i would like help finding the inverse

Answer:

[tex] \frac{1}{3} \pi( {3.5}^{2} )(11) = 44.9\pi[/tex]

C is the correct answer.

The bond price at 12% maturity is $435.42, at 10% maturity is $500.00, at 8% maturity is $607.28, and at 6% maturity is $748.65. The balance at the end of 28 months is approximately $41,097,019.67.

To determine the price of the bond at different yield to maturity rates, we need to use the bond pricing formula

Bond price = (Coupon payment / (1 + YTM)¹) + (Coupon payment / (1 + YTM)²) + ... + (Coupon payment + Face value) / (1 + YTM)ⁿ

Where Coupon payment = Annual coupon rate x Face value

YTM = Yield to maturity

n = Number of years to maturity x Number of coupon payments per year

Using $1,000 as the face value and an annual coupon rate of 10%, we have

At 12% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.12)¹) + ($100 / (1 + 0.12)²) + ... + ($100 + $1,000) / (1 + 0.12)⁴⁰

Bond price = $435.42

At 10% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.10)¹) + ($100 / (1 + 0.10)²) + ... + ($100 + $1,000) / (1 + 0.10)⁴⁰

Bond price = $500.00

At 8% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.08)¹) + ($100 / (1 + 0.08)²) + ... + ($100 + $1,000) / (1 + 0.08)⁴⁰

Bond price = $607.28

At 6% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.06)¹) + ($100 / (1 + 0.06)²) + ... + ($100 + $1,000) / (1 + 0.06)⁴⁰

Bond price = $748.65

To calculate the monthly payment and balance of the loan from the bank, we can use the formula for the monthly payment of an amortizing loan

P = (r × A) / (1 - (1 + r)⁻ⁿ)

where P is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), A is the loan amount, and n is the total number of months in the loan.

First, we need to calculate the values of r, A, and n

r = 0.08 / 12 = 0.00667 (monthly interest rate)

A = $50,000,000 (loan amount)

n = 5 years × 12 months/year = 60 months (total number of months in the loan)

Now, we can plug these values into the formula to calculate the monthly payment

P = (0.00667 × $50,000,000) / (1 - (1 + 0.00667)⁻⁶⁰)

P ≈ $1,029,299.29

Therefore, the monthly payment on the loan is approximately $1,029,299.29.

To find the balance at the end of 28 months, we can use the formula for the remaining balance of an amortizing loan

B = (P * (1 - (1 + r)⁻ⁿ')) / r

where B is the remaining balance, r is the monthly interest rate, P is the monthly payment, and n' is the number of months remaining in the loan (which is equal to the total number of months minus the number of months already paid).

After 28 months, the number of months remaining in the loan is

n' = 60 - 28 = 32

We can now plug the values of P, r, and n' into the formula to find the balance

B = ($1,029,299.29 × (1 - (1 + 0.00667)⁻³²)) / 0.00667

B ≈ $41,097,019.67

Therefore, the balance at the end of 28 months is approximately $41,097,019.67.

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The length of GF is 4 cm minus half the length of side FH.

To do this, we can use the fact that point S is the midpoint of FH. This means that FS = 1/2 FH. Similarly, point T is the midpoint of GH, so TG = 1/2 GH. We can now use these equalities and the fact that SG = 4 cm and HT = 6 cm to set up an equation involving FH:

SG + GF + HT = ST + TG + FH

Substituting the given values and using the fact that TG = GH - TG = GH - 1/2 GH = 1/2 GH, we get:

4 cm + GF + 6 cm = 8 cm + 1/2 GH + FH

Simplifying and substituting FS = 1/2 FH and TG = 1/2 GH, we get:

10 cm + GF = 8 cm + FS + TG

GF = 8 cm + FS + TG - 10 cm

GF = 1/2 FH - 1/2 GH

Now, substituting the values we know, we get:

GF = 1/2 FH - 1/2 GH

GF = 1/2 (FS + SH) - 1/2 (GH)

GF = 1/2 (8 cm + SH) - 1/2 (GH)

GF = 1/2 (8 cm + FS) - 1/2 (GH)

GF = 1/2 (8 cm + 1/2 GH) - 1/2 (GH)

GF = 3 cm - 1/4 GH

We can now substitute TG = 1/2 GH and solve for GH:

TG = 1/2 GH

8 cm - FS = 1/2 GH

GH = 16 cm - 2 FS

Substituting this value into the expression for GF, we get:

GF = 3 cm - 1/4 (16 cm - 2 FS)

GF = 3 cm - 4 cm + 1/2 FS

GF = 1/2 FS - 1 cm

Finally, substituting FS = 8 cm - SH, we get:

GF = 1/2 (8 cm - SH) - 1 cm

GF = 4 cm - 1/2 SH

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Complete Question:

Points S and T are midpoints of the sides of triangle FGH

when HT = 6cm, ST = 8 cm, SG = 4CM

what is GF ?

