Basic Math Questions and Answers

Answer the questions below about the quadratic function. g(x)=2x² + 12x+22 Does the function have a minimum or maximum value? What is the function's minimum or maximum value? Where does the minimum or maximum value occur?

Justin notices that his electric bill reflected a monthly fee of $40 as well as a charge of $0.0743 kilowatt-hour of electricity used. a) Write a function that will help Justin determine the monthly cost of his electricity bill.

The Football Boosters bought pizza for $900 to sell at the game. They kept 10 pizzas to feed the players after the game and sold the rest for $1040. There were 8 slices in each pizza. Their profit was 50 cents a slice a) How many pizzas were in the original order? What was the original price of each pizza? b) What did they charge per slice? c) If they bought plain cheese pizza, the original price would be $10 per pizza. What would this make their profit be per slice if they sold it for the same price as before and still saved 10 pizzas for the players?

For the function f(x)=2x-9, determine whether f(x) is one-to-one. If so, (a) write an equation for the inverse function in the form y=f(x). (b) graph fand f¹ on the same axes, and (c) give the domain and the range of f and if the function is not one-to-one, say so.

Bridget wants to purchase a mix of candy. She decides to make a mix of jelly beans worth $18 per kg and chocolate worth $21 per kg. Together, she gets 84 kg of the mixture worth $19 per kg. How many kg of each type of candy did she buy?

Susan invested her savings in two investment funds. The $12,000 that she invested in Fund A returned a 10% profit. The amount that she invested in Fund B returned a 3% profit. How much did she invest in Fund B, if both funds together returned a 6% profit?

What is the relationship between the value of the 4 in the circle and the value of the 4 in the square in the number above?? A. The value of the 4 in the circle is 10 times the value of the 4 in the square. B. The value of the 4 in the circle is 100 times the value of the 4 in the square. C. The value of the 4 in the circle is 1/100 the value of the 4 in the square. D. The value of the 4 in the circle is 1/100 the value of the 4 in the square.

The height of an object t seconds after it is dropped from a height of 300 meters is s(t) = -4.9t² + 300. (a) Find the average velocity of the object during the first 6 seconds. (b) Use the Mean Value Theorem to verify that at some time during the first 6 seconds of fall, the Instantaneous velocity equals the average velocity. Find that time

Suppose that after a company introduces a new product, the number of months before its market share is x percent is given by m = 20 In ( 40/40 - X), where x < 40. After how many months is the market share more than 37%, according to this model?

From an elevation of 4.5 m below the surface of the water, a dolphin dives at a rate of 1.6 m/s. What is the function rule for this if the dolphin's depth, d, and time, t? A d = (-4.5)t + (-1.6) · B d = (-1.6)t + (-4.5) C d = (-1.6t) + 4.5 D d = 1.6t+ 4.5

their annual reunion should take place, they found that out of all the family members, 7 would not go to a park, 7 would not go to a beach, 9 would not go to the family cottage, 2 would go to neither a park nor a beach, 3 would go to neither a beach nor the family cottage, 4 would go to neither a park nor the family cottage, 1 would not go to a park or a beach or to the family cottage, and 1 would go to all three places. What is the total number of family members? There are total family members. (Simplify your answer.)

The flight path of a rocket, launched from the ground, is modeled by y = 0.25(60x-x²), where y is the height of the rocket in meters from the ground and x is the time in seconds after it was launched. Find the vertex of the parabola and explain what it represents in terms of the context. (30, 225); rocket reaches maximum height of 225 feet after 30 seconds (60, 0); rocket lands at 0 feet after 60 seconds (30, 225); rocket reaches maximum height of 30 feet after 225 seconds (60, 0); rocket reaches 60 feet after 0 seconds

Diana has 160 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?

A ball is inside a glass case in the shape of a cube. The diameter of the ball and length of the glass case are both 3.4 cm. What is the volume of the air outside the ball that is inside the glass case? Use the π button on your calculator.

What property or identity is described in each of the following? A) If 17+0=17, then 0+17 = 17 B) 17(0) = 0 C) If 17.0=0, then 0-17 = 0 D) If (1+17) +2= 20, then 1 + (17+ 2) = 20

Mark owns a lawn service company. He used the function f(t) = 10t + 25 to determine the cost in dollars of his services where t is the time, in hours, he spent mowing. How much will Mark charge for working 2.5 hours?

