pls analyze the accuracy of this json for a math quiz:

[
  {
    "text": "If $f(x) = 2x^2 - 3x + 5$, what is the value of $f(-2)$?",
    "type": "multiple-choice-single-answer",
    "id": 1,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "To find $f(-2)$, substitute -2 for x in the function: $f(-2) = 2(-2)^2 - 3(-2) + 5$. Simplify: $2(4) + 6 + 5 = 8 + 6 + 5 = 19$. The correct answer is 19.",
    "options": [
      {
        "text": "13",
        "id": "a"
      },
      {
        "text": "15",
        "id": "b"
      },
      {
        "text": "17",
        "id": "c"
      },
      {
        "text": "19",
        "id": "d"
      }
    ]
  },
  {
    "text": "The line $y = mx + b$ passes through the points $(2, 5)$ and $(4, 9)$. What is the value of $m$?",
    "type": "multiple-choice-single-answer",
    "id": 2,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The slope $m$ can be calculated using the formula $m = \\frac{y_2 - y_1}{x_2 - x_1}$. Plugging in the given points: $m = \\frac{9 - 5}{4 - 2} = \\frac{4}{2} = 2$. The correct answer is 2.",
    "options": [
      {
        "text": "1",
        "id": "a"
      },
      {
        "text": "2",
        "id": "b"
      },
      {
        "text": "3",
        "id": "c"
      },
      {
        "text": "4",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $\\log_2 x = 5$, what is the value of $x$?",
    "type": "multiple-choice-single-answer",
    "id": 3,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "The equation $\\log_2 x = 5$ means that $2^5 = x$. Calculate $2^5$: $2 \\times 2 \\times 2 \\times 2 \\times 2 = 32$. Therefore, $x = 32$.",
    "options": [
      {
        "text": "10",
        "id": "a"
      },
      {
        "text": "25",
        "id": "b"
      },
      {
        "text": "32",
        "id": "c"
      },
      {
        "text": "64",
        "id": "d"
      }
    ]
  },
  {
    "text": "In triangle ABC, $\\sin A = \\frac{3}{5}$ and $\\cos B = \\frac{4}{5}$. What is the value of $\\tan C$?",
    "type": "multiple-choice-single-answer",
    "id": 4,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "In any triangle, $\\sin A = \\cos B = \\frac{3}{5}$, so this is a 3-4-5 right triangle. $\\tan C = \\frac{opposite}{adjacent} = \\frac{3}{4}$. The correct answer is $\\frac{3}{4}$.",
    "options": [
      {
        "text": "$\\frac{3}{4}$",
        "id": "a"
      },
      {
        "text": "$\\frac{4}{3}$",
        "id": "b"
      },
      {
        "text": "$\\frac{5}{3}$",
        "id": "c"
      },
      {
        "text": "$\\frac{5}{4}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $y = 3x + 7$ and $x = 4$, what is the value of $y$?",
    "type": "multiple-choice-single-answer",
    "id": 5,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find y, substitute $x = 4$ into the equation $y = 3x + 7$. This gives $y = 3(4) + 7$. Simplify: $y = 12 + 7 = 19$. Therefore, the correct answer is 19.",
    "options": [
      {
        "text": "15",
        "id": "a"
      },
      {
        "text": "17",
        "id": "b"
      },
      {
        "text": "19",
        "id": "c"
      },
      {
        "text": "21",
        "id": "d"
      }
    ]
  },
  {
    "text": "Solve for $x$: $2x + 5 = 13$",
    "type": "multiple-choice-single-answer",
    "id": 6,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To solve for x, first subtract 5 from both sides: $2x = 8$. Then divide both sides by 2: $x = 4$. The correct answer is 4.",
    "options": [
      {
        "text": "3",
        "id": "a"
      },
      {
        "text": "4",
        "id": "b"
      },
      {
        "text": "5",
        "id": "c"
      },
      {
        "text": "6",
        "id": "d"
      }
    ]
  },
  {
    "text": "What is the value of $\\frac{1}{2} + \\frac{3}{4}$?",
