Nokea
A farmer plans to install fencing around a certain field. If each side of the hexagonal field is 320 feet long, and fencing costs $1.75 per foot, how much will the farmer need to spend on fencing material to enclose the perimeter of the field?
- A. $2,240
- B. $2,800
- C. $3,360
- D. $4,480
Correct Answer: C
Rationale: To find the perimeter of a hexagonal field with 6 sides, multiply the length of one side (320 feet) by the number of sides (6): 320 x 6 = 1920 feet. The total cost of the fencing material can be calculated by multiplying the perimeter by the cost per foot: 1920 feet x $1.75 = $3360. Therefore, the farmer will need to spend $3,360 on fencing material to enclose the perimeter of the field. Choice A, B, and D are incorrect as they do not accurately calculate the total cost based on the given measurements and cost per foot.
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Solve for y: 2y + 5 = 25 * 10
- A. y = 25
- B. y = 100
- C. y = 150
- D. y = 200
Correct Answer: B
Rationale: To solve the equation 2y + 5 = 25 * 10, start by simplifying the right side: 25 * 10 = 250. Then, subtract 5 from both sides to isolate 2y: 2y = 250 - 5 = 245. Finally, divide by 2 to find the value of y: y = 245 / 2 = 122.5. Therefore, the correct answer is y = 122.5. Choices A, C, and D are incorrect as they do not result from the correct calculation steps.
Arrange the following numbers from least to greatest: 7/3, 9/2, 10/9, 7/8
- A. 10/9, 7/3, 9/2, 7/8
- B. 9/2, 7/3, 10/9, 7/8
- C. 7/3, 9/2, 10/9, 7/8
- D. 7/8, 10/9, 7/3, 9/2
Correct Answer: D
Rationale: To arrange the numbers from least to greatest, first convert them to decimals:
1. 7/3 is approximately 2.33
2. 9/2 equals 4.5
3. 10/9 is approximately 1.11
4. 7/8 equals 0.875
Now, arrange the decimals from least to greatest: 0.875 (7/8), 1.11 (10/9), 2.33 (7/3), 4.5 (9/2). Therefore, the correct order is 7/8, 10/9, 7/3, 9/2. Choice A is incorrect because it doesn't follow the correct order. Choice B is incorrect as it places 9/2 before 7/3, which is not the right arrangement. Choice C is incorrect as it places 7/3 before 9/2 and 10/9, which is incorrect. Thus, the correct answer is choice D.
Joshua has to earn more than 92 points on a state test to qualify for a scholarship. Each question is worth 4 points, and the test has 30 questions. Which inequality can be solved to determine the number of questions Joshua must answer correctly?
- A. 4x < 30
- B. 4x < 92
- C. 4x > 30
- D. 4x > 92
Correct Answer: D
Rationale: Joshua must answer more than 92 points' worth of questions. Since each question is worth 4 points, the inequality is 4x > 92. Choice A (4x < 30) is incorrect as it represents that Joshua must answer less than 30 questions correctly, not earning more than 92 points. Choice B (4x < 92) is incorrect as it signifies that Joshua must earn less than 92 points, which contradicts the requirement. Choice C (4x > 30) is incorrect as it implies that Joshua must answer more than 30 questions correctly, but the threshold is 92 points, not 30 points.
If Hannah spends at least $16 on 4 packages of coffee, which of the following inequalities represents the possible costs?
- A. 16 ≥ 4p
- B. 16 < 4p
- C. 16 > 4p
- D. 16 ≤ 4p
Correct Answer: D
Rationale: To represent the relationship between the number of packages of coffee and the minimum cost, the inequality can be written as 4p ≥ 16 (cost is at least $16). This inequality can also be expressed as 16 ≤ 4p, which reads as the cost being less than or equal to $16. Therefore, the correct answer is D. Choice A (16 ≥ 4p) implies that the cost can be greater than or equal to $16, which does not align with the statement that Hannah spends at least $16. Choice B (16 < 4p) suggests that the cost is less than $16, which contradicts the given information. Choice C (16 > 4p) indicates that the cost is greater than $16, which is not accurate based on the scenario provided.
What is the probability of flipping a coin and getting heads?
- A. 1/2
- B. 1/3
- C. 1/4
- D. 1/5
Correct Answer: A
Rationale: The correct answer is A: 1/2. When flipping a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1 out of 2 possible outcomes, which can be expressed as 1/2. Choice B, 1/3, is incorrect because a fair coin only has two sides. Choices C and D, 1/4 and 1/5, are also incorrect as they do not represent the correct probability of getting heads when flipping a coin.