Math Questions

3) A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults? How many were children?

A woman has nine skirts and six blouses. Assuming that they all match, how many different skirt-and-blouse combinations can she wear? different skirt-and-blouse combinations. The woman can wear (Type a whole number.)

Let R be the region bounded above by the graph of y = 1-² and below by the graph of y= 2²-1, for-1 ≤ ≤ 1, as shaded in the figure above. What is the volume of the solid generated when region R is revolved about the horizontal line y = 3? A 64π/15 B 8π/3 C 12π D 16π

Divide and simplify: x + 4/3x + 12/ x + 5/8x + 40 Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

If you have 240 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area = (include units)

(d) A wind turbine has a capacity of 3 MW. Assuming the turbine operates at 50 percent of its capacity all day and every day for a week, calculate how many kWh of electricity the wind turbine will produce by the end of the week. Show your work (e) if a typical house uses 10,900 kWh per year, calculate how many bouses could have their full energy needs provided for one year by the turbine above if it continued to operate as described for one year. Show your work

You have 268 feet of fencing to enclose a rectangular region. What is the maximum area of the region? A. 17,956 square feet B. 4,485 square feet C. 4,489 square feet D. 71,824 square feet

In the lab, Dale has two solutions that contain alcohol and is mixing them with each other. He uses twice as much Solution A as Solution B. Solution A is 17% alcohol and Solution B is 13% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 376 milliliters of pure alcohol? Number of milliliters of Solution B:[] X S ?

T If sin 0= 77,0 <0</2₁ 7,0<8<, (a) sin (20) find the exact value of each of the following. (b) cos (20) 7|2 0 (c) sin (c) sin 2 (a) sin (20) = 12√13 49 (Type an exact answer, using radicals as needed.) -23 (b) cos (20) = 49 (Type an exact answer, using radicals as needed.) 0 2 (Type an exact answer, using radicals as needed.) - (d) cos 2

Analyze the polynomial function f(x) = x²(x + 4) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = x3 for large values of |x|. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are 0,-4. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is 0. (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of f is/are 0,-4. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The lesser zero of the function is of multiplicity, so the graph of f at x = the x-axis at x = The greater zero of the function is of multiplicity, so the graph of f the x-axis

Question 1 (13 points total): Consider the linear homogeneous differential equation y"-x²y'-3xy=0: a) (5 pts) For a series solution y=a, +qx+a₂x²+...+₂x+, find a recurrence relation for the coefficients a A₁, A₂, A

A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

Suppose a survey of 500 people age 18 to 34 indicated that 32.2% of them live with one or both of their parents. Construct and interpret a 99% confidence interval to estimate the true proportion of all people age 18 to 34 who live with one or both parents.

Coast Guard Station Able is located L = 120 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E. Use this information to answer the questions below. (a) How far is each station from the ship?

A contractor finds that Crew A takes 9 1/2 hours to construct a retaining wall and Crew B can do the same job in 7 1/2 hours. If Crew A and Crew B work together, how long will it take them to construct the retaining 2 wall? a) Let h = the time to complete the job. Write the equation you would use to solve this problem. b) Now solve your equation. Give your answer first as a reduced fraction, and then a decimal rounded to 3 places. Working together, the two crews will construct the wall in which as a decimal is hours. hours (fraction),

A) The luxury tax threshold in a professional sports league is the amount in total payroll that teams must stay under to prevent being levied a competitive balance tax by the league's commissioner. One model that could be used to represent the amount of the league's luxury threshold A, in millions of dollars, t years since 2003 is A (t) = 120(1.033)'. Suppose a second model assumed that the league's luxury threshold was $117 million in 2003 and increased by 3.5% each year. How would the function A (t) change to represent the second model? (1 point) The coefficient changes from 120 to 103.5, and the base changes from 1.033 to 0.17. The function that represents the second model is A (t) = 103.5(0.17t). The coefficient changes from 120 to 103.5, and the base changes from 1.033 to 1.17. The function that represents the second model is A (t) = 103.5(1.17)t. The coefficient changes from 120 to 117, and the base changes from 1.033 to 0.035. The function that represents the second model is A (t) = 117(0.035)t. The coefficient changes from 120 to 117, and the base changes from 1.033 to 1.035. The function that represents the second model is A (t) = 117(1.035)t.

