Basic Math Questions and Answers

A small lake is stocked with a certain species of fish. The fish population is modeled by the function 10 P = 1+ 4e-0.4t where P is the number of fish in thousands and t is measured in years since the lake was stocked. (a) Find the fish population after 4 years. (Round your answer to the nearest whole fish.) fish (b) After how many years will the fish population reach 5000 fish? (Round your answer to two decimal places. yr

A couple just had a baby. How much should they invest now at 5.7% compounded daily in order to have $35,000 for the child's education 17 years from now? Compute the answer to the nearest dollar. (Assume a 365-day year.)

Groom Lawn Equipment pays Kim Jones a $1520 monthly salary plus a 15% commission on merchandise she sells each month. Assume Kim's sales were $83,100 for last month. Calculate the following amounts: 1. Amount of Commission: 2. Gross Pay: $1 ?

A man invests $3000 in an account that pays 7.5% interest per year, compounded quarterly. (a) Find the amount after 3 years? (Round your answer to the nearest cent.) (b) How long will it take for the investment to double? (Round your answer to two decimal places.)

Do the side lengths 4, 8, and 10 form a triangle? Select the correct answer and reasoning. A) Yes, because the sum of any two side lengths is greater than the third side length. B) Yes, because the sum of all three side lengths is greater than 20. C) No, because the third side length is greater than the sum of the other two side lengths. D) No, because 4 + 8 is greater than 10.

1.7.PS-16 A company's stock began the day at $30.12 per share. That price drops by $1.59 each hour. a. What is the price per share after 4 hours? b. What will it be after 21 hours if this rate continues? c. Explain what the signs of the answers mean in this context. OA. The price per share after 4 hours is $23.51. OB. The price per share after 4 hours is $23.76. OC. The price per share after 4 hours is $3.77. OD. The price per share after 4 hours is $3.27.

Solve the system of equations by graphing: y = 2x8 Y=2-6 First graph each line, then place a dot indicating the solution to the system.

Match each exercise with the first step needed to perform the operation. Do not actually perform the operation. x+1 X-1 X X Choose the correct answer below. ***** OA. Multiply the numerators and multiply the denominators. B. Multiply the first rational expression by the reciprocal of the second rational expression. C. Subtract the numerators. Place the difference over a common denominator. D. Multiply the second rational expression by the reciprocal of the first rational expression.

Given sets X, Y, Z, and U, find the set Xn(X-Y) using the listing method. X={e, b, g, a) Y-{e, d, b) Z-{d, b, f, g, c) U-(a, b, c, d, e, f, g Xn(X-Y)={ (Use a comma to separate answers as needed.) www

The function V(r) = πr³ can be used to find the volume of air inside a basketball given its radius. What does V(r) represent? O the radius of the basketball when the volume is V the volume of the basketball when the radius is r the volume of the basketball when the radius is V O the radius of the basketball when the volume is r

Find the equation of the line perpendicular to the given line and passing through the given point. y=-4x+2; (-1,4) Enter the correct equation in the box.

Explain how a cardinal number formula can be derived for the case where three sets occur. Specifically, give a formula relating n(A UBUC) to n(A), n(B), n(C), n(An B), n(An C), n(B n C), and n(A n B nC). Illustrate with a Venn diagram. Extend the procedure for cardinality from three sets to two sets. Which of the following formulas does this give? A. n(AUBU C) = n(A) + n(B) + n(C) - n(An B)-n(An C)- n(B nC) B. n(AUB UC) = n(A) + n(B) + n(C) n(An B)-n(An C)- n(B nC) + n(An B nC) C. n(AUB UC) = n(A) + n(B) + n(C) - n(An B)- n(An C)- n(B nC) - n(AnBnC) D. n(A UBUC) = n(A) + n(B) + n(C)

Question 6 of 10 Which statement is an inference about The Odyssey? A. The Cyclops reflects negative cultural values of ancient Greece. B. Odysseus escapes the Cyclops through trickery. C. The Odyssey is an epic poem retold by generations. D. The Odyssey was composed by Homer around 750 BC. SUBMIT

A radioactive substance has a decay rate of 0.073 per minute. How many grams of a 120 gram sample will remain radioactive after 30 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer.

A chemist is estimating the volume of a solution in a test tube. The actual volume of the solution is 27.2 ml. The chemist's estimate is 30 ml. Find the absolute error and the percent error of the chemist's estimate. If necessary, round your answers to the nearest tenth.

