Basic Math Questions and Answers

A website got 4 x10⁹ views on Saturday and 8 x106 views on Sunday. How many times more views were on Saturday than Sunday?

Write the exponential equation x = 12^y in logarithmic form.

Michelle and Michael collect baseball cards. Michael has 5 more cards than Michelle. Together they have 27 cards. How many cards does each have?

When the sun is at a certain angle in the sky, a 100-foot building will cast a 25-foot shadow. How tall is a person if he casts a 1.5-foot shadow at the same time? Enter only the number.

Graph the equatiob y=-x² - 2x + 3 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Keith's school is due west of his house and due south of his friend Mary's house. The distance between the school and Mary's house is 15 kilometers and the straight-line distance between Keith's house and Mary's house is 17 kilometers. How far is Keith's house from school?

Plot the intercepts to graph the equation. x+4y=8 Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Diana has 360 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W) = -w² +180w (b) The area is largest for W= (Simplify your ans

Alice loaned Juan $8080 at an interest rate of 15 % for 116 days. How much will Juan pay Alice at the end of 116 days? Round your answer to the nearest cent. Note: Assume 365 days in a year and 30 days in a month.

Which choice correctly compares the two decimal numbers to hundredths? A) 28.14> 29.11 B) 28.61 > 28.48 C) 29.13 < 28.37 D) 29.19 < 28.32

Graph the linear equation. y=-2/3x+1

Solve the equation 19t² + 4t =-12t³ State your answers as integers or reduced fractions, separated by commas.

At which points is the function continuous? y = 4√3x-2 The function is continuous on (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

There are 630 dishes that need to be rinsed. Omar can rinse them in 105 minutes by himself. It will take his friend Brian 70 minutes to rinse these dishes. How long will it take them if they rinse these 630 dishes together?

Solve for using the square root property. 2t²-12=-2

Graph the equation y = x² + 12x + 35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Click to plot points. Click points to delete them.

John is in a club that collects annual dues. In the first year that he was a member, he paid $20 in club dues. However, the club dues increase by $2 each year. Identify the function that describes the relationship between the number of years that John has been a member of the club and the dues he pays that year. f(n) = 20 + 2(n-1) f(n) = 20 + 2(n+1) f(n) = 20 + 2n f(n) = 20 + 2(n - 2)

Outside temperature over a day can be modelled sa sinusoidal function. Suppose you know the high temperature for the day is 95 degrees and the low temperature of 65 degrees occurs at 4 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Does the function f(x) = (0.85)x represent exponential growth, decay, or neither? A) Exponential decay B) Impossible to determine with the information given. C) Exponential growth D) Neither

Dominique is allowed to play up to 8 hours of video games this week. They want to play video games for at least 4 hours this weekend. Which of the following can be used to represent t, the number of hours they can play video games before the weekend?

The decay rate, k, for a particular radioactive element is 2.5%, where time is measured in years. Find the half-life of the element. The half-life is years. (Round to one decimal place as needed.)

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 15 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own? Do not do any rounding.

A voltage V across a resistance R generates a current I=V/R. If a constant voltage of 6 volts is put across a resistance that is increasing at a rate of 0.2 ohms per second when the resistance is 4 ohms, at what rate is the current changing? (Give units.) rate =

Find two points on the graph of this function, other than the origin, that fit within the given [-10, 10] by [-10, 10] grid. Express each coordinate as an integer or simplified fraction, or round to four decimal places as necessary.

Write in factored form by factoring out the greatest common factor. 6y³ - 3y

A population numbers 18,000 organisms initially and grows by 15.2% each year. Suppose Prepresents population, and t the number of years of growth. An exponential model for the population can be written in the form P = abt where P=

Richard mows 5 lawns for $25 each. He spends $15 on gas, then gives his dad half of what is left to cover his car insurance. He then spends $20 for himself and puts the remaining amount in his savings account. How many dollars did he put in his savings account? 20 2 55 42 35

If a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d = 3.57√h. Suppose the person's eye level is 8.41 meters above sea level. How far can she see to the horizon? Round your answer to the nearest tenth.