A paddle for adults costs $10 more than a paddle for kids. The boating center bought 4 of each type of paddle. The total cost was $312. What was the total cost for 4 adult-sized paddles?

A semi-ellipse-shaped gate has a maximum height of 20 feet and a width of 15 feet, both measured along the center. Can a truck with a height of 12 feet and a width of 16 feet with a load and 10 feet without a load pass through the gate? A. Yes, It can pass either with or without the load. B No, it can't pass with or without the load. C Yes, it can pass without the load. D. It depends on the foci of the semi-ellipse.

Jamal calculates the mean and standard deviation of a data set of the salaries of 10 employees. He then calculates the mean of the salaries after each employee receives a pay increase of $2,000. Which statement is true? The mean of the new data set decreases. The mean of the new data set increases. The mean of both data sets stays the same. There is not enough information to know how the mean will change.

Each statement describes a transformation of the graph of the parent functiony = x². Which statement correctly describes the graph of y=(x-4)² +5? A. It is the graph of y=x² translated 4 units down and 5 units to the right B. It is the graph of y=x² translated 5 units down and 4 units to the left C. It is the graph of y=x² translated 5 units up and 4 units to the right D. It is the graph of y=x² translated 5 units up and 4 units to the left.

A large random sample of soda cans found that the volume of soda in a can had a normal distribution with a mean volume of 12 fl oz of soda and a standard deviation of 0.11 fl'oz. Based on this, what percent of soda cans would have a volume less than 11.8 fl oz? Use the standard normal table to look up the percent. Put your answer in percent form, and round to two decimal places. Do not include the percent symbol.

During a 5-year period of constant inflation, the value of a $113,000 property increases according to the equation v= 113,000 e 0.04t dollars. In how many years will the value of this building be double its current value?

Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 a month plus $0.01 per copy. Which equation can be used to find the number of copies, c, both companies need in order to charge the same amount? 0.05c+ 600 = 0.01c + 300 0.05c-300= 0.01 + 600 0.05c + 300 = 0.01c + 600 0.05c+0.01c = 300 + 600

In an IB school 47 students study biology, 53 students study chemistry and 34 students do not study either of these two subjects. There are 109 students in this school. A student is selected at random. Given that this student does not study chemistry, find the probability that he/she studies biology. Give an exact answer as a fraction in fully simplified form or an approximate answer as a decimal rounded to three significant figures.

Write a polynomial, P(x), in factored form given the following requirements. • Degree: 5 • Leading coefficient 1 • x-intercepts at (1, 0), (-9, 0), (2, 0) and (-2, 0) • y-intercept at (0, -180)

An object is launched straight up from the ground with an initial velocity of 80 feet per second. The height is found using the equation below. At how many seconds will the height be at 64 feet? h = - 16t² + 80t 1 second and 4 seconds 2 seconds 3 seconds and 6 seconds 5 seconds

graph the solution of the system of linear inequalities. X≤8 y≥-7

In an effort to reduce global warming, it has been proposed that a tax be levied based on the emissions of carbon dioxide into the atmosphere. Suppose the cost-benefit equation In (1-P)= -0.0038 -0.0054t estimates the relationship between the percent reduction of emissions of carbon dioxide P (as a decimal) and the tax t in dollars per ton of carbon dioxide. Use this information to answer parts (a) and (b) a. Solve the equation for t, giving t as a function of P. Graph the function. t= (Do not simplify. Type an exact answer. Use integers or decimals for any numbers in the expression.)

A jar is filled with black pebbles, white pebbles, and jade pebbles. The number of jade pebbles is greater than half the number of black pebbles, and the number of white pebbles is less than twice the number of black pebbles. If there are 32 jade pebbles in the jar, what is the maximum number of white pebbles that could be in the jar?

A collector bought a rare coin for $30. The coin is now valued at $37.50. Select all the true statements. The scenario represents a percent increase. The scenario represents a percent decrease. The percent of change was 20%. The percent of change was 25%. The percent of change was 75%.

