_Semester 1 Study Guide 15 complete
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School
University of Florida *
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Course
500
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
10
Uploaded by ColonelLeopard3628
Pick 15 questions to answer. Make sure you show all of your work
1.
Write an example of the Associative Property of Addition.
(2 + 3) + 4 = 2 + (3 + 4) is an illustration of the Associative Property of Addition. This demonstrates that when adding three integers, the order of the numbers has no effect on the result.
2.
To which subset of real numbers does the number 1
2
belong? (Hint: there may be more than one)?
The number 1/2 belongs to two subsets of real numbers: the rational numbers (Q) and the positive numbers (R+).
3.
What is the algebraic expression for the following word phrase: the product of 4 more than x and 6?
The algebraic expression for the word phrase "the product of 4 more than x and 6" is 6(4 + x).
4.
What is the simplified form of the expression √
❑
The simplified form of the expression √196 is 14. This is because the square root of 196 equals 14.
5.
Evaluate 2
x
y
7
for x
=
3
and y
=
6
6.
Evaluate (
4
5
)
2
Evaluating (4/5)^2, we get (4/5)^2 = (4/5) × (4/5) = 16/25. So, the value is 16/25.
7.
What is the simplified form of the expression 3
[
14
÷
(
4
2
−
3
2
)−
5
]
?
The simplified form of the expression 3[14 ÷ (4^2-3^2)-5] is 3[14 ÷ (16-9)-5] = 3[14 ÷ (7)-5] = 3[2-5] = 3[-3] = -
9.
8.
Which ordered pair is the solution of the equation y
=
5
x
+
3
?
a.
(
3,18
)
b.
(3,0)
The ordered pair (3,0) is the solution of the equation y=5x+3.
9.
Solve the equation for m: 3
m
−
4
=
26
To solve the equation 3m-4=26, we can start by isolating the variable m by adding 4 to both sides: 3m-
4+4=26+4, which simplifies to 3m=30. Then, we divide both sides by 3 to solve for m: (3m)/3=30/3, which simplifies to m=10. So, the solution to the equation is m=10.
10. Solve the equation for p:
−
18
=
p
2
To solve the equation -18=p^2, we can start by isolating the variable p by taking the square root of both sides (considering both the positive and negative square roots): √(-
18)=±√(p^2). This simplifies to √(-18)=±p. Since the square root of a negative number is not a real number, there are no real solutions for this equation.
11. Solve the equation for y: 4
(
2
y
−
6
)+
3
=
11
To solve the equation 4(2y-6)+3=11, we can start by distributing the 4 to the terms inside the parentheses: 8y-24+3=11. This simplifies to 8y-21=11. Next, we isolate the variable y by adding 21 to
both sides: 8y-21+21=11+21, which simplifies to 8y=32. Finally, we divide both sides by 8 to solve for
y: (8y)/8=32/8, which simplifies to y=4. So, the solution to the equation is y=4.
12. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {1, 2, 3, 4}. What is P'?
P' is the complement of P, which consists of all the elements in the universal set U that are not in P. Therefore, P' = {5, 6, 7, 8}.
13. Solve the inequality: 4
x
−
3
≥
21
To solve the inequality 4x - 3 ≥ 21, first add 3 to both sides to isolate the variable: 4x ≥ 24. Then, divide both sides by 4 to solve for x: x ≥ 6.
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14. Your goal is to save at least $360.00 over the next 6 weeks. How much money must you save each week to meet that goal? Write and solve an inequality.
Let x represent the amount of money to save each week. Since the goal is to save at least $360.00 over 6 weeks, the inequality would be 6x ≥ 360. Divide both sides by 6 to solve for x: x ≥ 60. Therefore, you must save at least $60.00 each week to meet the goal.
15. Of 256 consumers polled, some like only thriller movies, some prefer just comedies, and some like both. If 78 people like only thrillers, and 116 like both, how many people prefer only comedies?
Let T represent the number of people who like only thriller movies, C represent the number of people who like only comedies, and B represent the number of people who like both. Since the total number of people polled is 256, we can set up the following equation: T + C + B = 256.
Given that 78 people like only thrillers (T = 78) and 116 like both (B = 116), we can substitute these values into the equation: 78 + C + 116 = 256.
Simplifying, we have C + 194 = 256. Subtracting 194 from both sides, we get C = 62. Therefore, 62 people prefer only comedies.
16. Solve and graph the inequality -3x > 24
17.
Solve and graph the inequality: 7x + 2 ≥ 30 or 2x – 3 ≤ –11
18.
Solve the absolute value equation: |x − 10| = 5
To solve the absolute value equation |x - 10| = 5, we consider two cases:
Case 1: x - 10 = 5. In this case, we can add 10 to both sides to solve for x: x = 15.
Case 2: -(x - 10) = 5. Here, we need to distribute the negative sign: -x + 10 = 5. Subtracting 10 from both sides, we find -x = -5. Finally, multiplying both sides by -1, we get x = 5.
Therefore, the solutions to the absolute value equation are x = 15 and x = 5.
19. Shirts with a school’s mascot were printed, and the table shows the number of people who bought
them the first, second, third, and fourth weeks after their release. Draw the graph that represents the data shown in the table.
20. The table shows the relationship between two variables. Is the table linear? Nonlinear? Increasing? Decreasing? 21. Suppose soda is on sale for $0.50 a can, and you have a coupon for $0.30 off your total purchase. Write a function rule for the cost of n cans of soda. `
22. Which mapping is not a function? 23. Draw the graph of the function rule y
=
¿
3
x
∨+
2
24. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
25. Graph the equation 3
x
−
6
y
=−
18
26. Find the slope of the line graphed below
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27. What is the slope of the line that passes through the pair of points (3, 6) (-2, -4)? (hint: use slope formula to solve)
28. What is the slope of the line graphed below? 29. Write an equation in point-slope form for the line through the given point with the given slope.
(−
4,6
)
;m
=
3
4
30. Rewrite this equation this standard form: y
=
−
3
5
x
−
5
. Using integer coefficients. 31. How many solutions does this system of equations have?
y
=−
4
x
+
1
24
x
+
6
y
=
6
32. Write the inequality that is represented by the graph below. 33. Andre has $30, and Erin has $14. Andre is saving $5 per day, and Erin is saving $9 per day. After how many days will Andre and Erin have the same amount of money?
34. Write the equation of each line below.
35. Which type of correlation is suggested by the scatter plot?
A runner times herself to see how long it takes her to run different distances. The table shows the runner's times (in minutes) for running several distances (in miles).
36. What is the correlation coefficient of the set of data? Round your answer to the nearest thousandth.
37. About how long would you expect it to take this runner to run 17 miles? Find a line of best fit for this data and use it to make your prediction.
38. Write the linear equation that represents the table below.
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39. Determine whether the pair of lines listed are parallel, perpendicular, or neither. y
=
1
4
x
−
3
y
=−
4
x
+
3
y
=
−
1
3
x
+
2
3
x
+
y
=
5
2
x
+
3
y
=
6
y
=
−
2
3
x
+
3
40. Create a linear equation with point (5,4) that is perpendicular to the line y
=
2
x
+
1
.
41. What is the solution to the system?