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Question:

A new cancer treatment provides a 50% success rate for patients with lung tumors. Lung tumors make up 10% of all cancer patients. What percentage of all cancer patients will this new drug work on?

A 5%

explanation

A simple way to solve this is to multiply the two percentages. Therefore 50% × 10% = 0.05 or 5%.

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If Carol can write 3 articles for the newspaper every \(2 \frac{\mathrm{1} }{\mathrm{2} } \) hours, how many articles can she write in 10 hours?

12 articles

Convert the mixed number to an improper fraction by multiplying the denominator by the base number and adding it to the numerator. \(2 \frac{\mathrm{1} }{\mathrm{2} } = \frac{\mathrm{2 \times 2 + 1} }{\mathrm{2} } = \frac{\mathrm{5} }{\mathrm{2} x} \). Divide 10 hours by 5/2. Remember that when dividing by a fraction, you can multiply it by its reciprocal instead. \(10 \div \frac{\mathrm{5} }{\mathrm{2} } = 10 \times \frac{\mathrm{2} }{\mathrm{5} } = \frac{\mathrm{20} }{\mathrm{5} } = 4\) . Since Carol can write 3 articles in each \(2 \frac{\mathrm{1} }{\mathrm{2} } \) hour time period, multiply 4 by 3 to find the total number of articles she can write in 10 hours. \(4 \times 3 = 12\) articles

Which of the following is NOT an integer?

\(\frac{\mathrm{1} }{\mathrm{2} } \)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

If there were a total of 450 raffle tickets sold and you bought 13 tickets, what's the probability that you'll win the raffle?

About 3%

You have 13 out of the total of 450 raffle tickets sold so you have a \( \frac{\mathrm{13} }{\mathrm{450} } \times 100 = 3 \% \)

A steak dinner at a restaurant costs $15.99. If a man buys a steak dinner for himself and 4 friends, what will the total cost be?

$79.95

In total, the man is buying 5 steak dinners (one for himself and 4 for his friends). To find the total amount he will have to spend, multiply the cost of one dinner ($15.99) by the number of dinners purchased (5): 15.99 x 5 = 79.95

How long will it take to reach a town 250 miles away if you drive 50 miles per hour?

5 hours

\( \frac{\mathrm{250miles} }{\mathrm{50miles per hour} } = 5 hours\)

If you invest $10,000 at an annual rate of 7%, how much interest will you earn after one year?

$700

Interest = Principal x Rate = $10,000 x 0.07 = $700

What is \(4 \sqrt{45} - 7 \sqrt{5}\)?

\(5 \sqrt{5}\)

To subtract these radicals together their radicals must be the same:
\([4 \sqrt{45} - 7 \sqrt{5}] \) = \(4 \sqrt{ 3^2 \times 5 } - 7 \sqrt{5} \) = \(4 \times 3 \sqrt{5} - 7 \sqrt{5} = 5 \sqrt{5} \)

Continue the pattern: 6, 9, 13.5, 20.25, ?

30.375

The pattern is the previous number multiplied by 1.5. Therefore, \(6 \times 1.5 = 9\); \(9 \times 1.5 = 13.5\); \(13.5 \times 1.5 = 20.25\); \(20.25 \times 1.5 = 30.375\)

If a store adds 50 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 40%, what will the new inventory of chairs be?

140

This word problem requires careful translation. Let’s say t = total current inventory of chairs. The first sentence states that \(50 + t = \frac{\mathrm{3} }{\mathrm{2}} t\). First solve for the current inventory:
\(50 + t = \frac{\mathrm{3} }{\mathrm{2}} t\)
50 = 3t/2 - t
\(50 = \frac{\mathrm{1} }{\mathrm{2}}t\)
t = 100.
The manager wants to increase this by 40%. We know that 40% of 100 is 40, so the new inventory will be 140.

A woman must drive 298 miles to reach her destination. If she travels 42 miles during the first day, how many miles will she have yet to travel?

256

To calculate how many miles the woman still has to travel, subtract the distance she has traveled (42 miles) from the distance she originally had to travel (298 miles):
298 miles – 42 miles = 256 miles

How much time is there between 7:45 am today and 3:15 pm tomorrow?

\(31 \frac{\mathrm{1} }{\mathrm{2}}\) hours

From 7:45 am today to 7:45 am tomorrow is 24 hours. From 7:45 am tomorrow to 3:15 pm tomorrow is \(7 \frac{\mathrm{1} }{\mathrm{2}}\) hours. Add them up and we get the correct answer.

A diver can hold his breath for two minutes under water. After practicing for a week, he can hold his breath for 5% longer. How long will he be able to hold his breath after the first week of practice?

2.1 minutes

First, calculate 5% of 2: 2 × 0.05 = 0.1
Then, add this increase to the amount of time the diver could originally hold his breath:
2 + 0.1 = 2.1 minutes

Divide: \((8.8 \times 10^{-8})\) \(\div (2.2 \times 10^{-6}) = \)

\(4.0 \times 10^{-2}\)

First divide the nonexponential terms: \(8.8 \div 2.2 = 4.0\) When dividing, subtract exponents from each other (when multiplying, add the exponents together). –8 – (–6) = –2

Tina bought a scarf for $16.65. She gave the clerk $20. How much change should she get back?

$3.35

$20 - $16.65 = $3.35