Match each equation on the left with its solution on the right. No answer on the right will be used twice. 3x + 2(x-4)= 4(x - 1) + x x = 2 4x + 2(x-4)= 8(x - 1) - 2x 3x + 2(x-4)= 4(x - 1) - x 4x + 2(x-4)= 4(x - 2) + x No solution All real numbers x=0

= (1 point) Solve for all solutions to the trigonometric equation 1 - sin² (0) - 3 cos² (0) = = -0.7 on the interval [0, 2π]. Find exact answers if possible, and enter your answer as a comma separated list.

13. DETAILS LARMPMT1 16.2.018. MY NOTES You roll a pair of six-sided number cubes, numbered 1 through 6. What is the probability of rolling two odd numbers? (Enter your probability as a fraction.) Need Help? Read It ASK YOUR TEACHER

0 Finish solving the triangle: A . ZA= 64° ZB= 55° LC= b degrees a = b= C= 7 C Enter your answer as a decimal value. • You must be accurate to at least 3 decimal places. . Note that for these problems, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

4) In the early spring, the trout at Big Blue Lake swim at a depth of 30 feet below sea level. When the lake warms up in the summer, the trout swim 20 feet deeper than that. At what position relative to sea level do the trout swim in the summer? Submit feet

Match the given exercise with the first step needed to perform the operation. Do not actually perform the operation. 2/a * 3/(a+6) Choose the correct answer below. ***.. OA. Multiply the first rational expression by the reciprocal of the second rational expression. B. Find the LCD. Write each expression as an equivalent expression with the LCD as the denominator. C. Subtract numerators. Place the difference over a common denominator. D. Multiply numerators and multiply denominators.

A vector with magnitude 6 points in a direction 295 degrees counterclockwise from the positive x axis. Write the vector in component form. Vector = Give each value accurate to at least 1 decimal place

(a) Find the values of the constants m and n for which the equation (xy² + x²)dx + (x²y + y³)dy = 0 is exact. Hence solve the equation using the values of m and n obtained. (b) Let f(r) 2

Ian's investment in his savings account matured to $5,510.89 at the end of 135 days. If the account was earning simple interest at a rate of 1.50% p.a., answer the following. a. What was Ian's initial investment? $0.00 Round to the nearest cent

Identify the values for which the given rational expression is undefined. s²+49 52-49 The values for which the rational expression is undefined are s = (Use a comma to separate answers as needed.)

If an object is projected upward with an initial velocity of 127 ft per sec, its height h after t seconds is h=-161²2 + 127t. Find the height of the object after 4 seconds. The height of the object after 4 seconds is (Simplify your answer.) ft. DOE

Simplify the expression. x+1 x² - 6x - 7 Select the correct choice below and fill in any answer boxes in your choice. x + 1 x² - 6x - 7 OB. The expression cannot be simplified. OA. (Simplify your answer.) *****

This, and Esther) form a club, N={A, B, C, D, E). Callie and Esther are women, and the others are men. If they choose a secretary randomly, fir the odds against a person whose name begins with a vowel becoming secretary. The odds against a person whose name begins with a vowel becoming secretary are (Type whole numbers.) to 0

A parabola is the set of all points P in the plane that are equidistant from a fixed line called the A parabola is the set of all points P in the plane that are equidistant from a fixed line called the and a fixed point not on the line called the and a fixed point not on the line called the

8. Louis wants to take out a $14,000 loan with a 6.8% APR. He can afford to pay no more than $400 per month for loan payments. What would be the length of his loan? Round to the nearest tenth of a year.

As Jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. Convert this speed to kilometers per second. At this speed, how many kilometers will Jupiter travel in 2 seconds? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers. Speed: Distance traveled in 2 seconds: km X 5 ?

ASK YOUR TEACHER Scholarship A is worth $1000 and costs $10 to apply. Scholarship B is worth $5000 and costs $25 to apply. You have a 5% chance of receiving Scholarship A and a 2% chance of receiving the Scholarship B. (a) What is your expected value for Scholarship A? $ X (b) What is your expected value for Scholarship B? $ X (c) You can only apply for one scholarship. Which one should you choose? Scholarship A Scholarship B MY NOTES

Ashley made $25,000 in taxable income last year. Suppose the income tax rate is 10% for the first $8000 plus 16% for the amount over $8000. How much must Ashley pay in income tax for last year? X 5

The sides of AABC are a, b, and c. If the lengths of a = 7 and b= 10, what are the possible lengths of c? A) 3 < c < 10 B) 3<c< 6 C) 3 < c < 17 D) 7 < c < 10

