Investment The future value S of an investment earning 6% compounded continuously is a function of the principal P and the length of time t that the principal has been invested. It is given by
S = f(P, t) = Pe0.06t
Find f(2000, 20), and interpret your answer.

Answer:

2 2/7 - 4 5/7      

= -2 3/7

Step-by-step explanation:

Frequency is the number of occurrences of a repeating event.

The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.

The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.

The number of times a specific data value occurs is the frequency of that data. We use f to symbolise the frequency of a data value.

As an illustration, the grade A is said to occur frequently if five students received an A in science.

Here we have the events:

shopping time between occurrences frequency

18 to 22: 20, 18 2

23 to 27: 27, 24, 26, 24, 24 5

28 to 32 29, 31 2

33 to 37 37, 34, 35, 33, 36, 32 6

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Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map f: X --> X such that f(x) = x- 1 is an example of continuous map is one to one and honto but is not a homemorphism .

A function f: A --> B is said to be bijective or bijection if it satisfies both injective (one-to-one function) and surjective (over-function) properties. Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map

f : X--> X such that f(x) = x- 1 ; x∈X (domain)

Now, we show that it is bijective, so

One to One : let x₁ and x₂ belongs to X such that f(x₁) = f(x₂) we have to show x₁= x₂

f(x₁) = f(x₂) => x₁ - 1 = x₂ - 1

=> x₁ = x₂ -1 + 1

=> x₁ = x₂

So, f(x) is one to one.

Onto : let y be a element of X ( co-domain) We can show that there exists x∈A such that f(x)=y. Choose x= f⁻¹(y) and so f(f⁻¹(y))=y. So for all y∈B, there exists an x∈A such that f(x)=y. Therefore, it is onto. Thus, f(x) is one to one and onto and continus( due to polynomial nature) i.e it is a continuous bijection from X to itself, but it is not a

homeomorphism, since the image of N is not open.

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2.833 10 6 is the largest error as a result.

Finding a function's derivative, or rate of change, is the process of differentiation in mathematics.

The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

The three fundamental derivatives (D) are: (1) D(xn) = nxn 1 for algebraic functions, where n is any real number; (2) D(sin x) = cos x and D(cos x) = sin x for trigonometric functions; and (3) D(ex) = ex for exponential functions.

Hence, 2.833 10 6 is the largest error as a result.

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Answer:

39960

Step-by-step explanation:

first you have to divide how much money they made by the products to find the base price of each product so 13,000 / 325 which has a quotient of $40 per product then you multiply 40 by 999, so 40 x 999 has a product of 39960

You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will  increase by $100.

Hence, You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will  increase by $100.

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Answer: you need to have at least $312,500 in your account at the beginning.

Step-by-step explanation:

The total amount of money you will need to withdraw over the 25-year period is $30,000 * 25 years = $750,000. To find the total amount of interest you will earn, we need to use a compound interest formula. The formula for compound interest is:

A = P(1 + r/n)^nt

where A is the total amount of money you will have in your account after 25 years, P is the initial amount of money in your account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In our case, we have A = $750,000, P = ?, r = 8%, n = 1 (since the interest is compounded annually), and t = 25. Plugging these values into the formula, we get:

$750,000 = P * (1 + 0.08/1)^1 * 25

We can simplify this equation to:

$750,000 = P * 1.08^25

To find the value of P, we can divide both sides of the equation by 1.08^25:

$750,000 / 1.08^25 = P

We can use a calculator to compute the value of 1.08^25, which is approximately 2.4. This means that the initial amount of money you need in your account is $750,000 / 2.4 = $312,500.

Therefore, to be able to withdraw $30,000 each year for 25 years and earn 8% interest on your account, you need to have at least $312,500 in your account at the beginning.

You can then add up the lengths of the sides to find the perimeter, and add up the areas of the faces to find the total surface area of the gift box.

What is a perimeter?

The perimeter of a shape is the total length of the outer boundary of the shape. It is the sum of all the sides of the shape.

To find the perimeter and the area of a gift box, you can use the given dimensions of the net to calculate the lengths of the sides and the areas of the faces. You can then add up the lengths of the sides to find the perimeter, and add up the areas of the faces to find the total surface area of the gift box.

Hence, you can then add up the lengths of the sides to find the perimeter, and add up the areas of the faces to find the total surface area of the gift box.

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Answer:

1656

Step-by-step explanation:

Answer: 1656

Step-by-step explanation:

just trust me, that's the answer! I did the same question.

The SSS congruence theorem is used to prove that triangles MAH and THA are congruent to each other. See proof below.

"SSS" stands for side-side-side congruence theorem, which says that given the criteria that two triangles both have three corresponding sides that are equal or congruent to each other, both triangles are congruent.

