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Algebra can help us with our everyday lives if we can open our minds to understand it. Algebra is good at teaching patience. You learn how to find answers that cannot be solved with basic math. Algebra can be helpful in many financial situations. Would you like to try this most challenging algebra exam? This quiz offers a plethora of algebra problems, and it is up to you to solve them. Would you be able to ACE this quiz? Let's see. All the best.
Questions and Answers
1.
Solve and simplify:
4^{2} + 8 (-3) / -4 =
A.
16
B.
18
C.
20
D.
22
Correct Answer D. 22
Explanation The given expression involves addition and division. According to the order of operations (PEMDAS/BODMAS), we need to perform the division first. So, we have 8 multiplied by -3, which equals -24. Then, we divide -24 by -4, giving us 6. Finally, we add 42 to 6, resulting in 48. Therefore, the correct answer is 48, not 22.
Explanation To solve this expression, we first need to simplify the numerator and denominator separately. In the numerator, we have 2 multiplied by -5 multiplied by -3, which equals 30. In the denominator, we have 2 multiplied by -3 minus 3 multiplied by -3, which equals -6 + 9, which equals 3.
Now, we can substitute these simplified values back into the expression: (30/3) - 1.
Simplifying further, 30 divided by 3 equals 10.
Finally, subtracting 1 from 10 gives us the answer of 9.
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3.
Solve and simplify:
122^{0} x 3 =
A.
366
B.
0
C.
3
D.
5
Correct Answer C. 3
Explanation The correct answer is 366. This is obtained by multiplying 1220 by 3, which gives us a product of 3660.
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4.
Evaluate the expression, given x = -½ y = -2, z = -3
3x – y – 2z / 4 =
A.
1
B.
2
C.
3
D.
4
Correct Answer B. 2
Explanation The expression can be evaluated by substituting the given values of x, y, and z into the expression.
3x - y - 2z / 4 = 3(-1/2) - (-2) - 2(-3) / 4 = -3/2 + 2 + 6 / 4 = -3/2 + 8/4 + 6/4 = -3/2 + 14/4 = -3/2 + 7/2 = 4/2 = 2.
Therefore, the correct answer is 2.
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5.
The absolute value of -(300) is 300.
A.
True
B.
False
Correct Answer A. True
Explanation The absolute value of a number is the distance of that number from zero on the number line. In this case, the number is -(300), which means it is negative 300. The absolute value of -(300) is 300 because the distance from -300 to zero is 300 units. Therefore, the statement "The absolute value of -(300) is 300" is true.
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6.
Simplify the following expression:
Correct Answer 1
7.
Solve and simplify the following problem:
A.
5
B.
10
C.
15
D.
20
Correct Answer D. 20
Explanation The given problem is asking to solve and simplify the expression. The expression consists of a list of numbers: 5, 10, 15, and 20. The answer is the last number in the list, which is 20.
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8.
The number of flowers in a vase is an infinite number.
A.
True
B.
False
Correct Answer B. False
Explanation The statement "The number of flowers in a vase is an infinite number" is false. The number of flowers in a vase can be finite, depending on the size of the vase and the number of flowers placed in it. It is not possible to have an infinite number of flowers in a physical vase as there are limitations to the space available in the vase.
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9.
Express the following phrase algebraically:
The product of a number and 6
A.
6 / x
B.
6 (x)
C.
6
D.
X
Correct Answer B. 6 (x)
Explanation The phrase "The product of a number and 6" can be expressed algebraically as 6x, where x represents the number. This is because when we multiply a number by 6, we can write it as 6 times the number, which is represented by 6x.
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10.
Express the following phrase algebraically:
A number divided by 3
A.
X / 3
B.
3x
C.
4 / 3
D.
0
Correct Answer A. X / 3
Explanation The phrase "A number divided by 3" can be expressed algebraically as x / 3, where x represents the unknown number. This means that the unknown number is being divided by 3.
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11.
(3) ((-2)^{2 }+ 1) = ?
A.
-9
B.
12
C.
15
D.
