Mathematics

2 answers:

mafiozo [28]2 years ago

6 0

Answer:

Option D is the correct answer.

Step-by-step explanation:

$-2\frac{2}{3}=-\frac{8}{3}\\\\-5\frac{1}{3}=-\frac{16}{3}\\\\-10\frac{2}{3}=-\frac{32}{3}\\\\-21\frac{1}{3}=-\frac{64}{3}$

So the series is

$-\frac{8}{3},-\frac{16}{3},-\frac{32}{3},-\frac{64}{3}.............$

$\frac{-\frac{16}{3}}{-\frac{8}{3}}=2\\\\\frac{-\frac{32}{3}}{-\frac{16}{3}}=2\\\\\frac{-\frac{64}{3}}{-\frac{32}{3}}=2$

We can see that each term is twice of the previous term

So, f(x + 1) = 2f(x)

Option D is the correct answer.

Vesna [10]2 years ago

5 0

D. f(x+1)=2f(x)

f(x+1)=2(-2 2/3)=-5 1/3
f(x+1)=2(-5 1/3)=-10 2/3
f(x+1)=2(-10 2/3)=-21 1/3
f(x+1)=2(-21 1/3)=-42 2/3

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Snowcat [4.5K]

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2. Slope = - 1/2, through (3,0)

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0 = -1/2(3) + b

0 = -1.5 + b

0 + 1.5 = b

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2 years ago

Noah was assigned 64 cookies for the bake sale. He mad 125% of that number. 90% of the cookies he made were sold. How many of No

Mice21 [21]

Noah made 80 cookies and sold 72. This means that 8 cookies were left.

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2 years ago

If the principal is $300 rate 3% time 4 years then what is the interest earned and the new balance

Tomtit [17]

Answer:

a) Interest earned = $36

New Balance = $336

b) Interest rate = 0.05 or 5%

New Balance = $517.5

c) time t = 5

New Balance = $612.5

d) Principal Amount = $675

New Balance = $783

Step-by-step explanation:

We are given:

a) Principal (P) = $300

Rate (r) = 3% or 0.03

Time (t)= 4 years

Interest earned = ?

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding interest

$Simple \ Interest (I)= P\times r\times t\\Simple \ Interest (I)= 300\times 0.03\times 4\\Simple \ Interest (I)= 36$

So, Interest earned = $36

New Balance = Principal + Interest = 300+36 = $336

b) a) Principal (P) = $300

Rate (r) = ?

Time (t)= 3 years

Interest earned = 67.50

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding rate

$Simple \ Interest (I)= P\times r\times t\\67.50= 450\times r\times 3\\67.50=1350\times r\\r=\frac{67.50}{1350}\\r=0.05 \ or \ 5\%$

So, Interest rate = 0.05 or 5%

New Balance = Principal + Interest = 450+67.50 = $517.5

c) Principal (P) = $500

Rate (r) = 4.5% or 0.045

Time (t)= ?

Interest earned = $112.50

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding time

$Simple \ Interest (I)= P\times r\times t\\112.50= 500\times 0.045\times t\\112.50=22.5 \times t\\t=\frac{112.50}{22.5}\\t=5$

So, time t = 5

New Balance = Principal + Interest = 500+112.50 = $612.5

d) Principal (P) = ?

Rate (r) = 8% or 0.08

Time (t)= 2 years

Interest earned = 108.00

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding Principal

$Simple \ Interest (I)= P\times r\times t\\108=P\times 0.08 \times 2\\108=P\times 0.16\\P=\frac{108}{0.16}\\P=675$

So, Principal Amount = $675

New Balance = Principal + Interest = 675+108 = $783

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2 years ago

Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t

juin [17]

Answer:

a. 73; b. 48.9; c. 2; d. 33.8; e. 73

Step-by-step explanation:

Assume the function was

S(t)= 73 - 15 ln(t + 1), t ≥ 0

a. Average score at t = 0

S(0) = 73 - 15 ln(0 + 1) = 73 - 15 ln(1) = 73 - 15(0) =73 - 0 = 73

b. Average score at t = 4

S(4) = 73 - 15 ln(4 + 1) = 73 - 15 ln(5) = 73 - 15(1.61) =73 - 24.14 = 48.9

c. Average score at t =24

S(24) = 73 - 15 ln(24 + 1) = 73 - 15 ln(25) = 73 - 15(3.22) =73 - 48.28 = 24.7

d. Percent of answers retained

At t = 0. the students retained 73 % of the answers.

At t = 24, they retained 24.7 % of the answers.

$\text{Percent retention} = \dfrac{\text{24.7}}{\text{73}} \times 100 \, \% = \text{33.8 \%}\\\\\text{The students retained $\large \boxed{\mathbf{33.8 \, \%}}$ of their original knowledge after two years.}$

e. Maximum of the function

The maximum of the function is at t= 0.

Max = 73 %

The graph below shows your knowledge decay curve. Knowledge decays rapidly at first but slows as time goes on.

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2 years ago

the point (- 7, 4) is reflected over the line x = - 3 . Then , the resulting point is reflected over the line y = x . Where is t

uysha [10]

Answer:

(-10,-7)

Step-by-step explanation:

first reflect over x=-3

(-7,-10)

then reflect over y=x

(-10,-7)

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2 years ago