Math Questions

The duration of a professor's class has a continuous uniform distribution between 50.0 minutes and 52.0 minutes. If one class is randomly selected, find the probability that the professor's class duration is between 51.2 and 51.5 minutes. P(51.2 < X < 51.5) =

The top of a 5 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 3 feet per second. How fast is the bottom of the ladder sliding along the ground away from the wall when the bottom of the ladder is 4 feet away from the base of the wall?

You invest $2500 in an account at interest rate r, compounded continuously. Find the time required for the amount to double and triple. (Round your answers to two decimal places.) r = 0.0485 (a) double (b) triple

For the function f(x) = - 1/12x, construct and simplify the difference quotient f(x+h)-f(x)/ h The difference quotient for f(x) = - 1/12x is (Simplify your answer. Use integers or fractions for any numbers in the expression.)

The area of a square is increasing at a rate of 12 centimeters squared per second. Find the rate of change of the side of the square when it is 2 centimeters.

A bicyclist rides 24 mi against a wind and returns 24 mi with the same wind. His average speed for the return trip traveling with the wind is 8 mph faster, than his speed going out against the wind. If x represents the bicyclist's speed going out against the wind, then the total time, t required for the round trip is given by t = 24/x +24/x+8 where t is measured in hours a) Find the time required for the round trip if the cyclist rides 12 mph against the wind b) Find the time required for the round trip if the cyclist rides 24 mph against the wind

The running lanes at the Emery Sears track at Bluffton College are 1 m wide. The inside radius of lane 1 is 33 m, and the inside radius of lane 2 is 34 m. How much longer is lane 2 than lane 1 around one turn? * (25 Points) 106.814 m 103.673 m 3.142 m 4.142 m

Jessica Cardenas has a sprinkler that has several varieties of coverage. The quarter-circle sprinkler head sprays water a distance of up to 20 feet from the head. What area will be covered by the spray of the quarter-circle sprinkler head to the nearest square foot? * (25 Points) 493 ft² 314 ft² 25 ft² 31 ft²

The functions=t³-15t² +75t,0≤t≤ 5, gives the position of a body moving on a coordinate line, with s in meters and t in seconds. a. Find the body's displacement and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval. c. When, if ever, during the interval does the body change direction? a. What is the body's displacement for the given time interval? m (Simplify your answer.) What is the average velocity for the given time interval? m/s (Simplify your answer.) b. What is the body's speed at t=0? m/s (Simplify your answer.) *****

A 95 kg basketball player jumped in the air to secure a rebound. During the last step before jumping in the air, 1,792 N of ground reaction force was applied to the basketball player over a duration of 400 ms a.What is the average net vertical force during the jump? b.What is the impulse the basketball player experienced during the jump? c. What is the momentum the basketball player experienced during the jump? d. What is the basketball player's vertical velocity at the instant of takeoff? e. How high did the basketball player's center of mass rise during his jump?

The cost of renting a space for up to 400 people is a $700 flat fee. The cost of catering a dinner for x attendees is given by C(x) = 300+ 32x. Write an equation for the total cost, T(x), of putting on a prom if these are the only two expenses.

11 Mr. Davis and Ms. Lee saved the same amount of money. Mr. Davis spent $1,140 on a television and Ms. Lee spent $580 on a stand mixer. Ms. Lee then had 9 times as much money as Mr. Davis. How much money did Mr. Davis have at first?

For every three girls taking classes at a martial arts school, there are 4 boys who are taking classes. Suppose there are 236 boys taking classes at the school. Write a proportion that could be used to predict the number of girls taking classes at the school. Use x to represent the number of girls.

The cost of reserving a particular domain name is $21 up front plus $4.49 per month. Find the cost of reserving that domain name for the following:

Given that f(x)=x²-19 and g(x) = 6x +1, find (fg)(-1/6) A. (fg)(-1/6)= (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. The value for (fg)(-1/6) does not exist.

a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x) = 2x² +3x, a = -2

For a given input value u, the function g outputs a value v to satisfy the following equation. -12u + 3 = 8v + 1 Write a formula for g(u) in terms of u. g(u) =

Insert the proper sign, > or < or =, between the given expressions. Explain your answer. cos 0° 3 cos 60° Because cos 0° = and 3 cos 60° =, the correct comparison is cos 0° 3 cos 60°. (Round to three decimal places as needed.)

Find the coordinates of both intercepts for the line. Express numbers in exact simplified form. -8x-3y=-23 The X intercept has the coordinates The intercept has the coordinates

A mirror should be centered on a wall. The mirror is 36 inches wide and the wall is 18 feet wide. Which equation helps determine the distance x on each side of the mirror? A) X + 3 + x = 18 B) X = 18 + 3 C) X + 36 + x = 18 D) 3 + x + 3 = 18

27) A-Plus Advertising charges a fee of $27 plust $0.10 per flyer to print and deliver flyers. Print and More charges $0.25 per flyer. For how many flyers is the cost at A-plus Advertising less than the cost at Print and More?

State if the given functions are inverses. * g(x)=2x+4 f(x) = x-4/2 A) Yes B) No

A box of chocolates contains six milk chocolates and seven dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. What is the probability that the first piece is milk chocolate and the second is dark chocolate?

Solve the equation by using the quadratic formula. 2p² = -8p+3 Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The solution is p = (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. There are no real roots.

