Math Questions

The polar coordinates of a point are (9,3π/2). Find the rectangular coordinates of this point. The rectangular coordinates are (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.)

A machine produces 264 bolts in 42 minutes. At the same rate, how many minutes would it take to produce 308 bolts?

The math department needs to buy new textbooks and laptops for the computer science classroom. The textbooks cost $116.00 each, and the laptops cost $439.00 each. If the math department has $6500 to spend and purchases 30 textbooks, how many laptops can they buy? 1) 6 2) 7 3) 11 4) 12

When using substitution to solve this system of equations, what is the result of the first step? x = 6y + 3 x + 2y = 5 A. x + 2(6x + 3) = 5 B. x + 2(6y + 3) = 5 C. 6y +3+ 2y = 5 D. 6x + 3 + 2y = 5

5 lbs. of organic red potatoes cost $6.00. What is the price per lb.? A. $0.83 B. $1.20 C. $0.91 D. $1.00

Solve, using a proportion. If there are 75 pepperoni on 5 large pizzas, how many pepperoni are there on 3 large pizzas? pepperoni

A 75-horsepower outboard motor at full throttle will rotate its propeller at exactly 4100 revolutions per min. Find the angular speed of the propeller in radians per second.

Suppose that you are headed toward a plateau 37.8 meters high. If the angle of elevation to the top of the plateau is 24.5°, how far are you from the base of the plateau? What is your distance from the base of the plateau? ___meters (Round to one decimal place as needed.)

A farmer has a house at the point (0, 0). He has a corn field that can be found by driving 2 units left, 2 units up, and 4 units right. If he instead walks diagonally to his corn field, how far has he gone? Round to 2 decimal places.

A surveyor measures the length of a surveying chain containing 1000 chain links. The length is 0.052 km. What is the length of a single chain link in centimeters? Write your answer as a decimal.

Vera needs repairs on her car. The mechanic's estimate says that he will provide 7.3 hours of labor. His rate is $55 per hour. The total cost of the labor will be a. $165.00 b. $172.00 c. $385.00 d. $401.50

Forrest is purchasing a car priced at $7,299. His down payment is $299 and his monthly payments are $165 per month for 48 months. The deferred cost of the car is a. $7,000 b. $7,299 c. $7,920 d. $8,219

What is the radius of a hemisphere with a volume of 5320 in³, to the nearest tenth of an inch?

Geraldine opened a savings account with a principal amount of $100. The interest is 105 compounded quarterly. At the end of six months, the amount of money in her savings account will be a. $100.00 b. $102.50 c. $102.56 d. $105.06

Which of the following is a disadvantage to using tables? Check all that apply. A. Graphs are much easier to work with for all problems. B. They organize the data. C. It is often difficult to solve complicated problems with tables alone. D. They force you to do every problem twice, once with a table and once with an equation.

Lorenzo is planning a 285-mile trip. His car's EPA rating is 18 mpg. The number of gallons of gas that Lorenzo will need for the trip is about a. 15.8 gallons b. 18.0 gallons c. 26.7 gallons d. 28.5 gallons

How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to make f continuous at 3? f(x) =x²-x--6/x - 3 f(3) =

A new Youth Sports Center is being built in Hadleyville. The perimeter of the rectangular playing field is 320 yards. The length of the field is 8 yards less than double the width. What are the dimensions of the playing field?

Ellen is purchasing a used car. She is paying $89 down plus $128.57 per month for 36 months. The total amount paid for the car financed in this manner is a. $1,424.54 b. $4,628.52 c. $4,717.52 d. $7,832.52

You roll a six-sided die and select a card from a standard deck of cards. Find the probability that you roll a number less than five on the die and select a face card from the deck of cards. Write your answer as a reduced fraction. (Use the / symbol to write your fraction, ex. 1/2.) Hint (they are independent events). P(A)*P(B) The probability is

Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is the largest data value. C. The mean does not represent the center because it is not a data value. D. The mean does not represent the center because it is the smallest data value.

(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 3 8 8 6 1 9 8 7 9 6 9 5 1 6 2 9 8 7 7 9 (a) Min = 1 (Simplify your answer.)

If 0= 135°, find the exact value of each expression below. (a) cos (-θ) = 1 (b)cos ²θ= (c) cos 2θ = .0

Solve the right triangle ABC, where C = 90°. a = 76.3 yd, b = 42.7 yd

Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line? y-7=3(x-1) y-1=3(x-7) y-7=4(x-1) y-1=4(x-7)

Solve the equation for exact solutions over the interval [0, 21). 7 cos²x+14 cos x + 7 = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an exact answer, using as needed. Type your answer in radians. Use integers or fractions for any numbers in the express Use a comma to separate answers as needed.) B. The solution is the empty set.

