Sequences & Series Questions and Answers

Replace the? with the correct symbol, <, >, or =, which will make a true statement from the following expression: 10/15 ? 6/10

Using the Pythagorean Theorem, if in a right triangle leg b = 11 and the hypotenuse, c = 19, what does the other leg, a equal? a≈ 15.49 a≈ 21.95 a 16.31 a≈ 12.8

If triangle ABC is similar to triangle MNO and side AB = 21 when side MN = 12, what is the length of side BC when side NO 25? Round your answer to the nearest hundredth. BC=

If an 8-hour workday includes a total break time of 14%, how many hours are used for breaks? Round your answer to the nearest hundredth of an hour, or the nearest minute. 1.29 hours, or 1 hour and 17 minutes. 1.13 hours, or 1 hour and 8 minutes. 1.19 hours, or 1 hour and 11 minutes.

Suppose $7000 is invested at an annual interest rate of 4% compounded daily for 3 yr. What is the accumulated amount in the account at the end of the 3 yr? (Assume there are 365 days in a year. Round to two decimals.)

The half-life of Radium-226 is 1600 yr. The decay model A(t) 70e-0.000433t describes the amount of Radium-226 present after t years for a sample of 70 g. How many grams of Radium-226 will remain after 2000 yr? Round to two decimals.

Compute the amount in an account after 4 years if $4550 is invested at an annual interest rate of 3.5% compounded semiannually. Round to two decimals.

When we write 0.000 000 027 in scientific notation, it becomes 2.7 x 10" for what value of n?

Use a calculator to approximate the value. Enter your answer rounded to three decimal places. 104.12

The number 1/100 is a power of 10 because it can be written as 10x for what value of X?

Enter the value of each exponential expression. When needed, round answers to three decimal places. a. 10° b. 10³ c. 10 ² d. 10¹/2 e. 10⁰

When the number 2 is written as an exponential expression with a base of 8, what is the exponent? (Use /to indicate a fraction; for example, 1/6.)

When the number 32 is written as an exponential expression with a base of 1/2 what is the exponent?

When 0.00053 is written in scientific notation, it is equivalent to 5.3 x 10 for what value of n?

A railroad track follows an inclination of 3.5°. How far must the train travel along the track to gain 18 meters in altitude?

Answer the following completely. Show your complete solutions. Number 1.) 2, 12, 40, 98, 198, ... General Rule = ? 23rd term = ? 32nd term = ? Number 2.) 8, 21, 46, 89, 156, ... General Rule = ? 23rd term = ? 32nd term = ? Number 3.) 3, 20, 63, 144, 275, ... General Rule = ? 23nd term = ? 32nd term = ?

The moment magnitude scale, denoted Mw, is a scale that measures the energy released by an earthquake and is now preferred over the Richter scale for medium to large earthquakes. The formula Mw = 2/3 log(Mo) 10.7, where Mo is the magnitude of the seismic moment, or the energy released in dyne centimeters. An earthquake in 1964 in Alaska had a moment of 7.5X10^29 dyn-cm. Compute the moment magnitude for this earthquake. Round your answer to the nearest tenth. (Source: USGS) Type your numeric answer and submit

Courtney has invested $3,500 into a savings account with a 4% APR compounding quarterly. How many years will it take for the investment to double? Round to two decimal places.

Complete and submit the assignment below, then you can proceed onto the next lesson. Can the Law of Sines be used to solve a right triangle? Write a short paragraph explaining why it can or cannot be used. If it can be used explain how to use it. Is there an easier way to solve the triangle? Explain.

Use a calculator to determine the value of each expression. Enter each value rounded to three decimal places. a. log 20 b. log 0.05 c. log 200 d. log 75.000 e. In 100 f. In 0.004

Fill in each blank with the appropriate value if it exists. To enter a fraction, use /as in 2/3. If the expression is undefined, enter undefined in the blank. a. In 1 = b. In e= c.Ine^5= d. In √e= e. In (1/e)= f.In0=

What is the equation of the vertical asymptote of the function? (Write the answer in the form of an equation. Do not enter any spaces in your answer.) f(x) = log(x + 2) + 1

A normal conversation is about 10^7 times the of hearing. Compute the intensity level (in decibels) for a normal conversation.

Let f(x) = - In(x). Fill in the blanks with the appropriate information. a.f(1/e)= b. f(1) = c. f(e) = d. f (e²) = e. Domain of f: f. Range of f: g. Vertical asymptote of graph:

Given that f(x)= 3x² + 5x + 3 and g(x)=-2x-6,determine each of the following. Make sure to fully simplify your answer.

Find functions f and g so that h(x) = (fog)(x). h(x)=1/(x^2-3) f(x) = 1/3, g(x) = x²-3 f(x) = 1/x², g(x) = - 1/3 f(x) = 1/x, g(x)=x²-3 f(x) = 1/x², g(x) = x - 3

3, 20, 63, 144, 275, ... General Rule = ? 23nd term = ? 32nd term = ?

