how many different collections of 30 coins can be chosen if there are at least 30 of each kind of coin?

The number of estimates of expected returns, variances, and covariances are needed to optimize this portfolio is 1,830.

Portfolio

A the definition of portfolio refers the asset allocation refers to an investment strategy whose main goal is to balance the risk and to recompense by allocating the assets portfolio with respective to the individual's objectives, tenure of the investment, and the risk capacity.

Given,

A portfolio management organization analyzes 60 stocks and constructs a mean-variance efficient portfolio using only these 60 securities.

Here we need to find the  estimates of expected returns, variances, and covariances are needed to optimize this portfolio.

As per the Markowitz procedure,

The estimation as follows

Here the Variance as N,

And Co variance will be as follows:

Co variance = (N² -  N) / 2

And the total estimation is calculated as,

=> N +  (N² -  N) / 2

Here, the number of assets is 60

So, the value of N=60

Then the Covariance and estimates will be as follows:

=> 60 +  (60² - 60) / 2

=> 1830.

Therefore, the estimates of expected returns, variances, and covariances are needed to optimize this portfolio is 1830.

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The correct option are; b. Perpendicular and d. Transversal; are the lines that intersects and are coplaner lines.

Perpendicular lines:

Transversal:

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Answer:

[tex]\frac{27}{4}[/tex] or [tex]6\frac{3}{4}[/tex]

Step-by-step explanation:

6.75 = [tex]6\frac{3}{4}[/tex] = [tex]\frac{27}{4}[/tex]

Because 0.75 = [tex]\frac{3}{4}[/tex]

I would appreciate it if you mark my answer as brainliest.

Answer:

6 3/4

Step-by-step explanation:

so first 1/4 equals to 0.25

so if 1/4 is 0.25 than 3/4 would be 0.75

6 in this equation represents 24/4

so it would be (24+3)/4

which is 27/4

after simplifying you would get 6 3/4

Approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

Given,

In the question:

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds.

Central Limit Theorem:-

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 140, standard deviation of 20, sample of 4:

By the Central Limit Theorem, the distribution is approximately normal.

Mean is the same, of 140.

n = 4 , σ = 20, thus:

s = σ / [tex]\sqrt{n}[/tex]  = 20/[tex]\sqrt{4}[/tex] = 10

Thus, the correct answer is:

Approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

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Answer:

50

Step-by-step explanation:

b

"Reflection and dilation" are the series of transformations that would produce a square that was comparable to the original square but not congruent.

Reflection:

Reflection is a method of transformation which it flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance as from mirror line as its mirrored point.

Dilation:

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The term "Daily Allowance" refers to a sum of money given to an employee for each day he or she is away from the office, covering the employee's regular daily expenses as a result of the absence.

What are daily expenses?

As the name suggests, basic living expenses are those required for daily existence, with the main categories being housing, food, clothing, transportation, healthcare, and pertinent miscellaneous items.

An allowance in the workplace is money given to a worker to cover costs or make up for certain working circumstances. For instance, many employees receive an allowance to cover the cost of entertainment or vacation. In some circumstances, employees may also be required to accept their allowances.

There are three different classifications of allowances: non-taxable, partially taxable, and taxable.

How to Plan Your Allowance Budget;

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The expression √n^2 can be simplified as n

The square root of a number is that factor of a number which when multiplied by itself gives the original number.

Squares and square roots are special exponents. Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 32. Here, the exponent is 2, and we call it a square. Now when the exponent is 1/2, it refers to the square root of the number. For example, √n = n^½, where n is a positive integer.

Therefore √n^2 = n^½×2= n

the value of √n^2 = 2

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The trigonometric expression (cos²α - cot²α)/(sin²α - tan²α) = cot⁶α

Trigonometric expressions are equations that contain the trigonometric ratios.

