Math Questions

Of the last 75 people who went to the cash register at a department store, 19 had blond hair, 21 had black hair, 30 had brown hair, and 5 had red hair. Determine the empirical probability that the next person to come to the cash register has red hair. 2/5 14/15 21/25 1/15 3/5 19/25

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.

The longer leg of a right triangle is 2 cm more than the shorter leg. The length of the hypotenuse is 4 cm more than the shorter leg. Find the length of the hypotenuse. Show your work and be sure to assign a variable. The length of the hypotenuse is 6 cm. The length of the hypotenuse is 8 cm. The length of the hypotenuse is 10 cm. The length of the hypotenuse is 2 cm.

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?

From the sample space S={1, 2, 3, 4,..., 15) a single number is to be selected at random. Given event A, that the selected number is even, and event C, that the selected number is a prime number, find P(CIA). P(CIA)= (Simplify your answer. Type an integer or a fraction.)

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.

Job Elimination In the past year, 15% of businesses have eliminated jobs. If 3 businesses are selected at random, find the probability that at least 1 has eliminated jobs during the last year. Round your answer to at least three decimal places. Do not round your intermediate calculations. P(at least 1 has eliminated jobs during the last year) =

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 telescope contains both a parabolic mirror and a hyperbolic mirror. They share focus F₁, which is 42 feet above the vertex of the parabola. The hyperbola's second focus F2 is 6 ft above the parabola's vertex. The vertex of the hyperbolic mirror is 3 ft below F₁. Find the equation of the hyperbola if the center is at the origin of a coordinate system and the foci are on the y-axis. Complete the equation.

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.

From the sample space S= {1, 2, 3, 4,..., 15) a single number is to be selected at random. Given event A, that the selected number is even, and event B, that the selected number is a multiple of 4, find P(A/B). P(A/B)= (Simplify your answer. Type an integer or a fraction.)

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.

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.