All categories

3 years ago

Find the sum of the first 11 terms of the geometric sequence shown below. 2, 6, 18, 54, ...

Mathematics

1 answer:

Margarita [4]3 years ago

4 0

Answer:

177146

Step-by-step explanation:

2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098

You might be interested in

If given f(x) = –4x – 2 and g(x) = 2x, what is (f · g)(x)?

Rashid [163]

Answer:

-8x^2 -4x

Step-by-step explanation:

f(x) = –4x – 2

g(x) = 2x

(f · g)(x) = (-4x-2) * (2x)

distribute

= -2x*4x -2x*2

= -8x^2 -4x

4 0

3 years ago

A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes a) are there in total?

attashe74 [19]

Answer:

There are 256 ways in total.

There are 56 possible outcomes contain exactly three heads.

The possible outcomes contain at least three heads is 219.

The possible outcomes contain the same number of heads and tails are 70.

Step-by-step explanation:

Consider the provided information.

A coin is flipped eight times where each flip comes up either heads or tails.

Part (a) How many possible outcomes are there in total?

Each time we flip a coin it comes up either heads or tail.

Therefore the total number of ways are:

$2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^8=256$

Hence, there are 256 ways in total.

Part (b) contain exactly three heads?

We want exactly 3 heads, therefore,

n=8 and r=3

According to the definition of combination: $\binom{n}{r}=\frac{n!}{r!(n-r)!}$

$\binom{8}{3}=\frac{8!}{3!(5)!}=56$

Hence, there are 56 possible outcomes contain exactly three heads.

Part (c) contain at least three heads?

For 3 heads: $\binom{8}{3}=\frac{8!}{3!(5)!}=56$

For 4 heads: $\binom{8}{4}=\frac{8!}{4!(4)!}=70$

For 5 heads: $\binom{8}{5}=\frac{8!}{5!(3)!}=56$

For 6 heads: $\binom{8}{6}=\frac{8!}{6!(2)!}=28$

For 7 heads: $\binom{8}{7}=\frac{8!}{7!(1)!}=8$

For 8 heads: $\binom{8}{8}=1$

Now add them as shown:

56+70+56+28+8+1=219

Hence, the possible outcomes contain at least three heads is 219.

Part (d) contain the same number of heads and tails?

Same number of heads and tails means that the value of r=4.

Therefore,

$\binom{8}{4}=\frac{8!}{4!(4)!}=70$

Hence, the possible outcomes contain the same number of heads and tails are 70.

6 0

3 years ago

"Julie has six photos that she has taken, framed and are hanging in a row on the wall. If she wants to rearrange them so that th

erik [133]

Answer:

Julie has 6 photos that she wants to rearrange.

Two of them are fixed at the middle position.

=> There are 4 photos left for rearranging.

=> This is the permutation with n = 4, k = 4.

=> The number of ways Julie can arrange the photos:

N = 4 x 3 x 2 x 1 = 24 ways

Hope this helps!

5 0

3 years ago

Which expression is equivalent to 2(3g - 4) - (8g + 3)?

kolbaska11 [484]

Answer:

Step-by-step explanation:

6 0

3 years ago

Please help

ICE Princess25 [194]

brb for answer i got go find it

4 0

3 years ago

Read 2 more answers