Let n and m be positive integers, where the unique prime factorisations of n and m are given by: n = 2 · 3 ^a · 7^2 · 13^b for some fixed a, b ∈ Z + m = 3^k · 7 · 11 · 13^ℓ for some fixed k, ℓ ∈ Z +. If a < k and b > ℓ, determine the greatest common divisor of n and m and the least common multiple of n and m

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:

46%

Step-by-step explanation:

Answer:

factors

Step-by-step explanation:

To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.

a) The area of triangle PQR is:

Area = √(6)/2

b) The equation of the plane that contains P, Q, and R is:

x + y + 2z = 2

a) For the area of the triangle PQR, we can use the formula:

Area = 1/2 |PQ x PR|

where PQ and PR are the vectors from P to Q and R, respectively, and x denotes the cross product.

So, we have:

PQ = <1-0, -1-0, 2-1> = <1, -1, 1>

PR = <-1-0, 1-0, 1-1> = <-1, 1, 0>

Taking the cross product:

PQ x PR = <1, -1, 1> x <-1, 1, 0> = <-1, -1, -2>

Taking the magnitude:

|PQ x PR| = √((-1)² + (-1)² + (-2)²) = √(6)

So, the area of triangle PQR is:

Area = 1/2 × √(6) = √(6)/2

b) To find the equation of the plane that contains P, Q, and R, we can use the point-normal form of the equation:

n · (r - P) = 0

where n is the normal vector of the plane (which is perpendicular to the plane), r is any point on the plane, and · denotes the dot product.

To find the normal vector, we can take the cross product of PQ and PR:

n = PQ x PR = <-1, -1, -2>

Now, we can use any of the three points to find the equation of the plane. Let's use P:

n · (r - P) = 0

Substituting n and P:

<-1, -1, -2> · (r - <0, 0, 1>) = 0

Expanding the dot product:

-1(r_x - 0) - 1(r_y - 0) - 2(r_z - 1) = 0

Simplifying:

-r_x - r_y - 2r_z + 2 = 0

So, the equation of the plane that contains P, Q, and R is:

x + y + 2z = 2

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-4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

The physical concept of temperature indicates in numerical form how hot or cold something is.

A thermometer is used to determine temperature.

Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.

The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).

The lowest point on the thermodynamic temperature scale is absolute zero, or zero kelvin, or 273.15 °C. It can be very closely approximated experimentally but never actually reached, as stated in the third rule of thermodynamics.

Hence, -4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

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The predicted mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F is approximately 828.9 cubic feet.

To predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F, we will use the given regression line equation: y^ = 1425 - 19.87x.

Step 1: Substitute the value of x (mean temperature) with 30.
y^ = 1425 - 19.87(30)

Step 2: Perform the calculations.
y^ = 1425 - 596.1

Step 3: Simplify the equation.
y^ = 828.9

So, the predicted mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F is approximately 828.9 cubic feet.

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Answer: 0.024

Step-by-step explanation:

percents are out of 100 so 2.4% divided by 100 = the decimal. 2.4/100 = 0.024

To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

Step 1: Identify the critical value (z-score) for a 90% confidence interval. This can be found in a standard z-table or using a calculator. The critical value for a 90% confidence interval is 1.645.

Step 2: Use the margin of error (E) formula to calculate the sample size (n):
E = (z * σ) / √n

Where E is the margin of error (0.5 mph), z is the critical value (1.645), σ is the standard deviation (7 mph), and n is the sample size.

Step 3: Rearrange the formula to solve for n:
n = (z * σ / E)^2

Step 4: Plug in the values and calculate the sample size:
n = (1.645 * 7 / 0.5)^2
n ≈ 338.89

Since the sample size must be a whole number, round up to the nearest whole number.

