Basic Math Questions and Answers

Find the x-intercepts and y-intercept of the following function. f(x) = (x-6) (x − 3) (4x + 4) Write your answer in coordinate pairs of the form (x, y))

A photographer takes an average of 15 pictures per session. The total number of pictures p(s) is a function of the number of sessions s. a. Identify the independent and dependent variables. b. What values of the domain and range make sense for this situation? Explain. c. Write a function to represent the total number of pictures taken. Then determine the number of pictures taken in 22 sessions.

A total of 330 children and adults attended a school play. There were 21 times as many children in attendance as there were adults. This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children. c=21a a+c=330

A recreation the summer. On the first day of the offering, a family paid $96 for 4 pool passes and 2 gy memberships. Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership. She paid $72. 1. Write a system of equations that represents the relationships between pool passes, gym memberships, and the costs. Be sure to state what each variable represents.

Mr. Lings has a plank of wood 118 inches long. He cuts it into two pieces such that the longer piece is 5.5 inches longer than twice the length of the shorter piece. What is the length of the longer piece? 37.5 inches 59 inches 80.5 inches 56.25 inches

A study shows that 77% of the population was vaccinated against the Venusian flu but 2% of the vaccinated population got the flu anyway. Of the total population, 12% got this flu. Let V be the event that a person was vaccinated. Let F be the event that a person gets the flu. Compute the following values. P(V) = P(F) = P(V∩F) P(V∪F) What percentage of the population either got the vaccine or got the disease?

The polygon below was a square with 20-meter sides before a triangle was removed. What is the new perimeter of the polygon, in meters? F. 66 G. 70 H. 76 J. 78 K. 80

A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays, the appointment times are 15 minutes. On Wednesdays and Thursdays, they are 30 minutes. On Fridays, they are one hour long. The doctor works for no more than 8 hours a day. Here are some inequalities that represent this situation. 0.25 ≤ y ≤ 1 7≤x≤ 12 xy ≤8 a. What does each variable represent? b. What does the expression xy in the last inequality mean in this situation?

Diana has 120 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?

In a certain country, approximately 24 out of 100 people over the age of 12 smoke. How many smokers would you expect in a group of 550 people over the age of 12?

Find the remaining five trigonometic functions of θ. cot θ = 12/5, sin θ >0 Complete the following table. sin θ = cos θ = tan θ = csc θ = sec θ = cot θ = 12/5

In a product liability case, a company can settle out of court for a loss of $350,000, or go to trial, losing $800,000 if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-guilty verdi be 0.8. Complete parts (a) through (b) below.

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equation dependent. -9x - 6z = 19 x - 3y = 35 Select one: a. {(0, -18, 16)} b. {(-19/2,2,0)} c. {(-3,2,4)} d. {(-3,-38/3, 4/3,)}

Choose the correct expression equal to sin x. A. sinx= ± √1- cos x B. sinx= 1/1- cos x C. sinx=(1- cos x)(1+ cos x) D. sinx= ± √1- cos^2 x

Diana has 440 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 right circular cone is shown. The base of the cone is a circle with the center at point A. The distance from point A to point C is 16 inches. The distance from point to point B is 20 inches. What is the diameter, in inches, of the base of the cone?

It has been said that newspapers are disappearing, replaced by various electronic media. In 2001, newspaper circulation (the number of copies distributed in a day) in a country was about 58 million. In 2011, this ad dropped to 46 million. Assume that the relationship between time, x, and circulation, y, is a linear relationship. Write an equation describing the relationship between time and circulation. Use ordered pairs of the form (years past 2001, number of newspapers circulated in millions). Use this equation to predict newspaper circulation in 2015. The equation describing the relationship is type your answer in slope-intercept form. Use integers or decimals for any numbers in the equation.) million. In the year 2015, the newspaper circulation will be implify your answer. Type an integer or a decimal.)

The school that Imani goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 3 child tickets for a total of $69. The school took in $91 on the second day by selling 5 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?

Solve the system by the method of your choice. x²+2y² = 36 x+y = 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an ordered pair, using integers or simplified fractions for the coordinates. Use a comma to separate answers as needed.) B. There is no solution.

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

The area of a parallelogram is 18 square units. One side of the parallelogram is 24 units long. The other side is 6 units long. Which could be the parallelogram's height? Select all that apply. A 3/4 units B 4/3 units C 3 units D 4 units E 12 units

A 300. L kiln is used for vitrifying ceramics. It is currently operating at 1065 °C, and the pressure is 0.9250 atm. How many moles of air molecules are within the confines of the kiln?

Determine if the conclusion follows logically from the premises. All children are energetic. Some actors are children. Therefore, some actors are energetic. Valid argument Invalid argument All flowers need water. Roses need water. Therefore, roses are flowers. Valid argument Invalid argument

When factoring, which of of the following is the rule we follow? We just guess until we get something that works. We find what multiplies to "c" and adds to "b" We find what multiples to "a" and adds to "b" We find what multiples to "b" and adds to "c"

Describe and correct the error a student made when graphing y +5=-3/4(x-8)

Find the roots of the quadratic function: f(k)= 2k² - 3k - 9.

Graph the line through the point (0, -3), having a slope of 3/4

The mathematics faculty at a college consists of 4 professors, 7 associate professors, 5 assistant professors, and 9 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor.

Supply a conclusion to make each argument valid. 1. All shrimp are appetizing. Tiger is a shrimp. Therefore, Tiger is appetizing. 2. All flowers smell good. All things that smell good are tasty. Therefore, all flowers are tasty. 3. No New Yorker likes pecan pie. All Southerners like pecan pie. Select an answer 4. All sailors are big spenders. No big spenders are miserly. Select an answer 5. All violets are blue. Some flowers are violets. Select an answer

A company found that an experienced surveyor can survey a roadbed in 5 hours. An apprentice surveyor needs 8 hours to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.

A figure containing STU is dilated by a scale factor of 2/3 to form a new figure which contains S'T'U'. STU measures 140°. What is the measure of S'T'U'?

Solve the system by the substitution method. x+y = - 12 y = - 4x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There are infinitely many solutions. C. There is no solution.

Maya arranges some tiles in different arrays. One array has 4 rows with 3 tiles in each row. The other array has 2 rows with 6 tiles in each row. Maya says that she can use the Commutative Property of Multiplication to show that the arrays both have 12 tiles. Is she correct? Explain.

A ferris wheel is 15 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? What is the Midline? y = What is the Period? How High are you off of the ground after 4 minutes?

Kimani plans to paint the background of a mural on a wall in her school's cafeteria. The mural will be in the shape of a parallelogram. One quart of paint covers 100 square feet. How many quarts of paint does Kimani need? Show your work.

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.