interval - a set of real numbers that contains all real numbers lying between any two numbers of the set

-2 <= x +4 < 9

-2 <= x +4 < 9
Subtract 4 from each piece:
-2 - 4 <= x < 5
Simplify:
[B]-6 <= x < 5
[/B]
To find the interval notation, we set up our notation:
[LIST]
[*]The left side has a solid bracket, since we have an equal sign:
[*]The right side has an open parentheses, since we have no equal sign
[*][B][-6, 5)[/B]
[/LIST]

-3x<= -9 or 5+x<6

-3x<= -9 or 5+x<6
Take each piece:
-3x<= -9
Divide each side by -3:
x>=3
Now take 5 + x < 6
5 + x < 6
Subtract 5 from each side:
x < 1
Joining together the two inequalities, we have:
x<1 or x>=3
Use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3C1orx%3E%3D3&pl=Show+Interval+Notation']interval notion calculator[/URL] to find the interval notation of this compound inequality

30 people are selected randomly from a certain town. If their mean age is 60.5 and ? = 4.6, find a 9

30 people are selected randomly from a certain town. If their mean age is 60.5 and ? = 4.6, find a
95% confidence interval for the true mean age, ?, of everyone in the town.

6 times a number, x, is at least 22.

6 times a number, x, is at least 22.
6 times a number x:
6x
The phrase [I]is at least[/I] means greater than or equal to. So we have an inequality:
[B]6x >= 22[/B] <-- This is our algebraic expression
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6x%3E%3D22&pl=Show+Interval+Notation']To solve this for x, paste this into the search engine[/URL] and we get:
[B]x >= 3.666667[/B]

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is t

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is the better deal
Let the number of days be d. We have the inequality below where we show when the day to day cost is greater than the monthly pass:
1.5d > 24
To solve this inequality for d, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.5d%3E24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]d > 16[/B]

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of f

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of fish can you buy for your aquarium?
Let the number of fish be f. We have the following inequality where "at most" means less than or equal to:
3.19f <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.19f%3C%3D35&pl=Show+Interval+Notation']Typing this inequality into our search engine[/URL], we get:
f <= 10.917
Since we need a whole number of fish, we can buy a maximum of [B]10 fish[/B].

a confidence interval for a population mean has a margin of error of 0.081

a confidence interval for a population mean has a margin of error of 0.081

a confidence interval for a population mean has a margin of error of 0.081

Margin of error = Interval Size/2
0.081 = Interval Size/2
Cross Multiply:
Interval Size = 0.081 * 2
Interval Size = [B]0.162[/B]

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represe

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represents the number x of cups of coffee you must purchase for the monthly card to be a better deal?
Let c be the number of cups. We want to know how many cups (x) where:
1.75x > 25
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.75x%3E25&pl=Show+Interval+Notation']inequality solver[/URL], we see:
[B]x > 14.28[/B]

A lighthouse blinks every 12 minutes.A second lighthouse blinks every 10 minutes.If they both blink

A lighthouse blinks every 12 minutes.A second lighthouse blinks every 10 minutes.If they both blink at 8:10 P.M., at what time will they next blink together?
We want to know the least common multiple, so that 12 and 10 intervals meet again.[URL='https://www.mathcelebrity.com/gcflcm.php?num1=10&num2=12&num3=&pl=GCF+and+LCM'] We type in LCM(10,12) into our search engine[/URL] and we get 60.
60 minutes is 1 hour, so we add this to 8:10 to get [B]9:10[/B]

A local radio station sells time slots for programs in 20-minute intervals. If the station operates

A local radio station sells time slots for programs in 20-minute intervals. If the station operates 24 hours per day, what is the total number of 20-minute time slots the radio station can sell for Thursday and Friday?
Thursday and Friday = 2 days
With 24 hours per day, we have 24 * 2 = 48 hours for Thursday and Friday.
Since 20 minutes is 1/3 of an hour, then we have 3 20-minute time slots per hour.
3 20-minute time slots * 48 hours = [B]144[/B] total 20-minute time slots

A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population sta

A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime.
[B]2902 < u < 3098[/B] using our [URL='http://www.mathcelebrity.com/normconf.php?n=100&xbar=3000&stdev=500&conf=95&rdig=4&pl=Large+Sample']confidence interval for the mean calculator[/URL]

