Arithmetic, Geometric, and Sum sequences.
Determine whether or not the sequence below is Arithmetic, Geometric, or Neither.
1, 2, 3, 4, 5...
What is Arithmetic?
Determine x below
x + y = 2
2x - y = 4
What is x = 2?
If included y = 0, do NOT award credit.
If P(A) = 0.5 and P(B) = 0.2, state P(A∩B) given that the events are independent.
What is P(A∩B) = 0.1?
What is Observational Study?
State the name of the formula below
A = P(2)^(t/d)
What is the Double Life formula?
Determine whether or not the sequence below is Arithmetic, Geometric, or Neither.
1, 1, 2, 3, 5, 8, 13...
What is Neither?
Determine x and y below
3x + 2y = 12
x - 5y = 21
If P(A) = 0.8 and P(B) = 0.6, state P(A|B) given that the events are independent.
What is P(A|B) = 0.8?
An unfair statistic
What is Statistical Bias?
Bias by itself is also correct
State the name of the formula below
A = Pe^rt
What is the Continuous Compounding formula?
A recursive formula for the sequence 64, 48, 36, … is
(1) an = 64(0.75)^(n-1)
(2) a1 = 64
an = an-1 - 16
(3) an = 64 + (n-1)(-16)
(4) a1 = 64
an = 0.75(an-1)
What is (4) a1 = 64
an = 0.75(an-1)?
Solve for the value of y in the system shown below.
3x + 4y - 5z = -27
2x + 3y - z = -3
6x - y + 4z = 3
(1) -27 (2) 6 (3) 3 (4) 23
What is (3) 3?
Mr. Zachary posts review assignments on the Betamath website for his students. On his last test, 49% of his students used Betamath and passed. Overall, 68% of his students used Betamath. Approximate the percentage of Mr. Zachary’s students that passed, given that they used Betamath.
(1) 19% (3) 33% (2) 32% (4) 72%
In a small city, there are 22 gas stations. The mean price for a gallon of regular gas was $2.12 with a standard deviation of $0.05. The distribution of the data was approximately normal. Given this information, the middle 95% of the gas stations in this small city likely charge
(1) $1.90 to $2.34 for a gallon of gas
(2) $1.97 to $2.27 for a gallon of gas
(3) $2.02 to $2.22 for a gallon of gas
(4) $2.07 to $2.17 for a gallon of gas
What is (3) $2.02 to $2.22 for a gallon of gas ?
A rabbit population doubles every 4 weeks. There are currently five
rabbits in a restricted area. If t represents the time, in weeks, and P(t)
is the population of rabbits with respect to time, about how many
rabbits will there be in 98 days?
(1) 56 (2) 152 (3) 3688 (4) 81920
What is (1) 56?
When a ball bounces, the heights of consecutive bounces form a geometric sequence. The height of the first bounce is 121 centimeters and the height of the third bounce is 64 centimeters. To the nearest centimeter, calculate the height of the fifth bounce.
(1) 25 (2) 34 (3) 36 (4) 42
What is (2) 34?
Solve for the value of x in the system of equations below.
5x + 2y - z = -14
7y - z = 31
5y + 4z - 5x = -23
(1) -17 (2) 2 (3) -1/5 (4) -7
What is (4) -7 ?
The probability of having math homework is 1/3 and the probability of having English homework is 1/7 . The probability of having math homework or having English homework is 9/21 . State the probability of having both math and English homework.
(1)19/21 (2)1/5 (3)1/21 (4)10/21
What is (3) 1/21 ?
Anne has a coin. She does not know if it is a fair coin. She flipped the coin 100 times and obtained 73 heads and 27 tails. She ran a computer simulation of 200 samples of 100 fair coin flips. The output of the proportion of heads is shown below.
Samples = 200
Mean = 0.497
Standard Deviation = 0.050
Given the results of her coin flips and of her computer simulation, state the most accurate answer.
(1) 73 of the computer’s next 100 coin flips will be heads.
(2) 50 of her next 100 coin flips will be heads.
(3) Her coin is not fair.
(4) Her coin is fair.
What is (3) Her coin is not fair ?
To prepare for lacrosse tryouts, Kole is increasing the amount of time
he spends at the gym. This week he is spending 150 minutes there
and he plans to increase this amount by 2% each week. The amount of
time, in minutes, that he plans to spend at the gym t weeks from now
is given by the function A(t) = 150(1.02)^t.
In terms of a daily growth rate, the amount of time Kole is planning
to spend at the gym can best be modeled by the function
(1) A(t) = 150(1.14869)^(t/7)
(2) A(t) = 150(1.14869)^(7t)
(3) A(t) = 150(1.00283)^(t/7)
(4) A(t) = 150(1.00283)^(7t)
What is (4) A(t) = 150(1.00283)^(7t) ?
Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
1) Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
2) Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
1) What is (33,000 - 33,000(1.04)^n)/(1-1.04) ?
2) What is $660,778.39 ?
Solve the following system of equations algebraically for all values of x, y, and z.
2x + 3y - 4z = -1
x - 2y + 5z = 3
-4x + y + z = 16
What is (x = -2), (y = 5), and (z = 3)?
A public radio station held a fund-raiser. The table below summarizes the donor category and method of donation.
Supporter Patreon
Phone Calls 400 672
Online 1200 2016
1) To the nearest thousandth, find the probability that a randomly selected donor was categorized as a supporter, given that the donation was made online.
2) Do these data indicate that being a supporter is independent of donating online? Justify your answer.
1) What is 0.373 or 1200/3216?
2) What is Yes (1600/4218 = 0.373)?
In a packaging plant, a machine packs boxes with jars. The machine’s manufacturer states that a box is packed, on average, every 42 seconds. To test that claim, the packaging plant randomly selects a sample of 10 boxes and finds the sample mean to be 49.8 seconds. The company ran a simulation of 1000 trials based on the manufacturer's claim. The approximately normal results are shown below.
Mean = 42.029
SD = 3.105
n = 10
1) Based on the simulation, determine an interval containing the middle 95% of plausible mean times. Round your answer to the nearest hundredth.
2) Is the time 49.8 seconds unusual? Use statistical evidence to justify your answer.
1) What is (35.82, 48.24)?
2) What is Yes because 49.8 falls outside of the confidence interval?
On a certain tropical island, there are currently 500 palm trees and 200 flamingos. Suppose the palm tree population is decreasing at an annual rate of 3% per year and the flamingo population is growing at a continuous rate of 2% per year.
1) Write two functions, P(x) and F(x), that represent the number of palm trees and flamingos on this island, respectively, x years from now.
2) State the solution to the equation P(x) = F(x), rounded to the nearest year. Interpret the meaning
of this value within the given context.
Hint: It doesn't ask you to do it algebraically.
1) What is P(x) = 500(0.97)^x and F(x) = 200e^(0.02x)?
2) What is (The number of Palm Trees & Flamingos will be equal in 18 years)?