    "type": "multiple-choice-single-answer",
    "id": 7,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To add fractions with different denominators, find a common denominator. Here, the LCD is 4. Convert $\\frac{1}{2}$ to $\\frac{2}{4}$. Then add: $\\frac{2}{4} + \\frac{3}{4} = \\frac{5}{4}$ or $1.25$. The correct answer is 1.25.",
    "options": [
      {
        "text": "0.75",
        "id": "a"
      },
      {
        "text": "1",
        "id": "b"
      },
      {
        "text": "1.25",
        "id": "c"
      },
      {
        "text": "1.5",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $a^2 = 16$ and $a > 0$, what is the value of $a$?",
    "type": "multiple-choice-single-answer",
    "id": 8,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The equation $a^2 = 16$ means that a is a square root of 16. Since we're told $a > 0$, we're looking for the positive square root. $\\sqrt{16} = 4$, so $a = 4$.",
    "options": [
      {
        "text": "2",
        "id": "a"
      },
      {
        "text": "4",
        "id": "b"
      },
      {
        "text": "8",
        "id": "c"
      },
      {
        "text": "16",
        "id": "d"
      }
    ]
  },
  {
    "text": "A factory produces widgets at a constant rate. In $3$ hours, the factory produced $540$ widgets. If the factory continues at this rate, approximately how many widgets will it produce in $8$ hours?",
    "type": "multiple-choice-single-answer",
    "id": 9,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, calculate the rate of production: $540$ widgets ÷ $3$ hours = $180$ widgets per hour. Then, multiply this rate by $8$ hours: $180$ × $8$ = $1,440$ widgets. The correct answer is $1,440$.",
    "options": [
      {
        "text": "1,080",
        "id": "a"
      },
      {
        "text": "1,320",
        "id": "b"
      },
      {
        "text": "1,440",
        "id": "c"
      },
      {
        "text": "1,620",
        "id": "d"
      }
    ]
  },
  {
    "text": "A car travels from City A to City B, covering a distance of $360$ kilometers in $4$ hours. If the car maintains the same average speed, how long will it take to travel $495$ kilometers?",
    "type": "multiple-choice-single-answer",
    "id": 10,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Calculate the average speed: $360$ km ÷ $4$ hours = $90$ km/h. Then, use the formula Time = Distance ÷ Speed: $495$ km ÷ $90$ km/h = $5.5$ hours. The correct answer is $5.5$ hours.",
    "options": [
      {
        "text": "5 hours",
        "id": "a"
      },
      {
        "text": "5.5 hours",
        "id": "b"
      },
      {
        "text": "6 hours",
        "id": "c"
      },
      {
        "text": "6.5 hours",
        "id": "d"
      }
    ]
  },
  {
    "text": "A savings account earns interest at a constant rate. If the account balance increases from $\\$5,000$ to $\\$5,750$ in $2$ years, approximately how much will the balance be after $5$ years, assuming the same interest rate?",
    "type": "multiple-choice-single-answer",
    "id": 11,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, calculate the total interest earned in 2 years: $\\$5,750 - \\$5,000 = \\$750$. The yearly interest is $\\$750 ÷ 2 = \\$375$. For 5 years, the total interest would be $\\$375 × 5 = \\$1,875$. Add this to the initial balance: $\\$5,000 + \\$1,875 = \\$6,875$. The correct answer is $\\$6,875$.",
    "options": [
      {
        "text": "$6,250",
        "id": "a"
      },
      {
        "text": "$6,500",
        "id": "b"
      },
      {
        "text": "$6,875",
        "id": "c"
      },
      {
        "text": "$7,125",
        "id": "d"
      }
    ]
  },
  {
