A b = b a is an example of the property called the [B]commutative property of multiplication[/B].

A bacteria population increases every hour. At 12pm there are 5 cells. At 1pm there are 10 cells. At 2pm there are 20 cells. At 3pm there are 40 cells. If this pattern continues, how many cells will there be at 7pm? The bacteria cells double each hour in the example above. From 3pm to 7pm, we have 4 hours, meaning 4 doubling periods. Which is 2 * 2 * 2 * 2 or 2^4. So we have: 40 * 2^4 40 * 16 = [B]640 cells[/B]

A financial analyst computed the ROI for all companies listed on the NYSE. She found that the mean of this distribution was 10% with standard deviation of 5%. She is interested in examining further those companies whose ROI is between 14% and 16% of the approximately 1,500 companies listed on the exchange, how many are of interest of her? First, use our [URL='http://www.mathcelebrity.com/zscore.php?z=p%280.14%3Cz%3C0.16%29&pl=Calculate+Probability']z-score calculator[/URL] to get P(0.14 < z < 0.16) = 0.007889 Divide that by 2 for two-tail test to get0.003944729 Use the NORMSINV(0.003944729) in Excel to get the Z value of 2.66 Therefore, the companies of interest are 2.66 * 1500 * 0.10 = [B]399[/B]

A flea is very small, but can jump very high. For example, a flea that is 1/8 inch tall can jump 12 inches in height. If a child who is 4 feet tall had the ability to jump like a flea, how high could she jump? Set up a proportion of height to jump height where j is the jump height of the child: 1/8/12 = 4/j Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=0.125&num2=4&den1=12&den2=j&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: j = [B]384 feet[/B]

I brute forced this and got a wrong answer, logic tells me is right. I tried the calculator here but maybe messed up the equation using another users problem as an example. Having no luck. Problem: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 9 times the age of Clinton. How old are they now and how old were they 8 years ago?

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Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and only one test remains. If you need a mean score of 80% to earn a B for you final grade, is it possible for you to accomplish this? Assume there is no extra credit. Show work and explain why or why not. Hint: you're taking 4 tests total. Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=74%2C78%2C63&avg=80&pl=Calculate+Missing+Score']missing average calculator with our 3 given scores and target average[/URL], we get: A 4th score needed of 105. Since the most you can score on an exam is 100, [B][I]this is impossible[/I][/B].

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V = 1/3(pi)r^2h You want dv/dt. Here is an [URL='https://www.freemathhelp.com/forum/archive/index.php/t-77610.html']example[/URL]:

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Free Derivatives Calculator - This lesson walks you through the derivative definition, rules, and examples including the power rule, derivative of a constant, chain rule

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12. Our givens are: [LIST] [*]I = 450 [*]P = 3000 [*]t = 3 [*]We want r [/LIST] 450 = 3000(r)(3) 450 = 9000r Divide each side by 9000 [B]r = 0.05[/B]

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Explain the relationship between "squaring" a number and finding the "square root" of a number. Use an example to further explain your answer. Squaring a number means raising it to the power of 2 The square root of a number [I]undoes[/I] a square of a number. So square root of x^2 is x x squared is x^2 Let x = 5. x squared = 5^2 = 25 Square root of 25 = square root of 5^2 = 5

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Finding a 20% tip no calculator We have 2 methods to calculate a 20% tip. [LIST=1] [*]Divide by 5 [*]Shift one decimal place left and take the value. Multiply by 2 [/LIST] Example: 180 tip, find a 20% tip: Method 1: 180/5 = 36 Method 2: Move decimal place left = 18 Multiply this value by 2: 18 * 2 = 36 [MEDIA=youtube]UW4GYWfMhsE[/MEDIA]

First four exams scores were 78%, 76%, 82% and 84%. What is needed on the final exam to receive a 90% exam average? We need a missing average. [URL='https://www.mathcelebrity.com/missingaverage.php?num=78%2C+76%2C+82%2C84&avg=90&pl=Calculate+Missing+Score']Using our missing average calculator with our 4 test scores and a target average of 90%[/URL], we get: [B]130%[/B]

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If all A's are B's, then all B's are A's. Is this true? [B]No.[/B] Example: All dogs are mammals, but not all mammals are dogs. All squares are rectangles, but not all rectangles are squares.

