The probability of selecting a student that drink both coffee and tea is
1/10.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
From the algebra of sets, we know n(A∪B) = n(A) + n(B) - n(A∩B).
A university polls 200 students. 80 students drink tea, 140 drink coffee, and 30 drink neither.
Therefore,
200 = 140 = 80 - N(A∩B).
200 = 220 - N(A∩B).
N(A∩B) = 20.
So, out 0f 200 students 20 drink both.
Therefore the probability of students drink both is,
= 20/200.
= 1/10.
learn more about probability here :
https://brainly.com/question/743546
#SPJ1
3. The graph of function g(x) is shown below.
Answer:
Step-by-step explanation:
g(x) = 2*[tex]\sqrt{x}[/tex] + 4
Domain is the input so what limits are there to the input?
for the square root, you are told that you can't not put in negative numbers until you learn about imaginary number in the for m a+bi, but for now, just say the input is 0 to ∞, for now The domain is 0 to ∞
Range is the output
so that is from 4 to ∞
Answer:
a. translation 2 right and up 4
b. g(x) = √(x -2) +4
c. domain: x ≥ 2; range: y ≥ 4
Step-by-step explanation:
You have the graph of a square root function with its vertex at (2, 4). You want to know what transformation that represents, the equation of the graph, and the domain and range of the function.
a. TransformationThe vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged. This transformation is ...
translation right 2 units and up 4 units
b. EquationTranslation of function f(x) by h units right and k units up gives you ...
g(x) = f(x -h) +k
Here, we have (h, k) = (2, 4), and f(x) = √x, so the transformed function is ...
g(x) = √(x -2) +4
c. Domain and RangeThe domain is the horizontal extent of the graph. For a square root function it is the x-value of the vertex, and all points to the right of that.
domain of g(x): x ≥ 2
The range is the vertical extent of the graph. For a square root function it is the y-value of the vertex, and all points above that.
range of g(x): y ≥ 4
a response variable y has correlation coefficient 0.3 with each of the predictors x1 and x2. however, these predictors are heavily correlated r x1x2
If the response variable y has a correlation coefficient of 0.3 with each of the predictors x1 and x2, it means that there is a weak linear relationship between y and both x1 and x2.
This means that as x1 and x2 increase or decrease, y is likely to change by a small amount. If x1 and x2 are heavily correlated, it means that there is a strong linear relationship between the two variables. This means that as x1 increases or decreases, x2 is likely to change by a large amount in the same direction. When two predictors are highly correlated, it can be difficult to determine the individual contribution of each predictor to the response variable y.
In this situation, it may be useful to use techniques such as multi-collinearity analysis or principal component analysis to understand the relationship between the predictors and the response variable better.
Learn more about Correlation at:
brainly.com/question/28175782
#SPJ4
Find the centroid (x¯,y¯) of the triangle with vertices at (0,0), (10,0), and (0,6).
x¯=
y¯=
The triangle with vertices A(0 , 0), B(0 , 6), and C(10 , 0) has its centroid located at (5 , 3).
Centroid of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.
Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.
First, try to graph and visualize the triangle formed by the three vertices. (see photo)
From there, we can say that triangle ABC is a right-angled triangle with line BC as the hypotenuse.
One of the properties of the circumcenter of a triangle states that the circumcenter lies in the middle of a hypotenuse if it is a right-angled triangle.
To get the circumcenter, find the midpoint of the line BC.
midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]
M(xm ,ym) = [(0 + 10)/2 , (6 + 0)/2]
M(xm ,ym) = (5 , 3)
Hence, the centroid is located at (5 , 3).
To know more about centroid of a triangle:
https://brainly.com/question/11971285
#SPJ4
Let f(x) = –7x + 9. Suppose you add 2 to the input of f to create a new function g, then multiply the output of function g by –3 to create function h. What are the slope and y-intercept of the graph of function h?
We will see that the linear function h(x) is:
h(x) = -21x - 15
The slope is -21, and the y-intercept is -15.
What are the slope and y-intercept of function h?
