Is this number prime or composite

Aplicando las leyes de los exponentes de potencia, los resultados son los siguientes:

En este ejercicio debemos aplicar cualesquiera de las siguientes propiedades asociadas a los exponentes:

(i) \((a^{b})^{c} = a^{b\cdot c}\)

(ii) \(a^{c}\cdot b^{c} = (a\cdot b)^{c}\)

(iii) \(a^{-b} = \frac{1}{a^{b}}\)

(iv) \(a^{b} = a^{b}\), donde \(a\) es negativo o positivo y \(b\) es par.

(v) \((-a)^{b} = -a^{b}\), donde \(a\) es positivo y \(b\) es impar.

(vi) \(a^{b}\cdot a^{c} = a^{b+c}\)

A continuación, tenemos los siguientes resultados:

a) \((2^{3})^{7} = 8^{7} = 2097152\)

b) \((3^{3})^{-2} = 3^{-6} = \frac{1}{729}\)

c) \((b^{3})^{4}=b^{12}\)

d) \([(x^{2})^{3}]^{4} = (x^{6})^{4} = x^{24}\)

e) \(\left(x^{\frac{3}{5} }\right)^{2} = x^{\frac{6}{5} }\)

f) \((3\cdot 4\cdot 2)^{5} = 3^{2}\cdot 4^{2}\cdot 5^{2} = 9\cdot 16\cdot 25 = 3600\)

g) \((a^{3}\cdot b^{5}\cdot c^{-4})^{2} = (a^{3})^{2}\cdot (b^{5})^{2}\cdot (c^{-4})^{2} = a^{6}\cdot b^{10}\cdot c^{-8}\)

h) \((2\cdot x^{5})^{3}\cdot (-5\cdot x^{2})^{2} = (2^{3}\cdot x^{15})\cdot [(-5)^{2}\cdot x^{4}] = (8\cdot x^{15})\cdot (25\cdot x^{4}) = (8\cdot 25)\cdot x^{19} = 200\cdot x^{19}\)

i) \(\left(3\cdot y^{\frac{2}{3} }\right)^{3}\cdot (2\cdot y^{2})^{2} = (27\cdot y^{2})\cdot (4\cdot y^{4}) = 108\cdot y^{6}\)

Invitamos cordialmente a consultar esta pregunta sobre potencias: https://brainly.com/question/24239709

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.

To know more about Model specification, visit:

https://brainly.com/question/13326948?

#SPJ11

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.

for such more question on sample size

https://brainly.com/question/28583871

#SPJ11

Answer:

a, \(Books = 315\)

b, \(Total = 20s + 45l\)

Step-by-step explanation:

Given

\(Small\ Box = 20\)

\(Large\ Box = 45\)

Solving (a): Books using 5 small and 7 large boxes;

This is calculated as follows

\(Books = Size * quantity\)

For Small box

\(Books = 20 * 5\)

\(Books = 100\)

For large box:

\(Books = 45 * 7\)

\(Books = 315\)

\(Total = 100 + 315\)

\(Total = 415\ books\)

Solving (b): s small and l large

We use the same concept as (a) above:

For Small Box

\(Books = 20 * s\)

\(Books = 20s\)

For large box

\(Books = 45 * l\)

\(Books = 45l\)

\(Total = 20s + 45l\)

Answer:

How many kids own their own instruments? 18

How many kids rent instruments? 72

What percentage of kids rent their instruments? 80%

Step-by-step explanation:

Tell me if it's right

Answer:

2.8 liters

Step-by-step explanation:

So there are various ways to do this problem, this is just MY preferred way.

Since we are given 1/4th of a total value with 14 liters, we can actually make this 4/4 by multiplying our given value by 4. In this case, 14 liters for 25% becomes 56 liters for 100% antifreeze.

Since we know have a percent of 100%, we can proceed to take 10% increments, all the way up to 30%

10% is 5.6, multiplied by 3 is 16.8

While you might want to put 16.8 instantly, don't forget we are looking for how much is ADDED from 25%, not just how much there is.

