Card 0 of 2191
A number between 1 and 15 is selected at random. What are the odds the number selected is a multiple of 6?
In the set of 1 to 15, two numbers, 6 and 12, are multiples of 6. That means there are two chances out of 15 to select a multiple of 6.
2/15
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For the fall semester, three quizzes were given, a mid-term exam, and a final exam. To determine a final grade, the mid-term was worth three times as much as a quiz and the final was worth five times as much as a quiz. If Jonuse scored 85, 72 and 81 on the quizzes, 79 on the mid-term and 92 on the final exam, what was his average for the course?
The formula for a weighted average is the sum of the weight x values divided by the sum of the weights. Thus, for the above situation:
Average = (1 x 85 + 1 x 72 + 1 x 81 + 3 x 79 + 5 x 92) / ( 1 + 1 + 1 + 3 + 5)
= 935 / 11 = 85.
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If the average of 5k and 3l is equal to 50% of 6l, what is the value of k/l ?
Since the first part of the equation is the average of 5k and 3l, and there’s two terms, we put 5k plus 3l over 2. This equals 50% of 4l, so we put 6l over 2 so they have common denominators. We can then set 5k+3l equal to 6l. Next, we subtract the 3l on the left from the 6l on the right, giving us 5k=3l. To get the value of k divided by l, we divide 3l by 5, giving us k= 3/5 l. Last we divide by l, to give us our answer 3/5.
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A big box of crayons contains a total of 120 crayons.
The box is composed of 3 colors; red, blue, and orange. 30 of the crayons are red, 40 of the crayons are blue and the rest are orange. If one picks a crayon randomly from the box, what is the probability that it will be orange?
To solve the problem one must calculate that there are 50 orange crayons in the box. So 50/120 are orange. If we simplify that fraction by 10 we get 5/12.
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The St. Louis area has the following weather:
Monday High Temperature 76 Low Temperature 51
Tuesday High Temperature 82 Low Temperature 62
Wednesday High Temperature 67 Low Temperature 37
What is the difference between the high temperature average and the low temperature average over the three days?
Average = sum of data points ÷ number of data points
High temperature average = (76 + 82 + 67) ÷ 3 = 75
Low temperature average = (51 + 62 + 37) ÷ 3 = 50
The difference between the two averages is 25.
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In the following set of numbers, the arithmetic mean exceeds the mode by how much?
{2, 2, 4, 8, 10, 12, 20, 30}
The arithmetic mean is defined as:
The sum of a list of values divided by the number of values in the list.
Therefore for this problem, the arithmetic mean is:
(2+2+4+8+10+12+20+30) / 8 = (88/8) = 11
The mode is defined as the value that occurs the greatest number of times in a list of values.
In this case, it would be 2.
Therefore, the arithmetic mean (11) exceeds the mode (2) by 9.
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Doug has a cow farm. Some of Doug's cows are used for milk, some are used for reproduction and some are used for both. If he has a total of 40 cows and 10 are used only for milk and 3 are used for both milk and reproduction, then how many cows are used for reproduction?
Since we know that only 10 cows are for milk only we must subtract this number from the total amount of cows to get our answer: 40 – 10 = 30 cows. The cows that do both are still used for reproduction, so the correct answer is 30 cows.
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All students have to take at least one math class and one language class. Twenty students take calculus, and thirty students take statistics. Fifteen students take Spanish and twenty-five take French. If there are thirty-five students total, what is the maximum number of students taking both two math classes and two language classes.
Totalling the number in math there are 50 students on the rosters of all the math classes. With 35 total students this means that there are 15 students taking 2 math classes. For the language classes there are 40 students on the roster, showing that 5 students are taking 2 language classes. The maximum number of students taking two math classes and two language classes is only as great as the smallest number taking a double math or language class, which is 5 students (limited by the language doubles).
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At a certain college, some members of the baseball team are seniors and all seniors are in statistics class. Which statement is must be true?
The statement says all seniors take statistics so if you are a senior you are in statistics automatically. It also said some baseball team members are seniors which means at least some teammates must be in statistics.
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The average age of a certain group of 20 people is 25 years old. Another group of 10 people with an average age of 40 years comes in and joins the first group. What is the average age of the new group?
We cannot just take the average of the ages 25 and 40, which is 32.5 years old.
Instead, we need to take a weighted average, taking into account the varying number of people in each group.
Take the average age of each group and multiply it by the number of people in that group and then take the sum. Next divide by the total number of people to get the weighted average age of the new group.
(20 * 25 + 10 * 40)/30 = 30
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The average for 24 students on a test is 81%. Two more students take the test, averaging 74% between the two of them. What is the total class average (to the closest hundreth) if these two students are added to the 24?
The easiest way to solve this is to consider the total scores as follows:
Group 1: 81 * 24 = 1944
Group 2: 74 * 2 = 148
Therefore, the total percentage points earned for the class is 148 + 1944 = 2092. The new class average will be 2092/26 or 80.46. (For our purposes, this is 80.46%.)
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Find the mode of the following set of numbers:
1,5,14,17,22,23,23
To find the mode, you must remember that mode is the most frequently occurring number. Thus, you just look for the number that appears the most. Thus, our answer is 23.
