Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
What is integral ?
An integral is a mathematical concept that represents the area under a curve, or the accumulation of a quantity over a given interval. Integrals are a fundamental concept in calculus, which is the branch of mathematics that deals with the study of rates of change and accumulation. In other words, an integral can be thought of as the sum of an infinite number of infinitesimal "slices" of the quantity being measured, over a given interval. Integrals can be used to solve a wide variety of problems.
The integral is evaluated as follows,
∫[0,1]∫[0,1] 3yxy dydx
= 3∫[0,1] yxy dxdy
= 3 * (1/4) * ∫[0,1] x dxdy
= 3 * (1/4) * (1/2) * x^2 dy
= 3 * (1/4) * (1/2) * (1/3) = 3/24
Hence , Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
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to shift the graph of an equation a certain number of units down, you need to ______ the function equation
Answer:
Step-by-step explanation:
...You need to subtract that number of units from the function equation.
Example: given y = x^2, and wanting to shift the entire graph down 3 units, we subtract 3 from y = x^2, obtaining y = x^2 - 3.
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 19.
The probability of a student scoring less than 19 is.
(Round to four decimal places as needed.)
(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.7 and 27.1.
The probability of a student scoring between 17.7 and 27.1 is.
(Round to four decimal places as needed.)
(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 33.1.
The probability of a student scoring more than 33.1 is
3.1
is.
(Round to four decimal places as needed.)
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
OA. None of the events are unusual because all the probabilities are greater than 0.05.
B. The event in part (c) is unusual because its probability is less than 0.05.
C. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.
D. The event in part (a) is unusual because its probability is less than 0.05.
Help me solve this
Using the normal distribution, we have that:
a) The probability of a student scoring less than 19 is 0.2709 = 27.09%.
b) The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
c) The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
d) The correct option is: B. The event in part (c) is unusual because its probability is less than 0.05.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 22.4, \sigma = 5.1[/tex]
Item a:
The probability is the p-value of Z when X = 19, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22.4}{5.1}[/tex]
Z = -0.67.
Z = -0.67 has a p-value of 0.2709.
The probability of a student scoring less than 19 is 0.2709 = 27.09%.
Item b:
The probability is the p-value of Z when X = 27.1 subtracted by the p-value of Z when X = 17.7, hence:
X = 27.1:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27.1 - 22.4}{5.1}[/tex]
Z = 0.92.
Z = 0.92 has a p-value of 0.8212.
X = 17.7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.7 - 22.4}{5.1}[/tex]
Z = -0.92.
Z = -0.92 has a p-value of 0.1788.
0.8212 - 0.1788 = 0.6424.
The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
Item c:
The probability is one subtracted by the p-value of Z when X = 33.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33.1 - 22.4}{5.1}[/tex]
Z = 2.1.
Z = 2.1 has a p-value of 0.9821.
1 - 0.9821 = 0.0179.
The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
Item d:
Probabilities less than 0.05 are unusual, hence the correct option is:
B. The event in part (c) is unusual because its probability is less than 0.05.
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How many three-digit multiples of 5 have three different digits?
There are 180 numbers which are three-digit multiples of 5.
According to the statement
we have to find the three digit numbers which are multiples of 5.
we know that three digit numbers are start from 100 to 999 and in 1 line of counting means 100 to 110 there are 2 numbers are multiples of 5.
Here we use Multiplication method to find the number of digit which are a multiple of 5.
It means there are two numbers which are multiples of 5 in the one line of counting and there are 90 lines of counting from 100 to 999.
So, it means the answer will become
2*90 = 180.
So, There are 180 numbers which are three-digit multiples of 5.
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1. Name a career that requires data-analysis skills. Describe how data analysis is
used in this career. Be specific in your examples.
The career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.
Data analysis skillsData analysis skills are known as technical skills used by a data analyst to report insights and analyze data.
Some data analysis skills include;
Data VisualizationData CleaningPythonSQL and NoSQLMachine LearningLinear Algebra and CalculusMATLABA career that requires data analysis skills is a data scientists
A data scientist is one that computes and analyzes large amounts of data from different sources and makes useful interpretations from it.
