7.5 degrees C to -5.21 degrees C. Kayla and Jason were discussing the changes in temperature. Kayla said, "Wow, I can't believe the temperature fell 12.71 degrees C." Jason said, "What are you talking about? The temperature only fell 2.29 degrees C." Who is correct [B]Kayla[/B] is correct. The temperature change TC is: TC = High Temp - Low Temp TC = 7.5 - (-5.21) TC = 7.5 + 5.21 ([I]Since a minus negative is positive)[/I] TC = 12.71

A car is traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is traveling at 90 mph with the cruise control set at 90 mph. Which car has a higher acceleration? Acceleration means a change in speed. Neither car has a change in speed, [B]so both cars have the same acceleration which is 0[/B]

A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the ballon increasing when the radius is 2cm? [U]The volume (V) of the balloon with radius (r) is:[/U] V = 4/3?r^3 [U]Differentiating with respect to t, we get:[/U] dV/dt = 4/3? * 3r^2 * dr/dt dV/dt = 4?r^2 * dr/dt The rate of change of the volume is: dV/dt = 10cm^3s^?1 [U]So, we find dr/dt:[/U] dr/dt = 1/4?r^2 * dV/dt dr/dt = 10/4?r^2 dr/dt = 5/2?r^2 Therefore, dr/dt(2cm) is: dr/dt(2cm) = 5/2?(2)^2 dr/dt(2cm) = 5/2?4 dr/dt(2cm) = [B]5?/8[/B]

A city’s population in the 1987 was 125,524. In 2007 the population was 436,884. Determine the population rate of increase or decrease [U]Find the population change:[/U] Population Change = New Population - Old Population Population Change = 436,884 - 125,524 Population Change = 311,360 [U]Since the population change increased, we calculate the rate of increase:[/U] Rate of increase = 100% * Population Change / Starting Population Rate of increase = 100% * 311,360 / 125,524 Rate of increase = 100% * 2.48 Rate of increase = [B]248%[/B]

A customer buys 5 pounds of apples at $0.79 a pound. They hand the cashier a $10 bill. How much change will they get back? Calculate the total bill: Total Bill = Pounds of Apples * Cost per pound Total Bill = 5 * 0.79 Total Bill = $3.95 Calculate Change: Change = Money Offered - Total Bill Change = $10 - $3.95 Change = [B]$6.05[/B]

A dad gave his 3 sons each the same amount of money in an envelope. He took $20 from one son for getting a D on a math test and he gave another son an extra $35 for doing extra chores. Combined, the sons had $81. Figure out how much each son had. Let x, y, and z be the money each son received. To begin, x = y = z. But then, Dad took 20 from son X and gave it to son Y. So now, x = y - 20 Next, he gave Son Z an extra $35 for chores So z is now y + 35 since y and z used to be equal Combined, they all have 81. x + y + z = 181 But with the changes, it is: (y - 20) + y + (y + 35) Combine like terms: 3y - 20 + 35 = 81 3y + 15 = 81 Subtract 15 from each side: 3y = 66 Divide each side by 3 to isolate y y = 22 Since x = y - 20, x = 2 Since z = y + 35, we have z = 57 Checking our work, 2 + 22 + 57 = 81.

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 football team lost 7 yards each play for four consecutive plays. Represent the team’s total change in position for the four plays as an integer. A net loss in yardage for 7 yards is written as -7 4 plays * -7 yards equals [B]-28[/B]

A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives the value of the house, v, as a function of y, the number of years after 1989. Let's determine the years: 2000 - 1989 = 11 Let's determine the change in value: 125,000 - 70,000 = 55,000 Assuming a linear progression, we have: 55,000/11 = 5,000 per year increase [B]y = 70,000 + 5,000v[/B] where v is the number of years after 1989 Plug in 11 to check our work y = 70,000 + 5,000(11) y = 70,000 + 55,000 y = 125,000

