Basic Math Questions and Answers

Your itinerary contains a grid map of New York, with each unit on the grid representing 0.5 miles. If the Rockefeller Center is located at (2,-3) and Central Park is located at (6,-3), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? Round your answer to two decimal places, if necessary.

Answer the following. (a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 2.68 × 10-6 meters. Write this number in standard notation. (b) The diameter of Jupiter at its equator is approximately 143,000 kilometers. Write this number in scientific notation.

This exercise uses the radioactive decay model. Radium-221 has a half-life of 30 sec. How long will it take for 96% of a sample to decay? (Round our answer to the nearest whole number.)

Use dimensional analysis: Trent purchases 44 euros worth of souvenirs while on vacation in France. If $1 U.S.= 0.678 euros, find the cost of the souvenirs in United States dollars. Round to the nearest cent.

Connie and Rashim have to survey 2500 homeowners. Connie can do the job alone in 12 hours. If Rashim helps, they can get the job done in 4 hours. How long would it take Rashim to do the job by himself? Write your answer as a number only. No units. Round your answer to two decimal places, if necessary.

Consider the following. e5 - 3x = 15 (a) Find the exact solution of the exponential equation in terms of logarithms. (b) Use a calculator to find an approximation to the solution rounded to six decimal places.

Solve the given equation or inequality graphically. (a) x²= 6 - 7x (Enter your answers as a comma-separated list.) (b) -x² ≥ 6-7x (Enter your answer using interval notation.)

This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Imme of the surroundings is 70°F. (a) Find a function T(t) that models the temperature t hours after death. (b) If the temperature of the body is now 72°F, how long ago was the time of death? (Round your answer to the nearest whole number

Match the definitions in Column A with the correct words/terms in Column B. Write your answers on a separate sheet of paper. Column A 1. Statement that can either be written "If..., then form 2. Part of a conditional statement that follows it 3. Part of a conditional statement that follows "then" 4. Denial of a statement formed by adding or removing the word NOT from a statement 5. To add or remove the word NOT from a statement to change its truth value from true to faise or from false to true 6. Statement formed from a conditional statement 7. by switching the hypothesis and conclusion Statement formed from a conditional statement by negating the hypothesis and conclusion 8. Statement formed from a conditional statement by switching and negating the hypothesis and conclusion 9. Statement combining a conditional statement and its converse, using the phrase "if and only if Column B A. hypothesis B. conclusion C. Inverse D. contrapositive E. negation F. negate G. biconditional H. converse 1. conditional

Fill in the table using this function rule. f(x)=2√x Simplify your answers as much as possible. Click "Not a real number" if applicable.

A group of first ten shoppers in Town Mall have the following body temperature in Degree Celsius: 36.0, 36.2, 37, 35.9, 37, 36.2, 37.2, 36.0, 36.2 and 36.4. What is the percentile rank of the shopper with a body temperature of 36.4 Degree Celsius?

A rocket is fired upward with a velocity (v) of 680 feet per second. Find how many seconds pass before the rocket reaches the ground (S=0) again. Use the quadratic equation S = - 16t² +680t. It will take seconds until the rocket reaches the ground again. (Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)

Fill in the table using this function rule. f(x)=√x+2 Simplify your answers as much as possible. Click "Not a real number" if applicable.

From her camp, a hiker walks 550 meters north, then 425 meters southeast. How far, in meters, from the camp is the hiker? Select the correct answer below: 390.58 550.00 695.07 975.00 STION

If f(x) = 3x² + 2x, find each of the following. (a) f(0) (b) f(-3) (c) f(2) (a) f(0) = (Simplify your answer.) (b) f(-3)= (Simplify your answer.) (c) f(2)= (Simplify your answer.)

Marco has joined a bowling league, and is trying to raise his average to 170. On his last four games he scored 164, 170, 165, and 171. How much will he need to score on the next game to raise his mean to 170?

