A function f: RR is non-increasing on an interval I if Va e I, Vye I, r > y = f(x)
Answers
A function f: ℝ → ℝ is non-increasing on an interval I if for every pair of points a, b in I with a ≤ b, the value of f(a) is greater than or equal to f(b). In other words, as the input increases within the interval I, the corresponding output values of the function either remain the same or decrease.
To prove that a function f is non-increasing on an interval I, we need to show that for any two points a and b in I with a ≤ b, the inequality f(a) ≥ f(b) holds.
1. Start by assuming a and b are any two points in I such that a ≤ b.
2. Next, consider the values of f(a) and f(b) corresponding to these points.
3. Show that f(a) ≥ f(b) holds by comparing the values of f(a) and f(b) based on the definition of non-increasing function.
4. This comparison involves analyzing the behavior of the function f within the interval I and determining whether the output values remain the same or decrease as the input increases.
5. By demonstrating that f(a) ≥ f(b) for any pair of points a and b in I with a ≤ b, we establish that the function f is non-increasing on the interval I.
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Related Questions
Five boxes of candles contain a total of 60 candles. Each box holds the same number of candles. Complete the table and graph the relationship
Answers
Answer:
300
Step-by-step explanation:
you should muliple 60 and 5
true or false: of the range, the interquartile range, and the variance, the interquartile range is least influenced by an outlying value in the data set.
Answers
The interquartile range is least affected by an outlying value in the data set of the range, interquartile range, and variance is True.
Max to min value is the range. Range can substantially change if there are any outliers.
Since the threshold values for Q3 and Q1 are not outliers, the IQR won't change.
Outliers cause variance to be misinterpreted since they vastly increase variance.
Interquartile range:
You may determine the spread of the midpoint of your distribution using the interquartile range.
The interquartile range contains half of the values for any distribution that is ordered from low to high. The first 25% of values are found in the first quartile (Q1), while the last 25% are found in the fourth quartile (Q4).
The third quartile (Q3) less the first quartile (Q1) is the interquartile range (Q1). This provides us with the data set's middle half's range.
The interquartile range is calculated using only 2 values, much like the range. The IQR, however, is less impacted by outliers because the two values are more likely to be average scores because they are drawn from the middle of the data set.
The IQR provides a reliable indicator of variability for both skewed and normal distributions.
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A store has 1353
pair of socks. The socks are sold in pack of 3
pairs. How many packs of socks the store can sell?
Answers
Answer: The store can sell 451 packs of socks.
Step-by-step explanation: To find the number of packs of socks the store can sell, we need to divide the total number of socks by the number of socks in each pack.
Since each pack contains 3 pairs of socks, or 6 individual socks, we can find the number of packs by dividing the total number of socks by 6:
1353 socks ÷ 6 socks per pack = 225.5 packs
However, since we can't sell a fraction of a pack, we need to round up to the nearest whole number. Therefore, the store can sell 451 packs of socks.
Share Prompt
Explanation:
The store has a total of 1353 socks.
The store sells the socks in a pack of 3.
If we divide 1353 by 3 we’ll get 451.
Hence the store sells 451 packs of socks.
(2x-y)2-(y+2)2:::::::::::::::
Answers
Answer:
(2x - y )2 - (y + 2)2 = 4 (x - y - 1)
Step-by-step explanation:
\((2x -y) 2 - ( y + 2 ) 2 = (4x -2y) -(2y + 4) \\\\\)
\(= 4x - 2y -2y - 4\\\\=4x - 4y - 4\\\\=4(x-y-1)\)
ASAP PLEASE HELP WILL MARK BRAINLIEST
Rotate the point A (-4, 5) 270°about the origin. Plot A' on the grid.
Answers
Answer:
Clockwise 270° around the origin: (-5,-4)
Counterclockwise 270° around the origin: (5,4)
Step-by-step explanation:
Clockwise
A(x,y) -> A'(-y,x)
Counterclockwise 270° rotation rule:
A(x,y) -> A'(y,-x)
Decorative sheets of paper sell for
$0.16 per sheet. How many sheets
are sold for $7.84?
Answers
Answer:
42 sheet of paper
Step-by-step explanation:
$7.84 divided by $0.16
This equals 42
After spending 7 dollars and 84 cents, 42 sheets of paper will be sold.
NEEEDDDD HELP ASSAP. This is about math help
Answers
So 1st off you divide 25.2 by 36 since it miles is the x and the cost is y
the unit rate is 0.7 since i divided those 2 numbers
now i just have to do 0.7 times 47
The answer is $ 32.9
sorry if its wrong?
