Basic Math Questions and Answers

Write the algebraic expressions described by the following English phrases. Use the variable name "x" to describe the unknown. 1. a number less than six 2. a number less six

While shopping, Edna noticed that three different pancake mixes indicated that they were the best value for the price. She also noticed that all three packages cost the same amount. She wanted to know how they could all be the best value if they all cost the same. So, she decided to do a comparison of the mixes. Package A claims it makes 10 pancakes with a diameter of 6 inches. Package B claims it makes 25 pancakes with a radius of 2 inches. Package C claims it makes 50 pancakes with a circumference of 6.28 inches. Based on the total pancake area, order the packages from most valuable to least valuable. Assume all three types of pancakes have the same thickness. Use 3.14 for π.

Triangle ABC is congruent to triangle XYZ. In ΔABC, AB 12 cm and AC 14 cm. In ΔXYZ, YZ 10 cm and XZ = 14cm. What is the perimeter of ΔABC? 36 cm 38 cm 40 cm 50 cm

A certificate of deposit is worth P(1 + r)^2 dollars after years, where r is the annual interest rate expressed as a decimal, and P is the amount initially deposited. Which investment will be worth more? Investment A, in which P = $7200, r= 4%, and t = 5 years or investment B, in which P = $6100, r = 6%, and t = 7 years. Round your answers to two decimal places. The value of the certificate for investment A will be ,and the value for investment B will be

Use the quadratic formula to solve the equation. Be sure to simplify your answers. Enter both answers separated by a comma. x² - 8x + 10 = 0 For example, if x = -5± √15 / 4 you enter (-5-sqrt(15))/4 on the left and (-5+sqrt(15))/4 on the right. Note the important placement of parentheses! Use the PREVIEW button! X =

Hattle has recently inherited $8100, which she wants to deposit into an IRA account. She has determined that her two best bets are an account that compounds quarterly at an annual rate of 3.9 % (Account 1) and an account that compounds daily at an annual rate of 5.1% (Account 2). Step 2 of 2: How much would Hattie's balance be from Account 2 over 3.4 years? Round to two decimal places.

11) Jeff owns a watch repair shop. He has found that the cost of operating his shop is given by C (x) = 2x² - 108x+87, where C(x) is the cost and x is the number of watches repaired. How many watches x must he repair to have the lowest cost? 12) Ella works at Wendy's. On Monday she sells 15 fries and 10 burgers totaling $65.00. On Tuesday she sells 30 fries and 5 burgers totaling $77.50. How much does each burger cost?

Divide. 300√3619 Select the correct choice below and fill in any answer boxes in your choice. A. The quotient is B. The quotient is C. The quotient is undefined.

A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 72 in² and a perimeter of 34 in. Find the dimensions of the brochure. The longer side is in. The shorter side is in. (Type exact answers, using radicals as needed. Simplify your answers.)

A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 25 cm. (HINT: The altitude to the 25-cm side has length 12 cm.)

You own a home that was recently appraised for $390,000. The balance on your existing mortgage is $125,450. If your bank is willing to loan up to 70% of the appraised value, what is the potential amount (in $) of credit available on a home equity loan?

Divide. 91,900/21 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The quotient is B. The quotient is C. The quotient is undefined.

The revenue function is given by R(x) = x - p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x) = 42(4)^-s/4, find the revenue if 12 units are sold. Round to two decimal places.

Eva invests $8000 in a new savings account which earns 4.8% annual interest, compounded semi-annually. What will be the value of her investment after 7 years? Round to the nearest cent.

The volume, V, of a cylinder whose radius is 10 times its height is given by V = 1/10 πr³, where r is the radius. (a) Identify the coefficient and exponent of this power function. NOTE: Enter the exact answers. The exponent is The coefficient is (b) If the radius is 11 cm, what is the volume? NOTE: Enter the exact answer. (c) If the height is 0.9 cm, what is the volume? NOTE: Enter the exact answer.

