Use Calculus:
Solve for the second order sensitivity of a bond
Hint: You need to start from the second order Taylor approximation to get delta B and compute first and second order derivative for B and substitute in using Duration and Convexity.

Answer:

t = 7.875 seconds

Step-by-step explanation:

Comment

The formula itself gives you the answer almost directly.

Givens

S(t) = 217 feet

a = - 16

b = 12

Formula

S(t) = - 16t^2 + 126t

0 = -16t^2 + 126t - 217

Solution

You must use the formula for solving a quadratic.

t = (-b +/- (√b^2 - 4*ac)/2a               Substitute the gives into the quadratic formula

t = (-126 +/- √126^2 - 4(-16)(-217) )

t = (-126 +/- √15876) 2*-16

t = (-126 +/- 126) / 2* - 16

There are 2 values for t.                  One is not usable.

t = (-126 + 126)/-32 = 0

so t = 0 so that's impossible

t =  - 252 / - 32                                Combined -126 and - 126

t = 7.875 seconds.

After 7.875 seconds, the ball has gone up 217 feet. The reason you are getting only one answer is likely that you are getting the going up distance. But after the ball has reached its highest point if may have the going down distance = 217 feet from the ground. The formula does not provide it however.                          

Answer:

B.) 132.56 degrees

Step-by-step explanation:

================================================

Explanation:

Check out the diagram below.

Segment BD cuts angle EBC in half

So the two smaller pieces DBC and DBE are congruent. Let's call them x.

Let's make y = angle EBA.

Note how the diagram shows the angles x, x, and y forming a straight angle. So we can say

x+x+y = 180

2x+y = 180

y = -2x+180

We'll use this later.

For now, focus on triangle DEB. Angle E is 90 degrees and angle B is x.

D+E+B = 180

28+90+x = 180

x+118 = 180

x = 180-118

x = 62

Which means

y = -2x+180

y = -2*62+180

y = -124+180

y = 56

Now focus on triangle BEA. We have B = 56, E = 90 and A = z

B+E+A = 180

56+90+z = 180

146+z = 180

z = 180-146

z = 34

which is the measure of angle A.

Evaluating a function means finding the value of the function that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned.

Evaluating our function at x = -4 and x = 6, we have:

and those are our answers.

Answer:

Step-by-step explanation:

Conversion ratio = 8/5 = 1.6

So,

     25.9 miles = 25.9 x 1.6

                       = 41.44 km

Step-by-step explanation:

140/70=2 Therefore, 1 apple equals 2 percent

The remaining 30 percent times 2 equals 60

60 apples plus 140 apples equals 200 apples

Answer B

Answer:

200.

Step-by-step explanation:

70% is equivalent to 140

10 %  .............................. 140/7 = 20 apples

100% ................................. 10*20 = 200.

Answer:

$41.25

Step-by-step explanation:

The original price is $25. You want to sell it for 65% more. To find this amount, we need to find 65% of 25.

Let's make an equation.

65/100 • 25 = x

Multiply.

x = 16.25

Now we know how much you want to mark it up by.

Add this to your base of $25.

25 + 16.25

= 41.25

You want to sell it for $41.25.

Hope this helps!

The correct answer for the transformation will be:

translation up π/4

vertical stretch by 2

translation right π/4

The parent function of g(x) is y = sin(x), and g(x) is obtained from the parent function by performing the following transformations:

Translation: The argument of sin(x) is shifted by π/4 units to the left, which results in a horizontal translation to the right by π/4 units.

Vertical stretch: The amplitude of the sine function is multiplied by 2, which results in a vertical stretch by a factor of 2.

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Answer:

what´s the question????

Step-by-step explanation:

Answer:

$6.35

Step-by-step explanation:

10 quarters =

10 × .25 = $2.50

17 dimes =

17 × .10 = $1.70

40 nickels =

40 × .05 = $2.00

15 pennies =

15 × .01 = $0.15

2.50+1.70+2.00+.15

= 6.35

The total is $6.35.