An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 2 cm, and the height is 7 cm. Find the rate at which the water level is rising when the water level is 5 cm. cm/sec

You want to buy a bouquet of yellow roses and baby's breath for $16. The baby's breath costs $3.50 per bunch, and the roses cost $2.50 each. You want one bunch of baby's breath and some roses for our bouquet. How many roses can you buy?

Middle Creek High is selling tickets to a choral performance. On the first day of ticket sales the school sold 12 adult tickets and 3 child tickets for a total of $198. The school took in $172 on the second day by selling 3 adult tickets and 13 child tickets. Find the price of an adult ticket and the price of a child ticket. Make sure to set up the system first, and answer the question using proper units and a sentence. Enter your answer as a=# and c=#. Submit your work. *

At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per day and the sides of the square are increasing at a rate of 4 meters per day. When the radius is 3 meters, and the sides are 15 meters, then how fast is the AREA outside the circle but inside the square changing?

Use the given information to find the exact value of each of the following. a. sin 20 b. cos 20 c. tan 20 sinθ=5/7, θ lies in quadrant II a. sin 20 = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) b. cos 20 = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) c. tan 20 = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

John does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 10 hours. He spends at most 6 hours on weight training. He spends at most 12 hours doing cardiovascular work. Let x denote the time (in hours) that John spends doing cardiovascular work. Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.

A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function. The function has period 0.8 seconds, amplitude 6 cm, and midline H = 15 cm. At time t = 0.5 seconds, the bob is at its midline, moving towards the wall. Find the formula of the trigonometric function that models the distance H from the pendulum's bob to the wall after t seconds. Define the function using radians.

A baby weighs 14 pounds at 5 months and 21 pounds at 10 months. Assume the relationship is linear and that the baby gains the same number of pounds per month. Let x represent the number of months and y represent the weight in pounds. Write an equation in slope-intercept form that models the situation.

An aircraft (at Z) is spotted by two observers (at X and Y) who are L=1000 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure. If A=25°, and B=45°, how high is the airplane? The elevation of the plane is approximately feet. (Do not round until the final answer. Then round to two decimal places as needed.)

Which of the following would not be a correct description of slope? a. rise/run b. The height that a line rises. c. How gently or steeply something is slanted. d. The change in vertical distance compared to the change in horizontal distance.

A grocery store sells a bag of 7 oranges for $4.48. If Khloe spent $6.40 on did she buy? oranges, how many did she buy?

A car is purchased for $23,500. After each year, the resale value decreases by 35%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

Suppose there is a 22.1% probability that a randomly selected person aged 30 years or older is a jogger. In addition, there is a 25.8% probability that a randomly selected person aged 30 years or older is male, given that he or she jogs. What is the probability that a randomly selected person aged 30 years or older is male and jogs? Would it be unusual to randomly select a person aged 30 years or older who is male and jogs? The probability that a randomly selected person aged 30 years or older is male and jogs is 0.057 (Round to three decimal places as needed.). Would it be unusual? Yes No No

24. A shelf that is 18 cm wide is held up by a triangular bracket. The bracket makes a 37.5° angle with the bottom of the shelf. What is the height of the bracket? Hint: draw a diagram and think about trigonometry a.13.81 cm b.12.94 cm c.10.96 cm d.14.28 cm

How long is a ladder that reaches a height of 4.36 m up a wall and rests on the wall at an angle of elevation of 74°? Hint: Be sure to draw a picture a. 4.54 m b. 15.82 m c. 3.24 m d. 1.25 m

13. Jacob gets paid $21.25 an hour to work on a surveying team, plus $40.00 per day for food. Which of the following equations shows his earnings for a workday that is h hours long? a. earnings = 21.25h + 40 b. earnings = 21.25 × 40 c. earnings (21.25 +40)h d. earnings = 40h + 21.25

Between two telephone poles that are 40 feet apart, there is a wire suspended in the shape of a catenary y = 25 cosh (x/25) - 5, where and y are measured in feet and -20 ≤ x ≤ 20. What is the slope of the curve where the wire meets the right pole? Note: Round to the nearest thousanth.

