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3 years ago

Which choice is the explicit formula for the following geometric sequence? 0.2, -0.06, 0.018, -0.0054, 0.00162

Mathematics

1 answer:

Crazy boy [7]3 years ago

8 0

Answer:

aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾

Step-by-step explanation:

The geometric sequence with the first term a, a common ratio r has the nth term given as

Tₙ = arⁿ⁻¹

where Tₙ is the nth term

From the given sequence

a = 0.2

r = -0.06/0.2

= -0.3

Hence the nth term

= 0.2 * -0.3ⁿ⁻¹

The right option is E

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Joaquun is thinking hard about equations and inequalitjes an comes up with this idea: Jf 45+47=t, then t=45+47. so, If 45+47<

timama [110]

If 45 + 47 = t, then t = 45 + 47.....correct

if 45 + 47 < t , then t = 45 + 47....incorrect

45 + 47 < t
92 < t .....this is saying that t is greater then 92

t = 45 + 47
t = 92...this is saying t is equal to 92 (not greater)

8 0

3 years ago

How to do this guys im stuck on this one

OverLord2011 [107]

Answer:

x = 63°

y = 27°

Step-by-step explanation:

RECT is a rectangle.

By the property of interior angles of a polygon,

All interior angles of a rectangle measure 90°

m(∠RTC) = 90°

m(∠RTC) = m(∠RTE) + m(∠CTE) [Angle addition postulate]

x° + 27° = 90°

x = (90 - 27)°

x = 63°

Since, opposite sides of a rectangle are parallel and equal in measure,

RE║TC and TE is a transversal line,

m∠RET = m∠CTE [Alternate interior angles]

y = 27°

5 0

3 years ago

If a dart board was thrown randomly at the dartboard shown below, what is the probability that it will land in the bull’s-eye? T

vampirchik [111]

Answer:

Correct option: C -> 2%

Step-by-step explanation:

To find this probability we just need to divide the area of the bull's-eye circle by the total area of the outer circle.

The area of a circle is given by the equation:

$area = \pi * radius^2$

The outer radius is 14 cm, so:

$outer\ area = \pi * 14^2 = 196\pi\ cm^2$

The inner radius is 2 cm, so:

$inner\ area = \pi * 2^2 = 4\pi\ cm^2$

So the probability is:

$inner\ area / outer\ area = 4\pi / 196\pi = 0.02 = 2\%$

Correct option: C

3 0

3 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

What is 65/8 as a mixed number

lukranit [14]

8 1/65
thats the answer to the simple question

8 0

3 years ago

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