FL7_03: Finance Charges
Hugo is buying his first car, which costs $1 0 000. He wants to pay the car off in five years.
The following options are available.
Option A: Car Dealership Financing
No money down. $250 per month for five years.
Option B: Bank Loan
$250 processing fee. Interest is charged at a rate of per year simple interest for
borrowing $10 000. The total loan repayment, with interest, is due at the end of five years.
Option C: Family Financing
Hugo's mother will lend him $2000 interest free. He must borrow the rest of the money he
needs from a financial company at an annual rate of 9.5% simple interest.
1 . Determine the total finance charge of each option. Rank them in order from least to
greatest. You may use online interest calculators or other mathematical tools and
strategies.

The sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

We will use the method of percentage to solve the given question.

We are given:

A basketball backboard set that sold for $79 is discounted by 15%.

We need to find the sale price after the discount is given.

We will subtract the discount from the marked price.

Let us solve this;

Sale price = marked price - discount

Sale price =  $79 - $79 * 15%

Sale price =  $79 - $79 * 15 / 100

Sale price =  $79 - $11.85

Sale price = $67.15

So, the sale price will be $67.15.

Thus, the sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

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The probability that a student picked at random can speak French or German is 0.28

Total number of people = 100

People who can speak French = 20

People who can speak German = 14

People who can speak both = 6

Calculating the probability of the union of two events is:

P(A or B) = P(A) + P(B) - P(A and B)

Let the event that a person can speak French = A

Let the event that a person can speak German = B

Therefore.

P(A) = (20 out of 100 people can speak French)

= 20/100

= 0.2

P(B) = (14 out of 100 people can speak German)

14/100

= 0.14

P(A and B) = 6 out of 100 people can speak both French and German)

= 6/100

= 0.06

Therefore, the probability of the union of events A and B:

P(A or B) = P(A) + P(B) - P(A and B)

= 0.2 + 0.14 - 0.06

= 0.28

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We can start by using the standard normal distribution to find the z-scores for the two heights:

z1 = (176 - 180) / 4 = -1

z2 = (180 - 180) / 4 = 0

Then, we can use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores. From a table, we find that the area to the left of -1 is 0.1587 and the area to the left of 0 is 0.5. Therefore, the area between -1 and 0 is:

0.5 - 0.1587 = 0.3413

To find the percentage of the population, we can convert this decimal to a percentage by multiplying by 100:

0.3413 x 100 = 34.13%

Therefore, approximately 34.13% of the population would lie between 176cm and 180cm in height.

Answer:

1

Step-by-step explanation:

m=y2-y1/x2-x1

  =8-4/4-0

  =1

Answer:

1.5 cups of sugar

Step-by-step explanation:

Given:

-You need a 1/4 cup of sugar for 3 cups of Kool-Aid

-You need to find the amount of sugar you need for 18 cups of liquid

Solution:

You need to find how many recipes you need

3x = 18

So x = 6

Now you need to multiply 1/4 by 6 to find the amount of sugar

That would be 6/4 which is 1.5

So you need 1.5 cups of sugar for 18 cups of Kool-Aid

The standard deviation needed to achieve a process capability index of 2.0 is 0.003 feet.

To calculate the required standard deviation to achieve a process capability index of 2.0, we need to use the following formula:

Process Capability Index (Cpk) = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)

In this case, the upper specification limit is 1.788 feet, the lower specification limit is 1.752 feet, and the process capability index (Cpk) is 2.0.

Let's plug in the values into the formula and solve for the standard deviation:

2.0 = (1.788 - 1.752) / (6 * Standard Deviation)

Rearranging the equation:

Standard Deviation = (1.788 - 1.752) / (6 * 2.0)

Standard Deviation = 0.036 / 12

Standard Deviation = 0.003

Therefore, the standard deviation needed to achieve a process capability index of 2.0 is 0.003 feet.

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\(\bold{\huge{\blue{\underline{ Solution }}}}\)

We have,

Let the width of the rectangular trampoline be w

According to the question,

The length of the rectangular trampoline will be

\(\sf{ = (W + 6 )ft }\)

We know that,

\(\bold{\blue{ Area\: of\: rectangle = Length × Breath }}\)

Subsitute the required values,

\(\sf{ 135 = w(w + 6 ) }\)

\(\sf{ 135 = w² + 6w}\)

\(\sf{ = w² + 6w - 135 }\)

By factorization method,

\(\sf{ = w² - 9w + 15w - 135 }\)

\(\sf{ = w( w - 9) + 15( w - 9)}\)

\(\sf{ = ( w + 15) ( w - 9)}\)

Therefore,

Width of the rectangular trampoline

\(\sf{ w = - 15 \: or\: w = 9 }\)

[ Width of the rectangle can never be negative ]

Thus , The width of the rectangular trampoline is 9 feet

\(\bold{\pink{ Hence\:, Option \:D\: is\: correct }}\)

Answer :

Explanation :

Given :

To find :

Solution :

Let us assume the width of the rectangle as w and therefore the length becomes (w + 6) .

