Integrating Essential Skills
Shannon walked 1 2/3 miles on Wednesday and 2 3/5 miles on Thursday. What was the total distance, in miles, Shannon walked during those 2 days?
What is 4 4/15 miles?
4x3 x 3xy2 x 2xy2 is equivalent to:
What is 24x5y4?
(x3+2x2+3x- 2) - (2x3 x2 -4) is equivalent to:
What is -x3 + 3x2 +3x +2
What two number should be placed in the blanks below so that the difference between the consecutive numbers is the same? 13, _, _, 34
A. 19, 28 B. 20, 27 C. 21, 26
D. 23, 24 E. 24, 29
What is 20, 27
Reggie knows how to make 5 different entrees, 4 different side dishes, and 6 different desserts. How many distinct complete meals, each consisting of an entree, a side dish, and a dessert, can Reggie make?
What is 120?
Solution:
To find the number of distinct complete meals that Reggie can make from 5 different entrees, 4 different sides, and 6 different desserts, multiply the quantities in the 3 different groups together. Thus, there are (5)(4)(6), or 120 distinct meals that Reggie can make.
Mr. Wilk is a high math teacher whose salary is $33,660 for this school year, which has 180 days. In Mr. Wilk's school district, substitute teachers are paid $85 per day. If Mr. Wilk takes a day off without pay and a substitute teacher is paid to teach his classes, how much less does the school district pay in salary by paying a substitute teacher instead of Mr. Wilk for that day?
What is $102?
For any real numbers a and b, (10a2)(5ab)(2ab4) is equivalent to:
What is 100a4b5?
In the standard (x,y) coordinate plane, point X has coordinates (-4,0) and point Y has coordinates (0,-8). What are the coordinates of the midpoint of XY?
What i-4)s (-2,
The value of an investment grows based on the function V(t) = 1000(1 + 0.06)t, where V is the value in dollars and t is the time in years. To the nearest cent, what is the value of the investment after 8 years?
What is $1593.85?
If each element in a data set whose mean is x is multiplied by 3, and each resulting product is then reduced by 4, which of the following expressions gives the mean of the resulting data set in terms of x?
What is 3x - 4?
Solution:
For the sake of simplicity, let every element in the original set have the value x. If each element in the set is multiplied by 3, and then reduced by 4, each element then has the value 3x - 4. In a set where each value is 3x - 4, the mean is 3x - 4.
The expression a[(b-c) + d] is equivalent to:
ab - ac + ad
If 3 and 2 are factors of a, which of the following MUST be a factor of 14a?
What is 4?
The sides of a triangle are 9,12, and 15 centimeters long. What is the angle between the 2 shortest sides?
What is 900
If f(x) = -3x2 -8, then f (-4) =?
What is A -56
The average of five numbers is 12.4. The average of four of these numbers is 11. What is the value of the fifth number?
What is 18.0?
Solution:
Let the five numbers be represented by a, b, c, d, and e. Since the average of all five is 12.4, we know that a+b+c+d+e/5 = 12.4, or a +b+c+d+e = 12.4 x 5 = 62. We can say the four numbers that have an average of 11 are a, b, c, and d. This means that a+b+c+d/4 = 11, or a + b+ c +d = 44. Combining these equations, (a + b + c + d) + e = 62 = 44 + e, so e = 62 - 44 = 18.
There are 16 ounces in one pound. If 3.4 pounds of beef cost $4.95, what is the cost per ounce, to the nearest cent?
What is $0.09?
Solution:
To find the cost per ounce, first convert 3.4 pounds to ounces. Because there are 16 ounces in a pound, 3.4 is 3.4(16) = 54.4 ounces. To find the cost per ounce, divide the cost in dollars by the number of ounces, or $4.95/54.4 ounces = $0.09 per ounce.
For a real number m, (2m3)4=
What is 16m12?
A rectangle has a width of 5 meters and a length of 14 meters. If a similar rectangle has a width of 15 meters, what is its perimeter, in meters?
What is 114 meters?
Solution:
Since the rectangles are similar and 3(5)=15, the length of the larger rectangle is 3(14) = 42, and the perimeter is 15 + 42 + 15 + 42 = 114.
If f(x) = x2 + 3, then f(x + y) =?
What is x2 +2xy +y2 +3
How many different arrangements of the letters A, D, G, and F are possible?
What is 24?
Solution:
By the multiplication rule, there are 4 x 3 x 2 x 1 ways to arrange the letters.
One of three cards must be selected to continue a game. The probability the first card will be selected is 2/5, while the probability the second card will be selected is 1/8. What is the probability the third card will be selected?
What is 19/40?
Solutions:
The total of all the probabilities must be 1, since the events represent all possible choices:
1 - 2/5 - 1/8 = 40/40 - 16/40 - 5/40 = 19
The expression (x - a)(x + a) =
What is x2 - a2?
Triangle A and triangle B are equilateral triangles such that the ratioof the length of one side of triangle A to the length of one side of triangle B is 6 to 7. If the perimeter of triangle A is 9, what is the length of a single side of triangle B?
What is 7/2.
Solution:
Since A is equilateral, one side of A has a length of 9/3=3. Using the ratio, with b representing the length of one side of triangle B, 3/b=6/7, or 21=6b, Therefore, b=21/6=7/2.
If f(x) = 2x2 +3, then f(x+h) =?
What is 2x2 +4xh +2h2 + 3
If x = 7, what is the probability a randomly selected number from the set {x -5, 2x + 4, -x, x + 5, x + 3} will be even?
What is 4/5?
Solution:
Given that x = 7, the set can be written as {2, 18, -7, 12, 10}, which contains four even numbers. Since there are a total of five numbers in the set, the probability of selecting an even number is 4/5.