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blsea [12.9K]
3 years ago
14

There is an average of 3.5 x 10^−2 kilograms of dissolved salt in each liter of seawater. The Pacific Ocean contains approximate

ly ​ 6.6 × 10^20 ​ liters of seawater. About how many kilograms of dissolved salt are in the Pacific Ocean? Enter your answer, in scientific notation, in the boxes. __×__10 kg

Mathematics
2 answers:
nalin [4]3 years ago
7 0
The answer is: 
___________________________________________
   " 2.3 * 10^(19) "  kg  {dissolved salt in the Pacific Ocean} .
__________________________________________________
Explanation:
_____________________________
3.5 * 10⁻² * 6.6 * 10⁽²⁰⁾  = ? kg dissolved salt in the Pacific Ocean.
______________________________________________________
→ 3.5 * 10⁻² * 6.6 * 10⁽²⁰⁾  = 3.5 * 6.6 * 10⁻² * 10²⁰⁾ ;
___________________________________________
Note the following property of exponents:
___________________________________________
xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾ ;  so;  10⁻² * 10²⁰ = 10⁽⁻² ⁺ ²⁰⁾ = 10⁽ ¹⁸ ⁾ ;

→ So; we can rewrite our expression as:
___________________________________________
  3.5 * 6.6 * 10⁽ ¹⁸ ⁾ ;

→ Note: 3.5 * 6.6 = 23.1 ---> Round to 2 (two) significant figures:  23 ;

Answer:  23 * 10⁽ ¹⁸ ⁾ ;  to write in scientific notation; write the "whole number" as: "2.3" (a single digit, whole number integer, followed by a decimal", and adjust the exponent following the "10" accordingly, to make the value equal; and we have:
__________________________________________________ 
   " 2.3 * 10^(19) "  kg {dissolved salt in the Pacific Ocean} .
__________________________________________________
IgorC [24]3 years ago
3 0
This is the answer check it out

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Answer:4.75961

Step-by-step explanation:

7.7x0.35=2.695x1.79=<u>4.75961</u>

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3 years ago
Carly has 15 stuffed animals. How many ways are there to organize her top 3 favorites?
Ivanshal [37]
Well, the answer will depend on whether the order will count or not (based on Permutations and Combinations). <em>If the order counts</em>, then we would use the formula for Permutations, which is:
\frac{n!}{(n-r)!}
Where n is the number of items you have, and r is the number of times you choose from the items.
\frac{15!}{(15-3)!}
Which simplifies to
\frac{15!}{(12)!}
Which simplifies to 15*14*13 (because all the numbers 1-12 in the factorial canceled out), which gets us the answer 2730.

Now, if you wanted to find the number of ways to order the toys without replacement (<em>order doesn't count</em>), you would use the formula:
\frac{n!}{r!(n-r)!}
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\frac{15!}{3!(15-3)!}
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\frac{15!}{3!(12)!}
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\frac{2730}{3!}
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4 0
3 years ago
Each of six jars contains the same number of candies. Alice moves half of the candies from the first jar to the second jar. Then
tino4ka555 [31]

Answer:

The number of candies in the sixth jar is 42.

Step-by-step explanation:

Assume that there are <em>x</em> number of candies in each of the six jars.

⇒ After Alice moves half of the candies from the first jar to the second jar, the number of candies in the second jar is:

\text{Number of candies in the 2nd jar}=x+\fracx}{2}=\frac{3}{2}x

⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:

\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x

⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:

\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x

⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:

\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x

⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:

\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x

Now, it is provided that at the end, 30 candies are in the fourth jar.

Compute the value of <em>x</em> as follows:

\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}

Compute the number of candies in the sixth jar as follows:

\text{Number of candies in the 6th jar}=\frac{63}{32}x\\

                                                    =\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42

Thus, the number of candies in the sixth jar is 42.

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