A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population

A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population of 1,000. What is the 95% confidence interval for the unknown population?
[URL='http://www.mathcelebrity.com/normconf.php?n=144&xbar=100&stdev=70&conf=95&rdig=4&pl=Large+Sample']Large Sample Confidence Interval Mean Test[/URL]
[B]88.5667 < u < 111.4333[/B]

A random sample of 149 students has a test score average of 61 with a standard deviation of 10. Find

A random sample of 149 students has a test score average of 61 with a standard deviation of 10. Find the margin of error if the confidence level is 0.99. (Round answer to two decimal places)
Using our [URL='https://www.mathcelebrity.com/normconf.php?n=149&xbar=61&stdev=10&conf=99&rdig=4&pl=Large+Sample']confidence interval of the mean calculator[/URL], we get
[B]58.89 < u < 63.11[/B]

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afte

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 random sample of 40 adults with no children under the age of 18 years results in a mean daily leis

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.44 hours, with a standard deviation of 1.74 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children left parenthesis mu 1 minus mu 2 right parenthesis (?1 - ?2).
Using our confidence interval for [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=+2.31&n2=+40&xbar2=+4.44&stdev2=1.74&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means calculator[/URL], we get:
[B]0.0278 < ?1 - ?2 < 1.5322[/B]

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leis

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.29 hours, with a standard deviation of 1.58 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children (u1 - u2)
What is the interpretation of this confidence interval?
A. There is 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours
B. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
C. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
D. There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours
0.2021 < u1 - u2 < 1.6579 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=2.31&n2=40&xbar2=4.29&stdev2=1.58&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means confidence interval calculator[/URL]
[B]Choice D
There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours[/B]

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample stan

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample standard deviation S = 1 hr. is picked from a production line known to produce batteries with normally distributed operating lives. What's the 98% confidence interval for the unknown mean of the working life of the entire population of batteries?
[URL='http://www.mathcelebrity.com/normconf.php?n=10&xbar=5&stdev=1&conf=98&rdig=4&pl=Small+Sample']Small Sample Confidence Interval for the Mean test[/URL]
[B]4.1078 < u < 5.8922[/B]

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will excee

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage?
Let the number of inches be i. Remember 12 inches to a foot, so we have 2 feet = 12*2 = 24 inches.
[LIST]
[*]Inequality: 3i <= 24. (since more than means the river can go [U]up to[/U] 2 feet or 24 inches
[/LIST]
To solve the inequality for I, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3i%3C%3D24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]I <= 8
This means after 8 hours, the river will flood[/B]

A survey was conducted that asked 1007 people how many books they had read in the past year. Results

A survey was conducted that asked 1007 people how many books they had read in the past year. Results indicated that x overbarequals11.3 books and sequals16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval.
x bar = 11.3
s = 16.6
n = 1007
[URL='https://www.mathcelebrity.com/normconf.php?n=1007&xbar=11.3&stdev=16.6&conf=90&rdig=4&pl=Not+Sure']We use our confidence interval calculator[/URL] and get [B]10.4395 < u < 12.1605[/B].
[B][I]We interpret this as:
If we repeated experiments, the proportion of such intervals containing u would be 90%[/I][/B]

A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the te

A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the test and the 95% confidence interval of grades was (83, 90). Can you reject the teacher's assumption?
a. Yes
b. No
c. We cannot tell from the given information
[B]a. Yes[/B]
[I]At the 0.05 significance level, yes since 80 is not in the confidence interval.[/I]

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.20 per foot for the next 10 feet, and so on, at a price increase of $0.10 per foot for succeeding intervals of 10 feet. How much does it cost to drill a well to a depth of 150 feet?
Set up the cost function C(f) where f is the number of feet:
Cost = 9(10) + 9.1(10) + 9.2(10) + 9.3(10) + 9.4(10) + 9.5(10) + 9.6(10) + 9.7(10) + 9.8(10) + 9.9(10) + 10(10) + 10.1(10) + 10.2(10) + 10.3(10) + 10.4(10)
Cost = [B]1,455[/B]

Amanda runs each lap in 4 minutes. She will run less than 44 minutes today. What are the possible nu

