A portfolio has a value P(ES), so that the value P is a function of E, the price of a Euro in Canadian dollars, and S, the level of the TSX stock index. Presently the portfolio is worth $275.000, while a Euro is $1.50 Canadian, and the index is S = 18,000.
If the partial derivatives of P have values ϑP/ϑE = 62,000, and ϑP/ϑS = -29, what approximately will the portfolio value be if the price of a Euro goes down by 0.06 and the stock index goes down by 543?

Special angles in geometry are specific angle measures that have unique properties and are often encountered in geometric problems:

(1) Right angle      (2) Acute angle        (3)  Obtuse angle         (4)Straight angle              (5)Reflex angle

(6) Complementary angles          (7)Complementary angles

In geometry, special angles refer to specific angles that have special properties or characteristics. These angles include right angles, acute angles, and obtuse angles. A right angle is an angle that measures exactly 90 degrees, while an acute angle is an angle that measures less than 90 degrees. An obtuse angle, on the other hand, measures more than 90 degrees but less than 180 degrees. These angles are important in geometry as they form the foundation for many geometric shapes and concepts. Understanding the properties and characteristics of these special angles is crucial for solving geometry problems and constructing geometric figures accurately.

Special angles in geometry are specific angle measures that have unique properties and are often encountered in geometric problems. These angles include:

1. Right angle: A right angle is an angle that measures exactly 90 degrees. It is formed when two lines intersect perpendicularly.

2. Acute angle: An acute angle is an angle that measures between 0 and 90 degrees. It is smaller than a right angle.

3. Obtuse angle: An obtuse angle is an angle that measures between 90 and 180 degrees. It is larger than a right angle.

4. Straight angle: A straight angle is an angle that measures exactly 180 degrees. It is formed when two lines intersect in a straight line.

5. Reflex angle: A reflex angle is an angle that measures between 180 and 360 degrees. It is larger than a straight angle.

6. Complementary angles: Two angles are complementary if their sum is equal to 90 degrees.

7. Supplementary angles: Two angles are supplementary if their sum is equal to 180 degrees.

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Answer:

4.292

Step-by-step explanation:

(x+3)(x-1)=24

expand

x²+2x-3=24

x²+2x-27=0

Using the quadratic formula..

\(\frac{-2+\sqrt{2^2-4*1*-27}}{2}=\frac{-2+10.5830052443}{2}=4.292\)

there is another answer, but it doesn't make sense in the context of this question

the un-rounded answer is 4.29150262215

Answer:

$91.55

Step-by-step explanation:

The money belen pay in state taxes in 3 years is $91.84.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =P(1+r/n)^rt

We are given that;

Belen pays= $76.00

Rate= 6.4%

Now,

Plugging these values into the formula, we get:

A=76(1+0.064)3

A=76(1.064)3

A≈91.84

Therefore, by the interest the answer will be $91.84.

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The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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On solving we found that the given system of equations has infinitely many solutions as they have the same line.

What is a system of equations?

A group of equations comprising one or more variables is known as a system of equations. A system of equations consists of two or more equations and looks for common answers. Finding the values of the variables employed in a system of equations entails solving the set of equations.

While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system.

Given a system of equations as follows:

x + y = 3

4x  = 12 - 4y

1) Now we are asked to choose two numbers that add up to 3.

They are x = 4 and y = -1

2) The above values of x and y are solutions of the first equation. We have to check if it satisfies the second equation as well.

Now the second equation is:

 4x = 12 - 4y

 4x + 4y = 12

This can be simplified by dividing by 4 on both sides of the equation.

Then the equation becomes,

x + y = 3

This is the first equation.

Since the second equation is the multiple of the first equation, the values x = 4 and y = -1 will satisfy the second equation as well.

4 * 4 = 12 - 4 * -1

16 = 12 + 4

16 = 16

3) Both equations have the same line.

So this system of equations has infinitely many solutions.

When two equations in a system of equations are as follows:

ax + by = c

sx + ty = u

This has infinitely many solutions when,

a/s = b/t = c/u

For the given system of equations,

x + y = 3

4x + 4y = 12

1/4 = 1/4 = (3/12 = 1/4)

Therefore on solving we found that the given system of equations has infinitely many solutions as they have the same line.

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The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Answer:

107 cars

Step-by-step explanation:

Answer:

107 cars

Step-by-step explanation:

10+7+5+9+11+26+44=107

The answer is iii which are whole numbers

The correct way of representing different types of numbers is,

B. I and IV only

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set

                                   Complex numbers (a + ib)

Real numbers                                                                 Imaginary numbers.

(a + i0)                                                                                      (0 + ib)

Rational numbers               Irrational numbers

(perfect squares)              (non-perfects squares)

Fractions.  

(p/q, q ≠ 0)            

Integers.

