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3 years ago

The sequence {an } is defined by a of o = 1 and a of n + 1 = 2 a of n + 2 for n = 0, 1, 2.... What is the value of a of 3?

1 answer:

3 0

$\begin{cases}a(0)=1\\a(n+1)=2a(n)+2&\text{for }n\ge0\end{cases}$

Use the second part of the definition (the recursive one):

$a(1)=2a(0)+2=4$
$a(2)=2a(1)+2=10$
$a(3)=2a(2)+2=22$

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Brett has 2 1/2 pounds of bird seed left to share equally among 4 bird cages in his pet shop. How many pounds can he put in each

Ksju [112]

Answer:

Brett can put $\frac{5}{8}$ = 0.625 pounds in each bird cage.

Step-by-step explanation:

The total amount of bird seed left = $2\frac{1}{2}$ pounds

= $\frac{5}{2}$ pounds

Number of birds in pet shop = 4

So, the share of each bird = $\frac{\textrm{Total available seeds}}{\textrm{Total number of birds in the pet shop}}$

= $\frac{\frac{5}{2} }{4} = \frac{5}{2} \times \frac{1}{4} = \frac{5}{8}$

Hence, Brett can put $\frac{5}{8}$ = 0.625 pounds in each bird cage.

6 0

3 years ago

what are the factors of 47 (cuz im STUPID and i dont feel like doing this cuz im working on geogrophy)

Hitman42 [59]

Hey there! I'm happy to help!

The factors are the numbers you multiply to get 47. And they can't be fractions or numbers with fractions. They have to be integers (numbers without fractions).

So far, we see that we can multiply 1 and 47 to get 47. To see if there are any more, we see what numbers 1-10 we can divide by.

We cannot divide by 2 because 47 is odd.

We cannot divide by 3 because it gives us 15.6666...

We can't divide by 4 because 47 is odd.

We can't divide by 5 because 47 does not have a 5 or 0 in the ones place.

We can't divide by 6 because 47 is odd.

We can't divide by 7 because it gives us 6.714285....

We can't divide by 8 because 47 is odd.

We can't divide by 9 because it gives us 5.2222

And we obviously can't divide it by 10.

Therefore, the factors of 47 are 1 and 47. A number whose only factors are 1 and itself is called a prime number.

I hope that this helps! Have a wonderful day! :D

3 0

3 years ago

Read 2 more answers

What is the reason for each step in the solution of the equation?

Brums [2.3K]

The correct reason <span>for each step in the solution of the equation would be as follows:
</span>
12 − 5x + 6x = 4 - Given

12 + x = 4 - Combine Like Terms

x= −8 - Subtraction Property of Equality

Hope this answers the question. Have a nice day.

8 0

3 years ago

One third of a number t is equal to 7

Vikentia [17]

If one third of t is 7 than t is equal to 21

3 0

3 years ago

Read 2 more answers

can someone help me understand this, please? For some reason my answer is correct but I need to understand how did I found the c

Morgarella [4.7K]

Answer with step-by-step explanation:

The way the question is worded, this actually shouldn't be correct. The correct answer should be $3:4$ .

Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.

Why?

By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.

Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are $\overline{RS}$ and $\overline{AB}$ .

The ratio of $\overline{RS}:\overline{AB}$ is $18:24\implies \boxed{3:4}$ .

The reason why it ideally should be $3:4$ and not $4:3$ is because the question states $RTSU\sim ABCD$ , which mentions $RSTU$ first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.

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2 years ago