A flagpole is 12 feet fall. Its shadow is
11 feet long. How far is it from the top of the flagpole to the end of its shadow?

Answer:

3.15%

Step-by-step explanation:

To find the expected return and standard deviation of a portfolio that is invested in two assets A and B, we need to know the expected returns and standard deviations of those assets, as well as the correlation between them.

Let's assume that the expected return and standard deviation of asset A are 10% and 5%, respectively, and that the expected return and standard deviation of asset B are 8% and 3%, respectively. Let's also assume that the correlation between the two assets is 0.5.

To find the expected return of the portfolio, we can use the following formula:

Expected return of portfolio = weight of A * expected return of A + weight of B * expected return of B

where the weights are the proportions of the portfolio invested in each asset:

weight of A = 40% = 0.4

weight of B = 60% = 0.6

Expected return of portfolio = 0.4 * 10% + 0.6 * 8%

Expected return of portfolio = 9.2%

Therefore, the expected return of the portfolio is 9.2%.

To find the standard deviation of the portfolio, we can use the following formula:

Standard deviation of portfolio = sqrt(weight of A^2 * variance of A + weight of B^2 * variance of B + 2 * weight of A * weight of B * correlation * standard deviation of A * standard deviation of B)

where the variances are the square of the standard deviations of each asset:

variance of A = (5%)^2 = 0.0025

variance of B = (3%)^2 = 0.0009

Standard deviation of portfolio = sqrt(0.4^2 * 0.0025 + 0.6^2 * 0.0009 + 2 * 0.4 * 0.6 * 0.5 * 0.05 * 0.03)

Standard deviation of portfolio = 0.0315 or 3.15% (rounded to two decimal places)

Therefore, the standard deviation of the portfolio is 3.15%.

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Step-by-step explanation:

Volume = 20×70×80 = 112000 cm³

Volume of cubes = 20×20×20 ×5 = 8000 ×5 = 40000 cm³

Volume of space in the tank = 112000-40000 = 72000 cm³ = 72000 mL = 72 L

Volume of water from tap = 158 × 1 = 158 L

Volume of water spilt out = 158 - 72 = 86 L

Answer: 30000cm³

Step-by-step explanation:

Capacity of tank-> 30x70x80

                               =168000

Volume of 1 cube->20x20x20

                              =8000

Volume of 5 cubes->8000x5

                                  =40000

Volume of space which can be occupied by water->168000-40000

                                                                                        =128000

Volume of water running for 158 min-> 158x1000

                                                                  =158000

Volume of water spilt out->158000-128000

                                             =30000( Ans)

Answer:

0,-1

Step-by-step explanation:

Hope this helps! =D

Brainliest! =D

Answer:

-1

Remember y=mx+b

m is your slope and b is your y-int
m = -4/3

b = -1

We can compare and contrast the primary differences between the Job costing and Process costing processes as follows:

Job costing process:

Process costing:

We can classify the cost types by understanding their usage in the accounting industry. Process costing is used for calculating the costs for mass-produced materials while job costing is used for calculating the cost for customized products.

Process costing is used for accumulating costs and to ascertain the flow of costs through accounts. Job costing is the main document for tracking costs.

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Answer:

x = 4√3 y = 8/√2 = 4√2

(4 rad 3) (4 rad 2)

Answer:

Step-by-step explanation:

Greetings!Answer:[tex]\sqrt{85} or 9.22

Answer:

Step-by-step explanation:

The length of the Hypotenuse should be [tex]\sqrt{45}[/tex] , 6.70.

By Pythagoras' Theorem, [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].

so, Let a =6cm, b =3cm

[tex]6^{2}[/tex] + [tex]3^{2}[/tex] = 45

Therefore,

The length of the hypotenuse will be either [tex]\sqrt{45}[/tex]

Looking at the table, If Bridget has 10 animals in total with 30 legs, it only means she has 5 chicken.