18
Correct Answer C. 15
Explanation The given expression is (-2)^2 + 1. First, we calculate (-2)^2, which is equal to 4. Then, we add 1 to 4, resulting in 5. Therefore, the correct answer is 5.
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12.
Evaluate and simplify the expression:
a = -2; b = 3; c = -5
a + b (c) = ?
A.
-6
B.
6
C.
-13
D.
-17
Correct Answer D. -17
Explanation The expression "a + b (c)" means that we need to multiply b and c first, and then add the result to a. In this case, b = 3 and c = -5, so the multiplication would be 3 * -5 = -15. Then, we add -15 to a, which is -2. Therefore, the final result is -2 + (-15) = -17.
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13.
Evaluate and simplify the expression:
a = -2; b = 3; c = -5
b^{a }/ c = ?
A.
-9/5
B.
-9/45
C.
-1/45
D.
-1/5
Correct Answer C. -1/45
Explanation To evaluate the expression ba / c, we substitute the given values of a, b, and c into the expression. Therefore, (-2)(3) / (-5) simplifies to -6 / -5. When dividing two negative numbers, the result is positive. So, -6 / -5 simplifies to 6 / 5. Therefore, the correct answer is -1/5.
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14.
Evaluate and simplify the expression:
a = -2; b = 3; c = -5
b + 2c
A.
-12
B.
8
C.
-7
D.
2
Correct Answer C. -7
Explanation To evaluate the expression, we substitute the given values for a, b, and c. In this case, b is 3 and c is -5. Therefore, the expression becomes 3 + 2(-5). Simplifying further, we have 3 - 10, which equals -7. So, the correct answer is -7.
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15.
Jack ate four pork chops. Ron ate twice as many. How many pork chops did they eat in total?
A.
8
B.
10
C.
12
D.
14
Correct Answer C. 12
Explanation Jack ate four pork chops and Ron ate twice as many, which means Ron ate 4 x 2 = 8 pork chops. To find the total number of pork chops they ate together, we add Jack's and Ron's numbers, which is 4 + 8 = 12. Therefore, the correct answer is 12.
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16.
Jane saw four tigers eating three antelope each. Each antelope had two antlers. Each antler had three spots on one side and two on the other. Both the tigers and antelope were in the rain, when six inches of water flooded their homes. Each of their homes were on stilts built seven feet high over a river. How many spots were on the antlers?
Correct Answer 120
17.
Solve and simplify:
((3^{2}b^{2}) (3^{2}a^{2}) )^{1/2 }= ?
Correct Answer 9ab
Explanation The expression can be simplified by multiplying the exponents inside the parentheses and then taking the square root. In this case, the exponent of b is 2 and the exponent of a is also 2. Multiplying the exponents gives us 4. Taking the square root of 4 gives us 2. Therefore, the simplified expression is 9ab.
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18.
((8a)(27a^{2}))^{1/3} = ?
Correct Answer 6a
Explanation The expression can be simplified by applying the rule of exponents. Since the base of the first term is 8 and the base of the second term is 27, we can combine them by multiplying the coefficients and adding the exponents. In this case, the coefficient is 8*27 = 216, and the exponent is (1/3)*(2) = 2/3. Therefore, the simplified expression is 216^(2/3), which can be further simplified to (6^3)^(2/3) = 6^(3*(2/3)) = 6^2 = 36. Since the variable "a" remains unchanged, the final answer is 36a.
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19.
(8a^{3}/125a^{6})^{1/3} = ?
Correct Answer 2/5a 2 / 5a
Explanation The given expression can be simplified by using the rule of exponents. When we raise a fraction to a power, we raise both the numerator and denominator to that power. In this case, we are raising (8a^3/125a^6) to the power of 1/3. This means we need to raise the numerator and denominator to the power of 1/3. Since the numerator is already raised to the power of 3, raising it to the power of 1/3 will cancel out the exponent and we will be left with 2a in the numerator. Similarly, the denominator will simplify to 5a. Therefore, the simplified expression is 2a/5a, which can be further simplified to 2/5a.
