the optimum portfolio is said to occur at the point of tangency of which of the following two measures?

Answer:

There are 60 pieces of 20 cent coins

Step-by-step explanation:

Let the number of 50 cent coins be x.

Let the number of 20 cent coins by y.

Now, we are told that value of all coins is $27.

Also, 50 cent = $ 0.5 and 20 cents = $0. 2

Thus;

0.5x + 0.2y = 27 - - - - - (eq 1)

Now, we are told that there are twice as many 20 cent coins as there are 50 cent coins. So,

y = 2x - - - - (eq 2)

Putting 2x for y in eq 1,we have;

0.5x + 0.2(2x) = 27

0.5x + 0.4x = 27

0.9x = 27

x = 27/0.9

x = 30

Thus, y = 2 * 30 = 60

Thus,there are 60 pieces of 20 cent coins

The ladder is 13 m long and leans against a window 5 m high, then the ladder leaned to the other side without moving its feet to reach the 12 m high window.

if we imagine a leaning ladder it will look like a right triangle and it will remind us of the Pythagorean theorem. do you remember the pythagorean theorem?

The Pythagorean theorem explains the relationship or relationship between the lengths of the sides of a right triangle.

The Pythagorean theorem reads: "The square of the length of the hypotenuse (hypotenuse) in a right triangle is equal to the sum of the squares of the lengths of the other sides".

in the picture, let's say if the width of the street is a, the height of the window is b and the length of the stairs is c.

in this case we will find the width of the street, namely a, then we use formula a² = c² - b² .

then it will be

b = 12

c = 13

a² = c² - b²

a² = 13² - 12²

a² = 169 - 144

a² = 25

a = 5

The equation is 4x + y² - 2y + z² - 4z + 4 = 0 and To sketch the surface, plot the center point and the general shape of an elliptic paraboloid opening along the x-axis. This can be answered by the concept of Distance formula.

To find the equation of the surface consisting of all points P = (x, y, z) that are equidistant from point A = (-1, 1, 2) and the plane x = 1, we will use the distance formula for both the point and the plane.

The distance from point P to A is given by:
d₁ = √((x + 1)² + (y - 1)² + (z - 2)²)

The distance from point P to the plane x = 1 is given by:
d₂ = |x - 1|

Since the distances are equidistant, we have:
d₁ = d₂

Now, substitute the distance formulas and square both sides to get rid of the square root:
(x + 1)² + (y - 1)² + (z - 2)² = (x - 1)²

Expand and simplify the equation:
x² + 2x + 1 + y² - 2y + 1 + z² - 4z + 4 = x² - 2x + 1

Notice that x² terms on both sides cancel out. Then, simplify further:
4x + y² - 2y + z² - 4z + 4 = 0

This equation represents a surface in 3D space. Upon inspection, we can see that it is an elliptic paraboloid centered at (0, 1, 2). To sketch the surface, plot the center point and the general shape of an elliptic paraboloid opening along the x-axis.

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Answer: 0.16

Step-by-step explanation:

Statement 2) "The company ensures they dispose of byproducts in a way that does not affect the environment" demonstrates corporate social responsibility.

Corporate social responsibility refers to the ethical and responsible behavior of businesses towards society and the environment. In this statement, the company is actively taking steps to ensure that their waste disposal methods are environmentally friendly. By disposing of byproducts in a way that does not harm the environment, the company is demonstrating a commitment to minimizing their environmental impact and acting responsibly.

Statement 1) merely states that the company is a water treatment plant, which does not provide information about their social or environmental practices. Statement 3) mentions that the company is different from other similar companies that dispose of waste in the nearest rivulet. Although this statement implies that the company is not engaging in harmful practices like other companies, it does not explicitly demonstrate any proactive efforts towards corporate social responsibility.

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The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.

The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.

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Answer:

Question 1: ∠3 and ∠7 are corresponding angles.

Question 2: ∠2 and ∠8 are alternate interior angles.

Question 3: ∠4 and ∠6 are alternate exterior angles.

Question 4: ∠2 is congruent to ∠6.

Question 5: ∠8 is not congruent to ∠1.

Question 6: If ∠2 measures 132°, the measure of ∠7 would be 48°.

