Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten year term.


a. annual premium: $ a0

b. monthly premium: $ a1

Minimizing curve C is a helix, described by the equation :

C(t) = (a cos(t), a sin(t), C exp(-cot(t)) + h)

To express the length L(p) of curve C in terms of p, we can use the formula for the length of a curve in cylindrical coordinates. In cylindrical coordinates, the arc length element ds can be given by:

ds² = dr² + r² dt² + dz²

Since dr = 0 (as r = a is constant along the curve C), and dt = -a sin(t) dt (from the parametrization), we have:

ds² = a² sin²(t) dt² + dz²

Integrating ds over the curve C from t = 0 to t = tmax, we get:

L(p) = ∫[0,tmax] √(a² sin²(t) + p'(t)²) dt

where p'(t) denotes the derivative of p(t) with respect to t.

To find the differential equation for the function p(t) that minimizes L(p), we can apply the Euler-Lagrange equation of the calculus of variations. The Euler-Lagrange equation is given by:

d/dt (dL/dp') - dL/dp = 0

Differentiating L(p) with respect to p' and p, we have:

dL/dp' = 0 (since p does not appear explicitly in L(p))

dL/dp = d/dt (dL/dp') = d/dt (a² sin²(t) p'(t) / √(a² sin²(t) + p'(t)²))

Using the chain rule, we can simplify the expression:

dL/dp = (a² sin²(t) p''(t) - a² sin(t) cos(t) p'(t)²) / (a² sin²(t) + p'(t)²)^(3/2)

Setting the Euler-Lagrange equation equal to zero, we get:

(a² sin²(t) p''(t) - a² sin(t) cos(t) p'(t)²) / (a² sin²(t) + p'(t)²)^(3/2) = 0

Simplifying further, we have:

p''(t) - (sin(t) cos(t) / sin²(t)) p'(t)² = 0

This is the differential equation that the function p(t) must satisfy to minimize L(p).

To solve this differential equation, we can make the substitution u = p'(t). Then the equation becomes:

du/dt - (sin(t) cos(t) / sin²(t)) u² = 0

This is a separable first-order ordinary differential equation. By solving it, we can obtain the solution for u = p'(t). Integrating both sides and solving for p(t), we get:

p(t) = C exp(-cot(t)) + h

where C is a constant determined by the initial condition p(0) = 0, and h is the value of p at t = tmax.

Therefore, the minimizing curve C is a helix, described by the equation :

C(t) = (a cos(t), a sin(t), C exp(-cot(t)) + h)

where C is a constant determined by the initial condition, and h is the value of p at t = tmax.

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Answer:

caca

Step-by-step explanation:

Answer:

Diameter: 26cm

Circumference: 26π / 81.68cm

Area: 169π / 531cm²

Step-by-step explanation:

Diameter is radius x 2, so 13 x 2 = 26

Circumference is diameter x π, so 26 x π = 26π / 81.68cm

Area is π x r², so π x 13² = 169π / 531cm²

Answer:

s + r = 60 and 12s + 3r = 90

Step-by-step explanation:

I just took the quiz and it said this is correct

To approximate the stationary matrix S for the transition matrix P, we need to compute powers of the transition matrix P until it reaches a stable matrix.

Starting with P = [0.37 0.63; 0.19 0.81], we can compute powers of P as follows:

P^2 = P * P

= [0.37 0.63; 0.19 0.81] * [0.37 0.63; 0.19 0.81]

= [0.2746 0.7254; 0.1538 0.8462]

P^3 = P * P^2

= [0.37 0.63; 0.19 0.81] * [0.2746 0.7254; 0.1538 0.8462]

= [0.2421 0.7579; 0.1873 0.8127]

P^4 = P * P^3

= [0.37 0.63; 0.19 0.81] * [0.2421 0.7579; 0.1873 0.8127]

= [0.2222 0.7778; 0.1941 0.8059]

Continuing this process, we find:

P^5 = [0.2149 0.7851; 0.1957 0.8043]

P^6 = [0.2124 0.7876; 0.1961 0.8039]

P^7 = [0.2117 0.7883; 0.1961 0.8039]

As we can see, the matrix P^7 is very close to the stationary matrix S. Therefore, we can approximate the stationary matrix S as:

S ≈ [0.2117 0.7883; 0.1961 0.8039]

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Step-by-step explanation:

Radius = Half of Diameter

r = 8/2

= 4 in.