Write true or false for the statement. {b, h, j, k} = {j, k, h, b} Choose the correct answer below. False True

The human resources director for a commercial real estate company received the following numbers of applications from people with the information given to the right. Use a Venn diagram to answer parts (a) through (d). **** (a) How many applicants were there? applicants (b) How many applicants did not have sales experience? applicants (c) How many had sales experience and a college degree, but not a real estate license? applicants (d) How many only had a real estate license? applicants 63 with sales experience 38 with a college degree 28 with a real estate license 22 with sales experience and a college degree 18 with sales experience and a real estate license 14 with a college degree and a real estate license 12 with sales experience, a college degree, and a real estate license 25 with neither sales experience, a college degree, nor a real estate license

Write the expression as a constant times a power of the variable, and state the base, exponent, and coefficient 2πα + 2πα NOTE: Enter your answers exactly. The expression is The base is The exponent is The coefficient is

The population of a certain inner-city area is estimated to be declining according to the model P(t) = 221,000e^-0.021t, where t is the number of years from the present. What does this model predict the population will be in 4 years? Round to the nearest person.

You and a friend are playing horseshoes on a very uneven lawn. You both throw a horseshoe toward a stake in the ground. Think of the point where the stake enters the ground as the origin. Your horseshoe lands 2.3 feet east of the origin, 1.5 feet north of the origin, and 0.5 feet below the origin. Your friend's horseshoe lands 1.7 feet west of the origin, 2.5 feet north of the origin, and 0.5 feet above the origin. What is the distance between the horseshoes? √17 feet 3√ √2 feet √33 feet 6 feet

Pizza House offers 5 different salads, 7 different kinds of pizza, and 4 different desserts. How many different three course meals can be ordered? How many different meals can be ordered?

What is the probability of winning a lottery in which you must choose 6 numbers from the numbers 1 through 12? a. Assuming that order is unimportant. b. Assuming that the order matters.

David runs a small hotel with single and double room accommodations. Each single room costs $69 per night, and each double room costs $89 per night. David's nightly revenue goal is $1,000, and there are more single rooms than double rooms occupied on any given night. Which of the following is a possible description of the hotel occupancy on a night that David meets his goal? A. Tuesday: 5 single rooms and 8 double rooms occupied B. Sunday: 12 single rooms and 20 double rooms occupied C. Wednesday: 8 single rooms and 4 double rooms occupied D. Saturday: 15 single rooms and 10 double rooms occupied

Two people across the street from each other each put a hook below a window facing the street so that a banner can be hung from the hooks. One of the hooks is 104 ft. east and 20 ft. north from the street corner. It is hung at a height of 32 ft. The other hook is 4 ft. west and 22 ft. north from the same street corner. It is hung at a height of 35 ft. What is the distance between the hooks? Round your answer to the nearest foot. 100 ft. 108 ft. 127 ft. 134 ft.

A window is in the shape of a square with a semicircle on top. If the side of the square is I feet long then the area of the glass sheet in the T window is A = l² + π/2 (l/2)² 2 ft². (a) Is A a power function of l? Select an answer from the drop-down and, if so, enter the coefficient k and exponent p in the boxes that appear. (b) Without computing the area, say whether the area is larger when 1 = 3.5 feet or when l = 4.5 feet.

The radius of the wheel on a car is 19 inches. If the wheel is revolving at 421 revolutions per minute, what is the linear speed of the car in miles per hour? Round your answer to the nearest tenth.

Matthew wants to sell laptops and smartphones. He wants to sell at least 15 total devices and earn at least $4,800. L+S2 15 represents the number of laptops L and smartphones S Matthew should sell to achieve his goal of selling at least 15 devices. 425L+125S>4, 800 represents the number of laptops and smartphones he can sell to earn at least $4,800. If Matthew is only able to sell 4 laptops, the minimum number of smartphones must he sell in order to meet both of his goals is

Is the point (1, 2) a solution to the inequality y< -x+2?

Determine whether the two given events are independent. A pair of dice are rolled. The events are "odd on the first" and "even on the second." The two events are

Express all solutions in exact form. log8 (x + 2) + log8 (x+4)= log8 8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Type an exact solution, using radicals as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.

Consider the expression 5b + 3c - 20 + 3b - 15c +4. Part A Simplify the expression. Part B Factor the simplified expression using the GCF. Part C What is the value of the expression when b = 2 and c= -3?

The price of nails is $1.29/lb, the price of washers is $0.79/lb, and the price of bolts is $2.39/lb. Write an expression to represent the total price of n pounds of nails, w pounds of washers, and b pounds of bolts. What is the total cost of buying 2 pounds of nails, 4 pounds of washers, and 3 pounds of bolts?

