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malfutka [58]
4 years ago
13

Isabella save 2 nickels today, if she doubles the number of Nicole, she saves every day, how many days, including today, will it

take her to save more than 500 nickels?
Mathematics
1 answer:
Elden [556K]4 years ago
3 0

Answer:

  8 days

Step-by-step explanation:

On day 8, Isabella will save 256 nickels, bringing her total to 510.

_____

The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.

_____

The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.

__

The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...

  an = a1·r^(n-1) = 2·2^(n-1) = 2^n

The sum of n terms of the sequence is ...

  S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)

  S = 2^(n+1) -2

__

We want S > 500, so ...

  500 < 2^(n+1) -2

  502 < 2^(n+1)

  251 < 2^n

  log(251) < n·log(2)

  n > log(251)/log(2)

  n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels

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lions [1.4K]

Answer:

\frac{7}{9}

Step-by-step explanation:

\frac{9}{a} = \frac{7}{a^{2}}

9.a^{2} = 7a

9a = 7

a= 7/9

Hope this helps ^-^

3 0
3 years ago
The type of match to use in a Vlookup() function to assess the resort fee as a possible additional cost for a particular room is
schepotkina [342]

Answer:

An approximate match

Step-by-step explanation:

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The vlookup syntax is written as:

=VLOOKUP(value, table, col_index, [range_lookup])

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6 0
3 years ago
Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. . A. -20.5 . B. -151 . C. -22.75 . D. -144 . .
Dennis_Churaev [7]
In order to solve for a nth term in an arithmetic sequence, we use the formula written as:

an = a1 + (n-1)d

where an is the nth term, a1 is the first value in the sequence, n is the term position and d is the common difference.

First, we need to calculate for d from the given values above.  
<span>a1 = 38 and a17 = -74
</span>

an = a1 + (n-1)d
-74 = 38 + (17-1)d
d = -7

The 27th term is calculated as follows:

a27 = a1 + (n-1)d
a27= 38 + (27-1)(-7)
a27 = -144 -----------> OPTION D
7 0
4 years ago
Which of the following indicates a line segment?
Kazeer [188]

Answer:

A line segment is a line that starts somewhere and then ends somewhere.

Step-by-step explanation:

7 0
3 years ago
How many ways are there to select 3 of 15 flavors of juice at the grocery store?
m_a_m_a [10]
First, you need to distinguish if this is a permutation or a combination. The difference between the two is the order. In combination, order does not matter. Since there is no any restriction given, we assume this is a combination problem. The equation of determining the number of ways to choose 'r' objects out of total 'n' objects is:

Number of ways = n!/r!(n-r)! = 15!/3!(15-3)! = 455

There are 455 ways.
5 0
3 years ago
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