Basic Math Questions and Answers

Solve the following equation for B, where -π ≤ β < π. sec^2β-1/tan(-β) = -√3/3 Select the correct answer below: β = π/6 β = -π/6 β = -5π/6 and π/6 β = -π/6 and 5π/6

A ball is thrown from a height of 160 feet with an initial downward velocity of 12 ft/s. The ball's height h (in feet) after t seconds is given by the following. h=160-12t-167² How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

The average score of all golfers for a particular course has a mean of 70 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 71. 0.1293 0.0228 0.4772 0.3707

In the Bible, Joash was 7 years old when he became king; Uzziah was 16; Ahaz was 20; Manasseh was 12; Josiah was 8; and Jehoiachin was 18. What was the average age of these young men when they became kings of Judah? Write the remainder as a fraction. On the blank, write the answer in simplest form.

For f(x) = x² +4 and g(x)=√x-2, find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice. A. The domain of fog is {x}. (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of f o g is all real numbers. (b) (gof)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice.

Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not. D = Ga +3h³a

A pet store has 7 puppies, including 4 poodles, 2 terriers, and 1 retriever. Rebecka and Aaron, in that order, each select one puppy at random without replacement. Find the probability that Aaron selects a retriever, given Rebecka selects a retriever. The probability is (Type an integer or a simplified fraction.)

Three friends split the cost of a pizza and a salad. The pizza costs $15 and the salad costs $6. Which expression can you use to find how much each person owes? (15+6)÷3 15+(6x3) (15+3)+6

4. As you've heard, the smallest pair of amicable numbers, 220 and 284, were known to the ancient Greeks, the next pair of amicable numbers, 17296 and 18416, were discovered by the Islamic mathematician Ibn al-Banna in the 14th century (and rediscovered by Fermat). Thousands more have been found since. In Italy in 1866, however, 16-year-old Nicolo Paganini discovered a small pair of amicable numbers, 1184 and 1210, that had been overlooked for centuries. Verify that 1184 and 1210 are an amicable pair.

Considering only the values of β for which csc² βcos (2β) is defined, which of the following expressions is equivalent to csc² βcos (2β)? Select the correct answer below: 2 2 - sec² β 2sin²β - tan² β 2sin β cot²β - 1

Select the correct answer from each drop-down menu. ΔABC has vertices at A(11, 6), B(5, 6), and (5, 17). ΔXYZ has vertices at X-10, 5), -12, -2), and Z-4, 15). ΔMNO has vertices at M-9, -4), M-3, -4), and O(-3, -15). ΔJKL has vertices at 17, -2), K12, -2), and L(12, 7). ΔPQR has vertices at P(12, 3), Q(12, -2), and A(3,-2). Triangle ABC and triangle XYZ Triangle ABC and triangle MNO Triangle JKL and triangle ABC Triangle PQR and triangle XYZ can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.

Use synthetic division to rewrite the following fraction in the form g(x) +r(x) d(x) ,where d(x) is the denominator of the original fraction, q(x) is the quotient, and r(x) is 6x^6 + 12x³ − 2x³ − 4x² + 4x + 8 x + 2

State Gasoline Taxes A random sample of state gasoline taxes (in cents) is shown here for 11 states. Round sample statistics and final answers to at least two decimal places. 58.6 46.7 58.1 43.8 43.7 46.7 48.9 42.1 55.5 48.5 47.2 Use the data to estimate the true population mean gasoline tax with 98% confidence. Assume the variable is normally distributed. < µ <

A woman 5 ft tall is standing near a street lamp that is 12 ft tall, as shown in the figure. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp. L(d) =

Let f(x) = -x³ + 9x on [-3,5]. a. Locate the critical points of f. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) of f is/are x = (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. The function f has no critical points.

Consider the following equation. 3x - y = 1 Step 2 of 2: Determine the missing coordinate in the ordered pair (?, 3) so that it will satisfy the given equation.