(whole nos. -: 0 to ∞)

(negative integers -: - ∞ to - 1)

(positive integers -: 1 to ∞)

The type of numbers in which every next type is a subset of the previous type is Natural numbers ⊂ Whole numbers ⊂ Intergers ⊂Rational numbers.

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The scale that David used is 10 feet = 1 inch.

The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale.

On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.

So, we know that:

In reality, the diving board is 20 ft long.

In drawing the diving board is 2 inches long.

Then, the scale David used is:

20/2 = 10/1

10 feet = 1 inch

Therefore, the scale that David used is 10 feet = 1 inch.

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Answer:

-|b| < b

Step-by-step explanation:

-b where?

Answer:

a2 + 4b2

Step-by-step explanation:

The inequality that matches the graph is given as follows:

E. n ≥ 1.

The four most common inequality symbols, and how to interpret them, are presented as follows:

The graph in this problem is composed by the values to the right of n = 1, with a closed interval, hence the inequality is given as follows:

n ≥ 1.

The graph is presented at the end of the answer.

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The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

a) The differential equation expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is suffering from Warfarin  is given a pill containing 2.5 mg of Warfarin then,

dQ/dt = -kQ
here Q(0) = 2.5

b) The differential equation the expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is not suffering from Warfarin  is given a pill containing 0.5 mg/hr then,

dQ/dt = -kQ + r
where Q(0) = 0
Here
k = rate constant
r = rate of administration
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

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The rate at which Warfarin leaves the body should be proportional to the amount still in the body, not a constant rate of 2.5. So the correct differential equation for part (b) is:

Q' = 0.5 - kQ, where Q(0) = 0

Where k is the proportionality constant for the rate of elimination.

Explanation

(a) Let's denote the rate of elimination as k, where k > 0. Since the elimination rate is proportional to the amount of warfarin, we can write the differential equation as:

Q'(t) = -kQ(t)

Given that the initial condition is a 2.5 mg pill, the initial condition should be:

Q(0) = 2.5

So the differential equation for part (a) is:

Q'(t) = -kQ(t), Q(0) = 2.5

(b) In this case, the patient receives warfarin intravenously at a rate of 0.5 mg/hour. Thus, we should add the rate of administration to our equation:

Q'(t) = 0.5 - kQ(t)

The initial condition is still that the patient has no warfarin in her system:

Q(0) = 0

So the differential equation for part (b) is:

Q'(t) = 0.5 - kQ(t), Q(0) = 0

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Answer:

The correct answer is option D, 20ft

Step-by-step explanation:

After drawing the picture below, you can just use pythagorean theorem to solve for the diagonal, or the hypotenuse in this case;

(Length)² + (Width)² = (Diagonal)²

(16)² + (12)² = (Diagonal)²

256 + 144 = (Diagonal)²

400 = (Diagonal)²

\(\sqrt{400}\) = \(\sqrt{Diagonal^{2} }\)

20 = Diagonal

Hope this helps!

Answer:

D. 20 ft

Step-by-step explanation:

Use pythagorus! We can imagine the rectangle is split into 2 equal triangles, one side of the triangle being 12, and the width being 16.

Pythagorus theorum is used to calculate the hypotenuse (long side) of a right-angled triangle. This is the formula:

\(\sf{a^{2}+b^{2} = c^{2} }\)

So, we do 12^2 (squared) + 16^2 =

144 + 256 = 400

Now, we have to find the square root of 400, which is equal to

20

So our answer is 20ft

Hope this makes sense! If you need further explanation, do let me know...

- profparis

Answer:

63 %

Step-by-step explanation:

Percentage change in value value for any number is given by

percentage change = (new value - old value) /old value * 100

we can also write it as

percentage change = (change in value ) /old value * 100

________________________________________

cost of commercial in 1968 = $54000

cost of commercial in 1973 = $88000

change in cost of commercial = cost of commercial in 1973 - cost of commercial in 1973  = $(88000-54000) = $34000

thus,

percentage change in cost of commercial

         = change in cost of commercial/cost of commercial in 1968 * 100

         = 34000/54000*100 = 62.96 %

Thus, percentage change in cost of commercial is 62.96 %

we have to round it to nearest whole number

rounded value of 62.96 is 63

in that case

percentage change in cost of commercial is 63 %

Hey there! I'm happy to help!

We want to get m all by itself on one side of the equation. To do this, we use inverse operations on both sides of the equation to cancel out variables on one side to isolate m.

am/c=n

We multiply both sides by c.

am=nc

We divide both sides by a.

m=(nc)/a

I hope that this helps! Have a wonderful day! :D

It will take at least 25 weeks for you to save enough money to purchase the car, assuming you currently have $350 in the bank and save an additional $60 per week.

To determine the number of weeks it will take for you to save enough money to purchase the car, we can set up an equation and solve for the number of weeks.

Let's denote the number of weeks as "w".