    "text": "A bathtub is being filled at a constant rate. After $3$ minutes, the water level is $12$ cm deep. After $7$ minutes, the water level is $28$ cm deep. If this rate continues, how deep will the water be after $12$ minutes?",
    "type": "multiple-choice-single-answer",
    "id": 12,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Calculate the rate of water level increase: $(28\\text{ cm} - 12\\text{ cm}) \\div (7\\text{ min} - 3\\text{ min}) = 16\\text{ cm} \\div 4\\text{ min} = 4\\text{ cm/min}$. The water level increases by $4$ cm each minute. For $9$ additional minutes (from $3$ to $12$), the total increase would be $9 \\times 4 = 36$ cm. Add this to the initial level: $12\\text{ cm} + 36\\text{ cm} = 48\\text{ cm}$. The correct answer is $48$ cm.",
    "options": [
      {
        "text": "48 cm",
        "id": "a"
      },
      {
        "text": "52 cm",
        "id": "b"
      },
      {
        "text": "56 cm",
        "id": "c"
      },
      {
        "text": "60 cm",
        "id": "d"
      }
    ]
  },
  {
    "text": "Solve the system of equations:\n\n$2x + 3y = 12$\n$4x - y = 1$\n\nWhat is the value of $x + y$?",
    "type": "multiple-choice-single-answer",
    "id": 13,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n$2x + 3y = 12$\n$4x - y = 1$\n\nWe get: $x = \\frac{15}{14}$ and $y = \\frac{23}{7}$\n\nCalculating $x + y$:\n$\\frac{15}{14} + \\frac{23}{7} = \\frac{15}{14} + \\frac{46}{14} = \\frac{61}{14} \\approx 4.3571429$\n\nThe exact answer, $\\frac{61}{14}$, is provided as an option.",
    "options": [
      {
        "text": "4",
        "id": "a"
      },
      {
        "text": "61/14",
        "id": "b"
      },
      {
        "text": "31/7",
        "id": "c"
      },
      {
        "text": "5",
        "id": "d"
      }
    ]
  },
  {
    "text": "Given the system of equations:\n\n$3x - 2y = 6$\n$5x + y = 29$\n\nWhat is the value of $2x - y$?",
    "type": "multiple-choice-single-answer",
    "id": 14,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n$3x - 2y = 6$\n$5x + y = 29$\n\nWe get: $x = \\frac{64}{13}$ and $y = \\frac{57}{13}$\n\nCalculating $2x - y$:\n$2(\\frac{64}{13}) - \\frac{57}{13} = \\frac{128}{13} - \\frac{57}{13} = \\frac{71}{13} \\approx 5.4615385$\n\nThe exact answer, $\\frac{71}{13}$, is provided as an option.",
    "options": [
      {
        "text": "5",
        "id": "a"
      },
      {
        "text": "16/3",
        "id": "b"
      },
      {
        "text": "71/13",
        "id": "c"
      },
      {
        "text": "6",
        "id": "d"
      }
    ]
  },
  {
    "text": "For the system of equations:\n\n$x + y = 10$\n$2x - y = 3$\n\nWhat is the value of $3x + 2y$?",
    "type": "multiple-choice-single-answer",
    "id": 15,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n$x + y = 10$\n$2x - y = 3$\n\nWe get: $x = \\frac{13}{3}$ and $y = \\frac{17}{3}$\n\nCalculating $3x + 2y$:\n$3(\\frac{13}{3}) + 2(\\frac{17}{3}) = 13 + \\frac{34}{3} = \\frac{73}{3} \\approx 24.3333333$\n\nThe exact answer, $\\frac{73}{3}$, is provided as an option.",
    "options": [
      {
        "text": "23",
        "id": "a"
      },
      {
        "text": "24",
        "id": "b"
      },
      {
        "text": "73/3",
        "id": "c"
      },
      {
        "text": "25",
        "id": "d"
      }
    ]
  },
  {
    "text": "Solve the system of equations:\n\n$7x - y = 14$\n$3x + 2y = 12$\n\nWhat is the value of $x - y$?",
    "type": "multiple-choice-single-answer",
    "id": 16,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n$7x - y = 14$\n$3x + 2y = 12$\n\nWe get: $x = \\frac{40}{17}$ and $y = \\frac{42}{17}$\n\nCalculating $x - y$:\n$\\frac{40}{17} - \\frac{42}{17} = -\\frac{2}{17} \\approx -0.1176471$\n\nThe exact answer, $-\\frac{2}{17}$, is provided as an option.",
    "options": [
      {
        "text": "-2/17",
        "id": "a"
      },
      {
