Sequences & Series Questions and Answers

For each of the following proportions, write a corresponding word problem. Make sure to include an unknown variable and to define the units. (Hint: Since you are asked to include a variable, you will leave one of the components of each proportion out so that I can solve for it when I read your word problems).

If we accept that scalar multiplication is effectively multiplying each component of the vector by the scalar value, it becomes much more straightforward to multiply by more than just integer-valued scalars.

If the following box plot data represents the heights of 160 students, how many of the students are between 43.5 and 46.5 inches tall? Max 50 Q3 46.5 Q2 43.5 Q1 41.5 Min 37 60 students 80 students 120 students At least 75 students 40 students

Solve the equation: 1/3|9-2×|-2=-1 List solutions below. If there's two solutions, list each separately below from least to greatest. If there's one solution, type the solution in the first box and an X in the second box. If there's no solution, then type an X in both boxes. First solution: x= Second solution: x-

Translate into a variable expression. (Use x for your variable.) the quotient of four more than twice a number and the number

Solve the triangle. B=37°, C=23°, b=28 .... A = (Do not round until the final answer. Then round to the nearest degree as needed.) a (Do not round until the final answer. Then round to the nearest tenth as needed.) (Do not round until the final answer. Then round to the nearest tenth as needed.)

Consider the following. a number decreased by the difference between eight and the number Translate into a variable expression. (Use x for your variable. Do not simplify.) x(8-x) Simplify, 2x 8 Suggested tutorials:

Solve the inequality. Graph the solution set, and write it using interval notation. 3k+2<-22 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is Ø. Choose the correct graph of the solution below.

If the average person has an IQ of 100 and if IQ is normally distributed with a standard deviation of 15, what percentage of people have an IQ above 115? 6.68% None of those listed 93.32% 84.13 % 15.87%

Which of the following is a fixed expense? Your car insurance A flat tire A field trip All of the choices

Suppose that the 'true' regression model is Yi = β₀ + β₁ln(X₁i) + ui but, instead, you estimate Yi = β₀ + β₁X₁i+ui What are the consequences of this type of specification error for the OLS estimator?

Solve for g. t=5g+5w The solution is g = ______ (Use integers or fractions for any numbers in the expression. Simplify your answer.)

Samantha invests a total of $17,000 in two accounts. The first account earned an annual interest rate of 7% and the second account earned an annual interest of 2%. At the end of one year, the total amount of money gained was $715.00. How much was invested into each account? $_______ was invested in the account that earned 7% and $_______ was invested in the account that earned 2%.

Determine if -5x² + y = - 4 is an ellipse. Ellipse Not an Ellipse If it is an ellipse, write the equation of the ellipse in standard form (x-h)²/a² + (y-k)²/b² = 1 not an ellipse, leave the rest blank. h= k= a= b=

Divide polynomials using long division 32. x⁴ + 3x³ + 2x² - x-5/x² - 2 33. x⁴ – 5x² - 4x + 7/x²- 1 34. x⁴– 2x³ – 16/x²+ 5

Government agencies keep data about the income distribution of the population. The Gonzalez family and Allen family live in a county with 5000 families. The Gonzalez family's income is at the 38th percentile. The Allen family's income is at the 73rd percentile. (a) Which of the following must be true about the Gonzalez family's income? About 38% of the families in their county earn less than the Gonzalez family. The Gonzalez family earns about 38% of the highest income in their county. The Gonzalez family's income is in the top half of incomes in their county. The Gonzalez family earns $38,000. (b) Which of the following must be true about the Gonzalez family's and the Allen family's incomes? Both the Gonzalez family and the Allen family earn more than the median income. Both the Gonzalez family and the Allen family earn less than the median income. The Allen family earns more than the Gonzalez family. The Gonzalez family earns more than the Allen family.

Evaluate the function. f(x) = 3x² + 5x – 14 Find f(-3)

Find the 55th term of the arithmetic sequence 8, 24, 40, ...

What is the standard deviation of the following data set rounded to the nearest tenth? 78, 90, 456, 676, 111, 381, 21 229.2 259 229.1 258

An oblique triangular prism has a base area of 18 square units and a volume of 252 cubic units. What is the height of the pyramid?

Dylan invested $7,200 in an account paying an interest rate of 2.3% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 12 years?