Amanda runs each lap in 4 minutes. She will run less than 44 minutes today. What are the possible number of laps she will run today?
Notes for this problem:
[LIST]
[*]Let laps be l.
[*]Lap time = Time per lap * number of laps (l)
[*]Less than means we have an inequality using the < sign
[/LIST]
We have the inequality:
4l < 44
To solve this inequality for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C44&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
[B]l < 11[/B]

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the eleva

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the elevator? (Use "p" to represent the number of people)
Maximum means less than or equal to. We have the inequality:
150p <= 3000
To solve this inequality for p, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=150p%3C%3D3000&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]p <= 20[/B]

based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an

based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an aptitude test is from 60 to 66. Find the margin of error

Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admissio

Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admission to the park. Each ride costs $1.50 to ride. Write an inequality to represent the possible number of rides she can ride?
First, we subtract the food and admission cost from Beverly's starting balance of $50:
Cost available for rides = Starting Balance - Food - Admission
Cost available for rides = 50 - 10 - 15
Cost available for rides = 25
Now we set up an inequality for the number of rides (r) that Beverly can ride with the remaining balance:
1.50r <= 25
To solve for r, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.50r%3C%3D25&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]r <=[/B] [B]16.67[/B]

Compute a 75% Chebyshev interval around the mean for x values and also for y values.

Compute a 75% Chebyshev interval around the mean for [I]x[/I] values and also for [I]y[/I] values.
[B][U]Grid E: [I]x[/I] variable[/U][/B]
11.92 34.86 26.72 24.50 38.93 8.59 29.31
23.39 24.13 30.05 21.54 35.97 7.48 35.97
[B][U]Grid H: [I]y[/I] variable[/U][/B]
27.86 13.29 33.03 44.31 16.58 42.43
39.61 25.51 39.14 16.58 47.13 14.70 57.47 34.44
According to Chebyshev's Theorem,
[1 - (1/k^2)] proportion of values will fall between Mean +/- (k*SD)
k in this case equal to z
z = (X-Mean)/SD
X = Mean + (z*SD)
1 - 1/k^2 = 0.75
- 1/k^2 = 0.75 - 1= - 0.25
1/k^2 = 0.25
k^2 = 1/0.25
k^2 = 4
k = 2
Therefore, z = k = 2
First, [URL='http://www.mathcelebrity.com/statbasic.php?num1=11.92%2C34.86%2C26.72%2C24.50%2C38.93%2C8.59%2C29.31%2C23.39%2C24.13%2C30.05%2C21.54%2C35.97%2C7.48%2C35.97&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of x[/URL]
Mean(x) = 25.24
SD(x) = 9.7873
Required Interval for x is:
Mean - (z * SD) < X < Mean + (z * SD)
25.24 - (2 * 9.7873) < X < 25.24 - (2 * 9.7873)
25.24 - 19.5746 < X < 25.24 + 19.5746
5.6654 < X < 44.8146
Next, [URL='http://www.mathcelebrity.com/statbasic.php?num1=27.86%2C13.29%2C33.03%2C44.31%2C16.58%2C42.43%2C39.61%2C25.51%2C39.14%2C16.58%2C47.13%2C14.70%2C57.47%2C34.44&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of y[/URL]
Mean(y) = 32.29
SD(y) = 9.7873
Required Interval for y is:
Mean - (z * SD) < Y < Mean + (z * SD)
32.29 - (2 * 13.1932) < Y < 32.29 - (2 * 13.1932)
32.29 - 26.3864 < Y < 32.29 + 26.3864
5.9036 < X < 58.6764

Confidence Interval for the Mean

Free Confidence Interval for the Mean Calculator - Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean

Confidence Interval for Variance and Standard Deviation

Free Confidence Interval for Variance and Standard Deviation Calculator - Calculates a (95% - 99%) estimation of confidence interval for the standard deviation or variance using the χ^{2} method with (n - 1) degrees of freedom.

Confidence Interval of a Proportion

Free Confidence Interval of a Proportion Calculator - Given N, n, and a confidence percentage, this will calculate the estimation of confidence interval for the population proportion π including the margin of error. confidence interval of the population proportion

Confidence Interval/Hypothesis Testing for the Difference of Means

Free Confidence Interval/Hypothesis Testing for the Difference of Means Calculator - Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.

Also performs hypothesis testing including standard error calculation.

Also performs hypothesis testing including standard error calculation.

