All categories

3 years ago

Which answer describes the pattern in this sequence? 2,1,12,14,...

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

3 0

Answer:

$a_n = 2( \frac{1}{2})^{n - 1}$

Step-by-step explanation:

The given pattern is:

$2,1, \frac{1}{2} , \frac{1}{4}$

The first term is

$a_1=2$

The common ratio is the previous term of any consecutive two terms over the previous term.

$r = \frac{1}{2}$

The explicit formula that describes this pattern is:

$a_n = a_1 {r}^{n - 1}$

We substitute the common ratio and the first term to get:

$a_n = 2( \frac{1}{2} )^{n - 1}$

You might be interested in

Bill booked a ride to the airport. If it rains, the traffic will be bad and the probability that he will miss his flight is 0.06

kvasek [131]

Answer:0.614

Step-by-step explanation:

Given

Probability he will miss flight if it rains=0.06

Probability he will miss flight it does not rain=0.01

Given the probability of rain=0.21

Therefore Probability that it will not rain=1-0.21=0.79

Probability that he will miss the flight $=0.21\times 0.06+0.79\times 0.01=0.0205$

P(actual raining and he missed the flight| he miss the flight) $=\frac{0.21\times 0.06}{0.21\times 0.06+0.79\times 0.01}$

$=\frac{0.0126}{0.0205}=0.614$

7 0

3 years ago

A device produces random 64-bit integers at a rate of one billion per second. After how many years of running is it unavoidable

nikitadnepr [17]

Answer:

3171 × 10^(44) years

Step-by-step explanation:

For each bit, since we are looking how many years of running it is unavoidable that the device produces an output for the second time, the possible integers are from 0 to 9. This is 10 possible integers for each bit.

Thus, total number of possible 64 bit integers = 10^(64) integers

Now, we are told that the device produces random integers at a rate of one billion per second (10^(9) billion per second)

Let's calculate how many it can produce in a year.

1 year = 365 × 24 × 60 × 60 seconds = 31,536,000 seconds

Thus, per year it will produce;

(10^(9) billion per second) × 31,536,000 seconds = 3.1536 × 10^(16)

Thus;

Number of years of running is it unavoidable that the device produces an output for the second time is;

(10^(64))/(3.1536 × 10^(16)) = 3171 × 10^(44) years

6 0

3 years ago

The product of 1540 and m is a square number. find the smallest possible value of m

aliina [53]

The smallest possible value of m according to the task is; 1/1540.

<h3>What is the smallest possible value of m?</h3>

Since it follows from the task content that the product of 1540 and m is a square number and the smallest possible small number is; 1.

The equation which holds true is; 1540 × m = 1

Consequently, m = 1/1540.

Read more on square numbers;

brainly.com/question/123907

#SPJ1

5 0

1 year ago

In the below system, solve for y in the first equation.

fiasKO [112]

The correct answer should be A.

4 0

3 years ago

Read 2 more answers

Enter your answer and show all the steps that you use to solve this problem in the space provided. Find the values of x and y.

satela [25.4K]

Answer : The value of x and y is, $90^o$ and $43^oC$

Step-by-step explanation :

First we have to calculate the angle B.

As we know that,

The given triangle is an isosceles triangle in which the angles opposite to equal sides are always equal.

Thus, $\angle B=\angle C$

Given : $\angle C=47^o$

$\angle B=\angle C=47^o$

$\angle B=47^o$

Now have to calculate the angle A.

As we know that the sum of interior angles of a triangle is equal to $180^o$ .

$\angle A+\angle B+\angle C=180^o$

$\angle A+47^o+47^o=180^o$

$\angle A+94^o=180^o$

$\angle A=180^o-94^o$

$\angle A=86^o$

Now we have to determine the angle y.

As we know that, line AD is an angle bisector. That means, it divides into two equal angles. So,

$\angle y=\frac{\angle A}{2}$

$\angle y=\frac{86^o}{2}$

$\angle y=43^o$

Now we have to determine the angle x.

As we know that the sum of interior angles of a triangle is equal to $180^o$ .

$\angle y+\angle B+\angle x=180^o$

$43^oc+47^o+\angle x=180^o$

$\angle x+90^o=180^o$

$\angle x=180^o-90^o$

$\angle x=90^o$

Thus, the value of x and y is, $90^o$ and $43^oC$

6 0

3 years ago