A circular plate is measured to have a diameter of 14 inches. A student wants to cover the entire area of the top of the plate with mashed potatoes. If her calculations are correct, what area should she find to the nearest whole number? (round pi to 3.14)
Answer: 154 inches Solution: First, know that the area of a circle is equal to pi times the radius squared. You know the diameter of the plate, but you need the radius to find area, so you must divide the diamter by 2 to know the radius. 14 divided by 2 is 7. Then, you plug 7 into the equation for radius. 7 squared is 49, then multiply 49 by pi, which we have chosen to round to 3.14, and get 153.86. Since the problem said to round to the nearest whole number, we round 153.86 up to 154.
In a small high school, there are 450 students enrolled. One fifth of all students are in their freshman year. Two thirds of all students have brown eyes. What is the different between the number of all students with brown eyes and the number of all students enrolled in their freshman year?
Answer: 210 Solution: First, you know there are 450 total students. Next, you know, of the 450 students, a fifth of them are freshmen, meaning that to find the number of freshmen, you must multiply 450 by 1/5, or divide 450 by 5. The answer is 90 freshmen. Next, you know that of the total 450 students, two thirds have brown eyes. That means you must multiply 450 by 2/3, or multiply 450 by 2, then divide that answer by 3. You should get 300. Finally, you subtract the number of freshmen students from the number of brown-eyed students (300-90) and get 210.
A field is split into four quadrants. The North-East (top right from ariel view) quadrant is labelled A. The North-West (top left) quadrant is labelled B. The South-West (bottom left) quadrant is C. The South-East (bottom right) quadrant is D. A person begins at the very center of the field (0,0), then walks eastward 15 feet, and walks north 10 feet. From this new position, what distance would they have to walk in the southern direction and in the western direction in order to be 5 feet south and 5 feet west within the D quadrant?
Answer: 15 feet South and 20 feet West. Solution: First, draw a picture. The field is split in such a way as to look like an ordinary x-y plane. North contains the positive y-coordinates, South contains the negative y-coordinates, East contains the negative x-coordinates, and West contains the positive x-coordinates. So, first you place the person on the origin of your graph, then you move them 15 units (feet in this case) in the negative x direction (left), and 10 feet in the positive y direction (up), to have them at the (-15, 10) coordinate. The person's location should be in the B quadrant. Now, you wnat to know how far they must travel to be 5 feet both west and south of the origin and within the D quadrant. So, your desired location is at the (5, -5) coordinate. So, draw a dot on that location, and either count how many units it takes to go from y position -5 (final position) to y position 10 (initial position), or subtract -5-10, (the answer will be negative, but distance is always a positive number). You should get 15, and that is your southern movement. Next, do the same thing, except you subtract initial position -15 from final position 5. 5-(-15) (subtracting a negative is the same as adding a positive), and get 20. Thus, your eastern movement is 20.