Math Chapters 1-5

A book contains an average of 300 words per page. If you read one page in 68 seconds, what is your reading rate in words per minute? In pages per hour?

Approximately 265 words per minute or 53 pages per hour.

Rewrite each of these products as a sum. 6x(2x + y - 5) (2x2 - 11) (x2 + 4) (7x)(2xy) (x - 2)(3 + y)

a. 12x2 + 6xy - 30x b. 2x4 - 3x2 - 44 c. 14x2y d. 3x + xy - 6 - 2y

Simplify each expression. −2(−3) (−4) √49 −18 −7 −52

-24 7 -25 -25

Write each expression below as an equivalent expression without negative exponents. 3-2 m-4

1/9 1/m⁴

Evaluate each absolute value expression: |-27+33| |65-12| |13+(24⁻²)|

6 53 13¹/₅₇₆

M(16, -8), J(16, 2), and N(4, 0). What is the area of ΔMJN?

60 square units

Figure one has 6 tiles, figure 3 has 14 tiles. How many tiles will Figure 10 have?

Figure it out, kid.

Shirley starts with $85 in the bank and saves $15 every two months. Write an equation for the balance of Shirley's bank account. Be sure to define your variable(s).

Let x = # of months that have passed. Let y = amount of money in the account. y = ¹⁵/₂x + 85

Determine if the following sequences are arithmetic, geometric, or neither: −7, −3, 1, 5, 9, ... −64, −16, −4, −1, ... 1, 0, 1, 4, 9, ... 0, 2, 4, ...

a. arithmetic b. geometric c. neither d. arithmetic

Rewrite each of the expressions below. y2 · y7 (7a4)2 5xy2 · 12x3y4

a. c5 b. y9 c. 49a8 d. 60x4y6

Solve each equation after first rewriting it in a simpler equivalent form. 3(2x − 1) + 12 = 4x − 3 4x(x − 2) = (2x + 1)(2x − 3)

a. x = −6 b. x = 4 c. x = 7.5 d. x = ¾

Graph the segment that connects the points A(-4, 8) and B(6, 3). What is the slope of AB? Write an equation for the line that connects points A and B. Write an equation for a line that is parallel to AB. Write an equation for a line that is perpendicular to AB.

a. −¹/₂ b. y = −¹/₂x + 6 c. Answers vary, but should be in the form y = −½x + b. d. Answers vary, but should have a slope of 2 and be written in the form y = 2x + b.

Evaluate the expressions below for the given values −2x2 + 1 for x = −3 2x for x = 3 4x − 4 for x = 3 2 · 3x for x = 5

a: -17 b: 8 c: 8 d: 486

If f(x) = 2x, then f(4) = 24= 16. Find the value of f(1) f(3) f(t)

a: 2 b: 8 c: 2t

Solve. −2x − 3 = 3 7 + 2x = 4x − 3 6x − 10 = −8 + 3x

a: x = -3 b: x = 5 c: x = 2

What value(s) of x will make each equation below true? x + 5 = 5 2x − 6 = 3x + 1 − x − 7 3x + 1 = 43 4x − 1 = 4x + 7

a: x = 0 b: all real numbers c: x = 14 d: no solution

For each equation below, determine the value of y if x = 2. y = 7 − 3x y = x2 − 1 y = ¹⁸/x

a: y = 1 b: y = 3 c: y = 9

Rewrite each expression into an equivalent, simpler form with no negative exponents or parentheses remaining. 2m3n2 · 3mn4 (s4tu2)(s7t−1) (3w−2)4 m−3

b. 6m4n6 d. s11u2 e. 81/w⁸ f. 1/m³

Mary helps prepare food in the Tiger Cafe. Mary notices that sales of fresh fruit cups seem to vary widely from day to day. This is a problem because preparing too many cups results in wasted fruit and making too few results in lost sales. She decides that the daily weather may have a strong association with demand. Mary chooses 12 days at random from last semester and pairs each day's high temperature with the number of fresh fruit cups sold each day. Temp (ºF) # of Cups 89 150 52 85 72 136 65 101 72 122 45 66 31 63 89 137 57 86 38 80 37 58 71 118 checksum 718 checksum 1202 b. Is a linear model appropriate? Create a residual plot to provide evidence. c. Compute the correlation coefficient and interpret R‑squared in context. d. Describe the association. Make sure you describe the form and provide evidence for the form. Provide numerical values for direction and strength and interpret them in context. Describe any outliers. e. If Mary wanted to be reasonably certain of not running out of fresh fruit cups on a day forecasted to be 90ºF, how many should she prepare? (Hint: Consider the upper and lower bounds of sales.)

b. Yes. There is random scatter in the residual plot with no apparent pattern. See graph at right. c. r = 0.956 and R2 = 91.3%. 91.3% of the variability in fruit cup sales can be explained by a linear relationship with the temperature. d. There is a strong positive linear association between the number of fruit cups sold and the temperature. The residual plot with random scatter confirms the relationship is linear. The association is positive with a slope of 1.54, so an increase in one degree in the weather is predicted to increase sales by 1.54 fruit cups. The association is strong: 91.3% of the variability in fruit cup sales can be explained by a linear relationship with the temperature. There are no apparent outliers. e. The largest residual is 17.09 fruit cups, so the boundary equations are c = 25.10 + 1.54t and c = -9.08 + 1.54t. On 90º days we predict sales will be between 129.5 and 163.7 fruit cups. Mary should prepare 164 fruit cups.

What is the word for: A function that has an equation of the form y = abx + k, where a is the initial value, b is positive and is the multiplier, and y = k is the equation of the horizontal line which has no limits (asymptote).

exponential function

Identify m and b in the following equations. What do m and b represent? y = 2x + 1 y = x − 4

m represents the slope and b represents the y-intercept. a. m = 2, b = 1 b. m = , b = −4

A line passes through the points A(-3, -2) and B(2, 1). Does it also pass through the point C(5, 3)?

no

To get the final output of 5 with an initial input of 6, what order must the following functions go in? y=√(x-5) y=x²-6

y = x²-6 and then y=√(x-5) Yes, reverse the order of the machines ( y = x ! 5 and then y = x2 ! 6 ) and use an input of x = 6.

Figure one has 3 blocks, two has 5, and three has 7. Write a y=mx+b equation.

y=2x+1