        "text": "-1/8",
        "id": "b"
      },
      {
        "text": "1/8",
        "id": "c"
      },
      {
        "text": "2/17",
        "id": "d"
      }
    ]
  },
  {
    "text": "A charity organization's monthly donations can be modeled by the function $D(t) = 250t + 3000$, where $D(t)$ represents the total donations in dollars $t$ months after implementing a new fundraising strategy. How many months will it take for the total donations to reach $8500?",
    "type": "multiple-choice-single-answer",
    "id": 17,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find when the donations reach $8500, we set up the equation: \\n$8500 = 250t + 3000$ \\n\\nSubtracting 3000 from both sides: \\n$5500 = 250t$ \\n\\nDividing both sides by 250: \\n$22 = t$ \\n\\nTherefore, it will take 22 months for the total donations to reach $8500.",
    "options": [
      {
        "text": "18 months",
        "id": "a"
      },
      {
        "text": "20 months",
        "id": "b"
      },
      {
        "text": "22 months",
        "id": "c"
      },
      {
        "text": "24 months",
        "id": "d"
      }
    ]
  },
  {
    "text": "The population of a small town is modeled by the function $P(y) = 150y + 5000$, where $P(y)$ represents the population $y$ years after a new factory opened. In how many years will the population reach $6800?",
    "type": "multiple-choice-single-answer",
    "id": 18,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To find when the population reaches 6800, we set up the equation: \\n$6800 = 150y + 5000$ \\n\\nSubtracting 5000 from both sides: \\n$1800 = 150y$ \\n\\nDividing both sides by 150: \\n$12 = y$ \\n\\nTherefore, it will take 12 years for the population to reach 6800.",
    "options": [
      {
        "text": "10 years",
        "id": "a"
      },
      {
        "text": "12 years",
        "id": "b"
      },
      {
        "text": "14 years",
        "id": "c"
      },
      {
        "text": "16 years",
        "id": "d"
      }
    ]
  },
  {
    "text": "A company's profit can be modeled by the function $P(x) = 500x - 10000$, where $P(x)$ represents the total profit in dollars after selling $x$ units of their product. How many units need to be sold for the company to break even (reach $0 profit)?",
    "type": "multiple-choice-single-answer",
    "id": 19,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find when the profit reaches $0, we set up the equation: \\n$0 = 500x - 10000$ \\n\\nAdding 10000 to both sides: \\n$10000 = 500x$ \\n\\nDividing both sides by 500: \\n$20 = x$ \\n\\nTherefore, the company needs to sell 20 units to break even.",
    "options": [
      {
        "text": "15 units",
        "id": "a"
      },
      {
        "text": "18 units",
        "id": "b"
      },
      {
        "text": "20 units",
        "id": "c"
      },
      {
        "text": "22 units",
        "id": "d"
      }
    ]
  },
  {
    "text": "The distance traveled by a car can be modeled by the function $D(h) = 65h - 5$, where $D(h)$ represents the distance in miles $h$ hours after starting a journey. How long will it take for the car to travel $450 miles?",
    "type": "multiple-choice-single-answer",
    "id": 20,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To find when the distance reaches 450 miles, we set up the equation: \\n$450 = 65h - 5$ \\n\\nAdding 5 to both sides: \\n$455 = 65h$ \\n\\nDividing both sides by 65: \\n$7 = h$ \\n\\nTherefore, it will take 7 hours for the car to travel 450 miles.",
    "options": [
      {
        "text": "6 hours",
        "id": "a"
      },
      {
        "text": "7 hours",
        "id": "b"
      },
      {
        "text": "8 hours",
        "id": "c"
      },
      {
        "text": "9 hours",
        "id": "d"
      }
    ]
  }
]