Basic Math Questions and Answers

Over a period of 120 days, Shawna Johnson earned $400 interest in a retirement account paying interest at a rate of 5%. Find (a) the principal at the beginning of the 120 days and (b) the amount in the account at the end of 120 days. (a) The principal was $ (b) The amount in the account at the end of 120 days is $.

Ayat's van traveled 88 miles on 6.5 gallons of gasoline. At this rate, how many gallons would be needed to travel 220 miles? Ayat will need gallons. (Type an integer or a decimal.) ……..

Solve the equation by factoring. 49 - 64x² = 0

The 30 introductory statistics students took another quiz worth 30 points. On this quiz, the standard deviation of the scores of that quiz was 1 point. Which of the following gives the most suitable interpretation? A. all of the individual scores are one point apart B. the difference between the highest and lowest score is 1 C. the difference between the upper and lower quartile is 1 D. a typical score is within 1 point of the mean

The approximate areas of Oregon and Hawaii are listed below: Oregon: 2.55 x 105 square kilometers Hawaii: 2.83 × 104 square kilometers What's the difference between the areas of the two states? Express your answer using scientific notation.

Keisha puts 4 oranges into each of 5 baskets. She puts 6 lemons into each of 2 baskets. What is the total number of oranges and lemons in the baskets?

Find the midpoint of PQ with endpoints P(-4, 3) and Q(4, -1). Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is called the perpendicular bisector.

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 45 minutes of calls is $23.25, and the remaining credit after 72 minutes of calls is $19.20. What is the remaining credit after 79 minutes of calls?

A sample of 300 g of lead-210 decays to polonium-210 according to the function given by A(t) = 300e^-0.032t, where t is time in years. What is the amount of the sample after 60 years (to the nearest g)? 2046 g 44 g 230 g 32 g

The population of Ukraine in 2015 was 44.4 million and the expected continuous annual rate of change k of the population is -0.006. (a) Find the exponential growth model P = Ce^kt (b) Use the model to predict the population of the country in 2031. ( (c) Discuss the relationship between the sign of k and the change in population for the country.

The approximate areas of South Carolina and Puerto Rico are listed below: South Carolina: 8.29 × 104 square kilometers Puerto Rico: 5.33 x 10³ square kilometers What's the difference between the areas of the two states? Express your answer using scientific notation.

Martina rents a room in her home to guests. She charges a $25 flat fee per night for one person. Additional guests are welcome to stay, but she charges $10 per person. She expects guests to check out by 10 a.m. and charges an extra $5 per hour for late checkouts. Select the linear equation that correctly represents how much Martina collects for one night of stay in her home. A) c+ 25 = 10p + 5h B) c= 25 +10+5 C) c= 25-10p - 5h

Think about the meaning of relative to. Then rephrase this sentence in your own words: The altitude of the bird is 4 feet relative to the rooftop.

In a busy flu season, the rate of infection on a college campus is proportional to the product of the number of people who have the flu and the number who do not have the flu. Let P be the total population and let F be the number of people who have the flu. Which differential equation models this event? a. dF/dt = kF (P-F) b. dF/dt = e^k(P-F) c. dF/dt = k(P-F) d. dF/dt = kP(P-F) e. None of these

Determine f^-1 if f (x) = x+1/2-2 where ≠ 2 f^-1 (x) = x-2/x+1 f^-1 (x) = x-1/x+2 f^-1 (x) = 2x+1/x-1 f^-1 (x) = x-1/2x+1

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