Basic Math Questions and Answers

Find the rate, or speed, as a ratio of distance to time. 1560 yd, 8 hr The rate is Type a whole number or decimal rounded to the nearest hundredth

Write the negation of the following conditional statement: "If you pass this course, you will graduate this semester." If you graduate this semester, then you pass this course You don't pass this course, and you do not graduate this semester If you don't pass this course, then you do not graduate this semester You pass this course, and you graduate this semester You don't pass this course, or you graduate this semester If you do not graduate this semester, then you don't pass this course You don't pass this course, and you graduate this semester You pass this course, and you do not graduate this semester

To prepare for a bake-off, Charlie used 0.94 kilogram of flour each day for 3 weeks. How many grams did Charlie use in those 3 weeks? Charlie used grams of flour in 3 weeks.

City A and city B are expensive cities for business travel. On the basis of the average total costs per day for each city (which include a hotel room, car rental, and three meals), 3 days in city A and 4 days in city B cost $5560, while 6 days in city A and 3 days in city B cost $7875. What was the average cost per day in each city? What is the average cost per day in city A? What is the average cost per day in city B?

Do these three points create a right triangle? Length of AB Length of BC Length of AC • Write your answer in exact form, do not use decimal approximations. • To write a square root such as √15, type in 'sqrt(15)' instead of using rational exponents. • You are not required to reduce your radicals for this problem. Which side would be our candidate for the hypotenuse? . In other words, which side is the longest? • Enter one of the following: AB, BC, or AC So do these three sides satisfy the Pythagorean Theorem? • Answer yes or no. Note: You can earn partial credit on this problem. A:(-3,-3), B:(-6, -2), C:(-1,3)

Sleep apnea: Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 420 people aged 65 and over, 114 of them had sleep apnea. Part 1 of 3 (a) Find a point estimate for the population proportion of those aged 65 and over who have sleep apnea. Round the answer to at least three decimal places. The point estimate for the proportion of those aged 65 and over who have sleep apnea is Part 2 of 3 (b) Construct a 99.8% confidence interval for the proportion of those aged 65 and over who have sleep apnea. Round the answer to at least three decimal places. A 99.8% confidence interval for the proportion of those aged 65 and over who have sleep apnea is <p< Part: 2/3 Part 3 of 3 (c) In another study, medical researchers concluded that more than 12% of elderly people have sleep apnea. Based on the confidence interval, does it appear that more than 12% of people aged 65 and over have sleep apnea? Explain. Since all of the values in the confidence interval are (Choose one) lesser than/greater than 0.12, then the confidence interval contradict the claim.

Online courses: A sample of 261 students who were taking online courses were asked to describe their overall impression of online learning on a scale of 1-7, with 7 representing the most favorable impression. The average score was 5.45, and the standard deviation was 0.90. Part 1 of 2 Construct a 99.5% interval for the mean score. Round the answers to two decimal places. A 99.5% confidence interval for the mean score is <μ< Part 2 of 2 Assume that the mean score for students taking traditional courses is 5.53. A college that offers online courses claims that the mean scores for online courses are the same. Does the confidence interval contradict this claim? Explain. The confidence interval (Choose one) does/does not contradict this belief.

foot piece of siding is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is four times as long as the first piece. If x represents the length of the first piece, find lengths of all three pieces. ho length of the first piece of siding is long, the longth of the second piece is long, and the length of the third piece is long.

The space probe Voyager I travels 3.255 x 108 miles in year At this rate, how far does the Voyager I travel during a period of 40 years?

You can afford a $250 per month car payment. You've found a 5 year loan at 4% interest. How big of a loan can you afford?

Before a detailed family budget can be created, your financial planner has advised you to examine the important aspects that affect a budget such as income, taxes, savings, and expenses. Work through the following questions to start thinking about these aspects of budgeting. As a student, you are able to earn extra money by assisting your neighbors with odd jobs. If you charged $10.25 an hour for your assistance, about how many hours would you need to work to earn $8,425?

A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the peak is one-half the total hang-time.)

One of the lamp posts at a bank has a motion detector on it, and the equation (x +15)² + (y - 12)² = 25 What is the greatest distance, in feet, a person could be from the lamp and be detected? 5 ft 10 ft 50 ft 125 ft

Which situations most likely involve the use of decimals? Choose more than one answer. Counting the number of apples in a basket Measuring a person's height in meters Calculating the price of an item after tax Predicting the next full moon Comparing the batting averages of two baseball players Estimating the weight of an elephant

The measure of a central angle is 5.3 radians and the corresponding arc length is 23 inches. What proportion would you use to solve for the radius? 5.3/2π = 23/πr^2 5.3/2π = 2πr/23 5.3/2π = 23/2πr 5.3/360 = 23/2πr

You're buying hand lotion. The lotion comes in rectangular pyramid-shaped bottles. Bottle A has a base of 1 in x 2 in, and a height of 6 in. Bottle B is a wider bottle with a base of 1.5 in x 3 in, and a height of 4 inches. Which bottle has more lotion? Bottle B contains 18 in^3 of lotion, and Bottle A contains 12 in^3. Bottle B contains more. Bottle B contains 6 in³ of lotion, and Bottle A contains 4 in³. Bottle B contains more. Bottle A contains 18 in^3 of lotion, and Bottle B contains 12 in^3. Bottle A contains more. Bottle A contains 6 in³ of lotion, and Bottle B contains 4 in³. Bottle A contains more.

