Sequences & Series Questions and Answers

Express sin(2-x) in terms of sinx and cosx.

Vladimir rolls a six-sided number cube 36 times. If getting a 3 is a success, what is the probability of a success?

Martha opened a savings account on January 1 with a deposit of $750. The following July 1, January 1, and July 1, she made three more deposits of $750 each. The account paid interest at 3.75% per annum, compounded quarterly. What amount was in her account at the end of the second year?

The president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip. Instead of asking the whole class, she surveys only the twelfth-grade members of the math club. She records their choices and plans to present the results to the school principal. What type of sampling did she use? systematic random sampling simple random sampling stratified sampling convenience sampling

Write the equation of an ellipse with foci at (0, 2) and (6, 2), and a vertex at (8, 2). b) Graph the ellipse.

Consider the following subsets of M_(2x2) W1={(a, b, c, a) in M_2x2(F) | a,b,c in F} W2={(0, a, -a, b) in M_2x2(F) | a,b in F} Show that W1 and W2 are subspaces of M_2x2(F) and find dim(W1), dim(W2)

Brett is performing a hypothesis test in which the population mean is 310 and the standard deviation is 20. His sample data has a mean of 295 and a sample size of 50. Which of the following correctly depicts the z-statistic for Brett's data? -5.30 -0.11 4.28 6.27

A periodic function f(t) is defined by f(t)-1-f², 0<t<1 f(t)=f(t+1) Sketch the graph of f(t) over the interval [-3,3]. Then, find the Fourier Series expansion of f(t).

A normal distribution of data has a mean of 90 and a standard deviation of 18. What is the approximate z-score for the value 64? -3.6 -1.4 1.4 3.6

David wants to complete a hypothesis test with the least amount of probability for error. If he sets the significance level to 1%, assuming his sample is truly random, what else could he adjust in the test in order to reduce error? He could change the population mean. He could increase the sample size. He could change the population standard deviation. He could decrease the sample size.

A simple random sample is drawn from a normally distributed population. The value of which of the following will not be known for certain but can be inferred? x s n

The components of v= 240i + 300j represent the respective number of gallons of regular and premium gas sold at a station. The components of w = 2.90i +3.07j represent the respective prices per gallon for each kind of gas. Find vw. For 3 points extra credit, describe what the answer means in practical terms.

Use the Binomial Theorem to find the coefficient of x in the expansion of (x + 1)¹0.

3. Find the x-intercept(s) of y x +17/x - 2.Write your answers as ordered pairs. x-intercept(s):

Express sin(2π-x) in terms of sinx and cosx.

Which of the following conditions must be met in order to make a statistical inference about a population based on a sample if the sample does not come from a normally distributed population? µ≥ 230 x≥ 30 n≥ 30 N≥30

The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the coordinates of P and find equations for the line in the plane through P perpendicular to L. (25 pts)

In 1626, an explorer convinced a group of indigenous peoples to sell him an island for $27. If the indigenous peoples had put the $27 into a bank account paying 8%, how much would the investment be worth in the year 2003 if the interest were compounded a. monthly? b. continuously?

The test scores of a geometry class are given below. 90, 75, 72, 88, 85 The teacher wants to find the variance for the class population. What is the value of the numerator of the calculation of the variance? -160 -6 16 258

Match the description of each distribution shape to the name of the distribution shape. Symmetric Skewed Right Skewed Left Bell-Shaped Uniform Bimodal a. When the right side of the distribution has more values farther from the bulk of the data. Has a 'tail' on the left. b. A distribution with two very common data values seen as distinct peaks. c. A distribution with a vertical line of symmetry in the center of the graphical representation. d. A distribution that takes the form of a bell with most of the data clustered near the center and fewer points farther from the center. e. When the side of the distribution has more values farther from the bulk of the data. Has a 'tail' on the right. f. A distribution which has the data values evenly distributed throughout the range of the data.

If a salesperson is paid a base salary of $100 a week plus 5% commission on his gross sales, then what is his weekly gross to earn $1,100 a week? A) $24,000 B) $200 C) None of the answers listed D) $20,000 E) $2,000

If you're given the magnitude of two vectors and the angle between them, how do you show ax + by?

The line L: x = 3 + 2t, y = 2t, z: = t intersects the plane x + 3y -z = -4 in a point P. Find the coordinates of P and find equations for the line in the plane through P perpendicular to L.

Consider the following LP problem: Min 16X+ 16Y; Subject to : 4 X + 4Y <= 34, and X + Y <= 102. Which one of the following is true?: O a. X=51, Y=51 is the only optimal solution. O b. Optimal Obj. function value is 0 O c. Slack for each constraint is zero. Od. Optimal Obj. function value is 136

If a data value in a normal distribution has a negative z-score, which of the following must be true? The data value must be negative. O The data value must be positive. O The data value must be less than the mean. O The data value must be greater than the mean.