Based on the information on the table,

For the number of chicken legs, we say

9 x 2 = 18       3 x 2 = 6          7 x 2= 14       14 x 2 = 28

If we sum these number to the total number of legs in each row, it would be;  4 + 18 = 22   8+6 = 14   12 + 14 = 26     16+28 = 44

This means that all the values provided so far does not give us the accurate number of legs of the animals.

If 5p = 20L the number of hen should be 30- 20 = 10/2 = 5

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The surface area and volume of the tent are 213.5 ft² and 148?75ft³ respectively.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as ;

SA = 2B + ph. Where p is the perimeter and h is the height of the prism. B is the base area

Base area = 1/2 bh

= 1/2 × 7 × 5 = 35/2

= 17.5ft²

perimeter = 7+6+6 = 21ft

SA = 2 × 17.5 + 21 ×8.5

SA = 35+178.5

SA = 213.5 ft²

Volume of prism is expressed as;

V = base area × height

= 17.5 × 8.5

= 148.75 ft³

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You would need to purchase 720 different tickets to guarantee a win.

You must pick the first three finishers in the correct order to win a trifecta race with 10 entries.

Since there are ten participants in the race, there are ten ways to select the winner of the first place prize. In the wake of choosing the primary spot finisher, there are just 9 passages remaining, so the quantity of ways of choosing the second-place finisher is 9.

Finally, since there are only eight entries left after selecting the first two, there are 8 ways to select the third-place finisher.

Therefore, the total number of possible winning trifecta combinations is:

10 x 9 x 8 = 720

This indicates that in order to guarantee a win, you would need to purchase 720 distinct tickets. However, it is essential to keep in mind that betting on a race in this manner may not always be the most profitable or efficient option, and that purchasing each and every possible combination can be very costly. It's vital to painstakingly think about the chances, payouts, and your financial plan prior to putting down any wagers.

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Answer:

First, we need to convert 1,200 meters to inches:

1,200 meters * 39.3701 inches/meter = 47,244.12 inches

Next, we need to find the circumference of the wheel:

Circumference = π * Diameter

Circumference = 3.14 * 12 inches

Circumference = 37.68 inches

To find the number of revolutions, we can divide the total distance traveled (47,244.12 inches) by the distance traveled per revolution (37.68 inches):

47,244.12 inches ÷ 37.68 inches/revolution ≈ 1,254 revolutions

Rounding to the nearest whole number, it will take approximately 1,254 revolutions of the wheel to travel 1,200 meters on a child's bicycle.

The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. The input values are often called the independent variable, while the output values are called the dependent variable. Functions are commonly denoted using functional notation, such as f(x), where x is the input and f(x) is the output. Functions are used to describe relationships between variables, such as in algebraic expressions or equations. They can take many forms, including linear, quadratic, polynomial, exponential, trigonometric, and logarithmic functions. Functions are fundamental to many areas of mathematics, science, engineering, and economics, and have many applications in real-world situations.

Here,

A. The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. In other words, the function is not a straight line, because y is not directly proportional to x. Instead, it is a linear equation in two variables x and y, where the graph of the equation is a straight line.

B. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change. In a linear function, the rate of change of the function (slope) is always constant, meaning that for any two points on the line, the change in y over the change in x is always the same. However, in this case, the rate of change of the function depends on the value of x, and thus the graph of the function is not a straight line. Instead, it is a quadratic function, where the graph is a parabola.

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Dimensions of the rectangle are 6 feet and 12 feet.

Rectangle is a quadrilateral whose each pair of opposite sides are equal in length and each two consecutive sides are in right angle to each other. In rectangle one pair of equal opposite sides is called Length and another one is called Width.  

If length of a rectangle is L and width of rectangle is W then the perimeter of that rectangle will be = 2(L+W)

Let W be the rectangle's width.

Here according to question the rectangle is twice as long as it is wide.

So, length of rectangle = 2W

Perimeter will be = 2(W+2W) = 2*(3W) = 6W

So, according to question,

6W = 36

W = 36/6 = 6

Thus the width of the rectangle is = 6 feet.