Answer:

Step-by-step explanation:

4 (x + 2) =30

4x + 8 = 30

4x = 30 - 8

4x = 22

x = 22 : 4

x = 5.5

check

(5.5 + 2) * 4 = 30

the answer is good

Answer:

the cost of each sandwich is 5.5

Step-by-step explanation:

we have,

4(x+2) = 30

we know a(b+c) = ab+ac

so, when we open the bracket we get,

4(x+2) = 4x+4*2 which is equal to 4x+8

so, 4x+8 = 30

=>   4x = 30 - 8         [transposing method]

=>   4x = 22

=>   x = 22/4

=>   x = 5.5

hope this helps

x = 1/2, 'x' represents the number of adults and children in the group, and since we can't have a fraction of a person, we can conclude that there is 1 adult and 1 child in the group.

Let's assume that the number of adults and children in the group is represented by the variable 'x'. Since the number of adults and children is the same, we can say that there are 'x' adults and 'x' children in the group.

Now, we know that the cost for each adult and each child to attend the carnival is $110. Since there are 'x' adults and 'x' children, the total amount paid by the group can be calculated by multiplying the cost per person by the total number of people:

Total amount paid = Cost per person * Total number of people

                 = $110 * (x + x)

                 = $110 * 2x

                 = $220x

We are given that the total amount paid by the group is $110, so we can set up the equation:

$220x = $110

To solve for 'x', we divide both sides of the equation by $220:

x = $110 / $220

x = 1/2

Therefore, 'x' represents the number of adults and children in the group, and since we can't have a fraction of a person, we can conclude that there is 1 adult and 1 child in the group.

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Therefore in each composite function we get different domains and ranges which is given below.

(1) f(x) = x+2 , g(x) = 3x - 1

(f + g)(x) = f(x) + g(x)

              =  x+2 + 3x - 1

             = 4x +1

Domain = (-∞ , ∞) and range = (-∞ , ∞)

(f - g )(x) = f(x) - g(x)

                =  x+2 -3x +1

               = -2x + 3

Domain = (-∞ , ∞) and range = (-∞ , ∞)

(f.g)(x) = f (x) g(x)

          = (x+2)( 3x - 1)

           = 3x²- x + 6x - 2

           = 3x²+ 5x -2

Domain = (-∞ , ∞) and range = [-49/12 ,∞)

(f/g)(x) = f(x)/g(x)

           = x+2/3x-1

Domain = (-∞ , 1/3) ∪ (1/3 ,∞) and range = (-∞ , 1/3) ∪ (1/3 ,∞)

(2) f(x) = x² - 5 and g(x) = -x +8

   (f + g)(x) = f(x) + g(x)

                 = x² - 5 -x +8

                 = x² - x +3

Domain = (-∞ , ∞) and range = [11/4 ,∞)

(f - g )(x) = f(x) - g(x)

              =  x² - 5 +x -8

              =  x² + x - 13

Domain = (-∞ , ∞) and range = [-53/4 ,∞)

(f.g)(x) = f (x) g(x)

          = ( x² - 5 )(- x +8)

          = -x³ + 8x² + 5x - 40

Domain = (-∞ , ∞) and range = (-∞ , ∞)

(f/g)(x) = f(x) / g(x)

          = x² - 5 / -x +8

Domain = (-∞ , 8) ∪ (8 ,∞) and range = (-∞ , -16 - 2√59 ) ∪ (-16 + 2√59  ,∞)

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The vector-valued function r(t) = 〈3 cos(t), 3 sin(t)〉 represents the plane curve x² y² = 9.

We are supposed to represent the plane curve by a vector-valued function. The plane curve x2 y2 = 9 can be represented by a vector-valued function

r(t) = 〈3 cos(t), 3 sin(t)〉.

To find the equation of the plane curve we have to make use of the following equation:

x² + y² = r², where x, y and r are the components of the vector r(t).

Here, we are supposed to represent the plane curve by a vector-valued function.

A vector-valued function can represent the plane curve x² y² = 9,

r(t) = 〈3 cos(t), 3 sin(t)〉.

