3 salads, 4 main dishes, and 2 desserts Total meal combinations are found by multiplying each salad, main dish, and dessert using the fundamental rule of counting. The fundamental rule of counting states, if there are a ways of doing one thing, b ways of doing another thing, and c ways of doing another thing, than the total combinations of all the ways are found by a * b * c. With 3 salads, 4 main dishes, and 2 desserts, our total meal combinations are: 3 * 4 * 2 = [B]24 different meal combinations.[/B]

3^14/27^4 = ? Understand that 27 = 3^3. Rewriting this, we have: 3^14/(3^3)^4 Exponent identity states (a^b)^c = a^bc, so we have: 3^14/3^12 Simplifying, we have: 3^(14 - 12) = 3^2 = [B]9[/B] [MEDIA=youtube]u_238Z7Mqk[/MEDIA]

A 128 ounce carton of milk states that there are 20 servings. How many ounces are in a serving? We divide 128 ounces by 20 servings to get ounces per serving: 128 ounces / 20 servings [B]6.4 ounces / serving[/B]

A bag contains 7 red, 9 white, and 4 blue marbles. Find the probability of picking 3 blue marbles if each marble is NOT returned to the bag before the next marble is picked. The problem states we will have no replacement. [LIST] [*]First draw probability is 4 blue marbles out of (7 red + 9 white + 4 blue) = 20 marbles (4/20) [*]Second draw probability is 3 blue marbles out of (7 red + 9 white + 3 blue) = 19 marbles (3/19) [*]Third draw probability is 2 blue marbles out of (7 red + 9 white + 2 blue) = 18 marbles (2/18) [/LIST] Each draw is independent, so we multiply the three draws together: 4/20 * 3/19 * 2/18 24/6840 [B]0.0035[/B]

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model that represents the number y of muffins that the bakery sells x years after 2010. Find the number of muffins sold after 2010 through 2015: 7,420 - 5,800 = 1,620 Now, since the problem states a linear sales model, we need to determine the sales per year: 1,620 muffins sold since 2010 / 5 years = 324 muffins per year. Build our linear model: [B]y = 5,800 + 324x [/B] Reading this out loud, we start with 5,800 muffins at the end of 2010, and we add 324 more muffins for each year after 2010.

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win? Using our percentage calculators, we type the following statements into our search engine and get: [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=45&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']45% of 30[/URL] = 13.5 [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=60&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']65% of 60[/URL] = 39 For a total of 52.5 games won The team played 30 + 60 = 90 games. So we want to know the pecent: [URL='https://www.mathcelebrity.com/perc.php?num=52&den=90&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']52/90[/URL] = [B]57.78%[/B]

A certain group of woman has a 0.69% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness? 0.69% = 0.0069. There exists a statistics theorem for an event A that states: P(A) + P(A') = 1 where A' is the event not happening In this case, A is the woman having red/green color blindness. So A' is the woman [U][B][I]not[/I][/B][/U][I] having red/green color blindness[/I] So we have: 0.0069 + P(A') = 1 Subtract 0.0069 from each side, we get: P(A') = 1 - 0.0069 P(A') = [B]0.9931[/B]

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in the top 30% of the distribution gets a certificate. (b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state? (a) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.70&pl=Calculate+Critical+Z+Value']Top 30% is 70% percentile[/URL] Inverse of normal distribution(0.7) = -0.5244005 Plug into z-score formula, -0.5244005 = (x - 25)/4 [B]x = 22.9024[/B] (b) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']Top 5% is 95% percentile[/URL] Inverse of normal distribution(0.95) = 1.644853627 Plug into z-score formula, 1.644853627 = (x - 25)/4 [B]x = 31.57941451[/B]

A house sold for $200,000 and the real estate agent earned a commission of $10,200.00. Find the commission rate. Commission Rate = 100 * Commission Amount / Sale Price Commission Rate = 100 * 10200/20000 Commission Rate = 100 * 0.051 Commission Rate = [B]5.51%[/B]

The mean credit card debt among households in one state is $8400. A hypothesis test is to be performed to decide whether the mean credit card debt for households in the formerly affluent town of Rich-No-More differs from the mean credit card debt for the state.