A cliff diver jumps from a height of 18m above sea level into the sea. She reaches a depth of -6m in the sea before rising back to sea level to take a breath. What difference in elevation did she experience from the top of the cliff to the lowest depth in the sea?

Select the statement below that is equivalent to the following statement: "If the light is on, someone is home." The light is on and someone is home If someone is home, the light is on. Either someone is not home, or the light is on. If someone is not home, the light is not on.

The position of an object moving in a straight line is given by s = t² - 3t, where s is in meters and t is time in seconds. How long (to the nearest tenth) will it take the object to move 12 meters?

The cost to purchase a song from iTunes is $0.99 per song. To purchase a song from Napster youmust be a member. The Napster membership fee is $10. In addition, each purchased song costs $0.89. Which equation represents when the cost for iTunes and Napster will cost the same? A. 0.99x+10=0.89x+10 B.0.99x=0.89x+10 C.0.99=0.89x+10x D0.99x=0.89x+10x

Deborah has two paintings in her portfolio and paints three more each week. Kayla has twelve paintings in her portfolio and paints two more each week. After how many weeks will Deborah and Kayla have the same number of paintings?

Smart phone: Among 242 cell phone owners aged 18-24 surveyed, 107 said their phone was an Android phone. Part 1 of 3 (a) Find a point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answer to at least three decimal places. The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.442 Part: 1/3 Part 2 of 3 (b) Construct a 95% confidence interval for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answers to at least three decimal places. A 95% confidence interval for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.370 <p< 0.494 3

Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x) = - x² + x + 2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground? 1 second 3 seconds 4 seconds 2 seconds

Michael breeds chickens and ducks. Last month, he sold 50 chickens and 30 ducks for $550. This month, he sold 44 chickens and 36 ducks for $532. How much does a chicken cost, and how much does a duck cost? A chicken costs $ and a duck costs $

Jan's car will go 403 miles on 15.5 gallons of gasoline in highway driving. a) How many gallons will it take to drive 2603 miles from her house to a friend's house? b) How far can the car be driven on 134 gallons of gasoline?

Find the arc length of a circle if the central angle is 312° and the radius is 17 centimeters. Round your answer to two decimal places. 786.45 cm 92.53 cm 5304 cm 46.27 cm

Erika needs a test average of 85 or higher to make the honor roll. . There are four tests in the term. . Her first three test grades were 78, 80, and 88. Which inequality could be used to find what she needs to score on her fourth test, x, in order to make the honor roll? B. es D. M 73 3 10- S 3 7-10 * + I - I ≤85 ≥ 85 ≤85 2 85

The mosquito population for the Eastern United States was predicted to be 23,467,899,213. Which number estimates the predicted mosquito population?

Jan's car will go 378 miles on 13.5 gallons of gasoline in highway driving. a) How many gallons will it take to drive 2691 miles from her house to a friend's house? b) How far can the car be driven on 136 gallons of gasoline?

For the given pair of equations, give the slopes of the lines, and then determine wheth 5x + 2y = 5 10x + + 4y = 3 OA. The slope of 5x + 2y = 5 is Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ... OA. The slope of 10x + 4y = 3 is (Type an integer or a simplified fraction.) OB. The slope of 10x + 4y = 3 is undefined. Next Question (Type an integer or a simplified fraction.) OB. The slope of 5x + 2y = 5 is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The lines are parallel, perpendicular, or neither.

Select ALL of the answers that apply. Which of the following are equivalent functions to f(x) = (x-6) (x - 2) A f(x) = (x-4)² - 4 B f(x)=x²-10x + 24 C f(x) = (x + 6)² - 2 D f(x) = x² - 8x + 12

An online retail company determined that their cost for each day, x, can be determined by the function C(x) = 2x² - 20x + 70 and their revenue by the function R(x) = -x^2 + 5x + 18. How many days will it take for the company to earn a profit? 4 5 20 22

Your parents have been advised to save 5% of their income for your college education, which would include money for housing, tuition, books, and fees. How much would your parents have saved in one year, following the recommended 5%, if they had an average household income of $48,948? Show your work. (5 points)

As a smart consumer, you are always on the lookout for sales, coupons, and rebates. While shopping for new clothes, you notice that one particular brand of shirts is on sale for 20% off the original price. You also have a coupon for $10 off a $40 purchase. Coupons are applied after the 20% discount is taken. If each shirt originally costs $17.99, how many shirts would you need to buy to be able to use your coupon? Show your work. (15 points)

