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Andreas93 [3]
3 years ago
11

Sarah converts the number 1,500,600 into scientific notation. She writes 1.5006 x 104. Which of the following statements is true

?
Sarah is correct.
Sarah is not correct because the exponent should be 6.
Sarah is not correct because 1.5006 should be 1.5.
Sarah is not correct because the exponent should be -4.
Mathematics
2 answers:
AlladinOne [14]3 years ago
6 0

Answer: Choice B) she is not correct; the exponent should be 6

I'm assuming you meant to say 1.5006 x 10^4

The exponent 4 means we move the decimal point four spots to the right to go from 1.5006 to 15,006

This result is a little over 15 thousand when we want closer to 1.5 million

The exponent should be 6. We move the decimal point six places to the right to go from 1.5006 to 1,500,600 which is the proper value we want

So Sarah should have written 1.5006 x 10^6

valentina_108 [34]3 years ago
5 0

Answer:

Choice B) she is not correct; the exponent should be 6

Step-by-step explanation:

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Step-by-step explanation:

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aₙ = 3*n^2 - 1

And the n-th term of another sequence is:

bₙ = 30 - n^2

Remember that in a sequence n is always an integer number.

We want to find a number that belongs to both sequences, then we want to find a pair of integers x and n, such that:

aₙ = bₓ

This is:

3*n^2 - 1 = 30 - x^2

Let's isolate one of the variables, i will isolate n.

3*n^2 = 30 - x^2 + 1 = 31 - x^2

n^2 = (31 - x^2)/3

n = √( (31 - x^2)/3)

Now we can try with different integer values of x, and see if n is also an integer.

if x = 1

n = √( (31 - 1^2)/3) = √10

We know that √10 is not an integer, so we need to try with another value of x.

if x = 2:

n = √( (31 - x^2)/3) = √(27/3) = √9 = 3

Then if we have x= 2, n is also an integer, n = 3.

Then we have:

a₃ = b₂

The common number between both sequences is:

a₃ = 3*(3)^2 - 1 = 26

b₂ = 30 - 2^2 = 26

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