Answer:

[tex] 36 < 47 < 49[/tex]

[tex] \sqrt{36} < \sqrt{47} < \sqrt{49} [/tex]

[tex]6 < \sqrt{47} < 7[/tex]

√47 is approximately 6.9

The graph of y=4[tex](2)^{x}[/tex]-3 is the same as the graph of y=4[tex](2)^{x}[/tex] shifted downwards by 3 units.

The function y=4[tex](2)^{x}[/tex] is an exponential function with base 2 and vertical intercept at (0, 4).

To translate this function to the graph of y=4[tex](2)^{x}[/tex]-3, we need to shift the graph downwards by 3 units. This can be achieved by subtracting 3 from the original function as follows:

y = 4[tex](2)^{x}[/tex] - 3

Now, the vertical intercept of the new function y=4[tex](2)^{x}[/tex]-3 is at (0, 1), which is 3 units below the intercept of the original function.

Notice how the entire graph has shifted down by 3 units, while maintaining the same shape as the original exponential function y=4[tex](2)^{x}[/tex].

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Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x-1)} +2[/tex]

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

Therefore, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 2) + 2

[tex]g(x) = -\sqrt{9(x-1)} +2[/tex]

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The median is 81.5.

The median of the lower half of the data is 67.

The median of the upper half of the data is 92.

Given a data set,

82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85

Median of a data set is the middle element when the data are arranged in a order.

Arranging in ascending order,

51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98

There are even number of data sets.

So, Median = Average of the middle two elements.

Median = (81 + 82) / 2 = 81.5

Lower half of the data set is,

51, 56, 62, 72, 79, 81

Median = (62 + 72) / 2 = 67

Upper half of the data set is,

82, 85, 89, 95, 97, 98

Median = (89 + 95) / 2 = 92

Hence the median is 81.5, lower half median is 67 and upper half median is 92.

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A sample size of 176 tenth graders would be needed in order to estimate the fraction of students with reading skills at or below the eighth grade level at a 99% confidence level having an error of at most 0.03.

To calculate the sample size required for estimating the fraction of tenth graders with reading skills at or below the eighth grade level, we can use the formula for sample size estimation for proportions;

n = (ZZ × p × (1 - p)) / (EE)

where; n = sample size

Z = Z-score corresponding to the desired confidence level (in this case, the Z-score for a 99% confidence level, which is approximately 2.626)

p = estimated population proportion (in this case, 0.22)

E = desired margin of error (in this case, 0.03)

Plugging in the given values;

n = (2.6262.626 × 0.22 × (1 - 0.22)) / (0.030.03)

n = 0.15774 / 0.0009

n ≈ 175.27

Since we need to round up to the next integer, the sample size required would be 176.

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Answer:

Step-by-step explanation:

No, the corresponding angles are not congruent.,

They have to be EXACTLY the same.

Lol i am learning this to.

The rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.

Use the formula A=pi*r^2 to calculate the area of the circle when the radius is 44cm.

A=pi*r^2

A= 3.14159*(44 cm)^2

A= 6081.816 cm^2    

Use the formula A'=2pi*r*r' to calculate the rate of change of the area.

A'=2pi*r*r'

A'= 2*3.14159*44 cm*(7 cm/s)

A'= 97.636 cm^2/s

The area of a circle is calculated by the equation A=pi*r^2, where r is the radius of the circle. At the instant when the radius of the circle is 44 centimeters, the area is 6081.816 cm^2.

To calculate the rate of change of the area, we use the equation A'=2pi*r*r', where r' is the rate of change of the radius.

In this case, the radius of the circle is decreasing at a rate of 7 cm/s, so r'=7 cm/s. Plugging these values into the equation, we get A'=2*3.14159*44 cm*(7 cm/s), which equals 97.636 cm^2/s.

Therefore, the rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.

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complete question:

the radius of a circle is decreasing at a constant rate of 7 centimeters per second. at the instant when the radius of the circle is 44 centimeters, what is the rate of change of the area? round your answer to three decimal places.

