Basic Math Questions and Answers

Consider the equation 1.5x + 4.5y = 18. For each question, explain or show your reasoning. 1. If we graph the equation, what is the slope of the graph?

Axel swam 32 laps at the pool. The number of laps that he swam was 2 more than 3 times as many laps as his friend Kelly swam. Which of the following equations could you use to determine the number of laps that Kelly swam?

A model rocket is launched from the ground. The height, s, of the rocket above the ground at time t seconds after it is launched can be found by the formula s=-16t² +67t. Find how long it will take for the rocket to reach a height of 44 feet. seconds (Round to two decimal places as needed. Use a comma to separate answers as needed.)

In a genetics class, 6 students have GREEN eyes, 3 students have BLUE eyes, and 11 have HAZEL eyes. If a single student is picked at random, what is the probability that their eyes are GREEN or HAZEL? • Provide the final answer as a fraction.

Troy opened a savings account and deposited $300.00. The account earns 6% interest, compounded annually. If he wants to use the money to buy a new bicycle in 3 years, how much will he be able to spend on the bike? Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent. 7

Logan earned $8 for each dog he walked last summer. This summer, he raised his fee to $9 per dog. Express the change in Logan's fees as a percent. Round to the nearest tenth of a percent. Enter the correct answer in the box.

An elevator can carry 26 adults or 30 children at one time. During the course of a day, the elevator carries a full passenger load 46 times. If all the passengers were children, how many more people would the elevator carry than if all the passengers were adults?

Vina has $4.60 in quarters, dimes and nickels in her purse. She has seven more dimes than quarters and six more nickels than quarters. How many of each coin are in her purse? nickels dimes quarters

Write an expression that is equivalent to 3y - 9. A common factor of 3 and 9 is 3y - 9 = So, 3y - 9 is equivalent to Why can you use properties of operations to write equivalent expressions?

Sam opens a savings account at the start of the school year. The amount of money in Sam's college savings account is given by the function: A(w): = 2400-60w Where w= the number of weeks since school started and A(w) represents the amount of money, in dollars, left in the account w weeks after school started Find the missing value in the ordered pair described by the function notation and then choose the option that best describes the meaning of that ordered pair. A(0) means... O After 0 weeks of school Sam has $2400 in the account. After 0 weeks of school Sam has $2,340 in the account. After 40 weeks of school Sam has $0 in the account. O After 0 weeks of school Sam has $40 in the account. O After 60 weeks of school Sam has $0 in the account.

Algebra 2 > T.13 Compound interest Troy opened a savings account and deposited $300.00. The account earns 6% interest, compounded annually. If he wants to use the money to buy a new bicycle in 3 years, how much will he be able to spend on the bike? nt I Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

A population of bears increased by 50% in 4 years. If the situation is modeled by an annual growth rate compounded continuously, which formula could be used to find the annual rate according to the exponential growth function? Leave your answer in terms of In.

When Deion was born, his grandfather gave him a 7.5-gram gold coin as a present. Today, Deion read in the newspaper that a gram of gold is worth $50.04. How much money is the gold coin worth?

4. A car traveled 180 miles at a constant rate. a. Complete the table to show the rate at which the car was traveling if it completed the same distance in each number of hours. b. Write an equation that would make it easy to find the rate at which the car was traveling in miles per hour r, if it traveled for hours. 180/F travel time (hours) 5 4.5 3 2.25 rate of travel (miles per hour)

Noah operates an orange juice stand. On Monday he used 3/10 of a bag of oranges. On Tuesday he used 1/3 as many oranges as on Monday. How many bags of oranges did Noah use on Tuesday? Write your answer as a fraction or as a whole or mixed number. bags

Mary needs to borrow $11,000. She can borrow the money at 5.5% simple interest for 3 3 yr. (a) How much total interest would Mary pay at 5.5% simple interest? (b) How much total interest would Mary pay at 5% interest compounded continuously? (c) Which option results in less total interest? Part 1 of 3 (a) How much total interest would Mary pay at 5.5% simple interest? At 5.5% simple interest, the total interest Mary would pay is $2733.875 Part: 1/3 Part 2 of 3 X (b) How much total interest would Mary pay at 5% interest compounded continuously? At 5% interest compounded continuously, the total interest Mary would pay is $ or she can borrow at 5% with interest compounded continuously for X S Submit Assignm Acressi

An account is opened with an initial deposit of $24,000 and earns 2.5% interest compounded quarterly. What will the account be worth in 15 years? Since we are dealing with money, round 2 decimals.

