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Chapter 0: Problem 101
Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. $$\frac{2.4 \times 10^{-2}}{4.8 \times 10^{-6}}$$
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In parts (a) and (b), complete each statement. $$\text { a. } b^{4} \cdot b^{3}=(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)=b^{?}$$ $$\text { b. } b^{5} \cdot b^{5}=(b \cdot b \cdot b \cdot b \cdot b)(b \cdot b \cdot b \cdot b \cdot b)=b^{7}$$ c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?
You had \(\$10,000\) to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression $$0.05 x+0.12(10,000-x)$$ a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested $6000 in the safe, government-insured certificate of deposit.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x-0.02(x+200)=0.98 x-4$$
In one short sentence, five words or less, explain what $$ \frac{\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}}{\frac{1}{x^{4}}+\frac{1}{x^{5}}+\frac{1}{x^{6}}} $$ does to each number \(x\).
Your computer store is having an incredible sale. The price on one model is reduced by 40%. Then the sale price is reduced by another 40%. If x is the computer鈥檚 original price, the sale price can be modeled by Your computer store is having an incredible sale. The price on one model is reduced by 40%. Then the sale price is reduced by another 40%. If x is the computer鈥檚 original price, the sale price can be modeled by $$ (x-0.4 x)-0.4(x-0.4 x)$$ A. Factor out \((x-0.4 x)\) from each term. Then simplify thre sulting expression. B. resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a 40% reduction followed by a 40% reduction, is the computer selling at 20% of its original price? If not, at what percentage of the original price is it selling?
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