Math Questions

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?

Solve the equation by factoring. x² = 6x +27 Rewrite the equation in factored form. (x+3)(x-9) = 0 (Factor completely.) The solution set is

A box contains 36 orange golf balls, 28 white golf balls, and 92 yellow golf balls. If a golf ball is drawn at random from the box, find the probability that it will NOT be an orange ball. Write your answer as a fraction in simplest form. (Use the /symbol to write your fraction, ex. 1/2) Hint: 1 - P(Orange Ball) The probability is

The average adult heart pumps about 84. mL/s of blood at 72 beats per minute. Suppose you need to calculate how long it would take the average heart to circulate 7300. mL of blood. Set the math up. But don't do any of it. Just leave your answer as a math expression. Also, be sure your answer includes all the correct unit symbols.

What is the diameter of a sphere with a volume of 89110 cm³, to the nearest tenth of a centimeter?

Solve the quadratic equation using the square root property. (x-7)² = -3 The solution set is (Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. 8 8 11 11 8 7 7 7 9 7 7 7 10 A. The mode(s) is/are 7. (Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as needed.) B. The data set does not have a mode. Does (Do) the mode(s) represent the center of the data? A. The mode(s) represent(s) the center. B. The mode(s) does (do) not represent the center because it (one) is the largest data value. C. The mode(s) does (do) not represent the center because it (they) is (are) not a data value. D. The mode(s) does (do) not represent the center because it (one) is the smallest data value. E. The data set does not have a mode.

Which of the following values of x makes the rational expression below equal to zero? x-3/x-9 A. 12 B. 9 C. 3 D. 6

There are 2.5 oranges per pour and 1.1 grapefruit per pound. With $50 you can buy 36 pounds of oranges or 45 pounds of grapefruit. If you have enough money to buy 37 pounds of grapefruit, how many oranges (to the nearest whole orange) could you buy instead? 116 74 90 30 33

What is the volume of a hemisphere with a diameter of 7.1 ft, rounded to the nearest tenth of a cubic foot?

A circle has a radius of 11 m. Find the radian measure of the central angle that intercepts an arc of length 5 m.

A bicyclist heads east at 19 km/h. After she has traveled 24.2 kilometers, another cyclist sets out in the same direction going 30 km/h. About how long will it take the second cyclist to catch up to the first cyclist? A It will take the second cyclist 3.2 hours to catch up the first cyclist. B It will take the second cyclist 2.2 hours to catch up the first cyclist. C It will take the second cyclist 3.7 hours to catch up the first cyclist. D It will take the second cyclist 1.7 hours to catch up the first cyclist.

A person came to work at 8:30 AM, went out at 11:45 AM, had lunch, came in at 12:30 PM, and left work at 5:15 PM. The total number of hours worked by this person was a. 7 hours b. 7 hours, 15 min c. 8 hours d. 8 hours, 45 min

If Tamara walks 3.5 miles in 0.75 hour, how far will she walk in 1 hour if she walks at the same pace? A. 0.078 miles C. 1.29 miles B. 4.67 miles D. 4.3 miles

A bag contains 18 red chips, 16 blue chips, and 14 yellow chips. A chip is selected, replaced, then another chip is chosen. Find each probability. (independent events) (Write your answers as a reduced fraction using the / symbol as your fraction bar.) P (blue then red) P(yellow then blue)

The years that a television show on a particular network won an award for best drama series are shown below. 1955 1971 1975 1983 1989 1993 2003 2005 2012 Determine the level of measurement of the data set. Explain your reasoning. What is the level of measurement of the data set? Explain your reasoning. A. Ratio. The data can be ordered and differences between data entries are meaningful, and a zero entry is an inherent zero. B. Ordinal. The data can be arranged in order, or ranked, but differences between data entries are not meaningful. C. Nominal. No mathematical computations can be made. D. Interval. The data can be ordered and differences between data entries are meaningful, but a zero entry is not an inherent zero.

A vector u has initial point (3, 4) and terminal point (5, 1). Write u in the form u = ai+bj. u=

The osmotic pressure exerted by a solution is equal to the molarity multiplied by the absolute temperature and the gas constant R. Suppose the osmotic pressure of a certain solution is measured to be 19. atm at an absolute temperature of 363. K. Write an equation that will let you calculate the molarity c of this solution. Your equation should contain only symbols. Be sure you define each symbol other than R.

Over the last three evenings, Jina received a total of 101 phone calls at the call center. The third evening, she received 4 times as many calls as the first evening. The second evening, she received 5 more calls than the first evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening:

Consider the line y=-9x+7. Find the equation of the line that is perpendicular to this line and passes through the point (5, 6). Find the equation of the line that is parallel to this line and passes through the point (5, 6). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

Solve the quadratic equation by the square root property. 6x²=24 The solution set is

Find the direction angle of the vector v=-8i-7j. That is, find the angle between 0° and 360° that v makes with the positive x-axis (measured counterclockwise), when v is in standard position. Do not round any intermediate computations, and round your answer to the nearest whole number.

Suppose the value R (d) of d dollars in euros is given by R (d)= 5/6 d. The cost P (n) in dollars to purchase and ship n purses is given by P (n)=55n+23. Write a formula for the cost Q (n) in euros to purchase and ship n purses. It is not necessary to simplify. Q(n) =

Consider the line y= 5/ 9x-1. Find the equation of the line that is perpendicular to this line and passes through the point (9, 3). Find the equation of the line that is parallel to this line and passes through the point (9, 3). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

The letters r and θ epresent polar coordinates. Write the given equation using rectangular coordinates (x,y). r = 16 Complete the general form of the equation using rectangular coordinates. 0=

The volume (r) (in cubic meters) of a spherical balloon with radius r meters is given by V(r) = 4/3πr³. The radius W (t) (in meters) after t seconds is given by W (t) = 5t+3. Write a formula for the volume M (t) (in cubic meters) of the balloon after t seconds. It is not necessary to simplify. M(t) =