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# Math Praxis Examples

### Stack #82051

Math Problems | Answers |
---|---|

5* + 15* = | 5*+15*= 5*+(3*)(5*)= 5*(1+3*) |

A 224-mile trip requires 6 gallons of gasoline. At this rate, how many gallons of gasoline would be required for a 168-mile trip? | 224miles/6 gallons = 168miles/ g gallons. Solving the proportion gives g=6 x 168/224 = 4.5 gallons |

Which of the following defines y as a function of x? (A) x - y*=4, (B) x* + y* = 4, or (C) y=x +1 | There is only one value of y that corresponds to any given value of x. The answer is (C) y = x + 1 |

If a and b are integers, then all of the following must be true EXCEPT (A) [a] = [b], (B) [ab] = [a] [b], (C) [ab] =<a^2 b^2>, (D) [a +b]=[a] + [b] | Choice (D) is not alsways true because the equality fails when the signs of a and b are opposite. [a] + [b] = [10]+[-8] = 10+8 = 18 |

A certain recipe calls for 1/4 cup of white sugar, 1/2 cup of brown cusgar, 2 1/4 cups of flour, 1/4 teaspoon of salt. and 2 tablespoons of cornstartch. The amount of cornstarch called for is approximately what fraction of the total amount of sugar? | The sugar is given in cups and the cornstarch is given in tablespoons(T). The total amount of sugar is 3/4 cup (add white & brown sugar). Using the conservation table, 2T = 1/8 cup. Comparing 1/8 to 3/4 is the same as comparing 1/8 to 6/8 = 1/6 |

2(x-2)(3x-5) = | 2(x-2)(3x-5)= 2(3x^2 - 6x - 5x +10)= 6x^2 -22 +20 |

Jane withdrew half of the money from her savings. She later withdrew an additional $5.00, leaving $12.75 balance. If no other transactions were performed, how much money was in Jane's account originally? | Notice that the balance of $12.75 + $5 = $17.75, which is half of Jane's original savings. Thus, Jane originally had $35.50 in her account. |

Step 1 has 1 dot, Step 2 has 3 dots, Step 3 has 6 dots. If the pattern continues indefinitely, what expression could be used to find the number of dots in step n? | Fom the figure, you can see that 2 dots are added at step 2 and 3 dots are added in step 3. Multiply the step number by the step number plus 1 and divide by 2. Algebraically, n(n+1)/2 = n^2 +n/ 2 |

What is the negation of the following statement "All p is q"? | When "All p is q" it also means "Some p is q", and this statement you need to negate. This is easlily done by saying, "Some p is not q". It often helps to draw a Venn diagram when solving logic problems that are not too complicated. |

If 1/(1 - 3/7) < 1/(1 - x) < 1/(1 - 3/4), then x could equal which of the following? I. 1/2, II. 3/5, III. 5/9 | The answer is I and III. Look at notes for comparison |

The original price of a ceratin car was 25% greater than its cost to the dealer. The actual selling price was 25% less than the original price. If c is the cost of the car and p is the selling price, which of the following represents p in terms of c? | The original price of the car was c + 0.25c = 1.25c. The selling price was p= 1.25c - 0.25(1.25c) = 1.25c(1- 0.25), which is = (1.25c)(0.75) |

The point with coordinates (-4,t) lies on the line m in the xy-plane. The other coordinates that lie on line m are (6,0) and (0,3)? | Line m has a slope of -1/2 since 3-0/0-6 = 3/ -6 = -1/2. By inspecting the graph you can see that its y-intercept is 3. The equation of the line m can be written as y = -1/2x + 3. The value of t when x = -4 is 5. |

In the equation 32 base 4 = x base 2, the subscript of each number identifies the base in which the number is expressed, What is the value of x? | In base 4, the number 32 is equal to 3 x 4^1 + 2 x 4^0, which is 14 (in base 10); and in base 2, the number "14" can be expressed as 14= 8+4+2+0= 1x2^3 + 1x2^2 + 1x2^1 + 0x2^0, which yeilds 1110. Therefore, x = 1110. |

According to a survey of 100 students, 73 of the students took a math course and 57 took a music course. Of those surveyed, 22 reportedly took a math course but not a music course. How many students took neither a music course nor a math course? | Use a Venn diagram. The entire rectangle region represents the 100 students. The region of the rectangle that is outside the circles represents the # of students who took neither course. 100 - (22+51+6) = 21 |

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