Remember that a general linear function is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we start with the linear function:
f(x) = -7x + 9
First, we need to add 2 to the input of f (the input is x) to get function g(x), so we have:
g(x) =f(x + 2)
Replacing the actual function we will get:
g(x) = -7*(x + 2) + 9
Now we multiply the output of function g by 3 to get h(x), then:
h(x) = 3*g(x)
We will get:
h(x) = 3*[-7*(x + 2) + 9]
h(x) = -21*(x + 2) + 27
h(x) = -21x - 42 + 27
h(x) = -21x - 15
So we can see that the slope of function h(x) is -21, while the y-intercept is -15.
Learn more about linear functions by reading:
https://brainly.com/question/4025726
#SPJ1
a price is discounted by 20 percentage and the discounted price is 200 euro. how many euros was the discount?
Answer:
Step-by-step explanation:
40
Find The length of the third side. If necessary, round to the nearest tenth. need answer ASAP
The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.
What is the Pythagoras theorem?The theorem is given by (hyp)² = (opp)² + (adj)².This theorem applies to a right-angle triangle only.Calculation:The given triangle is a right-angle triangle.
It has two lengths. They are
length of the hypotenuse = 21
length of the adjacent or base = 13
Then, the third side i.e., the opposite side length is calculated by
(hyp)² = (opp)² + (adj)²
⇒ (21)² = (opp)² + (13)²
⇒ 441 = (opp)² + 169
⇒ (opp)² = 441 - 169 = 272
⇒ opposite side length = √272 = 16.49 ≅ 16.5
Therefore, the length of the third side is 16.5.
Learn more about the Pythagoras theorem here:
https://brainly.com/question/16176867
#SPJ1
the table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. which statements about the function described by the table are true? check all that apply. the independent variable is the number of people. the initial value (initial fee) for the picnic is $40. the rate of change is $8.67 per person. as the number of people increases, the total cost of the picnic increases. if 4 people attended the picnic, the total cost would be $46.
Required function y = 2x + 40 to represents linear relationship between number of people and total cost shows following statements are true:
a. Independent variable represents the number of people.
b. Initial value for the picnic is $40.
d. Cost of the picnic increases as per the number of people.
As given in the question,
Let 'x' represents the number of people
And 'y' represents the total cost
Linear relationship between number of people and total cost is:
y = mx + b
Consider two points (x₁ , y₁) = (6, 52) and ( x₂ , y₂ ) = ( 9 , 58)
Slope 'm' = ( y₂ - y₁)/ (x₂ - x₁)
= (58 - 52)/ (9 -6)
= 6 / 3
= 2
y = 2x + b
Now for, (x. y) = ( 12,64)
64 = 2(12) +b
⇒b = 64 - 24
⇒b = 40
Hence, required function is :
y = 2x + 40
a. Independent variable is the number of people.
Here it is x which represents the number of people.
True.
b. Initial value for the picnic is $40
y- intercept when x =0 ⇒ y = $40
True.
c. Rate of change is $8.67 per person.
No, rate of change is $2 per person.
d. Number of people increases as total cost of picnic increases
True .
e. If x = 4
⇒y = 2(4) + 40
= 48 ≠46
False.
Therefore, function y = 2x + 40 represents that following statements are true:
a. Independent variable represents the number of people.
b. Initial value for the picnic is $40.
d. Cost of the picnic increases as per the number of people.
The above question is incomplete, the complete question :
The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which statements about the function described by the table are true? Check all that apply. a. The independent variable is the number of people.
b. The initial value (initial fee) for the picnic is $40.
c. The rate of change is $8.67 per person.
d. As the number of people increases, the total cost of the picnic increases.
e. If 4 people attended the picnic, the total cost would be $46.
Number of people Total cost ($)
6 52
9 58
12 64
15 70
Learn more about function here
brainly.com/question/12426369
#SPJ4
solve the system by using elementary row operations on the equations. follow the systematic elimination procedure. x1 3x2
On solving, the given system reduces to x1 = 12, & x2 = —7 which is the required solution.
What is matrix?Linear algebra is a subfield of mathematics that mostly uses matrices. When you start solving linear equation systems, linear algebra first starts to seem good. You may concentrate on the figures and greatly simplify the procedure by condensing all the information into a single large chart and leaving out the rest.
