# Math Topics

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Math

Sequences & SeriesWrite the first six terms of the arithmetic sequence with the first term, a₁, and common difference, d.
a₁ = 4, d = 1
a2
a3
24
=
a5 = 0
86 = 0
a6
...

Math

Basic MathFor q (x) = (-4x²+4x−1)/ (x²+2)
(a) Identify the horizontal asymptotes (if any). (b) If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the ho asymptote(s). Separate multiple equations of asymptotes with commas as necessary. Select "None" if applicable. The graph has no horizontal asymptotes. O The graph has at least one horizontal asymptote. Equation(s) of the horizontal asymptote(s): Crossover point(s):

Math

StatisticsYou want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 20.8. You would like to be 90% confident that your estimate is within 2 of the true population mean. How large of a sample size is required? n || Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places - this is important for the system to be able to give hints for incorrect answers.

Math

StatisticsYou want to obtain a sample to estimac population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 29.4. You would like to be 90% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?
n =
Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places - this is important for the system to be able to give hints for incorrect answers.

Math

Basic MathConnor is going to invest $83,000 and leave it in an account for 15 years. Assuming the interest is compounded monthly, what interest rate, to the nearest tenth of a percent, would be required in order for Connor to end up with $125,000?

Math

Basic MathYou are choosing between two health clubs. Club A offers membership for a fee of $11 plus a monthly fee of $22. Club B offers membership for a fee of $29 plus a monthly fee of $19. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
In months the total cost of each health club will be the same.
The total cost for each health club will be $

Math

Basic MathSuppose that the local sales tax rate is 4% and you purchase a car for $24,200.
a. How much tax is paid?
b. What is the car's total cost?
a. The amount of tax paid is $.
b. The total cost is $.

Math

Basic MathA small rock sits on the edge of a tall building. A strong wind blows the rock off the edge. The distance, in feet, between the rock and the ground t seconds after the rock leaves the edge is given by d = -16t² - 8t+470.
If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed.
How many seconds after the rock leaves the edge is it 443 feet from the ground?
seconds
How many seconds after the rock leaves the edge does it hit the ground?
seconds

Math

StatisticsYou want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 60.5. You would like to be 99% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?
n=
Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places - this is important for the system to be able to give hints for incorrect answers.

Math

Basic MathYou want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 68.6. You would like to be 98% confident that your estimate is within 1 of the true population mean. How large of a sample size is required?
n=
Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places - this is important for the system to be able to give hints for incorrect answers.

Math

Basic MathAssume that the situation can be expressed as a linear cost function. Find the cost function in this case.
Marginal cost: $20; 180 items cost $7500 to produce.
The linear cost function is C(x) =

Math

Basic MathThe principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t.
P= $12,000, r = 9.0%, t = 3 years

Math

Application of derivativesThe function h represents the height of an object t seconds after it is launched into the air. The function is defined by h(t) = -5t² + 20t+18. Height is measured in meters.
1) When will the object hit the ground? (round to the nearest hundredth)
seconds
2) At what 2 times does the object occupy a height of 33 meters?
seconds and seconds
3) When does the object reach its maximum
height? seconds
4) What is the maximum height that the
object reaches? meters

Math

LogarithmsWrite the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers.
log2(p3/mn)=

Math

Basic MathDetermine the difference in clock 12 arithmetic by starting at the first number and counting counterclockwise on the clock the number of units given by the second number.
2-8