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Vitek1552 [10]
3 years ago
13

Gouilleul Sequence.

Mathematics
1 answer:
harkovskaia [24]3 years ago
6 0

Answer:

Step-by-step explanation:

No idea what a gouilleul Sequence is, but hopefully it will help to show how I would find the answer.

A geometric  sequence means a term is multiplied by something over and over So say we start with 100 and the common ratio is .5 then the sequence would go 100,50,25,12.5,6.25 and so on.  Another way of writing it is:

100*.5^0 = 100

100*5^1 = 50

100*.5^2 = 100*.25 = 25

and so on.  

ANyway, here we have the first and fourth term.  so that's 3.5*x^0 and 3.5*x^3.  Keep in mind the exponent will be n-1 when the term you want to find is the nth term.  Anyway, we know 3.5*x^3 = 28, so we just use algebra to find x, which is the common ratio.

3.5*x^3 = 28

x^3 = 8

x = 2

So the common ratio is 2, or in other words it keeps doubling.  You could try it real quick, keep doubling the starting term 3.5

3.5, 7, 14, 28 and 28 is the fourth term.  

So we know the common ratio.  you could just add the four terms listed then for part b, but there is an equation, for in case they ask you to find the sum of say the first 100 terms.  that wouldn't be fun.  Anyway, the formula is a((1-r^n)/(1-r)) where a is the starting term, r is the common ratio and n is the number term.  In your case that's 3.5((1-2^4)/(1-2)) = 52.5.  You can actually check since it's only 4 terms.  3.5 + 7 + 14 + 28 = 52.5.

If you want to know how that formula was gotten let em know and I can explain or give a link to a video or something to show.

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3 years ago
1A technical magazine stated that the mean retail cost of all models of a particular laptop was $600. A random sample of 10 stor
My name is Ann [436]

Answer:

Yes

Step-by-step explanation:

Given,

Population mean Z = 600

Sample mean, µ = 586.50

Size of the sample, n = 10

Standard deviation, σ = 26.77

The testing hypothesis is,

Null hypothesis = µ<600

Alternative hypothesis = µ≥600

The test statistics is the calculated value of Z,

(Z- µ)/(σ/√n)

= (600-586.50)/(26.77/√10)

= (13.5*3.1623)/26.77

= 42.691/26.77

= 1.5947

And at 5% level of significance, the table value of Z = 1.644

Here, calculated Z<Table value of Z, so we accept the null hypothesis.

So, the null hypothesis is accepted. The mean value of the laptop is less than 600.

3 0
3 years ago
A gambler playing blackjack in a casino using four decks noticed that 20% of the cards that had been dealt were jacks, queens, k
Ksenya-84 [330]

Answer:

x = 162 cards need to be dealt with

Step-by-step explanation:

Given:

- Estimation of likelyhood of next card to be queen, a king, or an ace:

                                  ( 64 - 0.2*x ) / ( 208 - x )

Find:

For what values of x is this likelihood greater than 70%?

Solution:

- Use the likely-hood estimation relation and set up the inequality as follows:

                                 ( 64 - 0.2*x ) / ( 208 - x ) > 0.7

                                 ( 64 - 0.2*x ) > 0.7*( 208 - x )

                                   64 - 0.2*x > 145.6 - 0.7*x

                                          0.5*x > 81.6

                                                 x > 163.2

- It would require 162 cards to be dealt with for the probability of next card being queen, a king, or an ace is greater than 70%

6 0
2 years ago
Last year, Maria had $10,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she inv
denis-greek [22]

Answer:

$3,000 invested at 6%

$7,000 invested at 10%

Step-by-step explanation:

Maria had total $10,000 to invest.

Let x be the amount that Maria invested initially at 6% interest rate.

0.06x

Then she invested the remaining amount at 10% interest rate.

0.10(10,000 - x)

She received a total of $880 in interest.

0.06x + 0.10(10,000 - x) = 880

0.06x + 1000 - 0.10x = 880

-0.04x = 880 - 1000

-0.04x = -120

0.04x = 120

x = 120/0.04

x = $3,000

This is the amount that Maria invested initially at 6% interest rate.

The remaining amount is

10,000 - 3,000

$7,000

This is the remaining amount that she invested at 10% interest rate.

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2 years ago
Pete entered a lucky draw. The probability of winning a free ticket for a soccer game is 15%. What are the ODDS AGAINST winning
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Answer:

3 to 20

Step-by-step explanation:

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1 year ago
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