Math Questions

A resistor and an inductor connected in a series network impede the flow of an alternating current. This impedance Z is determined by the reactance X of the inductor and the resistance R of the resistor. The three quantities, all measured in ohms, can be represented by the sides of a right triangle as illustrated, so Z² = x² + R². The angle is called the phase angle. Suppose a series network has an inductive reactance of X=400 ohms and a resistance of R = 1000 ohms. (a) Find the impedance Z. (b) Find the values of the six trigonometric functions of the phase angle .

Geneva has learned that the expected value of an Insurance payment to a driver to cover the costs of an accident in her state Is $5,200 over the first three years. If her Insurance costs $2,000 a year and the average cost of an accident Is $1,000, which statement is most correct? If Geneva drives more recklessly than most other drivers, the insurance is a good decision for Geneva. If Geneva drives more carefully than most other drivers, the insurance is a good decision for Geneva. Geneva knows she will certainly come out ahead and make money by paying for the insurance. Geneva knows she will certainly lose money by paying for the insurance.

Three hundred students submitted an essay In a nationwide essay contest. The best essay will win a $2,000 scholarship. Ten other students will be given a $1,000 scholarship. What is the expected value of an essay submission? $40 $0.04 $12,000 $1,500

Bob runs each lap in 7 minutes. He will run at most 12 laps today. What are the possible numbers of minutes he will run today? Use for the number of minutes he will run today. Write your answer as an inequality solved for t.

You are on a treasure-diving ship that is hunting for gold and silver coins. You reel in a wire basket that contains gold and silver coins, among other things. The basket holds no more than 50 pounds of material. Each gold coin weighs about 0.5 ounce, and each silver coin weighs about 0.25 ounce. You want to know the different numbers of each type of coin that could be in the basket. Write an inequality that models the weight in the basket. Give three solutions to the inequality you wrote above

Use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle θ. cos θ = 1/11

Suppose the probability of a pitcher throwing a strike (the probability of success) is 0.5. After how any pitches is a strike expected? 1 2 3 5

Describe how you know the difference between a binomial distribution and other probability distributions. Give an example of a scenario involving a binomial distribution not discussed in this lesson.

Solve 9t2 + 30t + 25 = 36 by using the square root method. Enter each solution in the box below as a reduced fraction or integer. If there is more than 1 solution, separate the values with a comma (example: -3, 2).

A relative has set up an account for you to have access to in 15 years. The account is at a bank which pays 2% interest and compounds quarterly. If the original amount placed in the account is $10,000, how much will be in the account after 15 years?

The critical numbers for the function f(x) = 2x³-21x² + 36x - 7 are: -

If a 43.08 gram piece of brass which has a specific heat of 0.38 J/gºC absorbs 1,979.56 J of energy, how much did the temperature change? Round your answer to 2 numbers after the decimal and include the correct units.

A building contractor receives a new contract to consider. From past experience, he estimates that there is a 40% chance of making a $400,000 profit, a 40% chance of losing $300,000 and a 20% chance of losing $250,000. What Is the contractor's expected profit or loss from this contract? $1000 $200,000 -$100,000 -$10,000

You were given a table with the cost of a hamburger In a town and the associated probability of each cost. You found the expected value to be $2.87. Which statement is correct? The average cost of a hamburger is $2.87. You found the expected value by adding up the costs, then dividing by the sum of the probabilities. There are more restaurants that sell a hamburger for $2.87 than there are for any other price. You know the price of a hamburger at every restaurant in town.

Ron makes soap balls and sells them at his local farmers' market. First, he uses a large cylindrical pot to mix and melt the ingredients. The pot has a diameter of 10 inches, and he fills it to a height of 10 inches. When everything is melted, he pours the liquid soap into small spherical soap molds that each have a radius of 1.5 inches. What is the maximum number of soap molds that Ron can fill completely using his soap mixture?

Find all real solutions of the equation (4j-1)² = 25. Write your answers as a list of integers or reduced fractions in the form A/B. For example, if your answers 2/3 are and 5, you would enter 2/3,5

Solve 25t2-64-0 by using the square root method. Enter the solution(s) in the box below as reduced fractions or integers. If there is more than 1 solution, separate the values with a comma (example: 11/7, 11/7). The solution set fort is

Consider the function f(x) = 1/16 x² + 2x + 4. What is the maximum approximation of the area under the curve of f on the interval [-1, 3] with four equal subintervals?