Given the trigonometric expression

(cos²α - cot²α)/(sin²α - tan²α)

To simplify the expression, we proceed thus

(cos²α - cot²α)/(sin²α - tan²α) = (cos²α - 1/tan²α)/(sin²α - tan²α)

= (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

=  (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

Factorizing out cos²α and sin²α, we have

=  (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

=  cos²α(1 - 1/sin²α])/(sin²α(1 - 1/cos²α])

= [cos²α(sin²α - 1)/sin²α]/[sin²α(cos²α - 1)/cos²α]

= cos²α(sin²α - 1)/sin²α × cos²α/[sin²α(cos²α - 1)

= cos²α × -(1 - sin²α)/sin²α × cos²α/[sin²α × -(1 - cos²α)

= cos²α(1 - sin²α)/sin²α × cos²α/[sin²α(1 - cos²α)

= cos²α × cos²α/sin²α × cos²α/[sin²α × sin²α] (since cos²α = 1 - sin²α and sin²α = 1 - cos²α)

= cos²α × cos²α × cos²α/[sin²α × sin²α × sin²α]

= cos⁶α/sin⁶α

= (cosα/sinα)⁶

= cot⁶α

So, (cos²α - cot²α)/(sin²α - tan²α) = cot⁶α

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Answer:

c = 5m + 10

Step-by-step explanation:

Each moth 5 dollars is charge and a one time fee of 10

For

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

What is the slope of the line in the slope-intercept form of the line?

If y = mx + c line is given then 'm' represents the slope of the line. If any pair of lines are given and if they have the same value of the slopes then we can say that the given pair of lines will be parallel in nature and if the slope of the one line is the negative inverse of the other line then we can say that the pair of lines are perpendicular to each other.

For example 1:

      y = 3x + 4 and y = 3x +7

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 2:

     y = -4x + 1 and 4y = x + 3

    Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 3:

     y = 2x - 5 and y = 5x -5

   In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

For example 4:

     y = -1/3x + 2 and y = 3x - 5

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 5:

     y = 3/5x - 3 and 5y = 3x - 10

    The slopes of both lines are equal hence, these pair of lines are parallel.

For example 6:

     y = 4 and 4y = 6

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 7:

     y = 7x + 2 and x + 7y = 8

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 8:

     y = 5/6x - 6 and x + 5y = 4

    In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

Hence,

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

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This can be done using statistical tests such as the t-test or ANOVA, which can determine if there is a statistically significant difference between men and women.

Analysis of variance, or ANOVA, is the term. A statistical test is used to assess if the means of two or more groups differ significantly from one another. It is a method used to compare the means of several groups to see if they are comparable or whether there is a notable different purchase between them. ANOVA is frequently used to compare the means of several data sets, such as the means of various test scores or the means of various populations. The ANOVA test is a potent instrument that enables researchers to establish whether there is a significant difference between the means of various groups and to pinpoint which groups differ from one another.

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Shelly needs 168 blocks to cover the area of the square gap

A square is a two-dimensional shape quadrilateral with four sides equal and parallel to each other. The angles in this shape are measured as 90 degrees.

The gap is 36 mm deep and it's length is assumed to be 36 mm too

The area of the gap will be calculated using area of square

Area of square = L²

Area of square = 36²

Area of square = 1296mm²

However, the block has a shape of rectangle and the area of rectangle is given as

Area of Rectangle = L * W

Area of the rectangular blocks = 4 * 2 = 8mm²

The number of blocks required to fill the square gap will be

1296 / 8 = 162 blocks

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Tyler was gone for 45 minutes

Answer: 45 minutes

Step-by-step explanation: First, do 60-25 to find how much time there is till 3. (60-25=35) Then, add 10 because he came back at 3:10, not 3:00.

hope this helps!

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The number of terms and the degree of the polynomial are 3 and 2 respectively.

The terms of the polynomial = The parts of the polynomial

                                                = -8rt ,- s² ,- 3t

The number of terms of the polynomial  = 3    

The degree of the polynomial =  Highest degree of the polynomial

The highest degree of the polynomial = 2

So, the polynomial degree is 2

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184.04 ft high the tower with a lean of 6 degrees, the degree measure of this lean is 3.6 degrees and most likely because either the 13ft lean has not been measured to the top edge of the tower or the side of the tower isn't straight.

In the given question, the tower was 184.5 feet tall.

(a) If the article states that when work began the tower Leaned 6° or 13 feet, off the perpendicular then we have to draw a sketch and label the two measurements.

According to given statement the sketch is given below:

(b) We have to find how much high is the tower with a lean of 6 degrees.

From the graph using the Pythagorean Theorem:

H^2 = 184.5^2- 13^2

H^2 =34040.25-169

H^2 = 33871.25

Taking square root on both side

H=184.04 ft

(c) The article goes on to say that the tower now leans 16 inches less we have to draw a new sketch that shows this measurement.

The graph is given below:

(d) Now we have to find the degree measure of this lean.

We know that the tower leans 16 in less.