Given that you currently have $350 in the bank and plan to save an additional $60 per week, the amount of money you will have after "w" weeks can be represented as:

350 + 60w

We want this amount to be at least $1800, so we can set up the following inequality:

350 + 60w ≥ 1800

To find the number of weeks, we need to solve this inequality for "w".

Subtracting 350 from both sides of the inequality, we have:

60w ≥ 1450

Dividing both sides of the inequality by 60, we get:

w ≥ 24.167

Since the number of weeks must be a whole number, we can round up to the nearest whole number. Thus, it will take you at least 25 weeks to save enough money to purchase the car.

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Answer:

The measure of angle DCB = 125

Step-by-step explanation:

This is because angle ACD and angle DCB are supplementary.

Supplementary angles are two angles with a sum of 180 degrees, and we know these angles are supplementary by the fact that angle ACB = 180 degrees.

Answer:

Step-by-step explanation:

the odds of choosing a ginger ale is 1/21

Answer:

the first one

Step-by-step explanation:

all created functional values must always be negative, because "absolute value" Shays creates only positive numbers, and then the "-" in front makes then sure we have only negative numbers.

that rules out the third and fourth answer option.

to decide between first and second answer, I choose to see, when the function should deliver 0 as functional value.

f(x) is 0, when x+3 is 0. and that is only possible for x=-3.

so, at x=-3, y=0.

and that is only true for the first answer option.

Answer: i think D sorry if wrong

can we be friend

The weekly deposit of Neisha is given by the equation x = $ 12.35

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the weekly deposit of Neisha be x

Now , Neisha saves equal amount in every week

So , let the number of weeks be represented as n

Now , the equation will be

The total amount of money saved in n weeks = nx

Now , when the number of weeks = 6 weeks

The total amount of money saved in 6 weeks = 6x

The amount of money saved after 6 weeks = $ 74.10

Substituting the values in the equation , we get

6x = 74.10   be equation (1)

Dividing by 6 on both sides of the equation , we get

x = 74.10/6

x = $ 12.35

Hence , the amount of money saved each week is $ 12.35

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Answer: x=7.48 im positive

Answer:

The answer is 7.48.

Step-by-step explanation:

\(c^{2} - b^{2}\) = \(a^{2}\)

\(15^{2} - 13^{2} = a^{2}\)

\(225 - 169\) = \(a^{2}\)

\(56 = a^{2}\)

\(\sqrt{56} = \sqrt{a^{2} }\)

\(7.48 = a\)

The bicycle manufacturer is studying the reliability of its models and analyzing the probability of defects. They found the probability of a brake defect is 4 percent and the probability of both brake and chain defects is 1 percent.

Given that the probability of a defect with brakes or chain is 6 percent, we can find the probability of a chain defect using the formula: P(A and B) = P(A|B) * P(B), where P(A and B) is the probability of both events A and B occurring, P(A|B) is the probability of event A occurring given that event B has occurred, and P(B) is the probability of event B occurring.

In this case, we want to find the probability of a chain defect given that there is a defect with either the brakes or the chain. Let's use the events: A = brake defect, B = chain defect, From the problem statement, we know that: P(A) = 0.04 (probability of a brake defect), P(A and B) = 0.01 (probability of both a brake defect and a chain defect)
P(A or B) = 0.06 (probability of a defect with the brakes or the chain).

To find P(B|A or B), we can use the formula: P(B|A or B) = P(A and B) / P(A or B) = 0.01 / 0.06, = 1/6, = 0.1667, So the probability of a chain defect given that there is a defect with either the brakes or the chain is 16.67%, or approximately 2/12 or 1/6.

Therefore, the correct answer is option 2: 2%, Solving for the probability of a chain defect, we get: P(chain defect) = 0.06 - 0.04 + 0.01 = 0.03, So, the probability of a chain defect is 3 percent.

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Answer:

Hi! -5/3 :)

Step-by-step explanation:

Hope this helps!

Best of luck! ♥

Answer:

yes he is

Step-by-step explanation:

The approximate number of time does an average human heart beat in a lifetime is 3 x 10⁹

The term called average in math is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Here we need to find the number of time does an average human heart beat in a lifetime.

As we all know that a normal heart rate when you're not being active is generally between 60 – 100 beats per minute.

And this is called your resting heart rate.

Based on this we have calculated as average of 80 beats per minute, your heart beats about 4,800 times per hour. That's a whopping 115,200 times per day.

Then during an average lifetime, then the human heart will beat more than 2.5 billion times.

When we round off the value then we get approximately 3 billon.

In a scientific notation it can be written as,

=> 3 x 10⁹

Therefore option (c) is correct.

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Answer:

12

Step-by-step explanation:

20-6=14 (Distance between points) then 14*3/7=6.

3/7 of the distance from A=6 to B=20 is 6. Thus, we find the point that is

3/7 of the distance from A=6 to B=20 by adding 6 to 6.

6+6= 12

Therefore, the point that is

3/7 from A=6 to B=20 is 12.