The quadratic equation is in factored form. y = − 1.1(x+6)(x − 7) What are the x-intrecepts for the graph of this equation? Enter the left-most intercept first: Enter the right-most intercept next:

A ferris wheel is 50 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? What is the Midline? y = What is the Period? How High are you off of the ground after 3 minutes?

Guests at a wedding have an appetizer choice of soup or a salad, an entrée choice of chicken, steak, or vegetarian, then a dessert choice of vanilla or chocolate cake. How many different meals are possible?

Consider a student loan of $15,000 at a fixed APR of 9% for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Acme Life Insurance charges $650 for a $1,000,000 life Insurance policy. Historical research shows that 1 In 11,000 policyholders will dle and the company is forced to pay out $1,000,000. On average, what is the expected profit of Acme Life Insurance per policy? $649.94 $591.00 $559.03 $62.01

Which of the following correctly describes expected value? the long-term mean of all possible outcomes in a probability distribution the probability distribution of the means of all outcome variables the set of all outcomes in a discrete variable set the first value in a variable set greater than one

In a certain city in Washington, the grass grows at the rate of 1/2 Inch a day on sunny days. On cloudy days, the grass grows at the rate of 1/4 Inch per day. In a typical July, 75% of the days are sunny and 25% are cloudy. Determine the total number of Inches of expected growth In a typical July. 0.43 inches 12.5 inches 15.5 inches 2.34 inches

How can you use a simulation to collect data for an event that has two possible outcomes that each have a probability of 0.5? Use a coin and let heads represent one outcome and tails represent the other outcome. Use a random number generator and let each number represent the different outcomes. Use a deck of playing cards and let number cards represent one outcome and let face cards represent the other outcome. Use a spinner with four sections and let one section represent one outcome and three sections represent the other outcome.

Consider the quadratic function f(x) = x² + 2x − 3. Determine the following: (enter all numerical answers as integers, fractions, or decimals): The smallest (leftmost) z-intercept is a = The largest (rightmost) -intercept is a = The y-intercept is y = The vertex is The line of symmetry has the equation

What is the estimate of the area under the curve of f using rectangular approximations and sample points on the interval [-1.5, 1.5]? Evaluate the function at: x = -1.3 on [-1.5, -1] x= -0.7 on [-1,0] x = 0.7 on [0, 1] x = 1.3 on [1, 1.5]

Solve the system algebraically. 5x + 3y = -3 x = 3y - 15

Jenny runs a daycare center and charges $60 per day for each child. There are currently 50 children enrolled at the daycare. At a recent conference, Jenny was advised to lower her rates in order to stay competitive in her area. For each price decrease of $4 per day, the number of children enrolled at the center increases by two. Write the equation that can be used to determine the number of price decreases, x, in dollars, for which the daycare center has a daily revenue of $2,800. A. (60-4x)(50 + 2x) = 2,800 B. (60-2x)(50 +4x) = 2,800 C. (60+ 2x)(50-4x) = 2,800 D. (60+4x)(50-2x) = 2,800

Consider the function f(x) = − 1/2x²+2x+8. What is the overestimate of the area under the curve of f using rectangular approximations on the interval [-2, 4] with three equal subintervals? Note: Round to the nearest whole number.

Michael uses a blend of dark chocolate and milk chocolate to make the ice cream topping at his restaurant. He needs to buy 100 kg of chocolate in total for his next order. Dark chocolate costs $12 per kilogram, milk chocolate costs $10 per kilogram, and he wants to spend $1120 total. Let d be the number of kilograms of dark chocolate he buys and m be the number of kilograms of milk chocolate he buys. Which system of equations represents this situation?

The owner of a radio station wants to determine how much airtime songs take up. The owner collects the song length in seconds of 10 population songs. The data are reproduced in the table below. Calculate the mode(s) using a TI-83, TI-83 plus, or TI-84 graphing calculator. 279, 219, 298, 134, 206, 293, 165, 227, 230, 212 There is one mode. The mode is 223. There is no mode. There are two modes. The modes are 134 and 298. There is one mode. The mode is 298.