The proof below shows how we can apply the SSS to prove that triangles MAH and THA are congruent to each other.

Statement                                 Reason                                            

1. MA ≅ TH                               1. Given

2. MH ≅ AT                              2. Given

3. AH ≅ HA                              3. Reflexive property of congruence

4. ΔMAH ≅ ΔTHA                   4. SSS congruence theorem

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a) The thrust of the propeller is  23,834 lbf and b)  The induced velocity is 8.44 mph c)  The velocity in the downstream far field away from the propeller disc is 161.56 mph

a)The thrust of the propeller can be calculated using the equation,

Thrust = 2πρR^2V^2, where ρ is the air density, R is the propeller radius, and V is the average velocity of the propeller disc. For sea level at a speed of 150 mph, the air density is about 0.002377 slugs/ft^3.

the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf

b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph

c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph

d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp

e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp

f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%

Hence, d) The power absorbed by the fluid is  42.7 hp e)  the propeller power (thrust flight speed) is  4,844.08 hp f)  The propeller efficiency is 113.6%

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The angle C can be obtained rom the computation below as 16 degrees.

We know that the cosine is one of the angular measures that we have. The trigonometric ratios that we have are the sine the cosine and the tangent. We can be able to obtain the angle of the when we take the inverse of the cosine of the angle.

Now we know that the cosine of the angle can be defined as the ratio of the adjacent and the hypotenuse. The value of the cosine of the angle can be gotten from the table of the standard measure of the angles or by the use of a calculator.

We then have that;

Cos C= 0.9613

C = Cos-1( 0.9613)

By the time we make use of a good calculator we obtain the angle as;

C = 16 degrees

This is the value of the angle.

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Answer:

Step-by-step explanation:

Answer:

f slopes was  [tex]\frac{3}{2}[/tex]  ,the y intercepts was -3

g slopes was [tex]-\frac{1}{3}[/tex],the y intercepts was -2

Step-by-step explanation:

g slopes :

functions g has point (0,-2) and (3,-3)

the slopes =[tex]\frac{-2-(-3) }{0-3} =-\frac{1}{3}[/tex]

Answer:

miles: 55(36/60) = 55(0.6) = 33 miles

mins: 60(14/17.5) = 60(0.8) = 48 minutes

Total amount of time, in minutes

The total distance, in miles

Step-by-step explanation:

The required distance and time are 47 miles and 84 minutes, respectively.

Speed is measured as the ratio between the distance and time, and the SI unit of speed is m/s.

We know that speed = distance / time

Finding for distance =

55(36/60) = 55(0.6) = 33 miles

Therefore, The total distance, in miles =

= 33 miles + 14 miles

= 47 miles

For Time =

60(14/17.5) = 60(0.8) = 48 minutes

Therefore, Total amount of time, in minutes =

36 minutes + 48 minutes

= 84 minutes

Hence, The required distance and time are 47 miles and 84 minutes, respectively.

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The magnitude of the current induced in the wire is 1.2×10^{-8} and direction of the current induced in the wire is counter clockwise.

In the given question,

A rectangle (W = 20 cm, H = 30 cm) and has a resistance of(R) = 5.0 mΩ.

B(s) = 4.0 μT and B(b) = -2.5

t(s) = 2.0 s

From the question

dB(1)/dt = B(s)/t(s)

dB(1)/dt = 4 μT/2

As μ = 10^{-6}

dB(1)/dt = 2×10^{-6} T/s

dB(2)/dt = 1/2dB(1)/dt

dB(2)/dt = 2×10^{-6} /2

dB(2)/dt = 1×10^{-6} T/s

dB(3)/dt = B(b)dB(1)/dt

dB(3)/dt = -2.5×2×10^{-6} T/s

dB(3)/dt = -5×10^{-6} T/s

Now the change in magnetic field is,

dB/dt = dB(1)/dt + dB(2)/dt + dB(3)/dt

dB/dt = 2×10^{-6} + 1×10^{-6}/2 - 5×10^{-6}

dB/dt = - 2×10^{-6}

Now finding the area

Area = 1/2 wh

Firstly converting the w and h in m

So w = 0.20 m, h = 0.30 m

Area = 1/2 *0.20*0.30

Area = 0.03 square m

The induced EMF is

EMF = -AdB/dt

EMF = -(0.03)*(- 2×10^{-6})

EMF = 0.06×10^{-6}

The magnitude of the current induced in the wire is

I = EMF/R

I = 0.06×10^{-6}/5

I = 0.012×10^{-6}

I = 1.2×10^{-8}

Now, the direction of the current induced in the wire is counter clockwise.

