1.
If each of the figures is created from equilateral triangles of side length 1, what is the perimeter of the 5th figure?
Correct Answer
C. 15
Explanation
Each figure is created by adding an additional row of equilateral triangles to the previous figure. The first figure has 1 triangle, the second has 4 triangles, the third has 9 triangles, and so on. The number of triangles in each figure follows the pattern of square numbers. Therefore, the fifth figure will have 5^2 = 25 triangles. Since each triangle has a side length of 1, the perimeter of the fifth figure will be 25 * 1 = 25.
2.
What are the next three letters in the sequence below?J F M A M J J A S ___ ____ ____
Correct Answer
B. O N D
Explanation
The sequence follows the pattern of the first letter of each month in the year. The sequence starts with J for January, followed by F for February, M for March, A for April, M for May, J for June, J for July, A for August, S for September. The next three letters in the sequence would be O for October, N for November, and D for December.
3.
Simplify: (3x + 4) ( 3x - 4)
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
D. 9x^2 - 16
Explanation
The given expression is a product of two binomials: (3x + 4) and (3x - 4). To simplify the expression, we can use the distributive property to multiply the terms within each binomial. The first terms give us 9x^2, the outer terms give us -12x, the inner terms give us +12x, and the last terms give us -16. Simplifying further, we combine like terms and get 9x^2 - 16.
4.
In a group of 70 Spigghots there are 30 Reinholds, 25 Spahzbhotts and 15 Bluumps. What is the correct ratio of Bluumps to Spahzbhotts? CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 3 to 5
Explanation
The correct ratio of Bluumps to Spahzbhotts is 3 to 5. This can be determined by dividing the number of Bluumps (15) by the number of Spahzbhotts (25). Simplifying the ratio gives us 3 to 5.
5.
The Commutative Property of Addition says that you can add a set of numbers in any order, and still get the same answer. In other words, 8 + 3 = 3 + 8.Which example shows the Commutative Property of Multiplication? "x" is the multiplication sign, not a variable.CALCULATORS ARE NOT ALLOWED ON THIS QUIZ.
Correct Answer
C. A x B x C = C x A x B
Explanation
The given example A x B x C = C x A x B demonstrates the Commutative Property of Multiplication. This property states that the order of multiplication does not affect the result. In other words, you can multiply a set of numbers in any order and still get the same answer. In this example, rearranging the order of the variables A, B, and C does not change the product, showing the commutative property.
6.
Select the answer that is smaller than 66 2/3 %(sixty-six and two-thirds percent)CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
C. 5 / 8
Explanation
The answer 5/8 is smaller than 66 2/3% because when we convert 66 2/3% to a fraction, it becomes 2/3. Comparing this with 5/8, we can see that 5/8 is smaller.
7.
What does it mean to "Factor a quadratic expression"?
Correct Answer
B. To rewrite as a product of two linear expressions.
Explanation
To "Factor a quadratic expression" means to rewrite it as a product of two linear expressions. This involves finding two binomials that, when multiplied together, give the original quadratic expression. By factoring the quadratic expression, we can often simplify and solve equations more easily.
8.
Choose the correct factorized form of the expression:x^{2} + 7x + 12
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
D. (x + 3)(x + 4)
Explanation
The given expression is a quadratic expression in the form of ax^2 + bx + c. In order to factorize it, we need to find two binomials that when multiplied together, give us the original expression. In this case, we can see that the factors (x + 3) and (x + 4) when multiplied together, give us the expression x^2 + 7x + 12. Therefore, the correct factorized form of the expression is (x + 3)(x + 4).
9.
If 6 people can sit at one table, and 10 people can sit at two tables, and 14 people can sit at three tables, then how many tables do you need for 30 people? CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 7
Explanation
If 6 people can sit at one table, and 10 people can sit at two tables, and 14 people can sit at three tables, then we can determine the pattern. The number of people that can sit at each additional table is increasing by 4. So, for 30 people, we can calculate the number of tables needed by subtracting 6 (the number of people that can sit at one table) from 30 and then dividing the result by 4. This gives us 6 tables. However, since the question asks for the number of tables needed, we need to add 1 more table to the result, giving us a total of 7 tables.
10.
Simplify: (3k^{2} + 2k
-5) + (-2k^{2} -2k -1)
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 1k^2 -6
Explanation
The given expression is a combination of like terms. By combining the terms with the same exponent of k, we can simplify the expression. The coefficients of the like terms are added or subtracted based on their signs. In this case, the simplified expression is 1k^2 - 6, where 1k^2 represents the term with the coefficient 1 and exponent 2 of k, and -6 represents the constant term.
11.
