Basic Math Questions and Answers

The System of linear equation given by a11x1 + a12x2 + a13x3 = b₁ a21x1 + a22x2 + a23x3 = b₂ a31x1 + a32x2 + a33x3 = b3 Possess infinite solution if : Select one: a. Rank(A) = Rank(A:B) < 3 b. Rank(A) = Rank(A:B) = 3. c. Rank(A) = Rank(A:B) ≥ 3 d. Rank(A) = Rank(A:B)>3

The velocity function for an object is given to the right. Assuming that the object is at the origin at time t=0, find the position at time t = 20. v(t)= 1/10 if 0≥t≤ 10 1 if 10 <1≤20 The position of the object at time t=20 is

One safe investment pays 6% per year, and a more risky investment pays 14% per year. a. How much must be invested in each account if an investor of $94,000 would like a return of $7,400 per year? b. Why might the investor use two accounts rather than put all the money in the 14% investment? a. is invested in the 6% account. is invested in the 14% account. b. Why might the investor use two accounts? A. The 14% account does not earn as much interest as the 6% account B. Investing in two accounts always yields more money than investing in just one account. C. The 14% investment is riskier than the 6% investment. There is a greater chance the investor will lose money if it is all placed in the 14% account. D. Although the 14% account earns more interest, the 6% account has no hidden fees.

A dolphin jumped from 5 feet below the surface of the sea. Jane wrote -5 to represent the depth from which the dolphin jumped. What does 0 represent in this situation? the floor of the sea the surface of the sea the level to which the dolphin jumped the level from which the dolphin jumped

Write an equation of the line that passes through (-3,-1) and is parallel to the line defined by 4x+y=-3. Write the answer in slope-intercept form and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable. The equation of the line in slope-intercept form:

A construction company plans to invest in a housing project. There is a 30% chance that the company will lose $200,000 a 30% chance it will lose $100,000, and a 40% chance of a $300,000 profit. Based ONLY on this information, what should the company do? The expected value is $60,000, so the company should proceed with the project. The expected value is -$90,000, so the company should not proceed with the project. The expected value is $30,000, so the company should proceed with the project. The expected value is $90,000, so the company should proceed with the project.

The base of a triangle exceeds the height by 4 feet. If the area is 142.5 square feet, find the length of the base and the height of the triangle.

Working her way through school, Kathy works two part-time jobs for a total of 22 hours a week. Job A pays $6.20 per hour, and Job B pays $6.50 per hour. How many hours did she work at each job the week that she made $140.60? (Round to two decimal places if necessary.)

One number is 7 more than another. The difference between their squares is 161. What are the numbers? smaller number = larger number =

The length of a rectangle is 7 more than the width. The area is 744 square centimeters. Find the length and width of the rectangle.

The points (-8, 3) and (-9, 5) fall on a particular line. What is its equation in point- slope form? Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

A student at Pine Valley high school would like to find the mean number of extra credit points her fellow students earned on a statistics chapter test. She collects data from 11 students in her class. The graph shows the frequency for the number of extra credit points earned by her fellow classmates. Find the mean number of extra credit points earned by the 11 students, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.

The volume of a hexagonal prism is given by The area of the base is given by. Find an expression for the height of the hexagonal prism.

Suppose a bounty hunter captures a certain type of fugitive 62% of the time. On average the apprehension of this type of criminal costs him $9,000 in expenses, but if he captures the criminal he receives a bounty(monetary reward) of $50,000. Based on this information, should the bounty hunter take the job? The expected value is -$27,580, so the bounty hunter should not take the job. The expected value is $22,000, so the bounty hunter should not take the job. The expected value is $27,580, so the bounty hunter should take the job. The expected value is $22,000, so the bounty hunter should take the job.

Analyze the polynomial function f(x) = − 3(x + 2)(x-4)³ using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y =__for large values of |x|

Imagine that you work for a company that sells hardware to various businesses. You receive a commission based on your monthly sales, and your goal for commissions this month is $1,500. You receive a $10 commission for every tablet you sell, and $30 for every computer you sell. Part A Write a linear inequality to model this situation.

The formula for the volume of a pyramid is A.h/3 where A is the area of the pyramid's base and h is its height. The base of the Great Pyramid of Giza is about 53,000 square meters, and its height is about 150 meters. What calculation will give us the estimated volume of the Great Pyramid of Giza in cubic meters?

The total amount of money (in cents) in x nickels, (x + 3) dimes, and 2x quarters. (Hint: The value of a nickel is 5 cents, the value of a dime is 10 cents, and the value of a quarter is 25 cents.)

Determine which of the equations, y = 2x + 4 or y=0.5x+4, is the better fit for the data points. (0,4), (1,6.5), (2,8), (3,10.5) Which equation is a better fit for the data points? A. y=0.5x+4 B. y = 2x+4

Jamaal ran 6 miles in 30 minutes. Which expression shows how to correctly determine his speed in miles per minute? 6 miles 30 minutes 30 minutes = 6 miles 6 miles 1 minute 30 minutes + 1 mile

Solve the system using the substitution method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options.

A grocer stacks oranges in a pyramidke pille. If the bottom layer is rectangular with 5 rows of 20 oranges and the top layer has a single row of oranges, how many oranges are in the stack? There are ___oranges in the stack

A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. a. Express the surface area A of the box in terms of the width w of the base. b. If the material for the base and top costs 20 dollars/ft² and that for the sides costs 30 dollars/ft², express the total cost C as a function of the width.

Suppose f(x) represents the total number of children that have bought a defective product, and x is the number of days since it came out. Step 2 of 2: Interpret the meaning of f'(42) = 12. 12 is the rate of change in children who have bought a defective product after 42 days. 12 is the total change between the first day and 42 days later. 12 is the average change in the number of children who have bought a defective product between the first day and 42 days later. After 42 days 12 children have bought a defective product.