The vector-valued function r(t) represents the curve x² y² = 9 since if we plug the components of r(t) in the equation x² y² = 9, we get:

= 9 cos²(t) sin²(t)

= 9sin²(t) + 9cos²(t)

= 9

This is true for any value of t. Therefore, the vector r(t) traces the curve x² y² = 9. If we graph the curve x² y² = 9 we get a circle with radius 3 centered at the origin, and the vector-valued function r(t) traces the circle counterclockwise starting at the point 〈3, 0〉. The vector-valued function r(t) = 〈3 cos(t), 3 sin(t)〉 represents the plane curve x² y² = 9.

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The profit, y, can be written in terms of x, the number of computers sold.  as ​y = 150x

The table that completes the question is added at the end of this solution as an attachment

From the question, we have the following parameters that can be used in our computation:

Amount of items sold = x

Profit made by the company = y

The equation of a proportional relationship is represented as

k = Y/X * h

Where

(X, Y) is the coordinate of any ordered pair from the function or table

Using the above as a guide, we have the following:

(X, Y) = (3, 450)

Substitute the known values in the above equation, so, we have the following representation

y = 450/3 * x

Evaluate the quotients in the equation

y = 150 * x

Evaluate the products in the equation

y = 150x

Hence, the equation of the proportional relationship is y = 150x

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Answer:

x= 101

Step-by-step explanation:

Exterior angle of triangle states that the exterior angle of a triangle is the sum of the 2 opposite interior angles. This is abbreviated as 'ext. ∠ of ∆'. Thus using the exterior angle theorem,

x°= 64° +37° (ext. ∠ of ∆)

x°= 101°

x= 101

_____

Alternative method:

Let the third angle in the triangle be y°.

Since the sum of the angles in a triangle is 180°,

y° +64° +37°= 180° (∠ sum of ∆)

Simplify:

y° +101°= 180°

y°= 180° -101°

y°= 79°

The sum of the angles on a straight line is 180°.

x° +y°= 180° (adj. ∠s on a str. line)

Substitute y°= 79°:

x° +79°= 180°

x°= 180° -79°

x°= 101°

x= 101

Answer:

$1081.65

Step-by-step explanation:

866.71/5 gives you 173.34 as 20 percent

add that to the original fir an upmarket and it will be 1040.05.

4 percent of that is $41.60 so add that again and you get 1081.65 as the total amount paid.

The amount Jackie paid for the clothes dryer is  $1081.65.

Mark up means that the price of an item was increased by a certain percentage. Tax is a compulsory sum levied on the purchase of goods and services. Taxes increase the price of products.

The mark up price of the clothes dryer = 1.20 x $866.71 = $1040.05

Amount paid by Jackie = 1.04 x $1040.05 = $1081.65

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Answer:

Scientific Notation: 8.97 x 10^-3

Answer:

8.97 to the -3 power

Step-by-step explanation:

The entropy of the data set can be calculated using the formula: -p(log2p) - (1-p)(log2(1-p)), where p is the proportion of positive outcomes.

Plugging in the values, we get: -12/20(log2(12/20)) - (1-12/20)(log2(1-12/20)) = -0.971. Rounded to the nearest thousandths place, the entropy is -0.971.
The entropy of a dataset is a measure of its impurity or randomness. In your case, you have a dataset with 20 training outcomes, with 12 positive and 8 negative (since 20-12=8). To calculate the entropy, we use the formula:
Entropy = -p(positive) * log2(p(positive)) - p(negative) * log2(p(negative))
First, find the probabilities of positive and negative outcomes:
p(positive) = 12/20 = 0.6
p(negative) = 8/20 = 0.4
Next, plug these probabilities into the entropy formula:
Entropy = -0.6 * log2(0.6) - 0.4 * log2(0.4)
Entropy ≈ 0.971
Thus, the entropy of your dataset, rounded to the nearest thousandth, is 0.971.

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  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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The magnitude of the vector QP is √73.

To find the component form of the vector QP, we need to subtract the coordinates of point P from the coordinates of point Q. The component form of a vector is represented as (x, y), where x and y are the differences in the x-coordinates and y-coordinates, respectively.

Given that P = (4, 1) and Q = (-4, 4), we can calculate the component form of the vector QP as follows:

x-component of QP = x-coordinate of Q - x-coordinate of P

                 = (-4) - 4

                 = -8

y-component of QP = y-coordinate of Q - y-coordinate of P

                 = 4 - 1

                 = 3

Therefore, the component form of the vector QP is (-8, 3).