Construct a confidence interval of the population proportion at the given level of confidence. x = 1

Construct a confidence interval of the population proportion at the given level of confidence.
x = 120, n = 300, 99% confidence
Round to 3 decimal places as needed
[B]0.327 < p < 0.473[/B] using our [URL='http://www.mathcelebrity.com/propconf.php?bign=300&smalln=120&conf=99&pl=Proportion+Confidence+Interval']proportion confidence interval calculator[/URL]

Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit

Free Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit Calculator - Given two distributions X and Y, this calculates the following:

* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r^{2}

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

data below consists of the pulse rates (in beats per minute) of 32 students. Assuming ? = 10.66,

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

Dawn has less than $60. She wants to buy 3 sweaters. What price of sweaters can she afford if all th

Dawn has less than $60. She wants to buy 3 sweaters. What price of sweaters can she afford if all the sweaters are the same price? Let s be the price of each sweater. Write this as an inequality.
The phrase [I]less than[/I] means an inequality, so we have the following inequality:
3s < 60
To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3s%3C60&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
s < [B]20[/B]

Estimate a 15% tip on a dinner bell of $49.76 by first round the bill amount to the nearest $10

Estimate a 15% tip on a dinner bell of $49.76 by first round the bill amount to the nearest $10.
Round the bill to the nearest $10
[LIST]
[*]$49.76 is in between ($40, $50)
[*]1/2 of that interval is (40 + 50)/2 = 90/2 = 45
[*]Since $49.76 is greater than or equal to 45, we round up to $50
[/LIST]
Add a 15% tip
50(1 + 0.15) = 50 + 7.50 = [B]$57.50[/B]

Express the confidence interval 0.039 < p < 0.479 in the form of p ± E.

Express the confidence interval 0.039 < p < 0.479 in the form of p ± E.
We find the range of this interval:
Range = Upper Bound - Lower Bound
Range = 0.479 - 0.039
Range = 0.44
Each piece on opposite sides of p gets:
0.44/2 = 0.22
So our expression becomes
[B]p ± 0.22[/B]

Find Requested Confidence Value

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

Find the confidence interval specified.

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.

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?
So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next.
whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of:
[B]6, 8, 10, 12[/B]

Functions-Derivatives-Integrals

Free Functions-Derivatives-Integrals Calculator - Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ'(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ'(1)

3) 2^{nd} Derivative ƒ''(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ''(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1

3) 2

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

Gary is buying chips. Each bag costs $3.50. He has $40 to spend. Write an inequality to represent th

Gary is buying chips. Each bag costs $3.50. He has $40 to spend. Write an inequality to represent the number of chip bags, c, he can afford.
Gary's spend is found by this inequality:
[B]3.50c <= 40
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.50c%3C%3D40&pl=Show+Interval+Notation']we type it in our search engine[/URL] and we get:
[B]c <= 11.43[/B]

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the sta

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]

Interval Counting

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

Interval Notation and Set Builder Notation

Free Interval Notation and Set Builder Notation Calculator - This calculator translates the following inequality statements to interval notation and set builder notation:

* x < 5

* y <= 5

* z > 5

* a >= 5

* b < 5 or b > 20

* Compound Inequality such as 0 <= c < 4

* |x|<3

* Reverse Interval Notation to Inequality Statement such as (-7,5]

* {x|x<1}

* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8

* x < 5

* y <= 5

* z > 5

* a >= 5

* b < 5 or b > 20

* Compound Inequality such as 0 <= c < 4

* |x|<3

* Reverse Interval Notation to Inequality Statement such as (-7,5]

* {x|x<1}

* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8

Interval Partition

Free Interval Partition Calculator - Given a partitioned interval, this evaluates the norm (mesh) by calculating each subinterval

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours sh

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours she needs to work to earn at least $120.
A few things to note:
[LIST]
[*]Earnings = Rate * time
[*]Let h be the number of hours worked
[*]The phrase [I]at least[/I] means greater than or equal to, so we have the following inequality.
[/LIST]
We represent this with the following inequality:
7.5h < 120
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7.5h%3C120&pl=Show+Interval+Notation']type it into our math engine[/URL] and we get:
[B]h < 16[/B]

kim wants to buy candy for 4 dollars a pound. if she wants to spend less than 20 dollars, how many b

kim wants to buy candy for 4 dollars a pound. if she wants to spend less than 20 dollars, how many bags can she buy
Since cost = price * quantity, we have the following inequality with b as the number of bags:
4b < 20
To solve this inequality for b, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4b%3C20&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]b < 5[/B]