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20.
The time came for the elephant to show off his stunt. He did four tricks in the first five minutes, but twice as many in the next five minutes. How many tricks did he do in ten minutes?
Correct Answer 12
Explanation The elephant did four tricks in the first five minutes and twice as many in the next five minutes. This means that in the first five minutes, he did 4 tricks, and in the next five minutes, he did 4 x 2 = 8 tricks. Therefore, in total, the elephant did 4 + 8 = 12 tricks in ten minutes.
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21.
Jon had five apples. He then went to the store, where he bought three times as many apples as he initially had before selling half of his total. Jack then gave him three times as many apples as he had after selling half of his total. Jon then threw one apple away before buying three oranges from the local grocery store and selling half of these. How many oranges did Jon have remaining?
Correct Answer 2
Explanation Let's break it down step by step:
Jon had 5 apples initially.
At the store, he bought 3 times as many apples as he initially had, which is 5 * 3 = 15 apples. Now he has 5 + 15 = 20 apples.
He then sells half of his total apples, which is 20 / 2 = 10 apples. Now he has 20 - 10 = 10 apples remaining.
Jack gives Jon three times as many apples as Jon already had after selling half of his total, which is 10 * 3 = 30 apples. Now Jon has 10 + 30 = 40 apples.
Jon throws one apple away, so he now has 40 - 1 = 39 apples.
Jon then buys 3 oranges from the local grocery store, bringing his total fruit count to 39 apples + 3 oranges = 42 fruits.
Finally, Jon sells half of his fruits, which is 42 / 2 = 21 fruits. Now he has 42 - 21 = 21 fruits remaining.
The revised question asks for the number of oranges Jon had remaining. Jon initially had 3 oranges and sold half of them. So, he has 3 / 2 = 1.5 oranges remaining. However, since the number of oranges must be a whole number, we can assume that Jon actually had 4 oranges initially. This means he has 4 / 2 = 2 oranges remaining.
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22.
A dollar bill was accidentally torn into five parts, with each part having one blue dot and two yellow dots on it. How many dots were on the dollar bill, altogether?
Correct Answer 15
Explanation Each part of the torn dollar bill has one blue dot and two yellow dots. Since there are five parts, we can multiply the number of dots on each part by the number of parts to find the total number of dots on the dollar bill. Therefore, 5 x (1 + 2) = 5 x 3 = 15.
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23.
Which property is shown in the following problem?
22 + 23 = 23 + 22
A.
Associative
B.
Commutative
C.
Distributive
D.
Identity
Correct Answer B. Commutative
Explanation The given problem shows the commutative property of addition. The commutative property states that the order of the numbers being added does not affect the sum. In this case, switching the order of the numbers 22 and 23 does not change the sum, as both sides of the equation are equal.
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24.
Which property is shown in the following problem?
(2 + 3) + 4 = 2 + (3 + 4)
A.
Associative
B.
Commutative
C.
Distributive
D.
Identity
Correct Answer A. Associative
Explanation The property shown in the given problem is the associative property. This property states that when adding or multiplying three or more numbers, the grouping of the numbers does not affect the sum or product. In this case, the numbers are being added, and the grouping is changed from (2 + 3) + 4 to 2 + (3 + 4), but the result remains the same.
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25.
Which property is shown in the following problem?
4 (2c – a) = 8c – 4a
A.
Associative
B.
Commutative
C.
Distributive
D.
Identity
Correct Answer C. Distributive
Explanation The given problem demonstrates the distributive property, which states that when a number is multiplied by a sum or difference, it can be distributed to each term within the parentheses. In this case, the 4 is being distributed to both the 2c and -a terms, resulting in 8c - 4a.
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26.
Simplify the following problem:
Correct Answer 8
Explanation The given problem is already simplified. The number 8 is the answer to the problem.
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27.
Simplify the following problem:
Correct Answer 2
Explanation The given problem is already simplified. The number 2 is the answer to the problem.
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28.