A lady walks into a store and steals $100 bill from the register without the owners knowledge. She comes back 5 minutes later and buys $70 worth of goods with the $100 bill. The owner gives her $30 in change. How much did the owner lose? [LIST=1] [*]After the lady steals $100, the owner is down -$100. [*]The lady comes back, and buys $70 worth of goods. At this point, the owner has -$100 + $70 = $-30. [*]Next, the owner gives the lady another $30 in change, making the owner's loss -$30 - $30 = [B]-$60[/B]. [/LIST]

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes). Checkout Time (in minutes) | Frequency | Relative Frequency 1.0 - 1.9 | 2 | ? 2.0 - 2.9 | 8 | ? 3.0 - 3.9 | ? | ? 4.0 - 5.9 | 5 | ? Total | 25 | ? (a) Complete the frequency table with frequency and relative frequency. (b) What percentage of the checkout times was less than 3 minutes? (c)In what class interval must the median lie? Explain your answer. (d) Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why? (a) [B]Checkout Time (in minutes) | Frequency | Relative Frequency 1.0 - 1.9 | 2 | 2/25 2.0 - 2.9 | 8 | 8/25 3.0 - 3.9 | 10 (since 25 - 5 + 8 + 2) = 10 | 10/25 4.0 - 5.9 | 5 | 5/25 Total | 25 | ?[/B] (b) (2 + 8)/25 = 10/25 = [B]40%[/B] c) [B]3.0 - 3.9[/B] since 2 + 8 + 10 + 5 = 25 and 13 is the middle value which occurs in the 3.0 - 3.9 interval (d) [B]Mean increases[/B] since it's a higher value than usual. Median would not change as the median is the most frequent distribution and assuming the 5.8 is only recorded once.

A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds later. At what rate is the scuba diver going deeper down in the water If we take these as coordinates on a graph, where y is the depth and x is the time, we calculate our slope or rate of change where (x1, y1) = (10, 30) and (x2, y2) = (40, 100) Rate of change = (y2 - y1)/(x2 - x1) Rate of change = (100 - 30)/(40 - 10) Rate of change = 70/30 Rate of change =[B] 2.333 feet per second[/B]

A Septon who visited Earth used an Earth scale and found that he weighed 125 pounds. He is horrified that he lost so much weight. Translate 125 pounds base 10 into base 7. Using our [URL='https://www.mathcelebrity.com/binary.php?num=125&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we see that: 125 = [B]236[/B] (in base 7)

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 submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90 meters. What is the submarines new elevation? 3 times the current elevation is: 3 * -185 = -555 Elevating 90 meters means we have a positive change: -555 + 90 = [B]-465[/B]

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to have enough paintings so she can change the order of the arrangement each day for the next 41 years. (The same five paintings are okay as long as the hanging order is different.) What is the fewest number of paintings she can buy and still have a different arrangement every day for the next 41 years? 365 days * 41 years + 10 leap year days = 14,975 days what is the lowest permutations count of n such that nP5 >= 14,975 W[URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Permutations']e see that 9P5[/URL] = 15,120, so the answer is [B]9 paintings[/B]

Antonio has a change jar that contains $3.65 in half dollars and nickels. He has 7 more nickels than half dollars. How many of each type of coin does he have? Let h be half dollars Let n be nickels We're given two equations: [LIST=1] [*]n = h + 7 [*]0.5h + 0.05n = 3.65 [/LIST] Substitute equation (1) into equation (2) for n: 0.5h + 0.05(h + 7) = 3.65 To solve this equation for h, we[URL='https://www.mathcelebrity.com/1unk.php?num=0.5h%2B0.05%28h%2B7%29%3D3.65&pl=Solve'] type it in our search engine[/URL] and we get: h = [B]6 [/B] To get n, we substitute h = 6 into equation (1) above: n = 6 + 7 n = [B]13[/B]

