Which expression is equivalent to 3^4 x 3^-9?

The parametric equations for the motion of the particle will be : d) x(t) = (3t/20) + 6, y(t) = (2t/20) + 5.

To find the parametric equations for the motion of the particle, we need to determine how the x and y coordinates change with respect to time.

Given that the particle moves from point A = (6,5) to point B = (9,7) in 20 seconds at a constant rate, we can calculate the rate of change for each coordinate.

For the x-coordinate, the change is 9 - 6 = 3, and the time taken is 20 seconds. Therefore, the rate of change for x is 3/20.

For the y-coordinate, the change is 7 - 5 = 2, and the time taken is 20 seconds. Hence, the rate of change for y is 2/20.

Now, we can write the parametric equations for the motion of the particle:

x(t) = (3t/20) + 6

y(t) = (2t/20) + 5

Therefore, the correct answer is: d) x(t) = (3t/20) + 6, y(t) = (2t/20) + 5.

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The length of the shortest piece is 5, and the longest piece is 13 feet by solving the equations.

The length of the shortest piece is 5, and the longest piece is 13 feet.

the solution is as follows,

Greg has a piece of rope that is 18 ft long.

He wants to cut it into two pieces so that the longer piece is 2 ft less than three times the length of the.

Let the length of the shorter piece be x.

And the length of the longer piece is 3x -2.

Greg has a piece of rope that is 18 ft long.

Then,

longest piece+ shorter piece = 18

x + 3x -2 = 18

4x - 2 =18

4x = 18+2

4x = 20

x= 20/4

x = 5.

Therefore,

The length of the shorter piece is x =5.

And the length of the longer piece = 3x -2 = 3(5)-2 = 15-2 = 13

Hence, the length of the shortest piece is 5, and the longest piece is 13 feet.

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Answer:

x = 16 and y = 116

Step-by-step explanation

For the trapezoid, the sum of the adjacent side is 180. Hence;

6x+20 + 4x = 180

10x + 20 = 180

10x = 180-20

10x = 160

x = 160/10

x = 16

Also, the sum of opposite side is 180, hence;

4(16)+ y = 180

64 + y = 180

y = 180 - 64

y = 116 degrees

hence x = 16 and y = 116

Research that provides data which can be expressed with numbers is called quantitative research.

Quantitative research is a type of research that focuses on gathering and analyzing numerical data. It involves collecting information or data that can be measured and quantified, such as numerical values, statistics, or counts. This research method aims to objectively study and understand phenomena by using mathematical and statistical techniques to analyze the data.

Quantitative research typically involves the use of structured surveys, experiments, observations, or existing data sources to gather information. Researchers often employ statistical methods to analyze the data and draw conclusions or make predictions based on the numerical findings.

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Answer:

3000

Step-by-step explanation:

To simplify, 1 significant figure means a number that isn't zero. Although the zeros in 3000 do count as significant figures so this is a weird one.

All the missing angles of the triangles are;

m∠1 =  50°

m∠4 = m∠2 = 30°

m∠3 = 50°

m∠5 = 40°

m∠6 = 50°

m∠7 = 90°

We know that the sum of angles in a triangle is 180 degrees. Thus;

m∠1 = 180 - (90 + 40)

m∠1 =  50°

We know that sum of angles on a straight line is 180 degrees. Thus;

m∠4 = m∠2 = 180 - 50

m∠4 = m∠2 = 30°

Now, opposite angles are equal and as such;

m∠1 =  m∠3 = 50°

Using the first concept, we can say that;

m∠5 = 180 - (90 + 50)

m∠5 = 40°

Similarly,

m∠6 = 90 - 40

m∠6 = 50°

Similarly,

m∠7 = 90°

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Answer:

The slope is \(\frac{3}{5}\) because if you do the rise over run method, it goes up 3 times and right 5 times, therefor being \(\frac{3}{5}\).

Answer:

c

Step-by-step explanation:

Answer:

  {-√6, -1, 1, √6}

Step-by-step explanation:

You want the roots of the quartic 3x^4-21x^2+18.

We can find the roots by factoring to linear factors:

  = 3(x^4 -7x^2 +6)

  = 3(x^2 -6)(x^2 -1) . . . . . . . 6 = (-1)(-6) are factors with a sum of -7

  = 3(x -√6)(x +√6)(x -1)(x +1) . . . . . a^2 -b^2 = (a -b)(a +b)

The roots of the quartic are ±√6 and ±1.

Answer:

The answer is the last one!! 3/14

Step-by-step explanation:

Answer:

s increases

Step-by-step explanation:

2t is a positive value so it will make the value of a increase

A C++ function getNorm that returns its 1-norm is defined.