Write the following in scientific notation134.8 x 10^8
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
D. 1.348 x 10^10
Explanation
The given number, 134.8 x 10^8, is already in scientific notation. Scientific notation is a way to express very large or very small numbers in a compact form. It consists of a number between 1 and 10, multiplied by a power of 10. In this case, the number 134.8 is multiplied by 10^8, which means it is equal to 134.8 multiplied by 10 raised to the power of 8. Therefore, no changes are needed and the given number is already in scientific notation.
12.
Which set is in decreasing order?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. { 9.0X10^5 ... 0.9x10^5 ... 9.0x10^3 }
Explanation
The set { 9.0X10^5 ... 0.9x10^5 ... 9.0x10^3 } is in decreasing order because the numbers are arranged from largest to smallest. The first number, 9.0X10^5, is the largest, followed by 0.9x10^5, and finally 9.0x10^3, which is the smallest number in the set.
13.
Which set of coordinates contains points that are ONLY on the y-axis?
Correct Answer
D. { (0,-4) ( 0,8) (0,-33) }
Explanation
The set of coordinates { (0,-4) (0,8) (0,-33) } contains points that are ONLY on the y-axis because all the x-coordinates are zero, indicating that these points lie on the vertical line passing through the origin.
14.
If 80% of the population are considered DELLS, and 30% of DELLS are MINEOS, and 60% of MINEOS are also LORAXES, then...In a population of 230, about how many would you expect to be LORAXES?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
A. About 32 to 35
Explanation
Based on the information given, we can calculate the expected number of LORAXES in the population. First, we find the number of DELLS in the population by multiplying the population size (230) by the percentage of DELLS (80%). This gives us 184 DELLS. Then, we find the number of MINEOS by multiplying the number of DELLS (184) by the percentage of MINEOS (30%). This gives us 55.2 MINEOS. Finally, we find the number of LORAXES by multiplying the number of MINEOS (55.2) by the percentage of LORAXES (60%). This gives us approximately 33.12 LORAXES. Since we cannot have a fraction of a person, we can expect about 32 to 35 people to be LORAXES in the population.
15.
A ball is thrown up in the air with an initial upward velocity of 34 feet per second from a height of 5 feet. You want to determine the maximum height of the ball. Which process would best help you answer the question?
Correct Answer
C. Use the vertex formula, then plug your answer back into the "throw formula".
Explanation
The vertex formula is used to find the maximum or minimum point of a quadratic equation. In this case, the vertex formula can be used to find the maximum height of the ball. By plugging the values into the vertex formula, we can determine the time at which the ball reaches its maximum height. Then, by plugging this time back into the "throw formula" (which represents the height of the ball at any given time), we can find the maximum height of the ball.
16.
Solve: -11 = 2x -5CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
A. -3
Explanation
To solve the equation -11 = 2x - 5, we can start by isolating the variable term. Adding 5 to both sides of the equation, we get -11 + 5 = 2x - 5 + 5, which simplifies to -6 = 2x. Next, we can divide both sides of the equation by 2 to solve for x. Dividing -6 by 2, we get x = -3. Therefore, the correct answer is -3.
17.
Solve: -3x -1 â‰¤ 14CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
E. X is greater than or equal to -5
Explanation
The given inequality is -3x - 1 â‰¤ 14. To solve this inequality, we need to isolate the variable x. By adding 1 to both sides, we get -3x â‰¤ 15. Then, dividing both sides by -3 (remember that when dividing by a negative number, the direction of the inequality sign flips), we have x â‰¥ -5. Therefore, the correct answer is "x is greater than or equal to -5."
18.
Find the product of the solutions to each problem below:4 = -x + 3 and -x + 2 = 6In other words: Find the product of the solutions of the problems above. CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
C. 4
Explanation
The product of the solutions to each problem can be found by solving each equation separately and then multiplying the solutions together. For the first equation, -x + 3 = 4, we can subtract 3 from both sides to get -x = 1, and then multiply both sides by -1 to get x = -1. For the second equation, -x + 2 = 6, we can subtract 2 from both sides to get -x = 4, and then multiply both sides by -1 to get x = -4. The product of -1 and -4 is 4, so the answer is 4.
19.
Which quadratic trinomial has (x - 4) as a factor?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. X^2 + 2x -24
Explanation
The given quadratic trinomial has (x - 4) as a factor because when we factor out (x - 4) from x^2 + 2x - 24, we get (x - 4)(x + 6), which is the given quadratic trinomial.
20.
