1.
Two bowls of yellow beans are mixed with four bowls of white beans. If yellow beans cost £136 per bowl, and white beans cost £94 per bowl, find the average cost of one bowl of the mixture.
Correct Answer
C. £108
Explanation
The average cost of one bowl of the mixture can be found by taking the total cost of all the bowls and dividing it by the total number of bowls. In this case, there are 2 bowls of yellow beans and 4 bowls of white beans, so a total of 6 bowls. The total cost of the yellow beans is £136 per bowl multiplied by 2 bowls, which is £272. The total cost of the white beans is £94 per bowl multiplied by 4 bowls, which is £376. The total cost of all the bowls is £272 + £376 = £648. Dividing this by the total number of bowls, 6, gives an average cost of £108 per bowl.
2.
3(4a - 5) = 2(a - 5). Find a.
Correct Answer
D. 0.5
Explanation
To solve this equation, we can start by distributing the 3 to both terms inside the parentheses: 12a - 15 = 2(a - 5). Next, we can distribute the 2 to the terms inside the parentheses: 12a - 15 = 2a - 10. We can then move all the terms with a to one side of the equation and the constant terms to the other side: 12a - 2a = -10 + 15. Simplifying further, we get 10a = 5. Finally, we can divide both sides of the equation by 10 to solve for a, which gives us a = 0.5.
3.
Expand (x - 5)(7 +x)
Correct Answer
A. 2x + x^{2 }- 35
Explanation
The given expression is (x - 5)(7 + x). To expand this expression, we can use the distributive property. Multiplying x by 7 gives us 7x, and multiplying x by -5 gives us -5x. Similarly, multiplying -5 by 7 gives us -35, and multiplying -5 by x gives us -5x. Combining like terms, we have 7x - 5x - 35, which simplifies to 2x - 35. Therefore, the correct answer is 2x + x2 - 35.
4.
Find the reciprocal of 0.54037
Correct Answer
B. 2.477
Explanation
The reciprocal of a number is obtained by dividing 1 by that number. In this case, the reciprocal of 0.54037 is approximately 2.477. To verify this, we can perform the division 1/0.54037 and the result will be approximately 2.477.
5.
Find the reciprocal of 761.
Correct Answer
A. 0.001314
Explanation
The reciprocal of a number is obtained by dividing 1 by the given number. In this case, to find the reciprocal of 761, we divide 1 by 761. The result is approximately 0.001314.
6.
Two similar cones have corresponding slant heights of 8cm and 12cm. Find the ratio of their areas.
Correct Answer
B. 4/9
Explanation
The ratio of the areas of two similar cones is equal to the square of the ratio of their corresponding slant heights. In this case, the ratio of the slant heights is 8/12, which simplifies to 2/3. Squaring this ratio gives (2/3)^2 = 4/9. Therefore, the ratio of the areas of the two cones is 4/9.
7.
If y = 10x^{2 }- 20, find y when x = 3.
Correct Answer
A. 70
Explanation
When x is substituted with 3 in the equation y = 10x^2 - 20, we get y = 10(3)^2 - 20 = 10(9) - 20 = 90 - 20 = 70. Therefore, the value of y when x = 3 is 70.
8.
Two similar cones have a corresponding slant heights of 8cm and 12cm. The surface area of the smaller cone 102cm^{2}. Calculate the surface area of the larger cone.
Correct Answer
A. 229.5cm^{2}
Explanation
The surface area of a cone can be calculated using the formula: SA = πr(r + l), where SA is the surface area, r is the radius, and l is the slant height. Since the slant heights of the two cones are given as 8cm and 12cm, we can assume that the radii are proportional to the slant heights. Let the radius of the smaller cone be r1 and the radius of the larger cone be r2. We can set up the equation: r1/8 = r2/12. Solving for r2, we get r2 = (12/8) * r1 = (3/2) * r1. The surface area of the smaller cone is given as 102cm2. Plugging in the values into the formula, we have 102 = π * r1(r1 + 8). Solving for r1, we get r1 ≈ 3.65cm. Substituting this value into the equation r2 = (3/2) * r1, we get r2 ≈ 5.48cm. Finally, plugging in the values into the formula, we can calculate the surface area of the larger cone as 229.5cm2.
9.
Make y the subject of the equation x = y - 7.
Correct Answer
A. Y = x + 7
Explanation
To make y the subject of the equation x = y - 7, we need to isolate y on one side of the equation. By moving the constant term -7 to the other side, we get y = x + 7.
10.
3x + 5y = 8. Find y if x = 2.
Correct Answer
D. 0.4
Explanation
To find the value of y, we substitute the given value of x into the equation. Substituting x = 2 into the equation 3x + 5y = 8, we get 3(2) + 5y = 8. Simplifying this equation, we have 6 + 5y = 8. Subtracting 6 from both sides, we get 5y = 2. Dividing both sides by 5, we find y = 0.4. Therefore, the value of y is 0.4.