Express the confidence interval using the indicated format. Express the confidence interval 0.469 ± 0.077 in the form of - E<p <+E. 0.4305< p <0.5075 0.392 < p < 0.469 0.469 <p <0.546 0.392<p <0.546

If an object is dropped, the relationship between the distance it falls and the time that it has been falling is given by: d = 1/2 gt2 where: d is the distance the object falls, in feet t is the time the object falls, in seconds g is a constant due to gravity, 32.2 ft/sec² While standing on a bridge overlooking a river, you drop a rock and time how long it takes to hit the water. If the time is 1.5 seconds, how high is the bridge above the water, to the nearest whole foot? feet

Suppose you were asked to solve the following two problems on a test. (a) Find the remainder when 6x1000-12x562 + 15x + 25 is divided by x + 1. (b) Is x - 1 a factor of x567 - 2x400 + x +7? Obviously, it's impossible to solve these problems by dividing, because the polynomials are of such large degree. Use one or more of the theorems in this section to solve these problems without actually dividing (a) Find the remainder when 6x1000-12x562 + 15x + 25 is divided by x + 1. (b) Is x - 1 a factor of x567 - 2x400 + x9 +7? Yes No

The Coconut Delight Bakery can produce 500 coconut tarts in a week at a total cost of $2000 and 700 coconut tarts at a cost of $2500. What is the weekly fixed cost in dollars per coconut tart? Write your answer as an integer and donot use the dollar sign symbol.

Compute the discriminant of 8x² - 6x - 6 = 0. The discriminant is: How many real solutions does the equation, 8x2 - 6x - 6 = 0, have? No real solution One real solution Two real solutions None of the above

If P dollars is invested in an account that earns interest at 7% compounded annually, the amount available after t years is A = P(1 +0.07). How many years will it take for $1500 in this account to grow to $3000? It will take approximately years for $1500 in this account to grow to $3000. (Round to the nearest whole year.)

A plane is 115 mi north and 176 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree.

The formula for the braking distance of a car is: d =V²/2g(f+ G) where: d is the braking distance (in feet) V is the initial velocity of the car (in feet per second) G is the roadway grade (written in decimal form) f is the coefficient of friction between the tires and the roadway g is the acceleration constant due to gravity (32.2 ft/sec²) a) If a car's speed was 47 miles per hour, what value would be used in this formula for V? Round to the tenths place. Recall 1 mile = 5280 feet. feet per second b) If a car was going 86 feet per second when the driver applied the brakes, on a road with grade G = 0.03 and a coefficient of friction of f = 0.8, what distance would it go before stopping? Round to the tenths place. feet

Find the interest rate to the nearest hundredth of a percent that will produce $2000, if $1500 is left at interest compounded quarterly for 4.5 yr. Use the formula A=P (1+r/n)tn The interest rate to the nearest hundredth of a percent is. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Suppose that you are grading a classmate's work on a compound interest problem, shown below. If there is a mistake, select the step where the mistake was made. If there is no mistake, select "No mistake." Problem: How long will it take for an investment of $3500 to double if it is invested at 2.5% annual interest compounded monthly? Round your answer to three decimal places. Step 1: 7000-3500 (1 + 0.25) 12 Step 2: 2 = (1 + 0.25) 12 12 Step 3: log(2) = log ((1+0,25)¹²) Step 4: log(2) Step 5: t = O Step 1 Step 2 Step 3 Step 4 Step 5 No mistake 12t log(1 + 025) 12 log(2) (12 log (1+0)) 2.801 years 12

In a class, having more number of girls than boys, students were given a task of collecting flowers. Each boy collected 5 flowers whereas each girl collected 3 flowers. If a total of 46 flowers were collected, which of the following could be the number of girls in the class?

Landon went to the store to buy a new TV. The sales clerk asked "How large is your current TV?". Landon replied "It is 37 inches wide and 21 inches tall". The sales clerk explained that TVs are sold by the measurement along the diagonal of the screen. Save Landon a trip home to remeasure What is the diagonal measurement for Landon's current TV, rounded to one decimal place?

Use the multiplication principle to solve. An auto manufacturer produces 8 models, each available in 9 different colors, with 6 different upholstery fabrics and 7 interior colors. How many varieties of car are available?

The height of a trapezoid is 15 feet and the two bases are 10 and 11 feet. Find the area of the trapezoid.

Use A=(5, 6, 7, 8, 9) and B={1, 3, 7, 8) to find the set A∩B. A∩B= (Use a comma to separate answers as needed.)

Find the distance between the points (-10, -9) and (-2,-2).

In response to rising concerns about identity theft, the number of models of paper shredders a company manufactures increased approximately steadily from 5 models in 1997 to 37 models in 2008. Find the average rate of change of the number of shredder models manufactured per year between 1997 and 2008. The average rate of change of the number of paper shredders manufactured per year between 1997 and 2008 was (Type an integer or decimal rounded to two decimal places as needed.)

