Sequences & Series Questions and Answers

x² + y² - 4x + 4y + 7 = 0 is the equation of a circle with center (h, k) and radius r for: a)h = b)k= c)r= Graph the circle.

Ashley, who is currently a high school freshman, is saving money for a big school trip during her senior year. In the first month, she saved $20. She plans to save 2% more each month than the previous month. How much money will she have saved after three years? A) $540.83 B) $4,692.15 C) $35,720.00 D) $1,039.89

Find the quotient and remainder using long division for:(2x³-14x²+7x-28)/(2x²+5) The quotient is The remainder is

Calculate the sum: Σ 1000 (1.01). (A)1,000,000,000.001 (B)1,000,000.01 (C)100,000,000,000.0001 (D)Does not exist

Find the infinite sum of the geometric sequence with a₁ = 4,r= 3/7 if it exists.

Where i is the imaginary unit, the expression (x + 3i)² - (2x -3i)² is equivalent to (1) -3x² (2) -3x² - 18 (3) -3x² + 18xi (4) -3x² - 6xi-18

A bag contains 12 movie tickets and 8 concert tickets. You randomly choose 1 ticket and do not replace it. Then you randomly choose another ticket. Find the probability that both events A and B will occur. Round your answer to the nearest tenth. Event A: The first ticket is a concert ticket. Event B: The second ticket is a concert ticket.

The table contains data on the number of people visiting a historical landmark over a period of one week. Day 1 2 3 4 5 6 7 Visitors 45 86 124 138 145 158 162 45 86 124 138 145 158 162 Which type of function best models the relationship between the day and the number of visitors? A a quadratic function with a positive value of a B. a square root function C. a quadratic function with a negative value of a D. a linear function with a positive slope

Find the partial fraction decomposition of 5/x²+x-6

For the sequence aₙ = [(-1)ⁿ8]/n², its first term is ______ ; its second term is ____ ; its third term is ____ ; its fourth term is ____ ; its 100th term is ____ ;

Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two blends, robust and mild. A pound of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans. A pound of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans. Coffee is shipped in 105-pound burlap bags. The company has 52 bags of Colombian beans and 35 bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available beans?

Find a scalar equation of the hyperplane with vector equation: ~x = c1 (1, -2, 2, 1) + c2 (-1, 3, -2, 1) + c3 (2, -3, 5, 4), c1, c2, c3 ∈ R

Simplify. (Assume all variables represent nonzero numbers.) x¹¹y⁷ (3x-4y)²² /(x⁴y²(3x-4y) ¹⁷)

Show that the correlation coefficient satisfies the expression |⍴| = |µ11l / (√(µ02µ20)) ≤1

A jogger begins her workout by jogging to the park, a distance of 18 miles. She then jogs home at the same speed, but along a different route. This return trip is 24 miles, and her time is one hour longer. Find her jogging speed. Complete the accompanying chart and use it to find her jogging speed. Let r be the jogging speed.

Aubrey's dinner cost $85. She tips the waitstaff 30% for excellent service. How much does Aubrey tip the waitstaff?

Solve the equation for x. Give an exact solution and a four-decimal-place approximation. log 3x = 1.9 The exact answer is x= A four-decimal place approximation is x= (Round to four decimal places as needed.)

From a boat, the angle of elevation to the top of a lighthouse is 5". The tower is 50 ft. high. Find the distance from the boat to the lighthouse. Round your answer to the nearest tenth.* Do not include a comma in the answer. Distance =__ft. 10. From the top of an offshore oil rig that is 199 ft. above sea level, the angle of depression of a passing ship is 15°. Find the distance between the ship and the top of the oil rig. Round your answer to the nearest tenth. Distance =__ft.

If the fourth term of a geometric progression is -81/2 and the fifth term is 243 / 2 find a₁ and r. r= __ a₁ =__

Find the sum of the given infinite geometric series described as 3 + 2+ 4/3 + 8/9....

Find the first five terms of the geometric sequence a₁ = 4, r = √2. (a) {√2, 4√2, 16√2, 64√2, 256√2} (b) [4,4√2, 8, 8√2, 16) (c) {4,4+ √2, 4+2√2, 4+ 3√2, 4+4√2} (d) {4, 4√2, 16, 16√2, 64}

The Xs show the positions of two basketball teammates relative to the circular "key" on a basketball court. The player outside the key passes the ball to the player on the key. What is the length of the pass?

Find the sixteenth term of the arithmetic sequence whose first term is 4 and whose common difference is 1/5 a₁₆=?

What value of x makes the equation log10 x = -1 true over the set of real numbers? (A) X =5 (B)X =1/10 (C)X =10 (D)X=1/5

Given tan A =7/6 and that angle A is in Quadrant I, find the exact value of sin A in simplest radical form using a rational denominator.

For compound interest accounts, the amount A accumulated or due depends on the principle P, interest rate r, number of compounding per year n, and the time t in years according to the formula A = P(1 + 2) ^n t. Find r given A = $90,000, P = $60,000, and t = 15 years with interest compounded monthly.

A loan of $19,000 is made at 3.75% interest, compounded annually. If no payments are made towards this loan, in how many years will the amount due reach $33,000 or more, to the nearest year? Answer Record your answer in the boxes below. Be sure to use correct place value.

