Math Questions

If a cup of coffee has temperature 93°C in a room where the ambient air temperature is 20°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) = 20 + 73e-t/45. What is the average temperature of the coffee during the first 22 minutes?

Multiply and simplify: 4d/w. 3w/2r Be sure to use parentheses as needed when entering your answer.

The loudness, L, of a sound, (measured in decibels, dB) is inversely proportional to the square of the distance, d, from the source of the sound. When a person 5 feet from a jetski, it is 100 decibels loud. How loud is the jetski when the person is 49 feet away?

In ΔPQR, the measure of ∠R-90°, RP = 3.7 feet, and PQ = 9.5 feet. Find the measure of ∠Q to the nearest tenth of a degree.

Simplify the expression 5/x2+1/x² + x and give your answer in the form of f(x)/g(x) Your answer for the function f(x) is: Your answer for the function g(x) is:

Garrison deposited $480 in an account that earns 3% interest compounded annually. How much interest will the account earn after 72 months?

Find the future value and interest earned if $8804.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuously. (a) The future value when interest is compounded semiannually is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.) The interest earned is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.) (b) The future value when interest is compounded continuously is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.) The interest earned is approximately $ (Type an integer or decimal rounded to the nearest hundredth as needed.)

In ΔSTU, the measure of ∠U=90°, US = 5.9 feet, and TU = 2.6 feet. Find the measure of ∠T to the nearest tenth of a degree.

Carly deposited $800 in an account that earns 2.5% compounded annually. How much will Carla have in her account at the end of 8 years if she makes no withdrawals or deposits? The answer is $

The sum of the digits of a two digit number is 14. The difference between the tens digit and the units digit is 2. If x is the tens digit and y is the ones digit, which system of equations represents the word problem? x+y=14 and x-y=2 x+y=14 and y-x=2 xy-14 and x-y=2

Suppose you deposit $4000 at 8% interest compounded continuously. Find the average value of your account. during the first 4 years.

You decide that you want to make sure your estimate from part a is correct. You go out and gather 10 simple random samples of 25 people in your school and calculate the proportion of students within each sample whose Amazon packages arrive within two business days of ordering. The proportion of customers that receive their packages within two days of ordering are given below. 0.70, 0.75, 0.6, 0.95, 0.90, 0.73, 0.87, 0.86, 0.92, 0.97 a. Explain why all of the sample proportions are not the same. b. Find the average of all 10 proportions above.

A fireman invests $40,000 in a retirement account for 2 years. The interest rate is 6%. The interest is compounded monthly. What will his final balance be? The answer is $

If 1700 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = (include units)

A farmer has 380 feet of fencing and wants to fence off a rectangular field that borders the back of his property. The back of the property already has a fence. What is the largest possible area of the field in square feet?

A model rocket is launched with an initial upward velocity of 70 m/s. The rocket's height h (in meters) after t seconds is given by the following. h=70t-5t² Find all values of t for which the rocket's height is 35 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

In ΔNOP, the measure of ∠P-90°, NO = 83 feet, and OP = 49 feet. Find the measure of ∠0 to the nearest tenth of a degree.

Suppose a universal set consists of natural numbers that are at most 16. Two subsets are created from the universal set; Set A contains the multiples of 3 and Set B contains the odd numbers. Correctly place each element of the universal set in the Venn diagram to the right.

Suppose 30 cars start at a car race. In how many ways can the top 3 cars finish the race? The number of different top three finishes possible for this race of 30 cars is (Use integers for any number in the expression.)

A mall has four escalators, one elevator, and three stairwells to travel from the second floor to the first floor. They have six doors on the first floor to exit the mall. If Jane is on the second floor, how many ways can she exit the mall?

If you were going to use the distributive property as the first step in the equation, 4 − 2 (x + 1) = 10, what would your next step be? 4-2x+1=10 4-2x-2 = 10 4-2x-1-10 -2x+5 = 10

Consider the curve y = 5x3 - 3x. (a) Find dy/dx. The curve has a tangent at the point P(-1.-2). (b) Find the gradient of this tangent at point P. (c)Find the equation of this tangent. Give your answer in the form y = mx + c.

In Exercises 1-4, find the indicated measure. 1. area of a circle with a radius of 6.8 feet 2. area of a circle with a diameter of 19.2 centimeters 3. radius of a circle with an area of 1017.9 square meters 4.diameter of a circle with an area of 707 square inches

A manufacturer is making cylindrical cans that hold 300 cm³. The dimensions of the can are not mandated, so to save manufacturing costs, the manufacturer wants to make the can that uses the least material. What are the dimensions, to the nearest three decimal places, of the can that has the smallest surface area? Radius= Height =

Select the correct answer. The designers of a standardized test are interested in knowing how long people take, on average, to complete the writing portion of the test. They decide to conduct an observation study at a testing facility. To avold blas in their study, they create a list of the test takers scheduled to take the test this week. Then, they randomly select 50 test takers from the list to be part of the study. In this situation, what does the list of test takers represent? A. the frame B. a control group C. a sample D. the population

At a hockey game, a vender sold a combined total of 228 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

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.