A local store ordered a shipment of video game systems. The store sells 30 systems weekly to customers. As a result, the number of systems in stock decreased to 190 in the first week. Which statements correctly interpret the rate of change, or the y-intercept, of the given situation? Select all that apply. A There are 30 systems sold each week. B There are 190 systems in the shipment. C There were 220 systems in the shipment. D The situation can be modeled as y= 30x190. E The situation can be modeled as y=-30x + 220

Jasper is 43 years old and his daughter Freya is 7. In n-years Jasper will be four times as old as Freya is at that point. Set up and solve an equation for n. Then state both Jasper and Freya's ages after n-years.

Consider a triangle A whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of A is (1, 1), then the equation of the circle passing through the vertices of the triangle A is (A) x² + y² - 3x + y = 0 (C) x² + y² + 2y - 1 = 0 (B) x² + y² + x + 3y = 0 (D) x² + y² + x + y = 0

After the success of Sputnik 1 in October 1957 by USSR, they decided to launch Sputnik 2 by November, and this left them with only 4 weeks to design and build the spacecraft. Sputnik 2, therefore, was something of a rush job, with most elements of the spacecraft being constructed from rough sketches. It was decided that Sputnik 2 would carry a canine, thus repeating the triumph of Sputnik 1. Three dogs were trained for Sputnik 2 flight- Albina, Mushka and Laika.

Find an equation of the line satisfying the given conditions. Through (9,7) and perpendicular to y = 3x - 5 The equation of the line is (Simplify your answer.)

Find the arc length if the measure of the central angle is 80° and the radius is 8 inches. Round your answer to one decimal place. Hint: Draw a picture to help! 5.58 inches 11.16 inches 12.6 inches 44.65 inches

A large national women's retail store uses ink tags to help prevent shoplifting. The tag is fastened to clothing items, and if it is not removed with the correct device, it will "explode" and put a large ink stain on the clothing. It will also set off an alarm if taken out of the store. Five stores are selected at random to see if clerks are remembering to take the tags off before shoppers who have paid for clothing leave the store. It is determined that 48 out of 80 shoppers have an alarm go off even after having paid for their merchandise. (a) Determine whether the following statement is true or false. This sample size is large enough to find a margin of error. True False off even after having paid for their merchandise?

Verify that the equation is an identity. tan^x - sec^4x = 1 - 2 sec^2x

Write the equation of the parabola in vertex form with the given information. Vertex: (4,7) Point on graph: (2, -1) Oy = (x + 4)² + 7 Oy = -2(x-4)² + 7 Oy = -2(x + 4)² + 7 Oy = (x-4)² + 7 Oy = 2(x-4)² + 7 Oy = 2(x + 4)² + 7

Find the area of a sector that has a central angle of 200° and a diameter of 18 cm. Leave your answer in terms of л. Hint: Draw a picture to help! O 10 cm² O 1807cm² 457cm² O90лcm²

Harold cut 18 1/2 inches off a rope that was 60 inches long. How is the length of the remaining rope in inches written in decimal form?

During 1991, a total of 200,000 people visited Rave Amusement Park. During 1997, the number visiting the park had grown to 834,000. If the number of visitors to the park' obeys the law of uninhibited growth, find the exponential growth function that models this data.

Sometimes the problem will give the initial and final states in different units. In this case, you need to identify all of the pressures and all of the volumes by organizing them into a table (step 1 of our problem-solving method). Then, you need to convert all of your pressures to the same units (usually atmospheres works best) and all of your volumes to the same units (usually liters). Then you can set up the problem and solve. A balloon filled with 2.00 L of helium initially at 1.95 atm of pressure rises into the atmosphere. When the surrounding pressure reaches 470. mmHg, the balloon will burst. If 1 atm =760. mmHg, what volume will the balloon occupy in the instant before it bursts? Express your answer with the appropriate units.

A circle has a radius of 7.5mm. A sector of the circle has a central angle of 80°. Find the area of the sector. Do not round any intermediate computations. Round your answer to the nearest tenth. mm^2

Describe the transformations from the graph of f(x) = |x| to the graph of d(x)=-x-31+5. The transformations are a horizontal translation 3 units left, then a reflection in the y-axis, then a vertical translation 5 units down. The transformations are a horizontal translation 3 units right, then a reflection in the x-axis, then a vertical translation 5 units up. The transformations are a horizontal translation 3 units left, then a reflection in the y-axis, then a vertical translation 5 units up. The transformations are a horizontal translation 3 units right, then a reflection in the x-axis, then a vertical translation 5 units down. Graph the function. Ray Undo 4 2 a Redo x Reset 2

Find the distance between these two points: (4,-5) and (-4,-9)