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Math 70S Integrated Intermediate Algebra

• Sample of what you should know before Math 70S:
1. Given the formula for converting degrees Fahrenheit (F) to degrees Celsius (C), evaluate this formula when
2. On a map, 2 cm represents 15 miles. Ryan measures on the map and finds there are 11.5 cm between Springfield and Bloomton.  How many miles apart are the two cities?
3. A \$380 television is on sale for 25% off.  If the sales tax is 7.5%, what is the total price you would have to pay for the television?
4. Solve:
5. Simplify:
6. Simplify:
• Sample of what you will learn in Math 70S:
1. Suppose two salt solutions are to be mixed to create a 25-liter salt solution with 5 gm of salt per liter. The solutions to be mixed contain 2 gm per liter and 10 gm per liter respectively.  How much of each solution should be used?
• Solution
Let x represent the volume in liters of the 2 gm per liter solution.
Let y represent the volume in liters of the 10 gm per liter solution.
Adding the volume in liters, we want
Adding the mass in grams, we need
This gives us the system of equations
We can solve  for y to get
Substituting into the second equation, we get
So,
We should use 15.625 liters of the 2 gm per liter solution and 9.375 liters of the 10 gm per liter solution.
2. If you deposit \$10,000 into an account that earns a fixed 8% annual interest rate, compounded quarterly, when will the account balance reach \$25,000?
• Solution
Use the compound interest formula
Here P = 10000, r = 0.08, n = 4, A = 25000, and we're solving for t.
The account balance will reach \$25,000 after 12 quarters (or 3 years).
3. The following are root lengths (inches) of garlic cloves after soaking in water for one week. {2.23, 1.71, 1.45, 3.53, 2.57, 1.61, 1.64, 1.67, 1.79, 1.90, 3.04, 2.09, 1.42, 2.16, 1.52, 2.23, 2.26, 1.57, 2.33}.  Sketch a boxplot and identify outliers.  Describe the distribution of values in terms of center, shape and spread.
• Solution
First sort the data from smallest to largest:
{1.42, 1.45, 1.52, 1.57, 1.61, 1.64, 1.67, 1.71, 1.79, 1.9, 2.09, 2.16, 2.23, 2.23, 2.26, 2.33, 2.57, 3.04, 3.53}
The number of sample values is n = 19
First quartile:
Second quartile:
Third quartile:
There are no sample values less than 0.635.
3.53 is more than 3.235, so 3.53 is an outlier.
The center is 1.9.  The boxplot has a center of 1.9 and is skewed to the right.