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A wide range of mathematical problems and their solutions, including topics such as trigonometry, algebra, geometry, and probability. The problems cover various levels of difficulty, from basic arithmetic to more advanced concepts. Step-by-step explanations and solutions to help the reader understand the underlying principles and techniques used to solve these problems. The topics covered include finding the value of unknown variables, calculating areas and volumes, solving systems of equations, and analyzing probability and statistics. This document could be a valuable resource for students, teachers, or anyone interested in improving their mathematical problem-solving skills.
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If tan θ = 5/12 and sin θ > 0, then cos θ =? a. -5/ b. 12/ c. 13/ d. -12/ e. 0 - Answer-b. 12/ tanθ = opp/adj = 5/ c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13 cosθ = adj/hyp = 12/ If 60% of x equal to 30% of 20, then what is the value of (x + 5)^2? a. 25.
b. 26 c. 26. d. 2025 e. 225 - Answer-e. 225 0.6x = (0.3) x 20 → x = 10 (x + 5)^2 → (10 + 5)^2 = (15)^2 = 225 In the xy-plane, the point (4,3) and (3,2) are on line A. Which of the following equations of lines is parallel to line A? a. y = 3x b. y = 10 c. y = x d. y = 2x e. y = x - Answer-e. y = x Slope of line A is: m = (y2 - y1)/(x2 - x1) = (3 - 2)/(4 - 3) = 1 Parallel lines have the same slope and only choice (e.) has slope of 1. When point A (10,3) is reflected over the y-axis to get the point B, what are the coordinates of point B? a. (10,3) b. (-10,-3) c. (-10,3)
x = [8y + (r/r + 1)] / [(6/(z/3))] x = [8y + (r/r + 1)] / [(3 x 6/(z)] x/3 = [8y + (r/r + 1)] / [(3 x 6/(z)] x (1/3) A boat sails 40 miles south and then 30 miles east. How far is the boat from its start point? a. 45 miles b. 50 miles c. 60 miles d. 70 miles e. 80 miles - Answer-b. 50 miles Use Pythagorean Theorem: a^2 + b^2 = c^ 40^2 + 30^2 = c^ → 1600 + 900 = c^ → 2500 = c^2 → c = 50 x is y% of what number? a. 100x/y b. 100y/x c. x/100y d. y/100x e. xy/100 - Answer-a. 100x/y
Let the number be A. Then: x = y% * A Solve for A. x = y/100 * A Multiply both sides by 100/y: x * 100/y = y/100 * 100/y * A A = 100x/y If cotangent of an angle β is 1, then tangent of angle β is a. - b. 0 c. 1 d. 2 e. 3 - Answer-c. 1 Tangent = 1/cotangent = 1 What is the value of y in the following system of equations? 3x - 4y = - -x + 2y = 10 a. - b. - c. 1
e. 120 feet - Answer-d. 60 feet If 40% of a class are girls, and 25% of girls play tennis, what percentage of the class play tennis? a. 10 b. 15 c. 20 d. 40 e. 80 - Answer-a. 10 In five successive hours, a car travels 40 km, 45 km, 50 km, 35 km and 55 km. in the next 5 hours, it travels with an average speed of 50 km per hour. Find the total distance the car traveled in 10 hours. a. 425 km b. 450 km c. 475 km d. 500 km e. 1000 km - Answer-c. 475 km From last year, the price of gasoline has increased from $1.25 per gallon to $1.75 per gallon. The new price is what percent of the original price? a. 72% b. 120% c. 140% d. 160%
c. 4π - 8 d. 4π - 3 e. None of the above - Answer-a. 2π - 4 Two electrical poles are 12 feet apart. If one of the poles is 5 feet more in length than the other, what is the minimum length of the wire required for connecting them about their top? a. 8 feet b. 10 feet c. 12 feet d. 14 feet e. 13 feet - Answer-e. 13 feet The average salary of 3 people is $1,500. If one of them received a 100% raise, then the average salary becomes $2,000. What is the sum of the salary of the two people who did NOT get the raise? a. $2, b. $3, c. $4, d. $5, e. $6,000 - Answer-b. $3, Sum of salary of 3 people = 3 x $1500 = $ 1 person received a raise of 100%
Sum of new salaries = 3 x $2000 = $ The increased salary of 1 person = $ → Salary of 2 people who did NOT get the raise = $4500 - $1500 = $ A pair of playing dice is thrown. What is the probability of getting a sum of 5? a. 1/ b. 1/ c. 1/ d. 1/ e. 1/27 - Answer-d. 1/ A and B can do a job alone in 10 days and 12 days, respectively. A starts working along and 5 days later B joins to finish the work together. For how many days has B worked on the job? a. 32/ b. 24/ c. 30/ d. 24/ e. 2 - Answer-c. 30/
a. $30, b. $15, c. $18, d. $45, e. $60,000 - Answer-e. $60, If a + b > a - b, then which of the following must be true? a. b ≤ 0 b. a - b > b - a c. a > 0 d. a = 0 e. None of the above. - Answer-e. None of the above. What is the square root of (.25 x 2.25)? a. 2 b. 0. c. 0. d. 20 e. 75 - Answer-b. 0. A rectangle with a perimeter of 68 inches has one side that is 4 inches longer than the other. What is the area of this rectangle?
(x^2 -3) / (x-1) = 1 / (x-1)
Jen is building a playground with a perimeter of 280 feet. If the length is 10 feet less than twice the
d. 4.0 x 10^- e. 4.0 x 10^4 - Answer-e. 4.0 x 10^ y = (x+5) / (x-9)represent this in the form of x = a. (9y - 9)/(y + 5) b. (9y + 5)/y c. (9y + 5)/(y - 1) d. (y + 5)/(y - 9) e. 9y/(y - 1) - Answer-c. (9y + 5)/(y - 1) √(x^2 - 9) / √(x-3) = 4 For what value of x is this statement true? a. 3 b. 13 c. 23 d. 4 e. 14 - Answer-b. 13 Danny caught a fish that weighed 5 pounds 8 ounces, Glen caught a fish that weighed 6 pounds 2 ounces, and Michael caught a fish that weighed 4 pounds 8 ounces. What is the average weight of these fish? a. 5 lbs. 0 oz. b. 5 lbs. 5 2/3 oz.