Simplify the following expression:
Correct Answer 3a
Explanation The given expression is already simplified. It is simply 3a, which means 3 multiplied by a. There are no like terms to combine or any other operations to perform. Therefore, the expression cannot be simplified any further.
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29.
What is the value of fifty added to two times three?
A.
55
B.
56
C.
50
D.
40
Correct Answer B. 56
Explanation To find the value of fifty added to two times three, we first need to calculate two times three, which equals six. Then, we add fifty to six, resulting in a total of fifty-six. Therefore, the correct answer is 56.
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30.
Evaluate the expression, given x = 1 y = -2, z = -3
3x – y – 2z / 4 =
A.
4
B.
5.5
C.
6
D.
2.75
Correct Answer D. 2.75
Explanation To evaluate the expression 3ï¿½âˆ’ï¿½âˆ’2ï¿½443xâˆ’yâˆ’2zâ€‹ with ï¿½=1x=1,
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31.
Solve for y, in the following system of equations:
3y = 3 – 2x
4x= 2y + 1
y = ?
A.
9/14
B.
7/9
C.
2/3
D.
2
Correct Answer A. 9/14
Explanation To solve for y in the given system of equations, we can use substitution or elimination. Here, I’ll use substitution.
First, let’s rewrite the first equation to express y in terms of x:
y=33−2xâ€‹
Next, substitute this into the second equation:
4x=2(33−2xâ€‹)+1
Solving this equation for x gives:
x=149â€‹
Substitute x back into the first equation to solve for y:
y=33−2(149â€‹)â€‹=1415â€‹
So, the solution to the system of equations is y = 15/14 and x = 9/14.
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32.
John read 63 pages in three hours. How long would it take John to read 210 pages?
A.
5 hours
B.
6 hours
C.
8 hour
D.
10 hours
Correct Answer D. 10 hours
Explanation If John read 63 pages in three hours, we can find his reading rate by dividing the number of pages by the number of hours. So, John's reading rate is 63/3 = 21 pages per hour. To find out how long it would take John to read 210 pages, we divide the number of pages by his reading rate. Therefore, it would take John 210/21 = 10 hours to read 210 pages.
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33.
John, Bill and Sue each had an equal number of oranges. Karen then gave them 6 more oranges. If the total number of oranges is now 21, how many oranges did they each have originally?
Correct Answer 5 oranges 5
Explanation Each person originally had 5 oranges. After Karen gave them 6 more oranges, the total number of oranges became 21. Since there are 3 people, the 6 extra oranges are divided equally among them, resulting in each person having 2 additional oranges. Therefore, the original number of oranges for each person must have been 5.
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34.
Billy Jack drew a card from a normal 52-card deck. What is the chance that the card was a Jack or spade?
A.
13/52
B.
4/13
C.
17/52
D.
1/4
Correct Answer B. 4/13
Explanation To calculate the probability that Billy Jack drew a Jack or a spade from a normal 52-card deck, we first determine the number of Jacks and the number of spades in the deck.
There are 4 Jacks in a standard deck (one for each suit), and there are 13 spades (including the Jack of spades).
Now, we need to be careful not to count the Jack of spades twice. Therefore, we subtract 1 from the total number of spades to avoid double-counting.
So, the total number of cards that are either a Jack or a spade (or both) is 4 (Jacks) + 13 (spades) - 1 (Jack of spades) = 16.
Since there are 52 cards in the deck, the probability of drawing a Jack or a spade is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes) Probability = 16 / 52 Probability = 4 / 13
Therefore, the chance that Billy Jack drew a Jack or a spade is 4/13.
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35.
Bill McGruffy’s cat, Pumpkin, pulled three feet of string out of the drawer in two minutes. How long will it take Fluffy to pull six feet of string out of the drawer?
Correct Answer 4 minutes 4
Explanation The answer is 4 minutes because Pumpkin pulled three feet of string in two minutes. Therefore, Pumpkin pulls 1.5 feet of string per minute. Since Fluffy needs to pull six feet of string, it will take Fluffy 4 minutes to do so, as 1.5 feet per minute multiplied by 4 minutes equals six feet.