Here's an implementation of the 'getNorm' function in C++:

#include <iostream>

float getNorm(float **matrix, int N) {

   float norm = 0.0;    

   for (int j = 0; j < N; j++) {

       float sum = 0.0;

       for (int i = 0; i < N; i++) {

           sum += std::abs(matrix[i][j]);

       }

       if (sum > norm) {

           norm = sum;

       }

   }    

   return norm;

}

In this implementation, we iterate over each column of the matrix and calculate the sum of absolute values of elements in that column. We keep track of the maximum sum encountered so far and return it as the 1-norm of the matrix.

Complete Question:

Given a NxN matrix of floats, write a function getNorm that returns its 1-norm, defined as: || A||\(_1\) = max (i<=j<=n)\((\sum (i=1\ to\ n) |a_{ij}|\))

The prototype of getNorm should be: float getNorm(float **matrix, int N);

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The MSE for the regression models developed in parts (b) and (d) is Ŷ = 5.10 + 0.83X

Let's assume that the dependent variable in both models is denoted by Y, and the independent variable is denoted by X. The regression model developed in part (b) is expressed as:

Y = 5.10 + 0.83X

The regression model developed in part (d) is expressed as:

Y = 4.90 + 0.89X + 0.012X²

To calculate the MSE for the model developed in part (b), we need to first calculate the predicted values of Y using the equation:

Ŷ = 5.10 + 0.83X

Then, we can calculate the squared difference between the predicted value Ŷ and the actual value Y for each data point, and take the average of these squared differences. This gives us the MSE for the model developed in part (b).

Similarly, to calculate the MSE for the model developed in part (d), we need to first calculate the predicted values of Y using the equation:

Ŷ = 4.90 + 0.89X + 0.012X^2

Then, we can calculate the squared difference between the predicted value Ŷ and the actual value Y for each data point, and take the average of these squared differences. This gives us the MSE for the model developed in part (d).

After calculating the MSE for both models, we can compare them to determine which model is more effective. A lower MSE indicates that the model is more accurate in predicting the dependent variable.

Therefore, the model developed in either part (b) or (d) with the lower MSE is considered to be more effective.

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To find the sum of the vertex angles in various polygons, we need to sketch the polygons and then calculate the sum. For a hexagon, octagon, and dodecagon, the sums of the vertex angles are 720°, 1,080°, and 1,800°, respectively.

a. Hexagon: A hexagon is a polygon with six sides. To find the sum of the vertex angles, we can divide the hexagon into triangles. Since each triangle has an interior angle sum of 180°, the hexagon can be divided into four triangles. Therefore, the sum of the vertex angles in a hexagon is 4 * 180° = 720°.

b. Octagon: An octagon is a polygon with eight sides. Similar to the hexagon, we can divide the octagon into triangles. Dividing it into six triangles, each with an interior angle sum of 180°, the sum of the vertex angles in an octagon is 6 * 180° = 1,080°.

c. Dodecagon: A dodecagon is a polygon with twelve sides. Dividing it into ten triangles, each with an interior angle sum of 180°, the sum of the vertex angles in a dodecagon is 10 * 180° = 1,800°.

Therefore, the sum of the vertex angles in a hexagon is 720°, in an octagon is 1,080°, and in a dodecagon is 1,800°.

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Find the sum of the vertex angles of the following polygons---

a. A hexagon

b. An octagon

c. A dodecagon.

Answer:

C. Ry-axis(x, y) = (-x, y)

Step-by-step explanation:

Answer: D. Rx-axis (x, y) = (x, -y)

Step-by-step explanation:

A (-3, 5)  --> A' (-3, -5)

B (2, 8)  --> B' (2, -8)

C (-4, -5)   --> C' (-4, 5)

Hope this helped!

The chi-square goodness-of-fit test requires that all anticipated counts be at least five and observations be drawn from random sample in order to be valid. The correct statements are I and III only. Correct option is C.

I. The chi-square goodness-of-fit test requires that all anticipated counts be at least five and that observations be drawn from a random sample in order to be valid. This statement is correct. The chi-square goodness-of-fit test is based on the chi-square distribution, which approximates the sampling distribution of the test statistic.

To ensure the validity of the test, it is generally recommended that all expected counts in the cells of the contingency table have a minimum expected count of five. This guideline helps to ensure that the chi-square test statistic follows the chi-square distribution, which is approximately valid under this condition.

II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom. This statement is incorrect. The number of categories being assessed determines the degrees of freedom for the chi-square goodness-of-fit test. It is equal to the total categories less one. So, if there are n categories, the degrees of freedom for the test would be n - 1, not 1 - n.

III. A condition for using the chi-square goodness-of-fit test is that the observations are based on a random sample. This statement is correct. The chi-square goodness-of-fit test assumes that the observations are obtained from a random sample or represent a random selection from a population.

This assumption is important to ensure that the test results are generalizable to the population from which the sample is drawn. If the observations are not based on a random sample, the test results may not be valid or may be biased. Therefore, random sampling is a condition for using the chi-square goodness-of-fit test.

