Math Questions

Manny is deciding between two packages of yogurt. YoFruit costs $4.48 for 16 ounces. Yummy Yogurt costs $2.64 for 8 ounces. How much more does Yummy Yogurt cost per ounce? per ounce

Dakota and Justine are training to be in the Sweat for Fun Run. They ran the same distance on Saturday, but Dakota finished in less time. They each plan to run for the same amount of time on Sunday. If their average speeds are consistent, who will run farther on Sunday?

Exponential models and applications The number of bacteria in a culture is given by the function n(t) = 960e0.25t where t is measured in hours. (a) What is the relative rate of growth of this bacterium population? Your answer is percent (b) What is the initial population of the culture (at t=0)? Your answer is (c) How many bacteria will the culture contain at time t=5? Your answer is

Find a polynomial function f(x) with the given degree, zeros, and leading coefficient: Degree 4, x = - 3, multiplicity of 2; x = 1 multiplicity of 1; x = 3, multiplicity of 1 and a leading coefficient of 1. a) The factored form is: b) Find the polynomial equation in standard form.

Assume that a hypothesis test will be conducted using a significance level of a = 0.01 and null hypothesis Ho: μ = 21. Furthermore, assume that the following sample data will be used: n = 12, x-bar = 22.2, and s = 2.1 Find the p-value for the test. 0.9227 0.0478 0.0733 0.1466

Find the absolute maximum and absolute minimum values of f(t) = t√/9-t2 on the interval [-3, 3]. 1. Find the absolute maximum of f on the interval. 2. Find the absolute minimum of f on the interval.

On November 1st, Ben owes $500 on his credit card. On November 5th, Ben pays $60 towards the balance of the card. On November 12th, Ben makes $90 in purchases. On November 22nd, Ben pays $150 towards the balance of the card. The average daily balance of the card for the month of November is Question Help: Message instruct

The electromotive force V of an alternating current circuit at time t can be describe by the following function, where V is volts and t is in seconds. V(t) = 110sin (120) How many cycles will the circuit run through in 1 minute? 120 1320 1200 3600

A company observes the lifespan of 560 lightbulbs and finds that their data follows a normal distribution. What is the approximate number of light bulbs that fall within two standard deviations from the mean?

Change 648,951,239 to Roman numeral (Assume the Roman Numerals in blue have double bar over them and Roman Numerals in red have one bar over them) DCXLVIII CMLI CCXXXIX DCXLVIII MCLI CCXXIX CDCXLVIII CMLI COXXXXXIX DCCXLVII CMLI CCXIX

Convert the complex number 1 + 9i into polar form. Express the angle using degrees over the interval 0° ≤ 0 < 360°. You may round the argument to the nearest tenth of a degree (if necessary), but you must express your modulus in it's exact form.

The population of Washington has been decreasing exponentially since the major employer left town. After 8 years the population was 68,532 and after 9 years it was 65,791. Write an equation forp (t), the population of Washington, + years after the employer left town. Use the caret symbol (^) for exponents and the equation form: y = a(b)^x Use the variables: t = amount of time elapsed since the employer left town (years) P(t) = the population of the town after t years Round the base (constant multiplier/ratio) to the nearest hundredth. Use substitution to find an accurate initial value. Round the initial value to the nearest whole value. Do not use commas or spaces in your equation. Equation:

The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the clinder is decreasing at a rate of 4 meters per hour. At a certain instant, the base radius is 5 meters and the height is 8 meters. What is the rate of change of the volume of the cylinder at the instant? Recall that the volume of a cylinder is given by: V=πr²h B)-120 m³/hr C) 60 m³/hr D) - 80 m³/hr A) -60 m³/hr

Olivia's mom is ordering cupcakes for Olivia's birthday. A pack of 6 cupcakes from Baked Fresh costs $18. A pack of 12 cupcakes from Milk 'n' Creme Bakery costs $27.20. How much more does Milk 'n' Creme Bakery charge per cupcake?

A manufacturer claims that fewer than 6% of its fax machines are defective. To test this claim, he selects a random sample of 97 such fax machines and finds that 5% are defective. Find the P-value for the test of the manufacturer's claim. 0.1591 0.3264 0.1736 0.3630

A Global Positioning Satellite (GPS) system uses satellite information to locate ground position. Abu's surveying firm bought a GPS system for $12,500. The GPS depreciated by a fixed rate of 6% and is now worth $8600. How long ago did Abu buy the GPS system?

