Simplify as far as possible. Please include the working in your answer, step by step.
\( \frac{9 {x}^{2} - 4 }{15 {x}^{2} - 13x + 2} \)
​

The best choice for the small business owner would be the loan with continuously compounded interest, as it results in the lowest overall cost.

Part A: To determine the total value of the loan with simple interest, we need to calculate the interest accrued over the loan term and add it to the principal.Interest = Principal * Interest Rate * Time

= $50,000 * 0.0525 * (3 + 8/12) years

= $50,000 * 0.0525 * 3.67

= $9,573.75

Total Value of the Loan = Principal + Interest

= $50,000 + $9,573.75

= $59,573.75

Part B: For quarterly compounded interest, we use the formula A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the time in years.

A = $50,000(1 + 0.0525/4)^(4 * 3.67)

= $50,000(1.013125)^14.68

= $50,000 * 1.2071

= $60,355.00

Part C: For continuously compounded interest, we use the formula A = P * e^(r*t), where A is the final amount, P is the principal, r is the interest rate, e is the mathematical constant approximately equal to 2.71828, and t is the time in years.

A = $50,000 * e^(0.0525 * 3.67)

= $50,000 * e^(0.1922175)

= $50,000 * 1.2113

= $60,565.00

Part D: Comparing the total values of the loans, we can see that the loan with continuously compounded interest has the highest total value ($60,565.00), followed by the loan with quarterly compounded interest ($60,355.00), and the loan with simple interest ($59,573.75).

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According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Answer:

x= 23 y=88

Step-by-step explanation:

3x+23= 4x

x=23

x and y are supplementary angles so they add up to 180 so then if x is 23

23 x 4= 92

so 180-92 is 88

therefore y is 88 and x is 23

Answer:

20

Step-by-step explanation:

I got it correct on khan

Answer:

x = 1, x = -1

Step-by-step explanation:

-4x² = -4

x² = 1

x = \(\sqrt{1}\)

x = ±1

The symbols d and sd represent:

The differences in the mean of the paired data entries in the dependent samples.

What is the standard deviation?

A measure of a set of values' variance or dispersion is called the standard deviation.

Here,

d: the difference between paired data in the dependent samples.

sd:  standard deviation.

The dependent samples' dependent samples' standard deviation for the variance between the means of the paired data items.

Hence, the differences in the mean of the paired data entries in the dependent samples.

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Answers:

1.) x - 3, x < -3

2.) x - 3, x>3

3.) x - 3, -3 <_ x > 3

4.) 2/5, 3/6

5.) 8, 10

Answer:

-43

Step-b-y-step explanation:

f(x)= -x^2+7x-13  so

f(-3)= - (-3)^2 + 7(-3) - 13

= -9 - 21 - 13

= -43.

The region of the solutions to the system is (d) Region B

From the question, we have the following parameters that can be used in our computation:

The graph

This point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (2, 3)

This is located in region B and it means that

x = 2 and y = 3

Hence, the region of the solutions to the system is (d) Region B

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A statement that creates a list is my_nums= [5,10,15]. This is also known as array.

An array is a grouping of identically typed elements that are stored in adjacent memory locations and may each be separately referred to using an index to a special identifier. There is no need to declare five distinct variables when declaring an array of five integer values (each with its own identifier).

The three types of arrays are index, multidimensional and associative array.

my_nums= [5,10,15] is an array that stores multiples of 5.

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A statement that creates a list is my_nums= [5,10,15]. This is also known as array.

What is an array?

An array is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is a combination of a set of elements which are all of the same data type, organized in a particular way. Arrays are used to store multiple values in a single variable, structure data, and access data more efficiently. Arrays are generally used to represent data in a structured way, and they can be used to perform various mathematical operations and other calculations. Arrays are also useful for sorting and searching data in a predetermined order.

What are three types of array?
The three types of array are index, multidimensional and associative array.
my_nums= [5,10,15] is an array that stores multiples of 5.

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The total number of students born in these three months is 2/5 of the total number of students in the class.

What is ratio ?

Ratio can be defined as given value divided by total value.

Let's assume there are a total of "x" students in the class.

According to the problem, 1/5 of the students were born in January.

So the number of students born in January = 1/5 * x

Similarly, 1/10 of the students were born in February, which means the number of students born in February = 1/10 * x.

And 1/10 of the students were born in March, which means the number of students born in March = 1/10 * x.

To find the total number of students born in these three months, we add up the number of students born in January, February, and March:

1/5 * x + 1/10 * x + 1/10 * x

= (2/10 * x) + (1/10 * x) + (1/10 * x)

= 4/10 * x

= 2/5 * x

Therefore, the total number of students born in these three months is 2/5 of the total number of students in the class.

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ANSWERS

• Mean: 67.025

• Mode: 67

EXPLANATION

The mean is the sum of all the data, divided by the amount of data,

In this case, the amount of data is 80,

Hence, the mean of this data set is 67.025.

The mode is the value or values in the data set that occurs most frequently. It is easier to find if we order the data set,

The value 67 occurs 9 times, while the second most frequent value is 66, which occurs 7 times.

Hence, the mode of this data set is 67.

Answer:

17hrs 45mins

Step-by-step explanation:

Timespan is 17 hour(s) and 45 minute(s).

If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

Given,

The percentage of people own dogs= 51%

We know,

Probability = Number of favorable outcomes / Total outcomes.