Assume that you make random guesses for 5 true-or-false questions. (a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form) (b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form) (c) If event A is “Getting the correct answer in the 5th question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain. (a) Correct Answer on each one is 1/2 or 0.5. Since all are independent events, we have: (1/2)^5 = [B]1/32[/B] (b) We have [B]1/2[/B] (1/2)^4 * 1/2/((1/2)^4) c) [B]Independent since you could have gotten correct or wrong on any of the 4 and the probability does not change[/B]

At 2:18 Pm, a parachutist is 4900 feet above the ground. At 2:32 pm, the parachutist is 2100 above the ground. Find the average rate of change in feet per minute Average Rate of Change = Change in Distance / Change in time Average Rate of Change = (4900 - 2100) / (2:32 - 2:18) Average Rate of Change = 2800 / 14 Average Rate of Change = [B]200 feet per minute[/B]

At the movie theater, Celeste bought 2 large drinks and 2 large popcorns for $8.50. She paid with a twenty-dollar bill. What is the fewest number of bills and coins that she could have received as change?r of bills and coins that she could have received as change? Calculate change: Change = Amount Paid - Bill Change = $20.00 - $8.50 Change = $11.50 Largest bill we can start with is a 10 dollar bill: $11.50 - 10 = $1.50 Next largest bill is a $1 bill $1.50 - $1 = 0.50 Now we're down to coins. Largest coin(s) we can use are quarters (assuming no half-dollars) 2 quarters equals 0.50 0.50 - 0.50 = 0 [U]Therefore, our answer is:[/U] [B]Ten dollar Bill, 1 dollar bill, and 2 quarters[/B]

Free Base Change Conversions Calculator - Converts a positive integer to Binary-Octal-Hexadecimal Notation or Binary-Octal-Hexadecimal Notation to a positive integer. Also converts any positive integer in base 10 to another positive integer base (Change Base Rule or Base Change Rule or Base Conversion)

Have you tried the rate of change formula?

Carol bought a pair of jeans for $12.95 and a belt for $3.79. The sales tax is $1.01. Carol gave the store clerk a $20.00 bill. How much change should she get back? Calculate total cost: Total cost = Jeans + Belt + Sales Tax Total cost = $12.95 + $3.79 + $1.01 Total cost = $17.75 Calculate Change Change = Carol's payment - Total cost Change = $20 - $17.75 Change = [B]$2.25[/B]

Change 1/9 to a decimal This is the same as 100/9 = 11.1111% or [B]0.1111[/B]

Change Base 10 number of 25 into base 2 Using our [URL='https://www.mathcelebrity.com/binary.php?num=25&check1=7&bchoice=2&pl=Convert']base change calculator[/URL], we get: 25 = [B]11001[/B] (in base 2)

Free Change Counting Calculator - This shows you how to make change using the least amount of bills/coins by taking a bill amount and a cash tendered amount from a customer and figuring out the fastest way to make change. Maximum denomination is $100

Change the base 10 number 100 into base 5 Using our [URL='https://www.mathcelebrity.com/binary.php?num=100&check1=7&bchoice=5&pl=Convert']base change calculator[/URL], we get: 100 = [B]400 (Base 5)[/B]

Change the base 2 number 1000 into base 10 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0 8 + 0 + 0 + 0 = [B]8[/B]

Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5 percent sales tax, how much change would she receive from a $10 bill 1. Change = $10 - Total Bill Total Bill = (Soda + Candy Bar + Bag of Chips) * 1.035 Total Bill = ($0.90 + $1.20 + $2.90) * 1.035 Total Bill = $5 * 1.035 2. Total Bill = $5.18 Plug Equation (2) into Equation (1), we have: Change = $10 - $5.18 Change = [B]$4.82[/B]

Elli is purchasing 2.75 pounds of jelly beans which are priced at 4.85 per pound. How much change should she get back from a 20? The total bill is 4.85 per pound * 2.75 pounds = 13.34 Her change from a 20 is 20 - 13.34 = [B]6.66[/B].

