Basic Math Questions and Answers

Write √-27 in simplest radical form.

Factor the expression completely. 63x² +18

A candle that is 11 inches tall burns 1/4 inch every hour. A 13-inch candle burns 2/3 inch every hour. After how many hours will the candles be the same height? Round to the nearest hour.

Write √-200 in simplest radical form.

Write the explicit equation for the table of values. Please enter the answer in f (x) = mx + b x f(x)

While visiting Crimson Lake, Sally decided to go kayaking. The rangers charge $8.50 per hour in addition to a $25.00 deposit to rent the kayak. If she rented the kayak from 11:30 a.m. until 2:30 p.m., write and solve a linear equation to find the total cost to rent the kayak.

For a project in his Geometry class, Magan uses a mirror on the ground to measure the height of his school building. He walks a distance of 7.95 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 1.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.

You work as a nurse. One of your patients has a fluid limit of 20 ounces per day. Each IV bag contains 3 ounces of fluid. How many IV bags can the patient have in a day before going over his fluid limit?

If you want to earn 2% annual simple interest on an investment, how much should you pay for a note that will be worth $19,500 in 10 months? (Round your answer to two decimal places.)

The ratio of white socks to black socks in Terry's drawer is 4/5. Which of the following combinations could NOT be the actual numbers of white and black socks in Terry's drawer? A 25 black socks; 20 white socks B 35 black socks; 28 white socks C 24 black socks; 30 white socks D 15 black socks; 12 white socks

Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = x-4 s(x)=2x-6 Write the expressions for (r+s) (x) and (r-s) (x) and evaluate (r.s)(1).

Solve the quadratic by factoring. 5x² - 39x - 4 = 4

Given the polynomial function, f(x) = (x² + 2)(x + 5)(x-3)². Which statement must be true about this polynomial? A. It has 5 distinct roots that are all real numbers. B. It has 5 distinct roots that are real and complex numbers. C. It has 4 distinct roots that are all real numbers. D. It has 4 distinct roots that are real and complex numbers.

Fully simplify using only positive exponents. 4x²y/2x8y4

Ava is required to take at least 200 shots at basketball practice each week. During the first practice this week, Ava took 80 shots. She has three remaining practices this week, and she plans to take an equal number of shots at each of those practices. Let s represent the number of shots taken at each of the remaining three practices. a. Type an inequality to represent the situation. b. What is the smallest number of shots she needs to take at each of the remaining practices to meet the weekly requirement? The smallest number of shots Ava needs to take at each remaining practice is

Solve the quadratic by factoring. x² = 4x +32

You and a friend are heading to the movies. You each buy a ticket and you also want to buy some refreshments. The total cost of admission per person, a, is $7.50 and you spent $15.50 on refreshments. Write an expression to represent the total cost of the trip. Then, find the total cost. Total Cost: $

Which of the following is NOT true of the graph y = x³ - 6x² + 11x - 6? As x → ∞o, f(x) - -0. As x +∞o, f(x) → +00. For values of x > 3, the function will be positive. The graph will have no x intercepts.

A fan of trigonometry is building a right triangular pool in his backyard. The hypotenuse of the right triangle is 30 feet long and the height of the right triangle is 24 feet long. If the fan of trigonometry wants to purchase a pool cover, how many square feet of material should he purchase?

Suppose a part inside a computer chip has been measured to be 0.0000266m wide, 0.0000014m long and 0.000284m high. The part has the shape of a rectangular box. What is its volume? Write your answer in scientific notation.

A gas station sells regular gas for $2.10 per gallon and premium gas for $2.60 a gallon. At the end of a business day 290 gallons of gas had been sold, and receipts totaled $639. How many gallons of each type of gas had been sold?

The manager of a 90-unit apartment complex knows from experience that at a rent of $1500 per month, all units will be rented. However, for each increase of $30 ir[ rent, he can expect one unit to be vacated. Let x represent the number of $30 increases over $1500. Complete parts (a) through (e) below. (a) Express, in terms of x, the number of apartments that will be rented if x increases of $30 are made. (For example, with three such increases, the number of apartments rented will be 90-3=87.) The number of apartments that will be rented if x increases of $30 are made is 90-x. (b) Express the rent per apartment if x increases of $30 are made. (For example, if he increases rent by $90=3-$30, the rent per apartment is given by 1500+3 (30) = $1590.) The rent per apartment if x increases of $30 are made is 1500 + 30x. (c) Determine a revenue function R in terms of x that will give the revenue generated as a function of the number of $30 increases. A revenue function R in terms of x that will give the revenue generated as a function of the number of $30 increases is R(x) = -30x² +1200x + 135,000. (Simplify your answer.) (d) For what number of increases will the revenue be $142,680? The number of increases is (Use a comma to separate answers as needed.)

If the radius of a right circular cylinder is 4x and the height of the cylinder is 3y, which of the following represents the volume of the cylinder? 12π* 2y 24π* 2y 48π*2y 144π* 2y .

Find the second derivative of the function. (Simplify your answer completely.) g(x) = ex In x g" (x). = (Express your answer as a single fraction. Factor the numerator, if possible.

A farmer classifies his carrots as 'small', 'medium' or 'large'. His harvest follows a normal distribution, with a mean length of 15 cm and standard deviation 5 cm. If 18% of his carrots are classified as small, what is the longest carrot in the small classification? Give your answer correct to 3 significant figures.