An item is regularly priced at $95. It is now priced at a discount of 45% off the regular price. Use the ALEKS calculator to find the price now.

In a survey of 356 people who attended a local professional soccer team's most recent home game, 135 said that they were fans of the visiting team. Create a 95% confidence interval for the population proportion of attendees who were fans of the visiting team. Use a TI-84 (plus) calculator, rounding your answers to three decimal places.

A ferris wheel is 20 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? What is the Midline? y What is the Period? How High are you off of the ground after 4 minutes?

Sarah has two tests at school next week, a math test and a physics test. Let A represent the event that she passes her math test and B represents the event that she passes her physics test. If A and B are independent events with P(A) = 0.30. and P(A and B) = 0.21, find P(B). Give your answer as a decimal rounded to two decimal places.

Charlie has to carry 272 apples from a farm to the market. How many baskets will he need, given that each basket can hold 49 apples?

Describe how the change would affect the graph of f(x) = x². f(x) = x² + 2 If it is shifted to the left 4 units, you would write "left four" with no quotes. If it is compressed or stretched, write "compressed" or "stretched" with no quotes. If it is reflected over the x-axis, type "reflected" with no quotes.

The height of a right cylindrical can of peas is greater than the diameter of the base of the can. The can is sliced into two equal parts through its bases. Which of the following figures BEST describes the cross section of the cylinder? A. circle B. rectangle C. triangle D. semicircle

The amount of time it takes Emma to wait for the train is continuous and Uniformly distributed between 4 minutes and 11 minutes. What is the probability that it take Emma more than 5 minutes to wait for the train? 4/7 3/14 5/7 5/14 6/7

In a large city's recent mayoral election, 131,506 out of 309,153 registered voters actually turned out to vote. If 20 registered voters are randomly selected, find the probability that 7 of them voted in the mayoral election. Use TI-84 (plus) calculator to find the binomial probability. Round your answer to three decimal places.

Nathan drew a circle on a grid with a radius of 4 units and the point (2, -1) as its center. Which of the following pairs of coordinates represent points on the circle? A (2,-5) and (6, -1) B. (4,0) and (0,4) C. (8,-4) and (6, -3) D. (2, 3) and (-1, -1)

Which of the following is NOT a characteristic of all parallelograms? a) Diagonal bisect each other b) Diagonals are angle bisectors c) Opposite angles are congruent d) Opposite sides are congruent

The Business Entity Concept means A business is an important legal entity Businesses can be stand alone or combined The entity is an profit earning business The accounting for a business is separate from that of its owners or other businesses .

Your grandparents invested $1500 in a college fund paying 7.2% interest when you were starting first grade. a) What is the equation that you would write to represent this situation? (annual interest, not compounded continuously) b) If you don't pull any money out of the account, how much money will you have when you enter college? Show the equation you used to answer this question. c) If you don't pull any money out of the account, how long will it take to reach $5000? Show your algebraic work.

A new motorcycle costs $5500 and depreciates at a rate of 18 % each year. How many years will it be until the motorcycle is worth $1000? (round to the nearest 3 decimal places)

Pietro is planning a patio using paving stones that are circles, semicircles, and quarter-circles. All stones have a radius of 10 inches. What is the area of one pattern of stones that has 5 circles, 10 semicircles, and 100 quarter-circles? Then, select the total area. total area= 8,164 in² 5 circles = 1,570 in² total area = 10,990 in² 5 circles= 2,198 in² 10 semicircles = 1,570 in² 100 quarter circles= 2,826 in² 100 quarter-circles = 7,850 in² 10 semicircles= 2,198 in²

A person standing close to the edge on top of a 108-foot building throws a ball vertically upward. The quadratic function h(t) = − 16t² + 132t + 108 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? b) How many seconds does it take until the ball hits the ground?

Diane buys candy that costs $4 per pound. She will spend more than $20 on candy. What are the possible numbers of pounds she will buy? Use p for the number of pounds Diane will buy. Write your answer as an inequality solved for p.