We know that,

\({ \qquad \dashrightarrow \bf{Length \times Width =Area _{(rectangle)} }}\)

Substituting the values in the formula :

\( {\qquad \sf \dashrightarrow (w + 6)w = 135}\)

\({\qquad \sf \dashrightarrow {w}^{2} + 6w = 135}\)

\({\qquad \sf \dashrightarrow {w}^{2} + 6w - 135 = 0}\)

\({\qquad \sf \dashrightarrow {w}^{2} + 15w - 9w - 135 = 0}\)

\({\qquad \sf \dashrightarrow {w}(w + 15) - 9(w + 15) = 0}\)

\({\qquad \sf \dashrightarrow (w + 15) (w - 9) = 0}\)

\({\qquad \sf \dashrightarrow (w + 15) = 0}\)

\({\qquad \sf \dashrightarrow w = - 15}\)

\({\qquad \sf \dashrightarrow (w - 9) = 0}\)

\({\qquad \sf \dashrightarrow w = 9}\)

The width of the rectangle cannot be negative therefore the width of the rectangle must be 9 feet .

Answer:

It's the third option

Step-by-step explanation:

the domain is all the x values

Using the Integral Test, the correct choice is B. Since the integral ∫(k+7)dx diverges, the series also diverges.

We are supposed to use Integral Test to determine the convergence or divergence of the series, ∑(k+7)dx.

We can use the Integral Test to test for the convergence of series if the function in the series is continuous, positive, and decreasing for all x greater than or equal to some value N.

The Integral Test states that a series converges if and only if the integral of the series term is convergent, i.e. if the integral of u(x)dx is convergent. Also, if the integral of u(x)dx diverges, the series is divergent.

So we need to check whether the function in the given series is continuous, positive, and decreasing for all x greater than or equal to some value N.

If we integrate the series, ∑(k+7)dx, we get:∫(k+7)dx= ∫k

dx + ∫7dx= (k²/2) + 7x+ C

where C is the constant of integration.

Since the value of C is not given, we cannot say anything about the exact value of the integral.

However, the value of the constant of integration does not matter in this case as we only need to determine whether the integral converges or diverges.

Therefore, we can use the Integral Test to determine the convergence or divergence of the series.

Using the Integral Test, the correct choice is B.

Since the integral ∫(k+7)dx diverges, the series also diverges.

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Answer:

DC⊥EF as the 2 angles in smallest triangle are 30 and 60 degrees, so the last one is 90 making Line DC perpendicular to Line EF.

Step-by-step explanation:

DC⊥EF means that Line DC is perpendicular (90 degrees) to EF.

To prove this, we can use the two angles of the small triangle created by the intersection of the triangles AEF and DCB.

The remaining angle of triangle AEF is 60, as all angles of triangles add up to 180 (so 180 - 12 = 60). This angle at F is shared with the little triangle.

Now we will get the angle at D using the triangle DCB. Since we are given two angles 90 and 60, angle D has to be 30.

So of our little triangle, we have angles 30 and 60, meaning the last one is 90 degrees and hence, DC⊥EF

Answer:

-3 or 6 I would put -3 but... its your wish

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

3x + 12 - 2x = 9

Subtract 3x - 2x

x + 12 = 9

subtract 12 to both sides

x = -3

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the probability that at least 3 phones are defective in a random sample of 37 phones is approximately 0.7889

To calculate the probability that at least 3 phones are defective in a random sample of 37 phones, we can use the binomial probability formula. The formula for the probability of at least a certain number of successes in a binomial distribution is:

P(X ≥ k) = 1 - P(X < k)

Where:

P(X ≥ k) is the probability of at least k successes

P(X < k) is the probability of less than k successes

In this case, "success" refers to a defective phone, and the probability of a phone being defective is 11% or 0.11. The sample size is 37 phones.