A ferris wheel is 45 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. The function h-f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters What is the Midline? y= meters What is the Period? minutes How High are you off of the ground after 1 minutes? meters

Which of the following is true about the graph of f(x) = 2 sin³(x) + 3 sin(x) + 2 on the interval [0, π]? a) f(x) has a local minimum at the point (π,7). b) f(x) has points of inflection at the points (π/4,2√2+2) and (3π/4, 2√2+2). c) f(x) is concave down on the interval (0, π). d) f(x) is concave up on the interval (0, π). e) f(x) is increasing on the interval (π/2, π).

Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, the ends of these mats are right triangles. If the height of the mat is 28 inches shorter than the length of the mat and the hypotenuse is 8 inches longer than the length of the mat, what is the length of the mat?

To rent a certain meeting room, a college charges a reservation fee of $14 and an additional fee of $4 per hour. The chemistry club wants to spend less than $50 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room? Use / for the number of hours. Write your answer as an inequality solved for t.

Differentiate the function, and find the slope of the tangent line at the given value of the independent variable. f(x) = 5x + 4/x, x = -5 The derivative of the function f(x) = 5x + 4/x is The slope of the tangent line at x = -5 is

A company pays its sales people a base salary of $38,500 per annum plus a commission of 12% on all sales. Stephen, one of the company's salespeople, made sales worth $105,000 in his first year. a. Calculate the commission Stephen earned during the year. Round to the nearest cent b. Calculate the total salary Stephen earned during the year.

A store pays $39.27 for a quilt. The store marks up the price by 26%. What is the new price? Round your answer to the nearest cent: $

Identify the zeros and y-intercept for the following function graphed below. a. zeros: (0, -3), (0, 5); y-intercept: (90, 0) b. zeros: (-3, 0), (5, 0); y-intercept: (0, 90) c. zeros: (5, 0); y-intercept: (0, 90) d. zeros: (0, 90); y-intercept: (5, 0)

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 70 workers to build a 80 story building? It will take years

On the planet Golgafrincham there are two systems for measuring temperature. Using the Celia scale, water freezes at 0° C and boils at 50° C. Using the Furryhat scale, water freezes at 10° F and boils at 110° F. Both systems divide the temperatures in between into equal increments. Let x be the temperature in degrees Celia and y be the temperature in degrees Furryhat. a. Find a formula which converts temperatures measured in Celia into Furryhat. y(x) = b. Find a formula which does the inverse. c. What temperature is the same in both Celia and Furryhat?

From recent survey data, its known that the proportion of adults in the United States who are smokers is 18%. For a random sample of size 150, what is the standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?

Given that the point (160, -36) is on the terminal side of an angle, θ, find the exact value of the following: sin(θ)= cos(θ)= tan(θ)= csc (θ)= sec (θ)= cot (θ)=

A student has student loans of $96,000. He would like to pay it back in 10 years. (10 points) a) Calculate the monthly payments if his loan has a fixed APR of 8%. b) What is the total amount that the student paid for his college education (principal and interest)?

The average cost of a 4-year college education is projected to be $130,000 in 20 years. How much money should be invested now at 8% compounded quarterly to provide $130,000 in 20 years?

Without using a calculator, compute the sine and cosine 5π/3 of by using the reference angle. What is the reference angle? In what quadrant is the original angle?

Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous f(x)= (2x-2) / (x2+2x-3) is discontinuous at x =

A student has student loans of $96,000. He would like to pay it back in 10 years. a) Calculate the monthly payments if his loan has a fixed APR of 8%.

For each sum or product, determine whether the result is a rational number or an irrational number. Then choose the appropriate reason for each. Result is Rational Result is irrrational reason (a) 2/11 + 17/19 (b) 16+√13 (c) 20 + 8/9 (d) √2+38

If y=ex is reflected about the x-axis, what is the formula for the resulting function? y = help (formulas)

Suppose that $10,000 is invested at an APR of 6% for 4 years. a) Determine the accumulated balance assuming that interest is compounded annually. b) Determine the accumulated balance assuming that interest is compounded monthly. c) Determine the accumulated balance assuming that interest is compounded continuously.

Patricia receives a gross pay of $1,850 bi-weekly from his employer. If his employer changed his pay period to monthly instead of bi-weekly, calculate the monthly payment that he would receive. Round to two decimal places

Alexander, a sales representative at a jewelry store, receives a 1.50% commission for the first $12,000 in sales he makes, 3.50% for the next $25,000, and 6.50% thereafter. If he was paid $2,000.00 in commissions last month, calculate the amount of sales he made.

Express the following equations in logarithmic form: (a) 5^4 = 625 is equivalent to the logarithmic equation: (b) 10^ 3 =0.001 is equivalent to the logarithmic equation:

A school superintendent purchase a new car for $26,788. A. If the sales tax is 7.75%, find the amount of sales tax. The sales tax is B.The superintendent makes a $3000 down payment and the license fee is $145. Find the amount the superintendent must finance. The amount financed is C. Assuming the superintendent gets the loan for the amount in part B at an annual interest rate of 8.1% for 5 years, determine the superintendent's monthly car payment. The monthly payment is

A random number generator picks a number from 13 to 38 in a uniform manner. Round answers to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the number will be exactly 24 is P(x = 24) = d. The probability that the number will be between 22 and 29 is P(22 < x < 29) = e. The probability that the number will be larger than 28 is P(x> 28) = f. P(x> 16 | x < 32) = g. Find the 22nd percentile. h. Find the minimum for the upper quartile.

Select the different types of transformations you can have with a function: Select one or more: a. Reflection about y axis b. Reflection about origin c. Reflection about x axis d. Horizontal Shifts e. Bolding f. Restriction g. Reflection about line y=x h. Shading i. Stretching j, Vertical Shifts k. Compression