Find a formula for the exponential function passing through the points (-2,768) and (2,3)

Answer: 10

Step-by-step explanation:

Since both points have the same y value, we just need to find the change of x, which would be the distance of the points.

Reading the points from left to right on an imaginary graph, point B would come first as it has the lesser x value.

To find the change of x subtract the x value of the second point from the first, so...

6 - (-4) = 10

The change of x = 10

The distance between the points is 10

Hope this helps!

Answer:

CD = 22

Step-by-step explanation:

You would double the side lengths given since this is a rectangle and set them equal to 80 cause that is the perimeter. So the equation would be 6z + 6 + 8z + 4 = 80. You would use the PEDMAS rule and subtract 6 from both sides which gives you:

6z + 8z +4 = 74

Subtract 4 from both sides

6z + 8z = 70

Add 6z + 8z

14z = 70

Divide 70 and 14z

z = 5.

AB and CD is equal in length so all you have to do is plug in 5 to z in the AB equation.

4(5) + 2

= 22

Answer: EF, DF, DE

Step-by-step explanation:

The smaller the opposite angle, the smaller the side, and vice versa.

∠EDF = 85°

∠DEF = 60° (Because the total degrees in a triangle must be 180°)

∠DFE = 35°

EF, DF, DE

Hope this helps!

Assuming the number of people who listen to the video increases by 45% each day, there would be approximately 24 new people who listen to the video on the 7th day after the initial 8 people.

According to the problem, the number of people listening to the video increases by 45% each day. Therefore, we can use the formula for compound interest to calculate the number of new people who listen to the video on the 7th day.

Let P be the initial number of people who listened to the video, which is 8.

Let r be the daily increase rate, which is 45% or 0.45 as a decimal.

Let n be the number of days, which is 7.

Then, the formula for compound interest is:

A = P(1 + r)^n

where A is the final number of people who listen to the video.

Plugging in the values, we get:

A = 8(1 + 0.45)^7

A ≈ 32

Therefore, the number of new people who listen to the video on the 7th day is approximately 32 - 8 = 24 people.

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Answer:

Step-by-step explanation:

Let's use the variable "a" to represent the number of stamps Angela has.

From the problem, we know that Nicolas has 48 stamps, and that this is 2 times 5 less than the number of stamps Angela has. "2 times 5 less than the number of stamps Angela has" can be written as:

2(a - 5)

So the equation that relates the number of stamps Nicolas and Angela have is:

48 = 2(a - 5)

We can simplify this equation by first distributing the 2:

48 = 2a - 10

Then, we can add 10 to both sides of the equation:

58 = 2a

Finally, we can solve for a by dividing both sides by 2:

a = 29

Therefore, the equation we can use to find the number of stamps Angela has is:

2(a - 5) = 48

or, simplified:

a = 29

When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).

According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.

When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.

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To find the ground distance traveled by the aircraft, we can use the trigonometric function tangent. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the aircraft (30,000 ft) and the adjacent side is the ground distance traveled (x).
Therefore, we can set up the following equation:
tan10° = 30,000/x

We are given that tan10° = 0.176, so we can substitute that value into the equation:
0.176 = 30,000/x
Next, we can cross-multiply and solve for x:
x = 30,000/0.176
x ≈ 170,455 ft
Finally, we can convert the ground distance traveled from feet to nautical miles using the conversion factor 1 Nm = 6076 ft:
170,455 ft * (1 Nm/6076 ft) ≈ 28.06 Nm
Therefore, the ground distance traveled by the aircraft is approximately 28.06 nautical miles.

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The local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.

Using a graphing Utility, we can approximate the local maximum value and local minimum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6.

1. The local maximum value occurs at the highest point on the graph within the given interval of -6. By observing the graph, we can see that the local maximum value is y=2.2 and it occurs at x=-1.2.

2. The local minimum value occurs at the lowest point on the graph within the given interval of -6. By observing the graph, we can see that the local minimum value is y=-4.6 and it occurs at x=-4.8.

It is important to note that these values are approximations and may not be exact. The graphing Utility is a useful tool for visualizing the function and finding approximate values, but it is not always precise.

the local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.