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The right question is:

Figure (a) shows a wire that forms a rectangle (W = 20 cm, H = 30 cm) and has a resistance of 5.0 mΩ. Its interior is split into three equal areas, with magnetic fields B(1), B(2), and B(3). The fields are uniform within each region and directly out of or into the page as indicated. Figure (b) gives the change in the z components B(z) of the three fields with time t; the vertical axis scale is set by B(s) = 4.0 μT and B(b) = -2.5 B(s) and the horizontal axis scale is set by t(s) = 2.0 s. What are the magnitude and direction of the current induced in the wire?

The slope of the linear relationship will be 2.

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

A linear relationship is given in the table.

Now,

Let two point on the table are (- 1, - 3) and (2, 3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - (-3)) / (2 - (-1))

m = 6 / 3

m = 2

Thus, The slope of the linear relationship = 2.

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Answer: -6

Step-by-step explanation: Since 9 is being subtracted from 3, we know that it will be a negative number. So, 9-3 = 6, and a greater number subtracted from a smaller number is a negative number. So, that results in this being -6. I hoped this helped.

[tex]3-9[/tex]

[tex]3+(-9)[/tex]

[tex]=\fbox{-6}[/tex]

[tex]3+(-9)[/tex] on a number line:

The standard deviation of Alex's new probability distribution is given as follows:

0.775.

The standard deviation of a discrete distribution is calculated as the square root of the sum of the differences squared between each observation and the mean, multiplied by their respective probabilities.

Hence the standard deviation of Alex's new probability distribution is calculated as follows:

S(X) = square root(0.035 x (0 - 1.471)² + 0.579 x (1 - 1.471)² + 0.286 x (2 - 1.471)² + 0.08 x (3 - 1.471)² + 0.02 x (4 - 1.471)²)

S(X) = 0.775.

Meaning that the second option is correct.

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A matrix B that has V as its nullspace. (c) Multiply A and B is [tex]I (4 by 4 ).[/tex]

[tex]\mathbb{R}^4[/tex]

What is a Nullspace vector?

The null space of A is all the vectors x for which Ax = 0, and it is denoted by null(A). This means that to check to see if a vector x is in the null space we need only to compute Ax and see if it is the zero vector.

- All vectors whose components are equal.

- All vectors whose components add to zero.

- All vectors that are perpendicular to [tex](1,1,0,0)$ and $(1,0,1,1)$.[/tex]

- The column space and the nullspace of  (4 by 4 ).

Solution. These bases are not unique.

[tex]- $(1,1,1,1)$.- $(1,-1,0,0),(1,0,-1,0)$, and $(1,0,0,-1)$.- $(1,-1,-1,0)$ and $(1,-1,0,-1)$.[/tex]

- The columns of are a basis of its column space: [tex]$(1,0,0,0),(0,1,0,0)$, $(0,0,1,0)$, and $(0,0,0,1)$.[/tex]The nullspace contains the zero vector only. By convention, the empty set is the basis of such a space.

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The rate at which the energy pass through an area of 1.0 m² at 2.0 km is equal to 1.97 × 10⁹ J/s.

At a constant power, the intensity of a wave is inversely proportional to the distance from the source. Mathematically, the intensity of a wave with respect to the distance from a source can be modeled (represented) by this mathematical expression;

I ∝ 1/r²

Where:

Next, we would re-write the mathematical expression and then determine the intensity of a wave from source as follows;

I₁/I₂ = r₂²/r₁²

I₁ = I₂(r₂²/r₁²)

Note: We know that its intensity when it passed a point from the source is 2.0 km.

Substituting the given parameters into the formula, we have;

I₁ = 2.8 × 10⁶ × (53²/2²)

I₁ = 1.97 × 10⁹ J/m²s.

Now, we can calculate the rate of the energy by using this formula;

Power = intensity × area

Power = 1.97 × 10⁹ × 1.0

Power = 1.97 × 10⁹ J/s.

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Answer: $0.75

Step-by-step explanation:

-We know that the line must also contain the point (0,0), as 0 pounds of potatoes would cost $0. Thus we can find the slope of the line and write an equation:

slope = Δy/Δx = (3-0)/(4-0) = 3/4

y = (3/4)x

(The y-int (aka b) is 0 since the line passes through (0,0))

Plugging in 1 yields $0.75

Answer:

-------------------------------------------------------

Proportional relationship equation:

Given point (4, 3).

Use its coordinates to find the value of k:

This is representing the price of 1 pound of potatoes.

Answer:

K = 4

Step-by-step explanation:

The x-y point  ( K, -5 ) means that ...

x = K and y = -5

Let's plug in K and -5 for y in the equation to find the value of K (which is the same as x).