For every 40 pounds of body weight, the dosage for a medication is 1/2 ounce. If a person weighs 180 pounds, how many ounces of medication should be given? a. 1 oz. c. 2.5 oz d. 2.25 oz b. 2 oz

Graph the polar equation below by first selecting the correct symmetry, then selecting the correct radius. r = -5 cos (θ)+5 Provide your answer below:

A consumer agency wants to estimate the proportion of all drivers who wear seat belts while driving. What is the most conservative estimate of the sample size that would limit the margin of error to within 0.47 of the population proportion for a 99% confidence interval? Round your answer up to the nearest whole number.

Over what interval is the cosine graph negative and the sine graph positive? [0, π] [3π/2, 2π] [π/2, π] [π/2,3π/2] Compare the graphs of sine and cosine and make sure you find the intervals where sine is positive and cosine is negative.

Which of the following cannot be the lengths of the three sides of a triangle? A 6 inches, 8 inches, 10 inches B 7 centimeters, 8 centimeters, 15 centimeters C 3 yards, 5 yards, 7 yards D 4 millimeters, 6 millimeters, 9 millimeters

Solve the equation 5 (2x - 1)^2/3 = 125 Assume x is positive. Give your answer as a simplified integer or improper fraction, if necessary. Note: Divide both sides with 5. first. Provide your answer below: x=

Ossie owns some property which has an assessed value of $179,800. Find the tax due if the tax rate is $8.28 per $100 of the assessed value. (Round your answer to the nearest cent.) $1,488.74 $14,204.20 $14,887.44 $17,980.00

Your local pizza store sells medium pizzas for $6.89 each, and breadsticks for $2.49 per order. For a party, you decide to order 5 pizzas and 2 orders of breadsticks. There is a $2 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax?

A game has 49 green balls and 1 red ball in a bag, and you will randomly select one ball from the bag. If the selected ball is green, you lose $1. And, if the ball is red, you win $100. What is the expected value of the game?

There are 15 black balls, 14 red balls, and 11 white balls in a jar, and you get to randomly pick one ball without looking. If you draw a black ball, you win $500. If you pick a red one, you lose $10. If you pick a white one, you lose $100. What is the expected value of picking a ball?

College Courses At a large university, the probability that a student takes calculus and is on the dean's list is 0.049. The probability that a student is on the dean's list is 0.29. Find the probability that the student is taking calculus, given that he or she is on the dean's list. Please round the final answer to 2 or 3 decimal places. P (the student is taking calculus given that he or she is on the dean's list)=

Name the property used to go from step to step each time the (why?) occurs. Choose the correct property for each step below. 5+2(x+6) = 5+ (2x+12) (why?) =5+(12+2x) (why?) = (5+12)+2x (why?) = 17+ 2x = 2x+17 (why?) commutative property of addition associative property of multiplication distributive property commutative property of multiplication associative property of addition ..... 5+2(x+6) = 5+ (2x+12) = 5+ (12+2x) = (5+12) + 2x = 17 + 2x = 2x + 17

Find the all solutions of this equation in the interval [0, 2π): 2 cos(x) sin(x) + sin(x) = 0 X= Give your answers in radians. Do not use decimal approximations. Use 'pi' to represent . Use commas to separate your answers.

A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 10 cm at the top and 9 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom. A(w) = cm²

A commuter railway has 800 passengers a day and charges each one 2 dollars. For each 6 cents the fare is increased, 5 fewer people will ride the train. Express the income I from the train in terms of the ticket price p (in dollars). I (p) = $

2 sandwiches and a bag of chips costs $4.25. A sandwich costs $0.50 more than a bag of chips. Find the cost of a sandwich and a bag of chips

Use the long division method to find the result when 3x³-4x^2+10x - 11 is divided by x – 1. If there is a remainder, express the result in the form q(x) + r(x)/b(x)

If f(x)= a*, show that f(A + B) = f(A). f(B). Rewrite f(A + B) by substituting A + B for x in the given function. f(A + B)= Which law of exponents can be used to rewrite the expression above as a product? A. a^-s= 1/a^s= (1/a)^s C. a^0 = 1 E. (ab)^s = a^s.b^s B. a^s.a^t = a^(s+t) D. 1^5=1 F. (a^s)^t = a^st

The area of a right triangle is 210 square inches. The height of the right triangle is 35 inches. What is the length of the hypotenuse of the right triangle? Enter your answer in the box.

