Basic Math Questions and Answers

Use a transformation of the graph of y=x4 to graph the function. f(x) = (x+2)4 Which transformation is needed to graph the function f(x) = (x + 2)4? Choose the correct answer below. A. The graph of y=x4 should be shifted vertically up 2 units. B. The graph of y=x4 should be shifted horizontally left 2 units. C. The graph of y=x4 should be shifted vertically down 2 units. D. The graph of y=x4 should be shifted horizontally right 2 units.

An object is dropped from a tower, 163 ft above the ground. The object's height above ground t sec into the fall is s=163-161². a. What is the object's velocity, speed, and acceleration at time t? b. About how long does it take the object to hit the ground? c. What is the object's velocity at the moment of impact?

plot the intercepts to graph the equation. 3x-6y=-6

Solve the system by the method of your choice. x²+2y² = 324 x+y = 18

A pencil cup with a capacity of 40 in.3 is to be constructed in the shape of a rectangular box with a square base and an open top. If the material for the sides costs 12¢/in.² and the material for the base costs 49¢/in.2, what should the dimensions of the cup be to minimize the construction cost (in ¢)? Round your answer to two decimal places, if necessary.

A rectangular picture frame measures 20 cm by 30 cm. A matte is made of uniform width to go inside the frame and make a nice border for the picture. The area of the matte is to be equal to the area of the picture. What is the width of the matte?

Every week at the Cougar Scouts meeting, Jenna is in charge of the craft activity. This week, she decides to make pinecone bird feeders. At the meeting, Jenna divides a bag of birdseed evenly among 15 Cougar Scouts, and each scout gets 1/3 of a cup of birdseed. Use an equation to find the amount of birdseed in the bag .

A plane can fly 1260 miles in the same time as it takes a car to go 420 miles. If the car travels 120 mph slower than the plane, find the speed of the plane. Using r as your variable to represent the speed of the plane in miles per hour, write an equation using the information above that can be solved to find the answer to this problem.

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. 0.01x -0.02y = 0.006 0.03x -0.04y = 0.06 Select one: a. {(-4.8, -2.1)} b. {(4.8, 2.1)} c. { }; The system is inconsistent. d. {(x, y) 1 0.01x -0.02y = 0.006); The equations are dependent.

The famous iris dataset (the first sheet of the spreadsheet linked above) was first published in 1936 by Ronald Fisher. The dataset contains 50 samples from 3 iris species: setosa, virginia, and versicolor. Four features are measured, all in cm: sepal length, sepal width, petal length, and petal width. What is the equation for the least square regression line where the independent or predictor variable is petal length and the dependent or response variable is petal width for iris setosa?

5 1/4 yards of ribbon cost $9.17.

Jim began a 209-mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 9 hours. If Jim walks at a rate of 3 miles per hour and rides at 31 miles per hour, find the amount of time he spent on the bicycle.

A car travels 292 miles in the same time that a motorcycle travels 252 miles. If the car's speed is 10 miles per hour more than the motorcycle's, find the speed of the car and the speed of the motorcycle.

For log430, (a) Estimate the value of the logarithm between two consecutive integers. For example, log2 7 is between 2 and 3 because 2² <7<2³. (b) Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. (c) Check the result by using the related exponential form.

Of the cartons produced by a company, 8% have a puncture, 5% have a smashed corner, and 0.8% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed comer.

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