Then the length = 2*6 = 12 feet.

Hence dimensions of the rectangle are 12 feet and 6 feet respectively.

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Aaron's algebraic expression is:

14 * (18 - 3x)

an algebraic expression is an expression built up from constant algebraic numbers, variables, and the addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number.

This expression represents the product of 14 and the difference of 18 and 3x. The factors of this expression are:

14: This is a constant factor that multiplies the difference of 18 and 3x.

(18 - 3x): This is the distinction of 18 and 3x, which is being duplicated by 14. It is a two-term binomial expression: 18 and -3x. The first term, which has a coefficient of -3, is a variable, while the second term, which has a coefficient of -3, is a constant.

To work on the articulation, we can utilize the distributive property of augmentation to get:

14 * (18 - 3x) = 14*18 - 14*3x = 252 - 42x

In this worked on structure, the elements are as yet 14 and (18 - 3x). However, additional factors of the simplified expression, such as 2 and 21, which are factors of 42 (the coefficient of x), can also be identified.

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1) The length of the segments BC =√53   FG =√53  JK =√53

2) The statements that are true are;

BC ≅ FG

BC ≅ JK

FG ≅ JK

To find the lengths of the segments, we use the formula d = √((x2 - x1)² + (y2 - y1)²)

For BC, it would be √((1 - (-6))² + (2 - 4)²) = √53.

It would ordinarily be 7.3. However, since approximations are not needed, it has been left in the form of squareroot

For  FG: √((-5 - (-7))² + (-1 - 6)²) = √53.

The answers provided are based on the questions seen in the image

Here are the endpoints of the segment BC, FG and JK.

B (-6, 4)  C (1, 2)        F (-7, 6),  G (-5, -1)        J (1, -8), K (3, -1)

Find the length of each segment. give an exact answer (not a decimal approximate)

BC =     FG =      JK =

Check all the statement that are true below;

BC ≅ FG

BC ≅ JK

FG ≅ JK

None of these are true.

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The geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

It should be noted that to find the geometric mean of two numbers, we multiply them together and then take the square root of the result. So, for each pair of numbers, we can follow these steps:

Multiply the two numbers together.

Take the square root of the product.

Using this formula, we get:

7.16 and 27:

Geometric mean = √(7.16 × 27) ≈ 14.85

5 and 36:

Geometric mean = √(5 × 36) = √180 ≈ 13.42

10.8 and 48:

Geometric mean = √(10.8 × 48) ≈ 22.94

Therefore, the geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

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The probability that someone with a credit score of 650 or below defaulted on the loan is 0.14.

The probability that someone with a credit score of 650 or below defaulted on the loan is calculated below:

Probability = number of defaulters/ number of loan recipients

From graph:

The total number of defaulters = 30 + 30 + 30

The total number of defaulters = 90

The total number of loan recipients = 120 + 240 + 270

The total number of loan recipients = 630

Probability to default = 90/630

Probability to default = 0.14

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answer:

17%

I hope this helps

The proof of the three distributions as required as shown in the explanation part.

For x² distribution:

Let's start with the sample variance, which is defined as:

s^2 = ∑(y_i - y_bar)² / (n-1)

where;

We can rewrite this formula as:

s^2 = (∑y_i² - n*y_bar²) / (n-1)

Multiplying both sides by (n-1)/σ², we get:

s^2 / σ² = (∑y_i² - ny_bar²) / (σ²(n-1))

Now, let's define a new variable:

x² = ∑y_i² / σ²

Substituting x² into the above equation, we get:

s^2 / σ² = (x² - n*y_bar²/σ²) / (n-1)

Notice that n*y_bar²/σ² is just the sample mean squared in units of variance. We can rewrite it as:

n*y_bar²/σ² = (y_bar - μ)² / (σ²/n)

where;

Substituting this into the above equation, we get:

s^2 / σ² = (x² - (y_bar - μ)² / (σ²/n)) / (n-1)

Now, let's define a new variable:

ss = ∑(y_i - y_bar)² / σ²

Substituting ss into the above equation, we get:

s^2 / σ² = (x² - ss/(n-1)) / n

This is the desired result. We have shown that s²/σ² follows a x² distribution with n-1 degrees of freedom.