In this case, subtract 14 from 16.8 to come out with a grand total of 2.8 liters added.

Answer:

a^ (5/2)

Step-by-step explanation:

a^5 ÷ a ^ (5/2)

We know that x^b ÷ x^c = x^ ( b-c)

a^ ( 5 - 5/2)

a^ ( 10/2 - 5/2)

a^ (5/2)

Answer:

\(a^{\frac{5}{2} }\)

Step-by-step explanation:

Using exponent rules, if we have \(a^x \div a^y\) then the result can simplify to \(a^{x-y}\)

So \(a^5 \div a^{\frac{5}{2}}\) is the same as \(a^{5 - \frac{5}{2}}\).

\(\frac{5}{1} - \frac{5}{2} = \frac{10}{2} - \frac {5}{2} = \frac {5}{2}\)

So \(a^{\frac{5}{2}}\).

Hope this helped!

Lucy's dog needs to gain 6 pounds.

Lucy's dog lost 6 pounds so the dog will have to gain 6 pounds.

Answer:

 a) cannot tell

  b) congruent

  c) not congruent

Step-by-step explanation:

You want to know if the triangles in the given figures are congruent.

In order to prove congruence, we must have information to establish one of SSS, SAS, ASA, AAS congruence.

Congruence only of corresponding angles demonstrates the triangles are similar, which means they may or may not be congruent.

These triangles have congruent corresponding angles, so are similar. It is impossible to tell if they are congruent.

These triangles meet the conditions for demonstrating AAS congruence. The triangles are congruent.

Looking at the figure from an AAS or ASA or SAS point of view, the corresponding sides are not congruent, but the corresponding angles are. These triangles are similar, but are not congruent.

__

Additional comment

In the triangles of (c), for the given long side, the short side shown will be 25.73 in the larger triangle and 16.73 in the smaller one. That is, the angles indicate the triangles should be similar, but the given side ratios are not proportional.

<95141404393>

Step-by-step explanation:

3^x =3^2(y-1)

I changed 9 to 3^2.

3^x = 3^2y-2

Drop 3 both sides.

x=2y-1

Using the Bisection method, we need to find solutions accurate to within \(10^{-5}\) for the equations \(x^{2}\)+ 2x - 3 = 0 in the range -2 < x < 2 and x - \(2^{-4}\) = 0 in the range 0 < x < 1.

For the equation \(x^{2}\) + 2x - 3 = 0:

We start with an initial interval [-2, 2] and evaluate the function at the midpoint of the interval. If the function value is close to 0, we consider it as the solution. Otherwise, we narrow down the interval by dividing it in half and selecting the subinterval where the function changes sign. This process is repeated until the desired accuracy is achieved (within \(10^{-5}\)). The number of iterations required will be recorded.

For the equation x - \(2^{-4}\)= 0:

We follow the same steps as above but with the initial interval [0, 1]. Again, we iterate until the desired accuracy is reached and keep track of the number of iterations.

By applying the Bisection method and counting the number of iterations for each equation, we can find solutions accurate to within 10^-5 for both equations and determine the required number of iterations for each case.

Learn more about bisection here:

brainly.com/question/32563551

#SPJ11

Based on the given residual plot, it is essential to evaluate whether the linear model is a good fit for predicting the cost of a standard postage stamp.

A well-fitted linear model should display a random scatter of residuals, without any noticeable patterns or trends.

To determine if the model is a good fit, examine the residual plot for the following:

1. A random distribution of residuals around the horizontal axis (i.e., no discernible patterns or trends).

2. A constant spread of residuals throughout the entire range of predictor values (i.e., homoscedasticity). If these conditions are met in the residual plot, then the linear model is likely a good fit for the data. If not, a different model should be considered for better prediction accuracy.

learn more about plot here: brainly.com/question/15579115

#SPJ11

Answer:

Its "B"

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\rm\Large\red{\underline{Required\:Solution:}}\)

\( \implies 426 \times 373 \\ \bf = 158898\)

Trina should buy the $6 packages to get 24 necklaces for the least price as calculated by using multiplication and division.