To calculate the probability, we need to sum up the probabilities of having 3, 4, 5, ..., up to 37 defective phones. We can use this formula:

P(X < k) = Σ (n choose i) * p^i * (1 - p)^(n - i)

Where:

n is the sample size (37)

i is the number of defective phones (ranging from 0 to k-1)

p is the probability of a defective phone (0.11)

Let's calculate the probability:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the formula above, we can calculate each term:

P(X = 0) = (37 choose 0) * 0.11⁰ * (1 - 0.11)³⁷

P(X = 1) = (37 choose 1) * 0.11¹ * (1 - 0.11)³⁷

P(X = 2) = (37 choose 2) * 0.11² * (1 - 0.11)³⁵

Now, let's calculate each term and sum them up:

P(X = 0) = (1) * (1) * (0.89)³⁷ = 0.0134

P(X = 1) = (37) * (0.11) * (0.89)³⁶ = 0.0613

P(X = 2) = (666) * (0.11)² * (0.89)³⁵ = 0.1364

Finally, calculate the probability:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.0134 + 0.0613 + 0.1364

= 0.2111

P(X ≥ 3) = 1 - P(X<3)

= 1 - 0.2111

=  0.7889

Calculating this value, the probability that at least 3 phones are defective in a random sample of 37 phones is approximately 0.7889

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To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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The answer is x = 3 1/2. To solve, you must multiply both sides of the equation by the denominator of the fraction on the left side, which is 3. This will cancel out the fraction and you will be left with 4 1/3 - x = -3, which can then be solved by adding x to both sides.

4 1/4 - 1/3x

= (12/3) - (1/3)x

= 4 1/3 - x

= 4 1/3 - x -3

= x - 3

= x + 3

= 3 1/2

To solve the equation 4 1/4 − 1/3x = −3/4, you must first multiply both sides of the equation by the denominator of the fraction on the left side, which is 3. This will cancel out the fraction and you will be left with 4 1/3 - x = -3. Then you can add x to both sides of the equation to get 4 1/3 = x - 3. Then you can add 3 to both sides of the equation to get x = 3 1/2. So the answer is x = 3 1/2. This process is necessary because fractions need to be canceled out before you can solve the equation. If you do not cancel out the fractions first, then you will not be able to solve the equation correctly. It is important to remember that when you are solving equations with fractions, you must cancel out the fractions before you solve the equation.

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Answer: 9,585

Step-by-step explanation:

Answer:

$9,585.00

6.5x9000 over 100

Declare X As Integer

Declare Y As Integer

For (X = 1; X <=2; X++)

For (Y = 3; Y <= 4; Y++)

Write X * Y

End For(Y)

End For(X)

3, 4, 6, 8

1, 3, 2, 4

4, 5, 5, 6

None of these are correct output

None of these are correct output3, 4, 6, 8

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.

Therefore, the correct answer is as given above

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The percent increase in the flight increase is \(18.35\)%

Definition of percentages.

A percentage is a ratio of some value out of a hundred.

With this definition in mind, if \(20\)% of \(200\) students have a test tomorrow, then a total of \(40\) students have a test tomorrow.

Percentage Increase Calculation Example #1

For the first example, we find the percentage increase for the following scenario:

If your total savings of $\(60\) at the beginning of the week grew to $\(90\) by the end of the week, what is the percentage increase?

This is where our three-step process comes in:

Step 1: Find the difference in values ​​by subtracting the initial value from the final value.

In this case, the final value minus the initial value can be calculated as follows:

\(90 -60 = 30\)

So in this example, the difference between the two values ​​would be \(30\). Remember that when calculating the percentage increase, you will always subtract the smaller value from the larger value.

Step 2:Divide the difference by the initial number

The next step is to take the difference (\(30\) in this example) and divide it by the starting number (\(60\) in this example) like this:

\(30/60 = 0.50\)

Always express your answer as a decimal (this will make your life a lot easier when you get to step three).

Step 3: Multiply by \(100\)

The last step is to multiply the decimal result from step two by one hundred and express the final result as a percentage.

\(0.50 * 100 = 50\)

Final answer: 50% increase

That is all! Using three steps, you can conclude that there was a \(50\)% increase in the money you had from the beginning of the week to the end of the week.