Free Equation of Exchange Calculator - Solves for any of the 4 variables in the Equation of Exchange: money, velocity, price, quantity

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.

How MUCH Change would be returned from a $50.00 bill for the purchase of 26 stainless Steel 8-in. bolts at the Price Of 79.5 cents each? Calculate the Stainless Steel Bolts Cost: Stainless Steel Bolts Cost = Number of Stainless Steel Bolts * Price per bolt Stainless Steel Bolts Cost = 26 * 0.795 Stainless Steel Bolts Cost = $20.67 Calculate the change: Change = Cash Offered - Stainless Steel Bolts Cost Change = $50 - $20.67 Change = [B]$29.33[/B]

In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000? Let w be the size of the workforce before any changes. We have: [LIST] [*]w(2000) = w(1999) * 1.5 [I](50% increase is the same as multiplying by 1.5)[/I] [*]w(2001) = w(2000)/1.5 [I](50% decrease is the same as dividing by 1.5)[/I] [/LIST] Substitute the first equation back into the second equation w(2001) = w(1999) * 1.5/1.5 Cancel the 1.5 on top and bottom w(2001) = w(1999) This means the workforce had [B]zero net change[/B] from the beginning of 2000 to the end of 2001.

in 6th grade, veronica reads 45 books. in 7th grade she reads 63 books. what is the percent change? Percent Change = 100% * (New Value - Old Value)/Old Value Percent Change = 100% * (63 - 45)/45 Percent Change = 100% * 18/45 Percent Change = 100% * 0.4 Percent Change = [B]40%[/B] [B] There is a percentage increase[/B]

In January 2017 the cost of postage stamps increased from 47 cents to 49 cents. What was the percent of increase? [URL='https://www.mathcelebrity.com/percentage-change-calculator.php?num=thecostofpostagestampsincreasedfrom47centsto49cents.whatwasthepercentofincrease&pl=Calculate']Using our percentage change calculator[/URL], we get: [B]4.26% increase[/B]

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year Let the starting book count be b. We have: [LIST] [*]We start with b books [*]Buying 237 books means we add (+237) [*]Removing 67 books means we subtract (-67) [*]We end up with 5745 books [/LIST] Our change during the year is found by the equation: b + 237 - 67 = 5745 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]5575[/B]

Free Income Elasticity of Demand Calculator - Calculates the income elasticity of demand using demand changes and income changes. Inputs are demand 1 and demand 0 and income 1 and income 0.

Jina's test score average decreased by 10 points this semester. Write a signed number to represent this change in average. Let A be the original average. The new average is: A + (-10)

Jose bought a shirt for $25.00. The sales tax was 8%. If Jose paid with $40, what was his change? Total Bill is 25 * 1.08 = $27 Change due = 40 - 27 = $[B]13[/B]

Leo and Zach went to lunch at a cafe. They ordered a spinach salad for $6.55, a tuna sandwich for $4.75, and 2 glasses of lemonade for $0.85 each. The tax was $1.30. They gave the waiter $15.00. How much change should they have received? Change = Cash - Total Bill - Tax Change = $15 - ($6.55 + $4.75 + 2($0.85)) - $1.30 Change = $15 - ($6.55 + $4.75 + $1.70) - $1.30 Change = $15 - $13 - $1.30 Change = $15 - $14.30 Change = [B]$0.70 or 70 cents[/B]

Free Logarithms and Natural Logarithms and Eulers Constant (e) Calculator - This calculator does the following:
* Takes the Natural Log base e of a number x Ln(x) → log_ex
* Raises e to a power of y, e^y
* Performs the change of base rule on log_b(x)
* Solves equations in the form b^cx = d where b, c, and d are constants and x is any variable a-z
* Solves equations in the form ce^dx=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z
* Exponential form to logarithmic form for expressions such as 5³ = 125 to logarithmic form
* Logarithmic form to exponential form for expressions such as Log₅125 = 3

