The value of the integral is -π/6.
To change the order of integration, we need to visualize the region of
integration. The limits of integration suggest that we are integrating over
a rectangular solid in the first octant (i.e., all coordinates are positive),
with a base in the xy-plane and height extending along the z-axis.
The bounds for x go from 0 to 5 cos(\(x^2\)), the bounds for y go from 0 to
3y, and the bounds for z go from 0 to 16.
So, we can write the integral as:
∫(∫(∫5cos(\(x^2\)) dz)dy)dx, where the limits of integration are:
0 ≤ z ≤ 16
0 ≤ y ≤ 3z/2
0 ≤ x ≤ √(arccos(z/5))
To change the order of integration, we integrate first with respect to z, then with respect to y, and finally with respect to x.
∫(∫(∫5cos(\(x^2\)) dz)dy)dx = ∫(∫(16-5y/3)cos(\(x^2\)) dy)dx
= ∫[0, √(π/2)] (∫[0, 3\(x^2\)/2] (16-5y/3)cos(\(x^2\)) dy)dx
= ∫[0, √(π/2)] [16x(3\(x^2\)-4)/9sin(x^2) + (5/9)cos(\(x^2\))]dx
= [8/9sin(\(x^2\))(3\(x^2\)-8)-5/9xcos(\(x^2\))] [0, √(π/2)]
= 2/9sin(π/2)(3π/2-8)-5/9(π/2)cos(π/2)
= -2/9(π/2) - 5/9(π/2)cos(π/2)
= -π/6
for such more question on integral
https://brainly.com/question/22008756
#SPJ11
find the value of x
please help me out here ill do anything
Answer:
let's find the value of x:
4)
10x=6(5)10x=30x=35)
9(x+4)=8(8+10)9x+81=1449x=63x=76)
y^2=2(2+9)y^2=2×11y^2=22y=√(22)y= 4.69 or 4.7What is the IQR of:
45, 32, 62, 26, 22, 29
Answer:
The first quartile is 26.
The third quartile is 45
The median is 30.5
The interquartile range is 19.
Hope that helped :)
Step-by-step explanation:
i don’t understand help
Answer:
rational as it can be expressed as the quotient of two integers
Answer:
that is a rational number
Step-by-step explanation:
A rational number is a number that can be express as the ratio of two integers. ... Likewise, any integer can be expressed as the ratio of two integers, thus all integers are rational.
Example: 17 and −34 are rational numbers. (Note that there is more than one way to write the same rational number as a ratio of integers. For example, 17 and 214 represent the same rational number.) All integers are rational numbers.
An irrational number is real number that cannot be expressed as a ratio of two integers. ... The number "pi" or π (3.14159...) is a common example of an irrational number since it has an infinite number of digits after the decimal point. Many square roots are also irrational since they cannot be reduced to fractio
how to find the missing value when given the median
The median is the middle value in a set of data when the values are arranged in ascending or descending order.
Here's how you can obtain the missing value:
1. Determine the known values: Identify the values you have in the dataset, excluding the missing value. Let's call the known values n.
2. Calculate the number of known values: Count the number of known values in the dataset and denote it as k.
3. Determine the position of the median: If the dataset has an odd number of values, the median will be the middle value. If the dataset has an even number of values, the median will be the average of the two middle values.
4. Identify the missing value's position: Determine the position of the missing value relative to the known values.
If the missing value is before the median, it will be located at position (k + 1) / 2. If the missing value is after the median, it will be located at position (k + 1) / 2 + 1.
5. Obtain the missing value: Now that you have the position of the missing value, you can determine its value by looking at the known values.
If the position is a whole number, the missing value will be the same as the value at that position.
If the position is a decimal fraction, the missing value will be the average of the values at the two nearest positions.
By following these steps, you can obtain the missing value when the median and the other values in the dataset are provided.
To know more about median refer here:
https://brainly.com/question/11237736#
#SPJ11
Simplify:
3(9 + 2d) + 4d
Answer:
27 + 10d
Step-by-step explanation:
Answer:
10d+27
Step-by-step explanation:
Rearrange terms
3
(
9
+
2
)
+
4
3
(
2
+
9
)
+
4
2
Distribute
3
(
2
+
9
)
+
4
6
+
2
7
+
4
3
Combine like terms
6
+
2
7
+
4
1
0
+
2
7
Answer this correct and you are a true legend 9 + 10 = ? ...