A number t is no less than 30 and fewer than 40. This is a compound inequality. Take it in 3 parts: Step 1: fewer than 40 means less than (does not include 40) t < 40 Step 2: no less than 30 means greater than or equal to t >= 30 Step 3: Combine these 2 statements into one compound inequality: [B]30 <= t < 40[/B]

A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $50. What was her profit or loss She lost, since the sale price was less than the purchase price. The loss is calculated as: 50 - 60 = [B]-$10[/B]

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?" Let the number of children be c. Let the number of parents be p We're given: [LIST=1] [*]c = p + 9 [I](9 more children than parents)[/I] [*]c + p = 25 [/LIST] to solve this system of equations, we plug equation (1) into equation (2) for c: (p + 9) + p = 25 Group like terms: 2p + 9 = 25 To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p%2B9%3D25&pl=Solve']type it in our search engine[/URL] and we get: p = [B]8[/B]

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remainder. How much commission is received on the sale of a $450,000 property? Calculate commission on first $100,000 (Commission 1): Commission 1 = $100,000 * 0.035 Commission 1 = $3,500 Calculate commission on the remainder (Commission 2): Commission 2 = 0.025 * ($450,000 - $100,000) Commission 2 = 0.025 * ($350,000) Commission 2 = $8,750 Calculate Total Commission: Total Commission = Commission 1 + Commission 2 Total Commission = $3,500 + $8,750 Total Commission = [B]$12,250[/B]

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads as she can afford, how much money will the real estate agent have left over? We want to know the remainder of 920/6. We can type 920 mod 6 into our search engine and get: [URL='https://www.mathcelebrity.com/modulus.php?num=920mod6&pl=Calculate+Modulus']920 mod 6[/URL] = [B]2[/B]

A real estate agent sells a house for $229,605. A sales commission of 6% is charged. The agent gets 45% of this commission. How much money does the agent get? The agents Commission (C) is: C = Sale price * sales commission percent * agent commission percent Since 6% = 0.06 and 45% = 0.45, we have: C = 229605 * 0.06 * 0.45 C = [B]6,199.34[/B]

A Septonian won the lottery in the United States and won $1,000,000. How many dollars in that in base 7? Using our [URL='https://www.mathcelebrity.com/binary.php?num=1000000&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we get: 1,000,000 in base 7 = [B]11,333,311[/B]

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights. The cost in dollars C is found below: [B]C = 7.50n + 6[/B]

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights. We write this as: cost per night of camping * n nights + entry fee [B]7.50n + 6[/B]

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies? We set up our exponential function where n is the number of days after today: Z(n) = 25 * 2^n We want to know n where Z(n) = 25,000. 25 * 2^n = 25,000 Divide each side of the equation by 25, to isolate 2^n: 25 * 2^n / 25 = 25,000 / 25 The 25's cancel on the left side, so we have: 2^n = 1,000 Take the natural log of each side to isolate n: Ln(2^n) = Ln(1000) There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have: n * Ln(2) = Ln(1,000) 0.69315n = 6.9077 [URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get: [B]n = 9.9657 days ~ 10 days[/B]

A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt? State this as an equation. Let the price of the shirt be s. 5 times as much means we multiply s by 5: 5s = 40 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D40&pl=Solve']Type this equation into the search engine[/URL], we get: s = [B]8[/B]

Aaron bought a guitar for n dollars. The tax in his state is 6%. What is the total cost of the guitar including tax? Sale price is n Tax on sale is 0.06n Add them together n + 0.06n = [B]1.06n[/B]

Free Algebraic Substitutions Calculator - Given an algebraic statement with variables [a-z], this calculator takes a set of given substitution values, i.e., x=2,y=3,z=4, and evaluates your statement using the substitution values.