Free Integrals Calculator - This lesson walks you through the integral definition, rules, and examples

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this. At least means greater than or equal to, so we have: [B]3x + 4y >= 76[/B]

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Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What could N be? Is there more than one answer? For example, for 23 P(23) = 6 and S(23) = 5, but 23 could not be the N that we want since 23 <> 5 + 6 Let t = tens digit and o = ones digit P(n) = to S(n) = t + o P(n) + S(n) = to + t + o N = 10t + o Set them equal to each other N = P(N) + S(N) 10t + o = to + t + o o's cancel, so we have 10t = to + t Subtract t from each side, we have 9t = to Divide each side by t o = 9 So any two-digit number with 9 as the ones digit will work: [B]{19,29,39,49,59,69,79,89,99}[/B]

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per book. What is the royalty he receives? Remember to put the $ symbol in your answer. For example, if your answer is 10 dollars, write $10 in the answer box. [U]Calculate total sales:[/U] Total Sales = Number of Books * Price per book Total Sales = 50,000 * $35 Total Sales = $1,750,000 [U]Now calculate Mike's royalties:[/U] Royalties = Total Sales * Royalty Percent Royalties = $1,750,000 * 15% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=15&den1=1750000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Royalties[/URL] = [B]$262,500[/B]

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Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include:
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Free Random Number Generator Calculator - This program generates (n) random numbers between a set of values you specify.
Example: Generate 5 random numbers between 0 and 100.

Rob has scores of 73,75 and 79 on three exams. what does he need on the last exam to get an average of no less than 80 Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=73%2C75%2C79&avg=80&pl=Calculate+Missing+Score']missing average calculator[/URL], we find the missing score must be: [B]93[/B]

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Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include:
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Take a look at the following sums: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25 a. Come up with a conjecture about the sum when you add the first n odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What if wanted to add the first 10 odd numbers? Or 100? b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have 4 squares and add on 5 more, what can you make? c. Is there a similar pattern for adding the first n even numbers? 2 = 2 2 + 4 = 6 2 + 4 + 6 = 12 2 + 4 + 6 + 8 = 20 a. The formula is [B]n^2[/B]. The sum of the first 10 odd numbers is [B]100[/B] seen on our s[URL='http://www.mathcelebrity.com/sumofthefirst.php?num=10&pl=Odd+Numbers']um of the first calculator[/URL] The sum of the first 100 odd numbers is [B]10,000[/B] seen on our [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=100&pl=Odd+Numbers']sum of the first calculator[/URL] b. Geometric is 1, 4, 9 which is our [B]n^2[/B] c. The sum of the first n even numbers is denoted as [B]n(n + 1)[/B] seen here for the [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=+10&pl=Even+Numbers']first 10 numbers[/URL]

the absolute value of a number is its _____ from 0 The answer is [B]distance[/B]. As an example: 2 and -2 are 2 units away from 0.

The astronomer found that 0.017 at the stars examined were red dwarfs. if 29,000 stars or examined, how many were not red dwarfs? [U]If 0.017 were red dwarfs, then we have a not red dwarfs percent of:[/U] Not red dwarfs pct = 1 - red dwarfs Not red dwarfs pct = 1 - 0.017 Not red dwarfs pct = 0.983 [U]For 29,000 stars, we have[/U] Not red dwarfs = Starts * not red dwarfs pct Not red dwarfs = 29000 * 0.983 Not red dwarfs = [B]28,507[/B]

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Digit, Probability 1, 0.301 2, 0.176 3, 0.125 4, 0.097 5, 0.079 6, 0.067 7, 0.058 8, 0.051 9, 0.046 [B][U]Fradulent Checks[/U][/B] Digit, Frequency 1, 36 2, 32 3, 45 4, 20 5, 24 6, 36 7, 15 8, 16 9, 7 Complete parts (a) and (b). (a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?
Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

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x% of y is the same as y% of x Example 1: 18% of 10 is the same as 10% of 18 10% is easy because we move the decimal one place left to get [B]1.8[/B] Example 2: 40% of 50 is the same as 50% of 40 50% is easy because we cut a number in half 40/2 = [B]20 [MEDIA=youtube]aiKsvYWEo0c[/MEDIA][/B]

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what is a well defined set? A well defined set is with no ambiguity or confusion about what belongs to the set. Think of it as a collection of distinct objects: Examples: [LIST] [*]Set of the first 5 even numbers: {2, 4, 6, 8, 10} [*]Set of weekend days: {Saturday, Sunday} [/LIST]

When finding the power of a power, you _____________________ the exponents [B]Multiply [/B] Example: (a^b)^c = a^bc

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Write a fraction with a denominator of 9. The fraction should be less than 1/2 Let n be the numerator. We have: n/9 < 1/2 multiply each side by 9: 9n/9 < 9/2 n < 9/2 Examples are 8/2, 7/2, 6/2, 5/2, 4/2, 3/2,

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