Answer:
AcORdinG To MY CaLCulAtIoNS ItS 21
Step-by-step explanation:
Logic :)
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The probability of landing on yellow is less than the probability of landing on blue
How to determine which statement about probability is true?Probability is the likelihood of a desired event happening.
Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.
Thus, we can write the probabilities as follow:
probability of orange = 1/8
probability of purple = 2/8 = 1/4
probability of yellow = 2/8 = 1/4
probability of blue = 3/8
Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement
Learn more about probability on:
brainly.com/question/251701
#SPJ1
NEED HELP! Will give brainiest!! And thanks if you even answer one of them
Answer:
In the questions you are asked to evaluate by substituting the variables to the given number.
PLZ EXCUSE MY HANDWRITING.
What is the length of the leaf to the nearest one fourth inch
is there a picture to the leaf
which measure of validility is based on showing a substantial correlation between selection test scores and job performance scores
The measure of validity based on showing a substantial correlation between selection test scores and job performance scores is known as criterion-related validity.
Criterion-related validity is a type of validity that examines the relationship between scores on a selection test and an external criterion, which is typically job performance in this case. The purpose is to determine how well the test predicts or correlates with an individual's ability to perform successfully in a specific job or role.
To establish criterion-related validity, data is collected from individuals who have taken the selection test and their subsequent job performance is measured. By analyzing the correlation between test scores and job performance scores, researchers can determine the extent to which the test accurately predicts future job performance.
If there is a substantial positive correlation between selection test scores and job performance scores, it indicates that the test is valid and can effectively differentiate between individuals who are likely to perform well in the job and those who are not. This provides evidence that the test is a useful tool for selecting candidates who have the potential to succeed in the specific job or role.
In summary, criterion-related validity is demonstrated when there is a significant correlation between selection test scores and job performance scores, indicating the test's ability to predict future job success.
Know more about Correlation here:
https://brainly.com/question/13879362
#SPJ11
Solve the system by substitution. 5x+2y=5 y=(-2x+3
Answer:
(x, y) = (-1, 5)
Step-by-step explanation:
You want to solve this system of equations by substitution.
5x +2y = 5y = -2x +3SubstitutionThe idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.
Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:
5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y
x +6 = 5 . . . . . . . . . . simplify
x = -1 . . . . . . . . . subtract 6
y = -2(-1) +3 = 5 . . . . . use the second equation to find y
The solution is (x, y) = (-1, 5).
__
Additional comment
Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.
Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.
4x -y = 3 ⇒ y = 4x -3 . . . . . for example
The attached graph confirms the solution above.
Wrestling wins
5 7 13 24 16 22 13 7 6
Which of the following factors does NOT control the stability of a slope?
the angle of repose for intact bedrock
whether the slope is rock or soil
the amount of water in the soil
the orientation of fractures, cleavage, and bedding
The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.
Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.
The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.
To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.
know more about Bedrock.
https://brainly.com/question/2948854
#SPJ11
Blair & Rosen, Inc. (B&R), is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $85,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 9%, whereas the Blue Chip fund has a projected annual return of 8%. The investment advisor requires that at most $55,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be
6(10) + 4(10) = 100.
Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 410.
(a)
Formulate a linear programming model to find the best investment strategy for this client. (Assume N is the amount invested in the internet fund project and B is the amount invested in the Blue Chip fund. Express the amounts invested in thousands of dollars.)
Max _______________ s.t.
Available investment funds
Maximum investment in the internet fund
Maximum risk for a moderate investor
N, B ≥ 0
(b)
Build a spreadsheet model and solve the problem using Excel Solver. What is the recommended investment portfolio (in dollars) for this client?
internet fund$
blue chip fund$
What is the annual return (in dollars) for the portfolio?
$
(b)
Suppose that a second client with $85,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 450. What is the recommended investment portfolio (in dollars) for this aggressive investor?
internet fund$
blue chip fund$
(d)
Suppose that a third client with $85,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 320. Develop the recommended investment portfolio (in dollars) for the conservative investor.
internet fund$
blue chip fund$
A. N, B ≥ 0 (non-negativity constraint)
B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
C. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(a)
The linear programming model to find the best investment strategy for this client can be formulated as follows:
Maximize: 0.09N + 0.08B
Subject to:
N + B ≤ 85 (maximum investment of $85,000)
N ≤ 55 (maximum investment of $55,000 in the internet fund)
6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)
N, B ≥ 0 (non-negativity constraint)
(b)
To solve the problem using Excel Solver, you can set up the following spreadsheet model:
Cell A1: N (amount invested in the internet fund)
Cell B1: B (amount invested in the Blue Chip fund)
Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)
Constraints:
Cell A2: ≤ 85
Cell B2: ≤ 85
Cell C2: ≤ 55
Cell D2: ≤ 410
The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.
Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.
The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
(b)
For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 450
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(d)
For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 320
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
Learn more about investment from
https://brainly.com/question/24703884
#SPJ11
The half-life of strontium is 29 years. If strontium was released in the Chernobyl nuclear accident and 41.3% of it remains, how long ago did this accident occur? What year did it
happen?
Answer:
Happened in 1986
Maybe 37 years ago?
Calculate the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria: 95% confidence, within 5 percentage points, and a previous estimate of 0.25 288.12 0/2 pts Question 16 Calculate the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria: 95% confidence, within 5 percentage points, and a previous estimate is not known 384
the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.
The minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is as follows:
95% confidence, within 5 percentage points, and a previous estimate of 0.25.
The formula to calculate the sample size required for the study to determine the proportion is given by:
`n = Z²pq / E²`
Where n = sample size
Z = z-value (1.96 at 95% confidence interval)
E = margin of error
p = estimated proportion of the population
q = 1 - pp
q = estimated proportion of population without the condition (1 - 0.25 = 0.75)
Given,
Z = 1.96E = 0.05p = 0.25q = 0.75
Substituting these values in the above formula, we get;
`n = (1.96)²(0.25)(0.75) / (0.05)²``n = 384.16`
Therefore, the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria is 384.12, which can be rounded up to 385.
learn more about proportion here:
https://brainly.com/question/31548894
#SPJ11
Using a special discount you download 15 songs for $10.86 the regular price of each song is $0.89. What is the percent of the discount?
Answer:
18.65%
Step-by-step explanation:
We know
The regular price of each song is $0.89
0.89 x 15 = $13.35
Using a special discount, you download 15 songs for $10.86
What is the percentage of the discount?
We Take
13.35 - 10.86 = $2.49
Then we take
2.49 divided by 13.35, time 100 = 18.65%
So, the percent of the discount is 18.65%
In a class of 120 students, 95 like Account, 80 like Biology and there are some students who like both subjects.
Find the number of students like Account only.
Find the number of students like Biology only
Show the above information in a Venn-diagram.
Answer:
I don't know dldlskskdkdkdbdndbdkyyknmdlsöskxkLyksKnsslymdlysyyby
Suppose there are two producers in a market with the following supply functions. Supply 1: P=6+0.7Q Supply 2:P=16+0.6Q When the price is [Answer], the total quantity supplied is 250. (In decimal numbers, with two decimal places, please.) Answer:
The price at which the total quantity supplied is 250 is $11.58.
In order to find the price at which the total quantity supplied is 250, we need to equate the total quantity supplied by both producers (Supply 1 and Supply 2) and solve for the price.
Supply 1: P = 6 + 0.7Q
Supply 2: P = 16 + 0.6Q
To find the equilibrium price, we set the total quantity supplied equal to 250:
0.7Q + 0.6Q = 250
1.3Q = 250
Q = 250 / 1.3 ≈ 192.31
Now that we have the quantity, we can substitute it back into either supply function to find the price. Let's use Supply 1:
P = 6 + 0.7Q
P = 6 + 0.7 * 192.31
P ≈ 6 + 134.62
P ≈ 140.62
Therefore, the price at which the total quantity supplied is 250 is approximately $11.58.
Learn more about Equilibrium price
brainly.com/question/29099220
#SPJ11
. If a number is decreased by 4 and divided by 6, the result is
8.What would be the result if 2 is subtracted from the number
and then it is divided by 5 ?
Answer:
10
Step-by-step explanation:
The number is 52. If you subtract 2 you get 50, then after dividing by 5 you get 10.
56°
101°
Find the value of the missing angle a.
Answer:
the x angle = 45 ............. 45
Help 90 points pls help
Answer: Probably D not sure though
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The equation g(x) = f(x-6) = 10(x-6) states that the graph is shifted to the left 6 units ( hints the -6)
Given f(x) = x²+x-6, find f(0).
Answer:
-6
Step-by-step explanation:
replace x with 0
Plz help me this is due today HELP and show work
Answer:use the caculater
Step-by-step explanation:
thats all
One hundred people were surveyed about their breakfast preferences. They had between french toast and pancakes and between sausage and bacon. The results the table below.