Alonzo needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of 48 pencils for $9.98. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent. Using our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=8.52&p2=9.98&q1=36&q2=48&pl=Better+Buy']better buy calculator[/URL], we see the following unit prices: [LIST] [*][B]Brand A = $0.24[/B] [*][B]Brand B = $0.21[/B]. [*][B]Brand B has the better unit price by 3 cents.[/B] [/LIST]

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings which need 3 lamps each. Write a formula to find z, the total number of lamps needed on the estate. z = 6(x * 1 + 3 * y) z = [B]6(x + 3y)[/B]

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest? Let's assume payments are made at the end of each month, since the problem does not state it. We have an annuity immediate formula. Interest rate per month is 6.6%/12 = .55%, or 0.0055. 7 years * 12 months per year gives us 84 deposits. Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=950&n=84&i=0.55&check1=1&pl=Calculate']present value of an annuity immediate calculator[/URL], we get the following: [LIST=1] [*]Accumulated Value After 7 years = [B]$101,086.45[/B] [*]Principal = 79,800 [*]Interest Paid = (1) - (2) = 101,086.45 - 79,800 = [B]$21,286.45[/B] [/LIST]

Arizona became a state in 1912. This was 5 years after Oklahoma became a state. Which equation can be used to find the year Oklahoma became a state? In what year did Oklahoma become a state? Let o be the year Oklahoma became a state: o = 1912 - 5 o = [B]1907[/B]

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years. At any time t, the Bangladesh population at year t is: [B]y = 170,000,000(1.015)^t[/B]

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this. We have: 25f + 100c < 50 Note: We use < and not <= because it states less than in the problem.

Chris has 6 cds that he is going to give away. He let his best friend choose 2 of the 6 cds. How many different groups of 2cds are possible? We want 6 choose 2 using combinations. We use combinations because the problem states the word [I]different[/I]. [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=2&pl=Combinations']6 C 2[/URL] using our calculator is [B]15[/B].

Common Core State Standards List

Dan bought a computer in a state that has a sales tax rate of 7%. If he paid $67.20 sales tax, what did the computer cost? Set up the equation for price p: p * 0.07 = 67.20 p = 67.20 / 0.07 p = [B]$960[/B]

Determine if the statement below is True or False If B ? A, then A ? B = B Is this statement True or False? [B]True:[/B] If B ? A, then B ? A So A ? B is the similar elements of both. B contains itself as a subset. So this is [U]true[/U]

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2 For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x. Add 2: x + 2 Multiply your answer to 3: 3(x + 2) And minus 2 which means we subtract: [B]3(x + 2) - 2[/B]

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of customers arriving at a bank between noon and 1:00 P.M. (i) The random variable is continuous. The possible values are x >= 0. (ii) The random variable is discrete. The possible values are x = 0, 1, 2,... (iii) The random variable is continuous. The possible values are x = 0, 1, 2,... (iv) The random variable is discrete. The possible values are x >= 0. (b) The amount of snowfall (i) The random variable is continuous. The possible values are s = 0, 1, 2,... (ii) The random variable is discrete. The possible values are s >= 0. (iii) The random variable is discrete. The possible values are s = 0, 1, 2,... (iv) The random variable is continuous. The possible values are s >= 0. [B](a) (ii) The random variable is discrete. The possible values are x = 0, 1, 2,... Discrete variables are limited in the values they can take between 9 and ? (b) (iv) The random variable is continuous. The possible values are s >= 0. Snowfall can be a decimal and can vary between 0 and ?[/B]

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b We have a logarithmic property that states: ln(a) - ln(b) = ln (a / b) We're given a < b, so (a / b) < 1 Therefore: ln (a / b) < 0 And since ln(a) - ln(b) = ln (a / b) Then Ln(a) - Ln(b) < 0 Add Ln(b) to each side and we get: Ln(a) - Ln(b) + Ln(b) < 0 + Ln(b) Cancel the Ln(b) on the left side and we get: Ln(a)

Determine whether the statement is true or false. If y = e^2, then y’ = 2e e^2 is a constant, and the derivative of a constant is 0. So y' = 0 So this is [B]FALSE[/B]

Determine whether the statement is true or false. You can always divide by e^x [B]True. As x --> infinity, 1/e^x approaches 0 but never touches it.[/B]

does the equation y= x/3 represent a direct variation? If so, state the value of k [B]Yes[/B], it's a direct variation equation. We rewrite this as: y = 1/3 * x So k = 1/3, and y varies directly as x.

Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to translate the above statements into algebraic equation. Our algebraic expression is: [B]0.25x = 2 [/B] To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%3D2&pl=Solve']type it in our search engine[/URL] and we get: x = [B]8[/B]

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2 equations. Let g be the number of German states. Let a be the number of Austrian states. We're given two equations: [LIST=1] [*]a + g = 25 [*]g = a + 7 [/LIST] To solve this system of equations, we substitute equation (2) into equation (1) for g: a + (a + 7) = 25 Combine like terms: 2a + 7 = 25 To solve for a, we[URL='https://www.mathcelebrity.com/1unk.php?num=2a%2B7%3D25&pl=Solve'] type this equation into our search engine[/URL] and we get: [B]a = 9[/B] To solve for g, we plug in a = 9 into equation (2): g = 9 + 7 [B]g = 16[/B]

Hayden bought 48 new trading cards. Three-fourths of the new cards are baseball cards. How many baseball cards did Hayden buy? We want 3/4 of 48. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=48&frac2=3/4&pl=Multiply']type this statement into our calculator[/URL] and we get: [B]36[/B]

Perform a one-sample z-test for a population mean. Be sure to state the hypotheses and the significance level, to compute the value of the test statistic, to obtain the P-value, and to state your conclusion. Five years ago, the average math SAT score for students at one school was 475. A teacher wants to perform a hypothesis test to determine whether the mean math SAT score of students at the school has changed. The mean math SAT score for a random sample of 40 students from this school is 469. Do the data provide sufficient evidence to conclude that the mean math SAT score for students at the school has changed from the previous mean of 475? Perform the appropriate hypothesis test using a significance level of 10%. Assume that ? = 73.

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the standard deviation for the distribution, according to the empirical rule, is The empirical rule states 68% of the values lie within 1 standard deviation of the mean. The mean is the midpoint of the interval above: (59.9 + 40.7)/2 = 50.3 Standard deviation is the absolute value of the mean - endpoint |59.9 - 50.3| = [B]9.6[/B]

If the probability of rain is 15%, what is the probability that it won't rain? If we assign the probability of raining as event A, then A' (A complement) is the probability it won't rain. Since it either rains or doesn't rain are the only two events. There exists an axiom in statistics that states: P(A) + P(A') = 1 Rearranging this, we get: P(A') = 1 - P(A) If we assign the probability of raining as event A which is 0.15, we get: P(A') = 1 - 0.15 P(A') = [B]0.85[/B]

If x2 is added to x, the sum is 42. x^2 + x = 42 Subtract 42 from both sides: x^2 + x - 42 = 0 We have a quadratic equation. Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-42%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation solver[/URL], we get: [B]x = 6 and x = -7 [/B] Since the problem does not state positive number solutions, they are both answers.

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose State ran the 100-yard dash in 9.1 seconds. Which runner had the faster average speed? We [URL='https://www.mathcelebrity.com/linearcon.php?quant=100&type=yard&pl=Calculate']convert yards to meters using our conversion calculator[/URL] and we get: 100 yards = 91.44 meters Now we set up a proportion of time per meter: [LIST] [*]Ato Boldon: 9.92/100 = 0.992 per meter [*]John Carlos: 9.1/91.44 = 0.995 per meter [/LIST] [B]Since Ato Boldon's time was [I]less per meter[/I], he had the faster average speed[/B]

Free Interval Counting Calculator - Evaluates a set of interval counting statements in the form a(b)c.

Free Interval Notation and Set Builder Notation Calculator - This calculator translates the following inequality statements to interval notation and set builder notation:
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* Compound Inequality such as 0 <= c < 4
* |x|<3
* Reverse Interval Notation to Inequality Statement such as (-7,5]
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* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8

Is there any other statement in mathematics for this with the "upper" definition? Replace "50" with "x" x + 10% x

When are you selling tickets? That is not stated in the problem.

