60% of the freshman ate pizza [URL='http://www.mathcelebrity.com/community/x-apple-data-detectors://3']at lunch today[/URL]. If 180 freshman ate pizza, how many freshman are enrolled at our school? 60% of x = 180 We write this as 0.6x = 180 Divide each side by 0.6 to isolate x. We get x = 300 freshman

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same? Let g be the number of GB. The limited plan has a cost as follows: C = 10(g - 5) + 55 C = 10g - 50 + 55 C = 10g + 5 We want to set the limited plan equal to the unlimited plan and solve for g: 10g + 5 = 70 Solve for [I]g[/I] in the equation 10g + 5 = 70 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 5 and 70. To do that, we subtract 5 from both sides 10g + 5 - 5 = 70 - 5 [SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE] 10g = 65 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10g/10 = 65/10 g = [B]6.5[/B] Check our work for g = 6.5: 10(6.5) + 5 65 + 5 70

A Government antipollution spokeperson asserts that more than 80% of the plants in the Glassboro area meet the antipollution standards. An antipollution advocate does not believe the government claim. She takes a random sample of published data on pollution emission for 64 plants in the area and finds that 56 plants meet the pollution standards. Do the sample data support the government claim at the 1% level of significance? (H0: ρ=0.8; H_a: ρ>0.8) [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+56&n=64&ptype==&p=+0.8&alpha=+0.01&pl=Proportion+Hypothesis+Testing']Perform a hypothesis testing of a proportion[/URL] [B]Accept null hypothesis[/B]

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the monthly charge and use d to represent data We multiply gigabyte fee by d and add the usage fee: [B]15d + 30[/B]

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 set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is the new mean? We know the mean formula is: Sum of scores / Number of Scores = Mean We're given mean = 6.3 and number of scores = 19, so we have: Sum of scores / 19 = 6.3 Cross multiply: Sum of scores = 19 * 6.3 Sum of scores = 119.7 Now a new score is added of 8, so we have: Sum of scores = 119.7 + 8 = 127.7 Number of scores = 19 + 1 = 20 So our new mean is: Mean = Sum of scores / Number of Scores Mean = 127.7/20 Mean = [B]6.385[/B] [COLOR=rgb(0, 0, 0)][SIZE=5][FONT=arial][B][/B][/FONT][/SIZE][/COLOR]

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest value in the set of data? High Value - Low Value = Range Let the high value be h. We're given: h - 22 = 30 We [URL='https://www.mathcelebrity.com/1unk.php?num=h-22%3D30&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]52[/B]

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Free Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:
Expected Value
Mean = μ
Variance = σ²
Standard Deviation = σ
Standard Error of the Mean
Skewness
Mid-Range
Average Deviation (Mean Absolute Deviation)
Median
Mode
Range
Pearsons Skewness Coefficients
Entropy
Upper Quartile (hinge) (75th Percentile)
Lower Quartile (hinge) (25th Percentile)
InnerQuartile Range
Inner Fences (Lower Inner Fence and Upper Inner Fence)
Outer Fences (Lower Outer Fence and Upper Outer Fence)
Suspect Outliers
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Ranked Data Set
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Frequency Distribution
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Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data. A score trial B score trial 2 C Score trial 3 4 6 7 3 7 8 2 8 5 1 4 7 4 6 9 2 4 2 (a) Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject. (b) Compute a one-sample t-test on this column (with the L values for each subject) you created. Formula t = To computer a one-sample t-test first know the meaning of each letter (a) Each L column value is just -1(Column 1) + 0(Column2) + 1(Column 3) A score trial B score trial 2 C Score trial 3 L = (-1)(a) + (0)(b) + (1)(c) 4 6 7 3 3 7 8 5 2 8 5 3 1 4 7 6 4 6 9 5 2 4 2 0 (b) Mean = (3 + 5 + 3 + 6 + 5 + 0)/6 = 22/6 = 3.666666667 Standard Deviation = 2.160246899 Use 3 as our test mean (3.666667 - 3)/(2.160246899/sqrt(6)) = 0.755928946

Free Benfords Law Calculator - Shows you Benfords Law and evaluates a data set compared to Benfords Law

Can a coefficient of determination be negative? Why or why not? [B]Yes, reasons below[/B] [LIST] [*] predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data [*] where linear regression is conducted without including an intercept [*] Yes, negative values of R2 may occur when fitting non-linear functions to data [/LIST]

Carilah asimtot-asimtot tegak dan datar dari grafik f(x) = 2x/(x - 1) Asimptot dijumpai apabila penyebut sama dengan 0. x - 1 = 0, jadi [B]x = 1[/B]

Free Class Frequency Goodness of Fit Calculator - Performs a goodness of fit test on a set of data with class boundaries (class boundary) with critical value test and conclusion.

Consider the case of a manufacturer who has an automatic machine that produces an important part. Past records indicate that at the beginning of the data the machine is set up correctly 70 percent of the time. Past experience also shows that if the machine is set up correctly it will produce good parts 90 percent of the time. If it is set up incorrectly, it will produce good parts 40 percent of the time. Since the machine will produce 60 percent bad parts, the manufacturer is considering using a testing procedure. If the machine is set up and produces a good part, what is the revised probability that it is set up correctly? [U]Determine our events:[/U] [LIST] [*]C = Correctly Set Machine = 0.7 [*]C|G = Correctly Set Machine And Good Part = 0.9 [*]I = Incorrectly Set Machine = 1 - 0.7 = 0.3 [*]I|G = Incorrectly Set Machine And Good Part = 0.4 [*]B< = BAD PARTS = 0.60 [/LIST] P[correctly set & part ok] = P(C) * P(C|G) P[correctly set & part ok] = 70% * 90% = 63% P[correctly set & part ok] = P(I) * P(I|G) P[incorrectly set & part ok] = 30% *40% = 12% P[correctly set | part ok] = P[correctly set & part ok]/(P[correctly set & part ok] + P[incorrectly set & part ok]) P[correctly set | part ok] = 63/(63+12) = [B]0.84 or 84%[/B]