To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

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Answer:

x = 1.155

x = -1.155

Step-by-step explanation:

4x² = x² + 4

4x² - x² = 4

3x² = 4

\( \frac{ {3x}^{2} }{3} = \frac{4}{3} \)

\( {x}^{2} = \frac{4}{3} \)

\(x = + - \sqrt{ \frac{4}{ 3} } \)

\(x = \sqrt{ \frac{4}{3} } \: or \: 1.155\)

\(x = - \sqrt{ \frac{4}{3} } \: or - 1.155\)

Answer:

Step-by-step explanation:

\(c(9 - 2) \cdot 3=21\\\\\mathrm{Divide\:both\:sides\:by\:}21\\\\\frac{c\left(9-2\right)\cdot \:3}{21}=\frac{21}{21}\\\\c = 1\)

When comparing means of three or more conditions, an analysis of variance (ANOVA) should be used instead of multiple t-tests. This is because using multiple t-tests increases the risk of a type I error, where a significant difference is found when there is none. ANOVA controls for this by using a single test to determine if there is a significant difference between the means. Additionally, using multiple t-tests increases the risk of a type II error, where a significant difference is not found when there is one.

ANOVA is also more likely to detect statistical significance between the means because it takes into account the variability within each condition as well as the variability between conditions. This increases the power of the test and reduces the chances of missing a significant difference between the means.

When using ANOVA, the results can indicate that there are no differences between any of the population means (option a), that at least one of the three population means is different from another population mean (option b), that all three of the population means are different from each other (option c), or that one population mean is different from one of the other population means, but not the other population mean (option d).

Finally, ANOVA provides a measure of effect size, typically reported as r2, which indicates the proportion of variability in the data that can be attributed to the differences between the conditions. This can be useful in determining the practical significance of the results.

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Answer: 3

Step-by-step explanation: I looked it up.

Answer:

the greatest common factor of 45 and 12 if 3

Step-by-step explanation:

Rate of change=35000-25000=10000

Time=6years

Total cost

\(\\ \sf\longmapsto 10000(6)=\$60000\)

Answer:

3 and 1/3 of an hour

Step-by-step explanation:

The most appropriate measure of center is the mean which describes the average weight of oranges.

For the given data:

5,6,7,7,8,8,10,11,11,14,16,19,20,21

The most appropriate measure of center from the data given is the mean. The mean value gives the average weight of the oranges in the scenario given above.

The mean can be calculated thus :

(Sum of weight / Number of values)

Mean = (163 / 14)

Mean = 11.64

Hence, the most appropriate measure of center is the mean and it describes the average weight of oranges.

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The percent of adult American males could enter this contest is 2.23%

Normal usually refers to the word "normal" in a normal distribution.

The word normal is used when something occurs that has occurred frequently. The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

We solve using z score formula

z = (x-μ)/σ,

where, x is the raw score = < 64 inches

μ is the population mean = 69

σ is the population standard deviation = 2.5

Here Participants must be less than 64 inches tall.

For x < 64 inches

z = 64 - 69/2.5

z = -2

Probability value from Z-Table:

P(x<64) = 0.02275

Converting to percentage;

= 0.02275 × 100

= 2.275%

Approximately = 2.23%

The participants must be less than 64 inches tall to participate in this limbo contest, the percent of adult American males thag could enter this contest is 2.23%

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Answer:

a = 7.4

b = 9.6

Step-by-step explanation:

set up a proportion to find 'b':

XN / NY = MN / NO

8/b = 13/(b+6)

cross-multiply:

13b = 8(b+6)

13b = 8b + 48

5b = 48

b = 9.6

set up a proportion to find 'a':

XN / XY = MN / MO

8/a = 13/12

cross-multiply:

13a = 96

a ≈ 7.4

Answer:

I will say A because is the one that makes more sense and is actually the one that is discrimination the equation

Answer:

y= -7

Step-by-step explanation:

There's no need to include x as the y-value will always be -7, but if your question requires it then you could say something like y=(x-x)-7

Constructing a 98% confidence interval with a larger sample size would result in a wider, yet more precise interval compared to a 95% confidence interval with a smaller sample size.

If you construct a 98% confidence interval for the population mean instead of a 95% confidence interval and the sample size is larger for the 98% interval, with everything else being the same, the confidence interval would:

1. Be wider than the 95% confidence interval:

A higher confidence level (98% vs. 95%) requires a wider interval to capture the true population mean with greater certainty.