Which 4 types of matrices are there?Almost as their name implies, square, symmetric, triangular, and diagonal matrices. All-zero identity matrices except along the major diagonal, where the values are
T he augmented matrix of the given system is B =
[tex][AB] = \left[\begin{array}{ccc}2&4&-4\\5&7&11\\\end{array}\right] \\on solving we get \\ [AB] = \left[\begin{array}{ccc}1&0&12\\0&1&-7\\\end{array}\right] \\[/tex]
Hence the given system reduces to x1 = 12 x2 = -7
Hence the given system reduces to
x1 = 12, & x2 = —7
which is the required solution.
To know more about matrix visit:
https://brainly.com/question/28180105
#SPJ4
The sum of the interior angles of a triangle is sometimes, but not always, 180º.
True
False
The sum of the interior angles of a triangle is sometimes, but not always, 180º is false.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
There are three angles in a triangle.
The sum is always 180 degrees.
Thus,
The sum of the interior angles of a triangle is always 180°.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ1
in the xyxyx, y-plane, if (0, 0)(0,0)(, 0, comma, 0, )is a solution to the system of inequalities above, which of the following relationships between aaa and bbb must be true?
As a result, if (0,0) is a solution to the system of inequalities above, the connection between a and b is a>b in the xy-plane.
What is inequality?In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. Inequality originates from a lack of equilibrium. To solve an inequality, isolate the variable on one side from the other constants. To do so, use opposing procedures to modify the inequality. To begin, separate the x by multiplying each side by two. Whatever you do on one side must equally be done to the other.
Here,
Given, y<−x+a and y>x+b
As given, (0,0) is a solution to the above inequalities.
0<0+a and 0>0+b
a>0 and b<0
Thus, we can conclude from the above inequalities that a is a positive number and b is a negative quantity.
Therefore, it can be surely said that a>b.
Hence, the relationship between a and b is a>b in the xy-plane, if (0,0) is a solution to the system of inequalities above.
To know more about inequality,
https://brainly.com/question/29139290
#SPJ4
consider the modified keynesian model with a change in the way that taxes are incorporated:
a) The Keynesian cross graphs an economy's planned expenditure function,
[tex]$\mathrm{E}=\mathrm{C}(\mathrm{Y}-\mathrm{T})+\mathrm{I}+\mathrm{G}$[/tex],
and the equilibrium condition that actual expenditure equals planned expenditure.
How do you find the expenditure function?
To derive the expenditure function we can either (i) invert V(·) and solve for M, or (ii) set up the dual of the consumer's choice problem, solve for Hicksian demand functions and substitute them into the objective (i.e., expenditure) function.
The amount by which[tex]$\mathrm{Y}$[/tex]falls is given by the product of the tax multiplier and the increase in taxes
[tex]: $\Delta \mathrm{Y}=[-\mathrm{MPC} /(1-\mathrm{MPC})] \Delta \mathrm{T}$.[/tex]
c) We can calculate the effect of an equal increase in government expenditure and taxes by adding the two multiplier effects that we used in parts a and b :
[tex]\Delta \mathrm{Y}=\left[(1 /(1-\mathrm{MPC}))^* \Delta \mathrm{G}\right]-[(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{T}[/tex]
Because government purchases and taxes increase by the same amount, we know that [tex]\Delta \mathrm{G}=\Delta \mathrm{T}$. Therefore we can rewrite the equation as:$$\Delta \mathrm{Y}=[(1 /(1-\mathrm{MPC}))-(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{G}=\Delta \mathrm{G}[/tex]
This expression tells us that an equal increase in government purchases and taxes increases [tex]$\mathrm{Y}$[/tex] by the amount that [tex]$\mathrm{G}$[/tex] increases. That is, the balanced-budget multiplier is exactly 1 .
Complete question: Consider the Keynesian model with a change in the way that taxes are incorporated: (1) PAE = C + IP + G + NX Definition of Planned Aggregate Expenditure (2) C = C+ mpc (1-1) .y Consumption Function (3) PAE = Y Short-run Equilibrium Condition In this case, taxes paid are proportional to income, i.e. taxes paid are t - Y, where t is the tax rate and 0<t< 1. Disposable income is the part of income after taxes, i.e., (1-t). Y. Solve for the PAE spending line with PAE as a function of Y. What is the slope?