Answer:

310 miles

Step-by-step explanation:

Hello,

62 mph for 5 hours

it means that in 1 hour he drives 62 miles

so in 5 hours he drives 5*62 = 310 miles

hope this helps

Answer:

310 miles

Step-by-step explanation:

he drove an average speed of 62 mph for 5 hours

62x5=310

so he drove 310 miles

Answer:

Yes, it is a rational number

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃  = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

What is a nonlinear function?

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃ = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

Answer:

The correct answer is 5b²-b-2

The effective interest method is used to amortize the bond premium. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond. The journal entry for bond issuance is as follows: Dr. Cash 205,000, Dr. Premium on Bonds Payable 5,000, Cr. Bonds Payable 210,000

The effective interest method is a method of amortizing bond premium or discount that takes into account the time value of money. The effective interest is the interest that would be earned if the bond were purchased at its market value and held to maturity. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond.

The journal entry for bond issuance records the proceeds from the sale of the bonds, the premium on bonds payable, and the bonds payable. The proceeds from the sale of the bonds are equal to the face value of the bonds plus the premium.

The premium on bonds payable is a liability that represents the excess of the issue price of the bonds over their face value. The bonds payable account is a long-term liability that represents the amount that the company owes to the bondholders.

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The formula for for Rn is given as Rn = Σ 18/n (1 - 12i/n + 36i²/n²).

We are given the function f(x) = 3x² on the interval [-1, 5] . This gives

Δx =6/n and xi= -1 + 6i/n.

Therefore,

Rn =  Σ f(xi) Δx

     = Σ 3 (-1 + 6i/n)² 6/n

     = Σ 18/n (1 - 12i/n + 36i²/n²)

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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a) The state transition graph for the HMM would show the two states as nodes, with directed edges. b) the most likely sequence for the three days would be Los Angeles (S2), Los Angeles (S2), and San Diego (S1). c) We can use the forward-backward algorithm.

(a) The Hidden Markov Model (HMM) for this scenario can be represented using matrices and vectors. Let's define the following:

- States:

 - S1: San Diego office

 - S2: Los Angeles office

- Observation symbols:

 - O1: Working between six and eight hours

 - O2: Working more than eight hours

 - O3: Working less than six hours

- Initial state probability:

 - π = [0.6, 0.4] (new employee assigned to Los Angeles with probability 0.4 and San Diego with probability 0.6)

- Transition matrix:

 - A = [[0.65, 0.35],

        [0.8, 0.2]] (probability of transitioning from one office to another)

- Observation matrix:

 - B = [[0.7, 0.2, 0.1],

        [0.15, 0.25, 0.6]] (probability of observing each working hour category in each office)

- Final state probabilities (not needed for this question).

The state transition graph for the HMM would show the two states (San Diego and Los Angeles) as nodes, with directed edges indicating the transition probabilities between states.

(b) To find the most likely sequence of places the employee worked in the first three days, we can use the Viterbi algorithm. Given the observations: 6.5, 10, 7 (representing the number of hours worked each day), we want to find the sequence of states that maximizes the probability of observing these hours.

Using the HMM parameters defined in part (a), we can apply the Viterbi algorithm to calculate the most likely sequence of states. In this case, the most likely sequence for the three days would be Los Angeles (S2), Los Angeles (S2), and San Diego (S1).

(c) To find the sequence of three places that has the maximum expected number of correct places, we can use the forward-backward algorithm. This algorithm calculates the probability of being in a certain state at a given time, given the observations.

Using the HMM parameters from part (a), we can apply the forward-backward algorithm to compute the probabilities of being in each state at each time step. By examining these probabilities, we can determine the sequence of three places that has the maximum expected number of correct places. The specific sequence would depend on the calculated probabilities and may vary based on the given observations and the HMM parameters.