☞ user58580~ ♥
Mr. Shelton paid $19.55 for 8.5 gallons of gas. How much did
he pay for EACH gallon of gas he bought? (Don't forget the $
Answers
Answer:
He paid $2.30 for each gallon of gas he got.
if 60! is written out as an integer, with how many consecutive 0’s will that integer end?
Answers
Answer:
14
Step-by-step explanation:
Ok, 60! is a really big number
\(x!=x(x-1)(x-2)...1\)
So we have 60*59*58...*1
2 times 5 is 10 which makes a terminal zero (ending zero)
We need to count how many fives and twos are in 60!
There are 60/5=12 5^1's
There are 60/25=2 5^2's
So 12+2=14
There are way more 2's than fives so we take the lesser number
So the answer is 14
*Note that 60/25 is not 2, we need an integer rounded down
Suppose the length of each sude of a square is decreased by 4 ft if the perimeter of the square is now 32 feet what was the original length of each side
Answers
Answer:
12ft
Step-by-step explanation:
length of one side of the square now
32ft / 4 = 8ft
length of one side of the square before decreasing the length
(original lenght)
8ft +4ft = 12ft
Dakota arrived at school at 7:59 a.m. He left at 2:33 p.m. How long was Dakota at school
Answers
Answer:
6 hours and 34 minutes
Step-by-step explanation:
If we add 1 minute to 7:59 it is 8 which makes it easier to see the length of time. Then we add that 1 back in to find the exact amount of time Dakota was in school.
Brainliest please . . . .
An angle measures 73.6° less than the measure of its supplementary angle. What is the measure of each angle?
Answers
Answer:
Smaller angle = 53.2
Larger angle = 126.8
Step-by-step explanation:
Lets say x is the measure of the supplement. Since we know they're supplementary, we know their angle measure sum will equal 180. We can set up our equation like this \(x + (x-73.6) = 180\). Note: (x - 73.6) is the measure of the smaller angle. By solving, we get 126.8 degrees for the measure of the supplement. If we plug in the value of x into (x-73.6), we get 53.2 degrees as the angle measure of the smaller angle.
The table shows the change in the annual sales turnover of a company in millions of dollars, S(x), where x represents the years since the company was founded. X 1 3 5 7 9 S(x) $495 $598. 95 $724. 73 $876. 92 $1,061. 08 What is the predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11]? A. $111. 42 per year B. $184. 15 per year C. $92. 08 per year D. $222. 83 per year
Answers
The predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is $92.08 per year.
To find the predicted average rate of change of the company's sales turnover over the interval [9, 11], we need to find the slope of the line that best fits the data points provided.
The slope of the line can be calculated using the formula:
(change in y) / (change in x) = (S(x2) - S(x1)) / (x2 - x1)
We can use any two of the provided data points to find the slope. Using the data points (9, $1,061.08) and (7, $876.92), we get:
(change in y) / (change in x) = ($1,061.08 - $876.92) / (9 - 7) = $184.15 / 2 = $92.08 per year
This is the average rate of change of the company's sales turnover over the interval [9, 11]. So the answer is C. $92.08 per year.
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Awnse choice cAnswer:
Step-by-step explanation:
a flower is chosen at random from the garden. what is the probability that the flower is purple? type as:
Answers
The probability of choosing a purple flower at random from a garden with 10 purple flowers and 40 total flowers is 1/4 or 25%.
To calculate the probability of an event, we divide the number of ways that event can occur by the total number of possible outcomes. In this case, we need to determine the number of purple flowers in the garden and divide it by the total number of flowers in the garden.
Let's say there are 10 purple flowers and 40 total flowers in the garden. The probability of choosing a purple flower at random would be:
Number of ways to choose a purple flower = 10
Total number of flowers = 40
Probability of choosing a purple flower = 10/40
Simplifying this fraction, we get:
Probability of choosing a purple flower = 1/4 or 25%
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Complete Question:
10 flower is chosen at random number of 40 from the garden. what is the probability that the flower is purple?
Can someone help me slove this plss. :-)
Answers
Answer:
Step-by-step explanation:
.
SS ZONE
Block 5> Topic 3> Applications of Percent
Dre is painting a mural for his school.
Each can of spray paint costs $5 before
sales tax. The sales tax rate is 10%.
Plot a point that represents how Dre can
spend money on spray paint.