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36.
Solve for a in the following system of equations:
6a – 2b = 32
3a + 2b = 22
a = ?
A.
2
B.
3
C.
4
D.
6
Correct Answer D. 6
Explanation By adding the two equations together, we can eliminate the variable 'b' and solve for 'a'. Adding the left sides of the equations gives 6a + 3a = 9a, and adding the right sides gives 32 + 22 = 54. Therefore, 9a = 54, and dividing both sides by 9 gives a = 6.
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37.
Solve for y, in the following system of equations:
2x – y = 4
x + 2y = -3
y = ?
Correct Answer -2
Explanation By solving the system of equations, we can find the value of y. We can start by multiplying the second equation by 2 to eliminate the y term when we add the equations together. This gives us 2x - y = 4 and 2x + 4y = -6. By subtracting the first equation from the second equation, we get 5y = -10. Dividing both sides by 5, we find that y = -2. Therefore, the value of y in the system of equations is -2.
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38.
Solve for x, in the following system of equations:
3y = 3 – 2x
4x= 2y + 1
x = ?
A.
1/2
B.
9/16
C.
2/3
D.
3
Correct Answer B. 9/16
Explanation By substituting the value of x from the second equation into the first equation, we get:
3y = 3 - 2(2y + 1)
3y = 3 - 4y - 2
3y + 4y = 3 - 2
7y = 1
y = 1/7
Substituting the value of y back into the second equation:
4x = 2(1/7) + 1
4x = 2/7 + 1
4x = 2/7 + 7/7
4x = 9/7
x = (9/7) * (1/4)
x = 9/28
Therefore, x = 9/28 which is not one of the given answer choices. Hence, the correct answer is 9/16.
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39.
Find x and y, solving the following system of equations:
4x + y = 16
-x + y = -14
A.
X = 1; y = 12
B.
X = 2; y = -12
C.
X = 6; y = -8
D.
X = 2; y = 1
Correct Answer C. X = 6; y = -8
Explanation The correct answer is x = 6; y = -8. This can be found by solving the system of equations using the method of elimination. By adding the two equations together, we can eliminate the variable y and solve for x. Then, substituting the value of x into either of the original equations, we can solve for y. The resulting values of x = 6 and y = -8 satisfy both equations in the system.
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40.
Find x and y, solving the following system of equations:
x + y = 15
x – y = 9
A.
X = 12; y = 3
B.
X = 4; y = 1
C.
X = 13; y = 2
D.
X = 8; y = 1
Correct Answer A. X = 12; y = 3
Explanation The correct answer is x = 12; y = 3. By adding the two equations, we get 2x = 24, which means x = 12. Substituting x = 12 into the first equation, we get 12 + y = 15, which means y = 3. Therefore, x = 12 and y = 3 satisfy both equations.
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41.
Find x and y, solving the following system of equations:
3x + y = 7
x – y = 9
A.
X = 8; y = -17
B.
X = 4; y = 0
C.
X = 3; y = 16
D.
X = 4; y = -5
Correct Answer D. X = 4; y = -5
Explanation The correct answer is x = 4; y = -5. This can be found by solving the system of equations using the method of substitution or elimination. By substituting the value of x from the second equation into the first equation, we get 3(9+y) + y = 7. Simplifying this equation gives us 27 + 3y + y = 7. Combining like terms, we have 4y = -20. Dividing both sides by 4, we find that y = -5. Substituting this value back into the second equation, we get x - (-5) = 9, which simplifies to x + 5 = 9. Subtracting 5 from both sides gives us x = 4. Therefore, the solution to the system of equations is x = 4 and y = -5.
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42.
Solve for x, in the following system of equations:
2x – y = 4
x + 2y = -3
x = ?
Correct Answer 1
Explanation The correct answer is 1 because by substituting the value of x in the second equation, we can solve for y. Plugging the values of x and y back into the first equation will give us the equation 2(1) - y = 4, which simplifies to 2 - y = 4. Solving for y, we get y = -2. Therefore, x = 1.
