Math Questions

f(x)=x-1. Find the inverse of f(x). A. f^-1(x) = 1-x B. f^-1(x) = x C. f^-1(x) = x + 1 D. f^-1(x) = x −1

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

A certain culture of bacteria initially has 10 bacteria and is observed to double every 1.5 hours. a. Find an exponential model n(t) =n0*2¹/a for the number of bacteria in the culture after t hours. b. Estimate the number of bacteria after 35 hours. c. After how many hours will the bacteria count reach 10,000?

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

Let f (x) = 5x - 2. Describe the transformations from the graph of f to the graphs of g(x) = f(x - 5) and h(x) = f(x) +2. The graph of g is a of the graph of f. The graph of h is a of the graph of f.

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.

A pet store has 9 puppies, including 2 poodles, 2 terriers, and 5 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement, find the probability that Aaron selects a retriever, given that Rebecka selects a poodle. The probability is (Type an integer or a fraction.)

Let U = { 14, 15, 16, 17, 18, 19, 20}, A={17, 18, 19, 20). Use the roster method to write the set A'. A'= (Use a comma to separate answers as needed.)

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?

You are dealt one card from a standard 52-card deck. Find the probability of being dealt a card greater than 5 and less than 10. The probability of being dealt a card greater than 5 and less than 10 is (Type an integer or a simplified fraction.)

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

For an outdoor concert by the city orchestra, concert organizers estimate that 10,000 people will attend if it is not raining. If it is raining, concert organizers estimate that 3000 people will attend. On the day of the concert, meteorologists predict a 35% chance of rain. Determine the expected number of people who will attend this concert. Enter your answer in the space provided using number keys only.

Suppose Exam 1 has a normal distribution with mean = 78 and standard deviation = 14.9. Select one student at random, a. find the probability that the student got at least 90 on Exam 1. Write answer in 2 decimals. b. find the probability that the student got between 70 and 80 on Exam 1.

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.

For a segment of a radio show, a disc jockey can play 5 records. If there are 9 records to select from, in how many ways can the program for this segment be arranged?

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

Let Ln denote the left - endpoint sum u sing n subintervals and let Rn denote the corresponding right - endpoint sum. In the following exercises, compute the indicated left and right sums for the given functions on the indicated interval. L4 for f(x) =1/x²+1 on [-2, 2]. Write your answer to two decimal places.

Assume that cans of Coke are filled so that, the actual amounts have a mean of 12 oz and standard deviation of 0.14 oz. If a random sample of 40 cans of Coke is selected, hind the probability that the mean content is: a) At least 12.16 oz ? b) Less than 11.94 OZ

A farmer is growing a type of apple with a known mean weight of 0.3 lbs. and a standard deviation of 0.05 lbs. After looking through his orchard, he believes his apples might weigh less on average. He selects a random sample of 35 apples and finds the mean weight to be 0.28 lbs. Write null and alternative hypotheses to describe this situation.

The circle-shaped part of the necklace above has a diameter of 5 mm. The circumference of the circle-shaped part of each of the earrings is one-half the circumference of the necklace. What is the circumference of the circle-shaped part of one of the earrings? (Use 3.14 for .) A. 3.925 mm B. 7.85 mm C. 15.7 mm D. 31.4 mm

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

If h(x) = {(0, -9), (5,2), (8, -3), (10, 11)}, which set of ordered pairs represents the inverse of h(x)? A. ((0, 9), (-5,-2), (-8, 3), (-10, -11)} B. ((-9,0), (2, 5), (-3, 8), (11, 10)} C. {(9, 0), (-2,-5), (3, -8), (-11, -10)} D. ((0.-9), (5,2), (8, -3), (10, 11)}

If three people are selected, find the probability that all three were born in January. Write your answer as a fraction in simplest terms. The probability that all three people were born in January is

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.

The eccentricity of a hyperbola is defined as e = c/a. Find an equation of a hyperbola with vertices (1,-1) and (-5, -1) and e=5/3 The equation of the hyperbola is

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?

A small motorboat travels 15 mph in still water. It takes 2 hours longer to travel 69 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 15 + x = rate going downstream and 15 - x = rate going upstream.)(Round your answer to the nearest tenth.)

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?

The Earth's Orbit. The maximum distance of the earth from the sun is 9.3 × 10^7 mi. The minimum dis- tance is 9.1 x 10^7 mi. The sun is at one focus of the elliptical orbit. Find the distance from the sun to the other focus.

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.

Line A has a slope of -2/5 and passes through the point (2, 6). Line B has a slope of 1/3 and passes through the point (-33, -2). Find the point where line A intersects line B. A. x = -1, y = 8² B. I = -3, y = 8 C. I = 8, y = -3 D. I = 17, y = 0

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?

Kari is purchasing a home for $260,000. The down payment is 25% and the balance will be financed with a 15 year mortgage at 8% and 4 discount points. Kari made a deposit of $20,000 (applied to the down payment) when the sales contract was signed. Kari also has these expenses: credit report, $70; appraisal fee, $110; title insurance premium, 1% of amount financed; title search, $200; and attorney's fees, $500. Find the closing costs (in $).

A nursing student can be assigned to one of six different floors each day depending on staffing needs. How many different ways can she be assigned during a 4- day work week?

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.