Eric determines that the length of a bus journey is normally distributed with mean 20 minutes and standard deviation 5 minutes. He wants to calculate the probability that the journey lasts at least 25 minutes. Which of the following curves shows the area of the normal distribution he needs to determine?

Express the following fraction in simplest form, only using positive exponents. 3x10c10/-4(x³ c²)-4

A sun in a distant galaxy has an estimated Mass of 1.67216 x 1030 kg and the earth has a mass of 5.972 x 1024 kg, how many earths would it take to equal the mass of the sun? Write your answer in scientific notation. It would take earths to equal the mass of the sun.

The random variable X is normally distributed with mean µ = 7.4 and standard deviation o = 2.1. Find the value of k if P(X > k) = 0.32. Give your answer as a decimal, rounded to three significant figures.

A typical human red blood cell has an average diameter of 8.2 x 10-6m, while a typical human skin cell has an average diameter of 30 x 10-6m. How many times larger is the diameter of a skin cell than a red blood cell?

A group of adult males has foot lengths with a mean of 27.27 cm and a standard deviation of 1.15 cm. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 24.6 cm significantly low or significantly high? Explain. Significantly low values are cm or lower. (Type an integer or a decimal. Do not round.) Significantly high values are 0 cm or higher. (Type an integer or a decimal. Do not round.) Select the correct choice below and fill in the answer box(es) to complete your choice. The adult male foot length of 24.6 cm is significantly high because it is greater than (Type an integer or a decimal. Do not round.) The adult male foot length of 24.6 cm is not significant because it is between (Type integers or decimals. Do not round.) The adult male foot length of 24.6 cm is significantly low because it is less than (Type an integer or a decimal. Do not round.)

Use synthetic division to find the result when 2x4 - 10x³ + 16x² - 7x - 4 is r(x) 2. If there is a remainder, express the result in the form q(x) + b(x)* divided by x-2. If there is a reminder, express the result in form q(x) + r(x)/b(x)

Pocahontas received an 80.7% on the most recent French test. What fraction of the questions did Pocahontas answer correctly?

Simplify the expression to a + bi form: (12 - 9i)²

Factor the expression completely. 18x² - 3

Solve for all values of x by factoring. x²+x=2=0

You are a lumber jack. You are chopping down a tree that is 91 cm thick. Every time you pull the you cut through 2 cm of the tree. If 24 cm of the tree were already cut through when you started, how many pulls of the saw would be necessary for you to completely cut the tree down?

The wheels on Noah's bike have a circumference of about 5 feet. 1. How far does the bike travel as the wheel makes 15 complete rotations? 2. How many times do the wheels rotate if Noah rides 40 feet?

Junior is buying bags of grass seed and flower pots to do some work on his yard. Each bag of grass seed cost $23 and each flower pot cost $15. He has at most $120 total to spend on this project. As Junior is at the store shopping, he fills his cart with 3 bags of grass seed and 3 flower pots. Does he have enough money to purchase all the items in his cart? o Yes O No o Not enough information to determine

You are in charge of the marketing budget for a company. You have allowed a maximum budget of $10,000 for banners on various websites. It costs $600 to run a single banner for one year. How many banners can be run for one year without exceeding the maximum budget?

You are crossing a toll bridge. You currently have $40 on your toll pass and each crossing costs you $3. How many times can you cross the toll bridge without having to adding money to your toll pass?

Factor the expression completely. 80x² +50

A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 35,000 miles and a standard deviation of 2600 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?

Mr. Wells tells his class of 24 that when they have completed the assignment, they may play online math games. At the end of class, 40% of the class is playing online math games. Approximately how many students st need to complete their assignment?

A consonant digraph is two consonants together that stand for only one sound. A. Read the word. Circle the consonant digraph in each word. The consonant digraph may be at the beginning or the end of the word. 1. phone 3. chop 5. fish 2. whale 4. ring 6. thin

Let P(x) = x32 — x25 + x18x11 + x4 – x³ + 1. Which of the following are CORRECT ? Number of real roots of P(x) = 0 are zero. Number of imaginary roots of P(x) = 0 are 32. Number of negative roots of P(x) = 0 are zero. Number of imaginary roots of P(x) + P(-x) = 0 are 32.

John drove 138 miles in 3 hours. Use the formula d = rt, where d is distance, r is rate, and t is time, to find John's rate of speed in miles perhour. 135 miles per hour 46 miles per hour 0.02 miles per hour 414 miles per hour

Jacob is working two summer jobs, making $12 per hour washing cars and making $8 per hour landscaping. In a given week, he can work no more than 13 total hours and must earn a minimum of $120. Also, he must work no more than 10 hours washing cars and at least 3 hours landscaping. If a represents the number of hours washing cars and y represents the number of hours landscaping, write and solve a system of inequalities graphically and determine one possible solution.

Two mountain peaks are known to be 15 kilometers apart. A person located at a vista point such that a right angle is spanned when he looks from one peak to the other is told that the distances from the vista point to each peak differ by 3 kilometers. How far is the vista point from each mountain peak?

A flower shop sells two types of bouquets. Bouquet A consists of a dozen roses and some carnations. Bouquet B consists of a dozen peonies and some lilies. The price of one dozen peonies is 3 times the price of one dozen roses, as shown in the table. The cost of five Bouquets A is the same as the cost of two Bouquets B. What is the cost of a dozen roses?