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3 years ago

Find the nth term -1 8 19 32 47

1 answer:

4 0

$\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6$

Step-by-step explanation:

-1 → 8 = +9

8 → 19 = +11

19 → 32 = +13

32 → 47 = + 15

a₁ = -1

d = 2n + 5

Recursive formula is: the previous term plus the difference (d)

$\large\boxed{a_n=a_{n-1}+2n+5}$

Explicit formula is the first term plus the product of d and n-1:

$a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}$

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grigory [225]

<h3>Answer: Approximately 191 bees</h3>

================================================

Work Shown:

One way to express exponential form is to use

y = a*b^x

where 'a' is the initial value and 'b' is linked to the growth rate.

Since we're told 34 bees are there initially, we know a = 34.

Then after 4 days, we have 48 bees. So we can say,

y = a*b^x

y = 34*b^x

48 = 34*b^4

48/34 = b^4

24/17 = b^4

b^4 = 24/17

b = (24/17)^(1/4)

b = 1.090035

Which is approximate.

The function updates to

y = a*b^x

y = 34*(1.090035)^x

------------------------

As a way to check to see if we have the right function, plug in x = 0 and we find:

y = 34*(1.090035)^x

y = 34*(1.090035)^0

y = 34*(1)

y = 34

So there are 34 bees on day 0, ie the starting day.

Plug in x = 4

y = 34*(1.090035)^x

y = 34*(1.090035)^4

y = 34*1.4117629

y = 47.9999386

Due to rounding error we don't land on 48 exactly, but we can round to this value.

We see that after 4 days, there are 48 bees.

So we confirmed the correct exponential function.

------------------------

At this point we can find out how many bees there are expected to be after 20 days.

Plug in x = 20 to get

y = 34*(1.090035)^x

y = 34*(1.090035)^20

y = 190.672374978452

Round to the nearest whole number to get 191.

There are expected to be roughly 191 bees on day 20.

4 0

2 years ago

What is 79 1/2% of $7570?

Mariulka [41]

Answer:

$6018.15

Step-by-step explanation:

"is" number always goes on TOP "of" number.

"is" number is 79 1/2%

"of" number is $7570

79 1/2 % / $7570 * 100 = $6018.15 

To find out if the answer is correct :

6018.15 / 7570 * 100 = 79.12%

5 0

3 years ago

X/4 < -1.5 for a million dollars and Brainliest. Send cash app too

pogonyaev

Answer:

x < -6

Step-by-step explanation:

X/4 < -1.5

Multiply each side by 4

X/4*4 < -1.5*4

x < -6

3 0

2 years ago

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aivan3 [116]

What is this caption

6 0

3 years ago

In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. Three of the 8 are in one family

lianna [129]

There are 14 chairs and 8 people to be seated. But among the 8. three will be seated together:

So 5 people and (3) could be considered as 6 entities:

Since the order matters, we have to use permutation:

¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆ x 3!

2,162,160 x 6 = 12,972,960 ways.

Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways
The 2nd has a choice among 13 ways
The 3rd has a choice among 12 ways
The 4th has a choice among 11 ways
The 5th has a choice among 10 ways
The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways
But the 3 (that formed one group) could seat among themselves in 3!
or 6 ways:

Total number of permutation = 2,162,160 x 6 = 12,972,960

4 0

2 years ago