Area of Circle =

[tex]\pi {r}^{2} \\ = \pi( {4}^{2} ) \\ = 16\pi \: {in}^{2} [/tex]

Answer:

42 inches

Step-by-step explanation:

1 FT=12 inches

One half FT=6 inches

12×3=36

36+6=42

Answer:

42 inches

Step-by-step explanation:

The question is basically asking you to convert 3 1/2 ft into inches. Since there are 12 inches in a feet you have to multiply 3 1/2 by 12. It easier to do it when you turn 3 1/2 into a decimal, which would be 3.5. So then, you multiply 3.5 by 12, to get 42 inches.

12 inches = 1 feet

3 1/2 = 3.5

3.5 x 12 = 42

The house will be 42 inches tall.

Answer:

d

Step-by-step explanation:

answer: he increased 40 pound

Step-by-step explanation: if it gives negative option please select that

Answer:

-3 for the first box and -69 for the second one.

Step-by-step explanation:

Answer:

Tasha has the greater balance at the end of the week.This balance is $381

The account balance is the remaining amount after the deduction of withdrawals from the deposits.

Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.

It is the remaining amount after the deduction of withdrawals from the deposits.

We have,

Tasha:

Initial deposits = $250

Withdrawals = $20

Deposits = $65

Debit card purchases = $46

Balance = $250 - $20 + $65 - $46 = $249

Jamal:

Initial deposits = $200

Withdrawals = $60

Deposits = $135

Debit card purchases = $27

Balance = $200 - $60 + $135 - $27 = $248

We see that Tasha has a greater balance than Jamal and Tasha's balance is greater than Jamal's by $1.

Thus,

Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.

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Answer:

Jackson's opponents planned to use the bank to defeat him in the 1832 presidential campaign. Senators Henry Clay and Daniel Webster were friends of Biddle. ... They thought that if Jackson tried to veto, or reject, the renewal of the charter, he would lose support.

Step-by-step explanation:

The solution to the system of equations by substitution is x = 3 and y = -8.

To solve the system of equations by substitution:

Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:

4x - y = 20

4x = y + 20

x = (y + 20)/4

Substitute this expression for x into the second equation:

-2x - 2y = 10

-2((y + 20)/4) - 2y = 10

(y + 20)/2 - 2y = 10

(y + 20) - 4y = 20

-y - 20 - 4y = 20

-5y = 40

y = -8

Substitute the value of y back into the first equation to find x:

4x - (-8) = 20

4x + 8 = 20

4x = 20 - 8

4x = 12

x = 12/4

x = 3

Therefore, the solution to the system of equations is x = 3 and y = -8.

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Answer:

tee shirt:4

sleeve shirt:3

Step-by-step explanation:

we are given two conditions

we want to figure out how many each type of shirt he bought

let tee and sleeve shirts be t and s respectively

according to the first condition

[tex] \displaystyle t + s = 7[/tex]

according to the second condition

[tex] \displaystyle5t + 6s = 38[/tex]

therefore

our system of linear equation is

[tex] \displaystyle\begin{cases}t + s = 7 \\ 5t + 6s = 38 \end{cases}[/tex]

so

now we need our algebra skills to figure out t and s

to do so we can use substitution method

cancel s from both sides of the first equation:

[tex] \displaystyle t = 7 - s \: \cdots \: i[/tex]

now substitute the value of i equation to the second equation:

[tex] \displaystyle 5(7 - s) + 6s = 38[/tex]

distribute:

[tex] \displaystyle 35 - 5s+ 6s = 38[/tex]

collect like terms:

[tex] \displaystyle s + 35 = 38[/tex]

cancel 35 to both sides:

[tex] \displaystyle \therefore s = 3[/tex]

now substitute the value of s to the i equation:

[tex] \displaystyle t = 7 - 3 \\ \therefore \: t = 4[/tex]

hence,

he bought tee shirt 4 and sleeve shirt 3

Answer:

1776.25

Step-by-step explanation:

35x7=245. 245x7.25=1776.25

Answer:

35 x 24 = 840, 840 hours

840 x 7.25 = $6090 for 35 days

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Hello There!

The circumference is equal to the diameter times π

The diameter given is 9m

NOTE: it says "leave answer in terms of π" meaning that we do not apply π to the diameter

So the answer would be just 9π

Answer:

9

Step by step:

C= 2 x pi x r

c = 2 x pi x 4.5

c=  9 x pi

Rounding the cutoff score to the nearest whole number, the cutoff score that will make a student eligible for the reading program is approximately 108.