There is a 60% chance that your math teacher will give a pop quiz tonight, and due to the fact that you have a soccer game, there is a 85% chance you will not be able to do your math homework. You decide that you will not do the homework if the probability of their being a pop quiz and your not doing the home is greater than 80%. What is the probability of there being a pop quiz and your not doing your homework? 0.51 0.34 0.06 0.09

If the density of New York City is 26,403 people per square mile, and the city is 302 square miles, how many people are living in New York City? 7,973,706 people 6,723, 874 people 880,000 people 1,346,395 people

Solve the following system of equations with the Write your answer as an Ordered Pair. on Hele If infinitely many solutions exist, enter ∞ (00). If no solution exists, enter DNE

Solve the equation for all values of x. -3(100x² - 49)(x² - 2) = 0

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?

An airplane takes 7 hours to travel a distance of 6468 kilometers against the wind. The return trip takes 6 hours with the wind. What is the rat in still air and what is the rate of the wind?

In the lab, Josh has two solutions that contain alcohol and is mixing them with each other. Solution A is 40% alcohol and Solution B is 10% alcohol. He uses 600 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 20% alcohol solution? Number of milliliters of Solution B:

Answer the questions about the following function. f(x)=3x²-x-2 (a) Is the point (-1,2) on the graph of f? (b) If x=2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercept(s), if any, of the graph of f. (1) List the y-intercept, if there is one, of the graph of f.

P is on the interior of ∠QMR. R is on the interior of ∠PMT. T is on the interior ∠RMS. m∠QMP = m∠TMS. Ray MR bisects ∠PMT. If m/QMP = 2x, m∠PMR = 3x + 8, and m∠QMS = x² + 13x - 12, find the m∠QMS.

Nicole bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $450, more than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 6% per year. The total finance charges for one year were $300. How much did each computer cost before finance charges?

The medians of a triangle have an intersection point in a triangle called the point of concurrency. This point of concurrency is called the Incenter Circumcenter Inscribed Centroid

Graph the polynomial function f(x) = -2(x - 3)²(x² - 16) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = for large values of |x|.

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 1 cm more than the shorter leg and the hypotenuse 2 cm more than the shorter leg. How long should the sides of the triangle be?

6. What is the equation of a sphere, with center at the origin, that passes through the point (2,3,4)? (x - 2)² + (y - 3)² + (z-4)² = 9 b. (x - 2)² + (y - 3)² + (z - 4)² = 29 c. x² + y² +2²= 9 d. x² + y² + z²= 29

Nick and Adam workout together. Nick weighs 160 pounds and is gaining about 3 pounds per week. Adam weighs 195 pounds and is losing about 2 pounds each week. Write an equation that can be used to find the number of weeks that it will take them to weigh the same amount. a. Equation: b. Solution: c. How much will Nick and Adam weigh?

Suppose a circle has a radius of 21 cm and central angle is 4.5 radians. What is the length of the arc intercepted by the central angle? 1.65 cm 44.1 cm 94.5 cm 22.1 cm

Line segment AB with endpoints A (2, 2) and B (4, 2) is translated 4 units up and 3 units right. Identify the coordinates of the endpoints of the translated line segment. A' (6,-5) and B' (8,-5) A' (5, 6) and B '(7,6) A' (-6, 5) and B' (-8,5) A' (-6, -5) and B' (-8,-5)

Out of 5000 policies for cell phones, a company received 585 claims. The average amount paid on the claims was $80. If the annual cost of the policy was $48, what was a customers expected value of the cell phone insurance policy?

Central park is a rectangle with an area of 840 acres. It is 1/2 a mile wide. One acre is 43,560 square feet. Two people start at the southwest corner at 1:30 pm and start walking round the park in opposite directions. One walks at 9 mph, the other walks at 2 mph. How long until they meet again? It may help to remember that a mile is 5280 feet.

Which is the possible length of the base of a parallelogram If the area is given by 20x^5 23x^4-41x³ +35x^2 + 40x-70 and the height is given by 4x-7 Select the correct answer below: 5x^4+3x³ +5x² + 10 5x^4-3x³-5x² + 10 5x^4+3x³ - 5x² + 10 5x^4 - 4x³ + 10x³ +8x² + 10x - 15 5x^4-4x³-10x³ + 8x² + 10x - 15

A and B are supplementary angles. If m A = (3x – 17)° and m B = (2x - 23)°, then find the measure of B.

State A and state B are among the states with the most remaining drive-in movie screens. State A has 6 more screens than state B, and there are 58 screens total in the two states. How many drive-in movie screens remain in each state?

A commercial fisherman fishes for haddock, sea bass, and red snapper. He is paid $1.25/lb for haddock, $0.75/lb for sea bass, and $2.00/lb for red snapper. Yesterday he caught 500 lb of fish worth $575. The haddock and the red snapper together are worth $320. How many pounds of each fish did he catch?

The volume of a great pyramid is 91,636,272 ft. If the height of the pyramid is 481 feet and the base is a square what is the length and width of the base? 571,536 feet 756 feet 436 feet 481 feet

A boat travels 15 miles upstream in 3 hours. Going downstream, it can travel 45 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water. mph What is the speed of the current? What is the speed of the boat in still water?mph

A new roller coaster at an amusement park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated that the heights of 10-year-old boys are normally distributed with u=54.0 inches and o=4 inches. a. What proportion of 10-year-old boys is tall enough to ride the coaster? b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10-year-old boys is tall enough to ride this coaster? c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a?