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The required solutions are as follows,
(a) The parabola will open downwards and have a maximum.
(b) The axis of symmetry for this function is t = 15.

A parabola is a cross-section cut out of the cone and represented by an equation shown in the question.

Here,
(a) The function C(t) is a quadratic function with a coefficient of -0.2 in front of the t² term. Since this coefficient is negative, the parabola will open downwards and have a maximum.

(b) The axis of symmetry of a quadratic function in the form of f(x) = ax² + bx + c is given by the formula x = -b/2a.

In this case, the function is C(t) = -0.2t² + 6t + 28.5, so a = -0.2 and b = 6. Thus, the axis of symmetry is:

t = -b/2a = -6/(2*(-0.2)) = 15

Therefore, the axis of symmetry for this function is t = 15.

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the factored form of the expression 9m^(2)-49 is (3m+7)(3m-7).

To factor the expression 9m^(2)-49, we need to use the difference of squares formula.

The difference of squares formula states that a^(2)-b^(2)=(a+b)(a-b).

In this case, we can see that 9m^(2) is a perfect square and 49 is also a perfect square. So, we can write the expression as (3m)^(2)-(7)^(2).

Using the difference of squares formula, we get:

(3m)^(2)-(7)^(2)=(3m+7)(3m-7)

So, the factored form of the expression 9m^(2)-49 is (3m+7)(3m-7).

Therefore, the answer is (3m+7)(3m-7).

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The graph of the function y=3x+1 is shown.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

We are given that;

The function is y=3x+1

Now,

When x = 0, y = 3(0) + 1 = 1, so one point on the function is (0, 1).

When x = 1, y = 3(1) + 1 = 4, so another point on the function is (1, 4).

When x = -1, y = 3(-1) + 1 = -2, so a third point on the function is (-1, -2).

Therefore, the graph will be given the attachment

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The caterer was able to make 72 (1)/(3) size pieces from the 24 sandwiches.

To find this answer, we can use the following equation:

24 sandwiches × 3 (1)/(3) size pieces per sandwich = 72 (1)/(3) size pieces

This equation tells us that for every sandwich, the caterer was able to make 3 (1)/(3) size pieces. By multiplying the number of sandwiches by the number of (1)/(3) size pieces per sandwich, we can find the total number of (1)/(3) size pieces the caterer was able to make.

Therefore, the caterer was able to make 72 (1)/(3) size pieces from the 24 sandwiches.

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The total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

What is meant by surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. A solid object's surface area is a measurement of the overall space that the object's surface takes up. Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces.

1) This figure is a cuboid.

  It has six faces and the opposite faces are of equal dimensions.

The surface area of a cuboid is the sum of the areas of each face.

Length l = 10 ft

Width w = 6 ft

Height h = 8 ft

Surface area = 2lw+2lh+2hw = 2 ( lw+ lh+ hw)

                                     = 2 ( 10*6 + 10*8 + 8*6) = 376 sq. feet

2) This figure has 2 similar right triangle faces.

Sum of area of both triangles = 2 * 1/2 * base * height = 3 * 4 = 12 sq. feet

There are two rectangular faces.

Area of front rectangular face = 10 * 5 = 50 sq. feet

Area of base rectangular face = 10*3 = 30 sq. feet

 Total surface area = 12 + 50 + 30 = 92sq. feet

Therefore the total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

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The missing values are 2 and 35 respectively. The points plotted have been attached below. The solution has been obtained by using equivalent ratio.

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another.

We are given that Bashir walked 10 miles in 4 hours and the table is of equivalent ratios.

The ratio comes out to be 2.5.

So, he will walk 5 miles in 2 hours.

Similarly, in 14 hours he will walk 35 miles.

The points have been plotted on the coordinate axes and has been attached below.

Hence, the missing values are 2 and 35 respectively.

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The journal entry to record the expenses with the annual amortization expense list is present in above figure.

a) Amortization per year = $43750 per year.

b) Amortization per year = $5230 per year.

c) Amortization per year = $14000 per year.