Cost Including Sales Tax (5)
132
88
44
20
40
60
Cost Before Sales Tax ($)
Answers
A point that represents how Dre can spend money on spray paint is plotted on the proportional relationship graphed at the end of the answer.
How to model the money spent?The money spent after sales tax is obtained multiplying the money spent before sales tax by a constant, hence a proportional relationship models the situation.
The general format of a proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality.
In this problem, the sales tax rate is of 10%, meaning that the total amount paid is composed as follows:
Cost before sales tax.10% of the cost before sales tax.Considering x as the cost before sales tax, the equation is given as follows:
y = x + 0.1x
y = 1.1x.
Meaning that one point is given as follows:
(5,5.5).
Meaning that when the cost before sales tax is of $5, the cost including sales tax is of $5.5.
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Please help!
Identify the slope of the function: f(x)=2(3x-7)
A:3
B:6
C:7
D:2
Answers
Answer:
The slope is 6
Step-by-step explanation:
f(x)=2(3x-7)
Distribute the 2
f(x)=2*3x-2*7
f(x) = 6x -14
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 6 and the y intercept is -14
The slope is 6
What value for x will make the equation −3x+1=2(4x−5)true?
Answers
The table lists data on the hair length and the age of nine girls. Select the points that represent this data.
Answers
The points that represent this data are shown in the scatter plot attached below.
How to construct and plot the data in a scatter plot?In this scenario, the age (in years) would be plotted on the x-axis (x-coordinate) of the scatter plot while the hair length (in inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the age (in years) and the hair length (in inches), a linear equation for the line of best fit is given by:
y = 0.0502x + 7.73
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solve 3y + 6 = 30 - 7y
Answers
Answer:
y= 12/5
Step-by-step explanation:
in convex hexagon , all six sides are congruent, and are right angles, and , , , and are congruent. the area of the hexagonal region is . find .
Answers
In a convex hexagon, if the area of the hexagonal region is 2116 (√2 + 1), then the value of AB is 46.
What is a convex hexagon?A convex hexagon is a hexagon in which all of the inner angles and all of the vertices have to be smaller than 180 degrees. There are both regular and irregular convex hexagons. Inside a convex hexagon, there are no angles. More specifically, no internal angle will exceed 180 degrees. Any internal angle which exceeds 180 degrees is concave.
Let the side length be x.
So, the diagonal BF = √(AB^2 + A F^2) = √(x^2 + x^2) = x√2.
Then, the areas of the triangles AFB and CDE in total equals (x^2 / 2) * 2, and the area of the rectangle BCEF equals x * x√2 = x^2 √2.
Now, let the equation be:
2116 (√2 + 1) = x^2√2 + x^2
And by simplifying the above equation, we will get:
2116 (√2 + 1) = x^2 (√2 + 1)
2116 = x^2
By taking root both sides, then it will be:
x = 46
Hence, the value of AB is 46.
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Although part of your question is missing, you might be referring to this full question: In a convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles. And ∠B, ∠C, ∠E and ∠F are congruent. The area of the hexagonal region is 2116 (√2 + 1). Find AB.
using the formula for a confidence interval percentage indicate the role of: a) sample finding (percentage) b) variability c) level of confidence
Answers
A higher level of confidence results in a wider confidence interval, which means that there is a greater chance that the true value lies within the confidence interval.
The role of the following factors can be determined using the formula for a confidence interval percentage:
a) Sample size (percentage): The sample size (percentage) determines the size of the standard error in the estimate. The formula for calculating a confidence interval percentage takes into account the sample size and the variability of the data.
b) Variability: The variability is a measure of how much the data deviates from the mean or expected value. The variability is represented by the standard deviation of the data.
A higher variability results in a larger confidence interval, which means that there is a greater chance that the true value lies outside the confidence interval.
c) Level of confidence: The level of confidence determines the size of the confidence interval. The level of confidence is typically set to 95%, which means that there is a 95% chance that the true value lies within the confidence interval.
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Sam is 1.5 meters tall and casts a 3-meter shadow. At the same time, a trees shadow is 10 meters long. How high is the tree? (Note that similar triangles result)
Answers
The height of the tree casting a shadow of 10 meters is 5 meters.
What is the height of tree?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
Given the data in the question;
Height of Sam = 1.5mShadow of Sam = 3mHeight of tree = xShadow of tree = 10mRatio of height of tree and its shadow = x/10
Ratio of height of Sam and his shadow = 1.5/3
Equate the two to get the height of the tree.
x/10 = 1.5/3
Cross multiply
3x = 10 × 1.5
3x = 15
x = 15/3
x = 5m
Therefore, 5 meters is the height of the tree.