From the attached table let us calculate the cost of buying necklaces in the various packages by using multiplication and division.

For the $4 package:

Number of necklaces in the package = 3

Number of packages Trina should buy (division used) = 24 ÷ 3 = 8

Cost of 8 packages =$ 4 × 8 = $ 32

For the $5 package:

Number of necklaces in the package = 4

Number of packages Trina should buy(division used) = 24 ÷ 4 = 6

Cost of 8 packages =$ 5 × 6 = $ 30

For the $6 package:

Number of necklaces in the package = 6

Number of packages Trina should buy(division used) = 24 ÷ 6 = 4

Cost of 8 packages =$ 6 × 4 = $ 24

Therefore buying the $24 package is the cheapest.

To learn more about multiplication and division visit:

https://brainly.com/question/1292482

Disclaimer: The missing table is attached below.

#SPJ9

Answer:

Sam had 80 dollars in his pocket. He was feeling generous, so he handed out equal amount of money to each of his friends. After he handed out the money, he had 53 dollars left. How much did Sam give out to each one of his friends?

Step-by-step explanation:

In this real-world problem, the money he had at the beginning resembles the 80 in the equation. The -3x is the money he gives out to each of his friends. The 53 on the right-hand side is the money he has left after he gives the money away.

To determine if parents feel differently today compared to twenty years ago, we can conduct a hypothesis test using the given data. Let's set up the null and alternative hypotheses:

Null hypothesis (H0): The proportion of parents who feel it is a serious problem that high school students are not being taught enough math and science is the same today as it was twenty years ago.

Alternative hypothesis (Ha): The proportion of parents who feel it is a serious problem that high school students are not being taught enough math and science is different today compared to twenty years ago.

We can use a hypothesis test for a single proportion to compare the proportions. Let p1 represent the proportion twenty years ago, and p2 represent the proportion today.

Given information:

Twenty years ago: 53% of parents felt it was a serious problem.

Recent survey: 325 out of 850 parents felt it was a serious problem.

Using the recent survey data, we can calculate the sample proportion of parents who feel it is a serious problem today:

p2 = 325/850 = 0.3824

To calculate the test statistic, we need to compare the sample proportion today to the proportion twenty years ago.

Under the null hypothesis, we assume that p1 = p2. Thus, we can estimate the common proportion using the combined sample proportion:

p = (x1 + x2) / (n1 + n2)

where x1 is the number of parents who felt it was a serious problem twenty years ago, and n1 is the total number of parents twenty years ago.

Assuming p1 = p2 = p, we can calculate the test statistic:

z = (p2 - p) / sqrt(p(1-p)(1/n1 + 1/n2))

We can then compare the test statistic to the critical value at the α = 0.1 level of significance.

If the test statistic falls in the rejection region (beyond the critical value), we reject the null hypothesis and conclude that parents feel differently today compared to twenty years ago. Otherwise, if the test statistic falls within the non-rejection region, we fail to reject the null hypothesis and do not conclude a significant difference.

Since the exact values for the number of parents and the total number of parents twenty years ago are not provided, we cannot calculate the precise test statistic or critical value.

However, you can use the provided formula and the specific values to perform the calculations and draw a conclusion based on the test statistic and critical value for α = 0.1.

To learn more about hypothesis test go to:

https://brainly.com/question/28331914

#SPJ11

Answer:

5

25/5=5

Step-by-step explanation:

The solutions to the system of equations are: y=2, x=0.