It is known that 45% of men snore an 25% of women snore. A doctor looked at these numbers and made the following statement: "If you put a man and a woman together, there is a 70% chance that someone is snoring." Explain why the doctor's math is wrong. The doctor added the percents together: 45% + 25% = 70%. Here's why this is incorrect: [LIST] [*]45% of men snore means 100% - 45% = 55% of men do not snore [*]25% of women snore means 100% - 25% = 75% of women do not snore [*]Both men and women not snoring is: 55% * 75% = 41.25% neither of them snore [*]100% - 41.25% = [B]58.75%[/B] somebody is snoring [/LIST]

John mows 3 lawns in 4 hours, Paul mows 5 lawns in 6 hours. Who mows faster? To see who mows faster, we set up fractions with a common denominator. You can see this by running this statement in the calculator: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3/4&frac2=5/6&pl=Compare']3/4 or 5/6[/URL] You'll see that 5/6 is larger, so Paul mores more lawns per hour.

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month? [U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 10% written as a decimal is 0.1. We want decimals to solve equations easier. S(m) = 0.1m + 1500 [U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 15% written as a decimal is 0.15. We want decimals to solve equations easier. S(m) = 0.15m + 1200 [U]The question asks what is m when both S(m)'s equal each other[/U]: The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other 0.1m + 1500 = 0.15m + 1200 We want to isolate m terms on one side of the equation. Subtract 1200 from each side: 0.1m + 1500 - 1200 = 0.15m + 1200 - 1200 Cancel the 1200's on the right side and we get: 0.1m - 300 = 0.15m Next, we subtract 0.1m from each side of the equation to isolate m 0.1m - 0.1m + 300 = 0.15m - 0.1m Cancel the 0.1m terms on the left side and we get: 300 = 0.05m Flip the statement since it's an equal sign to get the variable on the left side: 0.05m = 300 To solve for m, we divide each side of the equation by 0.05: 0.05m/0.05 = 300/0.05 Cancelling the 0.05 on the left side, we get: m = [B]6000[/B]

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Free Phonetic Algorithms Calculator - Given a name, this calculator translates a name to one of the following 3 phonetic algorithms:
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We are given, using the word word problem combined formula, that: 1/j + 1/p + 1/m = 1/3 However, you state the hours working alone, but then ask how much it would take working alone. I'm confused on the last part. Can you clarify?

Take an integer n. The next alternate consecutive integer is n + 2 Subtract the difference of the squares: (n + 2)^2 - n^2 n^2 + 4n + 4 - n^2 n^2 terms cancel, we get: 4n + 4 Factor out a 4: 4(n + 1) If n is odd, n + 1 is even. 4 * even is always even If n is even, n + 1 is odd. 4 * odd is always odd Since both cases are even, we've proven our statement. [MEDIA=youtube]J_E9lR5qFY0[/MEDIA]

Take an integer n. The next consecutive integer is n + 1 Subtract the difference of the squares: (n + 1)^2 - n^2 n^2 + 2n + 1 - n^2 n^2 terms cancel, we get: 2n + 1 2 is even. For n, if we use an even: we have even * even = Even Add 1 we have Odd 2 is even. For n, if we use an odd: we have even * odd = Even Add 1 we have Odd Since both cases are odd, we've proven our statement. [MEDIA=youtube]RAi0HbH5bqc[/MEDIA]

Prove the following statement for non-zero integers a, b, c, If a divides b and b divides c, then a divides c. If an integer a divides an integer b, then we have: b = ax for some non-zero integer x If an integer b divides an integer c, then we have: c = by for some non-zero integer y Since b = ax, we substitute this into c = by for b: c = axy We can write this as: c = a(xy) [LIST] [*]Since x and y are integers, then xy is also an integer. [*]Therefore, c is the product of some integer multiplied by a [*]This means a divides c [/LIST] [MEDIA=youtube]VUIUFAFFVU4[/MEDIA]

Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent. Let d be the cost of each drink, and p be the price of each popcorn bag. We have 2 equations for our system of equations: [LIST=1] [*][B]4d + 9p = 65.25[/B] [*][B]8d + 3p = 51.75[/B] [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+9p+%3D+65.25&term2=8d+%2B+3p+%3D+51.75&pl=Cramers+Method']system of equations calculator[/URL], we get: [LIST] [*]d = 4.5 [*][B]p = 5.25 <-- Since the problem asks for the cost of each popcorn bag[/B] [/LIST]

States that begin with the letter C Our set has 3 elements: [B]{California, Colorado, Connecticut}[/B]

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. a. If X = distance in feet for a fly ball, then X ~ b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability. c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement. a. [B]N(250, 50/sqrt(1))[/B] b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL] Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B] c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL] Z-score formula: 0.8416 = (x - 250)/50
x = [B]292.08[/B]

The negative of the sum of C and D is equal to the difference of the negative of C and D The negative of the sum of C and D means -1 times the sum of C and D -(C + D) Distribute the negative sign: -C - D the difference of the negative of C and D means we subtract D from negative C -C - D So this statement is [B]true[/B] since -C - D = -C - D

The NJ state education department finds that in a random sample of 100 persons who attended college, 40 received a college degree. What's the 95% confidence interval for the proportion of college graduates out of all the persons who attended college? [URL='http://www.mathcelebrity.com/propconf.php?bign=100&smalln=40&conf=95&pl=Proportion+Confidence+Interval']Proportion Confidence Interval Test[/URL] 0.304 < p < 0.496 --> [B]30.4% < p < 49.6%[/B]

Let's take this by pieces. The product of 8 and a number k is written as: 8k. Since it's greater than 4, but not more than 16, we include this in the middle of an inequality statement. 4 < 8k <= 16 Notice no more than has an equal sign, it means less than or equal to. Greater does not include an equal sign.

The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other. Let the 2 numbers be x and y. We have: [LIST=1] [*]xy = 96 [*]x = y - 4 [/LIST] [U]Substitute (2) into (1)[/U] (y - 4)y = 96 y^2 - 4y = 96 [U]Subtract 96 from both sides:[/U] y^2 - 4y - 96 = 0 [U]Factoring using our quadratic calculator, we get:[/U] (y - 12)(y + 8) So y = 12 and y = -8. Since the problem states positive numbers, we use [B]y = 12[/B]. Substituting y = 12 into (2), we get: x = 12 - 4 [B]x = 8[/B] [B]We have (x, y) = (8, 12)[/B]

The senior class at high school A and high school B planned separate trips to the state fair. There senior class and high school A rented and filled 10 vans and 6 buses with 276 students. High school B rented and filled 5 vans and 2 buses with 117 students. Every van had the same number of students in them as did the buses. How many students can a van carry?? How many students can a bus carry?? Let b be the number of students a bus can carry. Let v be the number of students a van can carry. We're given: [LIST=1] [*]High School A: 10v + 6b = 276 [*]High School B: 5v + 2b = 117 [/LIST] We have a system of equations. We can solve this 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get: [LIST] [*][B]b = 21[/B] [*][B]v = 15[/B] [/LIST]

The square of a positive integer minus twice its consecutive integer is equal to 22. Find the integers. Let x = the original positive integer. We have: [LIST] [*]Consecutive integer is x + 1 [*]x^2 - 2(x + 1) = 22 [/LIST] Multiply through: x^2 - 2x - 2 = 22 Subtract 22 from each side: x^2 - 2x - 24 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2-2x-24%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: x = 6 and x = -4 Since the problem states [U]positive integers[/U], we use: x = 6 and x + 1 = 7 [B](6, 7)[/B]

The sum of a number and its square is 72. find the numbers? Let the number be n. We have: n^2 + n = 72 Subtract 72 from each side: n^2 + n - 72 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we have: [B]n = 8 or n = -9 [/B] Since the numbers do not state positive or negative, these are the two solutions.