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discou

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discount coupon for $4 off. What are the possible numbers of hours Lisa could rent the boat?
Calculate discounted cost:
Discounted cost = Full Cost - Coupon
Discounted cost = 52 - 7
Discounted cost = 45
Since price equals rate * hours (h), and we want the inequality (less than) we have:
7h < 52
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7h%3C52&pl=Show+Interval+Notation']inequality calculator,[/URL] we see that:
[B]h < 7.42[/B]

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to m

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to make the 15% option the best one?
Let the total bill be b. We have:
0.15b > 21 <-- Since 15% is 0.15
Using our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=0.15b%3E21&pl=Show+Interval+Notation']inequality calculator[/URL], we get [B]b>140[/B].
So any bill greater than $140 will make the 15% off option the best one, since the discount will be higher than $21.

Margin of Error from Confidence Interval

Free Margin of Error from Confidence Interval Calculator - Given a confidence interval, this determines the margin of error and sample mean.

Nine less than the product of 2 and y is not less than 15

The product of 2 and y means we multiply
2y
Nine less than that product means we subtract 9
2y - 9
Finally, the entire expression is not less than 15, which means 15 or more. We use greater than or equal to
[B]2y - 9 >= 15
[/B]
If you want to solve this inequality and write the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=2y-9%3E%3D15&pl=Solve']our calculator[/URL].

P-Hat Confidence Interval

Free P-Hat Confidence Interval Calculator - Given a large sized distribution, and a success amount for a certain criteria x, and a confidence percentage, this will calculate the confidence interval for that criteria.

Paired Means Difference

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

People with a drivers license are at least 16 years old and no older than 85 years old

People with a drivers license are at least 16 years old and no older than 85 years old.
Set up the inequality, where p represents the people:
[LIST=1]
[*]The phrase [I]at least[/I] means greater than or equal to. So we use the >= sign. 16 <= p
[*]The phrase [I]no older than[/I] means less than or equal to. So we use the <= sign. p <= 85
[/LIST]
Combine these inequalities, and we get:
[B]16 <= p <= 85[/B]
To see the interval notation for this inequality and all possible values, visit the [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=16%3C%3Dp%3C%3D85&pl=Show+Interval+Notation']interval notation calculator[/URL].

Solve Problem

based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an aptitude test is from 60 to 66. Find the margin of error

Solve the problem

a confidence interval for a population mean has a margin of error of 0.081. Determine the length of the confidence interval

The cost of 25 apples is less than $9.50. The cost of 12 apples is more than 3.60. What are the poss

The cost of 25 apples is less than $9.50. The cost of 12 apples is more than 3.60. What are the possible prices of one apple?
Let a be the price of each apple. We're given 2 inequalities:
[LIST=1]
[*]25a < 9.50
[*]12a > 3.60
[/LIST]
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=25a%3C9.50&pl=Show+Interval+Notation']Typing 25a < 9.50 into our search engine[/URL], we get a < 0.38
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12a%3E3.60&pl=Show+Interval+Notation']Typing 12a > 360 into our search engine[/URL], we get a > 0.3
Therefore, the possible prices a of one apple are expressed as the inequality:
[B]0.3 < a < 0.38[/B]

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An av

The minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement?
Let a be the number of apples required. The phrase [I]at least[/I] means greater than or equal to, so we have the inequality:
6a >= 50
To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6a%3E%3D50&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
[B]a >= 8.3333 apples or rounded up to a full number, we get 9 apples[/B]

The NJ state education department finds that in a random sample of 100 persons who attended college,

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]

The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9

The principal randomly selected six students to take an aptitude test.
Their scores were: 87.4 86.9 89.9 78.3 75.1 70.6
Determine a 90% confidence interval for the mean score for all students.

The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9

First, determine the [URL='http://www.mathcelebrity.com/statbasic.php?num1=87.4%2C86.9%2C89.9%2C78.3%2C75.1%2C70.6&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']mean and standard deviation[/URL] for the [I]sample[/I]
Mean = 81.3667
SD = 7.803
Next, use our [URL='http://www.mathcelebrity.com/normconf.php?n=6&xbar=81.3667&stdev=7.803&conf=90&rdig=4&pl=Small+Sample']confidence interval for the mean calculator[/URL] with these values and n = 6
[B]74.9478 < u < 87.7856[/B]

The product of x and 7 is not greater than 21

The product of x and 7 is not greater than 21
The product of x and 7:
7x
Is not greater than means less than or equal to, so we have our algebraic expression:
7x <= 21
If you want to solve this inequality and interval notation, use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=7x%3C%3D21&pl=Show+Interval+Notation']calculator[/URL].