What is equations?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

\($$\left[\begin{array}{c}y=3 x+2 \\y=-2 x+2\end{array}\right]$$\)

Substitute \($y=-2 x+2$\)

\($$[-2 x+2=3 x+2]$$\)

Isolate x for \($-2 x+2=3 x+2: \quad x=0$\)

For\($y=-2 x+2$\)

Substitute \($x=0$\)

\($$y=-2 \cdot 0+2$$\)

Simplify

y=2

The solutions to the system of equations are: y=2, x=0.

To learn more about equations visit:https://brainly.com/question/29657983

#SPJ1

The solutions to the system of equations are: y=2, x=0.

What is equations?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

\($$\left[\begin{array}{c}y=3 x+2 \\y=-2 x+2\end{array}\right]$$\)

Substitute y=-2 x+2

[-2 x+2=3 x+2]

Isolate \($\mathrm{x}$\) for \($-2 x+2=3 x+2: \quad x=0$\)

Fory =-2 x+2

Substitute x=0

\(y=-2 \cdot 0+2\)

Simplify

y=2

The solutions to the system of equations are: y=2, x=0.

To learn more about equations visit:brainly.com/question/29657983

#SPJ1

Answer:

According to the model, in 2025 the world population will be 8,493,750,000

Step-by-step explanation:

Rate at which population was growing per year = 0.09125 billion

Initial population figure in 1990 = 5.3 billion

World population prediction in 2010 ;

Predicted population figure :

Initial population + (population growth value per year * number of years)

number of years = (2025 - 1990) = 35 years

Predicted population figure in 2025 :

5.3 + (0.09125 * 35)

5.3 + 3.19375

= 8.49375 billion.

8,493,750,000 by 2025

Answer:

b

Step-by-step explanation:

edge 2021

To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.

The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.

For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.

To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.

Learn more about median here https://brainly.com/question/28060453

#SPJ4

Theorem of Angle-Angle-Side (AAS) Congruence: The two triangles are congruent if two angles and a non-included side of one triangle are congruent with two angles and the corresponding non-included side of a second triangle.

To learn more about Angle-Angle-Side refer to:

https://brainly.com/question/3168048

#SPJ1

Answer:

the daylilies cost: $5

The roses cost:$3

The tulips cost:$1

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Solve for x

x - 1  = -2x + 5

3x = 6

x = 2

Answer: 3

Step-by-step explanation:

1×-2=-2

-2+5=3

-2×1+5=3

I hope this helps, have a good day or night:)

The population parameter is the average amount of time for all students to complete the standardized test. The 90% confidence interval [108.6, 143.4] means that we are 90% assured that the true population means lies within this range.

The population parameter in this case is the average amount of time, in minutes, for all students to complete the standardized test.

The interpretation of the 90% confidence interval [108.6, 143.4] is that we are 90% confident that the true population means that it falls within this interval. It means that if we were to repeat the sampling process multiple times and construct 90% confidence intervals, approximately 90% of these intervals would capture the true population mean. In this specific case, we can be 90% assured that the average time for all students taken to complete the standardized test must be between 108.6 and 143.4 minutes.

Learn more about the calculation of population here: https://brainly.com/question/29159915

#SPJ11

An arrow diagram represents a relation between elements using arrows. Each element in the matrix corresponds to a point in the diagram, and the arrows indicate the relationship between the elements. The task is to create an arrow diagram and express the relation as a set of ordered pairs for a three-row matrix with entries [[0, 1, 0], [1, 0, 0], [0, 0, 1]].

An arrow diagram represents a relation between elements using arrows. Each element in the matrix corresponds to a point in the diagram, and the arrows indicate the relationship between the elements.

For the given three-row matrix, we can represent it as an arrow diagram with three points labeled as A, B, and C. The arrows will connect the elements based on the entries in the matrix. In this case, the matrix has a 1 in the first row and second column, indicating a relation between the first and second points. Similarly, there is a 1 in the second row and first column, and a 1 in the third row and third column.

Expressing the relation as a set of ordered pairs, we can observe the connections between the elements in the arrow diagram. Based on the arrows, the set of ordered pairs representing the relation would be        {(A, B), (B, A), (C, C)}. These ordered pairs indicate the pairs of elements that have a direct relation based on the matrix entries.

Learn more about arrow diagram here:

https://brainly.com/question/8223738

#SPJ11

The equation of the sphere that passes through the point (5, 8, 3) and has center (8, 1, -5) is (x - 8)² + (y - 1)² + (z + 5)² = 122.

To find the equation of a sphere that passes through the point (5, 8, 3) and has a center at (8, 1, -5), we can use the standard form equation of a sphere:

(x - h)² + (y - k)² + (z - l)² = r²,

where (h, k, l) represents the center of the sphere, and r represents the radius.

Given that the center is (8, 1, -5), we can substitute these values into the equation:

(x - 8)² + (y - 1)² + (z + 5)² = r².

Now, we need to find the radius, which is the distance between the center (8, 1, -5) and the point (5, 8, 3).

We can use the distance formula:

r = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²],

where (x₁, y₁, z₁) represents the center and (x₂, y₂, z₂) represents the given point.

Substituting the values, we get:

r = √[(5 - 8)² + (8 - 1)² + (3 - (-5))²]

= √[(-3)² + 7² + 8²]

= √[9 + 49 + 64]

= √[122]

= √122.

Now we can write the equation of the sphere:

(x - 8)² + (y - 1)² + (z + 5)² = (√122)²

(x - 8)² + (y - 1)² + (z + 5)² = 122.

For similar question on sphere.

https://brainly.com/question/30522100

#SPJ8

Answer:

A. $15

B.  x - .25x

C.  $12.50

Step-by-step explanation:

A. .25 x $20 = $5

$20-$5 = $15 discounted price of T-shirt

B. x - .25x

C. x + .25x = $10

1.25x = $10

x = $12.50

The solutions to the equation 6(x+1)^2 + 4 = 0 using square roots are x = -1 + (√(2/3)) * i and x = -1 - (√(2/3)) * i.

To solve the equation 6(x+1)^2 + 4 = 0 using square roots, we will follow these steps:

Step 1: Move the constant term to the other side of the equation.

\(6(x+1)^2 = -4\)

Step 2: Divide both sides of the equation by the coefficient of the squared term.

\((x+1)^2 = -4/6\)

Step 3: Simplify the right side of the equation.

\((x+1)^2 = -2/3\)

Step 4: Take the square root of both sides of the equation.

√\([(x+1)^2\)] = ±√(-2/3)

Step 5: Simplify the left side of the equation.

x+1 = ±√(-2/3)

Step 6: Rewrite the square root of a negative number using imaginary unit 'i'.

x+1 = ±√[(2/3)(-1)] * i

Step 7: Simplify the right side of the equation.

x+1 = ±(√(2/3)) * i

Step 8: Subtract 1 from both sides of the equation.

x = -1 ± (√(2/3)) * i

Therefore, the solutions to the equation 6(x+1)^2 + 4 = 0 using square roots are x = -1 + (√(2/3)) * i and x = -1 - (√(2/3)) * i.

It's important to note that when we encounter the square root of a negative number, we introduce the imaginary unit 'i' to represent the square root of -1. The solutions in this case involve complex numbers, where the real part is -1 and the imaginary part is ±(√(2/3)).

For more such questions on equation visit:

https://brainly.com/question/22688504

#SPJ8

If the parent function \(\sf y=(1.6)^x\) is translated 5 units up and 9 units to the right, then you should subtract 9 from x and add 5 to the whole function. Thus,

1) translation the parent function \(\sf y=(1.6)^x\) 9 units to the right gives you the function \(\sf y=(1.6)^{x-9}\).

2) translation the function \(\sf y=(1.6)^{x-9}\) 5 units up gives you the function \(\sf y=(1.6)^{x-9}+5\)

Therefore, the correct choice is C

Learn more: brainly.com/question/11468584