If, in a monopoly market, the demand function for a product is p = 130 -0.40x and the revenue function is R = px, where x is the number of units sold and p is the price per unit, what price will maximize revenue? $

A shipment of 1000 small lab mice arrives at the animal care facility with a nominal weight of 10 g per mouse. A simple random sample of 100 mice is selected and weighed, and the resulting 95% confidence interval for the mean weight is from 9.9 g to 10.5 Which of the given statements is correct? O About 95% of samples will have mean weights between 9.9 g and 10.5 g. O About 95% of individual mice in our sample weigh between 9.9 g and 10.5 g. This type of quality control is repeated across the country whenever a shipment of mice is received. About 95% of the quality control tests will have confidence intervals that contain the true mean. About 95% of individuals will have confidence intervals that contain the value of 10.

In AJKL, JL is extended through point L to point M, m/LJK = (2x + 2)°, m/KLM = (8x - 16), and m/JKL = (3x+6)°. Find m/KLM.

An individual plans to buy a house for $200,000. She will put 20% down, and finance the rest with a 20 year mortgage at a fixed rate of 5%. a) What will be the monthly payment for the loan? b) In total, how much interest will be paid over the term of the loan? c) How much interest is paid in the first month?

4. The doubling time for a city's population is 10 years. In 30 years the population will be times the initial population a) 2 b) 3 c) 4 d) 8 5. Which of the following is not a good approximation of doubling time? a) A population growing at 2% per year will double in 35 years. b) A population growing at 1% per year will double in 70 years. c) A population growing at 10% per year will double in 7 years. d) A population growing at 35% per year will double in 2 years. 6. The half-life of a drug in the bloodstream is 14 hours. What fraction of the original dose is left in the bloodstream after 56 hours? a) 1/4 b) 1/8 c) 1/16 d) 1/32

Dance Company Students The number of students who belong to the dance company at each of several randomly selected small universities is shown below. Round sample statistics and final answers to at least one decimal place. 30 26 25 26 21 29 21 40 Send data to Excel 47 47 21 35 35 35 2 Estimate the true population mean size of a university dance company with 80% confidence. Assume the variable is normally distributed. 0<<0 X

3. Write an equation to model the scenario, and then solve it. (2 pts) Mariah filled her dog treat jar with 72 dog treats. Her dogs eat 4 treats each day. How many treats are left in the jar after one week (7 days)?

Country A has an exponential growth rate of 4.9% per year. The population is currently 5,025,000, and the land area of Country A is 29,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?

Write a system of linear equations in three variables, and then use matrices to solve the system. A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 10 hours to fire. A tree takes 15 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 16 hours to paint, and 7 hours to fire. If the workshop has 93 hours for prep time, 74 hours for painting, and 107 hours for firing, how many of each can be made? O 3 wreaths; 7 trees; 4 sleighs O 7 wreaths; 4 trees; 3 sleighs 8 wreaths; 5 trees; 4 sleighs O4 wreaths; 3 trees; 7 sleighs

Find the zeros of the following polynomial. Include complex zeros if any occur. P(x) = (x+3)(x² - 2x + 3) (Give your answer in the form of a comma-separated list if needed. Express numbers in exact form. Use symbolic notation and fractions where needed.) x =

You perform a statistical test to examine if a new machine that fills soft drink cans has a higher mean amount filled than the old machine. Which of the given statements is an example of a Type II error? Conclude that the new machine increased the mean amount filled when in fact it does not. Conclude that the new machine did not increase the mean amount filled when in fact it does. Conclude that the new machine did not increase the mean amount filled when in fact it does not. Conclude that the new machine increased the mean amount filled when in fact it does.

Courtney and Joe are power washing the patio. Courtney can power wash the entire patio in 7 hours while it takes Joe just 5 hours to power wash the patio. How long will it take Courtney and Joe to power wash the patio together? Choose the equation that should be used to solve this problem and state the solution. O7t + 5t = 12; t = 1 hour O = + = 1; t = 2 hours 7t + 5t = 1; t = 12 hours O + = 1; t = 5 hours

Use the function equation to find the x-intercept of the linear function algebraically. G(x): =-220x + 5500 Write the ordered pair using parentheses like this: (x,y) with no spaces but with the appropriate numerical coordinates instead of x and y. If there is no 'x'-intercept type "N/A" in the blank. The x-intercept is

Write an expression to represent: Eight minus the quotient of two and a number .

The goat population in a certain region has an annual growth rate of 8% per year. In the year 2012, there were 24,900 goats counted in the area. What is the goat population predicted to be in the year 2020?

3. Suppose you have a rectangular garden that is 10 ft by 40 ft. The garden has become too much to manage, so you plan to install a square-shaped fountain in the middle. Square-shaped fountains come in all sizes, so you decide to buy one that will leave only 100 ft² of garden to maintain, which is all you have the energy for. What should the side length of the fountain be? After finding your two "answers", explain why neither actually makes sense in this problem! [WISE. VIZ]

Caitlin has a $10 gift certificate to the music store. She has chosen a number of CDs from the $7 bargain bin. If the cost of the CDs is $32 after the gift certificate is credited, how many CDs did Caitlin buy?