Nicole accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Nicole's salary will be $100000 and after working for the company for 5 years, she will have a salary of $110000. Write an equation for S, in terms of n, representing Nicole's salary after working n years for the company. Answer S=

A banquet hall has a maximum seating capacity of 168 people. For a particular event, the banquet manager must use an arrangement of short tables and long tables to ensure that there is enough seating to meet that capacity. Each short table seats 4 people and each long table seats 8 people. If no more than 32 tables can be placed inside the banquet hall, what is the maximum number of short tables that can be used? A) 10 B) 14 C) 18 D) 22

A gardener makes a new circular flower bed. The bed is fourteen feet in diameter. Calculate the circumference and the area of the circular flower bed. circumference =14 π feet, area = 196π square feet circumference = 7 π feet, area = 49 π square feet circumference = 14π feet, area = 49π square feet circumference = 14 π feet, area = 14л square feet

A German shepherd puppy weighed 25 pounds at 4 months old and 31 pounds at 5 months old. What is the percent increase or decrease of its weight? A 24% increase B 35% decrease C 35% increase D 54% decrease

A three-dimensional figure has the following properties: * It has a circular base. * It has a second, circular base parallel to the first, with a round smooth face between them. What kind of solid is it? sphere cone cylinder rectangular prism

Maria has a jewelry box and wants to increase its size. She decides she will double the length, width and height. How many times bigger will the volume of the new box be?

Solve csc(4x)-3 = 0 for the four smallest positive solutions x = Give your answers accurate to at least two decimal places, as a list separated by commas

A certain bran of razor blades comes in packages of 6, 12, and 24 blades. costing $2, $3, and $4 per package, respectively. A store sold 12 packages containing a total of 162 razor blades and took in $35. How many packages of each type were sold?

A stack of nickels has a mass of 45 grams. There are 9 nickels in the stack. What is the mass of one nickel?

Find the value of c that will allow you to solve by completing the square. x²-8x-7=8 4 16 -16 2 -2

A body moves on a coordinate line such that it has a position s= f(t)=t²-6t+5 on the interval 0 ≤t≤9, with s in meters and t in seconds. a. Find the body's displacement and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval. c. When, if ever, during the interval does the body change direction?

A license plate is to consist of 3 letters followed by 3 digits. Determine the number of different license plates possible if the first letter must be an K, L, or M and repetition of letters and numbers is not permitted. 162,000 9,072,000 1,386,000 1,296,000

A population of rabbits oscillates 150 above and below an average of 720 during the year, hitting the lowest value in January (t = 0). a. Find an equation for the population, P, in terms of the months since January, t. b. Find an equation if the lowest value of the rabbit population occurred in March (instead of January).

Jake and his friends went to the Dye Storm paint-tag course to celebrate the end of the school semester. The course charges $36 for an hour of group tag plus a rental fee for each paint marker. Jake's group played for one hour, rented 5 paint markers, and paid a total of $86. How much did it cost to rent each paint marker?

The number of violent crimes committed in a day possesses a distribution with a mean of 1.7 crimes per day and a standard deviation of four crimes per day. A random sample of 60 days was observed, and the sample mean number of crimes for the sample was calculated. The data that was collected in this experiment could be measured with a random variable. continuous discrete

After riding a bicycle at a steady speed for 40 miles, John had a flat tire and walked 5 miles to a repair shop. His cycling rate was 4 times faster than his walking rate. If the time spent cycling and walking was 5 hours, at what rate was the cyclist riding?

Harry is making bouquets of balloons. He makes the bouquets so that 2 out of every 5 balloons are red. Which equation correctly compares the number of balloons he uses, x, to the number of red balloons, y?

A triangle, Δ ABC, has angle measures of 45°, 45°, and 90° and two congruent (equal) sides. How would this triangle be classified? Isosceles acute Scalene acute Scalene right Isosceles right

Evaluate the following logarithms. (a) log 9 (b) In 56 (c) log 69,790

A real estate agent works on a 11 % commission. What is her commission on a house that she sold for $657,300? Follow the problem- solving process and round your answer to the nearest cent, if necessary.