Sequences & Series Questions and Answers

Which of the following statements is true for an angle of 10π/9 radians, rotated from standard position? a) Only the tangent ratio would be positive b) Only the cosine ratio would be positive c) Only the sine ratio would be positive d) Both tangent and cotangent would be positive.

The weight of an object on a particular scale is 175.2 lbs. The measured weight may vary from the actual weight by at most 0.1 lbs. What is the range of actual weights of the object? A. 175.12 ≥ x ≥175.3 B. 175.1 ≤ x ≤ 175.3 C. 175.12≥ x ≤ 175.3 D. x≤175.1 or x ≥ 175.3

Which of the following are solutions to |x+3 |= 4x-7? Check all that apply. A. X=-4/5 B. X=-10/3 C. X=10/3 D.X=4/5

Solve the equation. 7ˣ = 75 O a x ≈2.219 O b x ≈0.093 O c x ≈1.875 O d x ≈ 10.714

Describe the changes to the graph of f(x) = log₂ x when x is replaced by 8x a) Translated up 3 units b) Vertically compressed by factor of 8 c) Vertically stretched by factor of 3 d) Horizontally stretched by a factor of 8

Consider the formula p=(1+i)ᶜ-1 . If the interest conversion period is shorter than the payment period, then c is : Select one: a. a number >1 b. a negative integer c. a fraction < 1 d. a negative fraction

Mrs. Appleton bought 8 pizzas and 6 bottles of soda for a party. Each bottle of soda was $2.25 and she spent a total of $124.30. Write and solve an equation to determine the cost of one pizza.

In △NOP, the measure of ∠P=90°, PO =13, NP=84, and ON=85. What ratio represents the secant of ∠N?

For the curve f(x) = -2(3)ˣ +3, the horizontal asymptote occurs at: a) y = 1 b) y = 3 c) y = 1/2 d) y = -1

You anticipate an investment of $45 000 to grow by 7% each year. How long will the investment take to double? a) 10 years 3 months b) 10 years c) 3 years 10 months d) 11 years

A high-end bracelet maker has a fixed cost of $1,192.50 and an average unit cost of $23.50 per bracelet made. If she charges $89.75 per bracelet, how many bracelets must she sell in order to break even? Setup an equation and solve. Label your answer.

Justin had $44 before spending q dollars on jeans. How much money remains? The translation is $ (Do not include the $ symbol in your answer.)

Write and solve an equation that can be used to determine the value of x if the perimeter of the rectangle is 50 inches.

Austin invested $11,000 in an account paying an interest rate of 5.7% compounded money, to the quarterly. Assuming no deposits or withdrawals are made, how much nearest dollar, would be in the account after 6 years?

A couple purchased a home for $225,000. At the end of each year the home increases in value by 3%. What is the value of the home after the tenth year?

For the function y = -5x -4, answers parts a. through c. a. Find the slope and y-intercept (if possible) of the graph of the function. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined.

On (-∞, ∞), there are an infinite number of solutions. Write the general form of the solution. Your answer X =

If quadrilateral ABCD is a Saccheri quadrilateral, then which of the following are true? Choose all that apply. Select one or more: a. The lower base and upper base have the same length. b. The upper base angles are congruent. c. The diagonals have the same length. d. The upper base is parallel to the lower base. e. The upper base is equidistant from the lower base.

Write following products with a single base. Do not simplify further. x^5.x^6=____

Solve. √8x+9 = x-3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are___. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

Find the domain of the following function. Do not use a graphing calculator. f(x) =1/x^2-2x-8 The domain is___.

Determine whether the vectors are parallel, perpendicular, or neither. v= (3, 2), w = (6,4) parallel perpendicular neither

A sine function has an amplitude of 3 and a vertical shift of 2 units down. The equation of the function is: a) f(x) = -3 sin x - 2 b) f(x) = 3 sin x - 2 c) f(x) = -3 sin x + 2 d) f(x) = 3 sin x + 2

Evaluate the sum ₖ=₁Σ∞ 4(1/5)ᵏ-¹ . You should give an exact answer (as a fraction), not a decimal approximation.

Rewrite the function in the form y = a(1+r)ᵗ or y = a(1 - r) ᵗ. Then state the growth or decay rate. y = a(8) ᵗ/¹¹ A) y = a(1+1.208) ᵗ; 120.8% growth B) y = a(1-0.208)ᵗ ; 20.8% decay C) y = a (1 + 0.208)ᵗ ; 20.8% growth D) y = a(1-1.208) ᵗ ; 120.8% decay

There is a 6% tax on a $750 refrigerator. How much is paid altogether for the refrigerator?

