Sequences & Series Questions and Answers

In the equation: x³x²14x + 24 = 0 * = 2 is a solution. Which of the following represents the other real solution(s), if any?

The mean number of books read last year by a group of students is normally distributed with a mean of 10 and a standard deviation of 6. If Austin is 0.5 standard deviations below the mean and Kaleigh is 2 standard deviations above the mean, how many more books did Kaleigh read than Austin?

How many years will it take for $1,200 to double if your compound interest rate is 11% ? Round to nearest tenth. 6.5 years 6.4 years 5.9 years 5.6 years

Brad has $1,000 in a savings account which earns 5% interest compounded quarterly. He made no additional withdrawals or deposits. What was the amount in the account at the end of the second quarter?

Find the area of the shaded sector. A. 7.75 m² B. 64.25 m² C. 85.64 m² D. 92.99 m²

Find the slope of the line 2x + 5y = 6.

A new car is purchased for $28,000 and over time its value depreciates by one half every 4.5 years. Write a function showing the value of the car after t years, where the annual decay rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of decay per year, to the nearest hundredth of a percent.

Solve the following compound inequality. -7x-8-2x+7<-7x-3 Give your answer in interval notation. For example, if you found 3 < x < 5, you would enter (3,5).

In a lab experiment, 40 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 4 hours. Write a function showing the number of bacteria after t hours, where the hourly growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per hour, to the nearest hundredth of a percent.

Which of these intervals are possible confidence interval estimates of a population mean given a sample mean of 42.8 feet and some confidence level? (Assume that the population standard deviation is known and that the sample size is fixed.) a. 37.8 feet to 47.8 feet b. 39.3 feet to 46.3 feet c. 40.0 feet to 45.0 feet d. 40.0 feet to 45.6 feet 40.3 feet to 44.3 feet f. 41.0 feet to 44.6 feet e.

Find the vertical asymptotes (VA), horizontal asymptotes (HA), and slant asymptotes (SA) if any, for the function: f(x)

Recall that the z' value for a 90% confidence interval is 1.96. If you are testing a hypothesis and find this as the z-score associated to the observation given the (one-sided) null hypothesis, you would know without using technology that the P-value would be what.

Sarah sets off on her hike from the lodge at a bearing of S71°W. After 3.3 miles, she changes her bearing to $23°W and continues hiking for 6.6 miles. Find her distance and bearing from the lodge at this point. your answer to the nearest hundredth of a mile. Sarah's distance from the lodge = 7.58 x miles The bearing to the lodge from Sarah's current position with the angle rounded to the nearest degree is

Maria Elena is collecting college pennants. She has five fewer pennants from Washington campuses than from California campuses and twice as many pennants from California campuses as from Pennsylvania campuses. She has 40 pennants in her collection. Write and solve a system of equations to determine the number of pennants from each state.

Ms. Brown invested $20,000 in two accounts, one yielding 8% interest and the other yielding 10%. If she received a total of $1,860 in interest at the end of the year, how much did she invest in each account? The amount invested at 8% was The amount invested at 10% was S

Solve the following compound inequality. -3x6-x+2<-3x+6 Give your answer in interval notation. For example, if you found 3 < x < 5, you would enter (3,5].

The net of a rectangular prism is shown below. The surface area of each face is labeled. Which values represent the dimensions, in feet, of the rectangular prism? (Note: diagram is NOT to scale)

A wooden artifact from an ancient tomb contains 20 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)

At the beginning of an experiment, a scientist has 344 grams of radioactive goo. After 210 minutes, her sample has decayed to 10.75 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. How many grams of goo will remain after 80 minutes? You may enter the exact value or round to 2 decimal places.

Find the equation of a sine wave that is obtained by shifting the graph of y= cos(x) to the right 7 units and downward 5 units and is vertically stretched by a factor of 4 when compared to y= cos(x)

Solve the following compound inequality. -4x-10<-2x-8<-4x+10 Give your answer in interval notation. For example, if you found 3 < x < 5, you would enter (3,5).

You go to the doctor and he gives you 11 milligrams of radioactive dye. After 12 minutes, 4 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office.

If the constant 2 of the function y = x2 + 2 is changed to 5, how will the new graph differ from the graph of y = x² + 2? The new graph is obtained by shifting the old graph 3 units down. The new graph is obtained by shifting the old graph 5 units up. The new graph is obtained by shifting the old graph 3 units up.