Given that y varies directly with e, find the equation of direct variation when x=12 and y=20. (A) y= 5x/3 (B) y= 3x/5 (C) y= 15x (D) y= 8x

Each of these relationships reflects a correlation. Which relationship most likely reflects correlation but not causation? A) When seamstresses make more dresses, they sew more pants. B) When seamstresses mend more garments, they use more thread. C) When seamstresses alter more wedding gowns, they meet more brides.

A sports-and-exercise shop sampled its customer base one morning and asked 8 customers their age. Their responses are shown below. 24, 24, 25, 26, 28, 31, 36, 45 Which interval estimates the mean age of customers with a margin of error of 1.8? (A) 25.2 < µ < 28.8 (B) 26.1< µ < 27.9 (C) 28.1 < µ <31.7 (D) 29.0< µ < 30.8µ

Use synthetic division to find the result when x³ – 10x² + 21x – 1 is divided by x – 2. If there is a remainder, express the result in the form q(x) + [r(x) / b(x)].

Over the course of July, the high temperatures of 6 random days were collected. The data is shown below. 93°F 82°F X°F 79°F 92°F 84°F If the average temperature of the data set is 86°F, determine the missing temperature. Show all work in the space below.

Evaluate the summation below. 6 4 ∑ (-m - 3) m=0

Financial responsibility means_______ generating further income protecting the families protecting the dependents All of the choices

The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval - 6 < x < -3?

Find the radius of a sphere with a volume of 2304π

Evaluate the summation below. 3 ∑ (5p+ 2p^2) p=0

If your new balance is $425 and you made the minimum payment of $45, what was your original balance?

Use the binomial theorem to find: (a) the coefficient of r4 in the expansion of (x + 3)²⁰ (b) the sum 1 + 3n +9(n 2) +......+3ᵏ(n k)+...+ 3ⁿ-²(n n-2)+3ⁿ-¹n+ 3ⁿ

How can a relation be represented? Set of ordered pairs Mapping Graph Table Equation All of the above

Use synthetic division to find the result when x4 + 8x3 + 24x2 + 25x - 14 is divided by x + 3. If there is a remainder, express the result in the form q(x) + r(x)/ b(x)

Study the following spending chart: On which day was the most money spent? 1. 1ˢᵗ 2. 7ᵗʰ 3. 3ʳᵈ

A spotlight is mounted on the eaves of a house 45 feet above the ground. A flower bed runs between the house and the sidewalk, so the closest the ladder can be placed to the house is 28 feet. How long a ladder is needed so that an electrician can reach the place where the light is mounted? The length of the ladder needs to be _____ft

In your notebook, create a t-chart and evaluate the function f(x) = ¾x +2 for the values of x= 0, 1, 2, 3, 4, 5, 6, 7, and 8. Write your answer as decimals. Then, answer the following questions using complete sentences. Which values of x generated output values that would be easy to graph in the coordinate plane (integers)? Do you see a pattern in the x-values that created integer outputs?

Choose the correct answer. . . .is the material resource for a person to achieve a goal. (a) Talents (b) Time (c) Skill

For the function g(x) =(1/3)x+2, what values of x would generate integer outputs? Select all that apply. Since m=1/3 , multiples of the denominator (3) will generate integers for the output of the function. (A) 0 (B) 3 (C) 6

Name the point that coordinates with this notation: f(-1) = 1

If the unpaid balance is $3,400 and the interest rate is 19%, your final monthly payment is $3,453.62. (A) True (B) False

Solve the equation using logarithm: 88x-5=92x-9

Use the distributive property to remove the parentheses. -9 ( -5v + 4x - 3)

What does this image Indicate? A) Financial responsibilities B) Wise investments C) Generation of more income

If f(x) = x³+3x²–46x-48 and x - 6 is a factor of f(x), then find all of the zeros of f(x). a. x=2, x= 4 b. x=-2, x=4 c. X=-8, x=1 d. x=-8, x=-1

Which number line shows the solution set for |g+2| > 3?

When a data set is normally distributed, about how much of the data fall within one standard deviation of the mean? (a)95% (b)34% (c)68% (d)13.5%

The formula v=√2gh gives the velocity v, in feet per second, of an object when it falls h feet accelerated by gravity g, in feet per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 128 feet per second.

Find a sinusoidal function with the following four attributes: (1) amplitude is 10, (2) period is 4, (3) midline is y = 45, and (4) f(5) = 55. f(x)=