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Bond [772]
3 years ago
7

Calculate 8 ∙ 10-4 divided by 2 ∙ 102. (box after the "10" in answer is for the exponent.). ∙ 10

Mathematics
1 answer:
Korolek [52]3 years ago
6 0

Given problem: \frac{8*10^{-4}}{2*10^2}.

Solution: We can see that first we have 8 and 2 numbers in front of 10's powers.

So, we need to simplify 8 over 2 first.

If we divide 8 by 2, we get 4.

Now, let us work on 10's and their powers.

10^{-4} is being divided by 10^{2}.

We can apply quotient rule of exponents remaining part.

According to quotient rule of exponents, \frac{a^m}{a^n}=a^{m-n}

If we apply same rule, we need to subtract exponents of 10's.

\frac{10^{-4}}{10^2}=10^{-4-(-2)}

If we simplify exponent part -4-(-2), it will give us -4+2 =-2.

So, 10^{-4-(-2)}=10^{-2}

And final answer would be 4 \times 10^{-2}.


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Answer:

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<h3><u>Part (a)</u></h3>

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This set of data is presented as a <u>stem and leaf diagram</u>, where the units and tenths are split.  The units column is the 'stem' and the tenths become the 'leaf'.

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Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4

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\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}

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