A ball is thrown upward, with an initial velocity of 30 meters per second, at an angle of 61° with respect to the horizontal. The ball is thrown from a height of 6 meters off the ground. The horizontal distance x from the starting point and the height y above the ground of the ball / seconds after it is thrown are given by the parametric equations below. x=(vocosθ) t y=-4.9t² + (vosinθ)t + h Here vo is the initial velocity, 8 is the initial angle with respect to the horizontal, and h is the initial height. Use the equations to answer the following questions. (a) How long is the ball in the air before it first touches the ground? Do not round any intermediate computations. Round your answer to the nearest hundredth. seconds (b) What is the horizontal distance that the ball travels before it first touches the ground? Round your answer to the nearest whole number. meters

Rewrite this measurement with a simpler unit, if possible. 3.6 m² m Note: If you can simplify the unit at all, it may be possible to make more than one simplification. Be sure your final answer uses the simplest possible u

The polar coordinates of a point are (-12,-2π). Find the rectangular coordinates of this point. The rectangular coordinates are__ (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.)

There are 5 roses in a vase of 13 flowers. The rest are dalsies. (a) What is the ratio of dalsles to roses? (b) What is the ratio of daisies to all flowers in the vase?

If pencils cost $2.40 for twelve, What is the unit price per pencil? A. $0.20 C. $0.05 B. $5.00 D. $2.00

Compute the discriminant. Then determine the number and type of solutions of the given equation. x^2-4x-6=0 What is the discriminant? (Simplify your answer.) Choose the sentence that describes the number and type of solutions of the quadratic equation. A. There are two imaginary solutions. B. There are two unequal real solutions. C. There is one real solution. D. There are an infinite number of real solutions.

The base of a 10-foot ladder is 4 feet from a building. If the ladder reaches the flat roof, how tall is the building? The height of the building is

David made $40,000 in taxable income last year. Suppose the income tax rate is 10% for the first $7500 plus 16% for the amount over $7500. How much inust David pay in income tax for last year?

When writing a check for $3,476.89, the words that should be written out are a. Three thousand b. Three thousand four hundred c. Three thousand, four hundred seventy-six dollars d. Three thousand, four hundred seventy-six dollars and eighty-nine cents

Find the rectangular equation of the line given by the parametric equations below. Then graph the line and show its orientation. Assume that I can be any real number. x=t/4+2, y=t+3 Rectangular equation:

A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. If there are 16 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary. (Give your answer as a whole or exact number.) length of fencing perpendicular to the riverbank: length of fencing parallel to the riverbank:

Find the equation of the line through P = (9,8) such that the triangle bounded by this line and the axes in the first quadrant has the minimal area. (Use symbolic notation and fractions where needed. Use x as a variable.)

A student sets up and solves the following equation to solve a problem in solution stoichiometry. Fill in the missing part of the student's equation. (0.46__)( 1 mL/10^-3 L)( 1.36 g/mL)(1kg/10^3 g) = 0.63 kg

The temperature T (d) in degrees Fahrenheit in terms of the Celsius temperature d is given by T (d)= 9/5d+32. The temperature C (v) in degrees Celsius in terms of the Kelvin temperature v is given by C (v)=v-273. Write a formula for the temperature F (v) in degrees Fahrenheit in terms of the Kelvin temperature v. It is not necessary to simplify. F (v) = 0

A poster of area 6000 cm² has blank margins of 10 cm wide on the top and bottom and cm wide on the sides. Find the dimensions that maximize the printed area. (Use decimal notation. Give your answers as whole or exact numbers.)

Alexa randomly withdraws a card from a well shuffled standard deck of cards. What is the probability that the number on the card is a King or Queen? 1/13 11/13 2/13

A chemistry student needs 30.0 mL of chloroform for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of chloroform is 1.48 g/cm3 . Calculate the mass of chloroform the student should weigh out. Be sure your answer has the correct number of significant digits.

Find an equation of the circle whose diameter has endpoints (-4, 5) and (2, 3).

Find the solution to the system by the substitution method. Check your answer. -x+3y = -27 3x - y = 33 The solution is. (Type an ordered pair.)

An employment agency specializing in temporary construction help pays heavy equipment operators $125 per day and general laborers $83 per day. If thirty people were hired and the payroll was $3624, how many heavy equipment operators were employed? How many laborers? The number of heavy equipment operators hired was The number of general laborers hired was

The functions f and g are defined as follows. f(x)=x²-x-2 and g(x)= 7x-3/5x-1 Find f(x+8) and g(x/4) Write your answers without parentheses and simplify them as much as possible.

Use the remainder theorem to find P (3) for P(x)=2x-5x³+2x-3. Specifically, give the quotient and the remainder for the associated division and the value of P (3). Quotient = Remainder = P (3) =

Find an equation of the ellipse that has center (1,-4), a minor axis of length 4, and a vertex at (-2,-4).

Solve, using a proportion. If a 6-lb. turkey takes 120 minutes to cook, how long would a 9-lb. turkey take to cook?