In the hyperbola shown below, one focus is at F1(-2,12) and the other at F2(-2,-8). The points A(-2,8) and B(-2,-4) lie on the graph of the hyperbola.

The figure below is a net for a right rectangular prism. What is the surface area of the right rectangular prism, in square meters?

Which of the following methods needs vertex to be specified to solve the quadratic equation? Factoring method Graphical method Completing square method

Find the length of the second base of a trapezoid with one base measuring 15 feet, a height of 7.6 feet, and an area of 98.8 square feet. A. 9 ft B. 10 ft C. 11 ft D. 12 ft

At the beginning of an experiment, a scientist has 400 grams of radioactive goo. After 150 minutes, her sample has decayed to 25 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 14 minutes?

A wagon is on sale for 20% off. The sale price of the wagon is $114. What was the original price of the wagon assuming no sales tax is paid on the item? Report your answer to two decimal places. Do not include the dollar sign, $, in the answer box below.

A - the measure of the amplitude of the earthquake wave Ao the amplitude of the smallest detectable wave (or standard wave). An earthquake is measured with a wave amplitude 570 times as great as Ao. What is the magnitude of this earthquake using the Richter scale, to the nearest tenth? The earthquake registered on the Richter scale.

The denominator of a fraction is four more than twice the numerator. If both numerator and denominator are decreased by nine, the simplified result is original fraction. (Do NOT simplify.)

Determine whether the given graph is a function or not. Function Not a function Cannot be determined

Define the sentence symbols t = "I drink tea," c = "I drink coffee," and a = "I am thirsty." Write down a single logical statement that uses all three of these sentence symbols, and then write down your translation to the English version. Be sure that (a) your sentence is really one sentence! and (b) your translation matches the meaning of the symbolic version.

Sophia rolls a pair of six-sided fair dice with sides numbered 1 through 6. Fill in the following chart to find the sums of the dice rolled. What is the probability that the sum of the numbers she rolls is an odd number or a multiple of 3?

Use the function below to answer the following questions. y-log, (x-5) (a) Use transformations of the graph of y-log₂x to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.

Amy starts with 145 candies. Her mom then gives her 78 more candies: . a. Using the "standard addition algorithm," determine how many candies Amy has now. b. Using base-ten blocks, determine how many pieces of candy Amy has afterwards. Draw a picture of base ten blocks representing this problem to get your solution. c. Explain how your two solutions show the same process involving place value (hint: carrying ones and exchanging multiple small blocks for bigger ones is important here).

Which expression fits this description? • The expression is the sum of two terms. • The first term is the product of 2 and a. • The second term is the quotient of b and 4.

In a lab experiment, 10 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 29 hours. How many bacteria would there be after 21 hours, to the nearest whole number?

Find the solution to the following absolute value inequality. -2x + 5 ≥ 6 Give your answer in interval notation. For example, if you found a <-3 or x > 1, you would enter (-∞, -3) U (1, ∞).

To help support a flag pole, a 50-foot-long tether is tied to the pole at a point 40 feet above the ground. The tether is pulled tightly and tied to an anchor in the ground. How far away from the base of the pole is the anchor?

You pay a babysitter $30 each week for driving your children to school and $9 for each hour she watches them. Write a function in x that represents the total amount you pay your babysitter in a week. Be sure to indicate any domain restrictions.

Solve the compound inequality. 0<2-7X <7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is Ø.

Solve the compound inequality. 4(x-5)<16 or x+3>8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is Ø.

Solve the absolute value equation. |5x–5| = |15–5x| Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. B. The solution set is Ø.

What effect does the graph y= kf(x) have on its parent function when k> 0? The graph is stretched vertically. The graph is stretched horizontally. The graph is compressed vertically.

ve the absolute value equation. |x-4|+4=9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is Ø.

Solve the equation using the factoring method: 3x² - 8x+5=0 x= -1,-5/3 x = 1,53 x=-1,5/3

In circle B, the length of arc ADC is 14 cm, and the the measure of the marked angle is 210 degrees. Determine the area circle B. Give an exact answer, typing pi to represent the letter n. The area of circle B is

Find each probability. Express the result as a reduced fraction and then a decimal rounded to the nearest thousandth.

Refer to functions m and n. Find the function (nom) (x) and write the domain in interval notation. Write any number in the intervals as an integer or a simplified fraction. m (x)=√x+3 n(x)=x-9