Multiply. (20-4 i)(5+ i) (Simplify your answer. Type your answer in the form a + bi.) (20-4 i)(5+ i) =

Using a random sample with 100 observations, the regression of Y on X and W yields an R-squared of 3%. Then the homoscedasticity-only F-statistic testing the joint significance of X and W's coefficients is given by ______with a p-value ________________than 5% (use "greater" or "smaller"). This suggests that the coefficients of X and W are jointly_____________ at 5% level. (use "significant" or "insignificant"). Treat the sample size as large when answering the questions. Critical values for chi-squared(q)/q: when q = 1; 3.84 (5 % level), 6.63 (1% level): when q = 2: 3.00 ( 5 % level), 4.61 ( 1% level): when q = 3; 2.60 (5% level), 3.78 (1% level).

Some values for the function f(x) = log x are given in Table 1. Table 1 Table 2 x f(x) x g(x) 10 1 1 10 100 2 2 100 1,000 3 3 1,000 10,000 4 4 10,000 Which function can generate of the values in Table 2? Answer (F) g(x) = x^10 (G) g(x) = 10^x (H) g(x) = 10x (J) g(x) = 10/x

What value of r makes the equation below true? 19/(4r-1)=5 F. 1 G. 1.(1/5) H. 5 J. 1.(4/5)

The number of cases of a new infectious disease is doubling every year such that the number of cases is modeled by a sequence beginning whose general term is an=75(2)^n-1.where n is the number of the year beginning. Find how many cases there will be at the beginning of the fourth year. Find how many cases there were at the beginning of the first year. At the beginning of the fourth year, the number of cases will be At the beginning of the first year, the number of cases was.

Evaluate cos [tan -¹(1) - cos-¹(-√3/2)]. (1) If cos x = -1/2 with in Qll then find sin(x/2). (2) Solve for 0 ≤ θ < 2π : 4sinx - 2cscx = 0 (3)Solve for 0° < θ <360° : 2sinx + cotx - cscx =0

How many years will it take $3,000 to grow to $4,700 if it is invested at 4.25% compounded continuously?

Which square root equation shows a vertical compression, a right horizontal translation, and a downward vertical translation? y=1/8√x-1-3 y=-4√x+1−5 y= 2√x+1+2 y=√x−4+5

Given the logarithmic equation log4 6 = x, what would be the equation rewritten in exponential form? F) 6^x = 4 G) x^4 = 6 H 4^x = 6 J) 6^4 = x

Assume all variables represent nonzero numbers.) {a.a³.a²}\{(a²)³}

What is the inverse function for the rational function shown below? ƒ(x)=x/5z-8 5x-8 (a)ƒ-¹ (x)=5x/8x-1 (b)ƒ-¹ (x)=8x/5x+1 (c)ƒ-¹ (x)=8x/5x-1 (d)ƒ-¹ (x)=x/8x-1

What is the solution to the logarithmic equation shown below? log32 x = 1/3 Record your answer in the boxes below. Be sure to use correct place value.

Solving Differential Equations: Solve the following differential equation y" + 2y' + y = 0 Subject to the initial conditions y'(0) = 3 & y(0) = 2

Suppose is an angle such that cos(θ)=-1/3 If 0 < θ < π, then cos(θ/2)=____ and sin(θ/2)=_____ If π < θ < 2π, then cos(θ/2)=______ and sin(θ/2)=____ If 2π < θ < 3π, then cos(θ/2)=_____ and sin(θ/2)=______

Given the arithmetic sequence -4, 16, 36, 56, . . ..Find the a₃₅

Solve. √(2x²-15x + 25) = √(x+5)(x – 5) If there are multiple answers, list them separated by a comma. For example 1, 2. If there is no solution, indicate this with the empty set Ø. Provide your answer below:

Rewrite 2x²y in exponential form. A) 2³ * x² * y B) 2^(1/2) * x^(2/4) * y^(1/2) C) 2^(1/3) * x(1/3) * y(2/3) D) 2^(1/3) * x^(2/3) * y^(1/3)

A mining company is mining silver. The relationship between the mass of the material mined in metric tons and the number of carts required to transport the material is given by the function V(n) = 0.5n. Additionally, the relationship between the amount of silver and the material mined is given by the function G(V)= 0.00001V. Which function can be used to determine the mass of silver in metric tons as a function of the number of carts required to transport the materials out of the mine? A) G(V(n)) B) V(G(n)) C) n(G(V)) D) n(V(G))

Use a sample space to determine whether the events are independent. There are three green apples and one red apple in a bowl. You randomly select one apple to eat now and another apple to eat with lunch. Determine whether randomly selecting a green apple first and randomly selecting a green apple second are independent events. The events are

In the diagram below is P and Q the midpoints of two circles with equations (x-7)² + (y + 2)² = 49 and x² + y² + 10x - 6y = 30, respectively. Determine the radius of circle centre Q. Determine the length of PQ. Show that the equation of PQ is 5x+12y = 11 Determine the coordinates of A. Determine the equation of the chord CD.

Events A and B are independent. Let P(B) = 0.4 and P(A and B)-0.13. Find P(A). Write your answer as a decimal rounded to the nearest thousandth. P(A) =

Choose all of the true statements regarding the graph. Select all that apply. The graph passes the vertical line test. The graph is a function that has an inverse function. The inverse of the graph is not a function. The graph is a function. The graph passes the horizontal line test. The graph is a one-to-one function.

Consider to fit the data set {(xi, yi), i = 1,...,n} by the regression model yi = 3x² + €i, Find the least squares estimator of β.