To learn more about expenditure function, visit
https://brainly.com/question/28955497
#SPJ4
24. Name a point on ∠MNO
Only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.
In the given question we have to name a point on ∠MNO.
As we know that;
Evaluating the number of points in the curve of the triangle's vertices that are close to the location in question is the easiest method for determining whether a point is inside a triangle. The point on the curve is inside the triangle if it has three points; if it has four, it is outside the triangle.
When we check in the graph then only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.
To learn more about point on the curve link is here
brainly.com/question/28715687
#SPJ4
What is the value of x in the figure shown below?
x =
C
xo
32°
3.2
A
115°
4
4
D
3.2
B
A roller coaster ride holds a total of 48 passengers. The ratio of males to females on the ride is 5 : 7. Let x represent the number of males on the ride. Let y represent the number of females on the ride. Which two linear equations form a system that you can use to find the number of males and the number of females on the ride?
Answer:
5x + 7y = 48 (total number of passengers on the ride)
x + y = 48 (total number of males and females on the ride)
Step-by-step explanation:
To find the number of males and the number of females on the roller coaster ride, you can use the following two linear equations to form a system:
5x + 7y = 48 (total number of passengers on the ride)
x + y = 48 (total number of males and females on the ride)
The first equation states that the total number of passengers on the ride is equal to the sum of the number of males (5x) and the number of females (7y). The second equation states that the total number of males and females on the ride is equal to the sum of the number of males (x) and the number of females (y).
To solve this system, you can use algebraic techniques to eliminate one of the variables and solve for the other. For example, you could multiply the first equation by 5 and the second equation by 7, then subtract the two equations to eliminate the y variable:
5 * 5x + 7 * 7y = 5 * 48
7 * x + 7 * y = 7 * 48
25x + 49y = 240
49x + 49y = 336
24x = 336 - 240
24x = 96
x = 4
Substituting this value for x in the first equation, we can solve for y:
5 * 4 + 7 * y = 48
20 + 7 * y = 48
7 * y = 28
y = 4
Therefore, there are 4 males and 4 females on the roller coaster ride.
An entry-level civil engineer earns an average bi-weekly net pay of $2,175.25. The engineer has created a monthly budget using the following percentages for expenses:
Percent
Housing 35%
Food/Household 10%
Savings 10%
Transportation 15%
Debt 5%
Entertainment 6%
Medical/Personal Care 5%
Giving 5%
Clothing 4%
Miscellaneous 5%
Which balance sheet correctly represents the engineer's income, expenses, and balance?
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $2,175.25
Expenses
Percent Amount
Housing 35% $761.34
Food/Household 10% $217.53
Savings 10% $217.53
Transportation 15% $326.29
Debt 5% $108.76
Entertainment 6% $130.52
Medical/Personal Care 5% $108.76
Giving 5% $108.76
Clothing 4% $87.01
Miscellaneous 5% $108.76
$2,175.25
Balance
Income $2,175.25
Expenses $2,175.25
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $3,262.88
Expenses
Percent Amount
Housing 35% $1,142.01
Food/Household 10% $326.29
Savings 10% $326.29
Transportation 15% $489.43
Debt 5% $163.14
Entertainment 6% $195.77
Medical/Personal Care 5% $163.14
Giving 5% $163.14
Clothing 4% $130.52
Miscellaneous 5% $163.14
$3,262.88
Balance
Income $3,262.88
Expenses $3,262.88
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,713.04
Expenses
Percent Amount
Housing 35% $1,649.56
Food/Household 10% $471.30
Savings 10% $471.30
Transportation 15% $706.96
Debt 5% $235.65
Entertainment 6% $282.78
Medical/Personal Care 5% $235.65
Giving 5% $235.65
Clothing 4% $188.52
Miscellaneous 5% $235.65
$4,713.04
Balance
Income $4,713.04
Expenses $4,713.04
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses
Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $-
PLEASE HELP
The balance sheet that correctly represents the engineer's income, expenses and balance is balance number 4.
How tp determine percentages of income?We should know that balance sheet is a summary of assets and liabilities and income and expenses of a legal person.
We are told that the the balance sheet shows a bi-weekly net pay
This implies that a month has two bi-weeks. therefore every income and expenses is multiplied by 2 to get the following figures.
