General Mathematics 2020 Quiz

Explanation
The answer 2:5 is the correct ratio because it is the only option where the first number is smaller than the second number. In a ratio, the first number represents one quantity and the second number represents another quantity. The ratio 2:5 indicates that the first quantity is smaller than the second quantity, which is not the case in the other options.

Explanation
The given number, 0.0000407, has 4 significant figures. When rounding to 2 significant figures, we look at the digit after the second significant figure, which is 0. Since the digit after 0 is less than 5, we do not round up. Therefore, the correct answer is 0.000041.

Explanation
To express log 35 in terms of a and b, we can use the property of logarithms that states log(ab) = log(a) + log(b).

We know that log 35 = log(7 * 5).

Since a = log 7, we can rewrite log(7 * 5) as log 7 + log 5.

We don't have the value of log 5, but we can express it in terms of a and b by using the property log(ab) = log(a) + log(b).

log 5 = log(2 * 2.5) = log 2 + log 2.5 = log 2 + log(2 * 1.25) = log 2 + log 2 + log 1.25 = 2b + log 1.25.

Therefore, log 35 = log 7 + log 5 = a + 2b + log 1.25.

Since log 1.25 is a constant, we can simplify this expression to a + 2b + C, where C represents log 1.25.

This can further be simplified to a + 2b + 1, as C = 1.

Thus, log 35 can be expressed as a - b + 1.

Explanation
Each boy takes N20.00 more than each girl, so we can set up the equation: (boy's share) = (girl's share) + N20.00. Since there are 5 boys and 4 girls, the total amount shared among them is N18,100. We can express this as: 5(boy's share) + 4(girl's share) = N18,100. By substituting the equation from the first statement, we get: 5((girl's share) + N20.00) + 4(girl's share) = N18,100. Solving this equation, we find that the girl's share is N1,820.00. Substituting this back into the first equation, we can find the boy's share to be N2,020.00.

Explanation
The given expression is a quadratic trinomial. To find a factor, we can use the fact that if a quadratic trinomial can be factored, then the factors will have the form (ax + b)(cx + d), where a and c are the coefficients of the squared term and b and d are the constant terms. In this case, the coefficient of the squared term is 7, and the constant term is -10. To find the factors, we need to find two numbers that multiply to give -10 and add up to 33. The numbers 5 and -2 satisfy these conditions, so the factors are (7x + 5)(x - 2). Therefore, the correct answer is 7x - 2.

Explanation
The volume of a rectangular prism can be calculated by multiplying its length, width, and height. In this case, the dimensions of the water tank are given as 13cm, 10cm, and 70cm. Since the tank is half-filled with water, we need to find the volume of half of the tank. The volume of half of the tank can be calculated by dividing the volume of the whole tank by 2. Therefore, the volume of water in litres is (13cm x 10cm x 70cm) / 2 = 4550cm³. Since 1 litre is equal to 1000cm³, the volume of water in litres is 4550cm³ / 1000 = 4.55 litres.

Explanation
The correct phone number of the Mathematics teacher is 08028427234.