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2 years ago

Whats the formula of the sequence 13, 27, 41, 55, .....?

Mathematics

1 answer:

Bogdan [553]2 years ago

4 0

Answer:

Step-by-step explanation:

Note the common difference between consecutive terms in the sequence.

d = 27 - 13 = 41 - 27 = 55 - 41 = 14

This indicates the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 13 and d = 14, thus

$a_{n}$ = 13 + 14(n - 1) → A

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One in a hundred million people is a genius. If they are a genius, the probability that the person is acting extremely quirky is

Mila [183]

Answer:

The correct option is E) About 1 in a million.

Step-by-step explanation:

Consider the provided information.

It is given that one in a hundred million people is a genius.

Let G represents the Genius and Q represents the quirky.

We need to find the probability that someone is acting quirky- what is the probability that they are a genius.

The probability that person is quirky is: $P(Q)=0.999\cdot0.00000001+0.01\cdot0.99999999$

The probability of $P(Q\cap G)=0.999\cdot0.00000001$

Hence, the required probability is:

$P(G|Q)=\frac{P(Q\cap G)}{P(Q)}$

$P(G|Q)=\frac{0.999\cdot0.00000001}{0.999\cdot0.00000001+0.01\cdot0.99999999}$

$P(G|Q)\approx 9.98999\times10^{-7}$

Which is near about 1 in a million.

Hence, the correct option is E) About 1 in a million.

5 0

2 years ago

Miss Croft made snack bags for the picnic that contain three types of snacks: packages of crackers, packages of cookies, and can

jek_recluse [69]

Answer: $1.25

Step-by-step explanation:

Let the cost of cracker be a.

Let the cost of cookies be b.

Let the cost of candy bars be c.

From the question,

6a + 6b + 6c = $21

8a + 5b + 10c = $26

5a + 4b + 7c = $18.50

To solve this, we first pick any two pairs of equation. This will be:

6a + 6b + 6c = $21 ....... i

8a + 5b + 10c = $26 ....... ii

Multiply equation i by 8

Multiply equation ii by 6

48a + 48b + 48c = $168 ....... iii

48a + 30b + 60c = $156 ....... iv

Subtract equation iv from iii

18b - 12c = 12

We then pick another two pairs

8a + 5b + 10c = $26

5a + 4b + 7c = $18.50

Multiply equation i by 5

Multiply equation ii by 8

40a + 25b + 50c = $130

40a + 32b + 56c = $148

Subtract the equations

-7b - 6c = -18

Then, solve the new equations formed

18b - 12c = 12 ....... v

-7b - 6c = -18 ....... vi

Multiply equation i by -7

Multiply equation ii by 18

-126b + 84c = -84

-126b - 108c = -324

Subtract the equations

192c = 240

c = 240/129

c = $1.25

From equation v, put the value of c

18b - 12c = 12

18b - 12($1.25) = 12

18b - $15 = $12

18b = $27

b = $27/18

b = $1.5

Since,

6a + 6b + 6c = $21

6a + 6($1.5) + 6($1.25) = $21

6a + $9 + $7.5 = $21

6a + $16.5 = $21

6a = $21 - $16.5

6a = $4.5

a = $4.5/6

a = $0.75

One candy bar cost $1.25

6 0

2 years ago

The two parts to a recursive formula are the starting term and the ____ used to find the next term.

DIA [1.3K]

Answer:

Recursive formulas give us two pieces of information:

The first term of the sequence

The pattern rule to get any term from the term that comes before it

So I think A.Pattern

6 0

2 years ago

Read 2 more answers

A machine needs 2 of its gears replaced. You find 2 gears, one manufactured 5 years ago and the other manufactured 10 years ago.

Tcecarenko [31]

Probability that gear 1 will fail = 5/100 (upto 10 years)
and 8/100 (after 10 years)

Probability that both will fail = 5/100 * 8/100
= 40/10000
= 0.4 %

8 0

2 years ago

Solve for the value<br> 14/5 = z/25

Sladkaya [172]

Answer:

z = 70

Step-by-step explanation:

Multiply by 25 on both sides:

14/5 = z/25

25(14/5) = (z/25)

25(14/5) = z

Divide:

25(14/5) = z

25(2.8)‬ = z

Multiply:

25(2.8)‬ = z

70 = z

8 0

2 years ago

Read 2 more answers