Simplify the following expressions completely: A) √49 = B)√144=

The police department in your city was asked by the mayor's office to estimate the cost of crime. The police began their study with burglary records, taking a random sample of 500 files since there were too many crime records to calculate statistics for all of the crimes committed. If the average dollar loss in a burglary, for this sample size 500 is $678, with a standard deviation of $560, construct the 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount. We can be 95% confident that the upper limit of our interval of dollar loss in crimes committed is

If 7000 dollars is invested in a bank account at an interest rate of 7 per cent per year, Find the amount in the bank after 5 years if interest is compounded annually: Find the amount in the bank after 5 years if interest is compounded quarterly: Find the amount in the bank after 5 years if interest is compounded monthly. Finally, find the amount in the bank after 5 years if interest is compounded continuously.

Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years. A) A = 100 + te² B) A = 100+ e²t C) A = 100e²t D) A = 100+ 2et

Approximate the number using a calculator. Round your answer to three decimal places. 3.2π 10.053 38.635 38.983 36.462

Decide whether a line with the given slope slants upward or downward or is horizontal or vertical m=3/2 Choose the correct answer below A horizontal B. upward C. downward D. vertical

A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 23 feet long, 17 feet wide, and 9 inches deep. a) Determine the volume, in cubic feet, of mulch the contractor will need. When appropriate, use the key on your calculator. b) If mulch costs $9 per cubic foot, what will the cost of mulch be? a) The volume is ft³. (Type an integer or decimal.)

Let f (x) = log2 (x) + 2 and g(x) = log2 (x³) - 4. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)

Carl owns a company that washes the windows of office buildings. He recently signed a contract for a large office building and estimates that it would take 2 days for 4 workers to wash the windows. Write an equation to describe the relationship between time (t) and the number of workers (n), which are inversely proportional. A) t = 2/n B) t = 6/n C) t = 16/n D) t = 8/n

The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 7 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds. Assume the confidence level to be 99%. Sample Size =

A population of bacteria triples every hour. Is this situation linear or exponential? A) Linear, because the function increases B) Linear, because the function increases by a common difference C) Exponential, because the function decreases D) Exponential, because the function grows by a common ratio

A station wagon covered a total distance of 3343 kilometres averaging a speed of 32 km/h in slow-moving traffic and 79 km/h in fast-moving traffic. The journey took 56 hours. How many hours did the station wagon spend in slow-moving traffic? (Hint distance = speed x time)

Beth can travel 203 miles in the same length of time it takes Anna to travel 192 miles. If Beth's speed is 4 mph greater than Anna's, find both rates. Hint: You'll be using the d = r*t formula, but in a different form. For the time column in the table below, you should put in expressions using the formula t= d/r a.Write down the unknown(s) you're being asked to find and assign a variable or expression to represent it (them). b. Organize the information provided in the table below. Rate Time Distance Beth Anna c.Using the information given in the problem and your table, write an equation representing this scenario. Then solve the equation. d. Write a sentence answering the question asked in the exercise using the appropriate units of measure. e.Assess your solution. Write a sentence indicating whether your solution makes sense. If it doesn't make sense, explain why.

toy company recently added some made-to-scale models of racecars to their product line. The length of a certain racecar is 19 ft. Its width is 7 ft. The width of the e-cast replica is 1.75 in. Find the length of the model.

Factor each expression: 125x³ +216 = 8a³-276³=

Use a graphing device to solve the inequality, as in Example 5. Express your answer using interval notation, with the endpoints of the intervals rounded to two decimals. x3-8x2 - 11x + 18 ≥ 0

Suppose you have 60 kg of a radioactive material that decays 50% of its mass every year. How much material will you have left after 4 years? 8.12 kg 32.1 kg 12.14 kg 3.14 kg

Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a continuous rate of 25% every day (that's why they're magic). How many grams of crystals will you have after one week (7 days)? 85.28 g 47.68 g 100 g 57.55 g

According to a country's census, the number of people (in thousands) who are expected to be over 100 years old in year x is approximated by the function f(x)=0.27x² +3.54x+50.78, where x = 0 corresponds to the year 2000 and the formula is valid through 2045. (a) Find a formula giving the rate of change in the number of people over 100 years old. (b) What is the rate of change in the number of people expected to be over 100 years old in the year 2015? (c) Is the number of people expected to be over 100 years old increasing or decreasing in 2015? (a) The formula for the rate of change of the number of people over the age of 100 is f'(x) =

Find the difference. (-67x² +68x+25) - (31x^2 + 49) =

Solve the triangle. a=25.53 km, b=20.81 km, c= 18.57 km Find the measure of angle A. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A= (Round to two decimal places as needed.) B. There is no solution.

Divide the following and express your answer in appropriate scientific notation: 6.84 x 10(71)/1.2 × 10(43)