So 16in= 1 1/3ft = 4/3 ft = 1.33 ft

Consequently the lean after the work is: 13ft - 1.33= 11.67 ft

Then we can find the "lean" after the work as:

sin ("lean") =11.67/184.5

sin ("lean")= 0.0633

Angel of ("lean") after work = 3.6degrees.

(e) Now we have to find the height of the tower with this lean.

Height with reduced lean is found by using Pythagorean Theorem again:

H^2 = (184.5)^2 - (11.67)^2

H^2 = 34040.25 - 136.19

H^2 = 33904.06

Taking square root on both side, we get

H = 184.13

(f) Now comment on the fact that sin 4° =13/184.5 = 0.07046 while sin 6° = 0.10453. We have to check can we reconcile this seeming discrepancy.

Most likely because either the 13ft lean has not been measured to the top edge of the tower or the side of the tower isn't straight.

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Answer:

Step-by-step explanation:

answer is -25

Answer:

-25

Step-by-step explanation:

-15/1 / 3/5

(-15/1)(5/3) Do reciprocal on the second fraction  

(-5)(5) = -25 Cancel out common factors then multiply

The maximize revenue the ticket prices should be $5.5.

Consider a stadium that holds 58, 000 spectators, with ticket prices at $10, with an

Average attendance 5, 000.

Suppose the ticket prices were lowered to $8, then the average attendance rise to 15, 000.

Let R be the revenue, x be the average attendance, p(x) demand

The total revenue function R(x) is,

R (x) = p (x) x

=11 -x/5000*

=11x-x²/5000

Differentiate of R(x) with respect to x.

2x

R'(x) =11 - 2x/5000

=11-x/2500

Set R'(x ) = 0 to solve for x.

X = 27500

Therefore, the average attendance of spectators is 27,500 and, 27,500 fans will buy tickets.

Substitute x = 27,500 in p(x) =11-x/5000

p(x) = 5.5

Therefore, the maximize revenue the ticket prices should be $5.5.

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Answer:

y = -3x + 10

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

  m = -3

y = -3x + b

Now (6,-8) is passing through this line. So, substitute the x and y coordinates in the above equation and find the value of 'b'.

      -8 = -3*6 + b

     -8 = -18 + b

-8 +18 = b

   b = 10

Equation of the line:

    y = -3x + 10

Answer:

y=-3x+10

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

b is y intercept

So we fill in what we know to find b

-8=-3(6)+b

-8=-18+b

+18 +18

10=b

Now we can finish our equation

y=-3x+10

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Answer:

There’s no restrictions if I’m not mistaken.

Step-by-step explanation:

You’re correct

By solving a system of two simultaneous linear equation, it can be calculated that

There are 6 1p coin, 8 2p coin, 5 5p coin and 1 10p coins in the pot

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here a system of two simultaneous linear equation needs to be solved

Let the larger number be x and the smaller number be y

Two times the smaller of two number added with nine time the larger is 215.

9x + 2y = 215 ... (1)

Six time the larger added with seven time the smaller give -89.

6x + 7y = -89

Multiplying (1) by 2

18x + 4y = 430  ..... (3)

Multiplying (2) by 3

18x + 21y = -267 ... (4)

Subtracting (4) from (3)

-17y = 697

y = [tex]-\frac{697}{17}[/tex]

y = -41

Putting the value of y in (1)

9x + 2 [tex]\times[/tex] (-41)  = 215

9x = 215 + 82

9x = 297

x = [tex]\frac{297}{9}[/tex]

x = 33

The two numbers are 33 and -41

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Answer:

13.  7.5 square units

14.  24.5 square units

Step-by-step explanation:

Given vertices:

As points E and F share the same x-value and points F and G share the same y-value, the polygon is a right triangle with base GF and height FE.

As points F and G share the same y-value, the length of line segment GF is the difference between the x-values:

[tex]\begin{aligned} \implies \overline{GF}&=x_F-x_G\\&=3-(-2)\\&=3+2\\&=5\end{aligned}[/tex]

As points E and F share the same x-value, the length of line segment FE is the difference between the y-values:

[tex]\begin{aligned} \implies \overline{FE}&=y_E-x_F\\&=1-(-2)\\&=1+2\\&=3\end{aligned}[/tex]

Therefore, the area of polygon EFG is:

[tex]\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of polygon $EFG$}&=\dfrac{1}{2} \times \overline{GF} \times \overline{FE}\\\\&=\dfrac{1}{2} \times 5 \times 3\\\\&=\dfrac{15}{2}\\\\&=7.5\;\; \sf units^2\end{aligned}[/tex]

Given vertices:

As points J and K share the same y-value the polygon is a triangle with base JK and height of the difference in y-values of points K and L.