Income Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $0
Learn more about balance sheet https://brainly.com/question/26323001
#SPJ1
Which equation is the inverse of 2(x - 2)² = 8(7+ y)?
O-2(x-2)2 = -8(7+ y)
Oy-x²-x-6
O y=-2± √√28+4x
Oy-2± √√28+4x
Answer:
[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]
Step-by-step explanation:
The inverse of [tex]2(x-2)^2=8(7+y)[/tex] is
[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]
Suppose that events F and S are conditional independent events given D and ~D respectively with p(F|D)=p(S|D)=0.9, p(~F|~D)=p(~S|~D)=0.9, and p(D)=0.2. Find p(D|F∩S).
P(D|FS)=.9529
If F and S are conditionally independent given D and ~D, then
P(FSD)= P(D)P(F|D)P(S|D)
P(FS~D) = P(~D)P(F|~D)P(S|~D)
P(F|~D) = 1 - P(~F|~D)
P(S|~D) = 1 - P(~S|~D)
P(~D) = 1 - P(D)
P(D|FS) = P(FSD)/(P(FSD) + P(FS~D))
P(F|D) = P(S|D) = .9
P(~F|~D) = P(~S|~D) = .9
P(D = .2)
Then, P(FSD) = P(D)P(F|D)P(S|D) = .2*.9*.9 = .162
P(FS~D) = P(~D)P(F|~D)P(S|~D) = (1 - .2)(1 - .9)(1 - .9)= .008
P(D|FS) = P(FSD)/(P(FSD) + P(FS~D)) = .162/(.162+.008) = 162/170=81/85 = .9529
To learn more about conditional independent events follow link : https://brainly.com/question/12783373
in a simple linear regression analysis, the p-value associated with a test of the slope coefficient was equal to .028, which would lead us to do what at the 3% level of significance? group of answer choices accept the null hypothesis. not enough information is given to answer this question. conclude that the true slope for the population is equal to zero. conclude that a linear relationship exists between the two variables.
Out of the given choices, we choose 'not enough information given to answer this question' and concluded that the true slope for the population is equal to zero.
Since, we are given a p-value associated with a test of the slope coefficient equal to 0.028 which leads to 3% level of significance, it means that there is 3% chance of finding difference which is larger than the one given in our study given that the null hypothesis is true. Since, it is less than 5% level of significance, the null hypothesis is rejected and accept an alternative hypothesis. As this hypothesis is not given, we conclude that there is not enough information to give an answer to the question.
To know more about p-value here:
https://brainly.com/question/29585239
#SPJ4
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to exhibit 8-3. If we are interested in determined an interval estimate for mu at 86.9% confidence the z value to use is 1.96 1.31 1.51 2.00 Refer to exhibit 8-3. The value to use for the standard error of the mean is 13.5 9 2.26 1.5 Refer to exhibit 8-3. The 86.9% confidence interval for mu is 46.500 to 73.500 57.735 to 62.265 59.131 to 60.869 50 to 70
Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.
To find the confidence interval for the mean speed (mu) of all cars on this section of the highway, we can use the following formula:
Confidence interval for mu = sample mean +/- z * standard error of the mean
Where:
sample mean is the average speed of the 81 cars in the sample, which is 60 mph
z is the z-score corresponding to the desired confidence level. In this case, the desired confidence level is 86.9%, which corresponds to a z-score of 1.96.
standard error of the mean is the standard deviation of the sampling distribution of the mean, which is calculated as the standard deviation of the population divided by the square root of the sample size.
In this case, the standard error of the mean is 13.5 / sqrt(81) = 2.26 mph.
Plugging these values into the formula, we get:
Confidence interval for mu = 60 +/- 1.96 * 2.26 = 59.131 to 60.869
Therefore, at a confidence level of 86.9%, we can be confident that the interval between 59.131 and 60.869 mph includes the true mean speed of all cars on this section of the highway.
Learn more about probability, here https://brainly.com/question/11234923
#SPJ4
What is the slope in the given line?
Answer:
[tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
The slope/gradient of a line is defined by this formula:
[tex]\frac{y_{1}-y_{0} }{x_{1}-x_{0} }[/tex]
Where you pick two coordinates, find the change in the [tex]y[/tex] values, and divide it by the change in the [tex]x[/tex] values.
