Math Questions

Let u = (0, -2, 2) and v= (1,3,-1). Which of the following vectors are in span {u, v}? (i) (1,-1,2) (ii) (1, 1, 1) (iii) (5, 3, 7) (a) all of them (b) (ii) only (c) (iii) only (d) (i) and (iii) only (e) (ii) and (iii) only

Fireman Bob leans a 40 foot ladder against a building at an angle of elevation of 70°. How far is the base of the ladder from the building (round your answer to the nearest thousandth)? Distance from base of the building = ft

A pair of dice is rolled. What is the probability that the sum is 3, given that the sum is odd? Write a fraction in simplest form For example, 12/17

The element plutonium-239 is highly radioactive. Nuclear reactors can produce and also use this element. The heat that plutonium-239 emits has helped to power equipment on the moon. If the half-life of plutonium-239 is 24,360 years, what is the value of k for this element?

The results of a statewide exam for assessing the mathematics skills of realtors were normally distributed with a mean score of 72 and a standard deviation of 12. The realtors who scored in the top 10% are to receive a special certificate. What score does a realtor need in order to receive a certificate?

The sides of a triangle are 12 inches, 15 inches, and 8 inches. Does the triangle contain a right angle? No, the sides of 8 inches and 12 inches do not add up to 15 inches. No, the sides of 8 inches and 12 inches squared and added together does not equal the side of 15 inches squared. Yes, the sides of 8 inches and 12 inches squared and added together equal the side of 15 inches squared. Yes, the sides of 8 inches and 12 inches are less than 15 inches.

A bacterial culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour there were 400 bacteria. When will the population reach 1000?

The members of a youth football program are required to sell tickets to chicken dinners for the program's fundraiser. They can sell adult tickets for $10 and child tickets for $5. Each athlete must bring in at least $350 from the ticket sales. a. Write an expression to represent the total amount of money an athlete makes from ticket sales. Let x represent the number of adult tickets sold and let y represent the number of child tickets sold. b. Write an inequality in two variables to represent the amount an athlete must make. c. Graph the inequality from part (b). d. Use the graph to determine whether an athlete will bring in at least $350 if they sell 10 adult tickets and 30 child tickets. Explain your reasoning.

Dave bought a new car 8 years ago for $8400 to buy a new car comparably equipped new would cost $12,500. Assuming a steady rate of increase, what was the yearly rate of inflation in car prices over the 8-year period?

A wheelchair ramp is 24 ft long and connects with a building 4 ft above the ground. What is the angle of elevation of the ramp? Round your answer to the nearest WHOLE degree. Angle of elevation =

What factors must be taken into account in order to form a meaningful conclusion? Randomization Replication and treatments Controlling variables, randomization, and replication and treatments Controlling variables

Mike wants to find the confidence interval for a set of data. He knows the sample size and the sample proportion. Which other piece of Information does he need to determine the confidence interval? A. the critical value B. the standard deviation C. the number of favorable responses D. the standard error of the mean

Emma's Pet Shop sells aquariums in the shape of a right rectangular prism. Each aquarium measures 50 inches long, 20 inches wide, and 30 inches tall. The recommended density of each aquarium is no greater than 0.002 fish per cubic inch. Based on the recommendation, what is the greatest number of fish that should be in one aquarium? 15 fish 60 fish 600 fish 15,000,000 fish

Find the equation of the plane containing the point P(3, 0, -1) and the line (x, y, z) = (2, 1, 3) + t(3, -1, -2). (a) 2x 6y + 2z = 4 (d) 3x - 17y + 5z = 4 (b) x + 5y-z = 4 (c) x+6y-z = 4 (e) 16y - 4z = 4

Fill in the type of market that matches each feature mentioned below. Feature Firm sets market price depending on other firm's market price. Firms with zero ability to affect price. A product with no close substitutes.

A wire is tied from the top of a telephone pole to a stake in the ground. If the stake is 12 ft from the bottom of the pole and the wire makes a 78° angle with the ground, how long is the wire? Round your answer to the nearest tenth.

AIR PURIFICATION To test air purifiers, engineers ran a purifier in a smoke-filled 10-ft X 20-ft room. While con- ducting a test for a certain brand of air purifier, they determined that the amount of smoke in the room was decreasing at the rate of R(t) = 0.00032t4 -0.01872t³ + 0.39481² - 3.83t+ 17.63 (0 ≤t≤20) percent of the (original) amount of the smoke per minute, t min after the start of the test. How much smoke was left in the room 5 min after the start of the test? 10 min after the start of the test?