For t distribution:

Let's start with the sample mean, which is defined as:

y_bar = ∑y_i / n

We can rewrite this formula as:

y_bar - μ = (∑y_i - n*μ) / n

Now, let's define a new variable:

t = (y_bar - μ) / (s/√n)

where;

Substituting y_bar - μ and s into the above equation, we get:

t = (∑y_i - nμ) / (s√n)

This is the desired result. We have shown that t follows a t distribution with n-1 degrees of freedom.

For F distribution:

Let's start with the sample variances, which are defined as:

s₁² = ∑(y_i - y₁)² / (n₁-1)

s₂² = ∑(y_i - y₂)² / (n₂-1)

where;

We can rewrite these formulas as:

s₁² = (ss₁ - n₁*(y₁-μ)²) / (n₁-1)

s₂² = (ss₂ - n₂*(y₂-μ)²) / (n₂-1)

where;

ss₁ = ∑(y_i - y₁)²

ss₂ = ∑(y_i - y₂)²

Dividing these equations, we get:

s₁² / s₂² = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

Now, let's define a new variable:

F = s₁² / s₂

Substituting s₁² / s₂² into the above equation, we get:

F = (ss₁ / (n₁-1)) / (ss₂ / (n₂-1))

This is the desired result. We have shown that F follows an F distribution with (n₁-1) and (n₂-1) degrees of freedom.

It's worth noting that the F distribution is only defined for positive values. Therefore, if s₁² / s₂² is less than 1, we need to take the reciprocal of the above equation to ensure that F is positive:

F = (ss₂ / (n₂-1)) / (ss₁ / (n₁-1))

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Answer:

$98 a month

Step-by-step explanation:

1,176 divided by 12

The area of the shaded region = 30.903 in²

From the attached figure we can observe that the radius of the circle R is r = 6 in.

Using the forula for the area of circle, the area of circle R would be,

A₁ = πr²

A₁ = π × 6²

A₁ = 36π

A₁ = 113.097 in²

So, the diameter would be d = 6 × 2 = 12 in.

The circle R is inscribed in a square.

So, the side length of square is equal to the diameter of the circle.

This means the side length 'a' os square = 12 in.

Using the formula of the area of square,

A₂ = side²

A₂ = a²

A₂ = 12²

A₂ = 144 in²

so, the area of the shaded region would be,

A = A₂ - A₁

A = 144 -113.097

A = 30.903 in²

This is the required area.

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A statistical question would be:  What is the average salary of teachers in this school district?

When a question can be answered statistically, it can be done so by gathering and analysing data, for example. This particular question aims to comprehend a population or a phenomenon by using numerical data. In contrast to non-statistical questions, which are more concerned with acquiring information or opinions, statistical questions are more concerned with getting and analysing data. Statistical procedures including sampling, data analysis, and inference are frequently used to answer statistical issues.

A statistical question would be:  What is the average salary of teachers in this school district?

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None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.

what is rounding ?

Rounding is a mathematical process of approximating a number to a specified degree of accuracy. It involves replacing a number with a simpler, but close value that is easier to work with or understand.

In the given question,

The question asks us to find the annual premium for a $75,000 10-year term policy for a 25-year-old male, using the table of annual life insurance premiums per $1,000 of face value.

First, we need to find the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. Looking at the table, we can see that the premium for a 10-year term policy for a 25-year-old male is $4.79 per $1,000 face value.

To find the annual premium for a $75,000 policy, we need to multiply the premium per $1,000 face value by 75. So:

Annual premium = $4.79 per $1,000 x 75 = $359.25

Rounding this answer to the nearest cent gives us:

$359.25 ≈ $359.26

Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male is $359.26.

None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.

