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grandymaker [24]
3 years ago
11

What is the simplified form of (3.25x10^3)(7.8x10^6) written in scientific notation?

Mathematics
1 answer:
BabaBlast [244]3 years ago
3 0

Answer: 2.535*10^{10}


Step-by-step explanation:

1. By definition, scientific notation has the following form:

a*10^{b}

Where:

<em> a</em> is a number between 1 and 10 but does not include 10.

<em> b </em>an integer.

2. When you multiply 3.25 by 7.8  the result is 25.35 and when you multiply 10^{3} by 10^{6}, you obtain 10^{9}, but to write ree thsult in scientific notation, the decimal point must be after the first digit. Therefore, you must move the decimal point one place to the left. So, the exponent changes from 9 to 10:

(3.25*10^{3})(7.8*10^{6})=2.535*10^{10}

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<u>Completed Question</u>

Outputs to be matched to the functions are:

  • 1,2,3,4,5
  • 1,5,3,2,4
  • 1, 4, 3, 5, 2
  • 2, 18, 27, 43, 96

Answer:

  • sort(x): 2, 18, 27, 43, 96
  • order(x): 1, 5, 3, 2, 4
  • rank(x) : 1, 4, 3, 5, 2
  • none of these :  1, 2, 3, 4, 5

Step-by-step explanation:

Given the vector x: x <- c(2, 43, 27, 96, 18)

<u>Sort</u>

In R, the sort(x)  function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.

Therefore, the output that matches the sort function is:

sort(x): 2, 18, 27, 43, 96

<u>Rank</u>

The rank function returns a vector with the "rank" of each value.

x <- c(2, 43, 27, 96, 18)

  • 2 has a rank of 1
  • 43 has a rank of 4
  • 27 has a rank of 3
  • 96 has a rank of 5
  • 18 has a rank of 2

Therefore, the output of rank(x)  is: 1, 4, 3, 5, 2

<u>Order</u>

When the function is sorted, the order function gives the previous location of each of the element of the vector.

Using the sort(x) function, we obtain: 2, 18, 27, 43, 96

In the vector: x <- c(2, 43, 27, 96, 18)

  • 2 was in the 1st position
  • 18 was in the 5th position
  • 27 was in the 3rd position
  • 43 was in the 2nd position
  • 96 was in the 4th position

Therefore, the output of order(x) is: 1, 5, 3, 2, 4

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