A 2-column table titled Balloon Payment Mortgage has 7 rows. The first column has entries mortgage amount, term, interest rate, monthly payment, balloon payment, total interest, total payment. The second column has entries 170,000 dollars, 8 years, 4 percent, 811 dollars and 61 cents for 95 months, 143,152.99, 50,256, 220,256. By the end of year 8, Demarco and Tanya would have to pay a final payout of $120,887. $130,900. $143,152. $154,768.

Answers

Answer 1

A 2-column table titled Balloon Payment Mortgage has 7 rows. The first column has entries mortgage amount, term, interest rate, monthly payment, balloon payment, total interest, total payment. The second column has entries 170,000 dollars, 8 years, 4 percent, 811 dollars and 61 cents for 95 months, 143,152.99, 50,256, 220,256. By the end of year 8, Demarco and Tanya would have to pay a final payout of $143,152.

Hence, the correct option is C.

With the help of the given values, we know that the mortgage amount is $170,000 and the interest rate is 4%. The term of the loan is 8 years, which is equivalent to 96 months.

To calculate the monthly payment, we can use the following formula

P = (r * A) / (1 - (1 + r)^(-n))

Where P is the monthly payment, r is the monthly interest rate (which is 4% / 12 = 0.00333), A is the mortgage amount, and n is the total number of months (which is 96).

By putting the values, we get

P = (0.00333 * 170000) / (1 - (1 + 0.00333)^(-96))

P ≈ $811.61

Hence, the monthly payment is $811.61.

The total interest paid over the life of the loan can be calculated as the difference between the total payment and the mortgage amount.

Total interest = Total payment - Mortgage amount

Total interest = $220,256 - $170,000

Total interest = $50,256

Now, we can calculate the balloon payment using the formula

Balloon payment = A * (1 + r)^n - [P * ((1 + r)^n - 1) / r]

Where A is the mortgage amount, r is the monthly interest rate, P is the monthly payment, and n is the number of months until the balloon payment is due (which is 95 in this case).

By substituting the values, we get

Balloon payment = 170000 * (1 + 0.00333)^95 - [811.61 * ((1 + 0.00333)^95    - 1) / 0.00333]

Balloon payment ≈ $143,152.99

Hence, the correct option is C.

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Answer 2

Answer$143,152

Step-by-step explanation:


Related Questions

PLEASE HELPP SORRY ABT THE WRITING

Answers

Using relevant theorems the measures are:

1. x = 61°; y = 61°    2. x = 12; y = 7   3. x = 5; y = 13

4. x = 97°;    5. x = 6  6. x = 9

How to Find the Values of x and y Using Theorems?

1. x = 61° [based on the vertical angles theorem]

y = 61° [based on the corresponding angles theorem]

2. 8x = 96 [based on the corresponding angles theorem]

x = 96/8

x = 12

8x = 11y + 19 [based on the vertical angles theorem]

Plug in the value of x:

8(12) = 11y + 19

96 = 11y + 19

96 - 19 = 11y

77 = 11y

77/11 = y

y = 7

3. 8x + 2 = 42 [based on the alternate interior angles theorem]

8x = 42 - 2

8x = 40

x = 40/8

x = 5

8x + 2 + [6(2y - 3)] = 180 [based on the linear angles theorem]

8(5) + 2 + 12y - 18 = 180

40 + 12y - 16 = 180

24 + 12y = 180

12y = 180 - 24

12y = 156

y = 156/12

y = 13

4. x = 97° [corresponding angles theorem]

5. 8x = 4x + 24 [based on the alternate exterior angles theorem]

8x - 4x = 24

4x = 24

x = 6

6. 11x + 33 + 6x - 6 = 180

17x + 27 = 180

17x = 180 - 27

17x = 153

x = 9

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Factor.
2d² + 11d + 9

Answers

Answer:

(d + 1) (2d + 9)

Step-by-step explanation:

2d² + 11d + 9

First, we rewrite 11d as 2d + 9d, we have the equation:

2d² + 2d + 9d + 9

We group them, so the equation will be

(2d² + 2d) + (9d + 9)

Factor out the GCF of each group

2d (d + 1) + 9 (d + 1)

Factor the polynomial by factoring out the greatest common factor, d+1

(d + 1) (2d + 9)

So, the answer is (d + 1) (2d + 9)

if jimmy had 4/9 cups of juice and his friend give him 3/9 more cups juice how many cups of juice do jimmy have

Answers

Answer: 7/9

Step-by-step explanation: 3 + 4 = 9

add the /9 = 7/9

Jimmy would have 7/9 because 4+3=7 and they both have the same denominator

a probability distribution of the claim sizes for an auto insurance policy is given in the table below: claim size 20 30 40 50 60 70 80 probability 0.10 0.10 0.10 0.20 0.15 0.10 0.25 what percentage of the claims are within one standard deviation of the mean claim size?

Answers

55% of the claims are within one standard deviation of the mean claim size.

To find the percentage of claims that are within one standard deviation of the mean claim size, we first need to calculate the mean and standard deviation of the distribution.

The mean claim size is:

u = (20 × 0.10) + (30 × 0.10) + (40 × 0.10) + (50 × 0.20) + (60 × 0.15) + (70 × 0.10) + (80 × 0.25) = 54

The variance can be calculated as follows:

s^2 = [[tex](20-54)^{2}[/tex] × 0.10] + [[tex](30-54)^{2}[/tex] × 0.10] + [[tex](40-54)^{2}[/tex] × 0.10] + [[tex](50-54)^{2}[/tex] × 0.20] + [[tex](60-54)^{2}[/tex] × 0.15] + [[tex](70-54)^{2}[/tex] × 0.10] + [[tex](80-54)^{2}[/tex] × 0.25] = 340

The standard deviation is the square root of the variance:

s = √340 ≈ 18.44

To find the percentage of claims that are within one standard deviation of the mean claim size, we need to find the range of claim sizes that fall within the interval (u - s, u + s).

(u - s) = 54 - 18.44 = 35.56

(u + s) = 54 + 18.44 = 72.44

We can see from the table that the claim sizes 40, 50, 60, and 70 fall within this range, and their probabilities add up to:

0.10 + 0.20 + 0.15 + 0.10 = 0.55

Therefore, 55 percentage of the claims are within one standard deviation of the mean claim size.

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Ann fills her water bottle with 1 liter of water before school. She sets a goal to drink all of the water by the end of the school day. To stay on track, she drinks the same amount of water each hour for 8 hours. How many milliliters of water does Ann drink each hour?

Answers

Ann drinks 125 milliliters of water each hour to stay on track and finish her 1-liter water bottle by the end of the school day.

To solve this problem, we first need to convert the given volume of water from liters to milliliters since milliliters are a more appropriate unit of measurement for the amount of water that Ann drinks each hour.

1 liter = 1000 milliliters

Therefore, Ann drinks 1000 milliliters of water in total for the day.

To find out how many milliliters of water Ann drinks each hour, we can divide the total amount of water by the number of hours she drinks it for.

1000 milliliters / 8 hours = 125 milliliters per hour

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a(n) ▼ event sample space outcome experiment is any collection of outcomes from a probability experiment.

Answers

In probability theory, an event is any collection of outcomes or results from a probability experiment. option a) is correct event

It represents a particular occurrence or set of occurrences that we are interested in studying or analyzing. A sample space (option b) is the set of all possible outcomes in a probability experiment. An outcome (option c) is a particular result of a single trial of a probability experiment. An experiment (option d) refers to the process of conducting a trial or series of trials to observe the outcomes and collect data for analysis in probability theory. Therefore, the correct answer is option a) event.

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Complete Question

A(n) _______ is any collection of outcomes from a probability experiment.

a) event

b) sample space

c) outcome

d) experiment

To summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.



An experiment in probability refers to a process of observing or measuring some phenomenon, where the outcomes are uncertain. The collection of all possible outcomes from this experiment is known as the sample space. An outcome is a particular result that occurs as a result of the experiment.

Now, a set of outcomes chosen from the sample space is known as an event. An event can be as simple as a single outcome or as complex as a combination of outcomes. For example, flipping a coin and getting heads is a simple event, while flipping a coin and getting heads or rolling a dice and getting an even number is a compound event.

Finally, a collection of events is simply a group of events that share a common characteristic or property. In probability, we use collections of events to determine the likelihood of certain outcomes occurring. This allows us to make predictions about the experiment based on the available data.

So, to summarize, an outcome is a result of an experiment, a sample space is a collection of all possible outcomes, an event is a set of outcomes chosen from the sample space, and a collection is a group of events with a common property.

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What is the domain of the following graph?

Answers

Answer:

D

Step-by-step explanation:

Look at the graph and find the lowest x value and the highest x value. We don't use y in the inequality because it is not a range question. Domain relates to x-values and range relates to y-values.

When you have found the lowest and highest x-values, look at their dots. If it is shaded, then the answer would contain a less than sign between the number and variable. If it shaded, then it would contain a less than or equal to sign.

Both of the dots with the lowest and highest values are shaded. And the lowest and highest values are -4 and 4 respectively.

Therefore, the answer is D.

Mrs. Ades places tiles numbered 1 through 10 in a bag and assigns numbers 1-6 to Elias and tiles 7-10 to Maha. Each day, she draws a tile, and the person whose tile is drawn has to do chores. Is Mrs. Ades being fair? Explain.

Answers

Answer:

Mrs. Ades is not being fair. The probability of Elias and Maha getting chosen should be equal, but Elias has a 6/10 chance of being chosen, while Maha only has a 4/10 chance of being chosen. This is because Elias has 6 tiles assigned to him, while Maha only has 4 tiles assigned to her.

Explanation:

To make it fair, Mrs. Ades should assign each person an equal number of tiles, or draw from a bag with the tiles numbered 1 through 5 twice, assigning one to Elias and one to Maha each time, and then draw from a bag with tiles numbered 6 through 10 twice, assigning one to Elias and one to Maha each time.

Creating Ordered pairs

Answers

Answer:

either or

2,4 or 4,2

4,8 or 8,4

6,12 or 12,6

8,16 or 16,8

Step-by-step explanation:

if u tell me which one is x and would help even more good luck

The tables represent hat sizes measured in inches for two softball teams.


Pelicans
21.5 25 22
21 22 23
22.5 24 21.5
22 23.5 22
23.5 22 24.5
Falcons
22.5 20 23.5
21 24 22
20.5 21.5 23
23 22.5 21
24 22 24.5


Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
Falcons; they have a larger median value of 22.5 inches
Pelicans; they have a larger median value of 22 inches
Falcons; they have a larger mean value of about 22 inches
Pelicans; they have a larger mean value of about 23 inches

Answers

The team that has the largest overall size hat for their players is the Falcons; they have a larger mean value of about 22 inches

How to solve

In order to determine the average hat size per team, it is necessary to sum up each player's measurements and divide by the total number of players.

For the Pelicans: The combined sum equals 344.5, which results from adding up values such as 21.5, 25, 22, 24, and so on. With a team membership of 15 people, their mean measures out to approximately 22.97 inches.

The Falcon's equivalent calculation yields a total of 330 attained from summing head sizes, including those measuring 20, 23.5, 21, etc., with an equal number of members, coming close to an average measure of 22 inches thick.

As a result, comparisons between both teams reveal that the Falcons possess the larger collective hat size averages at roughly 22 inches in thickness.

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help pleasejhdfjg THIS ASSIGNMENT IS LIKE 2 WEEKS OVERDUE

Answers

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas (b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below. (c) The final total area is 2x² - 10x - 15.

What is an area model?

An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.

b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.

   2x⁴ − 3x³ − 2x² − 4x − 1

 +---------------------------------------

x  |   2x⁵    -3x⁴    -2x³    -4x²   -x

 |

3  |   6x⁴    -9x³    -6x²    -12x    -3

 +---------------------------------------

c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.

    x + 8      x - 5

 +--------------------

x  |  x² + 8x   x² - 5x

 |

-5 | -5x + -40   -5x + 25

 +--------------------

The final total area can be found by adding up the areas of the smaller rectangles:

Total area = x² + 8x + x² - 5x - 5x - 40 + 25

= 2x² - 10x - 15

= 2x² - 10x - 15.

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show that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

Answers

We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

What is rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.

To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.

Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.

Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.

Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

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change 0.56kilometres into metres

Answers

Answer: 560 metres.

Step-by-step explanation:  Here’s a step-by-step explanation of how to convert 0.56 kilometres into metres:

1. Start with the value in kilometres: 0.56 km

2. Know that there are 1000 metres in a kilometre.

3. Multiply the value in kilometres by the conversion factor (1000 m/km): 0.56 km x 1000 m/km = 560 m

4. The result is the value in metres: 560 m

So, 0.56 kilometres is equal to 560 metres.

To convert 0.56 kilometers to meters, we need to multiply the distance by 1000, since there are 1000 meters in one kilometer.

So, 0.56 kilometers = 0.56 x 1000 meters = 560 meters.

Therefore, 0.56 kilometers is equivalent to 560 meters.

Use the trading data for Friday, October 20 and Friday, October 27 to answer the questions. ( in the picture)

A) what was the difference between the high and low prices on October 20?

B) on October 27, what was the actual volume of discovery group shares posted? Write the volume in numerals.

C) at what price did discovery group clothes on October 19?

D) use the October 19 closing price from above and the October 20 opening price to find the difference in the prices as a percent increase. Round to the nearest hundredth place.

E) on October 21 discovery group announced that they would close one of their manufacturing plants. This resulted in a drop in their stock price. It closed at $32 express the number change from October 20 to October 21 as a percent rounded to the nearest tenth of a percent.

F) on October 28 discovery group announce that they would not be closing the plant this news cause the price of the stock to rise. It closed at $48.20 express the net change from October 27 to October 28 as a percent, rounded to the nearest tenth of a percent.

G) explain why 52 week high and 52 week low numbers are the same in both charts ?

H) examine the closing price of discover group on October 27 one year earlier one share closed at 30% higher than that amount, what was the closing price one year earlier?

Answers

The difference between the high and low prices on October 20 is $3.33  

On October 27, the actual volume of discovery group shares posted is 2360000

How to explain the value

The price that Discovery group clothes on October 19 is $36.94

The difference in the prices as a percent increase is 0.76%

The number change from October 20 to October 21 as a percent rounded to the nearest tenth of a percentage is -16.9%

The net change from October 27 to October 28 as a percent, rounded to the nearest tenth of a percent is 14.8%

The reason why 52 week high and 52 week low numbers are the same in both charts is that there was no price higher than $76.19 or lower than $22.78 for those weeks.

The closing price one year earlier is $54.60

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i need help someone . i need help on my iready

Answers

It wants you to multiply (5) x (8) = 40/3

HELP ASAP!!
Add. (5x + 8) + (2x + 5)

Answers

Answer:

7x + 13

Step-by-step explanation:

because the correct answer is 7x+13

Jaxson and his children went into a grocery store and where they sell bananas for

$0. 90 each and mangos for $0. 50 each. Jaxson has $9. 10 to spend and must buy at

least 11 bananas and mangos altogether. If Jaxson decided to buy 6 bananas,

determine the maximum number of mangos that he could buy. If there are no

possible solutions, submit an empty answer.

Answers

6 bananas = 0.90x6
=$5,40
$9,10-$5,40
=$3,70
$3,70÷$0,50
=7 mangoes
remainder: $0,20.

A PLOT MEASURING 1.2m by 9.1m IS SORROUNDED BY A PATH 0.5m WIDE. FIND THE AREA OF THE PATH IN SQUARE METRES?​

Answers

The area of the outer rectangle (including the path) is:

(1.2 + 2*0.5) * (9.1 + 2*0.5) = 2.2 * 10.1 = 22.22 square meters

The area of the inner rectangle (excluding the path) is:

1.2 * 9.1 = 10.92 square meters

Therefore, the area of the path is:

Area of outer rectangle - Area of inner rectangle = 22.22 - 10.92 = 11.3 square meters

The area of the path is 11.3 square meters.

1. Triangles

B = 4in, H = 5in
B = 6ft, H= 10ft
B = 12m, H = 15m
Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?
2. Parallelogram (H = height) and (B = base)

H = 9in, B = 6in
H = 5 ft, B = 2ft
H = 7yds, B = 3yds
Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?
Hint: Use the formula. Substitute the given values and then solve as an equation.

3. Rectangle (L = length) and (w = width)

rect. DKIF with L = 8 ft and w = 6 ft
rect. AOPU with L = 13 ft and w = 5 ft
Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.
4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)

rhombus with d1 = 12 yds and d2 = 12 yds
rhombus with d1 = 10 ft and d2 = 25 ft
rhombus with d1 = 16 in and d2 = 22 in
Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)

b1 = 6 ft, b2 = 7 ft, H = 10 ft
b1 = 5 yds, b2 = 8 yds, H = 4 yds
c. b1 = 9 in, b2 = 11 in, H = 13 in
d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?

Answers

The answers are:

Total area of two triangle tablecloths for one table with base of 2 ft and a height of 4 ft = 8 ft².Height of a parallelogram with base of 13 mm and an area of 78 mm² = 6 mm.Charles has enough paint to cover the den walls.Length of diagonals of a rhombus with an area of 72 ft² and the product of diagonals as 144 = 8 ft.Height of a trapezoid with bases of 16 km and an area of 32 km² = 4 km.

What is the explanation for the above response?

1) The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. For the given triangles:

Triangle 1: A = (1/2)(2ft)(4ft) = 4 sq ft (for one tablecloth), so for two tablecloths, the total area is 8 sq ft.

Triangle 2: A = (1/2)(6ft)(10ft) = 30 sq ft, so for two tablecloths, the total area is 60 sq ft.

Triangle 3: A = (1/2)(12m)(15m) = 90 sq m, so for two tablecloths, the total area is 180 sq m.

2) The area of a parallelogram is given by the formula A = Bh, where B is the base and h is the height. Rearranging this formula, we get h = A/B. For the given parallelogram:

A = 78 mm2 and B = 13 mm, so h = 78/13 = 6 mm.



3) The area of a rectangle is given by the formula A = LW, where L is the length and W is the width. For Charles' den:

The total wall space to be painted is (2 x 9 x 15) + (2 x 8 x 10) = 342 sq ft. One gallon of paint covers 440 sq ft, so Charles needs (342/440) = 0.7778 gallons of paint. Therefore, he does not have enough paint.


4) To calculate the total area of the walls to be painted, we can calculate the area of each wall and add them together.

The area of the two walls that are 9 ft high and 15 ft long is (9 x 15) = 135 sq ft each, for a total of 270 sq ft. The area of the other two walls that are 8 ft high and 10 ft long is (8 x 10) = 80 sq ft each, for a total of 160 sq ft. Adding them together, we get a total of 430 sq ft.

Since one gallon of paint covers 440 sq ft of wall space, Charles has enough paint to cover the den walls.

5) The area of a trapezoid is given by the formula A = (1/2)(b1 + b2)h, where b1 and b2 are the bases and h is the height. Rearranging this formula, we get h = 2A/(b1 + b2). For the given trapezoids:

A = (1/2)(6ft + 7ft)(10ft) = 65 sq ft and h = 2(65)/(6ft + 7ft) = 5 ft.

A = (1/2)(5yds + 8yds)(4yds) = 26 sq yds and h = 2(26)/(5yds + 8yds) = 2 sq yds.

A = (1/2)(9in + 11in)(13in) = 143.5 sq in and h = 2(143.5)/(9in + 11in) = 13.05 in.

For the application in part (d), we are given A = 32 km2 and (b1 + b2) = 16 km.

Rearranging the formula for A, we get h = 2A/(b1 + b2). Substituting the given values, we get h = 4

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Difference between problem with median nerve (C6-C8, T1) and with Klumpke's palsy (C7, C8, T1)

Answers

The median nerve and Klumpke's palsy are both related to nerve injuries in the arm, but they involve different nerve pathways and result in different symptoms.

The median nerve runs from the brachial plexus in the neck through the arm to the hand, and controls movement and sensation in the thumb, index, middle, and part of the ring fingers. Damage to the median nerve can result in symptoms such as weakness, numbness, and tingling in these fingers, as well as muscle wasting in the thumb.

Klumpke's palsy, on the other hand, involves damage to the lower brachial plexus nerves, specifically the C7, C8, and T1 nerve roots. This can result in weakness or paralysis in the hand and wrist, with symptoms such as a claw-like deformity, decreased grip strength, and loss of sensation in the affected areas.

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Consider the queueing model of the bank in Conceptual Problem 6.9. Suppose the arrival rate is 18 per hour, the mean service time is 10 minutes, and the lobby can handle 15 customers at one time. How many tellers should be used if the aim is to keep the mean queueing time to less than 5 minutes

Answers

The number of tellers that should be used if the aim is to keep the mean queuing time to less than 5 minutes is 3.

To determine the number of tellers follow these steps:

1. Arrival rate (λ) = 18 customers per hour
2. Mean service time (μ) = 10 minutes per customer = 1/6 customer per minute
3. Lobby capacity = 15 customers
4. Target mean queuing time = 5 minutes

Now, calculate the service rate and find the number of tellers needed to achieve the target mean queueing time.

Step 1: Convert arrival rate to customers per minute: λ = 18/60 = 0.3 customers per minute
Step 2: Calculate the service rate per teller: 1/μ = 1/(1/6) = 6 customers per hour = 0.1 customers per minute
Step 3: Determine the number of tellers (n) needed to achieve the target queuing time:

Using the formula:
n > λ / (μ * (Wq_target + 1/μ))

Here, Wq_target is the target mean queuing time in minutes.
n > 0.3 / (0.1 * (5/60 + 1/(6/60)))

After solving the inequality, we get:
n > 2.4

Since the number of tellers must be a whole number, therefore, at least 3 tellers should be used in the queueing model of the bank to keep the mean queueing time to less than 5 minutes.

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Question 3
Terry has a new retirement account. He plans to make deposits of $4,750 per year for the next 40 years. He expects the account to earn 9.1% for the first 25 years, 6.9% for the next ten years, and then 4.5% for the last five years. How much will have have at the end of the forty years based on these assumptions?

Answers

With an initial investment of $19,675.13 and yearly deposits of $3,000 at an interest rate of 9.25%, the account will be worth around $336,312.91 in 25 years.

what is unitary method ?

The unitary approach is a strategy for problem-solving in which the value of one piece of a quantity is determined, then the cost of an unique number of units associated with that quantity is subsequently determined using that value. In other words, it's a method of proportional used to resolve issues where one unit's value is known but another's value is needed. The unitary method's fundamental premise is to establish a percentage between two quantities, one of which is stated in the form of one unit and the other in terms of a greater number of units.

given

In the following ten years, we have:

P = $4,750 r = 6.9% = 0.069

n = 10

[tex]FV2 = $4,750 * ((1 + 0.069)^10 - 1) / 0.069[/tex]

= $74,894.87

In the previous five years, we have:

P = $4,750

r = 4.5% = 0.045

n = 5

= $127,756.44

Lastly, we can combine the two figures to determine the account's entire future value:

FV is $208,556.47 + $127,756.44 = $336,312.91 (annual deposits + initial investment).

With an initial investment of $19,675.13 and yearly deposits of $3,000 at an interest rate of 9.25%, the account will be worth around $336,312.91 in 25 years.

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A group of friends wanted to rent a cabin for the fourth of July.
The total cost to rent the cabin was $960. However, 4 of the
friends decided not to go. The remaining friends decided to
divide the $960 cost equally, which therefore increased each
share by $120. How many friends were originally in the group?
Show all your work!

Answers

If a group of friends wanted to rent a cabin for the fourth of July. The number of  friends that were originally in the group is 8.

How to find the number of friend?

Let x represent the number of friends in the group

Cost per person =960/x

After   the 4 friends dropped out the remaining number of friends was = x - 4

New cost per person =960/x + 120

New total cost of the cabin rental = (x - 4) * (960/x + 120)

Set the two expressions equal to each other

960 = (x - 4) * (960/x + 120)

960 = 960 - (3840/x) + 120(x - 4)

Simplifying

3840/x = 120x - 480

Multiplying both sides by x

3840 = 120x^2 - 480x

Rearranging

120x^2 - 480x - 3840 = 0

Dividing both sides by 120

x^2 - 4x - 32 = 0

Quadratic equation

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where:

a = 1, b = -4, and c = -32.

Plugin the formula

x = (4 ± √(16 + 128)) / 2

x = (4 ± √(144)) / 2

x = (4 ± 12) / 2

x = 8 or x = -4

Therefore the number of friends  is 8.

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name a secant in this circle

Answers

Answer: Line AB

Hope this helps

Translate the phrase into a variable expression. Use the letter c to name th
variable. If necessary, use the asterisk (*) for multiplication and the slash
(/) for division.
...
the value of the company divided by 96884 shares...

Answers

The variable expression would be:

Value of the company / 96884 = c

2 fractions with different denominators that add up to 6 1/3

Answers

The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

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imma be giving brainliest if you help me!!!???!!??

Answers

using trignometric ratio of sine thee measure of the angle x to the nearest degree is 28 degrees

What is Trignometric ratio?

Trigonometric ratios are ratios of the sides of a right triangle, such as sine, cosine, and tangent, that are used to find missing side lengths or angles.

What is angle?

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is typically measured in degrees or radians.

According the given information:

We can use the trigonometric ratio of sine to find the measure of the angle x.

sin(x) = opposite/hypotenuse

In this case, the opposite side is the height of the triangle, which is 13, and the hypotenuse is the length of the diagonal line connecting the base and the top of the triangle. We can use the Pythagorean theorem to find the length of the hypotenuse.

hypotenuse² = base² + height²

hypotenuse² = 22² + 13²

hypotenuse² = 769

hypotenuse ≈ 27.73

Now we can substitute the values into the sine ratio:

sin(x) = 13/27.73

x ≈ 28 degrees

Therefore, the measure of the angle x to the nearest degree is 28 degrees.

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A researcher was interested in comparing the resting pulse rate of people who exercise regularly and people who do not exercise regularly. Independent simple random samples of 16 people ages 30-40 who do not exercise regularly and 12 people ages 30-40 who do exercise regularly were selected and the resting pulse rate of each person was measured. The summary statistics are as follows. Do Not Exercise X1=72.3 s1=10.3 n1=16 Do Exercise X2=69.0 s2=8.9 n2=12 At the 2.5% significance level, do the data provide sufficient evidence to conclude that the mean resting pulse rate of people who do not exercise regularly is greater than the mean resting pulse rate of people who exercise regularly? Use the critical-value approach.

Answers

For a hypothesis testing by considering two samples related to rate of people who exercise and who do not exercise, the observed t-value < standard so, null hypothesis does not rejected and there is no evidence to support the claim.

We have a researcher who was interested in making a comparison of resting pulse rate of people who exercise regularly and who do not exercise regularly. There is two independent samples. In 1ˢᵗ sample, sample size, n₁= 16

Sample mean, [tex]\bar X_1[/tex] = 72.3

Standard deviations, s₁ = 10.3

In case of second sample, sample size, n₂ = 12

Sample mean, [tex] \bar X_2[/tex] = 69.0

Standard deviations, s₂ = 8.9

Level of significance = 2.5% = 0.25

Consider the null and alternative hypothesis for the test hypothesis are defined as [tex]H_0 : μ_1 =μ_2[/tex]

[tex]H_a : μ_1 >μ_2[/tex]

The test statistic : using t-test formula

[tex]t = \frac{ \bar X_1 - \bar X_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}}}[/tex]

[tex]= \frac{72.3- 69}{ \sqrt{ \frac {10.3^2}{16} + \frac{8.9^2}{12}}}[/tex]

= 0.91

Degree of freedom, df = n1 + n2 - 2

= 16 + 12 -2 = 26

Using the t-distribution table, the critical value for t(0.025, df = 26) is equals to the 2.06. Now, the observed t-value = 0.91 is less than 2.06 ( standard t value), so, we do not reject H₀ . Hence, no evidence to support the researcher claim.

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Line Segment BD and Line Segment CK are diameters of ⊙ A. Line Segment BP and Line Segment QP are tangents to ⊙ A. Find each of the following. Show your work.

11.) m∠ABP=_________
12.) m∠BAK=_________
13.) m∠AQP=_________
14.) m∠QAK=_________
15.) Measure of Arc BK=__________
16.) Measure of Arc BQ=__________
17.) m∠CAD=_________
18.) m∠CAB=_________
19.) Measure of Arc CB= __________
20.) m∠CDA=_________

Answers

The measure of angle ABP from the given circle is 90°.

From the given figure,

11) Measure of angle ABP is 90°.

12) Measure of angle BAK is 180°-(90°+25°)

= 180°-115°

= 65°

13) Measure of angle AQP is 90°.

14) Measure of angle QAK is 180°-(90°+25°) (Because ∠BPA=∠QPA=25°)

15) Measure of Arc BK = Measure of angle BAK = 65°

16) Measure of Arc BQ = Measure of angle BAQ = 65°×2

= 130°

17) m∠CAD=m∠BAK=65°

Therefore, the measure of angle ABP from the given circle is 90°.

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In a game, you can get 20 points, 10 points, 2 points. You calculated the expected value of the game; expected value = 5.6. If you play the game many times, how many points can you get on average?​

Answers

On average, you can expect to get about 4.24 points per game if you play many times.

How to calculate how many points can you get on average

To find the average number of points you can get by playing the game many times, you can use the expected value as a guide.

The expected value of the game is calculated as follows:

(20 points x probability of getting 20) + (10 points x probability of getting 10) + (2 points x probability of getting 2) = 5.6

Let's use the variables p20, p10, and p2 to represent the probabilities of getting 20 points, 10 points, and 2 points, respectively. Then we can set up the equation:

(20p20) + (10p10) + (2p2) = 5.6

We also know that the sum of the probabilities must equal 1:

p20 + p10 + p2 = 1

Now we have two equations and three variables. We need one more equation to solve for the variables. One way to do this is to assume that the probabilities of getting 20 points, 10 points, and 2 points are proportional to the point values themselves.

In other words, let's assume that:

p20 : p10 : p2 = 20 : 10 : 2

We can then use this proportion to write p20 and p2 in terms of p10:

p20 = 2p10

p2 = 4p10

Now we can substitute these expressions into the two equations we have:

(20p20) + (10p10) + (2p2) = 5.6

p20 + p10 + p2 = 1

Substituting the first equation gives:

(20(2p10)) + (10p10) + (2(4p10)) = 5.6

Simplifying:

80p10 + 10p10 = 5.6

90p10 = 5.6

p10 = 5.6/90

p10 = 0.062

Now we can use the proportions to find p20 and p2:

p20 = 2p10 = 2(0.062) = 0.124

p2 = 4p10 = 4(0.062) = 0.248

Finally, we can calculate the average number of points:

(20 points x 0.124) + (10 points x 0.062) + (2 points x 0.248) = 3.12 + 0.62 + 0.496 = 4.236

So, on average, you can expect to get about 4.24 points per game if you play many times.

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