Louis kept money through a hole inn his pocket. He started with 35 cents, lost 20 cents , put in 75 cents , spent 43 cents, lost 16 cents again, and then put in 14 cents. How much change should there be in his pocket? The phrase [I]put in[/I] mean we add money to the total The phrases s[I]pent or lost[/I] mean we subtract 35 - 20 + 75 - 43 - 16 + 14 = [B]45 cents[/B]

Free Matrix Properties Calculator - Given a matrix |A|, this calculates the following items if they exist:
* Determinant = det(A)
* Inverse = A^-1
* Transpose = A^T
* Adjoint = adj(A)
* Eigen equation (characteristic polynomial) = det|λI - A|
* Trace = tr(A)
* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form
* Dimensions of |A| m x n
* Order of a matrix
* Euclidean Norm ||A||
* Magic Sum if it exists
* Determines if |A| is an Exchange Matrix

Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanic’s mistake Let the cost for work be w. Let the cost for each tire be t. We're given; [LIST=1] [*]w = 5t [*]w + 4t = 1035 [/LIST] Substitute equation 1 into equation 2: (5t) + 4t = 1035 [URL='https://www.mathcelebrity.com/1unk.php?num=%285t%29%2B4t%3D1035&pl=Solve']Type this equation into our search engine[/URL], and we get: t = 115 Substitute this into equation (1): w = 5(115) w = [B]575[/B] The mechanic underestimated the work cost.

Mr. Crews goes to Publix and spends $81.25 on groceries. He pays the cashier with a hundred dollar bill. How much change will Mr. Crews get back from the cashier? Using our [URL='https://www.mathcelebrity.com/changecounter.php?cash=100&bill=81.25&pl=Calculate+Change+Amount']change calculator[/URL], we get: [B]$18.75[/B]

Free Percentage Change Calculator - Calculates the percentage change between two values. Percentage Increase or Percentage Decrease

Free Percentage-Decimal-Fraction Relations Calculator - Calculates the relational items between a fraction, a decimal (including repeating decimal and terminating decimal), a percentage, and the numerator and denominator piece of that fraction. Also calculates the percentage change going from one number to another or the amount increase or decrease of a percentage above/below a number. Round decimals. decimals into fractions

Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. (a) Which of the following is the hypothesis to be conducted? A. H0: p = 0.122, H1 p > 0.122 B. H0: p = 0.122, H1 p <> 0.122 C. H0: p = 0.122, H1 p < 0.122 (b) Which of the following is a Type I error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. c) Which of the following is a Type II error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% (a) [B]C H0: p = 0.122, H1: p < 0.122[/B] because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased. (b) [B]C.[/B] The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true c) [B]C.[/B] The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.

Free Strain Calculator - Solves for any of the 3 items in the strain equation: Change in Length, Strain, and Original Length

Free Temperature Change Calculator - This calculator determines the total temperature change

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph. [IMG]http://www.mathcelebrity.com/community/data/attachments/0/rate-of-change-wp.jpg[/IMG] Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope. Looking at a few points, we have: (0, 20), (12, 30) Using our [URL='https://www.mathcelebrity.com/slope.php?xone=0&yone=20&slope=+2%2F5&xtwo=12&ytwo=30&pl=You+entered+2+points']slope calculator for these 2 points[/URL], we get a slope (rate of change) of: [B]5/6[/B]

The next number in the series 38 36 30 28 22 is Notice the change of factors. Subtract 2, Subtract 6, Subtract 2, Subtract 6. So the next number should subtract 2. 22 - 2 = [B]20 [MEDIA=youtube]x7SHk_6-aok[/MEDIA][/B]