Convert the complex number -9 + Oi into polar form. Express the angle using degrees over the interval 0° ≤0 < 360°. You may round the argument to the nearest tenth of a degree (if necessary), but you must express your modulus in it's exact form.

A management consultant estimates that the number h of hours per day that employees will work and their daily pay of p dollars are related by the equation 90h5 + 18,000,000 = p³. Find dh/ dp at p = 300 and interpret your answer.

In order to predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables? Choose the correct answer below. A. The correlation between variables must be significant. B. The correlation between variables must be a y-value of a point on the graph. C. The correlation between variables must be greater than zero. D. The correlation between variables must be an x-value of a point on the graph.

We wish to test the claim that u > 32 at a level of significance of a = 0.05. The sample statistics are n = 50, and x-bar = 32.3. Moreover, it is known that the population standard deviation is a = 12. Compute the test statistic, rounded to two decimal places. 2.31 3.11 1.77 0.98

Manny is deciding between two packages of yogurt. YoFruit costs $4.48 for 16 ounces. Yummy Yogurt costs $2.64 for 8 ounces. How much more does Yummy Yogurt cost per ounce? per ounce

Dakota and Justine are training to be in the Sweat for Fun Run. They ran the same distance on Saturday, but Dakota finished in less time. They each plan to run for the same amount of time on Sunday. If their average speeds are consistent, who will run farther on Sunday?

Exponential models and applications The number of bacteria in a culture is given by the function n(t) = 960e0.25t where t is measured in hours. (a) What is the relative rate of growth of this bacterium population? Your answer is percent (b) What is the initial population of the culture (at t=0)? Your answer is (c) How many bacteria will the culture contain at time t=5? Your answer is

Find a polynomial function f(x) with the given degree, zeros, and leading coefficient: Degree 4, x = - 3, multiplicity of 2; x = 1 multiplicity of 1; x = 3, multiplicity of 1 and a leading coefficient of 1. a) The factored form is: b) Find the polynomial equation in standard form.

Assume that a hypothesis test will be conducted using a significance level of a = 0.01 and null hypothesis Ho: μ = 21. Furthermore, assume that the following sample data will be used: n = 12, x-bar = 22.2, and s = 2.1 Find the p-value for the test. 0.9227 0.0478 0.0733 0.1466

Find the absolute maximum and absolute minimum values of f(t) = t√/9-t2 on the interval [-3, 3]. 1. Find the absolute maximum of f on the interval. 2. Find the absolute minimum of f on the interval.

On November 1st, Ben owes $500 on his credit card. On November 5th, Ben pays $60 towards the balance of the card. On November 12th, Ben makes $90 in purchases. On November 22nd, Ben pays $150 towards the balance of the card. The average daily balance of the card for the month of November is Question Help: Message instruct

The electromotive force V of an alternating current circuit at time t can be describe by the following function, where V is volts and t is in seconds. V(t) = 110sin (120) How many cycles will the circuit run through in 1 minute? 120 1320 1200 3600

A company observes the lifespan of 560 lightbulbs and finds that their data follows a normal distribution. What is the approximate number of light bulbs that fall within two standard deviations from the mean?

Change 648,951,239 to Roman numeral (Assume the Roman Numerals in blue have double bar over them and Roman Numerals in red have one bar over them) DCXLVIII CMLI CCXXXIX DCXLVIII MCLI CCXXIX CDCXLVIII CMLI COXXXXXIX DCCXLVII CMLI CCXIX

Convert the complex number 1 + 9i into polar form. Express the angle using degrees over the interval 0° ≤ 0 < 360°. You may round the argument to the nearest tenth of a degree (if necessary), but you must express your modulus in it's exact form.

The population of Washington has been decreasing exponentially since the major employer left town. After 8 years the population was 68,532 and after 9 years it was 65,791. Write an equation forp (t), the population of Washington, + years after the employer left town. Use the caret symbol (^) for exponents and the equation form: y = a(b)^x Use the variables: t = amount of time elapsed since the employer left town (years) P(t) = the population of the town after t years Round the base (constant multiplier/ratio) to the nearest hundredth. Use substitution to find an accurate initial value. Round the initial value to the nearest whole value. Do not use commas or spaces in your equation. Equation:

The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the clinder is decreasing at a rate of 4 meters per hour. At a certain instant, the base radius is 5 meters and the height is 8 meters. What is the rate of change of the volume of the cylinder at the instant? Recall that the volume of a cylinder is given by: V=πr²h B)-120 m³/hr C) 60 m³/hr D) - 80 m³/hr A) -60 m³/hr

Olivia's mom is ordering cupcakes for Olivia's birthday. A pack of 6 cupcakes from Baked Fresh costs $18. A pack of 12 cupcakes from Milk 'n' Creme Bakery costs $27.20. How much more does Milk 'n' Creme Bakery charge per cupcake?