Category french toast pancakes
sausage 25 21
bacon 23 31
1. What is the probability that a randomly selected person from the survey prefers bacon.
2. What is the probability that a randomly selected person from the survey prefers pancakes?
3. What is the probability that a randomly selected person from the survey prefers french toast given that they prefer bacon and pancakes?
4. What is the probability that a randomly selected person from the survey prefers french toast given that they prefer sausage?
The probabilities are 1. 27/50, 2. 3/4, 3. 31/100, 4. 25/46, 5. 25/48
What is probability ?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
A probability is the number of desired outcomes divided by the number of total outcomes.
Item 1:
54 out of 100 people prefer bacon, hence:
P = 54/100
= 27/50
Item 2:
Out of 100 people, 54 prefer bacon, 21 prefer sausage but pancakes, hence 54 + 21 = 75 desired outcomes, hence:
P = 75/100
= 3/4
Item 3:
31 out of 100 people prefer bacon and pancakes, hence:
P = 31/100
Item 4:
Out of 46 people that prefer sausage, 25 prefer french toast, hence:
P = 46 / 25
Item 5:
Out of 48 people that prefer french toast, 25 prefer sausage, hence:
P = 48 / 25
To learn more about probability from the given link
https://brainly.com/question/11713135
#SPJ1
Katlin is choosing between two circular wall clocks one has the radius of 5 inches while the other one has a radius of 6 inches.How much more wall space will the clock with a radius of 6 inches cover?
Plz help i dont get any of these type of questions T-T
Answer:
Exact: \( 11 \pi~in.^2 \)
Approximate: \( 34.6~in.^2 \)
Step-by-step explanation:
The spaces the clocks occupy on the wall are the areas of the clocks.
The clocks are shaped like circles, so use the formula for the area of a circle to find the two areas. Then subtract the smaller area from the larger area.
\( A_{circle} = \pi r^2 \)
Larger clock, r = 6 in.
\(A_{large~clock} = \pi \times (6~in.)^2 = 36 \pi ~in.^2 = 113.1~in.^2\)
Smaller clock, r = 5 in.
\(A_{small~clock} = \pi \times (5~in.)^2 = 25 \pi ~in.^2 = 78.5~in.^2\)
Difference in areas:
Exact: \( 36 \pi~in.^2 - 25 \pi~in.^2 = 11 \pi~in.^2 \)
Approximate: \( 113.1~in.^2 - 78.5~in.^2 = 34.6~in.^2 \)
\(y = - .011x + 24.9\)
describe this relationship in words.
Step-by-step explanation:
The given relation is :
\(y=-0.11x+24.9\) ...(1)
We need to describe this relationship in words.
The general equation of a line is given by :
y = mx +c ...(2)
comparing equations (1) and (2).
m = -0.11 and c = 24.9
It shows that the slope of the line is -0.11 and the y-intercept is 24.9.
explain how the sequence 10.6, 11.8, and 13 is a function even though there are multiple rules that can represent it.
The correct option is Option C.
C.) The sequence is a function because each rule produces one output for each input.
Meaning of a sequence:
A grouping of any objects or a collection of numbers in a particular order that follows some rule is known as a sequence.
The difference between all the following terms in the sequence 10..6.11.8.13 is 12.
As a result, the series is an example of a linear function.
As a linear function, the sequence will always provide an output that complies with the rule.
As a result, the sequence is a function because each rule yields a single output for each input; hence, option C is the right response.
For such more question on Sequence:
brainly.com/question/9679397
#SPJ4
The following question may be like this:
Explain how the sequence 10.6, 11.8, and 13 is a function even though there are multiple rules that can represent it.
A)The sequence is a function because the domain is unrestricted.
B)The sequence is a function because more than one rule can represent it.
C)The sequence is a function because each rule produces one output for each input.
D)The sequence is a function because each rule produces multiple outputs for each input.
what would be the answer to 23 x 10^5
Answer:
2300000
Step-by-step explanation:
From a point 50m from the base of the Skylon Tower in Niagara Falls, the angle of elevation to the top of
the tower is 78o
. Find the height of the tower.
Answer:
The tower is about 235 m.
Step-by-step explanation:
Let x be the height of the tower
tan θ = opp / adj
tan 78 °= x / 50
x = 50 tan 78 °
x = 235
∴ The tower is about 235 m.
Hope this answer helps you :)
Have a great day
Mark brainliest