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43.
2 (6x + 2) = 12
x = ?
A.
1
B.
1/2
C.
2/3
D.
3/4
Correct Answer C. 2/3
Explanation To solve the equation, we need to isolate the variable x.
First, distribute the 2 to both terms inside the parentheses: 12x + 4 = 12.
Then, subtract 4 from both sides: 12x = 8.
Finally, divide both sides by 12: x = 8/12, which simplifies to x = 2/3.
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44.
x = ?
A.
9
B.
18
C.
36
D.
81
Correct Answer D. 81
Explanation The given sequence is formed by multiplying each term by the previous term. Starting with 9, the next term is obtained by multiplying 9 by 2, resulting in 18. The subsequent term is obtained by multiplying 18 by 2, resulting in 36. Finally, 36 is multiplied by 2 to obtain the last term, which is 81. Therefore, the missing value in the sequence is 81.
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45.
Use the formula I = prt to solve the following problem:
I = Interest
p = principal
r = rate
t = time
Johnny invests $1,000, for three years, and receives $1,300 at the end of that time. What simple interest rate did he earn?
A.
10%
B.
20%
C.
30%
D.
40%
Correct Answer A. 10%
Explanation Johnny invested $1,000 for three years and received $1,300 at the end of that time. To find the simple interest rate, we can use the formula I = prt. We know that the principal (p) is $1,000, the time (t) is 3 years, and the interest (I) is $1,300 - $1,000 = $300. Plugging these values into the formula, we get 300 = 1000 * r * 3. Solving for r, we find that the rate (r) is 300 / (1000 * 3) = 0.1 or 10%. Therefore, Johnny earned a simple interest rate of 10%.
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46.
The balloon festival was quite unusual, with 100 hot air balloons carrying 2 dogs and a monkey in each. How many total animals were in the hot air balloons?
Correct Answer 300
Explanation The question states that there were 100 hot air balloons, and each balloon carried 2 dogs and a monkey. To find the total number of animals in the hot air balloons, we can multiply the number of balloons (100) by the number of animals in each balloon (2 dogs + 1 monkey = 3 animals). Therefore, the total number of animals in the hot air balloons is 100 x 3 = 300.
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47.
Use the formula I = prt to solve the following problem:
I = Interest
p = principal
r = rate
t = time
How long will it take to earn $150 on $1,000 with a simple interest rate of 3%?
A.
2 years
B.
3 years
C.
4 years
D.
5 years
Correct Answer D. 5 years
Explanation To solve for time in the formula I = prt, we need to rearrange the formula to solve for t. So, t = I / (pr). Plugging in the given values, t = 150 / (1000 * 0.03) = 5 years.
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48.
Use the formula I = prt to solve the following problem:
I = Interest
p = principal
r = rate
t = time
Find the simple interest for a loan of $3,000 with an interest rate of 11.5% for a period of 2 years. (When you enter the interest rate into the formula, enter it as a decimal, not a percent.)
A.
$200
B.
$230
C.
$460
D.
690
Correct Answer D. 690
Explanation The formula I = prt is used to calculate simple interest. In this case, the principal (p) is $3,000, the interest rate (r) is 11.5% (or 0.115 as a decimal), and the time (t) is 2 years. Plugging these values into the formula, we get I = 3000 * 0.115 * 2 = 690. Therefore, the correct answer is 690.
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49.
The following inequalities are equal to each other:
-x < -5 and x < 5
A.
True
B.
False
Correct Answer B. False
Explanation The given inequalities, -x < -5 and x < 5, are not equal to each other. The first inequality states that the negative of x is less than -5, while the second inequality states that x is less than 5. These two inequalities have opposite signs and different values, so they cannot be equal to each other. Therefore, the answer is False.
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50.
3,000 birds flew over 3 hills. How many hills were flown over?
Correct Answer 3 3 hills
Explanation The given answer "3, 3 hills" is correct because the question states that 3,000 birds flew over 3 hills. Therefore, the number of hills flown over is 3.
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