Quiz On High School Math

Explanation
If a fair coin is flipped twice and both times it lands on heads, the outcome of each flip is independent of the others. Therefore, the chance of getting heads on the next flip is still 1 in 2, just like the chance of getting tails. Each flip has an equal probability of landing on either heads or tails, regardless of the previous outcomes.

Explanation
The range is the difference between the highest and lowest values in a set of numbers. In this case, the highest number is 45 and the lowest number is 1. Therefore, the range is 45 - 1 = 44. The other options, mode, mean, and median, do not involve finding the difference between the highest and lowest values.

Explanation
The reciprocal of the sine function is the cosecant function. The cosecant of an angle is equal to 1 divided by the sine of that angle. Therefore, the correct answer is cosecant.

Explanation
When a number is increased by 50%, it becomes 1.5 times its original value. Then, when the result is decreased by 50%, the number becomes half of the increased value. Therefore, the final number is 1/2 of 1.5 times the original value, which is equal to 3/4 of the original size of X.

Explanation
If an account yields 2% interest, it means that for every year, the account will earn 2% of the initial amount. Therefore, for two years, the account will earn a total of 4% (2% x 2) of the initial amount. In this case, the initial amount is $300, so the interest earned after two years will be 4% of $300, which is $12.

Explanation
To convert Celsius to Fahrenheit, you can use the formula: F = (C * 9/5) + 32. Plugging in the given temperature of 30 degrees Celsius, the calculation would be: (30 * 9/5) + 32 = 86 degrees Fahrenheit. Therefore, the correct answer is 86.

Explanation
A nonagon is a two-dimensional closed shape with nine straight sides. It is formed by connecting nine straight lines together to create a polygon with nine sides. The prefix "non-" in nonagon indicates the number nine. Therefore, a nonagon is the correct answer for a shape with nine sides.

Explanation
The given number, 315000, can be expressed in scientific notation as 3.15x10^5. In scientific notation, a number is written in the form of a decimal number multiplied by a power of 10. In this case, 3.15 is the decimal number and 10^5 represents the power of 10. This means that the original number, 315000, can be written as 3.15 multiplied by 10 raised to the power of 5.

Explanation
When x=2 and y=3, we can calculate x^x as 2^2=4 and y^y as 3^3=27. Adding these values together, we get 4+27=31. Therefore, the value of x^x+y^y is 31.

Explanation
The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius of the circle. In this question, the circumference of the circle is given as 44 cm. We know that the formula for the circumference of a circle is C = 2πr. By rearranging this formula, we can find the radius of the circle. Dividing the circumference by 2π gives us the radius, which is 7 cm. Substituting this value into the formula for the area of a circle, we get A = π(7)² = 49π ≈ 154 sq.cm. Therefore, the correct answer is 154 sq.cm.

Explanation
The given equation states that y is equal to 2 times x plus 3. We are also given that y is equal to 5. By substituting the value of y into the equation, we can solve for x. Therefore, if y is 5, then 5 is equal to 2 times x plus 3. By rearranging the equation, we can find that 2 times x is equal to 2, and thus x is equal to 1.

Explanation
The length of the taut string can be determined using the Pythagorean theorem. The pole forms the height of a right triangle, and the distance from the pole to your feet forms the base. By applying the theorem, which states that the square of the hypotenuse (the length of the string) is equal to the sum of the squares of the other two sides, we can calculate the length. In this case, the height of the pole is 12 feet, and the distance from the pole to your feet is 5 feet. By squaring these values and adding them together, we get 144 + 25 = 169. Taking the square root of 169 gives us 13 feet, which is the length of the taut string.

Explanation
To express x^-5 * y^-5 with positive exponents, we can use the rule that states when a term with a negative exponent is moved to the denominator, the exponent becomes positive. Therefore, x^-5 * y^-5 is equivalent to 1/x^5 * 1/y^5. Combining the terms, we get 1/(x^5 * y^5), which is the same as 1/x^5y^5.

Explanation
To express 3x^1/6 * 3x^-7/6 with positive exponents, we can simplify the expression by adding the exponents. The exponent of x in the numerator is 1/6, and the exponent of x in the denominator is -7/6. Adding these exponents gives us -6/6, which simplifies to -1. Therefore, the expression becomes 3x^-1. To express this with a positive exponent, we can rewrite it as 3/x^1. Simplifying further, we get the final answer of 9/x.

Explanation
When dividing powers with the same base, we subtract the exponents. In this case, 8^9 divided by 8^3 is equal to 8^(9-3) which simplifies to 8^6.