Remember to show your work! Practice Problem #1 (I love pandas!!) The population of pandas in China has been doubling every year. What is the estimated population of pandas in 5 years from now? This year there are 2500 pandas in China. 2500 5000 10000 20000 40000 80000 The estimated population of pandas five years from now is 80,000 pandas based on information provided. Express your final answer in scientific notation. 8.0 x 104 Practice Problem #2 The Johnson family has three times as many pepper plants than tomatoes in their garden. They have 63 plants in the garden. How many plants are tomatoes? How many plants are peppers? t = tomato plants p = pepper plants 3t = p t + p = 63 plants (three times as many pepper plants than tomatoes) Use substitution. Replace the p with 3t. New equation t + 3 t = 63 Combine like terms 4t = 63 Divide both sides by 4 t = 63/4 = 15.75 rounds up to 16 tomatoes 63 – 16 = 47 peppers The Johnson family would have approximately 16 tomato plants and 47 pepper plants in their garden based on information provided. Practice Problem #3 The angles of a triangle measure x, 3x, and 6x. What do you know about the sum of the interior angles of a triangle? Equals 180 degrees x + 3x + 6x = 10 x = 180 Practice Problem #4 Ali’s new business invest $5,000 in equipment to produce his new shoes design. Each shoe costs $5.00 to produce. Each shoe sells for $100.00. How many pairs of shoes must Ali sell in order for his business to recover the $5,000 he invested??!! $95.00 profit on each shoe. ($100-$5) $5,000 divided by $95.00 = number of shoes he needs to sell to break even. Ali needs to sell at least 53 shoes or 27 pairs of shoes. What is Ali’s profit if he sells 200 pairs of shoes? 200 pair x 2 = 400 shoes($95 profit for each shoe) 400 x 95 = $38,000 minus initial investment of $5,000 $33,000 Ali would make a profit of $33,000 if he sells 200 pairs of shoes. Practice Problem #5 Two angles of a triangle measure 400 and 600. Find the measure of the third angle. 180 – 40 – 60 = 80 degrees Two angles of a triangle measure 450 and 450. Find the measure of the third angle. 180 – 45 – 45 = 90 degrees Two angles of a triangle measure 900 and 300. Find the measure of the third angle. 180 – 90 – 30 = 60 degrees Practice Problem #6 P = Perimeter Solve the following equation for l. (l = length) P = 2 l + 2w l =( p - 2w)/2 w =( p – 2l)/2 Find P = 2l + 2w. Substitute in values for and w. The perimeter if l = 12 and w = 6. P = 2(12) + 2 (6) = 24 + 12 = 36 units The perimeter for this shape is 36 units. Practice Problem #7 Anya owns a business that sells jewelry. She must bring in more money in revenue that she pays out in costs in order to make or turn a profit. Use the information provided to see if Anya will make a profit and stay in business. It costs $10 per in labor and materials for each piece of jewelry sold. The rent for the retail space is $2,000.00 per month. She sells the jewelry for $75.00 per item. How many pieces of jewelry will Anya need to sell to make the minimum Profit? Profit on each piece of jewelry = $75 – $10 = $65.00 Cost of rent $2,000 per month So $2,000 divided by $65.00 = 31 pieces need to be sold to break even for month. To write as an inequality Anya needs to sell > 31. Practice Problem #8 Calculate distance travelled if travelling 75 mph for 1.5 hours. distance = rate times time d = rt = 75mph x 1.5 h = 112.5 miles Practice Problem #9 Remember distance = rate times time. Find the distance travelled in miles if you are going 90kph and travelling for 12 hours. (Use a conversion factor for 1.2 kilometer equals 1 mile (1.2 km = 1 mile.)) Convert the rate (speed) to miles first. 90 kph = 1m/1.2 kph = 90/1.2 = 75 miles perhour d = r t = 75mph (12)hrs = 900 miles Practice Problem #10 The slope of a function is defined using x and y coordinates. The ratio of the difference between the y values and x values is the calculation. To express this as a formula use Y2 - Y1 x2 - x1 (x1, y1) Represents the 1st point (x2, y2) Represents the 2nd point If 1st point is (10,5) and 2nd point is (4,2) what is the slope (m) between these two points. Y2 - Y1 = 2–5 x2 - x1 4 – 10 = - 3 = - 6 +1 2 The slope (m) is + ½ for these 2 points. Count up 1 and over to right two. If 1st point is (10,5) and 2nd point is (4,2) what is the slope (m) between these two points. 0 1 2 3 4 5 6 7 8 9 10 Draw or sketch the two points and connect the two points. Bonus: From looking at the graph can you determine a way or formula you could use to calculate the distance between the two points? Think of Pythagorean!!!!