To find the cutoff score that will make a student eligible for the reading program, we need to determine the score below which the bottom 14% of students fall.

Since the variable is normally distributed and we know the average score and standard deviation, we can use the Z-score formula to find the cutoff score.

The Z-score formula is:

[tex]\[Z = \frac{X - \mu}{\sigma}\][/tex]

Where:

Z is the Z-score,

X is the raw score,

[tex]\mu[/tex] (mu) is the mean, and

[tex]\sigma[/tex] (Sigma) is the standard deviation.

We want to find the Z-score that corresponds to the bottom 14% of students, which means the area to the left of the Z-score is 0.14.

Using a standard normal distribution table or calculator, we can find the Z-score that corresponds to an area of 0.14, which is approximately -1.08.

Now we can rearrange the Z-score formula to solve for X, the cutoff score:

[tex]\[X = Z \cdot \sigma + \mu\][/tex]

Substituting the values we have:

[tex]\[X = -1.08 \cdot 15 + 124.5\][/tex]

Calculating the expression:

[tex]\[X = -16.2 + 124.5\]\\X = 108.3[/tex]

Rounding the cutoff score to the nearest whole number, the cutoff score that will make a student eligible for the reading program is approximately 108.

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Answer:

3.3/2 = 1.65² x 3.14 = 8.54865

Answer:

it would be $1800

Step-by-step explanation:

if each hoop costs $600, and they buy 3, 600 x 3 = 1800

Answer:

1800

Step-by-step explanation:

600 * 3 = 1800

Answer:

1/3

Step-by-step explanation:

If you're talking about a 6-sided die, then there are 6 sides.  Rolling a 2 or a 3 would be a 2/6 chance.  To simplify if from there, you can also say that there is a 1/3 chance.

Answer:

5/8

Step-by-step explanation:

10 * 2^-4 = 10 * 1/16 = 10/16 = 5/8

Answer:

The last two.

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

For A and B to be mutually exclusive, the value of x must be 0. For A and B to be independent, the value of x can be any value between 0 and 0.3, inclusive.

Two events A and B are said to be mutually exclusive if they cannot occur at the same time, meaning that the intersection of A and B is an empty set. In probability terms, if A and B are mutually exclusive, then P(A and B) = 0.

Given that P(A) = 0.4 and P(A or B) = 0.7, we can use the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B). Since we want to find the values of x for which A and B are mutually exclusive, we set P(A and B) = 0:

0.7 = 0.4 + x - 0

0.7 = 0.4 + x

x = 0.3

Therefore, for A and B to be mutually exclusive, the value of x must be 0. For any other value of x, A and B will have a non-empty intersection and therefore will not be mutually exclusive.

On the other hand, two events A and B are considered independent if the occurrence of one event does not affect the probability of the other event. In probability terms, if A and B are independent, then P(A and B) = P(A) * P(B).

Since P(A) = 0.4 and P(B) = x, we can set up the equation:

P(A) * P(B) = 0.4 * x

For A and B to be independent, this equation must hold for any value of x. Therefore, A and B are independent for any value of x between 0 and 0.3, inclusive.

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Answer:

-6

Step-by-step explanation:

To find the slope, you do y₂ - y₁ / x₂ - x₁

y₂ - y₁ / x₂ - x₁

= -35 - 11 / 5 - 1

= -24 / 4

= -6

The slope is -6

Answer:

-6

Step-by-step explanation:

Hi,

To find the slope when given a table, just pick two points, subtract the y values, and then divide them by the x values after you subtract them as well. Here's what I mean...

Let's use 1, -11 and 5, -35

So...

-35 - (-11)

This is the change in y. -35 - (-11) is the same thing as -35 + 11 (subtracting  negative switches to adding it)

You get -24

Now, the change in x.

5 - 1 = 4

So, -24/4 and you get the slope of : -6

I hope this helps :)

Answer:

The last one is symmetrical.

The first one and the last one are correct.

Answer:

14

Step-by-step explanation:

Answer:

The Answer is B

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here diameter = 12, thus radius = 12 ÷ 2 = 6 and (h, k) = (2.5, - 3.5), thus

(x - 2.5)² + (y - (- 3.5))² = 6², that is

(x - 2.5)² + (y + 3.5)² = 36 ← equation of circle