The skills such career needs include statistics, calculus, probability, programming, excel, visualization, database management, and machine earning.
There is also need for a high level of accuracy when solving problems.
Thus, the career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.
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Combine like terms to simplify the following polynomial.
5a²b+7ab² +9c+ 11a²b-3ab² - 9c
Answer:
5a²b + 7ab² + 9c + 11a²b - 3ab² - 9c
= (5a²b + 11a²b) + (7ab² - 3ab²) + (9c - 9c)
= 16a²b + 4ab²
Mathematics word problem
75 miles per hour is the rate of train.
what is the formula of speed?Formula of speed = distance/time
let,
s1 , speed of A train = s
s2, Speed of B train = s
t1, time of travel for train A = 2.5h
t2, time of travel for train B = 4 h
d1, distance traveled by train A
distance travel by train A = speed*time
= s1*t1
d2, distance traveled by train B
distance travel by train A = speed*time
= s2*t2
Total distance between station A and station B = 562.5 mi
d1+d2=562.5 mi
s1t1+s2t2=562.5
s(2.5)+s(4)=562.5
6.5 s = 562.5
s = 562.5/6.5
s = 86.5 mph
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75 miles per hour is the rate of the train.
what is the rate of the train?Given:
Train A and Train B leave a central station at the same time.They travel at the same speed, but in opposite directions, with train A heading towards station A.Train B heading towards station B.Train A reaches station A after 2 and 1/2 hours.Train B reaches station B after 4 hours.Station A and Station B are 585 mi apart.Find:
Rate of the trains.Solution:
Formula of speed = distance/time
Let us consider
Speed of A train(s1) = s
Speed of B train(s2) = s
Time of travel for train A(t1) = 2.5h
Time of travel for train B(t2) = 4 h
Distance traveled by train A(d1)
= speed*time
= s1*t1
Distance traveled by train B(d2)
= speed*time
= s2*t2
The total distance between station A and station B = 562.5 mi
d1+d2=562.5 mi
s1t1+s2t2=562.5
s(2.5)+s(4)=562.5
6.5 s = 562.5
s = 562.5/6.5
s = 86.5 mph
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Which histogram represents the data? 1,2,12,14,15,16,18
Option b) is correct
In statistics, a histogram is a graphical representation of the distribution of data. A histogram is represented by a set of rectangles, adjacent to each other, where each column represents a certain type of data. Statistics is a stream of mathematics that is used in various fields. When figures are repeated in statistical data, this repetition is known as frequency and can be written in the form of a table, called a frequency distribution. Frequency distributions can be displayed graphically using different types of graphs and one of them is a histogram.
A histogram chart is used under certain conditions. They are:
Data should be numeric.
A histogram is used to check the shape of the data distribution.
It is used to check if the process changes from one period to another.
It is used to determine whether the output differs when it involves two or more processes.
It is used to analyze whether the given process meets the customer's requirements.
The data 1,2,12,14,15,16,18 is given
We need to find the histogram which best fits to the given data
Total number that falls between 0-9 is 2
Total Number that falls between 10-19 is 5
Total Number that falls between 20-29 is 1
Total Number that falls between 30-39 is 5
Total Number that falls between 40-49 is 3
Total Number that falls between 50-59 is 1
Hence the histogram is obtained
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Which of the following are equations for the line shown below? Check all that
apply.
(-2,-5)
(2,5)
A. y + 5 = 2.5(x+2)
B. y-5=2.5(x-2)
C. y-2=2.5(x - 5)
D. y+2=2.5(x+5)
Answer:
A
Step-by-step explanation:
first prime factor....
Answer:
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Which choice is equivalent to the product below?
√14•√10
A. 2√35
B. 4√7
C. 35
D. 4√35
Find the value of x.
helllppp
tysm
Answer:
Step-by-step explanation:
I need help with this slope
Answer:
Step-by-step explanation:
First, the y-intercept is -3 so from -3 the slop to the next point is 4/1.