3. Radium-225 is a metal with a half-life of 1600 years. Suppose a researcher has 30 kilograms of radium-225. How much will remain after 200 years? Round your answer to one decimal place. (3 points) 4. A rural community begins with a population of approximately 10,000 but declines at 6% per year. After how much time will the population reach half its size? (4 points) a) Use a formula that gives you the approximate half-life. bi Use the formula that gives the exact half-life, Round your answer to two decimal places

Select the correct description of each term. the point where all three medians meet the point where all three altitudes meet the point where all three perpendicular bisectors meet a segment connecting the midpoint of the side of a triangle to the opposite angle a line/segment perpendicular to a side at the midpoint of that side centroid othocenter circumcenter othocenter altitude perpendicular bisector median

Which of the following sample designs will result in a sample that is most representative of the population, or contain the least amount of bias? 300 math students in Math II are given a number. Ten numbers are chosen randomly and each winning number will get a $15 gift card to Target. A teacher wishes to know how his students at his high school feel about online homework. He emails a survey about the issue to a random sample of his students. Dancing with the Stars asks its viewers to text their vote for their favorite dancers. The school calls every person with a landline to ask the parents their opinion of using online textbooks over hardback textbooks. Not everyone in the school has a landline.

The exchange rate of a Chinese RMB to a US dollar is 1 RMB to 0.15 US dollar. How many RMB can an individual purchase if he or she has 250.00 US dollars? Round your answer to the second decimal place. Enter your answer as a number, such as: 410.56.

Find the distance between the pair of points. (22,12) and (14,8)

Suppose a line segment whose endpoints are C(7,3) and D(11,-5) is reflected over y=-x. What is the y- coordinate of D'? (2 Points)

Gina needs to cut a board to use for a project. The board is 10 feet long. She first has to cut off 1 feet from one end of the board She then cuts the remaining section of board into 3 equal pieces. Which equation can be used to determine the the length of each equal piece? 032-1-10 012-3-10 Ⓒ3z + 1 = 10 • 1z+3=10

Yesterday, in St. Petersburg, the temperature was -5.4°C at 8 am. The next three hours, the temperature decreased 7°C each hour. In the fourth hour, it increased by 4.5°C. What was the temperature at noon?

Mark owes his sister $15. He earned $20 for mowing the grass. He gave of his earnings to a local charity and then paid his sister. Does Mark have enough to repay his sister the full amount? Why or why not?

Select all that apply. Dangling constructions may be repaired by: expanding the dangling phrase into a subordinate clause changing the adjective into an adverb supplying a word for the modifier to describe placing the modifier close to the noun it modifies

8. Graph and completely describe the function f(x)=√x-4-2. Your description should include the following. • Domain ● Max/Min ● Range ● Is it symmetric? If so, what is the line of symmetry? • Identify at least 4 points with integer coordinates • x or y intercepts

Mary needs to borrow $12,000. She can borrow the money at 4.5% simple interest for 3 yr or she can borrow at 4% with interest compounded continuously for 3 yr. (a) How much total interest would Mary pay at 4.5% simple interest? (b) How much total interest would Mary pay at 4% interest compounded continuously? (c) Which option results in less total interest? (a) How much total interest would Mary pay at 4.5% simple interest? At 4.5% simple interest, the total interest Mary would pay is

Question Help An environmental engineer graphed the locations of a well and all of the drainage ditches in the vicinity. He positioned the well at (-6,3) and the farthest drainage ditch at (92,3). If each unit on the graph represents 1 foot, then how far away from the well is the farthest drainage ditch? ft

A population of 200 rabbits was introduced to an island. One week later the number of rabbits was 210. The number of rabbits, N, can be modelled by the function N(t)-200xb^t, t≥0, where t is the time, in weeks, since the rabbits were introduced to the island. a) Find the value of b. b) Calculate the number of rabbits on the island after 10 weeks. Round to the 3 sf. c) An ecologist estimates that the island has enough food to support a maximum population of 1000 rabbits. Calculate the number of weeks it takes for the rabbit population to reach this maximum. Round to 3 sf.

The average monthly sales volume (in thousands of dollars) for a company depends on the number of hours of training x of its sales staff, according to the function 60 X X 6 (a) Combine the terms of this function over a common denominator to create a rational function. S= + 10 + 10 ≤ x ≤ 100.

Complete the description of how you can use the information in a table showing a linear relationship to find the slope and y-intercept for the equation. Use two points from the table to find the slope slope to solve for the x-intercept and then use a point and the