Hence percent increase can be found as follows:

=$\((432-365)/365*100\)

=\(18.35\)%

Therefore, a percent increase in the flight increase is \(18.35\)%

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The largest profit for the sales of pencils and pen is 616 cents

We have

x = pencils

y = pens

So, we have

3 * 15 + 5 * 25 ≤ 400

Evaluate

170  ≤ 400 --- proved

Here, we have

The number of pens must not be greater than the number of pencils

This means that

y < x

Here, we have

There must be at least 35 pens

This means that

y ≥ 35

The inequalities to plot are

3x + 5y ≤ 400, y < x and y ≥ 35

See attachment for the three lines and the  regions shaded

Here, we have

x = 70

From the graph, we have

y = 38

Here, we have

Profit = Sum of products of items and individual profits

So, we have

Largest = 70 * 5 + 38 * 7

Largest = 616

Hence, the largest profit is 616 cents

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Slope = change in y over change in x:

Slope = (-6 6) / 2- -6) = -3/2

Equation of a line is y = Mx + b, where m is the slope and b is the y intercept.

Y = -3/2x + b

Replace y and x with one of the given points and solve for b:

6 = -3/2(-6) + b

6 = -9 + b

B = -9 + 6

B = -3

The equation of the line is y = -3/2x-3

Answer:

1/1000

Step-by-step explanation:

The dynamics of the asset price with constant mean and diffusion processes, and its solution is lognormally distributed.

The asset price SDE with constant mean and diffusion processes can be given by the equation below:

dSt = μSdt + σSdWt

where; μ: Constant mean

σ: Diffusion rate

Wt: Brownian motion

As we have assumed that the asset price is lognormally distributed, then its dynamics can be given by the following SDE:

dS = μSdt + σSdZ

where; Zt = dWt + μdt is a geometric Brownian motion

Therefore, to solve this SDE, we will use the following steps below:

Let's assume that S0 is the initial asset price;\(S1 = S0e^(μT + σZ√T)\)

where T is the time horizon

Let's now compute the expected value of S1;

\(E(S1) = E(S0e^(μT + σZ√T))= S0e^(μT + ½σ²T)\)

We can then compute the variance of S1;

Var(S1) = E(S1²) - [E(S1)]²Var(S1)

\(= [S0²e^(2μT + σ²T)] - [S0e^(μT + ½σ²T)]²Var(S1)\)

\(= S0²e^(2μT + σ²T) - S0²e^(2μT + σ²T)²\)

The solution to the SDE is then given by: \(St = S0e^(μt + σZ√t)\)

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The possible propagated error in computing the area of the triangle is approximately 8.8 cm².

To approximate the possible propagated error in computing the area of the triangle, we can use differentials.

Let's denote the base of the triangle as b and the altitude as h. We are given that b = 26 cm and h = 44 cm, with a possible error in each measurement of 0.25 cm.

The formula for the area of a triangle is A = (1/2) * b * h. To find the propagated error in the area, we will differentiate this formula with respect to both b and h.

∂A/∂b = (1/2) * h
∂A/∂h = (1/2) * b

Now, let's calculate the propagated error in the area. We will use the differentials (∆A, ∆b, and ∆h) to represent the changes in the area, base, and altitude, respectively.

∆A = (∂A/∂b) * ∆b + (∂A/∂h) * ∆h

Substituting the partial derivatives and the given possible errors, we have:

∆A = (1/2) * h * ∆b + (1/2) * b * ∆h

∆A = (1/2) * 44 cm * 0.25 cm + (1/2) * 26 cm * 0.25 cm

∆A = 5.5 cm² + 3.25 cm²

∆A ≈ 8.8 cm²

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Answer:

where's the picture. to the nearest mile...

Step-by-step explanation:

;-;

x + 3y + 1/2z

(4x + 12y + 2z)/4         <----- Divide the whole expression by 4

Answer:

x=53°

y=24°

m∠x+m∠y

53+24=77

Step-by-step explanation:

Option-C is correct that is increase, wider. If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.

Given that,

By completing the blanks, the sentence is complete. When generating a confidence interval, the margin of error and the confidence interval will be larger if the level of confidence grows.

We have to find the accuracy of the confidence interval will increase with a larger sample size, so the margin of error and the confidence interval will be-----.

We know that,

If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.

The margin of error is a phrase that conveys how much sampling error there is in the data that was gathered or in the parameter estimates. Accordingly, the credibility of the poll will decrease as the margin of error increases. It displays the degree of estimation accuracy.

Three things determine the margin of error:

Confidence level: The margin of error grows in proportion to the level of confidence.

Sample size: The margin of error gets smaller as the size of the random sample gets bigger.

Population standard deviation: The population's standard deviation is: For a given level of confidence, our interval will be wider the more dispersed the population is.

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