1.
Matt sold 35 tickets to the school play and Renee sold 45 tickets. What is the ratio of the number of tickets Matt sold to the number of tickets Renee sold?
Correct Answer
C. 7/9
Explanation
The ratio of the number of tickets Matt sold to the number of tickets Renee sold is 7/9. This can be found by dividing the number of tickets Matt sold (35) by the number of tickets Renee sold (45).
2.
Which ratios are equal to 4: 32?
Correct Answer
B. 12 : 96; 2 : 16
Explanation
The given ratios are 12:96 and 2:16. To check if they are equal to 4:32, we can simplify each ratio. 12:96 can be simplified to 1:8 by dividing both numbers by 12. Similarly, 2:16 can be simplified to 1:8 by dividing both numbers by 2. Therefore, both ratios are equal to 4:32.
3.
In mathematical analysis, the Ratio Test is used to determine the convergence or divergence of a series. What is the primary criterion of the Ratio Test for determining if a series Σa_n converges?
Correct Answer
B. The limit of |a_(n+1)/a_n| as n approaches infinity is less than 1.
Explanation
The Ratio Test states that a series Σa_n converges absolutely if the limit of the absolute value of the ratio of consecutive terms, |a_(n+1)/a_n|, as n approaches infinity is less than 1. This indicates that the terms of the series are getting progressively smaller at a rate sufficient to ensure the sum of the series converges. Conversely, if this limit is greater than 1, or if the limit does not exist, the series diverges. If the limit equals 1, the test is inconclusive, meaning that no determination can be made about the convergence or divergence of the series.
4.
Find a ratio equivalent to .
Correct Answer
C. 15/40
Explanation
The given ratio is 9/21. To find an equivalent ratio, we can simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 3. So, 9/21 simplifies to 3/7. Comparing this simplified ratio with the options, we can see that 15/40 is equivalent to 3/7. Therefore, the correct answer is 15/40.
5.
Write the ratio of 96 runners to 216 swimmers in simplest form.
Correct Answer
C. 4/9
Explanation
The ratio of 96 runners to 216 swimmers can be simplified by dividing both numbers by their greatest common divisor, which is 24. When we divide 96 by 24, we get 4, and when we divide 216 by 24, we get 9. Therefore, the simplified ratio is 4/9.
6.
Write the ratio of 2 cups to 3 qt as a fraction in simplest form.
Correct Answer
D. 1/6
7.
Find a ratio equivalent to 3:25.
Correct Answer
C. 9:75
Explanation
The given ratio is 3:25. To find an equivalent ratio, we need to multiply or divide both parts of the ratio by the same number. In this case, we can multiply both parts by 3 to get 9:75. Therefore, the ratio 9:75 is equivalent to 3:25.
8.
Which fraction shows the ratio of 3 dogs to 5 dogs?
Correct Answer
A. 6/10
Explanation
The fraction 6/10 shows the ratio of 3 dogs to 5 dogs. This can be determined by dividing the number of dogs in the ratio (3) by the total number of dogs (5). Simplifying this fraction gives us 6/10, which represents the ratio of 3 dogs to 5 dogs.
9.
Find a ratio equivalent to 27/81.
Correct Answer
C. 1:3
Explanation
The ratio 27/81 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 27. This simplifies the ratio to 1/3. Therefore, the ratio equivalent to 27/81 is 1:3.
10.
Maria tossed a coin 20 times and got 12 heads. What is the first step to find the ratio of the number of tails to the total number of tosses?
Correct Answer
B. Subtract 12 from 20
Explanation
To find the ratio of the number of tails to the total number of tosses, the first step is to subtract the number of heads (12) from the total number of tosses (20). This will give us the number of tails.
11.
12/24 = 50/100
Correct Answer
A. True
Explanation
The given statement "12/24 = 50/100" is true because both fractions are equivalent. When simplified, both fractions reduce to 1/2. Thus, the statement is correct.
12.
1/3 = 2/9
Correct Answer
B. False
Explanation
The given equation states that 1/3 is equal to 2/9. However, this is not true. In reality, 1/3 is equal to 3/9, not 2/9. Therefore, the correct answer is false.
13.
2/3 = 24/36
Correct Answer
A. True
Explanation
The given statement is true because when we simplify the fraction 2/3, we can multiply both the numerator and denominator by 12 to get 24/36. This means that 2/3 is equivalent to 24/36, making the answer true.
14.
16 to 3 equals 27 to 5.
Correct Answer
B. False
Explanation
The statement "16 to 3 equals 27 to 5" is false. This is because the expression "16 to 3" means 16 raised to the power of 3, which is equal to 4096. On the other hand, the expression "27 to 5" means 27 raised to the power of 5, which is equal to 143,489. Therefore, 16 to 3 is not equal to 27 to 5.