Amortisation of intangible assets : If any intangible assets are purchase and this will be amortized over the useful life of the assets and this will deduct the value of the intangible assets over the year completed. Now, we prepare a journal entry to record the expense:

a) A patent is a legal right granted to an individual or company to reproduce, use or sell an invention without interference from others.. A patent with 10-year remaining legal life was purchased for $350,000. Since the patent will be worthless after 8 years, the life will be considered to be 8 years. Amortization per year = $350000/8

= $43750 per year.

Amortization expense A/C.. Dr $43750 ( debit )

To Patents A/C $43750 ( credit)

b) Cost of the patent to date consisted in legal fee for handling the patent application = $52,300

Because the patent has commercial value during its remaining statutory life of 10 years. Only the original cost of patent will be amortized hence

Amortization per year = $52300/10

= $5230 per year

Amortization expense $5230 (debit)

Patents $5230 ( credit)

C) Since the additional cost will be incurred after 5 years and hence renewal is conditional , original life and cost will be considered.

Amortization per year = $70000/5 = $14000

Hence, required value is $14000.

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Complete question:

Amortization Expense : For each of the following unrelated situations, calculate the annual amortization expense and prepare a journal entry to record the expense:

a)A patent with a 10-year remaining legal life was purchased for $350,000. The patent will be commercially exploitable for another eight years. b) A patent was acquired on a device designed by a production worker. Although the cost of the patent to date consisted of $52,300 in legal fees for handling the patent application, the patent should be commercially valuable during its entire remaining legal life of 10 years and is currently worth $400,000.

c) A franchise granting exclusive distribution rights for a new solar water heater within a three-state area for five years was obtained at a cost of $70,000. Satisfactory sales performance over the five years permits renewal of the franchise for another three years (at an additional cost determined at renewal).

General Journal :

Ref. Description Debit Credit

a. To record patent amortization. ___ __

b. To record patent amortization. __ __

c. To record franchise amortization. __ ___

A frequency table is a type of statistic used to organize and display data.

A data set is a collection of related data records or observations, usually containing information about a particular subject or area of study. Data sets can be used to analyze trends, make predictions, and provide insights into various phenomena. Data sets can be collected from a variety of sources, such as surveys, experiments, simulations, or other research methods. They are typically organized into tables and can include both quantitative and qualitative data.

It is a chart that shows how often something occurs within a given set of data. The categories in a frequency table are the different values or categories of data, and the frequencies are the number of times each category occurs.

Relative frequency is the ratio of the number of times a category occurs in the data set to the total number of values in the data set. It is usually expressed as a percentage or decimal. For example, if the data set contains 20 values and the category "A" occurs 5 times, the relative frequency of "A" is 25%.

Cumulative frequency is the sum of the frequencies up to a given point in the data set. It is used to show how many values are below or above a certain category. For example, if the data set contains 20 values and the category "A" occurs 5 times, the cumulative frequency of "A" is 5. This means that there are 5 values that are below or equal to "A" in the data set.

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Answer:

A frequency table is a type of statistic used to organize and display data.

What is data set?

A data set is a collection of related data records or observations, usually containing information about a particular subject or area of study. Data sets can be used to analyze trends, make predictions, and provide insights into various phenomena. Data sets can be collected from a variety of sources, such as surveys, experiments, simulations, or other research methods. They are typically organized into tables and can include both quantitative and qualitative data.

It is a chart that shows how often something occurs within a given set of data. The categories in a frequency table are the different values or categories of data, and the frequencies are the number of times each category occurs.

Relative frequency is the ratio of the number of times a category occurs in the data set to the total number of values in the data set. It is usually expressed as a percentage or decimal. For example, if the data set contains 20 values and the category "A" occurs 5 times, the relative frequency of "A" is 25%.

Cumulative frequency is the sum of the frequencies up to a given point in the data set. It is used to show how many values are below or above a certain category. For example, if the data set contains 20 values and the category "A" occurs 5 times, the cumulative frequency of "A" is 5. This means that there are 5 values that are below or equal to "A" in the data set.

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Answer:

6 and -4

Step-by-step explanation:

Let the first number be n.

Other number= [tex]\frac{-24}{n}[/tex]

Their sum= 2

n + [tex]\frac{-24}{n}[/tex]= 2

[tex]\frac{n^{2-24} }{n}[/tex]= 2

n²-24= 2n

You can solve this problem in either of these 2 ways:

i) Square Completion method:

  n²-2n = 24

  Half of the coefficient= [tex]\frac{2}{2}[/tex] =1

  Its square= 1²= 1

  n²-2n+1= 24+1

      (n-1)²= 25

          n-1= [tex]\sqrt{25}[/tex]

          n-1= ±5

  If n-1= 5,

     n= 5+1

     n= 6

  If n-1= -5,

     n= -5+1

     n= -4

  ∴ the numbers are 6 and -4

ii) Equation Method:

   n²-24= 2n

   n²-2n-24= 0

   a= 1,

   b= -2,

  -b= 2,

   c= -24

   n= -b±[tex]\sqrt{b^{2}-4ac }[/tex]/2a

   n= 2±[tex]\sqrt{-2^{2}-4x1x-24[/tex]/2x1

   n= 2±[tex]\sqrt{4+96}[/tex]/2

   n= 2±[tex]\sqrt{100}[/tex]/2

   n= 2±10/2

   If n= [tex]\frac{2+10}{2}[/tex],

      n= [tex]\frac{12}{2}[/tex]

      n= 6

   If n= [tex]\frac{2-10}{2}[/tex],

      n= [tex]\frac{-8}{2}[/tex]

      n= -4

∴ the numbers are 6 and -4

There are 9 possible comparisons that Adnan can write using the temperatures of the three nearby cities.

Combinations are the procedures used in mathematics to pick k things from n different items without replacement.

The following formula computes the combinations of k items from n:

(n, k) = n! / k!×(n-k)!

Let's say that Adnan looks up the current temperature in three nearby cities and writes down their temperatures as T1, T2, and T3.

To compare the temperatures, Adnan can choose any two of the temperatures and write a comparison of them.

Since there are three temperatures, there are a total of three possible pairs of temperatures that Adnan can choose:

1. T1 and T2

2. T1 and T3

3. T2 and T3

For each pair of temperatures, Adnan can write a comparison in one of three ways:

T1 is greater than T2 (T1 > T2)

T1 is less than T2 (T1 < T2)

T1 is equal to T2 (T1 = T2)

So, Adnan can write a total of nine possible comparisons of the temperatures:

T1 > T2,

T1 < T2,

T1 = T2,

T1 > T3,

T1 < T3,

T1 = T3,

T2 > T3,

T2 < T3, and

T2 = T3.

These are all the possible comparisons that Adnan can write using the temperatures of the three nearby cities.

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Question 9: The standard error of the mean (SEM) is 0.0912 and the 95% confidence interval is (5.0213, 5.3787).

Question 10: This confidence interval indicates that we can be 95% confident that the true mean of acid rain in Winnipeg is between 5.0213 and 5.3787.

Question 11: The 90% and 99% confidence interval for the data is (5.0499, 5.3501) and (4.9650, 5.4350) respectively.

Question 12: As the confidence interval increases from 90% to 95% to 99%, the width of the interval also increases. This means that the range of values that we can be confident contains the true mean becomes larger.

Question 9:

The standard error of the mean (SEM) is calculated as:

SEM = s / √n

where s is the standard deviation of the sample and n is the sample size.

Assuming that the standard deviation and sample size from assignment #2 are 0.5 and 30, respectively, the SEM can be calculated as follows:

SEM = 0.5 / √30

SEM = 0.0912

The 95% confidence interval around the sample mean estimate can be calculated as:

CI = mean +/- (1.96 * SEM)

Assuming that the sample mean from assignment #2 is 5.2, the 95% confidence interval can be calculated as follows:

CI = 5.2 +/- (1.96 * 0.0912)

CI = 5.2 +/- 0.1787

CI = (5.0213, 5.3787)

Question 10:

This confidence interval indicates that we can be 95% confident that the true mean of acid rain in Winnipeg is between 5.0213 and 5.3787. In other words, if we were to take multiple samples from the population and calculate the mean for each sample, 95% of those means would fall within this confidence interval.

Question 11:

The 90% confidence interval can be calculated as:

CI = mean +/- (1.645 * SEM)

CI = 5.2 +/- (1.645 * 0.0912)

CI = 5.2 +/- 0.1501

CI = (5.0499, 5.3501)

The 99% confidence interval can be calculated as

CI = mean +/- (2.576 * SEM)

CI = 5.2 +/- (2.576 * 0.0912)

CI = 5.2 +/- 0.2350

CI = (4.9650, 5.4350)

Question 12:

As the confidence interval increases from 90% to 95% to 99%, the width of the interval also increases. This means that the range of values that we can be confident contains the true mean becomes larger. This pattern emerges because a higher confidence level requires a larger margin of error to account for more variability in the data. As a result, the confidence interval becomes wider to ensure that the true mean is captured within the interval with a higher level of confidence.

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According to the model, the expected salary for a CEO of a firm with $5,000,000 in sales and $20,000,000 in market value is $2,178,357 or between $1,139,522 and $4,056,537.  Therefore, asking for $500,000 as an annual salary would be significantly lower than what the model predicts.

According to the model from part (a), the equation for the logarithm of annual salary is:

log(salary) = 4.62 + 0.16 sales + 0.11 log(mktval) + u

where u is the error term. This model has a multiple R-squared of 0.30, which means that it explains 30% of the variation in salaries based on sales and market value.

log(salary) = 4.62 + 0.16 x log(500000) + 0.11 x log(20000000)

log(salary) = 4.62 + 0.16 x 13.122 + 0.11 x 16.811

log(salary) = 7.625

salary = exp(7.625)

salary = $2,178,357

We can also use the coefficients from the model to calculate the expected salary directly, without taking logarithms.

salary = exp(β0) x sales^β1 x mktval^β2 x e^u

salary = exp(4.62) x 5,000,000^0.16 x 20,000,000^0.11 x e^u

salary = $2,178,357 x e^u

Using this assumption, we can calculate a 95% confidence interval for the expected salary:

log(salary) = 7.625

standard error = 535.9 x sqrt(0.16^2 + 0.11^2) = 136.6

95% confidence interval = exp(log(salary) ± 1.96 x standard error)

95% confidence interval = $1,139,522 to $4,056,537

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One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.

A= [ 1 1 1] [ 1 2 3] [ 4 5 6] and v = [ 2 ] [ 3 ] [ -1]​​. To find the image of v under TA, we simply multiply A and v to get:

TA = [ 1 1 1] [ 2 ] = [ 4 ]
[ 1 2 3] [ 3 ] [ 7 ]
[ 4 5 6] [ -1]​​ [ 17 ]

So the image of v under TA is [ 4 7 17 ].

To find vectors w that are different from v but that get mapped to the same image, we can use the equation TA*w = TA*v. Since TA*v = [ 4 7 17 ], we can set up the following system of equations:

1w1 + 1w2 + 1w3 = 4
1w1 + 2w2 + 3w3 = 7
4w1 + 5w2 + 6w3 = 17

Solving this system of equations will give us all the possible vectors w that get mapped to the same image as v. One possible solution is w = [ 1 2 0 ], which is different from v but gets mapped to the same image.

To find all vectors z that get mapped to zero, we can use the equation TA*z = 0. This gives us the following system of equations:

1z1 + 1z2 + 1z3 = 0
1z1 + 2z2 + 3z3 = 0
4z1 + 5z2 + 6z3 = 0

Solving this system of equations will give us all the possible vectors z that get mapped to zero. One possible solution is z = [ -3 2 1 ], which gets mapped to zero under TA.

Finally, to write down a nontrivial linear dependence relation between the columns of A, we can use the equation c1*A1 + c2*A2 + c3*A3 = 0, where A1, A2, and A3 are the columns of A and c1, c2, and c3 are constants. One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.

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Carlota's rate on a bicycle who is 74 miles away is approximately 6.1667 miles per hour.

Carlota's rate can be found by using the formula: rate = distance ÷ time. To find her rate for the first part of the trip, we can plug in the given values:

To find her rate for the second part of the trip, we need to subtract the distance and time she had already traveled from the total distance and time:

Then we can plug these values into the formula:

Since Carlota's rate is the same for both parts of the trip, we can simply use the overall distance and time to find her rate:

Therefore, Carlota's rate is approximately 6.1667 miles per hour.

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A function type that could model the given situation is a linear function.

The rate of change in the truck's worth per year is -1400.

A model that describes this situation is y = -1400x + 43500

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (36,500 - 43,500)/(2020 - 2015)

Slope (m) = -7,000/5

Slope (m) = 1,400.

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Answer:

The difference in elevation between the bottom of the canyon and the bird's nest is the sum of the depths, which is:

72 1/2 + 719 2/5

To add these two mixed numbers, we first convert them to improper fractions:

72 1/2 = 145/2

719 2/5 = (3595/5) + (2/5) = 3597/5

Now we can add them:

145/2 + 3597/5

To add fractions with different denominators, we need to find a common denominator. The smallest common multiple of 2 and 5 is 10, so we can rewrite the fractions with a denominator of 10:

145/2 × 5/5 = 725/10

3597/5 × 2/2 = 7194/10

Now we can add the fractions:

725/10 + 7194/10 = 7929/10

Finally, we can simplify the fraction and convert it back to a mixed number:

7929/10 = 792 9/10

Therefore, the difference in elevation between the bottom of the canyon and the bird's nest is 792 9/10 feet.

Kai drives 470 miles in 10 hours at a constant speed of 47 miles per hour. To find out how far Kai drives in 10 hours, we can use the distance formula d=rt, where d is the distance, r is the rate (or speed), and t is the time.

First, we need to find Kai's rate (or speed). We can do this by rearranging the formula to solve for r:

r = d/t

Plug in the values we know:

r = 376 miles / 8 hours

Simplify:

r = 47 miles per hour

Now that we know Kai's rate, we can plug it back into the distance formula to find out how far he drives in 10 hours:

d = rt

d = (47 miles per hour) (10 hours)

Simplify:

d = 470 miles

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Answer:

9/7 is smallerrrr

The given expression -5x⁶-7x³+7x²+4 is a polynomial.

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable. The terms in a polynomial are called monomials, and they can be either constants or variables with a coefficient.

In the given expression, there are four terms: -5x⁶, -7x³, 7x², and 4. Each of these terms is a monomial. Since there are four terms in the expression, it is classified as a polynomial with four terms, also known as a quadrinomial.

Therefore, the given expression -5x⁶-7x³+7x²+4 is a quadrinomial, which is a type of polynomial.

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The maturity value of the loan is $13487.58 and the interest paid on the loan is $5487.58.

The maturity value of a loan is the amount that will be due at the end of the loan period. To calculate the maturity value of the loan, we will use the formula:
Maturity Value = Principal x (1 + Interest Rate/Compounding Periods)^(Compounding Periods x Number of Years)
(a) Maturity value of the loan
Maturity Value = 8000 x (1 + 0.11/12)^(12 x 5)
Maturity Value = 8000 x (1 + 0.0091666667)^60
Maturity Value = 8000 x 1.685947578
Maturity Value = $13487.58
The maturity value of the loan is $13487.58.
(b) Interest are you paying on the loan
To calculate the interest paid on the loan, we will subtract the principal from the maturity value.
Interest = Maturity Value - Principal
Interest = 13487.58 - 8000
Interest = $5487.58
The interest paid on the loan is $5487.58.

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If the number when rounded to 2 decimal places  is equal to 9.68, then the upper bound is 9.685 and lower bound is 9.675 .

In order to find the upper bound of the number y, we need to add 0.005,

and to find the lower bound of the number y, we need to subtract 0.005 ,

We know that, the number y, when rounded to 2 decimal places is equal to 9.68 ;

So, the Upper Bound is = 9.68 + 0.005 = 9.685, and

The Lower Bound is = 9.68 - 0.005 = 9.675.

Therefore, the lower bound of y is 9.675 and upper bound of y is 9.685.

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Answer:

(c+1)(c+2)

Step-by-step explanation:

you need to find the two numbers that get 2 when you multiply them and get 3 when you add them. those two numbers are 2 and 1 and c times c is c^2

you can check the answer by using foil like this:

(c+1)(c+2)

first: c times c= c^2

second: 2 times c= 2c

third: 1 times c= 1c

last: 1 times 2= 2

and all that together you get c^2+2c+1c+2

simply and get C^2+3c+2