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otez555 [7]
3 years ago
9

Simplify the expression. Write the answer using scientific notation. (4 x 10^13)^-2 -8 x 10^-26 6.25 x 10^-27 0.0625 x 10^-26 6.

25 x 10^-28
Mathematics
2 answers:
zimovet [89]3 years ago
6 0

Answer:

Option 4th is correct that is:6.25\cdot 10^{-28}

Step-by-step explanation:

We have been given an expression:

(4\cdot 10^{13})^{-2}

4^{-2}\cdot 10^{13\cdot -2}

Using x^{-a}=\frac{1}{x^a}

Here, x= and a= -2

\frac{1}{4^2}\cdot 10^{-26}

On simplification:

0.0625\cdot10^{-26}

When we right shift the decimal to 2 points power will be deducted by 2

6.25\cdot 10^{-28}

Therefore, Option 4th is correct that is:6.25\cdot 10^{-28}

ioda3 years ago
6 0

(4 x 10^13)^-2

(4)^-2 x (10^-26)

.0625 x 10^-26 = 6.25 x 10 ^ -28

                The underlined expression is the right answer because it follows the rule of scientific notation.

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A rectangular aquarium 3 ft. x 2 ft. 1 ft. is 2/3 full of water. In cubic feet, how much water is in the tank
tatuchka [14]

To find the volume of a rectangular prism, we must multiply the length * width * height.


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3 years ago
Suppose in a certain state, 60% of the people have a Visa credit card, 40% have a MasterCard, and 24% have both. Let V be the ev
REY [17]

Answer:

The question has some details missing; i.e

a. What is the probability that the shopper has neither type of card?

b. What is the probability that the shopper has both types of card?

c. What is the probability the individual has a Visa card but not a Mastercard? (Hint: You will use the answer)

a) 0.24

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Step-by-step explanation:

The detailed steps is shown in the attachment.

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(12) - (23 +131) =<br> Express your answer in the form (a + bi),
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Step-by-step explanation:

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5 0
2 years ago
3х - 30 = у<br> 7y - 6 = 3х
mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3<em>x</em> – 30 = <em>y</em>  and the second is 7<em>y</em> – 6 = 3<em>x</em>

As I look, I see 3 ways to use substitution to solve this:

  1. substitute 7<em>y</em> – 6 for 3<em>x</em>
  2. substitute 3<em>x</em> – 30 for <em>y</em>
  3. solve 3<em>x</em> – 30 = <em>y</em> for 3<em>x</em> and make it equal to 7<em>y</em> – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

<u>Method 1</u>:

3<em>x</em> – 30 = <em>y</em>

7<em>y</em> – 6 = 3<em>x</em>  — initial system of equations

7<em>y</em> – 6 – 30 = <em>y</em>  — substitute 7<em>y</em> – 6 for 3<em>x</em>

<u>7</u><u><em>y</em></u> – 6 – 30 = <u><em>y</em></u>  — marking like terms, bold for constants, <u>underlined</u> for variables

7<em>y</em> – 36 = <em>y</em>  — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract <em>y</em> from both sides, divide by 6 OR subtract 7<em>y</em> from both sides and divide by –6 . For the sake of time, I'm subtracting 7<em>y</em>, though I don't like dealing with negatives.

7<em>y</em> – 7<em>y</em> – 36 = <em>y</em> – 7<em>y</em>  — subtract 7<em>y</em> from both sides

–36 = –6<em>y</em>  — simplify

–36 ÷ –6 = –6<em>y</em> ÷ –6  — divide by –6 on both sides

<em>y</em> = 6  — simplify

Again, we can diverge here: substitute <em>y</em> into 3<em>x</em> – 30 = <em>y</em> or substitute <em>y</em> into 7<em>y</em> – 6 = 3<em>x</em>

I'm going to choose 3<em>x</em> – 30 = <em>y</em> but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3<em>x</em> – 30 = <em>y</em>  — initial equation

3<em>x</em> – 30 = 6  — substitute 6 for <em>y</em>

3<em>x</em> – 30 + 30 = 6 + 30  — add 30 to both sides to isolate 3<em>x</em>

3<em>x</em> = 36  — simplify the expression

3<em>x</em> ÷ 3 = 36 ÷ 3  — divide both sides by 3 to isolate <em>x</em>

<em>x</em> = 12  — simplify

So, we have <em>x</em> = 12 and <em>y</em> = 6 . We know they work for 3<em>x</em> – 30 = <em>y</em>  but not if they work for 7<em>y</em> – 6 = 3<em>x</em> . Let's substitute those in to see if (12, 6) really is the solution point.

7<em>y</em> – 6 = 3<em>x</em>  — original equation

7(6) – 6 ≟ 3(12)  — substitute 6 for <em>y</em> and 12 for <em>x</em>

42 – 6 ≟ 36  — simplify by multiplying

36 = 36 ✔  — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0
3 years ago
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