The sum of the interior angle of the regular hexagon is S = 720°

Given data ,

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

when n = 6 for a hexagon , we get

nθ = 180 ( 6 - 2 )

nθ = 180 x 4

nθ = 720°

Hence , the sum of interior angles of a hexagon is 720°

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Answer:kbef;eohrjkvoubwe

cv bojbDetectives are unsure whether Kendall Postwell will be able to testify at her trial. They say it is a question of competence. What does this MOST likely mean?

A.

Kendall might be determined to be insane and not qualified to testify.

B.

The evidence in Kendall’s case is inconclusive and doesn’t prove anything.

C.

Kendall is an expert witness who has testified many times before.

D.

The police think it will hurt their case if Kendall chooses to testify.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Arc length= [tex]\frac{interior angle}{360} 2\pi r[/tex]

The measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula. So option A is correct.

The secant tangent angle is the angle formed by a tangent and a secant that intersect outside of a circle. The measure of the secant tangent angle can be found using the following formula:

θ = 1/2 (arc EB - arc BD)

where arc EB and arc BD are the measures of the arcs intercepted by the secant and tangent, respectively.

From the question,

θ = m∠PQR

arc EB = 160°

arc BD = 60°

m∠PQR = 1/2(160° - 60°)

m∠PQR = 1/2 × 100°

m∠PQR = 50°

Therefore, the measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula.

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The amount of $5000 is invested at 12% and $2000 is invested at 8%.

Let x be the amount invested at 8% and y be the amount invested at 12%. We know that the total amount invested is $7000, so we have:

x + y = 7000

We also know that the annual interest earned is $580. The amount of interest earned from the investment at 8% is 0.08x, and the amount of interest earned from the investment at 12% is 0.12y. So we have:

0.08x + 0.12y = 580

We now have two equations with two variables. We can solve for one variable in terms of the other in the first equation and substitute it into the second equation:

x = 7000 - y

0.08(7000 - y) + 0.12y = 580

560 - 0.08y + 0.12y = 580

0.04y = 20

y = 500

So $5000 is invested at 12% and $2000 is invested at 8%.

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Answer:

Yes, it is possible to have a function f:A→B with an element b∈B so that f does not assign any element to b. This happens when b is not in the range of f 1.

I hope this helps!

Answer: 6

Step-by-step explanation:

Answer: option b

Step-by-step explanation:

The evaluated probability that 2 will find an excuse is 12.8%, under the condition that 35% of those failed will evaluate an excuse to avoid jury duty.

According to the data I found, about 23% of those evaluated to find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.
In the event 10 people are called for jury duty, then the evaluated probability that 2 will find an excuse can be found out using the binomial probability distribution formula.
The formula is:
[tex]P(X=k) = C(n,k) * p{^k }* (1-p)^{(n-k)}[/tex]

Here,
P(X=k) = successes  probability of k in n trials
C(n,k) =  combinations of number in n things taken k at a time
p=  success probability of any one trial
n = trial number
For the given case
k = 2
n = 10
p = 0.23
Staging these values into the formula
[tex]P(X=2) = C(10,2) * 0.23^{2}* (1-0.23)^{(10-2)}[/tex]
       = 45 × 0.0529 × 0.5225
       = 0.128

Hence, the probability that exactly 2 out of 10 people will evaluate an excuse to avoid jury duty is 0.128 or approximately 12.8%.
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The player can expect to win 1.67$ for each 3$ bet placed on the 5$ denomination.

In probability theory, the expected value or expectation is the value that a player would expect to receive on average if they repeated the same game many times under the same conditions.

To find the player's expectation, we need to use the formula:

Expectation = (Probability of Winning x Amount Won) - (Probability of Losing x Amount Lost)

Assuming that the player wins if the bet is successful, the probability of winning on a 5$ denomination bet is 1/3, since there are three possible outcomes (win, lose, or push). The probability of losing is 2/3, since the player will lose if the bet is unsuccessful or if the outcome is a push.

If the player bets 3$ on a 5$ denomination, there are two possible outcomes: they either win 5$ or lose 3$. Therefore, the player's expectation can be calculated as:

Expectation = (1/3 x 5$) - (2/3 x 3$) = 1.67$

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Answer:

830.53 in²

Step-by-step explanation:

Find the area of the full circle and divide it by 2:Use the circle area formula, A = r²Plug in 3.14 as pi, and plug in the radius:A = r²A = 3.14(23²)A = 1661.06Divide this by 2:1661.06 / 2= 830.53So, the area of one semicircle is 830.53 in²

Answer: The area of one semicircle is approximately 830.53 square inches.

