Math Questions

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.

A cone and a cylinder have the same radius and height. The volume of the cone is 100m cubic feet. What is the volume of the cylinder?

Which classification describes the following system of equations? 5x+y+2z-13 4x+3y+6z=17 x+2y=4 inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent

If the Laffite family deposits $8,500 in a savings account at 6.75% Interest, how much will the account make after 25 years if it is compounded... a) monthly? b) weekly? c) continuously?

Your credit card company uses the Unpaid Balance Method. Determine the finance charge at the end of the month for the following of transactions. Assume the interest rate is 12%. Previous Balance: $275.48 New Purchases: $429.95 . Return Credit: $106.99 Payment: $200.00

Which line is perpendicular to the line y = −1/2 x - 5 and passes through the point (-3, 2)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = − 3/4 x + 1, you would type your answer as y=(-3/4)x+1

What is the sales tax on a jacket priced at $325 if the sales tax rate is 7%? The sales tax is $.

Use Newton's method to approximate a root of the equation 3 sin(x) = x as follows. Let x1 = 2 be the initial approximation. The second approximation 2 is and the third approximation is

A pyramid has a height of 5 inches and a volume of 60 cubic inches. Which of the following figures could be the base for this pyramid? Select all that apply. A. a right triangle with one side 5 inches and the hypotenuse 13 inches. B. a 4-inch by 9-inch rectangle C, a circle with radius 4 inches D. a 3-inch by 4-inch rectangle E. a hexagon with an area of 36 square inches F. a square with side length 6 inches

A Toyota dealership receives a new shipment of Camrys and puts a sticker price of $23,485 in the window of each car. They arrived at this figure by marking up their cost for each car by 22%. What was the original cost that the dealership paid for the cars?

Boyle's law states that the volume of a gas varies inversely with applied pressure. Suppose the pressure on 60 cubic meters of gas is raised from 1 atmosphere to 3 atmospheres. What new volume does the gas occupy?

A town has an area of 10.4 mi². The town's population is 3619. What is the population density of the town? Round your answer to the nearest whole number. 37,368 people/mi² 348 people/mi² 1122 people/mi² 362 people/mi² None of the other answers are correct

According to Cavalieri's Principle, which pair of shapes would have equal volumes? A. a cylinder and a sphere with the same radius B. a cone and a pyramid with equal base areas and heights C. a cone and a cylinder with equal base areas and heights D. a cylinder and a right rectangular prism with equal heights

Carmen and Adela each spend the same amount of money at the dollar store. Carmen buys 3 bracelets and spends another $1.50 on candy. Adela buys one bracelet and a $5.00 hat. How much does one bracelet cost? A $1.17 B $1.50 C $1.75 D $2.00

Suppose you earn 3% on a $1,200 deposit for 5 years. Explain how the simple interest is affected if the rate is increased by 1%. What happens if the time is increased by 1 year?

Emily and Heather each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Emily spent $140 on 7 ft of grass sod and 10 geraniums. Heather spent $135 on 10 ft2 of grass sod and 5 geraniums. What is the cost of one ft2 of grass sod and the cost of one geranium?

An ant colony is growing according to an exponential growth model. The initial population of ants is 80 and after one day there are 92 ants. how many ants will be present after 30 days? * Approximately

Marcus finds that (3x² – 2y² +5x)+(4x² +12y²-7x) - 7x² - 10y²– 2x What error did Marcus make? He combined the terms 5x and -7x incorrectly. He combined the terms 3x² and 4x² incorrectly. He combined the terms -2y2 and 12y2 incorrectly. He subtracted the polynomials instead of adding.

Hector plays a game with a friend. They pay $1 and roll a 6-sided die. If the die comes up a number that is larger than 2, they win $7. If it doesn't, they win nothing. What is the expected value of the game? Give your answer to the closest cent (two decimal places).

Sani has at least 68 envelopes to address. He has addressed 17 of them. Write and solve an inequality that describes how many more envelopes, at most, Sani has left to address. n+ 172 68; n ≥ 85 n+ 17> 68; n> 51 n+ 17 ≤ 68; n ≤ 51 n+172 68; n ≥ 51

When treated with an antibiotic, 91% of all the dolphins are cured of an ear infection. If a group of 38 dolphins are treated with antibiotics, how many cured dolphins should be expected? The expected number of cured dolphins is

A county has a population density of 257 people per square mile. The county population is 4288. What is the area of this county? Round to the nearest square mile if necessary. None of the other answers are correct 1,102,016 mi² 283,218,112 mi² 6.5 mi² 16.7 mi^2

The geographic area of California is 1.637 x 105 sq. mi. The population of California, as of 2012, is approximately 3.804 x 107. What is the population density of California?? Note: Population/land area = population density. 232 per sq mi. 544 per sq mi. 3804 per sq mi. 1637 per sq mi

Central School is hosting a "Central Has Talent" show. They will award various prizes for the best 3 acts in the show. First place wins the most money, and each subsequent place after 1st wins $50 less than the previous place. Let x equal the amount of money first place wins. Which of the following expressions represents the total amount of prize money? Select all that apply.

Identify if the system of linear equations is parallel, perpendicular, coincident, or intersecting but, not perpendicular (IBNP). y = -3x = −3x − 2 Coincident Parallel IBNP Perpendicular

A company currently sells 905 units per year of a particular product, and sales are growing at a rate of 8% each year. How many years will it be until they are selling 3,218 units per year? Give your answer to two decimal places.

Write each power of 1+i in the form a + bi, where a and b are real numbers. If a or bis zero, you can ignore that part of the number. For example, 0+3i can simply be expressed as 3i. a. (1 + i)⁰ b. (1 + i)¹ c. (1 + i)² d. (1 + i)³ e. (1 + i)4