Construct a data set of seven temperature readings where the mean is positive and the median is negative. [B]{-20,-10.-5,-2,-1,20,40}[/B] [URL='https://www.mathcelebrity.com/statbasic.php?num1=-20%2C-10%2C-5%2C-2%2C-1%2C20%2C40&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Using our mean and median calculator[/URL], we see that: [B]Mean = 3.142857 (positive) Median = -2[/B]

The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66, obtain a 95.44% confidence interval for the population mean. 80 74 61 93 69 74 80 64 51 60 66 87 72 77 84 96 60 67 71 79 89 75 66 70 57 76 71 92 73 72 68 74

Dylan is playing darts. He hit the bullseye on 5 out of his last 20 tosses. Considering this data, how many bullseyes would you expect Dylan to get during his next 16 tosses? We have a proportion of bullseyes to tosses where b is the number of bullseyes for 16 tosses: 5/20 = b/16 [URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=b&den1=20&den2=16&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get: b = [B]4[/B]

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The data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66, obtain a 95.44% confidence interval for the population mean. 80 74 61 93 69 74 80 64 51 60 66 87 72 77 84 96 60 67 71 79 89 75 66 70 57 76 71 92 73 72 68 74

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters. 5.2 4.9 2.9 5.3 3.0 4.0 5.2 5.2 3.2 4.7 3.2 3.5 4.8 4.0 5.1 Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters. 5.1 4.9 4.7 3.1 4.3 3.7 3.7 4.3 3.5 5.2 3.2 3.5 4.8 4.0 5.1 Use the data to obtain a 95.44% confidence interval for the mean forced vital capacity for all asthmatics. Assume that ? = 0.7.

Find x [IMG]https://mathcelebrity.com/community/data/attachments/0/cong-angles.jpg[/IMG] Since both angles are congruent, we set them equal to each other: 6x - 20 = 4x To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x-20%3D4x&pl=Solve']type this equation into our math engine[/URL] and we get: x = [B]10[/B]

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a water park. How much shorter would their trip to the water park have been if they hadn’t stopped at the gas station and had driven along the diagonal path instead? [IMG]https://mathcelebrity.com/community/data/attachments/0/pythag-diagonal.jpg[/IMG] Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=14&side2input=48&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator[/URL], we see the diagonal route would be: 50 miles The original trip distance was: Original Trip Distance = 14 + 48 Original Trip Distance = 62 miles Diagonal Trip was 50 miles, so the difference is: Difference = Original Trip Distance - Diagonal Distance Difference = 62 - 50 Difference = [B]12 miles[/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.

Free Interpolation Calculator - Given a set of data, this interpolates using the following methods:
* Linear Interpolation
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Free Paired Means Difference Calculator - Calculates an estimation of confidence interval for a small or large sample difference of data. Confidence interval for paired means

Free Random Test Calculator - Given a set of data and an α value, this determines the test statistic and accept/reject hypothesis based on randomness of a dataset.

[IMG]https://mathcelebrity.com/community/data/attachments/0/supp-angles.jpg[/IMG] The angle with measurements of 148 degrees lies on a straight line, which means it's supplementanry angle is: 180 - 148 = 32 Since the angle of 2x - 16 and 32 lie on a straight line, their angle sum equals 180: 2x + 16 + 32 = 180 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B16%2B32%3D180&pl=Solve']type it in our math engine [/URL]and we get: x = [B]66[/B]

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an average of 4 cars arrive at a toll bridge each second. If it is assumed that cars arrive randomly, and can thus be modeled with Poisson distribution, what is the probability that in the next second, [U][B]NO[/B][/U] cars will arrive? Use the [I]Poisson Distribution[/I] with λ = 4 and x = 0 Using the [URL='http://www.mathcelebrity.com/poisson.php?n=+10&p=+0.4&k=+0&t=+3&pl=P%28X+=+k%29']Poisson Distribution calculator[/URL], we get P(0; 4) = [B]0.0183[/B]

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]

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]

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance from a data set is zero, then all the observations in this data set are identical. (c) P(A AND A^c)=1, where A^c is the complement of A. (d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis. (e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. [B](a) True, it's a bell curve symmetric about the mean (b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical (c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space. (d) False, we have sufficient evidence to reject H0. (e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

Yesterday a car rental agency rented 4 convertibles and 30 other vehicles. Considering this data, how many of the first 68 vehicles rented today should you expect to be convertibles? 30 other vehicles + 4 convertibles = 34 cars 34 * 2 = 68 30 * 2 other vehicles + 4 * 2 convertibles = 68 cars 60 other vehicles and [B]8 convertibles[/B]

You choose an alpha level of .01 and then analyze your data. (a) What is the probability that you will make a Type I error given that the null hypothesis is true? (b) What is the probability that you will make a Type I error given that the null hypothesis is false. [B](a) 0.01. Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B] [B](b) Impossible Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]

You work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls? We've got 2 questions here. Question 1: We want the cost function C(r) where r is the number of remotes: C(r) = Variable Cost per unit * r units + Fixed Cost (labor) [B]C(r) = 3r + 2000 [/B] Question 2: What is the cost of producing 2000 remote controls. In this case, r = 2000, so we want C(2000) C(2000) = 3(2000) + 2000 C(2000) = 6000 + 2000 C(2000) = [B]$8000[/B]