1. A block of clay contains twenty 4-ounce portions of clay. A ceramics teacher wants to use the block to make as many spheres of clay as possible, each weighing 2/5 pound. How many spheres can she make?

Consider these functions: f(x) = 5x² +2 g(x)=x²-1 What is the value of g(f(-1))? A. 2 B. 8 C.22 D.48

Answer the following. (a) The total surface area of Africa is approximately 11,700,000 square miles. Write this number in scientific notation. (b) The signal from a certain satellite takes approximately 1.3 × 10-3 seconds to reach Earth. Write this number in standard notation.

A waterfall has a height of 700 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The height of the pebble h in feet after t seconds is given by the equation h= - 16t² + 16t+ 700. How long after the pebble is thrown will it hit the ground? The time it takes for the pebble to hit the ground is about

Given that the polynomial f(x) has 7 x-intercepts, which of the following most accurately describes the degree of f(x)? Select the correct answer below: The degree of f(x) is at least 6. The degree of f(x) is at least 8. The degree of f(x) is at most 7. The degree of f(x) is at most 8. The degree of f(x) is at least 7. The degree of f(x) is at most 6.

Use the properties of exponents to simplify the following as much as positive. (X^5/6) / (x^3/5)=

A pharmacy produces a certain medication in a daytime variety and a nighttime variety. A bottle of the daytime variety contains 2 ounces of the active ingredient and 6 ounces of flavored syrup. A bottle of the nighttime variety contains 3 ounces of the active ingredient and 5 ounces of flavored syrup. The pharmacy currently has no more than 385 ounces of the active ingredient and no more than 850 ounces of flavored syrup available. If at least 65 bottles of the daytime variety must be filled, what is the maximum number of bottles of the nighttime variety that can be filled? A) 78 B) 85 C) 92 D) 106

Complete the sentence below. If 9^x = 9^6, then x = If 9^3x = 9^6, then x =

The palm tree on the left is 10 years old. The palm tree on the right is 8 years old. The trees grow at the same rate. b. a. Estimate the height y (in feet) of each tree. Plot the two points (x, y), where x is the age of each tree and y is the height of each tree. c. What is the rate of growth of the trees? d. Write an equation that represents the height of a palm tree in terms of its age.

Make a conjecture. Choose the correct answer below. A. cos 4x - sin 4x = (cos x)² B. cos x - sin^x= cos x C. cosx- sin^x= cos 2x D. cos 4x - sin4x = (cos 2x)² cos 4x - sin 4x = (cos²x- sin2x) (cos²x+ sin²x)

An airline finds that if it prices a cross-country ticket at $500, it will sell 300 tickets per day. It estimates that each $10 price reduction will result in 30 more tickets sold per day. Find the ticket price (and the number of tickets sold) that will maximize the airline's revenue. ticket price number of tickets

In a laboratory, it was observed that a colony of bacteria increases at the rate of 30% per hour. If the original number of bacteria is 10 000 how many will there be, (a). after 15 minutes? (b). in 30 minutes? (c). in 5 hours?

What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

The point (a, b) is on the terminal side of angle C in the coordinate plane. If a is a positive integer and b is a negative integer, which of the following statements is correct? Select all that apply. A.Angle C is in Quadrant II B.tan C < 0 C.sin C <0 D.cos C <0

The population of a parish is growing with an annual percentage rate compounded continuously. The population reaches 1.1 times its previous size in 2 years. Find the annual percentage rate according to the exponential growth function.Write your answer in exact form, using In (do not round). Note: When entering natural log in your answer, enter lowercase LN as "In". There is no "natural log" button on the Alta keyboard. Provide your answer below: