Find the area of a sector

Optimal allocation for estimating the population mean is 16.7 and 83.7 sample units.

Optimal allocation for estimating the difference of the means of the strata,μH-μL is 26.4 and 73.6 sample units.

a) To find the optimal allocation for estimating the population mean, we want to minimize the variance of the estimator. One common method for this is to use the proportional allocation, where the proportion of the sample allocated to each stratum is equal to the proportion of the population in that stratum.

In this case, the proportion of the population in stratum h is 100,000 / (100,000 + 500,000) = 0.167, and the proportion of the population in stratum L is 1 - 0.167 = 0.833.

So, the optimal allocation for estimating the population mean would be:

Stratum h: 16.7% of the sample, or 16.7% * 100 = 16.7 sample units

Stratum L: 83.3% of the sample, or 83.3% * 100 = 83.3 sample units

b) To find the optimal allocation for estimating the difference of the means of the strata, μH-μL, we again want to minimize the variance of the estimator. One method to achieve this is to use the Neyman allocation, where the sample size is allocated to each stratum in such a way that the variance of the estimator is minimized.

To do this, we need to know the variances of the strata, which are given as 20^2 and 12^2 respectively. The optimal allocation is given by the ratio of the variances, which is:

(12^2) / (20^2 + 12^2) = 144/544 = 0.264

So, the optimal allocation for estimating the difference of the means of the strata is:

Stratum h: 26.4% of the sample, or 26.4% * 100 = 26.4 sample units

Stratum L: 73.6% of the sample, or 73.6% * 100 = 73.6 sample units

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Answer:

180

Step-by-step explanation:

A = 16 + 25 + 36 + 49 + 64 + 81 = 271

B = 27 + 64 = 91

A - B = 271 - 91 = 180

Answer:

(7,13)

Step-by-step explanation:

\(\frac{x-1}{2}\) = 3  Multiple both sides by 2

x - 1 = 6     Add 1 to both sides

x = 7

\(\frac{y -3}{2}\) = 5  Multiple both sides 2

y - 3 = 10    Add 3 to both sides

y = 13

(7,13)

The coordinates of point is A ( 7 , 13 ) whose midpoint is M ( 3 , 5 )

What is the midpoint of two points?

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Measure the distance between the two end points, and divide by 2.

Let A ( x₁ , y₁ ) be the first point

Let B ( x₂ , y₂ ) be the second point

The midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Given data ,

Let the first point be A ( x , y )

Let the midpoint M between A and B be = M ( 3 , 5 )

Let the second point be = B ( -1 , -3 )

Now , from the midpoint formula ,

The midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Substituting the values in the equation , we get

3 = ( x + ( -1 ) ) / 2

Multiply by 2 on both sides of the equation , we get

x - 1 = 6

Adding 1 on both sides of the equation , we get

x = 7

And ,

5 = ( y + ( -3 ) ) / 2

Multiply by 2 on both sides of the equation , we get

y - 3 = 10

Adding 3 on both sides of the equation , we get

y = 13

Therefore , the point A is A ( 7 , 13 )

Hence , the point is A ( 7 , 13 )

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Answer:

(2w+2)(w+8) ≤ 100

Step-by-step explanation:

Answer:

●(2w+2)(w+8)< 100 represents the inequality that combined the area of Garden and walk away.

Step-by-step explanation:

this is correct!!

Answer:

D

Step-by-step explanation:

The explanation can be found at: https://brainly.com/question/2416795.

For the matrix A and B it is proved that AB has p linearly independent columns, which implies that rank of AB is p.

To show that the product AB has rank p,

Demonstrate that AB has p linearly independent columns.

A is a p × q matrix with rank p,

A has p linearly independent columns.

Let's denote these columns as a₁, a₂, ..., aₚ.

B is a p × r matrix, which means it has r columns.

Show that the product AB has p linearly independent columns,

which implies that these columns are formed by the columns of A.

To obtain the product AB,

multiply matrix A by matrix B.

The resulting matrix AB is a p × r matrix. Let's denote the columns of B as b₁, b₂, ..., bᵣ.

Now, let's consider the columns of the matrix AB.

Each column of AB is obtained by multiplying matrix A by a column of B,

AB = [Ab₁ Ab₂ ... Abᵣ]

Express each column of AB as a linear combination of the columns of A,

Abᵢ = c₁ᵢa₁ + c₂ᵢa₂ + ... + cₚᵢaₚ

where c₁ᵢ, c₂ᵢ, ..., cₚᵢ are scalars.

Since A has p linearly independent columns (a₁, a₂, ..., aₚ), any linear combination of these columns will also be linearly independent.

Therefore, the columns of AB (Ab₁, Ab₂, ..., Abᵣ) are linearly independent as well.

Hence, it is shown that AB has p linearly independent columns, which means the rank of AB is p.

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Answer:

3

Step-by-step explanation:

speed is distance divided by time

Answer:

20 minutes

Step-by-step explanation:

Answer:

Q2. angle 5 +angle 6=90°

angle 5+ 6°=90°

angle 5=90°-6°

angle 5=84°

Q.3 angle 8+angle 9=90°

angle 8 + 11°=90°

angle 8=90°-11°

angle 8=79°

Answer:

B and D

Step-by-step explanation:

quadrilaterals only have 4 sides hence the prefix quad

Answer:

B and D

Step-by-step explanation:

C has five sides and A has three sides with a curve, curve doesn't count as a side

Answer:

you have a 43?

Step-by-step explanation:

i need to know the percent of the C

Answer:

No correlation.

Step-by-step explanation:

We see that since all the points are scattered around with no clear direction, we have no correlation. We can confirm this by trying to draw a best line of fit, which would be impossible.

You could make an argument saying it is a positive correlation, but that would be very difficult to see.

Answer:

its d

Step-by-step explanation:just multiply 4 and 3 by 3

Answer:

Step-by-step explanation:

We have that

A = 51°, b = 14, c = 6

step 1

find the value of a

Applying the law of cosines

a²=c²+b²-2*c*b*cos A

a²=6²+14²-2*6*14*cos 51-------> 126.27

a=11.2

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

we have

a=11.2

b=14

c=6

so

(a+b) > c-------------> (11.2+14)=25.2

25.2 > 6-----> is not correct

therefore

the answer is the option

a. No triangles possible

I don't know if i am right sorry if this is wrong

Answer:

Step-by-step explanation:

ima a braintlest

The net force must all be equal to zero (0) for an object to be in mechanical equilibrium, in order for the sum of all forces to be equal to each other.

In Classical mechanics, mechanical equilibrium can be defined as a phenomenon in which the net force acting on a physical object or body is equal to zero because it is at rest or in an unaccelerated motion.

A net force can be defined as the vector sum of all the forces that are acting on a physical object or body. This ultimately implies that, a net force is a single (one) force which substitutes the effect of all the forces that are acting on a physical object or body when it is in mechanical equilibrium.

In this context, we can infer and logically deduce that the net force must all be equal to zero (0) for an object to be in mechanical equilibrium, in order for the sum of all forces to be equal to each other.

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Answer:

x = 4

Step-by-step explanation:

Given that AB = BC , substitute values

2x + 4 = x + 8 ( subtract x from both sides )

x + 4 = 8 ( subtract 4 from both sides )

x = 4

Answer:

24meters

Step-by-step explanation:

Given data

Joe walked 12m East

We are told that Joe continued to walk for another 12m east

Therefore, Joes displacement is

=12+12

=24m

His displacement is 24meters

Answer:A

Step-by-step explanation:  divide both by 5 and you get 3/4 because 15 divided by 5 = 3 and 20 divided by 5 =4

The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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Answer:

the ratio of boys to girls in Mr Hegarty's class is 5:3 (in its simplest form).

Step-by-step explanation:

For every 3 girls, there are 5 boys, which can be written as a ratio of 5:3 (boys to girls).

To simplify the ratio, we can divide both sides by the greatest common factor of 5 and 3, which is 1.

Answer: ok ok... If this is like pick one ima go for A. = b

Step-by-step explanation: i hope this helps<3

Answer:

The answer is C

Step-by-step explanation:

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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The commission for $750 at 3% is:

Commission can be defined as the fees or extra fees that is been paid to someone for a job well done or for rendering a service.

Now let find the commission amount using this formula

Commission = Earnings × rate

Where:

Earnings = $750

Rate =3%

Commission = $750 × 3%

Commission = $22.50

Therefore the commission is $22.50.

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The complete question is:

Find the commission.

Earning Commission

Sales Commission Rate Commission

$750

3%

?

The commission is $

Answer:

Vertex: ( 3 , 2 )

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex  ( h , k ) .

Axis of Symmetry:  x = 3

Vertex: ( 3 , 2 )

Graph: in pic

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

2.4x10^6

Step-by-step explanation:

Therefore, the mean of the data decreases by 15 when the number 646 changes to 639.

Median is a measure of central tendency that represents the middle value of a dataset when the data is arranged in order from least to greatest (or greatest to least). It is the value separating the higher half from the lower half of the data. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values. The median is a useful measure of central tendency because it is not affected by extreme values or outliers in the dataset.

Here,

(a) When the number 646 changes to 639, the median of the data changes as well. The new list of numbers of trading cards owned by the 7 middle-school students becomes:

360, 373, 402, 499, 548, 644, 639

The median is the middle value when the data is arranged in order from least to greatest. In the original list, the middle value was 499. But in the updated list, the middle value is now the average of the two middle values, which are 499 and 548. Therefore, the median of the updated list is:

Median = (499 + 548) / 2

= 523.5

So the median decreases by 523.5 - 499 = 24.5 when the number 646 changes to 639.

(b) To find out what happens to the mean when the number 646 changes to 639, we need to calculate the mean of the updated list of numbers. The new list of numbers of trading cards owned by the 7 middle-school students is:

360, 373, 402, 499, 548, 644, 639

The mean of the data is the sum of all the values divided by the total number of values. In the original list, the sum of all the values was:

Sum = 360 + 373 + 402 + 499 + 548 + 644 + 646

= 3472

And there were 7 values in the data. Therefore, the mean of the original list was:

Mean = Sum / Number of values

= 3472 / 7

= 496 (rounded to the nearest whole number)

To calculate the mean of the updated list, we need to subtract 646 and add 639, and then divide the new sum by 7. That is:

Mean = (Sum - 646 + 639) / 7

= (3472 - 646 + 639) / 7

= 481 (rounded to the nearest whole number)

Therefore, the mean of the data decreases by:

496 - 481 = 15

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Answer:

oh the answer is try your modest i hate this heh

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Can't have 0 in the denominator