As points J and K share the same y-value, the length of line segment JK is the difference between the x-values:

[tex]\begin{aligned} \implies \overline{JK}&=x_K-x_J\\&=4-(-3)\\&=4+3\\&=7\end{aligned}[/tex]

The height of the triangle is the difference between the y-values of points K and L:

[tex]\begin{aligned} \implies\sf Height&=y_K-y_L\\&=4-(-3)\\&=4+3\\&=7\end{aligned}[/tex]

Therefore, the area of polygon JKL is:

[tex]\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of polygon $JKL$}&=\dfrac{1}{2} \times \overline{JK} \times \sf height \\\\&=\dfrac{1}{2} \times 7 \times7\\\\&=\dfrac{49}{2}\\\\&=24.5\;\; \sf units^2\end{aligned}[/tex]

Answer:

The radius is 7.

Step-by-step explanation:

To find the radius of this circle, we would have to find the diameter first. This can be found by looking at both the directions of the origin (left and right) and counting how many spots it goes until the circle ends.

On the left, there is 6 spots. On the right, there is 8. So we would add to find the full way around or the diameter (6 + 8) and we get 14.

Now, since radius is halfway around or is half of the diameter, we simply divide 14 by 2 which is 7.

Therefore, the answer is 7.

(1) $132,000 is the net income

(2) $66,000 total income

Selling price per unit:

= Sales ÷ No. of units

= $456,000 ÷ 5,700

= $80

Variable cost per unit:

= variable cost ÷ No. of units

= $102600 ÷ 5,700

= $18

Alternative 1:

Contribution margin = Sales - variable cost

                                 = (5,700 × $80 × 1.1) - (5,700 × $18)

                                 = $440,000 - $210,000

                                 = $230,000

Net income = Contribution margin - Fixed cost

                  =  $230,000 - $98,000

                  = $132,000

Alternative 2:

Contribution margin:

= sales - variable cost

= $456,000 - ($456,000 × 59%)

= $456,000 - $236,000

= $164,000

Net income = Contribution margin - Fixed cost

                  =  $164,000 - $98,000

                  = $66,000

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The expression which gives a difference of 4 3/12 from the given options is 10 2/3 - 5 1/12 - 1 2/6. option C

The Subtraction of the expressions with different denominators are

The expression with a difference of 4 3/12

Check all that applies:

7 3/4 - 1 2/4 - 2 1/3

= 31/4 - 6/4 - 7/3

= (93-18-28) / 12

= 47/12

= 3 11/12

9 8/12 - 1 3/6 - 4 1/2

= 116/12 - 9/6 - 9/2

= (116-18-54) / 12

= 44/12

= 3 8/12

10 2/3 - 5 1/12 - 1 2/6

= 32/3 - 61/12 - 8/6

= (128-61-16) / 12

= 51/12

= 4 3/12

20 2/12 - 14 1/4 - 2 1/6

= 242/12 - 57/4 - 13/6

= (242-171 - 26) / 12

= 45/12

= 3 9/12

2.

= 23/3 - 19/6 - 20/9

common denominator is 18

= (138 - 57 - 40) / 18

= 41/18

= 2 5/18

= 119/12 - 10/3 - 34/8

common denominator is 24

= (238 - 80 - 102) / 24

= 56/24

= 2 8/24

= 2 1/8

In conclusion, the Subtraction of the mixed number with unlike denominators are:

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The roll with a better value, that is, cheap price is 9 packed toilet roll.

In order to determine the roll with a better value, we will consider the unit price of each roll and make comparison.

Unit price refers to the price of a commodity per each unit.

Unit price = Cost / units

= £2.04 / 4

= £0.51 per unit

Unit price = Cost / units

= £4.68 / 9

= £0.52 per unit

Therefore, it can be concluded that the the roll which has a better value is the 9 packed toilet roll.

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The point estimator is 0.0129, the 95% CI on variance ([tex]\sigma^2[/tex]) is (0.0082, 0.0233), the 95% CI on standard deviation (σ) is (0.0905, 0.1527), and it is surprised to hear the director that the standard deviation is more than 0.2 seconds.

n = total data = 30

[tex]\bar x[/tex] = mean or average

[tex]\sigma^2[/tex] = variance

σ = standard deviation

α = significance level = 1 - 95% = 0.05

A) First, calculate unbiased point estimator with this formula

[tex]\sigma^2[/tex] = [tex]\frac{1}{n-1}\times \sum(x_i-\bar x)^2[/tex]

[tex]\sigma^2[/tex] = 0.0129 (detail calculation in excel)

Before we calculate confidence interval, we first find out some of the values needed from the chi-square table.