If you invest $23010.00 at an interest rate of 2.90% per year compounded semi-annually, what will the total value of your investment be after 9 years? Hint: use compound interest formula a. $29801.62 b. $29816.29 C. $23853.03 d. $35779.54

The rectangular coordinates of a point are given. Find polar coordinates (r,0) of this point with 8 expressed in radians. Let r>0 and -2л<0<2л. (-10,10) One possibility for the polar coordinates of this point is. (Simplify your answer. Type an ordered pair. Type your answer in radians. Type exact answers, using as needed. Use integers or fractions for any numbers in the expression.)

The weight of 3-month-old Bullmastiffs follow approximately a normal distribution with a mean of 120 pounds and a variance of 25 pounds. If your 3-month-old Bullmastiff is 130 pounds, how many standard deviations above or below the mean is your pet (i.e., find the Z-score)? 0 1 1.5 2

CREDIT CARDS IN CHINA The total number of credit cards issued in China from 2009 through 2012 grew at the rate of r(t) = 153e0.21t (1 ≤1≤4) million/year, where (t = 1) corresponds to 2009. What was the average growth in the number of credit cards issued in China for the period under consideration?

An amount of $32,000 is borrowed for 11 years at 3.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back? Use the calculator provided and round your answer to the nearest dollar.

A certain forest covers an area of 2300 km. Suppose that each year this area decreases by 6.5%. What will the area be after 14 years? Use the calculator provided and round your answer to the nearest square kilometer.

Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $51,800?

The weight of golden hamsters follows a normal distribution with a mean weight of 4.3 ounces and a standard deviation of 0.25. What is the probability that a randomly chosen hamster weighs less than 4.6 ounces? 0.655 0.788 0.885 0.945

Consult the figure. To find the length of the span of a proposed ski lift from A to B, a surveyor measures the angle DAB to B be 25 and then walks off a distance of L= 1800 feet to C and measures the angle ACB to be 15°. What is the distance from A to B? The distance from A to B is approximately feet. (Do not round until the final answer. Then round to two decimal places as needed.) D

What are the coordinates of the point on the directed line segment from (-8, 1) (2, -7) that partitions the segment into a ratio of 3 to 1?

A perfectly spherical balloon is being inflated such that the radius of the balloon is increasing linearly at a rate of 0.3 inches per t seconds. What would be an expression for calculating the volume of the balloon att seconds? (Remember: Volume of a sphere: V = (4πr3/3)

6. Kelly works two jobs. She usually works at a retail store for 7 hours during the day and is paid $12 per hour by the store. In the evening she works at a restaurant as a manager for 5 hours and is paid $20 per hour. How much does she make on average per hour for the day?

A seventh grade English Language Arts teacher wants to order books for all the seventh grade classes. He wants to determine the favorite type of book among the seventh grade students. Which sample would be the most appropriate for this survey? A 7 girls in each of his classes B every fifth student in the seventh grade C 1 out of 7 students in his middle school D all of the boys in one of his seventh grade classes

8. Sketch a graph on the slope field through (-3,-1) and a point of your choice. Clearly indicate which point you chose.

Select all the correct answers. If the measure of angle is θ 7π/4, which statements are true? sin(θ)= - √2/2 cos(θ)= - √2/2 tan(θ)= -1 The measure of the reference angle is 60°. The measure of the reference angle is 30°. The measure of the reference angle is 45°

The revenue achieved by selling x graphing calculators is figured to be x(45-0.2x) dollars. The cost of each calculator is $33. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $160? A. Between 5 and 25 calculators B. Between 20 and 40 calculators C. Between 22 and 38 calculators D. Between 21 and 19 calculators