Two coordinates that this line passes through are (3, -2) and (-3, 2).
You can take the second [tex]y[/tex]-value (2) from the first [tex]y[/tex]-value (-2) or vice versa, so long as you do it in the same order the [tex]x[/tex] values.
For this example, I will take the first [tex]y[/tex]-value (-2) from the second [tex]y[/tex]-value (2), and take the first [tex]x[/tex]-value (3) from the second [tex]x[/tex]-value (-3).
The gradient/slope is defined by [tex]m[/tex] in the following:
[tex]m=\frac{2--2}{-3-3}=\frac{4}{-6}=-\frac{4}{6}=-\frac{2}{3}[/tex]
Evaluate the surface integral RR S x dS, where S is the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0, 0, 4). Sketch the surface S and the domain of integration D.
Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.
Surface S = √21
Define Surface integralA surface integral in mathematics is a generalization of multiple integrals to integration over surfaces, particularly in multivariable calculus. It can be viewed as the line integral's double integral equivalent. One can integrate a vector field or a scalar field across a given surface.
Equation of surface (S) is,
x/1 - y/2 + z/4 = 1
From here we get,
z = 4 - 4x + 2y
∫∫(S)xdS = ∫∫ (D)x(1 + (∂z/∂x)² + (∂z/∂y)²)^1/2 dxdy
Here (D) is projection of (S) on xy coordinate plane
so, (D) is triangle with vertices (1, 0, 0), (0, - 2, 0) and (0,0,0).
∂z/∂x = - 4, ∂z/∂y = 2.
In (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.
Now we have,
∫∫(S)xdS = ∫∫(D)x(1 + (- 4)² + 2²)^1/2 dxdy
= √21∫₋₂⁰dy ∫₀¹xdx
= √21y₋₂⁰x²/2₀¹
= √21
Hence, Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0 and Surface S = √21
To read more about Surface integral.
https://brainly.com/question/28171028
#SPJ4
There are 4 consecutive even integers that add up to 100. What is the least of the 4 integers?
The least among all 4 integers such that they sum up to 100 will be 22.
What is an integer?An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.
Integer; ....-2 , -1 , 0 , 1 , 2 , .....
Integers are non-decimal numbers and all integers are rational numbers.
Suppose the first integer is x.
The next three digits will be, x + 2, x + 4, and x + 6 correspondings.
Sum x + x + 2 + x + 4 + x + 6 = 100
(x + x + x + x) + (2 + 4 + 6) = 100
4x + 12 = 100
4x = 88
x = 22
Hence"The smallest of the four integers that add up to 100 is 22".
To learn more about integers,
brainly.com/question/1768254
#SPJ1
suppose dispatcher a takes a random sample of 9 response times from the log books in march. dispatcher a calculates x-
1. The first step is to determine the sample size. In this case, the sample size is 9 response times.
2. Next, the dispatcher should collect the response times from the log books.
3. After collecting the response times, the dispatcher should calculate the mean or average of the sample. This is known as the sample mean and is represented by the x-bar.
4. To calculate the sample mean, the dispatcher should add together the values of all the response times and divide this sum by the sample size (9). The result of this calculation is the sample mean or x-bar.
5. Finally, the dispatcher can use the value of the x-bar to calculate the standard deviation of the response times. This is done by taking the square root of the sum of the squares of the differences between each response time and the mean, divided by the total number of response times (in this case, 9). This will give us the standard deviation of the response times.
Question: Suppose dispatcher a takes a random sample of 9 response times from the log books in march. dispatcher a calculates x-bar
To learn more about the x-bar:
brainly.com/question/15586592
#SPJ4
You are refilling your inventory of welcome packets for new customers. For each packet, it takes 5 minutes to print, 2 minutes to organize, and 5 minutes to proofread. The ink in the printer will need to be changed every 5 packets, which takes 3 minutes. You have 3 hours to dedicate to this task. Assume thathe ink in the printer was already changed before beginning and that you have to complete each packet before completing any steps for the next one. How many welcome packets will you be able to fully complete in the time allotted?
The number of welcome packets that you will be able to fully complete in the time allotted would be = 14
What is the time for refilling the packets?The time allotted for the refilling of the whole welcome packets = 3 hours
To convert to mins = 3 × 60 = 180 mins.
To run each packet will take the following time:
5 minutes to print,
2 minutes to organize, and
5 minutes to proofread which is a total of 12mins
But for every 5 packets = 5×12+3 = 63 mins.
Therefore X packets = 180 mins.
Make X packets the subject of formula;
X packets = 5 × 180/63
= 900/63
= 14.2
Learn more about minutes here:
https://brainly.com/question/25800303
#SPJ1
ASAP HELP!! I think it’s A but I’m confused, please help!
Answer:
A
Step-by-step explanation:
5.7(3) can be expressed as a fraction
(573 -57)/90
516/90
i need help asap!!!!!
Answer:
The slope is same for both points.
Step-by-step explanation:
1st set of points: (1, 4) and (7, 2)
m = 2-4/7-1
m = -2/6
m = -1/3
2nd set of points: (7, 2) and (10, 1)
m = 1-2/10-7
m = -1/3
The slope is same for both points.
11 A fisherman wants to know how many fish there are in a lake. One day, he catches 50, marks them and puts them back. The next day he catches 80 fish. 20 of these fish have marks on them. Estimate the total number of fish in the lake.
The total number of fish in the lake would be = 60 fishes
What is total of a data set?The total of a data set is the addition of the various components that makes up a data set which gives a particular value.
On the first day the number of fish that was marked by the fisher man = 50 fishes.
On the second day the total amount of fishes that was caught = 80 fishes
The number of fishes that where among the 80 fishes that are marked= 20
Therefore the total amount of fishes in the lake = 80 - 20
= 60 fishes.
Learn more about addition here:
https://brainly.com/question/25421984
#SPJ1
if the 90 percent confidence interval for u is from 34 to 50 then there is a 10 percent chance that this interval does not contain u
AS per the given confidence interval, the z score is 0.54
The term confidence interval refers a parameter will fall between a pair of values around the mean.
Here we have given that if the 90 percent confidence interval for u is from 34 to 50 then there is a 10 percent
And we need to find the z value.
While we looking into the given situation, we have identified the following values,
Confidence interval = 95%
Interval = 34 - 50
Mean = 10
Through the given interval we have identified the that sample size was calculated as,
=> 50 - 34
=> 16
Then the z score is
=> z = 10/√16
=> z = 10/4
=> z = 2.5
Then according to the confidence interval, the value from the z table is obtained as.
=> z = 1.96
Then the difference is
=> 2.5 - 1.96
=> 0.54
To know more about Confidence interval here.
https://brainly.com/question/24131141
#SPJ4
the sugar sweet company delivers sugar to its customers. let be the total cost to transport the sugar (in dollars). let be the amount of sugar transported (in tons). the company can transport up to tons of sugar. suppose that gives as a function of . identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.
The domain and the range of a function are the possible input and output values of the function.
The function is given as:
C = 130S + 3500
The domain
This is the possible S values of the function.
S cannot be less than 0, because it represents a physical quantity (i.e. tons of sugar)
The value of S can be any value greater than 0
Hence, the domain of the function is [0, ∞)
The range
This is the possible C values of the function.
The function is given as:
C = 130S + 3500
When S = 0
C = 130(0) + 3500
C = 3500
The above means that:
C cannot be less than 3500
The value of C can be any value greater than 3500
Hence, the range of the function is [3500, ∞)
Read more about domain and range at:
brainly.com/question/4767962
#SPJ4
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
Answer:
Step-by-step explanation:
Since the domain of the function h is -3 ≤ x ≤ 11 and the range is 1 ≤ h(x) ≤ 25, the possible values of h(x) for a given value of x in the domain will be within the range of 1 to 25. Additionally, we are given that h(8) = 19 and h(-2) = 2, so for the values x = 8 and x = -2, the corresponding values of h(x) are 19 and 2, respectively.
Given this information, the statement that could be true for the function h is: "For every value of x in the domain of h, the corresponding value of h(x) is within the range of 1 to 25." This statement is true because the domain and range of h are such that the possible values of h(x) for any value of x in the domain will be within the range of 1 to 25.