Math Questions

A jet and a passenger plane left Nairobi at the same time. The planes flew in opposite directions. The passenger plane flew 255 km/h faster than the jet. After seven hours they were 5005 km apart. Find the jet's speed. 340 km/h 240 km/h 230 km/h 80 km/h 210 km/h

You buy fishing equipment costing $268. State taxes are 6.5% and the federal excise tax on this item is 11.45%. What is the total purchase price? (Round your answer to the nearest cent.) $285.42 $296.87 $298.69 $316.11

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

There are over 3 million students enrolled in community colleges in the U.S. A total of 443,818 students at 699 community colleges completed the Community College Survey of Student Engagement (CCSSE) between 2009 and 2011. About half (50%) of students reported that they "often" or "very often" prepare two or more drafts of a paper before turning it in. True or false? The 50% is a statistic representing a sample of 443,818 community college students. False True

Construct the sample space for a probability experiment where a coin is flipped, and then a 10-sided die is rolled. (H1, H2, H3, H4, H5, H6, H7, H8, H9, H10, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) This setup was used for a carnival game, and different amounts paid out for certain outcomes. Find the probability of each outcome: (a) There was a head on the coin and an odd number on the die. (b) There was a head on the coin and a prime number on the die. (c) There was a head on the coin and a number less than on the die. Write your answers in exact, simplified form.

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.

Write an equation that models the linear situation: The heater keeps the temperature of the pool at 78 degrees Fahrenheit all day long. Instructions: DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1 Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2) You may use decimals IF the decimal values are exact. (You cannot use 33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.) To write your equation, use the variables: h = amount of time since the day began (hours) T(h) temperature of the pool (Fahrenheit degrees) Equation:

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=

The vector PQ has initial point P(1, -3) and terminal point Q(4, -6). Find the magnitude and direction of PQ. Select the correct answer below: |PQ|=6√2; θ=315° |PQ|=3√/2 θ = 225° |PQ|-6√2; θ= 135° |PQ|=3√2; θ= 135° |PQ|=3√2; θ=315° |PQ|=6√2; θ = 225°

The second section of the walk continues from point B along Bell Avenue to the finish line at point C, as shown on the map. a. Each unit on the map represents 1 kilometer. What is the distance in kilometers from point B to point C? b. What is the total length of the race (from point A to point B and from point B to point C) in kilometers? c. A water station is located at the midpoint M of BC. Another water station is located at the midpoint N of MC. A race coordinator says that the map coordinates of point N are (6, 8). Is the race coordinator correct? Support your answer.

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?

Country Motorbikes Incorporated finds that it costs $200 to produce each motorbike, and that fixed costs are $1300 per day. The price function is p(x) = 500 - 5x, where p is the price (i dollars) at which exactly x motorbikes will be sold. Find the quantity Country Motorbikes should produce and the price it should charge to maximize profit. Also find the maximum profit.

Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log(8(1 + 3x)). Make sure to use parenthesis around your logarithm functions log(x + y).

Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. Replacement times for washing machines: 90% confidence; n=31, x= 10.4 years, σ = 2.4 years 0.1 yr 0.7 yr 3.1 yr 0.6 yr

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?

- In a class with 50 students, 25 of the students are sophomores, 15 of the students are mathematics majors, and 10 of the mathematics majors are sophomores. If a student in the class is to be selected at random, what is the probability that the student selected will be a sophomore or a mathematics major or both? A) 0.4 (B) 0.5 (C) 0.6 (D) 0.8

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)=

1. The table shows the number of turtles hatched at a zoo each year since 2003. a. Find the line of best fit. Predict the number of turtles to be hatched in 2011.

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.

Determine the point estimate of the population mean x̄ and margin of error (E) for each confident interval. Lower Bound: 15 Upper Bound: 35 (x)=25, E=15 (x)=10, E=25 (x)=25, E=10 (x)=15, E=10

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) = $

Write an equation that models the linear situation: A baby grows about an inch every month for the first year. She was born a foot and a half long. Instructions: DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs. For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1 Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2) You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.) To write your equation, use the variables: m = age of the baby (months) L(m) = length of the baby (inches) Equation:

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

Serial Killer The Murder Accountability Project has compiled a database of homicides in the United States from 1976-2017. This data set includes record: ID of the incident given as an integer number age of victim: in years age of perpetrator: in years sex: 1 female, 0 = male ethnicity of victim(s) ethnicity of perpetrator weapon used Which of the following variables is quantitative? sex age of victim record

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1200 miles. What is the probability a certain tire of this brand will last between 57,480 miles and 57,840 miles? 0.4649 0.0180 0.4920 0.9813

Curing diabetes: Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that less than 77% of those with diabetes who undergo this surgery will recover from diabetes? Use the α= 0.10 level of significance and the critical value method. State the appropriate null and alternate hypotheses. Ho: H₁: This hypothesis test is a (Choose one) test.

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

(1 point) Find the length of the arc on the unit cicle that is defined by the given angle. (a) π/4 radians (b) 2 radians (c) 1.6 radians (d) 46°

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.

A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a significant source of stress for me." To help form an estimate, the psychologist randomly selected 922 Americans and found that 59.6% of the sample agreed with the statement "the future of the nation is a significant source of stress for me." Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the true proportion of all Americans that say the "the future of the nation is a significant source of stress for me." Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary. The margin of error is given by E = A 96% confidence interval is given by

A sample of 650 grams of radioactive substance decays according to the function A(t)= 650e ^028t, where t is the time in years. How much of the substance will be left in the sample after 10 years? Round your answer to the nearest whole gram.

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