Simplify: (8 - 3)(9 + 3) + (4 -7)
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
C. 57
Explanation
To simplify the given expression, we need to follow the order of operations (PEMDAS/BODMAS). First, we simplify the parentheses: (8 - 3) = 5 and (9 + 3) = 12. Then, we perform the multiplication: 5 * 12 = 60. Finally, we subtract 7 from 4: 4 - 7 = -3. Adding these results together: 60 + (-3) = 57. Therefore, the correct answer is 57.
21.
A population of Pandas (P) decreases at a rate of 3% per year for five years. Which equation below represents this?
Correct Answer
D. P(1-.03)^5
Explanation
The equation P(1-.03)^5 represents the population of Pandas decreasing at a rate of 3% per year for five years. In this equation, P represents the initial population, (1-.03) represents the decrease in population each year (97% remaining), and the exponent 5 represents the number of years. By multiplying the initial population by the decrease factor raised to the power of the number of years, we can calculate the population after five years.
22.
There are 15 socks in a drawer; 4 are red and 3 are blue and the rest are green. What is the Probability of randomly choosing a blue sock?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
D. 1 / 5
Explanation
The probability of randomly choosing a blue sock can be calculated by dividing the number of blue socks by the total number of socks in the drawer. In this case, there are 3 blue socks out of a total of 15 socks. Therefore, the probability is 3/15, which simplifies to 1/5.
23.
Simplify: 24 - 57
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. -33
24.
Which is greater, five-sixths of a million dollars or seven-ninths of a million dollars?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
A. Five-sixths
Explanation
Five-sixths of a million dollars is greater than seven-ninths of a million dollars because when comparing fractions, a larger denominator indicates smaller parts. Since six is larger than nine, five-sixths represents a larger portion of the whole than seven-ninths. Therefore, five-sixths of a million dollars is the greater amount.
25.
Find the mean of the following three terms:(8y - 10) and (12y + 4) and (4y - 3)CALCULATORS ARE NOT ALLOWED ON THIS QUIZ(No, we have never done this. This is a "think and apply" question. You have to think about what you know about the word mean, then apply it to this problem which is a little different than a typical 'mean' problem.)
Correct Answer
D. (8y - 3)
26.
At 2:00 pm a 36 inch yardstick creates a 24 inch shadow. At the same time a tree casts a 36 foot shadow. How tall is the tree?CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
C. 54 feet
Explanation
The height of the tree can be determined using the concept of similar triangles. The ratio of the length of the yardstick to its shadow is the same as the ratio of the height of the tree to its shadow. Therefore, the height of the tree can be calculated by setting up the proportion: 36 inches (yardstick) / 24 inches (yardstick shadow) = x feet (tree height) / 36 feet (tree shadow). Solving for x, we get x = (36 inches * 36 feet) / 24 inches = 54 feet. Therefore, the height of the tree is 54 feet.
27.
Simplify: 8h - 9v + 12v + 3h - 7s
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 11h + 3v - 7s
Explanation
The given expression is a combination of terms with variables h, v, and s. To simplify the expression, we can combine like terms. Combining the terms with h, we have 8h + 3h = 11h. Combining the terms with v, we have -9v + 12v = 3v. Finally, combining the terms with s, we have -7s. Therefore, the simplified expression is 11h + 3v - 7s.
28.
Three people have a mean age of 17. If a fourth person is added, and the fourth person is 9 years old, then what is the new mean age?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 15 years
Explanation
When a fourth person who is 9 years old is added, the total age of the four people becomes 17 + 17 + 17 + 9 = 60 years. Since there are now four people, the new mean age is 60 divided by 4, which equals 15 years.
29.
Distribute: (4m - 5b)(4m + 5b)
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
A. 16m^2 - 25b^2
Explanation
The given expression is a product of two binomials, (4m - 5b) and (4m + 5b). To distribute these binomials, we multiply each term of the first binomial by each term of the second binomial. Using the FOIL method, we get:
(4m - 5b)(4m + 5b) = 4m * 4m + 4m * 5b - 5b * 4m - 5b * 5b
= 16m^2 + 20mb - 20mb - 25b^2
= 16m^2 - 25b^2
Therefore, the correct answer is 16m^2 - 25b^2.
30.
Three people (Aqua-man, Batman, and Catwoman) start walking/running around a one-quarter mile track. Aqua-Man can walk the track in 9 min, Batman can run the track in 6 min, and Catwoman can run the track in 4 min. All three of them start walking at the same time. Assuming that they keep the same pace and they take no breaks, how long will it be before they are all at the same place at the same time. In other words, in how many minutes will they all meet at the starting point again?(No, we have never done this. This is a "think and apply" question. Or, you could just make a table with three columns, and add a munch of numbers together, but this is tricky, because if you make ONE mistake out of 20 calculations, you'll never get the right answer.)
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
C. 36 min.
Explanation
In order to find the time it takes for all three people to meet at the starting point again, we need to find the least common multiple (LCM) of their individual times. The LCM of 9, 6, and 4 is 36. Therefore, it will take 36 minutes for Aqua-man, Batman, and Catwoman to all meet at the starting point again.
31.
Which selection below does NOT give you a PRIME answer.CALCULATORS ARE NOT ALLOWED ON THIS QUIZx is multiply/ is divide- is minus+ is plusHINT: Having trouble with what "Prime" means? Consider these prime numbers: 2, 7, 13, 23, 47, 59, 71, 203
Correct Answer
D. 45 x 9 / 5 - 1
Explanation
The given expression 45 x 9 / 5 - 1 is not a prime answer because it involves multiplication, division, and subtraction operations, which are not considered prime numbers.
32.
You have a babysitting business over the summer. You charge $12 per hour and in one week you work 15 hours. How much money did you earn that week?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
C. $180
Explanation
The correct answer is $180. This can be calculated by multiplying the number of hours worked (15) by the rate charged per hour ($12). 15 x $12 = $180.
33.
In a local soccer tournament there are 3 brackets with 4 team in each bracket. Each team has an average of 12 players, 2 coaches, 13 parents, and 3 goats. How many total players are at the tournament?
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 144
Explanation
There are 3 brackets with 4 teams in each bracket, so there are a total of 3 x 4 = 12 teams in the tournament. Each team has an average of 12 players, so there are a total of 12 x 12 = 144 players in the tournament.
34.
Simplify: [ 9 - (8 / 4) + (0.5 x 14) ] -1
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
A. 13
Explanation
The given expression involves a series of arithmetic operations. First, we divide 8 by 4, which gives us 2. Then, we multiply 0.5 by 14, resulting in 7. Next, we subtract 2 and 7 from 9, giving us 0. Finally, we subtract 1 from 0, resulting in -1. Therefore, the correct answer is 13.
35.
9 x 8
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
E. 72
Explanation
The correct answer is 72 because when you multiply 9 by 8, you get the product of 72.
36.
-4(-12y - 8)
CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 48y + 32
Explanation
The given expression is -4(-12y - 8). To simplify this expression, we distribute -4 to both terms inside the parentheses. This gives us -4 * -12y which is 48y, and -4 * -8 which is 32. Therefore, the simplified expression is 48y + 32.
37.
Which statement is correct?
Correct Answer
E. The opposite of Six and Three is the Opposite of Three.
Explanation
The correct answer is "The opposite of Six and Three is the Opposite of Three." This statement is correct because when we take the opposite of both Six and Three, we get -6 and -3 respectively. Therefore, the opposite of Six and Three is the opposite of Three.
38.
(3b - 4)(5b + 2)Simplify:
Correct Answer
B. 15b^2 - 14b - 8
Explanation
By using the distributive property, we can simplify the given expression. First, we multiply 3b by both terms in the second parentheses to get 15b^2 + 6b. Then, we multiply -4 by both terms in the second parentheses to get -20b - 8. Combining these results, we have 15b^2 + 6b - 20b - 8. Simplifying further, we can combine like terms by subtracting 20b from 6b to get -14b. Thus, the simplified expression is 15b^2 - 14b - 8.
39.
OPTION RR:: A cell phone company charges 20 cents for each the first 40 text messages sent per month then 15 cents for each of the next 40 text messages, then 5 cents for each text message after that. OPTION SS:: OR, you can pay a fixed amount and send all the message you want. Option SS costs $20. CALCULATORS ARE NOT ALLOWED ON THIS QUIZChoose the option that is the least expensive for you.
Correct Answer
C. Option SS is best if you send more than 190 txt msg / mth.
Explanation
Option SS is the best choice if you send more than 190 text messages per month because the fixed cost of $20 is cheaper than the cost of sending more than 190 text messages using Option RR. With Option RR, the cost per text message increases after the first 80 messages, so if you send more than 190 text messages, the total cost will likely be higher than $20.
40.
In this problem, each Capital Letter represents a mathematical operation. It is your job to (1) determine what operation each letter represents, (2) use that information to answer THE BIG QUESTION below: Parenthesis are used as normal in mathematics. CALCULATORS ARE NOT ALLOWED ON THIS QUIZEquation # 1: 6 Q 8 U 1 = 14Equation # 2: 12 E 3 U 8 = 32Equation #3: (160 T 40) E 12 = 10THE BIG QUESTION: SOLVE THE FOLLOWING(6 U 9 T 4 ) Q 16 = ????CALCULATORS ARE NOT ALLOWED ON THIS QUIZ
Correct Answer
B. 66