2. Be more precise due to the larger sample size:

A larger sample size provides more information about the population, which generally leads to a more precise estimate of the population mean.

To summarize, constructing a 98% confidence interval with a larger sample size would result in a wider, yet more precise interval compared to a 95% confidence interval with a smaller sample size.

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Answer:

so 6+30=36

we can use the distributive property

36-6=30

36-30=6

Hope This Helps!!!

Answer:

B.   x < -4  and x > 3

Step-by-step explanation:

Factor and set = to 0

\(x^{2} + x - 12\\( x + 4)(x - 3)\) = 0

x = - 4  or x = 3     I call these critical values

The two numbers would divide a number line into 3 intervals.  Pick a value in one of the intervals and put it in the original expression.  If it makes the function positive, then all the values in that interval make the function positive.  If the value you picked makes the function negative, then the values in the other intervals will make the function negative.  Let's pick the value of 0 and substitute it into the function

We get \(0^{2}\) + 0 - 12 = -12 which is not positive.  Therefore, all the values between -4 and 3 will make the function negative.  So, the values less than -4 or greater than 3 will make the function positive.  Therefore, B is the correct answer.

Another way to do this problem is to graph the function and see where the graph is above the x-axis.  But, sometimes it is not easy to graph the function.

The most likely production for a rainfall of 40 mm is 56.4 quintals.

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

          Rainfall (mm) Production (quintals)

Mean           35                  50

S.D                5                    8

Coefficient of correlation = 0.8​

First, we need to calculate the regression equation, which is:

y = a + bx

Where

To calculate the intercept and slope, we use the following formulas:

b = r * (SDy / SDx)

a = Ymean - b * Xmean

Plugging in the given values, we get:

b = 0.8 * (8 / 5) = 1.28

a = 50 - 1.28 * 35 = 5.2

Therefore, the regression equation is:

Y = 5.2 + 1.28x

To find the most likely production for a rainfall of 40 mm, we plug in x = 40 into the regression equation:

Y = 5.2 + 1.28 * 40

Y = 56.4

Hence, the most likely production is 56.4 quintals.

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Answer:

A = 7

Step-by-step explanation:

√50 = 7.07

approximating it will give you

= 7

At great axial distances x from a current-carrying loop, the magnetic field varies as:

b. x^-3

Here's the step-by-step explanation:

1. The magnetic field B at a point on the axis of a current-carrying loop can be given by the formula: B = (μ₀Ia²) / (2(a² + x²)^(3/2))

2. In this formula, μ₀ is the permeability of free space, I is current, a is the radius of the loop, and x is the axial distance from the loop.

3. When the axial distance x is much greater than the radius a (i.e., x >> a), the term a² in the denominator becomes negligible compared to x².

4. Therefore, the formula simplifies to: B ≈ (μ₀I) / (2x³)

As you can see, the magnetic field B varies as x^-3 at great axial distances from the current-carrying loop.

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Applying second fundamental theorem to the given function, f(x) = ∫[1 to 9x] t csc(t) dt, we can find its derivative, f'(x), by evaluating the integrand at the upper limit of integration, which is 9x.

The second fundamental theorem of calculus states that if we have a function defined as the integral of another function, then its derivative can be found by evaluating the integrand at the upper limit of integration. The derivative of f(x) is given by f'(x) = 9 csc(9x). This result comes from applying the second fundamental theorem of calculus. The integrand of the given function is t csc(t), and by evaluating it at the upper limit of integration, 9x, we obtain the derivative. The 9 outside the csc function is due to the fact that the derivative of 9x with respect to x is 9. Therefore, the derivative of f(x) with respect to x is simply 9 csc(9x).

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Answer:

1. 56.55

2. 150.8

Step-by-step explanation:

I didn't know if you were looking for the circumference or what

The height of Jeremy is 159 cm.

To find the height of Jeremy:

So,

Then, Jeremy = 135 + 24 = 159 cm.

Therefore, the height of Jeremy is 159 cm.

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