Nokea
Ratio and proportion: 6:10=24:x
- A. 40
- B. 25
- C. 240
- D. 4
Correct Answer: A
Rationale: To solve for x, use cross-multiplication:
6x = 10 x 24
6x = 240
Now, divide both sides by 6 to find x:
x = 240 / 6 = 40
Therefore, the correct answer is A. 40.
Choice B, 25, is incorrect because it does not satisfy the proportion.
Choice C, 240, is incorrect because it represents the value that is given in the proportion and not the value of x.
Choice D, 4, is incorrect as it does not align with the correct calculation for x.
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A set of temperature readings has a range of 5 degrees Celsius. What does this tell you about the data?
- A. The average temperature is 5 degrees Celsius.
- B. All temperatures are within 5 degrees of each other.
- C. The difference between the highest and lowest temperatures is 5 degrees.
- D. There are exactly 5 temperatures in the set.
Correct Answer: C
Rationale: Option A is incorrect because the range of 5 degrees does not necessarily mean that the average temperature is 5 degrees Celsius. The average temperature could be any value within the range. Option B is incorrect because the range of 5 degrees does not mean that all temperatures are within 5 degrees of each other. It only indicates the difference between the highest and lowest temperatures. Option C is correct because the range of 5 degrees specifically refers to the difference between the highest and lowest temperatures in the set. This is a common definition of range in statistics. Option D is incorrect because the range of 5 degrees does not determine the number of temperatures in the set. The set could have more or fewer than 5 temperatures.
Which of the following percentages is equal to 0.45?
- A. 4.5%
- B. 0.045%
- C. 0.45%
- D. 45%
Correct Answer: D
Rationale: To convert 0.45 to a percentage, you multiply by 100: 0.45 100 = 45%. Therefore, the correct answer is D. 45%.
Choice A, 4.5%, is incorrect. This percentage would be equal to 0.045, not 0.45. Choice B, 0.045%, is also incorrect. It represents 0.045, not 0.45. Choice C, 0.45%, is very close to the correct answer but actually represents 0.0045, not 0.45.
A farmer's production statistics find that it takes 2 chickens to produce 6 eggs in 24 hours. How many chickens will be needed to produce 24 eggs in 24 hours?
- A. 12 chickens
- B. 4 chickens
- C. 3 chickens
- D. 8 chickens
Correct Answer: D
Rationale: First, find how many eggs 1 chicken can produce in 24 hours. If 2 chickens produce 6 eggs: 6 eggs / 2 chickens = 3 eggs per chicken. To produce 24 eggs, we divide the required number of eggs by the production rate per chicken: 24 eggs / 3 eggs per chicken = 8 chickens. Therefore, the correct answer is D. 8 chickens. Choice A, 12 chickens, is incorrect because it does not consider the production rate per chicken. Choice B, 4 chickens, is incorrect as it does not account for the number of eggs needed. Choice C, 3 chickens, is incorrect because it miscalculates the production rate per chicken.
A lampshade is shaped like a frustum of a cone, with base diameters of 20cm and 10cm and a height of 15cm. What is its volume?
- A. 625 cu cm
- B. 1250 cu cm
- C. 1875 cu cm
- D. 2500 cu cm
Correct Answer: C
Rationale: To find the volume of the frustum of a cone, divide it into two cones and calculate their volumes separately. The formula for the volume of a cone frustum involves the radii of both bases and the height. The volume of the frustum cone can be calculated as V = 1/3 * π * h * (R^2 + r^2 + R * r), where R is the larger radius, r is the smaller radius, and h is the height. Substituting the values, V = 1/3 * π * 15 * (10^2 + 20*10 + 20^2) = 1875 cu cm. Therefore, the correct answer is 1875 cu cm. Choice A, B, and D are incorrect as they do not correspond to the correct calculation of the frustum's volume.
5\7 + 3\14 = ?
- A. 13\14
- B. 10/14
- C. 11/14
- D. 12/14
Correct Answer: A
Rationale: To add fractions with different denominators, first find a common denominator. The least common denominator between 7 and 14 is 14. Convert 5/7 to 10/14:
5
/
7
=
10
/
14
5/7=10/14
Now add the two fractions:
10
/
14
+
3
/
14
=
13
/
14
10/14+3/14=13/14