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr²

where A is the area of the circle and r is its radius.

The radius of the circle cut out of the piece of wood is about 23 inches. Therefore, its area is:

A = πr²

A = π(23)²

A = π(529)

A ≈ 1661.06 square inches

The carpenter cuts the circle into two semicircles. Therefore, the area of one semicircle is:

A/2 ≈ 830.53 square inches

Therefore, the area of one semicircle is approximately 830.53 square inches.

I hope this helps! Let me know if you have any other questions.

Answer:7

Step-by-step explanation:

a) The confidence level of 99% means that we are 99% sure that the interval contains the true population proportion.

b) The 99% confidence interval for the population proportion is given as follows: (0.3145, 0.4055). It means that we are 99% sure that the true population proportion is between 0.3145 and 0.4055.

c) The 95% confidence interval would be narrower, as it would have a lower critical value, thus the margin of error would also be lower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The parameters for this problem are given as follows:

[tex]\pi = 0.36, n = 739[/tex]

The lower bound of the interval is given as follows:

0.36 - 2.575 x sqrt(0.36 x 0.64/739) = 0.3145.

The upper bound of the interval is given as follows:

0.36 + 2.575 x sqrt(0.36 x 0.64/739) = 0.4055.

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Answer:

D.

Step-by-step explanation:

The set of data that contains two outliers is: 101, 135, 131, 99, 138, 136, 140. An outlier is a value that is significantly different from other values. In this set, both 99 and 138 are outliers because they are much lower and higher respectively than the other values. In the other sets, all values are relatively close to each other with no extreme deviations, thus they do not contain any outliers. Outliers can skew statistical analyses and should be removed or treated with caution.

Step-by-step explanation:

The set of data containing two outliers is the last one: 101, 135, 131, 99, 138, 136, 140. This can be determined by analyzing the range and distribution of the data. Two values, 99 and 140, are significantly different from the other values in the set and fall outside the typical range. These two extreme values are considered outliers and can impact the accuracy of any analysis or Scalculations based on the data.

Answer:

less than 60 is 59 and greater than 60 is 61

Answer:40 and 20

Step-by-step explanation: Mathematically the first fill in the blank can be any number less than 60 here in I have taken it as 40.In the second fill in the blank the it can be any number less than 40 so 20 can be answer I hv chosen here.

The Common factor:

a) 2x+6 = 2(x+3)

b) 9x² - 12x = 3x(3x - 4)

Expand and simplify:

a) [tex](x+3)(x+5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15[/tex]

b) [tex](x-6)(x+7) = x^2 + 7x - 6x - 42 = x^2 + x - 42[/tex]

Common factor:

a) 2x+6 = 2(x+3)

b) 9x² - 12x = 3x(3x - 4)

Factorization is the process of expressing a number or equation in terms of its factors, which are integers or individual terms that when combined together generate the original number or expression. This is an essential concept in algebra and number theory.

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Answer:

The answer would be 0.93!

Step-by-step explanation:

The solution to the inequality x² + 2x ≤ 24 is D. [-6, 4].

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factorization method as follows;

x² + 2x ≤ 24

x² + 2x - 24 ≤ 0

x² + 6x - 4x - 24 ≤ 0

x(x + 6) - x(x + 6) ≤ 0

(x + 6)(x - 4) ≤ 0

x = -6 or x = 4.

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Answer:

  d = (20/7)t

Step-by-step explanation:

You want the distance traveled as a function of travel time if Jack's speed going up was 2 mph and going down was 5 mph.

The relation between time, speed, and distance is ...

  t = d/s

If the total distance is d, the total travel time up and back is ...

  t = t1 +t2

  t = (d/2)/(2) +(d/2)/5 = d(1/4 +1/10) = 0.35d

Solving for distance, we have ...

  d = t/0.35

  d = (20/7)t . . . . miles, where t is in hours

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Using the future value,

Steven's grandmother needed to deposit $55,469.56 into the trust account.

We have,

We can use the formula for the future value of a present sum:

FV = PV(1 + r)^n

where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.

In this case, we have:

FV = $100,000

PV = unknown

r = 4% = 0.04

n = 15 years (18 - 3 = 15)

Substituting these values into the formula, we get:

$100,000 = PV(1 + 0.04)^15

Solving for PV, we get:

PV = $55,469.56

Thus,

Steven's grandmother needed to deposit $55,469.56 into the trust account.

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