Questions and Answers
Which equation has 1-i as a solution?
Which statement(s) about statistical studies is true?
To the nearest tenth, what is the value of x that satisfies $2^x = -2x + 11$?
2.6
What is the probability that a randomly selected 60 watt lightbulb's lifespan will be between 1440 and 1465 hours?
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Which factorization is incorrect?
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What is the highest ticket price to the nearest dollar that can be charged so that Sally's high school does not lose money on the event?
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What is the probability that a randomly selected person texts over 50 messages per month, given they are between the ages of 16 and 23?
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What is a recursive formula for the sequence 18, 9, 4.5...?
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If Kristen runs 8 miles in week one, what expression can help her find the total number of miles over the course of her 6-week training program?
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Over which interval is the height of the sine wave decreasing only?
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The expression $(x^3 + 2x^2 + x + 6)/(x + 2)$ is equivalent to?
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Given this output, what is the margin of error for the poll at a 95% confidence level?
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Which statement is not correct regarding the depreciation of a car represented by $v=32,000(0.81)^{(t/12)}$?
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Which equation represents an odd function?
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What is the completely factored form of $2d^4 + 6d^3 - 18d^2 - 54d$?
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Which diagram shows an angle rotation of one radian on the unit circle?
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When the equation is solved for J in terms of F and W, what does J equal?
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The sequence $a_1 = 6$ and $a_n = 3a_{n-1}$ can also be written as?
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Which equation represents the set of points equidistant from line L and point R shown on the graph?
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Mr. Fairson gave his class three mathematical rules. Which rules can be proved for all real numbers?
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What is the remainder when $p(x)$ is divided by $x + 4$?
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Which expression can be used to calculate the amount Remi would owe in dollars after one year if she did not make payments on a $300 payday loan?
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Which value is not contained in the solution of the systems shown below?
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Assuming a growth rate of 1.5%, what equation can predict the population of New York State t years after 2010, given the population was approximately 19,378,000?
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Study Notes
Algebraic Solutions and Functions
- The equation (X^2-2x+2=0) has the complex solution (1-i).
- The function representing revenue from ticket sales for a spring musical is (R(t)=-33t^2+360t) with a fixed production cost (C(t)=700+5t).
- The incorrect factorization of (M^3+3m^2-4m+12) is ( (m-2)^2(m+3) ).
Statistical Studies and Probability
- A survey of all English classes in a high school is a representative sample for studying student study hours.
- For ages between 16 and 23, the probability of texting over 50 messages per month is calculated as ( \frac{157}{229} ).
- Assuming a 95% confidence level, the margin of error for a poll is approximately 0.03.
Calculating Values and Sequences
- The solution for the equation (2^x=-2x+11) rounded to the nearest tenth is 2.6.
- A recursive formula for the sequence 18, 9, 4.5... is (G_1=18; G_n=(1/2)G_{n-1}).
- The sequence defined by (a_1=6) and (a_n=3a_{n-1}) simplifies to (a_n=2\cdot3^n).
- The total number of miles Kristen will run during her 6-week training program can be formulated as (E = 8(1.10)^{n-1}) where (n=1).
Statistical Distributions and Probabilities
- The lifespan of a 60-watt lightbulb is normally distributed with a mean of 1450 hours and standard deviation of 8.5 hours, with a probability of lasting between 1440 and 1465 hours being 0.8415.
- The population of New York State in 2010 was approximately 19.4 million, experiencing a growth rate of 1.5% annually, represented by (Pt = 1.015P_{t-1}).
Geometry and Functions
- A sine function representing light waves increases through the origin, and the height decreases in the interval (100, 300).
- The equation for a set of points equidistant from line (L) and point (R) is (y=-\frac{1}{8}(x-2)^2+1).
- The expression for the division of ( \frac{x^3+2x^2+x+6}{x+2} ) simplifies to (x^2+1+\frac{4}{x+2}).
Miscellaneous Mathematics
- The completely factored form of (2d^4+6d^3-18d^2-54d) is (2d(d+3)^2(d-3)).
- The remainder when dividing (p(x)) by (x+4) is 0, indicating (x+4) is a factor of (p(x)).
- The equation for calculating the amount owed on a $300 payday loan after one year with 30% interest compounded every 14 days is (300(1.30)^{365/14}).
- The odd function is represented by the equation (y=\sin x).
Logical Proofs
- Among the provided mathematical rules, rules 1 and 3 can be proved for all real numbers.
- A statement about the value of a car after 10 months, represented by (v=32000(0.81)^{t/12}), incorrectly states that the car loses 19% of its value each month.
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