Deb Cook is given the choice of two positions, one paying $3,200 per month and the other paying $2,300 per month plus a 5% commission on all sales made during the month. What amount must she sell in a month for the second position to be more profitable? The second position is more profitable if Deb sells more than $ per month. ...

01) 1574 Select one: 81 01) Functions:Question 7 What is the y-intercept of the function? 61 O (2,-2) O (0,4) O (0,2) (2,0)

Solve the system of linear equations by graphing. y = -2x 2x-y=8 Use the graphing tool to graph the system. Click to enlarge graph CICCOD Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution of the system is (Type an ordered pair.) OB. There are infinitely many solutions; {(x,y)ly=-2x) or ((x,y)|2x -y=8). Q Q

Q3. Define the Fibonacci sequence by f₁ = 1, f2 = 1, fn = fn-1 + fn-2 for n ≥ 3. Prove by induction that ged(fn, fa+1) = 1 for n 2 1.

7. A particle moves along a line according to the following information about its position s(t), velocity v(t), and acceleration a(t). Find the particle's position function s(t) for general t. (a) v(t) = 1.5t2 + 4t, s(4) = 50 (b) a(t) = 3 cost-2 sint, s(0) = 0, v(0) = 4

Write the number in standard notation. 6.2x10-3

Solve the system of equations by the addition method. [x-3y = - 12 - x + 2y = 9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution is (Simplify your answer. Type an ordered pair.) OB. There are infinitely many solutions; {(x,y)|x - 3y = - 12} or {(x,y)|-x+ 2y = 9}. OC. There is no solution; or Ø.

Gabe Amodeo, a nuclear physicist, needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 liters of 50% acid solution? Gabe needs 30 liters of the 30% solution. He also needs liters of the 60% solution. BELEID

Solve. That means find the missing value. Your work should indicate some of your thoughts steps. log7 2,401 = y

Write the number in standard notation. 4.5×10-3 4.5x10-3- =

Solve and state your answer in interval notation. x³ - 19x +30 ≥ 0

Assume the car can be purchased for 0% down for 60 months (in lieu of rebate). A car with a sticker price of $42,500 with factory and dealer rebates of $5,100 (a) Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.) $ X (b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.) X (c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.) x Your answer cannot be understood or graded. More Information % (d) State whether the 0% APR or the 2.5% add-on rate should be preferred. 0% APR 2.5% add-on rate

Suppose that $10,359 is invested at an interest rate of 5.3% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is P(t)= (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Find the exact values of the trigonometric function for a. 0 = 150° b. 0 = 7π/4

18. a. Sketch the graph of each of the following on the given coordinates plane. (4 points each) f(x) = x(x + 5)(x-7)

Q3. Define the Fibonacci sequence by fi= 1, f2 = 1, fn = fn-1 + fn-2 for n ≥ 3. Prove by induction that ged(fn: fn+1) = 1 for n > 1.

Find the maximum value of the equation below subject to the constraint x₁ + x₂ = 1 Q(x) = 7x² + 4x² - 6x₁x₂

The mean of a set of credit scores is = 690 and = 14. Which credit score is within a z-score of 3.3? O 634 O 640 O 720 O 750

Functions:Question 9 Which of the following relations is not a function? Select one: O (0, 1), (0, 2), (0, 3), (0,4)) O ((0.0), (2, 2), (4, 4), (6, 6)) O ((0, 1), (1, 1), (2, 1), (3, 1)) O ((0, 0), (3, 4), (5, 6), (8, 9))

Write the following number in standard notation. 5.722 x 10² 5.722 × 10²=

Solve for the antiderivative of each of the following: f'(x) = 12x² - 4x + 3 and f(1) = -4. f(x) = -300 dy=9e³t - 3 and y = 3 when t = 0. y = g(x) = 48x√4x²+28 and g(-3) = 2047. g(x) = Given f f(x) dx = 4 and f f(x) dx = 6, evaluate f f(x)dx. ff(x) dx

C5.Q50 | Perpetuities. A property will provide $10,000 a year forever. If its value is $125,000, what must be the discount rate? (LO4)

A factory costs $400,000. You forecast that it will produce cash inflows of $120,000 in year 1, $180,000 in year 2, and $300,000 in year 3. The discount rate is 12%. Is the factory a good investment? Explain. (L03)

Plot the intercepts to graph the equation . 8x-3y = -24 Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. Click to enlarge graph

Find an equation of the horizontal line through (-2, 5). The equation is (Type your answer in standard form.)