What is the solution of p - 12 > -18
p> -30
p<-6
p> -6
p < -30
Answer:
p > -6
Step-by-step explanation:
1) Add 12 to both sides.
p > -18 + 12
2) Simplify -18 + 12 to -6.
p > -6
Find the decimal. _. _ _ _ Clues: (a) The digits 0, 1 and 2 are not used in the decimal. (b) The digit in the ones place is the greatest 1-digit number. The hundredths digit is smaller than 5. The difference between the tenths digit and the ones digit is the hundredths digit. (c) (d) (e) (f) The thousandths digit is greater than 5 and is an odd number. All the digits are different.
Answer:
Step-by-step explanation:
143
or
121
We are accepting
does any of this help
I need help with this geometry question asap!
Answer:
True
Step-by-step explanation:
Lines in three dimensions can be one of ...
coincidentparallelintersecting (at one point)skewCoplanarLines are coplanar when a plane can be defined that includes the entirety of both of them. In the attached image, lines m₁ and n intersect and both lie in the gray plane. They are coplanar.
Lines m and m₁ are parallel, and both are contained in the turquoise plane. They are coplanar. A plane can always be drawn that will contain a pair of parallel lines. That is, any two parallel lines must be coplanar.
The lines m and n in the figure are skew, non-intersecting and non-parallel. They cannot be contained in a single plane.
__
Additional comment
Three or more parallel lines may not be coplanar. They will only definitely be coplanar when considered in pairs.
A train is traveling at a speed of 60 miles per hour. What happens to the number of miles when the number of hours
changes?
O When the number of hours increases, the number of miles decreases.
O When the number of hours increases, the number of miles increases.
O When the number of hours decreases, the number of miles increases.
O When the number of hours decreases, the number of miles stays the same.
Intro
Done
When the number of hours decreases, the number of miles increases.
What is the relationship between number of hours and number of miles travelled?
Average speed is the total distance travelled per time.
Average speed = total distance / total time
There is an inverse relationship between the distance travelled and the time travelled. If time increases, the distance travelled decreases.
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3.5.3 Test (CST): Functions
Does this graph show a function? Explain how you know.
-5
5-
OA. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
OC. Yes; there are no y-values that have more than one x-value.
D. Yes; the graph passes the vertical line test.
Jhy
Answer:
D
Step-by-step explanation:
It pass the vertical line test.
Hope this helps <3
As per the given graph, the graph fails the vertical line test. The correct option is B.
What is graph?A graph is a visual representation of data that uses lines, bars, or other symbols to show how different values are related to each other.
Graphs are often used to display information in a way that is easy to understand and interpret.
The vertical line test is a way to determine whether a given graph represents a function.
According to this test, if any vertical line intersects the graph at more than one point, then the graph does not represent a function.
In the given graph, we can see that there are some vertical lines that intersect the graph at more than one point, such as the vertical line passing through x = 2.
Therefore, the graph does not pass the vertical line test and does not represent a function.
Thus, the correct answer is B.
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The non-parallel sides of a trapezoid are called the
Answer:
Step-by-step explanation:
the legs
How did the temperature change if it increased by 50% and then decreased by 33 1/3%
The temperature does not change after the percentage increase and decrease.
What is the change in the temperature?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Assume the initial temperature is 10.
Temperature after the 50% increase : (1 + 0.5) x 10 = 15
Temperature after the 33 1/3% decrease : (1 - 0.333) x 15 = 10.00
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The graph shows f(x)and its transformation(x).
Enter the equation for g(x) in the box.
g(x) =
Using translation concepts, the equation for function g(x) given in the graph is:
[tex]g(x) = 2^{x + 2}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The parent function for this problem is given as follows:
[tex]f(x) = 2^x[/tex]
From the graph, function g(x) was shifted 2 units left, hence x -> x + 2 and the definition is:
[tex]g(x) = 2^{x + 2}[/tex]
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Can you help me in my work
Answer:
2-2 goes with 1 - 1
10 - 7 goes with 8 - 5
4 - 3 goes with 7 - 6
8 - 2 goes with 9 - 3
9 - 5 goes with 5 - 1
Have a nice day.
I am Clara btw.
Step-by-step explanation:
Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 101 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (12.4,13.3).
Given that a sample of 101 cookies and per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2.
From the given information,
Let n=101 represents the size of the sample.