Use the product rule to simplify the expression. Write your answer in exponential notation. (-6x²)(3x³) Select the correct choice below and fill in any answer boxes within your choice. A. (-6x²)(3x^8) = (Type exponential notation with positive exponents. Simplify your answer) B. The product rule does not apply.

Which of the following best describes the solution to the system of equations below? 3x+6y=10 9x + 18y=30 A. The system of equations has exactly one solution where x = 10/3 and y = 0. B. The system of equations has infinitely many solutions. C. The system of equations has exactly one solution where x = 1 and y = 3/2 D. The system of equations has no solution.

A good example of a positive sanction for conformity is which of the following: Caning Cash Spanking Waterboarding

A sum of $1000 is invested at an interest rate of 4% per year. Find the time required for the amount to grow to $4000 if interest is compounded continuously.

A rectangular auditorium seats 2408 people. The number of seats in each row exceeds the number of rows by 13. Find the number of seats in each row.

Follow the method in Step 1 to determine if the third expression is a perfect square trinomial. The first term and the third term of the third trinomial, h² - 13h + 36, are perfect squares. h² = (h)² 36 = (6)² Because the h-term is negative, if the trinomial is a perfect square, then it is the square of a binomial difference. Find the square of the binomial formed by the difference of the square roots of the perfect squares, (h - 6)². You can use the distributive property to square the binomial. Or you can use the rule for squaring a binomial difference, (a - b)² = a² - 2ab + b², with a = h and b = 6. Compare the original trinomial to the square of the binomial. (h-6)² = (h-6)(h-) =h² - (2)(h) ( ) + (6)² = h² - h + 36

When solving equations using the method of successive approximations, multiple iterations are performed. An approximate solution from three iterations is always an approximate solution from two iterations.

At the Pizza Dude restaurant, a 12-in. pizza costs $3.40 to make, and the manager wants to make at least $2.20 from the sale of each pizza. If the pizza will be sold by the slice and each pizza is cut into 6 pieces, what is the minimum charge per slice?

Select the correct statement in the table. A landscape architect is ordering trees to plant in a park she is designing. The cost of each maple tree is $40, and the cost of each birch tree is $60. Each maple tree requires 15 gallons of water per week, and each birch tree requires 10 gallons of water per week. The architect has a budget of $2,000 to spend on new trees for the park, and the trees must require no more than 400 gallons of water each week. Determine a system of linear inequalities to represent this situation, where x is the number of maple trees and yis the number of birch trees. Then, select the true statement about the system.

How much money does Barbara Mack owe at the end of 6 years if 7% interest is compounded continuously on her $1500 debt? Use the formula A = P ert to solve.

In the accompanying diagram, AB//CD and EF bisects AFG. m∠9 = 42°, find the measure of Each of the numbered angles.

9. (a) Let θ be an angle in standard position. Name the quadrant in which the angle θ lies given that sin θ <0 and sec θ < 0. (b) Let θ be an angle in standard position. Name the quadrant in which the angle θ lies given that cos θ <0 and csc θ > 0.

Samuel is hired at a small sales company. His monthly pay is calculated by the equation P= 150s + 500. s = the number of sales P = Samuel's pay in dollars. Which of the following statements are true? There may be more than one correct answer. Samuel earns a base salary of $500 each month. Samuel earns a base salary of $150 each month. Samuel earns $500 for each sale he makes. Samuel earns $150 for each sale he makes. The vertical intercept is (0, 150).

Completely factor the following polynomial: 90y² + 210y + 490. Factor out the greatest common factor (GCF) of the coefficients.

A. Write the following as whole numbers or decimals, without words. 3.2 thousand 26 thousand 14.5 million a rate of 85 per thousand a rate of 782 per million B. Find the square root of each number, to three decimal places, using your calculator: 0.91 0.452 C. There are two solutions to each of the following equations. What are they? x² = 25. x² = 0.64 x² = 0.0289

Find an approximate irrational solution to 2x = 3. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is {}. (Round to four decimal places.) B. The solution is the empty set.

A guitar factory has a cost of production C(x) = 75x + 50,000. If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar, and write the revenue function.

Divide. 7√1862 Select the correct choice below and fill in any answer boxes in your choice. A. The quotient is with no remainder. B. The quotient is with remainder C. The quotient is undefined.