Lower limit = [tex]X^2_{\alpha /2,n-1}[/tex] = [tex]X^2_{0.025,29}[/tex] = 45.722

Upper limit = [tex]X^2_{1-\alpha /2,n-1}[/tex] = [tex]X^2_{0.975,29}[/tex] = 16.047

B) Next, we calculate confidence interval on variance,

CI on [tex]\sigma^2[/tex] = ( [tex]\frac{(n-1)\times \sigma^2}{X^2_{\alpha /2,n-1}}[/tex], [tex]\frac{(n-1)\times \sigma^2}{X^2_{1-\alpha /2,n-1}}[/tex] )

= ( [tex]\frac{(30-1)\times 0.0129}{45.722}[/tex], [tex]\frac{(30-1)\times 0.0129}{16.047}[/tex] )

= (0.0082, 0.0233)

C) Then, for confidence interval on standard deviation,

CI on σ = [tex]\sqrt{\text{CI on }\sigma^2}[/tex] = ( [tex]\sqrt{\frac{(n-1)\times \sigma^2}{X^2_{\alpha /2,n-1}}}[/tex], [tex]\sqrt{\frac{(n-1)\times \sigma^2}{X^2_{1-\alpha /2,n-1}}}[/tex] )

= ([tex]\sqrt{0.0082}[/tex], [tex]\sqrt{0.0233}[/tex])

= (0.0905, 0.1527)

D) Confidence interval on standard deviation guarantee 95% that standard deviation in response time is between 0.0905 and 0.1527. So, it will be surprised if director claim that the standard deviation in response time is more than 0.2 seconds.

Thus, The point estimator of response time data is 0.0129, and the 95% confidence interval on variance is (0.0082, 0.0233), and the 95% confidence interval on standard deviation is (0.0905, 0.1527), and it's surprised if director said standard deviation is more than 0.2 seconds.

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Answer: Understand the context.

Make a plan.

Identify the “who” and “why”

Weigh the pros and cons.

Get a second opinion.

Limit your choices.

Set deadlines.

Evaluate the outcome.

Step-by-step explanation:

[tex]\huge \boxed{\sf 8+4\sqrt{5} }\\\\\\\displaystyle \sf Four\ lines\ are\ equal \\\\BC+CD+EF+FA = 2 \\\\Pythagorean\ theorem \\\\AB = DE= \sqrt{4^2 + 2^2} = 2\sqrt{5} \\\\ The\ sum\ of\ all\ individual\ segments \\\\ (4)2+(2 )2\sqrt{5}=8+4\sqrt{5}[/tex]

The perimeter of the polygon with the given vertices is 16.94 units.

From the graph:

Polygon ABCDEF with vertices A(0,4),B(2,0),C(2,-2),D(0,-2),E(-2,2) and F(-2,4).

Distance between AB = [tex]\sqrt{(2-0)^2+(0-4)^2}[/tex]

= [tex]\sqrt{2^2+4^2}[/tex]

= [tex]\sqrt{20}[/tex]

we know that opposite sides in polygon are equal.

AB = DE = [tex]\sqrt{20}[/tex]

Distance between BC = [tex]\sqrt{(2-2)^2+(-2-0)^2}[/tex]

= [tex]\sqrt{2^2}[/tex]

= [tex]\sqrt{4}[/tex]

= 2 units.

BC = EF = 2

Distance between CD = [tex]\sqrt{(2-0)^2+(-2+2)^2}[/tex]

= [tex]\sqrt{2^2}[/tex]

= 2

CD = FA = 2

The perimeter of polygon = [tex]\sqrt{20}[/tex] + 2+2+2+2+[tex]\sqrt{20}[/tex]

= 8+2[tex]\sqrt{20}[/tex]

= 8+4[tex]\sqrt{5}[/tex]

= 8+8.94

= 16.94 units

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Answer:

Below

Step-by-step explanation:

Move it to the other side of the fraction ( make it an inverse to change it to a + exponent)

Examples     5^-2 =   1/ ( 5^2)

      1 / (x^-23)   = x ^23

     x^2 y^-3  = x^2 / y^3           etc