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When the block is cut into smaller pieces, 512 pieces of cheese remain.

A cube is a solid three-dimensional shape with 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedral.

The volume V of a cube  is given by the formula V = a^3, where a = the length of one side of the cube. V = 4 ^ 3 = 64 cubic meters or inches ^ 3. The volume of a cube is 64 cubic meters

The total volume of the cheese block is obtained as follows:

V = edge length³ = 8³ = 512 cubic meters

Since the volume of each piece is 1 cubic inch, the total number of pieces is obtained by dividing the total volume by the volume of each piece:

Number of pieces = V / volume per piece = 512 / 1 = 512 pieces

Therefore, when the block is cut into smaller pieces, 512 pieces of cheese remain.

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The calculated line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

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Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation:

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

We have,

The area of the whole circle.

= πr²

Where r = 8

So,

= 3.14 x 8 x 8

= 200.96

Now,

Area of the red shaded circle = πr²

Where r = 4

So,

= 3.14 x 4 x 4

= 50.24

Now,

The probability that a randomly selected point within the circle falls in the red-shaded circle.

= Area of the red shaded circle / Area of the whole circle

= 50.24 / 200.96

= 1/4

= 0.25

Thus,

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

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B) The domain for #1 and #2 is  ≥ -7 and the domain for #3 is -∞ ≤  ≤ ∞.

1. [tex](f + g)(x) = f(x) + g(x)[/tex]

The domain of [tex](f + g)(x)[/tex] is the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex] (since we can't take the square root of a negative number), the domain of [tex](f + g)(x)[/tex] is [tex]x > = -7[/tex].

2. [tex](f - g)(x) = f(x) - g(x)[/tex]

The domain of [tex](f - g)(x)[/tex] is also the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for[tex]x > = -7[/tex], the domain of [tex](f - g)(x)[/tex] is also [tex]x > = -7[/tex].

3. [tex](fg)(x) - > (f(g(x))[/tex]

The domain of [tex]f(g(x))[/tex] is the set of all values of  [tex]x[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex]. Since the domain of [tex]f[/tex] is all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex]  is defined only for [tex]x > = -7[/tex], the domain of [tex]f(g(x))[/tex] is [tex]x > = -7[/tex].

Therefore, the correct answer is option:

B) The domain for 1) and 2) is [tex]> = -7[/tex] and the domain for 3) is -∞ ≤ [tex]x[/tex] ≤ ∞.

The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.

Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:

x(t) = 2 - t

y(t) = (t+3)²

To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.

When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.

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Therefore, the lawnmower can cut grass for 2.5 hours on 5/6 of a gallon of fuel in the gas can

To find out how long the lawnmower can cut grass with 5/6 of a gallon of gas, we first need to figure out how many gallons of gas the lawnmower will use per hour:

1 hour of grass cutting = 1/3 gallon of gas

1 gallon of gas = 3 hours of grass cutting

So the lawnmower uses 1/3 gallon of gas per hour, which means that 1 gallon of gas will last for 3 hours of grass cutting.

Now we can use this conversion factor to figure out how long 5/6 of a gallon of gas will last:

5/6 gallon of gas * 3 hours of grass cutting per 1 gallon of gas = 15/18 hours of grass cutting

Simplifying this fraction by dividing the numerator and denominator by 3:

15/18=3/6

So 5/6 of a gallon of gas will last for 5/6 of 3 hours, which is equal to 2.5 hours of grass cutting.

As a result, 5/6 of a gallon of gas will last for 5/6 of 3 hours, or 2.5 hours of mowing the lawn.

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Answer:

(m-3)^2

Step-by-step explanation:

(m^2-6m+9) is factored by using this formula:
(a-b)^2=a^2-2ab+b^2.

Therefore, we can substitute the values into this equation.

m^2=a^2,

-6m=-2ab,

9=b^2.

Solving for b in the third equation, b is equal to 3 or -3. However, as this equation is negative, then it must be -3.

(m-3)^2