The tax in a state is 5%. If Eric paid $4.60 tax for a bike, what was the cost of the bike before sales tax was added? 4.60 / 0.05 = [B]$92[/B]

The United States Department of Agriculture reports that 18% of Americans are now on food stamps. If there are 250,000,000 Americans, how many are on food stamps? Since 18% is 0.18, we have: 250,000 * 0.18 = 45,000

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue? Find the total number of marbles in the bag: Total marbles = 5 blue + 6 red + 2 green Total marbles = 13 The problem asks for exactly one blue in 2 draws [I]with replacement[/I]. Which means you could draw as follows: Blue, Not Blue Not Blue, Blue The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time. The probability of not drawing a blue is (6 + 2)/13 = 8/13 And since each of the 2 draws are independent of each other, we multiply the probability of each draw: Blue, Not Blue = 5/13 * 8/13 =40/169 Not Blue, Blue = 8/13 * 5/13 = 40/169 We add both probabilities since they both count under our scenario: 40/169 + 40/169 = 80/169 Checking our [URL='https://www.mathcelebrity.com/fraction.php?frac1=80%2F169&frac2=3%2F8&pl=Simplify']fraction simplification calculator[/URL], we see you cannot simplify this fraction anymore. So our probability stated in terms of a fraction is 80/169 [URL='https://www.mathcelebrity.com/perc.php?num=80&den=169&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Stated in terms of a decimal[/URL], it's 0.4734

The triangle sum theorem states the sum of the three angles in a triangle equals 180 degrees. So if you're given two angles and need too find the 3rd angle, add the 2 known angles up, and subtract them from 180 to get the 3rd angle measure.

Free Truth Tables Calculator - Sets up a truth table based on a logical statement of 1, 2 or 3 letters with statements such as propositions, equivalence, conjunction, disjunction, negation. Includes modus ponens.

Tyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at least 52 inches tall to ride. Which statements describe how much taller Tyrese’s sister must be to ride? Let h be the required additional height. The phrase [I]at least[/I] means an inequality, using the >= sign, so we have: h + 41 >= 52 If we want another way to express this, we [URL='https://www.mathcelebrity.com/1unk.php?num=h%2B41%3E%3D52&pl=Solve']type this inequality into our math engine[/URL] and we get: [B]h >= 11[/B]

Free What is a Variable Calculator - This lesson walks you through what a variable is and how to use it. Also demonstrates the let statement.

Which of the following involves making pairwise comparisons? a. Comparing the standard deviation of GRE grades between two states b. Comparing the variance of the amount of soda consumed by boys and girls in a high school c. Comparing the mean weight between children in grades 2, 3, 4 and 5 d. Comparing the number of restaurants in New York and Boston [B]c. Comparing the mean weight between children in grades 2, 3, 4 and 5[/B] Pairwise comparison generally refers to any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some quantitative property

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the rest of the money to buy shirts. Find the inequality. Let j be the number of jeans. Let s be the number of shirts. We are given: [LIST] [*]Mom told you to buy one pair of jeans. So we have $80 to start with - $29 for 1 pair of jeans = $51 left over [/LIST] Now, since shirts cost $12 each, and our total number of shirts we can buy is s, our inequality is [B]12s <= 51[/B]. We want to find the s that makes this inequality true. [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12s%3C%3D51&pl=Show+Interval+Notation']Run this statement through our calculator[/URL], and we get s <= 4.25. But, we need s to be an integer, so we have s <= 4.

You went to the State Fair and spent $20. If cotton candy costs $2 and a soda pop costs $1. Which equation represents the relation between the number of cotton candy (c) and soda pops (s) you can buy? Our total cost for 20 at the state fair is: Cost of Cotton Candy + Cost of Soda = 20 We know that price = cost * quantity, so we have: 2c + 1s = 20 Since 1s is written as s, we have: [B]2c + s = 20[/B]

Free Z Score Lookup Calculator - Given a Z-score probability statement from the list below, this will determine the probability using the normal distribution z-table.
* P(z < a)
* P(z <= a)
* P(z > a)
* P(z >= a)
* P(a < z < b) Calculates z score probability