Jerome is planning on tiling his bathroom floor with square tiles measuring 8 inches on each side. The bathroom measures 13 feet by 15 feet. a) What is the area of the floor, in square feet? b) Convert this area to square inches. c) How many 8 inch square tiles will Jerome need to cover the floor?

The value of a machine, V, at the end of t years is given by V = C(1-r)', where C is the original cost and r is the rate of depreciation. Find the value of a machine at the end of 4 years if the original cost was $2387 and r = 0.2. Round to the nearest cent.

A student has a credit card that is only used for school expenses. Their fall tuition was $1295, and the cost of books was $100. Both of these are put onto their credit card. a) Suppose these are the only two expenses on their credit card. When the bill arrives, they pay the minimum payment of $30. How much will be left on their credit card bill and therefore subject to interest? b) If the annual interest rate for their credit card is 17.99%, what is the periodic (monthly) interest rate, to 2 decimal places? c) How many dollars of interest will be added to their bill for the next month, to the nearest cent?

The hotness of chili peppers is usually measured in Scoville units. Using a log scale for Scoville units works well to compare the heat of peppers. a) A Jamaican Hot Pepper has hotness around 200,000 Scoville units. Plot this value on the log scale below. b) Another chili's hotness is shown on the number line below. What is, approximately, the hotness of the chili shown on the number line? Scoville units.

The population of foxes in a certain region over a 2-year period is estimated to be P₁(t) = 300 + 60 sin(πt/12) in month t, and the population of rabbits in the same region in month t is given by P₂(t) = 2000 + 300 cos((πt/12) Find the rate of change of the populations when t = 4. (Express a decrease in population as a negative rate of change. Round your answers to one decimal place.)

Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) = 3xex, a=0

The formula for changing Celsius (C) temperature to Fahrenheit (F) temperature is F = 1.8C + 32. To the nearest degree, what is the Fahrenheit temperature when the Celsius temperature is -8? A -18 degrees B -17 degrees C 17 degrees D 18 degrees

Emilio buys a sofa for a total purchase price of $1,309.79. State taxes were 4.4%. What is the sales tax amount for his purchase? (Round your answer to the nearest cent.) $50.38 $55.20 $57.63 $62.37

Randy buys a lawn tractor costing $975.90. The store charges $35 for assembly and $30 for delivery. State taxes are 4% and local sales taxes are 3%. What is the total purchase price? (Round your answer to the nearest cent.) $1,082.54 $1,109.21 $1,113.76 $1,115.01

Aliza had a tax liability of $6,218 last year. She was entitled to tax credits of $748 and withholding amounted to $540 per month. Aliza owed other taxes of $606. Calculate the amount of the refund or the amount of taxes due (as the case may be). $344 refund $404 refund $1,010 refund $4,930 due

Find the distance between the points (2, 9) and (-10, 1). Hint: Use the Pythagorean theorem.

Aaron's dad has a pickup truck and his mom has an SUV. Last week, his dad traveled 84 miles in the pickup truck on 4 gallons of gas. His mom traveled 72 miles in the SUV on 3 gallons of gas. How many more miles per gallon did the SUV get than the truck?

Jeremy has a total of $25 in dimes and nickels. He has 4 more dimes than nickels. Which system of equations can be used to determine the number of dimes, d, and the number of nickels, n, that Jeremy has?

Water is passed through a pipe containing porous material to filter out pollutants. Each inch of pipe removes 50% of the pollutant entering. (a) True or false: The first inch of the pipe removes 50 % of the pollutants and the second inch removes the remaining 50 %. (b) What length of pipe is needed to remove all but 8% of the pollutants? Round your answer to three decimal places. inches of pipe removes all but 8% of the pollutants.

Isosceles trapezoid ABCD with AB || CD has m (<A) = m (<B) = 60°, small base CD = 12 cm and non-parallel side BC = 24 cm. Find the large base AB and the lengths of the diagonals AC and BD.

Bernie and LuLu are selling fruit for a local fundraiser. Customers can buy boxes of apples or boxes of oranges. Bernie sold 7 boxes of apples and 7 boxes of oranges for a total of $147. LuLu sold 7 boxes of apples and 10 boxes of oranges for a total of $183. Determine the cost of one box of apples and one box of oranges.

Solve the equation 0.05e^-0.344t = 0.15 using natural logs. NOTE: Enter the exact answer. t =