Finite Math Examples

$z = \frac{0.29 - 0.3}{\sqrt{\frac{(0.3) (0.7)}{410}}}$

Step 1

Multiply $0.3$ by $0.7$ .

$z = \frac{0.29 - 0.3}{\sqrt{\frac{0.21}{410}}}$

Step 2

Subtract $0.3$ from $0.29$ .

$z = \frac{- 0.01}{\sqrt{\frac{0.21}{410}}}$

Step 3

Divide $0.21$ by $410$ .

$z = \frac{- 0.01}{\sqrt{0.00051219}}$

Step 4

Move the negative in front of the fraction.

$z = - \frac{0.01}{\sqrt{0.00051219}}$

Step 5

Multiply $\frac{0.01}{\sqrt{0.00051219}}$ by $\frac{\sqrt{0.00051219}}{\sqrt{0.00051219}}$ .

$z = - (\frac{0.01}{\sqrt{0.00051219}} \cdot \frac{\sqrt{0.00051219}}{\sqrt{0.00051219}})$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{0.01}{\sqrt{0.00051219}}$ by $\frac{\sqrt{0.00051219}}{\sqrt{0.00051219}}$ .

$z = - \frac{0.01 \sqrt{0.00051219}}{\sqrt{0.00051219} \sqrt{0.00051219}}$

Step 6.2

Raise $\sqrt{0.00051219}$ to the power of $1$ .

$z = - \frac{0.01 \sqrt{0.00051219}}{{\sqrt{0.00051219}}^{1} \sqrt{0.00051219}}$

Step 6.3

Raise $\sqrt{0.00051219}$ to the power of $1$ .

$z = - \frac{0.01 \sqrt{0.00051219}}{{\sqrt{0.00051219}}^{1} {\sqrt{0.00051219}}^{1}}$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z = - \frac{0.01 \sqrt{0.00051219}}{{\sqrt{0.00051219}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$z = - \frac{0.01 \sqrt{0.00051219}}{{\sqrt{0.00051219}}^{2}}$

Step 6.6

Rewrite ${\sqrt{0.00051219}}^{2}$ as $0.00051219$ .

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Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.00051219}$ as ${0.00051219}^{\frac{1}{2}}$ .

$z = - \frac{0.01 \sqrt{0.00051219}}{{({0.00051219}^{\frac{1}{2}})}^{2}}$

Step 6.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$z = - \frac{0.01 \sqrt{0.00051219}}{{0.00051219}^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

Combine $\frac{1}{2}$ and $2$ .

$z = - \frac{0.01 \sqrt{0.00051219}}{{0.00051219}^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$z = - \frac{0.01 \sqrt{0.00051219}}{{0.00051219}^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$z = - \frac{0.01 \sqrt{0.00051219}}{{0.00051219}^{1}}$

Step 6.6.5

Evaluate the exponent.

$z = - \frac{0.01 \sqrt{0.00051219}}{0.00051219}$

Step 7

Multiply $0.01$ by $\sqrt{0.00051219}$ .

$z = - \frac{0.00022631}{0.00051219}$

Step 8

Simplify the expression.

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Step 8.1

Divide $0.00022631$ by $0.00051219$ .

$z = - 1 \cdot 0.44185755$

Step 8.2

Multiply $- 1$ by $0.44185755$ .

$z = - 0.44185755$