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A bag of jellybeans has 20 watermelon jellybeans, 45 sour apple jellybeans, 30 orange jellybeans and 5 cotton candy jellybeans. If you reach in and grab one jelly bean, what is the probability that it will be watermelon flavored?
Add up the total number of jellybeans, 20 + 45 + 30 + 5 = 100.
Divide the number of watermelon jellybeans by the total: 20/100 and reduce the fraction to 1/5.
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Twenty students scored an average of 83% on a test. After three more took the exam, the class average was exactly 84%. Which of the following is a possible set of scores for these three students?
Let's think of the exams in terms of 100 points for a 100%. This means that the first 20 students received 20 * 83 or 1660 points.
Now, we must figure out how many points would be necessary for 23 students to have an average of exactly 84%. That would be found using the equation for a mean:
x / 23 = 84 → x = 1932
That means that our 3 students had to get a total of 1932 – 1660, or 272 points. The only answer that matches that among our answers is 84%, 92%, and 96%.
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If a = 2b = 4c = 8d, what is the average of a, b, c, and d, in terms of a?
Convert each term, so a = a, b = a/2, c = a/4, and d = a/8
so then the average would be (a + a/2 + a/4 + a/8)/4
= (8a/8 + 4a/8 + 2a/8 + a/8)/4
= (15a/8)/4 = 15a/32
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Daria plays darts often. She scores 25 points 1/5 of the time she plays. She also scores 50 points with probability 3/5, and 0 points with probability 1/5. What is the average number of points Daria scores when she plays darts?
To find the average number of points, we need to multiply the points by their corresponding weights and sum them up.
Average = 1/5 * 25 + 3/5 * 50 + 1/5 * 0 = 35.
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What is the probability of choosing three hearts in three draws from a standard deck of playing cards, if replacement of cards is not allowed?
The standard deck of cards has 52 cards: 13 cards in 4 suits.
Ways to choose three hearts: 13 * 12 * 11 = 1716
Ways to choose three cards: 52 * 51 * 50 = 132600
Probability is a number between 0 and 1 that is defines as the total ways of what you want ÷ by the total ways
The resulting simplified fraction is 11/850
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In a group of 83 gym members, 51 are taking kickboxing and 25 are taking yoga. Of the students taking kickboxing or yoga, 11 are taking both classes. How many members are not taking either course?
If 11 people are taking both courses, this means 51-11 or 40 are taking kickboxing only and 25-11 or 14 are taking yoga only. The number of people taking at least one course, therefore, is 40 + 14 + 11 = 65. The 83 members minus the 65 that are taking courses leaves 18 who are not taking any courses.
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In a school of 1250 students, 50% of the students take an art class and 50% of the students take a gym class. If 450 students take neither art nor gym class, then how many students take both art and gym?
You can construct a Venn diagran in which one circle represents art (A), the other represents gym (B), the region of overlap is designated (C), and the number of students not present in either circle is designated (S).
First, it is given that S=450.
50% of students take art and 50% take gym and the total number of students is 1250. 50% of 1250 is 625. Thus, A+C=625 and B+C=625.
Setting them equal to each other we get A+C=B+C.
Subtract C from both sides to get A=B; so the same number of students take art only and gym only.
Now 1250-450= A+B+C=800.
Since A=B we can use substitution to get 2A+C=800.
Finally you can solve the system of equations using the method of your choice (substitution or elimination) to solve the system with A+C=625 and 2A+C=800.
For substitution, we solve for C in the first equation to get C=625-A. Then we substitute this value into the second equation to get 2A+ (625-A)=800. Solve for A to get A=175, so B=175 also. Since A+B+C = 800, C=450.
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Sets P, Q, and R consist of the positive factors of 48, 90, and 56, respectively. If set T = P U (Q ∩ R), which of the following does NOT belong to T?
First, let's find the factors of 48, which will give us all of the elements in P. In order to find the factors of 48, list the pairs of numbers whose product is 48.
The pairs are as follows:
1 and 48; 2 and 24; 3 and 16; 4 and 12; 6 and 8
Therefore the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Now we can write P = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}.
Next, we need to find the factors of 90.
Again list the pairs:
1 and 90; 2 and 45; 3 and 30; 5 and 18; 6 and 15; 9 and 10
Then the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Thus, Q = {1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90}.
Next find the factors of 56:
1 and 56; 2 and 28; 4 and 14; 7 and 8
Set R = {1, 2, 4, 7, 8, 14, 28, 56}
Now, we need to find set T, which is P U (Q ∩ R).
We have to start inside the parantheses with Q ∩ R. The intersection of two sets consists of all of the elements that the two sets have in common. The only elements that Q and R have in common are 1 and 2.
Q ∩ R = {1, 2}
Lastly, we must find P U (Q ∩ R).
The union of two sets consists of any element that is in either of the two sets. Thus, the union of P and Q ∩ R will consist of the elements that are either in P or in Q ∩ R. The following elements are in either P or Q ∩ R:
{1, 2, 3, 4, 6, 8, 12, 16, 24, 48}
Therefore, T = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}.
The problem asks us to determine which choice does NOT belong to T. The number 28 doesn't belong to T.
The answer is 28.
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