To find the magnitude of the vector QP, we can use the formula:

Magnitude of a vector = √(\(x^2 + y^2\))

Substituting the x-component and y-component of QP into the formula, we get:

Magnitude of QP = √((\(-8)^2 + 3^2\))

              = √(64 + 9)

              = √73

Therefore, the magnitude of the vector QP is √73.

In summary, the component form of the vector QP is (-8, 3), and its magnitude is √73. The component form gives us the direction and the magnitude gives us the length or size of the vector.

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Answer:

112 in²

Step-by-step explanation:

width of the brick = (2 - - 5) = 7       this is the distance between the vertices in the y direction

length of the brick = (8 - -8) = 16  this is the distance between the vertices in the x direction

Area = length x width= 16 x 7 = 112 in²

Note:  it helps if you graph these points, then you can see the problem better

y -intercept #4 the starting value

(1 , 7.5) #3 the value after 1 year

because the x axis is the time (in years). When x = 0 (at the y-intercept) time = 0 or beginning time. When x = 1 one year has passed.

Answer:

117.65 miles

Step-by-step explanation:

Given data

Day one distance= 50.4miles

Day two distance= 67.25 miles

Total distance= Day one + Day two distance

Total distance= 50.4+67.25

Total distance= 117.65 miles

PreAlg students spend significantly less time doing homework compared to ElemAlg and InterAlg students, while there is no significant difference in homework time between ElemAlg and InterAlg students.

What is significantly ?

Significantly" is the keyword that indicates a notable or meaningful difference or result in the context of statistical analysis. It is often used to describe findings that have a high level of confidence and statistical significance, indicating that the observed difference or relationship is unlikely to have occurred by chance.

Based on the given data and statistical analysis, the conclusion is as follows:

PreAlg compared to ElemAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for ElemAlg (3.18) with a t-value of 5.08 and a p-value of 0.000. Therefore, we can conclude that PreAlg students spend significantly less time doing homework compared to ElemAlg students.

PreAlg compared to InterAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for InterAlg (4.42) with a t-value of 3.64 and a p-value of 0.003. Hence, we can conclude that PreAlg students spend significantly less time doing homework compared to InterAlg students.

ElemAlg compared to InterAlg:

The sample mean for ElemAlg (3.18) is not significantly different from the sample mean for InterAlg (4.42) with a t-value of 1.49 and a p-value of 0.163. Therefore, we fail to reject the null hypothesis, and we cannot conclude a significant difference in homework time between ElemAlg and InterAlg students.

In summary, the PreAlg students have significantly lower homework time compared to both ElemAlg and InterAlg students. However, there is no significant difference in homework time between ElemAlg and InterAlg students.

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To find the probability that the equipment is functioning properly, we need to consider the cases where 6, 7, 8, or all 9 components are operational.

Let's calculate the probability for each case and add them together.
For 6 components to be operational, we have to choose any 6 out of the 9 components. The probability of each chosen component working is p, and the probability of each unchosen component failing is (1 - p). So, the probability for 6 operational components is (9 choose 6) * \(p^6 * (1 - p)^3.\)
Similarly, for 7 operational components, the probability is (9 choose 7) \(* p^7 * (1 - p)^2.\)
For 8 operational components, the probability is (9 choose 8) * \(p^8 * (1 - p).\)
Lastly, for all 9 components to be operational, the probability is\(p^9.\)
Adding up these probabilities will give us the overall probability that the equipment is functioning properly.

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Answer:

48

Step-by-step explanation:

Simplify 80% to 0.8

Simplify=48

We could find the price of the item now by multiplying 80% by 60.

Answer:

\(2(9x+10)\)

Step-by-step explanation:

\(18x+20\)

First, we have to factor. We will have to factor out 2 to get the answer(Factor out 2 from 18x+20).

Answer:

\(2(9x+10)\)

Hope this helps!

There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

The dataset of doctor A is given as:

643 634 670 658 636 624 641 655 649 629

The dataset of doctor B is given as:

651 625 622 624 631 621 653 647 646 646

Using a statistical calculator, we have:

Doctor A

Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses

In a dataset, the larger the mean absolute deviations value, the larger the variation.

By comparison, 12 is greater than 11.28

Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

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Answer:

1st option

Step-by-step explanation: