Your professor has offered to give you $100, starting next year, and after that growing at 3% for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in the local bank so that the account will generate the money you would need to deposit in the local bank so that the account will generate the same cash flows as he is offering you. Your local bank will guarantee a 6% annual interest rate so long as you have money in your account.

1. How much money will you need to deposit into your account today?

2. Using an excel spreadsheet, show explicitly that you can deposit this amount of money into the account, and every year withdraw what your brother has promised, leaving the account with nothing after the last withdrawal.

3. Change the bank annual interest rate from 6% to 10% what is the difference?

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

The critical value for the 90% confidence interval is \(Z_c = 1.645\).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a p-value of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

The critical value for the 90% confidence interval is \(Z_c = 1.645\).

Answer:

0.3333333333 is right answer

Answer: ok i did :)

Step-by-step explanation: how are you?

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

t=3

Step-by-step explanation:

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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\(b=\frac{3A}{2m}\).

\(A = \frac{2}{3} mb\)

\(\frac{3}{2} A = \frac{2}{3} mb*\frac{3}{2}\\ \\\frac{3}{2} A =mb\)

\(\frac{\frac{3}{2} A}{m} =\frac{mb}{m} \\ \\\frac{\frac{3}{2} A}{m} = b\\ \\\frac{3}{2}*\frac{A}{m} =b\\ \\\frac{3A}{2m}=b\\\\ b=\frac{3A}{2m}\)

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

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If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

Probability is the likelihood of occurrance of an event. It is given by:

Probability = number of occurrence / total number of possible occurence

A cashier samples the transaction of every 10th person who goes though the line at a craft store out of 40 people, 32 used a coupon.

Probability of using coupon = 32/40 = 0.8

Hence if 750 people go to this store each day, number of people sampled = 75.

Number of people expected to use the coupon = 75 * 0.8 = 60

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

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Answer:

The linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven is 0.05*x + 20 and the cost of renting the truck if the truck is driven 107 miles is 25.35.

Step-by-step explanation:

A linear function is a polynomial function of the first degree that has the form:

f (x) = y = m*x + b

where m is the slope of the function and b is the y-intercept.

The graph of a linear function is always a line.

A truck rental company rents a moving truck for one day by charging $20 plus $0.05 per mile. So, the number of miles travel is represented by "x"  and the cost per mile is represented by "c". The y-intercept is the starting cost at zero miles or $20.  The slope is the rate per mile or $0.05. Then:

c= 0.05*x + 20

If the truck is driven 107 miles, then:

c= 0.05* 107 + 20

Solving:

c= 25.35

So, the linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven is 0.05*x + 20 and the cost of renting the truck if the truck is driven 107 miles is 25.35.

Answer: (x + 2) (x + 9)

Step-by-step explanation:

Factor using the AC method.

Answer:

4

Step-by-step explanation:

2*2=4

Hope this helps!

:)

Answer: Monke.

Step-by-step explanation:

get good.

The gratuity of the hotel server has to be $8.

The tax of the restaurant server is 8.5 percent

We have tro find this based on salary

40 dollars x 0.85 = 34

The income 34 - 18

= 16

Half of 16 = 8

Hence the amount that is the percentage of gratuity is 8 percent.

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Answer:

hi noah

Step-by-step explanation:

Answer:

Hi Noah is not an answer

Step-by-step explanation:

The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

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Answer:

Blac cack

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 \(g(h(x)) = \sqrt[4]{x^2 + x +5} + 3\)

b

 \(h(g(x))  = \sqrt{x}  + 7\sqrt[4]{x} + 17\)

c

 \(h(h(x)) =  [x^2 + x + 5 ]^2 + x^2 + x + 10\)

Step-by-step explanation:

From the question we are told that

    \(h(x) =  x^2  + x  + 5\)

and  

    \(g(x) = \sqrt[4]{x} + 3\)

Considering first question

Now we are told  g(h(x))

i.e

        \(g(h(x)) =  [x^2 + x + 5 ]^{\frac{1}{4} } + 3\)

=>     \(g(h(x)) = \sqrt[4]{x^2 + x +5} + 3\)

Considering second  question

   Now we are told  h(g(x))

i.e

    \(h(g(x)) =  [x^{\frac{1}{4} } + 3]^2 +  x^{\frac{1}{4} } + 3 + 5\)

=> \(h(g(x)) =  x^{\frac{1}{2} } + 6x^{\frac{1}{4} } + 9+ x^{\frac{1}{4}}  + 8\)

=>  \(h(g(x))  = x^{\frac{1}{2}} + 7x^{\frac{1}{4}} + 17\)

=>  \(h(g(x))  = \sqrt{x}  + 7\sqrt[4]{x} + 17\)

Considering third question

         \(h(h(x))= [x^2 + x + 5]^2 + [x^2 + x + 5 ] +  5\)

=>       \(h(h(x)) =  [x^2 + x + 5 ]^2 + x^2 + x + 10\)

The detailed answer of this question is:

P(X > 100 | X > 50)=0.455

Given that X follows an exponential distribution, we know that the probability density function (PDF) of X is given by:

f(x) = λe^(-λx) for x ≥ 0

where λ is the rate parameter of the distribution.

We are given that P(X < 50) = 0.25. Using the cumulative distribution function (CDF) of X, we can write:

P(X < 50) = 1 - e^(-λ*50) = 0.25

Solving this equation for λ, we get:

λ = -ln(0.75)/50 ≈ 0.0278

Now, we are asked to find P(X > 100 | X > 50). Using the definition of conditional probability, we can write:

P(X > 100 | X > 50) = P(X > 100 and X > 50) / P(X > 50)

= P(X > 100) / P(X > 50)

= e^(-λ100) / e^(-λ50)

= e^(-λ*50)

Substituting the value of λ, we get:

P(X > 100 | X > 50) = e^(-0.0278*50) ≈ 0.455

Therefore, the probability that a high-risk driver will have an accident after 100 days given that they have not had an accident for the first 50 days is approximately 0.455.

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Answer:

 =  1.6

Unless you meant to clarify what in the equation you needed, but that is the answer to it.

Answer:

A. -7

That's it

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

9.48

Step-by-step explanation:

Answer:

Direct V:

y=3x

y=(2/7)x

-0.5x=y

Not direct V:

y=2.2x+7

x=-1

y=4

Step-by-step explanation:

That was the answer on edge2020 :))

Direct variation usually conform to the general formula : \(y = kx \) where k is the proportionality constant. Hence sorting the equation into tbe appropriate category :

Direct variation :

y = 3x

y = (2/7)x

y = -0.5x

Non - direct variation :

y = 2.2x + 7

y = 4 and x = - 1

Therefore, only three of the expressions exhibit direct variation while the other three do not.

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The width of the duck pond is,

⇒ 27 feet

We can see that the given diagram is a rectangle,

And we know that,

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Now, By given diagram we have;

We have to given that;

Use the scale drawing to determine how wide the duck pond is.

And there are 4.5 feet in 1 square,

Therefore,

1 square is equal to 4.5 feet

So, we get;

The width of the duck pond is,

⇒ 6 square

We know that,

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Then to find width of duck pond in feet,

Multiply 6 with 4.5

⇒ 6 × 4.5 feet

⇒ 27 feet

Thus, The width of the duck pond is,

⇒ 27 feet

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Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

Explanation:

x is the number of years since 1988

x = 0 represents the year 1988

x = 1 is the year 1988+1 = 1989

x = 2 is the year 1988+2 = 1990

etc

x = 32 is the year 1988+32 = 2020

Answer:probably about 50 years

Step-by-step explanation:did for my family’s live oak

The probability that the three randomly selected students will have blood types A, B and AB is given as follows:

0.00164 = 0.164%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Hence the probability for this problem is calculated as follows:

41/100 x 1/10 x 1/25 = 0.00164 = 0.164%.

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