Basic Math Questions and Answers

On a scientific or graphing calculator, approximate the following value. In 0.9090

Graph the system below and write its solution. 6x-2y=-4 y=3x+3 Note that you can also answer "No solution" or "Infinitely many" solutions.

Consider the following absolute value inequality. |9x+6| < 24 Rewrite the given inequality as two linear inequalities.

Type the correct answer in the box. Round your answer to the nearest hundredth. Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26°. Scarlett's height is 1.65 meters, so the height of the dam is meters.

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.000165 moles per liter. Write this number in scientific notation. (b) A black rhinoceros can weigh up to 6.4 × 10³ pounds. Write this number in standard notation.

Which of the following are reasonable ways to estimate 15% of $29.95. There may be more than one reasonable method. 0.15 times 29.95 is $4.4925 30% is 3 out of 10, so that would be 9 out of 30. 15% is half of that, so $4.5 15 times 30 is $450. Adjusting the decimal place gives $45 10% of 30 is 3. 5% is half of that, so 1.5. Together, 15% is $4.5 15 times 30 is $450

Drag the blue point to a location on the coordinate plane so that the vector 7 (shown below in blue and centered at the origin) has magnitude 15 and direction 36.87° (relative to the positive x-axis). Provide your answer below:

Perform the following additions and/or subtractions: (10w² + 11w + 4) + (7w² + 8w + 3) =

Write an equation in point-slope form of the line that passes through the point (-8, -2) and has a slope of m = 5.

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. 12x-8y = 12 Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.

A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the number of videos. Identify the independent and dependent variables. Then, write a rule using function notation to represent the situation.

Suppose that the price - demand equation and the cost function for the production of table saws are given, respectively, by P = 300 81,000+ 90x where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost (in dollars) of producing x saws. Find the revenue function in terms of x. - 50 and C(x) Y

Suppose that the total cost (in dollars) of producing x food processors is given by C(x) = 1,800 + 36x -0.6 x². What is the average cos t (in dollars) of producing the 21st food processor? Round your answer to the nearest whole number.

The activity on Denise Hellings' Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previous balance was $155.27, and the annual simple interest rate is 21%. (Round your answers to the nearest cent.)

Consider the following points. (-3,7), (6,0) and (6, 7) Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene

Mia and Vincent are asked to choreograph a dance for the school musical.. Mia can choreograph the dance for the show in 20 hours and Vincent can choreograph the dance by himself in 16 hours. How long would it take to choregraph the dance for the musical if they worked together? Write your answer as a number only. No units. Round your answer to two decimal places, if necessary.

An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 2 IQ points of the true mean. Assume that o = 14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. (Round up to the nearest integer.) The required sample size is Would it be reasonable to sample this number of students? No. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly large number.

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.)