A manufacturer claims that fewer than 6% of its fax machines are defective. To test this claim, he selects a random sample of 97 such fax machines and finds that 5% are defective. Find the P-value for the test of the manufacturer's claim. 0.1591 0.3264 0.1736 0.3630

A Global Positioning Satellite (GPS) system uses satellite information to locate ground position. Abu's surveying firm bought a GPS system for $12,500. The GPS depreciated by a fixed rate of 6% and is now worth $8600. How long ago did Abu buy the GPS system?

4. Identify which of the following is a permutation question a. If there are 120 students in grade 11, how many ways can a seating chart be made for a group of 18 of the students? b. If there are eight classrooms on a school floor and twenty desks in each classroom, how many desks are there to choose from to sit in? c. How many groups of 10 students can be selected out of a class of 32 students?

Solve the equation using the quadratic formula. x² + 10x + 24 = 0 The solution set is (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

The function f(x) = 34,000(1.05)* can be used to determine Noah's cost of living in Houston over time. What does the 1.05 represent? A The cost of living will increase by approximately 1% each year B The cost of living will decrease by approximately 1% each year C The cost of living will increase by approximately 5% each year D The cost of living will decrease by approximately 5% each year

In both videos, Sal uses the mathematical operation factorial. Evaluate the following factorial expressions, and watch this video if you need help. Note: the answers to (a) and (b) are different!

Find the absolute maximum and minimum values of f(z) = (x²+x)^2/3 over the interval [-2, 3]. absolute maximum is and it occurs at x = absolute minimum is and it occurs at x = Notes: If there is more than one z value, enter as a comma separated list.

The soccer team is selling sweatshirts to raise money to pay for their season fees. Each sweatshirt costs $20. The team has already raised $100. The team's goal is to raise at least $500. Write, solve, AND graph an inequality that will show how many sweatshirts(s) the team needs to sell to meet their goal. Show all of your work in the sketchpad or text box. Use both sketchpads if needed.

Solve the equation by factoring. 9x² +21x-8=0 The solution set is (Use a comma to separate answers as needed. Type each solution only once.)

Thirty students raised money by selling frozen pizzas. In total, 400 pizzas were sold. The teacher wants to raffle off a prize proportional to the number of pizzas each student sold. Describe a process that the teacher can use.

19% of all college students volunteer their time. Is the percentage of college students who are volunteers different for students receiving financial aid? Of the 350 randomly selected students who receive financial aid, 53 of them volunteered their time. What can be concluded at the a = 0.10 level of significance? Write hypothesis, give test stat and p-value. Write conclusions about HO and claim. Select the correct conclusion below: a) Students who receive financial aid volunteer as much as the other students. b) Students who receive financial aid does not volunteer at the same rate as other students,

For a sale, a store decreases its prices on all soccer equipment by 20%. A pair of shoes before the sale is $120. Which expression(s) represent the new price? Select yes or no for each. $120 - 0.2($120) $120 0.8($120) 0.8($120) 0.2($120)

Find the domain of the function. f(x) = x+8/x³-4x²-x+4 What is the domain of f? (Type your answer in interval notation.)

Let f(x)=8(x-4)2/3 +2. (A) Find all critical values and list them below. Note: If there are no critical values, enter 'NONE'. (B) Use interval notation to indicate where f(x) is increasing. Note: Use 'INF' for co, '-INF' for -oo, and use 'U' for the union symbol. Increasing: (C) Use interval notation to indicate where f(x) is decreasing. Decreasing: (D) List the values of all local maxima of f. If there are no local maxima, enter 'NONE' I values of local maximums = (E) List the values of all local minima of f. If there are no local minima, enter 'NONE'. values of local minimums =

Representing Proportional Relationships with Equations: Maya is interning at a law firm over the summer and is paid by the hour. her hourly wage is $56, write two equations to represent the proportional relationship between the wages she earns (w) and the number of hours (h): Start with the proportion: Then solve for one of the variables: Then solve for the other variable: