Basic Math Questions and Answers

Suppose that W = span{V₁, V2, V3} where each v; is in R³. Consider the following statements. (i) If x is in W then x = C₁V₁1 + C2V2 + C3V3 for some scalars C1, C2, C3. (ii) 3v₁ - 2v2 is in W. (iii) W is a subspace of R³. Which of the above statements are always true? (a) (i) only (b) (ii) only (c) (ii) and (iii) only (d) (i) and (ii) only (e) (i), (ii), and (iii)

A manufacturer of face masks found out that the marginal revenue function is r(q) = 0.059q + 47.79 while the marginal cost function is c(q) = 0.0118q² - 1.18g + 59 where is the quantity of masks in thousands. Find the area between these two curves and the y-axis. Round your answer to 2 decimal(s).

I can find common factors and multiples. D Jerrie practices the piano every three days, and practices the trumpet every four days. Jerrie practices both the piano and the trumpet on May ST. When is the next day Jerrie will practice both Instruments at the same time?

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

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?

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

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

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 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

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?

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.

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)

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 =

An observer standing on the top of a 360 ft cliff spots a boat at an angle of depression of 28°. How far is the boat from the base of the cliff? Round your answer to the nearest tenth. Distance from the base of the cliff =

Two pools are being filled with water. To start, the first pool had 819 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 18 liters per minute. Water is being added to the second pool at a rate of 39 liters per minute. Let x be the number of minutes water has been added.

Over time, the value of the property at 397 West Lake Street increased by 215%. If the initial value of the property was P, what expression represents the property's current value? Why? 315 P 215 P 3.15 P 2.15 P

There were 1200 teams competing in the first annual world math tournament. After each round, the number of teams are cut in half. a= a. Find the a and the b for this problem. b = b. Write the equation that models this situation. C. How many teams will be left after 4 rounds? d. How many teams will be left after 8 rounds? y =

Suppose the statement below is true: "John wen to the gym or John wen to the bank." What can be said about the statement J = John went to the gym. insufficient information false true justified

The cooking time for a mini-loaf of bread is 5 minutes longer than half the time it takes to bake a regular-sized loaf of bread. If it takes 25 minutes to bake a mini-loaf, how long does it take to bake a regular-sized loaf? 10 minutes 20 minutes 30 minutes 40 minutes

An empty ice cream cone has a height of 3.02 inches and a radius of 0.98 inches. What is the approximate volume of ice cream it will hold within the cone (not h over)? 3 in³ 1 in ³ 12 in³ 9 in³

The graph of the function f(x) = e-* - 5 can be obtained from the graph of g(x) = e² by one of the following actions: (a) reflecting the graph of g(x) in the x-axis; (b) reflecting the graph of g(x) in the y-axis; your answer is (input a or b) then, by one of the following actions: (a) shifting the resulting graph to the right 5 units; (b) shifting the resulting graph to the left 5 units; (c) shifting the resulting graph upward 5 units; (d) shifting the resulting graph downward 5 units; Your answer is (input a, b, c, or d) Is the domain of the function f(x) still ( Your answer is (input Yes or No) The range of the function f(x) is (A, ∞), the value of A is ∞, ∞)?

Jaquin hopes to earn $700 in interest in 3.6 years time from $28,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds semi-annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Marsha gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.03 in change. Each pair of socks cost the same amount. What is the cost in dollars and cents for each pair of socks?

Sally worked 7 hours on Monday, 6 hours on Tuesday, 6.75 hours on Wednesday, 5.75 hours on Thursday, and 3.5 hours on Friday. If she is paid $10.18 per hour. Find her gross earnings for the week.

The harmonic motion function d (t) = 5cos(2t), in which dis measured in centimeters and t is measured in seconds, gives the distance a swinging pendulum is from its resting position at time t. How far was the pendulum from its resting position when the motion began? What is the period of the pendulum's motion? How far is the pendulum from its resting position after 7.5 seconds?

Carter Motor Company claims that its new sedan, the Libra, will average better than 31 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. There is not sufficient evidence to support the claim that the mean is less than 31 miles per gallon. There is not sufficient evidence to support the claim that the mean is greater than 31 miles per gallon. There is sufficient evidence to support the claim that the mean is less than 31 miles per gallon. There is sufficient evidence to support the claim that the mean is greater than 31 miles per gallon.

Eduardo wants to determine the fuel consumption of his vehicle. He knows that 20 L of gasoline will get him 220 km and that 11 L of gasoline will get him 115 km. a. What is the independent variable? b. What is the dependent variable? c. What would two coordinates be?

A radioisotope is used as a power source for a satellite. The power output is given by the equation P = 50e t/250, where P is the power in watts and t is the time in days. a. Find the power available after 100 days.

Zachary earns $8.00 per hour. He get paid time and a half for any hours over 40 that he works in a week. If Zachary works 9 hours per day from Monday through Friday, what are his gross earnings for the week?

A farmer is comparing the number of eggs laid by two hens. The first hen laid 6 eggs per week for x weeks. The second hen laid 9 eggs per week for y weeks. The total number of eggs laid by the first hen was greater than the total number of eggs laid by the second hen. Write an inequality showing this relationship.

The exponential model A = 883.1 e 0.014t describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.

Find the greatest common factor of 9m4 and 10n³.

Suppose there are five firms in an industry. Their sales (that is, total revenue) are as follows: • Firm 1: $96 million • Firm 2: $48 million • Firm 3: $36 million • Firm 4: $14 million • Firm 5: $6 million The Herfindahl-Hirschman Index (HHI) for this industry is (Enter your response as an integer.)

Grande Prairie to Medicine Hat, Alberta, is 1013 km and takes Suzie 10 hrs and 45 minutes to drive. Suzie's SUV is travelling at a constant rate of speed from Grande Prairie to Medicine Hat. a. What are the independent and dependent variables? b. How could you represent Suzie's starting coordinates and end coordinates?

After a 70% reduction, you purchase a new sofa on sale for $204. What was the original price of the sofa? The original price was $

A delivery truck is driving along a straight road, and after, hours its distance (in miles) east of its starting point is s = 24t² - 4t³ At time t = 2 hours, where is the truck located? B) 64 miles C) 48 miles A) 96 miles D) 100 miles

You invest $20,000 into an account that earns 5.2% interest every year. How much would you have after 18 years? a. Find the a and the b for this problem. b. Write the equation that models this situation. C. How much would you have after 18 years?

A bullet is fired straight up into the air. Its velocity after t seconds is given by v(t) = -9.81t + 345 m/sec. Find the total distance travelled by the bullet after 63 seconds. Round your answer to 2 decimal(s) Total distance: m