Let [tex]\bar{x}[/tex]= 12.9 represents the mean of the sample.
Let s= 3.2 represents the standard deviation of the sample.
Degrees of freedom:
df = n-1
df= 101-1
df= 100
The critical value of t at 0.2 level of significance with 100 degrees of freedom is,
[tex]\begin{aligned}t_{cric}&=t_{(\frac{\alpha}{2}, n-1)}\\ &=t_{(0.2,100)}\\ &=1.2900\end[/tex]
The 80% confidence interval for the number of chocolate chips per cookie for Big chip cookies is computed as follows:
[tex]\begin{aligned}CI_{80\%}&=\bar{x}\pm t_{(\frac{\alpha}{2},n-1)}\left(\frac{s}{\sqrt{n}}\right)\\ &=12.9\pm 1.2900\left(\frac{3.2}{\sqrt{101}}\right)\\ &=12.9\pm 1.2900\times 0.3184\\ &=12.9\pm 0.410736\\ &=12.489264,13.310736\end[/tex]
Hence, the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies when the mean is 12.9 and standard deviation is 3.2 is (12.4,13.3).
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The table shows various values of a linear function f (x).
x –4 0 2 5 9 13
f (x) –11 1 7 16 28 40
What is f –1(13)?
40
38
13
4
The value of f –1(13) is 4
How to determine the inverse value?The table of values is given as:
x –4 0 2 5 9 13
f (x) –11 1 7 16 28 40
A linear function is represented as:
y = mx + b
Where b represents the y-intercept and m represents the slope
From the graph, when x = 0, y = 1.
This means that b = 1
So, we have
y = mx + 1
Also from the graph, when x = 2, y = 7.
So, we have:
7 = 2m + 1
Subtract 1 from both sides
7 - 1 = 2m + 1 - 1
Evaluate the difference
6 = 2m
Rewrite the above equation as:
2m = 6
Divide both sides of the equation by 2
m = 3
Substitute m = 3 in y = mx + 1
y = 3x + 1
The notation f –1(13) implies that y = 13
So, we have
13 = 3x + 1
Subtract by 1
3x = 12
Divide by 3
x = 4
Hence, the value of f –1(13) is 4
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mrs.kingsleys has 102 inches of ribbon for her crafts she cut the ribbon into 8 pieces of equal length which statment best explains how mrs. kingsley cut the ribbon
Mrs Kingsley cut the ribbon into a length of 12.75 inches each.
How did Mrs Kingsley cut the ribbon?
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
Length of each ribbon = 102 / 8 = 12.75 inches
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find the lcm of 48,64,72,96,108
Please help me fast i will give you50 pts
2|48,64,72,96,108
2|24,32,36,48,54
2|12,16,18,24,27
2|6,8,9,12,27
2|3,4,9,6,27
2|3,2,9,3,27
3|3,1,9,3,27
3|1,1,3,1,9
3|1,1,1,1,3
LCM
2⁶×3⁴64×815184i know i just posted two in a row but im slow and im doing a test so expect more later
Answer:
D. is the answer of your questions
QUESTION 2
Which of the following is a quantitative variable?
Amount in fluid ounce of coffee
Name of a cell phone carrier
O Occupation
Anxiety rating (highly anxious, moderately anxious, or relaxed)
Answer:
Step-by-step explanation:
Amount in fluid ounce of coffee
Its the only one that deals with numbers
What is the value of the expression below when y = 4?
Answer:
6y²-7y+9
Submit Answer
What are the coordinates of the y-intercept of the line -3x+2y=6?
Answer:
y-intercept: (0,3)
Step-by-step explanation:
To find the y-intercept, we set x to equal 0, giving the equation:
-3(0)+2y = 6
0+2y = 6
y = 3
As an introduction to probability, a student asked to roll a fair, six sided number cube seven times the results of those seven rolls are shown below 1,4,4,4,4,6,5 what is the standard deviation of the data?
Using it's concept, the standard deviation of the data is of 3.742.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For this data-set, the mean is:
M = (1 + 4 + 4 + 4 + 4 + 6 + 5)/7 = 4.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(1 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (5 - 4)^2}{7}} = 3.742[/tex]
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