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. f(x) = (√x-1) - 4

The quotient of two more than the square of a number and the number.

7. The amount of snow on the grounddecreased by 12% each hour. Complete the table to show the amount of snow left on the ground after 5 hours. Round to the nearest hundredth. Time Inches of Snow 5 am 16 6 am 7am 8 am 9 am

Gigi is hanging a picture that is 12 inches wide, in the middle of a wall that is 29 inches wide. How far will the side of the picture be from the edge of the wall?

Vaneesha left a 22% tip on a $9.75 lunch bill. How much did he pay for lunch?

If an angle in a right triangle is π/4 and the length of the opposite side to this angle is 18 cm, how long would the hypotenuse of the triangle be? a) 12.73 cm b) 31.18 cm c) 18 cm d) 25.46 cm

$2,800 was deposited into an account for 16 years with a 1.25% interest rate. What is the final balance?

The weight W that a horizontal beam can support varies inversely as the length L of the beam. Suppose that an 8-m beam can support 1100 kg. How many kilograms can a 17-m beam support? A 17-m beam can support _____ kg. (Round to three decimal places as needed.)

Consider a point on a unit circle (x, y). Which of the following is an equivalent way of stating that point? a) (cos(θ), sin(θ)) b) (tan(θ), cot (θ)) c) (sin(θ), cos(θ)) d) ((1 - sin(θ)), (1 - cos(θ)))

What type of reflection symmetry does the graph of f(x)=sin x display? a) reflection in the line y = x b) reflection in the x-axis d reflection through the origin d) reflection in the y-axis

y=ax²+bx+c (blue) and y = px + q (green) are shown. Solve the system: y = ax²+bx+c y = px + q The solution(s) are: _____Enter your answers as ordered pairs (x, y). If no solution exists, enter DNE.

Determine the value of the angle whose terminal arm passes through the point (-1, √3). a) 5π/6 b) π/6 c) π/3 d) 2π/3

Find the unknown side lengths in this pair of similar triangles. Complete the table with the appropriate function values of the given quadrantal angles. If the value is undefined, say so. θ sinθ cosθ tanθ cotθ secθ cscθ 90° -360° 630° find the remaining trignometric function values of θ if sinθ=3/7

Which describes the following sequence? 3,9, 27, 81, 243, ... Arithmetic Sequence - sequence created by adding a fixed amount to each term to get to the next term Geometric Sequence - sequence created by multiplying the previous term by a fixed amount A arithmetic sequence B geometric sequence

Let A= 1 1/2 1/3 1/4 1/2 1/3 1/4 1/5 1/3 1/4 1/5 1/6 1/4 1/5 1/6 1/7 Show that A is invertible and find A-¹. Express A as the product of elementary matrices.

Kristin wants to buy a pair of jeans that cost $25. She gets a 20% discount since she works at the store. She must pay 6% sales tax. How much will she pay for the jeans?

What is the sample size for a box? Select one: a. 4 b. (top, bottom, side, side, side, side} c. 6 d. (side, side, side, side, top, bottom}

A company finds it can produce 30 heaters for $7800, while producing 35 heaters costs $9000. Express the cost, y, as Express the cost, y, as a linear function of the number of heaters, x. y = (Type an expression using x as the variable. Simplify your answer. Do not factor.) linear function of the number of heaters, x.

How long would it take to earn $450 in interest on a $12,000 investment with a 4% interest rate.

Moses assumed he could run a mile in 7.3 minutes. He completed the mile in 6.8 minutes. Calculate the percent error.

Show whether or not the following differential equationsn are separable: Show all working out dS/dt = t (In(S²t )) + 8t²

The following questions are about solving the following logarithmic equation. ln(4x + 2) = ln(7x)

An algae infection in a swimming pool is growing exponentially, and can be modelled by the function N(t) = 340.8 0.79t where t represents the time in days since the infection began, and N represents the total number of algae in the pool. How many algae will be in the pool in 3 days? Round to the nearest whole algae. According to the model, how many algae were in the pool to start the initial infection? Write the specific equation that can be solved to determine how long it will take the algae bloom to reach 900,000 algae.

(1 point) Find a basis of the subspace of R4 defined by the equation 5x₁ − 9x2 + 4x3 + 7x4 = 0.