The sum of 5x and 2x is at least 70

[I]Is at least [/I]means greater than or equal to:
5x + 2x >= 70
If we combine like terms, we have:
7x >=70
We can further simplify by dividing each side of the inequality by 7
x >=10
If you want the interval notation for that, use the [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3E%3D10&pl=Show+Interval+Notation']interval notation calculator[/URL].

the sum of a number times 3 and 30 is less than 17

the sum of a number times 3 and 30 is less than 17
A number is denoted as an arbitrary variable, let's call it x.
x
Times 3 means we multiply x by 3:
3x
The sum of a number times 3 and 30 means we add 30 to 3x above
3x + 30
Is less than 17 means we have an inequality, so we set 3x + 30 less than 17
3x + 30 < 17
To solve for x and see the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B30%3C17&pl=Solve']our calculator[/URL]:

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2
The Area (A) of a rectangle is given by:
A = lw
With an area of [I]less than[/I] 86 and a width of 4, we have the following inequality:
4l < 86
To solve for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C86&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]l < 21.5[/B]

Translate and solve: 30 times m is greater than ?330. (Write your solution in interval notation.)

Translate and solve: 30 times m is greater than ?330. (Write your solution in interval notation.)
30 times m:
30m
is greater than -330
30m > -330
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=30m%3E-330&pl=Show+Interval+Notation']equation and interval solver[/URL], we get:
m > -11

Use the definite integral to find the area between the x-axis and the function f(x)= x^2-x-12 over t

Use the definite integral to find the area between the x-axis and the function f(x)= x^2-x-12 over the interval [ -5, 10].
Using our [URL='http://www.mathcelebrity.com/dfii.php?term1=x%5E2-x-12&fpt=0&ptarget1=0&ptarget2=0&itarget=-5%2C10&starget=0%2C1&nsimp=8&pl=Integral']integral calculator[/URL], we get:
[B]157.5[/B]

Which of the following descriptions of confidence interval is correct? (Select all that apply) a. I

Which of the following descriptions of confidence interval is correct? (Select all that apply)
a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
b. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
d. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1
[B]a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
[/B]
[I]The lower the confidence interval, the wider the range, so if a higher confidence interval contains a point, a lower confidence interval will contain that point as well.[/I]

Write the interval (2,5) in set builder notation

Write the interval (2,5) in set builder notation
It's a closed interval, so [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=%5B2%2C5%5D&pl=Show+Interval+Notation']we type in [2,5] into the search engine[/URL], and we get:
[B]{x|2<= x <= 5}[/B]

X is a natural number greater than 6

I saw this ticket come through today.
The answer is x > 6.
Natural numbers are positive numbers not 0. So 1, 2, 3, ...
Let me build this shortcut into the calculator.
Also, here is the[URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3E6&pl=Show+Interval+Notation'] interval notation[/URL] for that expression.

x is smaller than 9 and greater than 4

x is smaller than 9 and greater than 4
Written as:
4 < x < 9
To display the interval notation, use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=4%3Cx%3C9&pl=Show+Interval+Notation']interval notation calculator[/URL].

You can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket

You can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket
We're given the number of tickets as 5.
We know cost = price * quantity
Let p = price
The phrase [B]at most[/B] means less than or equal to, so we have:
5p <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=5p%3C%3D35&pl=Show+Interval+Notation']Plugging this inequality into our search engine[/URL], we have:
[B]p <= 7[/B]

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the

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 have to pay 29 a month until you reach 850 how many months will that take

You have to pay 29 a month until you reach 850 how many months will that take.
Let m be the number of months. We set up the inequality:
29m > = 850 <-- We want to know when we meet or exceed 850, so we use greater than or equal to
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=29m%3E%3D850&pl=Show+Interval+Notation']Type this inequality into our search engine[/URL], and we get:
m >= 29.31
We round up to the next integer month, to get [B]m = 30[/B].