The temperature of a solution was -23C. After adding a substance to the solution, the temperature after adding the substance to the solution was 133C. What is the difference between the temperature of the solution before and after adding the substance Using our [URL='https://www.mathcelebrity.com/temp-change.php?num=thetemperatureofasolutionwas-23c.afteraddingasubstancetothesolutionthetemperaturefe133c.whatisthedifferencebetweenthetemperatureofthesolutionbeforeandafteraddingthesubstance%3E&pl=Calculate+Temp+Change']temperature difference calculator[/URL], we get: [B]156C[/B]

The temperature dropped 2 every hours for 6 hours. What was the total number of degrees the temperature changed in the 6 hours 2 degrees drop per hour * 6 hours = [B]12 degree drop[/B]

The temperature in Minneapolis changed from -7 fahrenheit at 6am to 7 fahrenheit at noon. What was the difference between high and low temperatures? Difference = High Temp - Low Temp Difference = 7 - -7 Difference = [B]14[/B]

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds. If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line? Change times to seconds: [LIST] [*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds [*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds [/LIST] Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line. 1 mile = 5280 feet: Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled 5280/276.5 = n/223.13 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: n = 4260.85 feet Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

There are 24 students in a class. Three new students joined the class. Work out the percentage change in the number of students in the class. We want to know how much an increase of 3 people is in a class of 24: 3/24 Using [URL='https://www.mathcelebrity.com/perc.php?num=3&den=24&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']our percentage/decimal calculator[/URL], we get: [B]12.5% increase[/B]

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will be 312,500 graphic designer jobs in 2020. (a) Using the data, find the number of graphic designer jobs as a linear function of the year. [B][U]Figure out the linear change from 2010 to 2020[/U][/B] Number of years = 2020 - 2010 Number of years = 10 [B][U]Figure out the number of graphic designer job increases:[/U][/B] Number of graphic designer job increases = 312,500 - 286,200 Number of graphic designer job increases = 26,300 [B][U]Figure out the number of graphic designer jobs added per year[/U][/B] Graphic designer jobs added per year = Total Number of Graphic Designer jobs added / Number of Years Graphic designer jobs added per year = 26,300 / 10 Graphic designer jobs added per year = 2,630 [U][B]Build the linear function for graphic designer jobs G(y) where y is the year:[/B][/U] G(y) = 286,200 + 2,630(y - 2010) [B][U]Multiply through and simplify:[/U][/B] G(y) = 286,200 + 2,630(y - 2010) G(y) = 286,200 + 2,630y - 5,286,300 [B]G(y) = 2,630y - 5,000,100[/B]

Two numbers have a sum of 20. Determine the lowest possible sum of their squares. If sum of two numbers is 20, let one number be x. Then the other number would be 20 - x. The sum of their squares is: x^2+(20 - x)^2 Expand this and we get: x^2 + 400 - 40x + x^2 Combine like terms: 2x^2 - 40x + 400 Rewrite this: 2(x^2 - 20x + 100 - 100) + 400 2(x - 10)^2 - 200 + 400 2(x?10)^2 + 200 The sum of squares of two numbers is sum of two positive numbers, one of which is a constant of 200. The other number, 2(x - 10)^2, can change according to the value of x. The least value could be 0, when x=10 Therefore, the minimum value of sum of squares of two numbers is 0 + 200 = 200 when x = 10. If x = 10, then the other number is 20 - 10 = 10.

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence. Given a first term a1 of 13 and a change amount of 7, expand the series The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d d represents the common difference between each term, an - an - 1 Looking at all the terms, we see the common difference is 7, and we have a1 = 13 Therefore, our explicit formula is an = 13 + 7(n - 1) If n = 15, then we plug it into our explicit formula above: an = 13 + 7(n - 1) a(15) = 15 + 7(15 - 1) a(15) = 15 + 7 * 14 a(15) = 15 + 98 a(15) = [B]113[/B]

What is the base 10 number 100 in base 7? Using our [URL='https://www.mathcelebrity.com/binary.php?num=100&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we see that: 100 in base 10 = [B]202[/B] in base 7