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Suppose that a researcher is interested in estimating the mean systolic blood pressure, μ, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate μ. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 24 mm Hg, what is the minimum sample size needed for the researcher to be 95% confident that his estimate is within 3 mm Hg of μ?Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
Answers
In order to find the sample size, we can use the following formula that relates the population and sample standard deviations:
\(\sigma_{\bar{x}}=z\frac{\sigma}{\sqrt{n}}\)For a confidence interval of 95%, we have z = 1.96.
Then, using the values of the standard deviations, we have:
\(\begin{gathered} 3=1.96\frac{24}{\sqrt{n}}\\ \\ 3=\frac{47.04}{\sqrt{n}}\\ \\ \sqrt{n}=11.76\\ \\ n=138.3 \end{gathered}\)Rounding to the next whole number, we have a sample size of 139.
Which digits are missing from this equation?
3. 58 × 100[(3 × 1) + (5 × 0. 1) + (8 × 0. 01)] × 100
= (3 × ) + (5 × ) + (8 × )
= 358
Answers
The digits missing from the equation are 100, 10 and 1 respectively. The solution has been obtained by using the concept of algebraic equation.
What is algebraic equation?
If a mathematical phrase has variables, constants, and algebraic operations, it is said to be "algebraic" (addition, subtraction, etc.). The expression must contain the equals sign and satisfy the algebraic equation.
We are given an expression as
3. 58 × 100[(3 × 1) + (5 × 0. 1) + (8 × 0. 01)] × 100
On multiplying, we get
= (3 × 100) + (5 × 10) + (8 × 1)
= 358
Hence, the digits missing from the equation are 100, 10 and 1 respectively.
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Graph :StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1
Answers
The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment
How to graph the equationThe expression that represents the function in words is given as
StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1
Express the equation properly
So, we have
x^2/49 + (y + 1)^2/4 = 1
The above equation is an ellipse
Next, we plot the graph on a coordinate plane using a graphing tool
See attachment for the graph of the equation
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The frequency table shows a set of data collected by a doctor for adult patients who were diagnosed with a strain of influenza. a 2-column table with 4 rows. the first column is labeled age range with entries 25 to 29, 30 to 34, 35 to 39, 40 to 45. the second column is labeled number of sick patients with entries 3, 6, 5, 4. which dot plot could represent the same data as the frequency table? a number line going from 25 to 45. there is 1 dot above 26, 28, 29, 33, 39, 44. there are 2 dots above 31, 35, 36, 38. there are 3 dots above 41. a number line going from 25 to 45. there is 1 dot above 26, 28, 29, 33, 44. there are 2 dots above 30, 35, 38. there are 3 dots above 32, 40. a number line going from 25 to 45. there is 1 dot above 26, 31, 33, 34, 41, 44. there are 2 dots above 30, 35, 37. there are 3 dots above 32, 40. a number line going from 25 to 45. there is 1 dot above 26, 27, 33, 40, 44. there are 2 dots above 29, 30, 32, 35, 38, 45. there are 3 dots above 39.
Answers
The dot plot that represents the same data as that in the frequency table is option 2.
What is a dot plot?
A dot plot is a graph that is used to display data using dot. The number of dots in the dot plot must be equal to the frequency in the frequency table.
For example, the frequency of the age range of 25 to 29 is 3. Thus, there must be 3 dots spread between 25 to 29.
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Answer:
the answer is B
Step-by-step explanation:
Using the data from problem 9 if student E had a z-score of -1.2,
what was the SAT score?
Answers
The SAT score, using the normal distribution, is obtained as follows:
373.6.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of SAT scores are given as follows:
\(\mu = 514, \sigma = 117\)
The z-score is of:
Z = -1.2.
Hence the score is obtained as follows:
-1.2 = (X - 514)/117
X - 514 = -1.2 x 117
X = 373.6.
Missing InformationThe mean and the standard deviation of the SAT scores are given as follows:
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What innovation was made possible in part because of the Carterfone decision in 1968? Select one a. COBOL b. radiospectrum allocation c. the public Internet d. SMS
Answers
The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C
The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.
This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.
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What is the y-intercept of the line graphed on the graph?
Answers
Answer:
y intercept is -5
Step-by-step explanation:
Answer:
it is -5 :)
Step-by-step explanation:
the y intercept is -5, you can easily see its -5 because thats where it crosses the y axis. good luck, hope this helped!!