3(K) + (-5) = 7

3K - 5 = 7

3K = 7 + 5

3K = 12

K = 4

Step-by-step explanation:

(-3x⁴)(-4x²)

as multiplication is commutative (that means the sequence of the factors is irrelevant), we get

-3×-4×x⁴×x²

we can combine everything of the same type (constants or variable names).

-3×-4 = 12

remember, -×- = +

x⁴×x² = x⁶

remember, when multiplying terms with the same base variable, we can simply add the exponents.

why ? because an exponent is a short way of saying that the base variable has to be multiplied by itself that many times.

e.g.

a³ = a×a×a

a⁷ = a×a×a×a×a×a×a

a³×a⁷ = a×a×a × a×a×a×a×a×a×a = a¹⁰

that's why.

so, the complete simplified expression is

12x⁶

The first blank as required to be filled in the task content should be filled with; two.

The second blank as required to be filled in the task content should be filled with; 134.1 in³.

According to the information given; the diameter of the beachball is; 8 inches. Therefore, it's radius is half that; 4 inches.

On this note, the volume of the beachball which is spherical in shape given by the formula;

Volume of a sphere = (4/3)πr³ where;

Radius, r = 4;

Therefore, volume of beachball is;

4/3 π (4)³ = 256π / 3.

Also, the volume of the cone which is given by the formula;

Volume of a cone = (1/3) π r² h

where; Radius, r = 4 and Height, h = 8.

Therefore, volume of the cone is;

(1/3) π (4²) × 8 = 128π / 3.

On this note, by dividing the volume of beachball by that of cone; we have that;

( 256π / 3 ) / ( 128π / 3 ) = 2.

On this note, the cone will fit into the beachball about 2 times.

Also, the volume of the cone given that; π = 22 / 7 can be evaluated as;

( 128 × 22 ) / ( 7 × 3 )

= 134.1 in³.

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The number of hours that each student work on the project is 2 hours.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, the equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute.

This will be:

(x + 28) /5 = 3x

Cross multiply

x + 28 = 15x

Collect like terms

15x - x = 28

14x = 28

Divide

x = 28 / 14

x = 2

The number of hours is 2 hours.

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Answer: that answer is right ^

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The solution set is the point(s) where the two plotted graphs intersect:

The relationship between 'h' and 't' when r=20 and rate = 1 rad/min is [tex]h=20sin(t)[/tex] and when r=30 and rate = 2 rad/min is [tex]h=30sin(2t)[/tex]

Given,

The Ferris wheel is rotating at constant angular speed.

"h" represents Alex's height above the center of the Ferris wheel (in feet)

"t" represents the number of minutes since the ride started.

a)

Here, the conditions are

the radius if ferris wheel is, r = 20 feet

and the ferris wheel is rotating at the ratei.e. angular speed, [tex]\omega = 1 rad/min[/tex]

Here, 'h' represents the height of Alex's measured in the y-direction.

As per the given conditions the relationship between 'h' and 't' can be determined by the equation,

[tex]y= rsin\theta[/tex]

Where, [tex]\theta =\omega t[/tex]

here y=h,

then,[tex]h=rsin(\omega t)\\\\h=20sin(t)...i[/tex]

b)

Now, the given conditions are

radius of ferris wheel is ,r = 30 feet

ferris wheel is rotating at ratei.e angular speed , [tex]\omega = 2 rad/min[/tex]

Now, the relationship between h and t becomes ,

[tex]h=30sin(2t)....ii[/tex]

Thus, the graph plots for eq. i and eq.ii are shown in the figure.

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Step-by-step explanation:

I don't know if this is valid but

We can think of this problem like

(6^7-6^6+6^5)/31 = x

Where x is a whole number so 6^7-6^6+6^5 is divisible by 31

Multiply each side with 31 :

6^7-6^6+6^5 = 31x

We can turn 6^7 into 6^5 x 6^2

We can also turn 6^6 into 6^5 x 6

So the equation turns into this :

(6^5 x 6^2) - (6^5 x 6) + (6^5 x 1) = 31x

We can factor out the 6^5 out of the left side of the equation, which turns into :

(6^5) x (6^2 - 6 + 1) = 31x

Which is also :

(6^5) x (31) = 31x

Divide each side with 31

6^5 = x

X is obviously a whole number

The t critical value and confidence interval must be determined.

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.

The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level.

For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.

The sample size, sample variability, and confidence level are all variables that have an impact on the width of the CI.

Assuming all other factors remain constant, a larger sample results in a narrower confidence interval, while a sample with more variability results in a wider confidence interval.

According to our question-

At a confidence level of 90%, we have α = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05.

Degree of freedom = 4-1 = 3

When we look this up in the t critical value table,

t critical = 2.353

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