Suman has a piece of land, which is in the shape of a rhombus. She wants her two sons to work on the land and produce different crops. She divides the land in two equal parts by drawing a diagonal. If its perimeter is 400 m and one of the
diagonals is of length 120 m, how much area each of them will get for his crops ?

Please help me with the question along with steps.

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

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Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.

Surface S = √21

A 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

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The least among all 4 integers such that they sum up to 100 will be 22.

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".

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The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.

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.

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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.

The 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

Translation 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

The 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

The total number of fish in the lake would be = 60 fishes

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.

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We will see that the linear function h(x) is:

h(x) = -21x - 15

The slope is -21, and the y-intercept is -15.

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.

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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.

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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

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The option a is giving the same value according the table. So the option a is correct answer.

In the given question, the table represents some points on the graph of linear function f.

We have to find which function represents f.

(a) f(x)= 32(3x-1)

(b) f(x)= -32(x-3)

(c) f(x)= -2(32x-3)

(d) f(x)= 16(2x-1)

We find the pattern we firstly observe the given table closely.

So from the given table;

f(-2) = -224, f(1) = 64, f(5) = 448, f(10) = 928

To check which option is giving the value of f(x) right according to table, we put the value in each option.

Firstly taking the option a.

f(x)= 32(3x-1)

Now checking the option 1.

Putting x=-2, if the value of f(-2) = -224, then the option is correct.

f(-2)= 32(3(-2)-1)

f(-2)= 32(-6-1)

f(-2)= 32*(-7)

f(-2)= -224 (True)

Now putting x=1 in the same option to cross check, if the value of f(1) = 64, then the option is correct.

f(1)= 32(3(1)-1)

f(1)= 32(3-1)

f(1)= 32(2)

f(1)= 64

Now the option a is giving the same value according the table. So the option a is correct answer.

We find the right answer so we don't check the further option. To check next option you can use the same way.

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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.

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.

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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]

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.

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The skier's distance to the east of the center of the ski trail is

x = 1.25cosθ

The skier's distance to the north of the center of the ski trail is

y = 1.25sinθ

When radius 'r' and the angle θ are given, the coordinates (x,y) as shown

x = east direction

y = north direction

In this case we get,

x = r cosθ

y = r sinθ

Given r = 1.25 km

We get,

x = 1.25 cosθ in east direction

y = 1.25 sinθ in north direction

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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.

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).

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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?

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Answer:

A

Step-by-step explanation:

5.7(3) can be expressed as a fraction

(573 -57)/90

516/90

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

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Answer:

Step-by-step explanation:

40

On solving, the given system reduces to x1 = 12, & x2 = —7 which is the required solution.

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.

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.

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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

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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.

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, ∞)

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The sum of the interior angles of a triangle is sometimes, but not always, 180º is false.

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°.

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The number of welcome packets that you will be able to fully complete in the time allotted would be = 14

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

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The balance sheet that correctly represents the engineer's income, expenses and balance is balance number 4.

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

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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.

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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

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