Sequences & Series Questions and Answers

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julle decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete? Oy-7.75x+4; discrete Oy-7.75x+4; continuous y4x+7.75; discrete y-4x+7.75; continuous

Solve the formula for the specified variable. V=ALT for A

$5000 invested at an APR of 5% for 3 years If interest is compounded annually, what is the amount of money after 3 years?

Consider an account with an APR of 45% Find the APY with quarterly compounding monthly compounding, and daily compounding Comment on how changing the compounding period affects the annual yield Cass When interest is compounded quarterly, the APY (Do not round until the final answer. Then round to two decimal places as needed)

4. Write down the sequence of the first twenty Fibonacci numbers and discover a relation between gcd (Fm, Fn) and Fgcd (m,n). Verify it for any eight (m, n) pairs. Show your work in detail.

Justify your response thoroughly to communicate your understanding of the concepts. Define and write the following relationship using function notation. A snowmobile travels through a 20 km trail. Determine a function for the speed of the snowmobile with respect to time.

You currently have $3,100 in an account that has an interest rate of 3.5% per year compounded continuously. After how many years will the account be worth $5.8907

Suppose that f(100) = 5000 and f'(100) = 20. Estimate each of the following. (b) f(100.5) (c) f(99) (e) f(99.75) (a) f(101) (d) f(98) (a) f(101)~ (Simplify your answer. Type an exact answer.)

Find the inverse of 2 multiplied by the cubed root of x-1, plus two

8200 where t is the number of 3+5e 0.021 months that have passed since the lake was stocked with catfish. How many catfish were in the lake three years after the lake was stocked? [round to the nearest catfish]. (4pts) The number of catfish in a lake is given by the formula: P(t) =

Determine whether the correspondence is a function. Domain f ON X + Range U Z V Is this correspondence a function? O No Ⓒ Yes

The sum of the measures of the angles of a triangle is 180°. Determine the measures of angles A, B, and C if the measure of angle B is 6° more than twice the measure of angle C and if the measure of angle A is 18° more than the measure of angle C.

Consider the function f(x) = -2x³ + k, where k is a constant. Find the decreasing interval(s) of f(x). a) {x|x > 0, x ∈ R} b) {x|x ≠ 0, x ∈ R} c) {x|x < k, x ∈ R} d) {x|x < 0, x ∈ R}

Let U be a unitary operator on an inner product space V and let W be a finite-dimensional U-invariant subspace of V. Prove: (a) U(W) = W (b) W⟂ is U-invariant

What is the function of sine that has an amplitude of 2, a period of, is reflected in the x-axis, and has a maximum value of 6? a) f(x) = -2 sin(8x) + 4 b) f(x) = 2 sin(8x) + 1 c) f(x) = -2 sin(8x) +1 d) f(x) = -2 sin(2x) +6

A vendor sells silk-screened T-shirts at community festivals and craft fairs. The costs incurred in the production and sale of the shirts are $90 plus $3.50 for each shirt sold and the vendor sells them for $9 each. a) Write the revenue, cost, and profit functions the model this situation. b) How many T-shirts must the vendor sell in order to break even? c) Find and interpret the slope of the profit function.

Let f(x) = √2x + 1 and g(x) = √2x-1. Find h(x) = f(x) = g(x). a) h(x) = √2x + 1 b) h(x)=√4x² - 1 c) h(r) = √4x²+1 d) h(z)=2x+1

Nick borrowed $6500 to help pay for school at a simple interest rate of 2.2% per year. At the end of five years, determine the following. Hint: Interest - Principal x Rate x Time a. How much did Nick pay in simple interest? b. How much did Nick pay back in all?

Exercise: Given = Find the following: a) f(-x)b) - f(x) 5x² - 4x + 9.

Calculate the distance from point P(2, 4, 1) to the line: Vector r = (1, 2, -1) + t(5, 1, -1), tER

Rewrite log x= w as an exponential equation. (a) a" = x b) a* = w c) x² = w d) wa = x

Solve the equation P= c + b + a for c. =(Simplify your answer.)

4. Write the equation of the line passing through the point (-9,2) that is perpendicular to the line 3x - y = 16.

If x-intercepts of the f(x) are (-1, 0) and (3, 0). What are the x-intercepts of y = af(x), where a is a constant? a) not enough information. b) (-1, 0) and (3, 0) c) (-a, 0) and (3a, 0). d) (-1,0) and (,0)

A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When she plants 3 stalks, each plant yields 115 ounces of beans. When she plants 8 stalks, each plant yields 190 ounces of beans. Write the linear equation, Y(n), that correctly represents this situation. Provide your answer below: Y(n) = FEEDBACK MORE INSTRUCTION SUBMIT

Match the inequality, x<-9, with its equivalent interval notation. Choose the correct answer below. OA. (0,-9) O C. [9,00) OE. (-∞, -9)U(-9,00) O G. (-∞0,00) OI. [-9,00) OB. (-6,9] O D. (-∞0,9] OF. (-∞, - 9) OH. [-6,9) O J. (-∞, -9]