4. Identify which of the following is a permutation question a. If there are 120 students in grade 11, how many ways can a seating chart be made for a group of 18 of the students? b. If there are eight classrooms on a school floor and twenty desks in each classroom, how many desks are there to choose from to sit in? c. How many groups of 10 students can be selected out of a class of 32 students?

Solve the equation using the quadratic formula. x² + 10x + 24 = 0 The solution set is (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

The function f(x) = 34,000(1.05)* can be used to determine Noah's cost of living in Houston over time. What does the 1.05 represent? A The cost of living will increase by approximately 1% each year B The cost of living will decrease by approximately 1% each year C The cost of living will increase by approximately 5% each year D The cost of living will decrease by approximately 5% each year

In both videos, Sal uses the mathematical operation factorial. Evaluate the following factorial expressions, and watch this video if you need help. Note: the answers to (a) and (b) are different!

Find the absolute maximum and minimum values of f(z) = (x²+x)^2/3 over the interval [-2, 3]. absolute maximum is and it occurs at x = absolute minimum is and it occurs at x = Notes: If there is more than one z value, enter as a comma separated list.

The soccer team is selling sweatshirts to raise money to pay for their season fees. Each sweatshirt costs $20. The team has already raised $100. The team's goal is to raise at least $500. Write, solve, AND graph an inequality that will show how many sweatshirts(s) the team needs to sell to meet their goal. Show all of your work in the sketchpad or text box. Use both sketchpads if needed.

Solve the equation by factoring. 9x² +21x-8=0 The solution set is (Use a comma to separate answers as needed. Type each solution only once.)

Thirty students raised money by selling frozen pizzas. In total, 400 pizzas were sold. The teacher wants to raffle off a prize proportional to the number of pizzas each student sold. Describe a process that the teacher can use.

19% of all college students volunteer their time. Is the percentage of college students who are volunteers different for students receiving financial aid? Of the 350 randomly selected students who receive financial aid, 53 of them volunteered their time. What can be concluded at the a = 0.10 level of significance? Write hypothesis, give test stat and p-value. Write conclusions about HO and claim. Select the correct conclusion below: a) Students who receive financial aid volunteer as much as the other students. b) Students who receive financial aid does not volunteer at the same rate as other students,

For a sale, a store decreases its prices on all soccer equipment by 20%. A pair of shoes before the sale is $120. Which expression(s) represent the new price? Select yes or no for each. $120 - 0.2($120) $120 0.8($120) 0.8($120) 0.2($120)

Find the domain of the function. f(x) = x+8/x³-4x²-x+4 What is the domain of f? (Type your answer in interval notation.)

Let f(x)=8(x-4)2/3 +2. (A) Find all critical values and list them below. Note: If there are no critical values, enter 'NONE'. (B) Use interval notation to indicate where f(x) is increasing. Note: Use 'INF' for co, '-INF' for -oo, and use 'U' for the union symbol. Increasing: (C) Use interval notation to indicate where f(x) is decreasing. Decreasing: (D) List the values of all local maxima of f. If there are no local maxima, enter 'NONE' I values of local maximums = (E) List the values of all local minima of f. If there are no local minima, enter 'NONE'. values of local minimums =

Representing Proportional Relationships with Equations: Maya is interning at a law firm over the summer and is paid by the hour. her hourly wage is $56, write two equations to represent the proportional relationship between the wages she earns (w) and the number of hours (h): Start with the proportion: Then solve for one of the variables: Then solve for the other variable:

The function f(x)=x+4 is one-to-one. Find an equation for f-1(x), the inverse function. (Type an expression for the inverse. Use integers or fractions for any numbers in the expression.)

An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river. Write the equation for this ellipse.

