Nokea
Jayden rides his bike for 5/8 miles. He takes a break and rides another 3/4 miles. How many miles does he ride?
- A. 1 3/8 miles
- B. 1 1/2 miles
- C. 1 7/8 miles
- D. 2 miles
Correct Answer: A
Rationale: To find the total distance Jayden rides, you need to add the fractions 5/8 + 3/4. To add these fractions, you must ensure they have a common denominator. In this case, the common denominator is 8. So, 5/8 + 3/4 = 5/8 + 6/8 = 11/8. Since 11/8 can be simplified to 1 3/8, Jayden rides a total of 1 3/8 miles. Choice B (1 1/2 miles), Choice C (1 7/8 miles), and Choice D (2 miles) are incorrect as they do not accurately represent the total distance calculated by adding the two fractions, which is 1 3/8 miles.
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What is the result of dividing 8 by 4?
- A. 2
- B. 4
- C. 6
- D. 8
Correct Answer: A
Rationale: To find the result of dividing 8 by 4, we divide 8 by 4, which equals 2. Choice B (4) is incorrect because it is the divisor, not the result of the division. Choice C (6) is incorrect as it is not the correct quotient. Choice D (8) is incorrect as it is the dividend, not the result of the division.
A sign stating 'Do Not Enter' is in the shape of a square with side lengths of 75 centimeters. What is the area in square centimeters?
- A. 150
- B. 300
- C. 5,325
- D. 5,625
Correct Answer: D
Rationale: The formula for the area of a square is given by the square of its side length: Area = side side. For this problem, the side length of the square is 75 centimeters. To find the area, you multiply 75 by itself: 75 75 = 5,625 square centimeters. Thus, the area of the square is 5,625 cm². This shows that option D is correct. Choices A, B, and C are incorrect as they do not correspond to the correct calculation of the area of a square with a side length of 75 centimeters.
Which proportion yields a different number for the unknown compared to the others?
- A. 2/3 = x/6
- B. 4/5 = x/10
- C. 3/4 = x/8
- D. 5/6 = x/12
Correct Answer: D
Rationale: To find the value of x in each proportion, cross multiply. For proportion A, x = 4; for B, x = 8; for C, x = 6; and for D, x = 10. Hence, proportion D yields a different value for x compared to the others. Choices A, B, and C all result in unique values for x, but these values are distinct from the value obtained in proportion D.
What is the mode of the data set: 2, 3, 3, 4, 4, 4, 5?
- A. 2
- B. 3
- C. 4
- D. 5
Correct Answer: C
Rationale: The mode of a data set is the value that appears most frequently. In this data set (2, 3, 3, 4, 4, 4, 5), the number 4 appears three times, which is more frequent than any other number in the set. Therefore, the correct answer is 4. Choice A (2), B (3), and D (5) do not appear as frequently as 4 in the data set, so they are not the mode.
Simplify (x^2 - y^2) / (x - y)
- A. x + y
- B. x - y
- C. 1
- D. (x + y)/(x - y)
Correct Answer: A
Rationale: The expression x^2 - y^2 is a difference of squares, which follows the identity: x^2 - y^2 = (x + y)(x - y). Therefore, the given expression becomes: (x^2 - y^2) / (x - y) = (x + y)(x - y) / (x - y). Since (x - y) appears in both the numerator and the denominator, they cancel each other out, leaving x + y. Thus, the simplified form of (x^2 - y^2) / (x - y) is x + y. Therefore, the correct answer is A (x + y). Option B (x - y) is incorrect as it does not result from simplifying the given expression. Option C (1) is incorrect as it does not account for the variables x and y present in the expression. Option D ((x + y)/(x - y)) is incorrect as it presents the simplified form in a different format than the correct answer.