Let x, y > 0. Use the AM-GM inequality to find the minimum value of S =1/x^2+1/y+ 2xy and determine the values of x and y at which this minimum value of S is attained.

An investment of $7000 is deposited into an account in which interest is compounded continuously. Complete the table by filling in the amounts to which the investment grows at the indicated interest rates. (Round your answers to the nearest cent.)

When x³ + cx + d is divided by x + 1, the remainder is 3, and when it is divided by x - 2, the remainder is -3. Determine the values of c and d.

Let a, b, c, d be fixed numbers, and suppose that a≠0 and a≠1. Which of the following types of common functions are one-to-one for any chosen values of a, b, c, and d? Select all that apply. The cubic function y = ax³ + bx² + cx + d The linear function y = ax + b The quadratic function ax²+bx+c The logarithmic function y = loga(x) (suppose a > 0) The exponential function y = a^x (suppose a > 0)

Today you have exactly $4817.81 in your savings account earning exactly 0.5% interest, compounded monthly. How many years will it take before that account reaches $15211.93? Use trial and error to find the number of years (t).

Determine the distance between the left right lines d₁: [x, y, z] [0, 2, 1] +t [3, 1,1] and d₂ : [ x, y, z] = [1, -3,0] +t [2,-1,1].

A ski resort has a lift from A to C, as shown in the figure below. Angle DAC measures 32". Mountain officials want to build a new ski lint from B to C. The base B will be 910 feet from A, and the new lift will be 2000 feet long. What will be the measure of angle B? Round your answer to the nearest tenth of a degree.

Let f(x) = 36ˣ. Find f(-1) Round your final answer to two decimal places.

a. Determine the remainder when 17^341 is divided by 5. b. Use the Chinese Remainder Theorem to find an x such that x ≡ 2 (mod 5 x ≡ 3 (mod 7) x ≡ 10 (mod 11)

Find functions f and g so that h(x) = (fog)(x). h(x) =3/x² + 9 f(x) = 1/x, g(x) = 3/x + 9 f(x) = x + 9, g(x) = 3/x² f(x) = x, g(x) = 3/x + 9 f(x) = 3/x², g(x) = 9

Given that p= the sun is shining and q- it is raining; write the statement below in English. q∧∽p

4. Find the first six terms of the following sequences starting with n = 1 and state whether the sequence is explicitly defined or defined recursively. (a) {1+ (-1)^n} (b) a₁=1 and an an-1 +n for n ≥2

Find the growth or decay rate in percent of the given exponential model. f(x) =49 (1.07)^x find the rate? 7% growth 7% decay 0.07 growth

Which is the most logical first step for solving for the variable in the inequality: 9z+8 < 11(17z+1) Reverse the inequality sign. Subtract 17z from both sides of the inequality. Use the distributive property to clear the parentheses by multiplying each of the terms in the parentheses by 11. Divide both sides of the inequality by 11.

Write the following in interval notation: 7>x or 19 ≤ x

Solve for x: -15≤- 6x-11 ≤ - 11 Write your answer in interval notation:

Solve the inequality. Graph it, write it in interval notation, and then inequality notation. 3x + 2 ≤5 and 5x + 2≥ - 23

For each of the following parts, state the quadrant (s), if any, for which the statements are true. 1. cost sint > 0 2. tant sect> 0 3. csc sint <0 4. sect cost > 0

The formula 1(x) =13.4 In x-11.6 gives the temperature increase in Fahrenheit in a vehicle when the outside air temperature is anywhere from 72°F. to 96°F., where "x" is the number of minutes during the first hour. If the temperature outside were 80°F. and the interior temperature were 60°F., what would the interior temperature be after 6 minutes? Round your answer to the nearest hundredths of a degree, and do not enter the units with your answer.

A swimming pool is filled with water by using two taps A and B. Alone, it takes tap A three hours less than B to fill the same pool. Together, taps A and B take 2 hours to fill the pool. How many hours does it take each tap to fill the swimming pool separately?

If θ =13π/6, then find exact values for the following: sec(θ) equals csc(θ) equals tan (θ) equals cot (θ) equals

The congruence 5 x^17 + x + 9 = 0 (mod 85) has exactly one integer solution such that 0 ≤ x₀ < 85. Enter this solution in the input box below. Hint: Note that 85 = 5.17 is the prime factorization of 85.

ΔABC is right-angled at A and has AB < AC. Point D is on BC so that AB = BD. Point L is the midpoint of AD. Let P be the point on the circumcircle of ΔADC so that ∠APB = 90°. (a) Prove that B, P, L, and A are concyclic. (b) Prove that ∠LPC = 90°.