Find the quotient using long division. 12a³-6a²-2a+9 4a+2

How many kiloseconds are in 3,450 milliseconds? 3,450 ms = [?] ks

When p(x) x4 4x³ + mx² + nx + 1 is divided by (x-1), the remainder is 7. When it is divided by (x + 1), the remainder is 3. Determine the values of m and n. O a) m = - = 3 and n = = 6 b) m = -1 and n = 6 c) m = -1 and n = 3 d) m = 2 and n = 3

A bank loaned out $19,000, part of it at the rate of 9% per year and the rest at 19% per year. If the interest received in one year totaled $3000, how much was loaned at 9%? How much of the $19,000 did the bank loan out at 9% ?

Ex: Solve the system using substitution. (3x + 5y = 26 y = 2x rium

Factor 11x²-10x-1. O (11x + 1)(x-1) (11x-1)(x-1) (11x-1)(x + 1) (11x + 1) (1 1x-1)

If log₂ (x + 5) = 5, then log3 (3) is: a) 27 b) 2 c) -2 d) 3

Solve the absolute value inequality. |x + 2| ≤6 Rewrite the inequality without absolute value bars. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) O A. ≤X+25 B. x+2s OC. x+2s …... or x + 22

Divide and simplify. 18a7b-5 45a b -3 OC. The Power Rule OD. Raising a Product to a Power The Quotient Rule states that any numbers a and any integers m and n, then What must be done to the expression in order to apply the Quotient Rule? 18a b 45a³b 5 A. Rewrite the expression in terms of m and n. B. Rewrite the expression such that all exponents are positive. OC. Rewrite the expression as the quotient of two numerical values with the same base. D. Rewrite the expression as a product of fractions whose numerators and denominators have the same bases. In order to simplify, rewrite the expression as the product of fractions whose numerator and denominator have the same base. 3 18 45 . a b a b am 3 a m-n

How many liters are in 1 decaliter? 1 dal = [?] L A. 10 L or 10¹ L B. 1/1000 L or 10-³ L C. 100 L or 10² L D. 1000 L or 10³ L

Problem 21. Suppose TEL(V) and U is a subspace of V. Show that if UC null T, then U is invariant under T.

A certain triangle has a perimeter of 3070 mi. The shortest side measures 74 mi less than the middle side, and the longest side measures 372 mi more than the middle side. Find the lengths of the three sides. The shortest side is mi long. ...

Simplify. Assume no division by zero. See Example 9. (Objective 5) y³y4 yy²

One roofer can put a new roof on a house three times faster than another. Working together they can roof a house in 5 days. How many days would it take the faster roofer to put a new roof on a house working alone? Round the answer to the nearest tenth. (Assume the roofs of the houses are similar sizes.) Type your numeric answer and submit O

Describe the transformation of g(x) = 2 f(2x + 1) - 1. a) Vertical stretch by a factor of 2, a horizontal compression by a factor of , a horizontal translation 1 unit to the right, and a vertical translation 1 unit down. Ob) A vertical stretch by a factor of 2, a horizontal compression by a factor of , a horizontal translation units to the right, and a vertical translation 1 unit down. 2 2 c) Vertical stretch by a factor of 2, horizontal compression by a factor of horizontal translation units to the left, and a vertical translation 1 unit down. a d) Vertical stretch by a factor of 2, a horizontal stretch by a factor of 2, a horizontal translation 1 unit to the left, and a vertical translation 1 unit down.

A newspaper article claimed that a new medication doubled the probability of successful treatment compared to an older medication. The odds of the older medication being successful in treatment were 3:7. According to the authors of the article, the odds in favour of the new medication being successful are 1) 3:5 2) 2:3 3) 5:3 4) 3:2

You want to determine how many grams are in 43 mg. 43 mg 10-3 g 1 mg Now divide the numerator by the denominator to find your answer. A. 43 g B. 4.3 x 10-² mg C. 4.3 x 10-² g

Subtract (4x+2) from the sum of (7x + 2) and (5x+4). The result is (Simplify your answer. Do not factor.)

Given f= {(0, 1), (2, 3), (5, 10)} and g = {(2, 1), (3, 1), (1, 2), (5,3), (4,5)}. determine the the value of gog(2). a) gog(2) - 1 b) gog(2) - 2 c)gog(2)=3 d) gog(2)=0

Consider an angle in quadrant 2 with reference angle (7/24). Assume θ is obtained by rotating counter-clockwise 6 times around the circle starting at the positive z-axis. Determine the angle

Solve the compound inequality. -7≤x-3<1 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.) B. The solution set is the empty set.

Solve the equation by the method of your choice. 2x² - 5x = 3

Give the following number in Base 16. 35 10 = [?]16

The one-to-one functions g and h are defined as follows. g={(-8, 3), (1, -9), (5, -5), (8, 1)) h(x)=2x-3 Find the following. g^-1 (1) = h^-1 (x) = (h^-1 o h) (6) =