If you choose random guy and probability that guy own a dog = 0.51

Here the probability of having a dog is independent events

Then,

Probability that they both own a dog = Probability of first person own a dog × Probability of second person own a dog

= 0.51×0.51

=0.2601

Hence, If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

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Answer:

f(5) = 3(5+2) - 8

f(5) = 15+6 -8

f(5) = 21 - 8

f(5) = 13

Answer: I can’t see the numbers dude.

Step-by-step explanation:

Sorry

The correct answer is B.

p(x) and q(x) have the same domain but different ranges.

Let's analyze the functions individually:

Function p(x) = 6 – x:

Domain: There are no restrictions on the values of x, so the domain of p(x) is all real numbers.

Range: As x increases, the value of 6 – x decreases. Therefore, the range of p(x) is also all real numbers.

Function q(x) = 6x:

Domain: Again, there are no restrictions on the values of x, so the domain of q(x) is all real numbers.

Range: As x increases, the value of 6x also increases.

Therefore, the range of q(x) is all real numbers greater than or equal to zero (0).

Since the ranges of p(x) and q(x) are different (all real numbers for p(x) and all real numbers greater than or equal to zero for q(x)), the correct answer is B. p(x) and q(x) have the same domain but different ranges.

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Answer:

-2 (k+3) > -2k -7 --> -2k-6 > -2k-7

                                +2k       +2k

                                      -6 > -7 = No Solution

Step-by-step explanation:

Using the probability, Carlos should use 4 blocks labeled with a 1 and 1 block labeled with a 0 to represent kicking 5 field goals in a single game with a 72% probability of making each one.

To represent kicking 5 field goals in a single game with a 72% probability of making each one, Carlos can use a block for each kick, and label the block with a 1 to represent making the kick and a 0 to represent missing the kick. Since there are 5 kicks in total, he would need 5 blocks in total.

To determine how many of each block Carlos should use to represent the situation, we need to calculate the probability of making each kick and use it to determine the number of blocks labeled with a 1 and a 0.

Since the probability of making each kick is 72%, the probability of missing each kick is 28% (100% - 72%). Therefore, to represent 5 kicks with a 72% probability of making each one, Carlos should use:

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The probability that it takes the player 2 tries to make a three-point shot is approximately 0.217.

To find the probability that it takes player 2 tries to make a three-point shot, we can use the concept of geometric probability.

The probability of making a three-point shot on any single attempt is 0.682. Therefore, the probability of missing a shot on a single attempt is 1 - 0.682 = 0.318.

Since we are interested in the player making the shot on the second attempt, we need to consider the following sequence of events:

1. Missing the shot on the first attempt (probability of 0.318).

2. Making the shot on the second attempt (probability of 0.682).

To find the probability of these events occurring in sequence, we multiply their probabilities together:

0.318 * 0.682 = 0.217276

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Answer:

3x+7y=2

7y=-3x+2

y=3/7x +2/7

Step-by-step explanation:

the forme slope intercept y=mx+b

so you find what y equal in equation

the slope its m so in this equation its 3/7

y intercept its b in this equation its 2/7

The probability that she makes no more than 20 of them is 0.394

We use Binomial Distribution in solving this question.

The discrete probability distribution known as the binomial distribution only offers two outcomes for an experiment: success or failure.

Sum of independent Bernoulli trials is binomial distribution; a random Variable x is said to be following binomial distribution if it's density is given as

P(X=x) = (nCx) px (1−p)n−x    where x=0,1,2…n

Let x denotes the number of throws that makes a free throw so here

x follows Binomial distribution with n=28 and p=0.603

Thus, we calculate

P(X≤20) =∑_(k=0)^1▒1= (28Ck)0.603k (1−0.603)28−k =0.3144

=0.394

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Answer:

1.7 degrees

Step-by-step explanation:

101.3-99.6= 1.7

Answer:

1.7 Degrees

Step-by-step explanation:

101.3-99.6= 1.7

\(4x + x = 180\)

\(5x = 180\)

\(x = \frac{180}{5} = 36\)

Answer:

36

Step-by-step explanation:

This is a Linear Pair. Adjacent (next to) angles that form a straight line. A good rule of thumb for 90% of Geometry, angle relationships are usually either supplementary or congruent. In this case, since they together form a straight line, they are supplementary.

x + 4x = 180

5x = 180

180/5 = 36

If you plug these numbers in, you have a 36 degree angle and a 144 degree angle (sum of 180). Easy way to check your work if ever unsure.

The price at which the total quantity supplied is 250 is $11.58.

In order to find the price at which the total quantity supplied is 250, we need to equate the total quantity supplied by both producers (Supply 1 and Supply 2) and solve for the price.

Supply 1: P = 6 + 0.7Q

Supply 2: P = 16 + 0.6Q

To find the equilibrium price, we set the total quantity supplied equal to 250:

0.7Q + 0.6Q = 250

1.3Q = 250

Q = 250 / 1.3 ≈ 192.31

Now that we have the quantity, we can substitute it back into either supply function to find the price. Let's use Supply 1:

P = 6 + 0.7Q

P = 6 + 0.7 * 192.31

P ≈ 6 + 134.62

P ≈ 140.62

Therefore, the price at which the total quantity supplied is 250 is approximately $11.58.

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limx→0sinaxcosbxsincx=limx→0(cosbx⋅sinaxax⋅cxsincx⋅ac)=ac