A car was valued at $26,000 in the year 1994. The value depreciated to $14,000 by the year 2008. A) What was the annual rate of change between 1994 and 2008? TR Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? T= 96. C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2012? Round to the nearest 50 dollars. value $ 20,150 = Question Help: Video Submit Question

A total of 120 high school students were surveyed about their winter break shopping habits. The results revealed that 45% shop for new clothes, 55% shop for school supplies, and 35% shop for clothes and school supplies. How many students shop for clothes or school supplies over the break? The number of students who shopped for clothes or school supplies over the break is

How long will it take for an investment of $1000 to double in value if the interest rate is 8.5% per year, compounded continuously? (Round your answer to two decimal places.) yr

Simplify. Do not use a calculator or round to a decimal. Write the exact simplified form, such as 3+√2/7 18+ √45 -18-3√5 3 X

In 2012, the population of a city was 5.38 million. The exponential growth rate was 2.95% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 8 million? d) Find the doubling time. b) The population of the city in 2018 is 6.4 million. (Round to one decimal place as needed.) CHURCZESNE a) The exponential growth function is P(t) = 5.38 0.0295t, where t is in terms of the number of years since 2012 and P(t) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.) c) The population of the city will be 8 million in about (Round to one decimal place as needed.) Part 3 of 4 years after 2012 Point

Heather participating in a 5-day cross country biking challenge.she biked for 53,68,64, and 65 miles on the four days. How many miles does she need to bike on the last day so that her average (mean) is 59

A bass guitarist worked on 14 music projects last year. He wrote and produced 5 projects. He wrote a total of 8 projects. He produced a total of 11 projects. Use a Venn diagram to determine (a) how many projects he wrote but did not produce, and (b) how many projects he produced but did not write. Complete the Venn diagram. Let W be the set of projects the bass guitarist wrote and P be the set of projects he produced.

Solve for all solutions to the trigonometric equation 5 sin (θ/3-1) = -1/5 on the interval [-π, 5]. Find exact answers if possible, and enter your answer as a comma separated list.

Whooping cough vaccine: Some parents fear that vaccinations may have adverse long-term effects on their children's health. In 2009 the Journal of the American Academy of Pediatrics published research on a routine childhood vaccine for whooping cough. The researchers studied 6811 children born between 1993 and 1997 in Leicestershire, UK. Parents answered questions over a 10+ year period about their children's respiratory symptoms. Researchers then linked this data to independently collected vaccination data from the National Health Service database. They divided the children into groups based on vaccine history (complete vaccines, partial vaccines, no vaccines) and compared respiratory symptoms. The study provided no evidence that vaccinated children were more likely to have respiratory problems such as wheeze and asthma. Which question is this observational study designed to answer? Are infants who are vaccinated against whooping cough more likely to develop wheezing disorders and asthma in later years? Does vaccinating infants against whooping cough cause wheezing disorders or asthma in later years? Are infants who receive a whooping cough vaccination less likely to develop whooping cough in later years?

How many three-digit numbers can be formed under each condition? (a) None of the digits can be 8. (b) The leading digit is one of the digits 0 through 6.

A car insurance company charges insurance premium in proportion to the car's value. For a $12,000 car, the monthly premium is $85. Laney pays a $120 monthly premium for her car. To the nearest dollar, how much is her car valued at?

Consider the expression √640, which simplifies to an expression in the form A√B. Simplify this expression completely and place the appropriate numbers in the boxes given.

At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $2.15 and the cost of a large greeting card is $5.40. How much would it cost to get 2 small greeting cards and 5 large greeting cards? How much would it cost to get a small greeting cards and y large greeting cards? Total cost, 2 small greeting cards and 5 large greeting cards: Total cost, a small greeting cards and y large greeting cards:

Choose the best answer. The dimensions of your living room are 13 ft. by 16 ft. What is the area of this room in square meters? Conversion factors: 1 meter = 3.28 feet. 19.3 m² 2.41 m2 18.45 m² 15.10 m² 3.54 m²

An investment banker deposited $50,000 in an account earning a nominal 6% per year compounded continuously. How much was in the account at the end of three years? Round the answer to nearest dollar. Select the correct answer below: 58,861 57,861 59,861 56,861 55,861 54,861

Use a standard normal distribution table to find the percent of the total area under the standard normal curve between the following z-scores. z = 0.55 and z=1.5 Click the icon to view the standard normal distribution table.