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The required probabilities for the events in question are:

Based on the parameters given :

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Total number of slots = 18+18+2 = 38

A.)

Probability of green slots 2 or more times :

(2/38)² × (36/38)²³ = 0.00080

B.)

Probability of ball not entering the green slots

1 - P(green slots)

P(not entering green slot ) = 1 - 0.0008 = 0.9992

C.)

probability that ball falls into black slot 15 or more times :

(18/38)¹⁵ * (20/38)¹⁰ = \(2.21\times10^{-8}\)

D.)

Probability that ball falls into red slot 10 or less times :

(10/38)¹⁰ * (28/38)¹⁵ = \(1.63\times10^{-8}\)

Therefore, the required probabilities are :

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Answer:

n = 4

Step-by-step explanation:

To solve for n, you need to undo what is being done to the variable. Since n is being multiplied by 5, you must divide both sides of the equation by 5.

1. (5n)/5 = 20/5

2. n = 4

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\(5n=20\)

Divide 5 from both sides.

\(5n/5=20/5\)

\(n\) does not have a coefficient now.

\(n=4\)

No, events A (the number is even) and B (the number is a multiple of 3) are not independent.

For events A and B to be independent, the probability of event A occurring should be unaffected by the occurrence or non-occurrence of event B, and vice versa. To determine if events A and B are independent, we examine the probabilities of each event separately.

Event A: The probability of selecting an even number from the given range is 25/50 = 1/2, as there are 50 integers in the range and half of them are even. Event B: The probability of selecting a multiple of 3 from the range is 16/50, as there are 16 integers in the range that are divisible by 3.

If events A and B are independent, then the probability of both events occurring should be equal to the product of their individual probabilities. However, in this case, the probability of both events occurring is (1/2) * (16/50) = 8/50, which is not equal to the product of their individual probabilities. Therefore, we can conclude that events A and B are not independent.

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Answer:

Step-by-step explanation: wjbsgstexrczlkcidgxtftwdcwdkfmw,d,f

Answer:

Step-by-step explanation:

There are five bars on a box-and-whisker graph, from left to right, that correspond to designated graph values. These five bars are the minimum, first quartile (Q1), median, third quartile (Q3) and maximum. You can tell the minimum and maximum bars from the quartile and median bar because they're the ones that stick outside of the box - hence the name box and whisker. Here's a graph to make it clearer.

OK, let's go through each of the problems one by one.

Answer:

(-45,0)

Step-by-step explanation:

The given data is,A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers.

Of the 60 subjects who participate in the study, 21 prefer the instant coffee. We need to find the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee, let's say p. The formula to calculate the proportion of the population is:

p = (n1 + n2) / (x1 + x2)n1 and n2 are the sample sizes of two categories and x1 and x2 are the number of favorable outcomes from the respective categories. Here, n1 = n2 = 60 and x1 = 39 (since 21 out of 60 prefer instant coffee, the remaining 39 must prefer fresh-brewed coffee).Now, p = (60 + 60) / (39 + 21) = 1.2. Since p is a probability, it must be between 0 and 1. But here, p is greater than 1, which is not possible. Therefore, there is an error in the given data and we cannot proceed with the calculation.

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Answer:

60%

Step-by-step explanation:

Tina has 3 quarters, 1 dime, and 6 nickels, or 10 coins in total.

They are asking for the probability of drawing a nickel (6 in total). Divide 6 from the total amount of coins:

6/10 = 0.60, or 60%

Tina has a 60% chance of drawing a nickel from her pocket.

~

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer:

The voltage is 110 V

Step-by-step explanation:

Given;

current in the circuit, I = 20 A

resistance in the circuit, R = 5.5 Ω

voltage in the circuit, V = ?

Voltage is given as = current x resistance

V = IR

V = 20 x 5.5

V = 110 V

Therefore, the voltage necessary to generate 20 amps of current in a circuit that has 5.5 ohms of resistance is 110 volts.