A bag has 2 red balls, 4 blue balls, and 3 yellow balls. Two balls are taken out of the bag 1 at a time. Is each statement True or False? A The probability of drawing 2 blue balls is 1/3. True False B If the first ball drawn is red, the probability that the second ball is also red is 1/36. True False C The probability of drawing a blue ball and then a red ball is 1/9. True False

An observer standing on the top of a 360 ft cliff spots a boat at an angle of depression of 28°. How far is the boat from the base of the cliff? Round your answer to the nearest tenth. Distance from the base of the cliff =

In a board game, players take turns spinning a wheel with four spaces and values of $100, $300, $400, $800. The probability of landing on $100 is 4/9. The probability of landing on $300 is 2/9. The probability of landing on $400 is 2/9. The probability of landing on $800 is 1/9. What is the expected value of spinning the wheel once?

The unemployment rate in a city is 14%. If 7 people from the city are sampled at random, find the probability that fewer than 3 of them are unemployed. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

Two pools are being filled with water. To start, the first pool had 819 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 18 liters per minute. Water is being added to the second pool at a rate of 39 liters per minute. Let x be the number of minutes water has been added.

The probability that Gary and Jane have a child with blue eyes is 0.4, and the probability that they have a child with blond hair is 0. 25. The probability that they have a child with both blue eyes and blond hair is 0. 1. Given this information, the events blue eyes and blond hair are 1: dependent II: independent III: mutually exclusive (A) I, only (B) II, only (C) I and III (D) II and III

A lottery system uses six digits. The possible entries in these digits are the numbers 1, 2, 3, 4, or letters n, m, o, q, s, w, and z. The numbers or letters drawn can be repeated. What is the total number of lottery sequences that can be made? 823,543 1,771,561 1,000,000 121,745

Over time, the value of the property at 397 West Lake Street increased by 215%. If the initial value of the property was P, what expression represents the property's current value? Why? 315 P 215 P 3.15 P 2.15 P

There were 1200 teams competing in the first annual world math tournament. After each round, the number of teams are cut in half. a= a. Find the a and the b for this problem. b = b. Write the equation that models this situation. C. How many teams will be left after 4 rounds? d. How many teams will be left after 8 rounds? y =

Suppose that the concentration y(t) of glucose in the bloodstream satisfies the following differential equation, dy/dt =r-ky, where r and k are positive constants. Determine the concentration at any time t by solving the above differential equation. (a) y = 1+ Ce(r/k)t (b) y=t+Ce-(r/k)t (c) y = // + Ce(r/k)t (d) y = / + Ce-kt (e) y = C + e-kt

Convince me that the equation of an ellipse that has foci at (2,0) and (-2,0) and a major axis length of 6 has an equation of x^2/9 + y^2/5 = 1

Suppose the statement below is true: "John wen to the gym or John wen to the bank." What can be said about the statement J = John went to the gym. insufficient information false true justified

The cooking time for a mini-loaf of bread is 5 minutes longer than half the time it takes to bake a regular-sized loaf of bread. If it takes 25 minutes to bake a mini-loaf, how long does it take to bake a regular-sized loaf? 10 minutes 20 minutes 30 minutes 40 minutes

An empty ice cream cone has a height of 3.02 inches and a radius of 0.98 inches. What is the approximate volume of ice cream it will hold within the cone (not h over)? 3 in³ 1 in ³ 12 in³ 9 in³

Let P(t) = 30000 (1.03)t be the population of a town t years after the year 2000. Estimate in which year the population will reach 32782. Year =

The graph of the function f(x) = e-* - 5 can be obtained from the graph of g(x) = e² by one of the following actions: (a) reflecting the graph of g(x) in the x-axis; (b) reflecting the graph of g(x) in the y-axis; your answer is (input a or b) then, by one of the following actions: (a) shifting the resulting graph to the right 5 units; (b) shifting the resulting graph to the left 5 units; (c) shifting the resulting graph upward 5 units; (d) shifting the resulting graph downward 5 units; Your answer is (input a, b, c, or d) Is the domain of the function f(x) still ( Your answer is (input Yes or No) The range of the function f(x) is (A, ∞), the value of A is ∞, ∞)?

Jaquin hopes to earn $700 in interest in 3.6 years time from $28,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds semi-annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

Marsha gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.03 in change. Each pair of socks cost the same amount. What is the cost in dollars and cents for each pair of socks?

Solve the equation using the quadratic formula. 5x^2 = 2x+4