The correct statements are I and III only. Correct option is C.

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Complete question is:

Which of the statements are correct?

I. A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five.

II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom.

III. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sample.

a) I only

b) II only

c) I and III only

d) II and III only

e) I, II, and III

Answer:

Your answer is 28/9 or the last one.

Step-by-step explanation:

28/9 = 3.111111111111.......

Answer:

C!

Step-by-step explanation:

The probability that represents the likelihood of a single event occurring by itself is called marginal probability.

Marginal probability refers to the probability of an individual event happening independently without considering any other events. It focuses on a single variable or outcome without considering the relationship or dependencies with other variables.

To calculate marginal probability, you divide the number of times the specific event occurs by the total number of observations. For example, if you have a bag of marbles with different colors and you want to find the marginal probability of drawing a red marble, you would count the number of red marbles and divide it by the total number of marbles in the bag.

Marginal probability is often used when working with categorical variables or when studying the probability of a single event without considering any other variables or conditions. It provides a fundamental understanding of the likelihood of an event occurring in isolation, independent of any other factors.

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The debits and credits for the four related entries for a sale of $15,000, with terms of 1/10, n/30, are presented in the following T accounts.

To understand the debits and credits for this sale, we need to consider the different accounts involved in the transaction.

1. Sales Account: This account records the revenue generated from the sale. The credit entry for the sale of $15,000 will be made in this account.

2. Accounts Receivable Account: This account tracks the amount owed to the company by the customer. Since the terms of the sale are 1/10, n/30, the customer is entitled to a 1% discount if payment is made within 10 days. The remaining balance is due within 30 days. Initially, we will debit the full amount of the sale ($15,000) in this account.

3. Cash Account: This account records the cash received from the customer. If the customer takes advantage of the discount and pays within 10 days, the cash received will be $15,000 minus the 1% discount. The remaining balance will be received if the customer pays after 10 days but within 30 days.

4. Sales Discounts Account: This account is used to track any discounts given to customers for early payment. If the customer pays within 10 days, a credit entry for the discount amount (1% of $15,000) will be made in this account.

In summary, the entries in the T accounts will be as follows:
- Sales Account: Credit $15,000
- Accounts Receivable Account: Debit $15,000
- Cash Account: Credit the discounted amount received (if payment is made within 10 days), and credit the remaining amount received (if payment is made after 10 days but within 30 days)
- Sales Discounts Account: Credit the discount amount (1% of $15,000) if payment is made within 10 days.

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Answer:

gdjsgsghdbdgdjdnvshskdndhdhdhdbbdbdhdhdhd

Since the limit of F(x) is infinity, we can conclude that F(x) = logx xlogx 5 grows at the same rate as logx as x approaches infinity. Therefore, F(x) = logx xlogx 5 is not ω(logx).

A function is a relation between sets that assigns to each element of a first set, exactly one element of the second set. Functions are typically written as an equation, with the first set (the domain) on the left side and the second set (the range) on the right side. The most common type of function is a function from real numbers to real numbers, which is often referred to as a real-valued function. Examples of real-valued functions include linear, polynomial, exponential, and trigonometric functions.


False. F(x) = logx xlogx 5 is not ω(logx). ω(logx) is a notation used to denote a function that grows faster than logx as x approaches infinity. However, F(x) = logx xlogx 5 grows at the same rate as logx as x approaches infinity. To prove this, we can calculate the limit of F(x) as x approaches infinity:

lim F(x) = lim (logx xlogx 5)

= lim (logx xlogx) lim 5

= ∞∞ 5

= ∞

Since the limit of F(x) is infinity, we can conclude that F(x) = logx xlogx 5 grows at the same rate as logx as x approaches infinity. Therefore, F(x) = logx xlogx 5 is not ω(logx).

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Answer:

yes you did

Step-by-step explanation:

I hate math and my math teacher

Answer:

301.733% increase

Step-by-step explanation:

The movie should be 2 hours and 15 minutes long.

Answer: My answer would be the movie was 2 hours and 55 minutes long.

Step-by-step explanation: I subtracted 4:10 by 1:55 and got 2:55.

                                               4:10-1:55=2:55

ANSWER

EXPLANATION

We are given the number 65,978.

To put it in scientific notation, we will need to put it in a format such that we have a number between 1 and 10 multiplying a power of ten.

So, to do that, we will move the decimal point from the end of the number (65978.) to just after the first number.

Then the number of times we move it will be the power of 10.

Since we will move it to the left, it will be a positive power.

So, we have that the number becomes:

The power is 4 because we moved the decimal four times.

y is a function of x because for each value of x, we can calculate a unique value of y

To determine whether y is a function of x, we need to check if for every value of x there is a unique corresponding value of y.

The given equation is y = 3/x - 11.

In this case, y is a function of x because for each value of x, we can calculate a unique value of y. The expression 3/x represents a rational function where the value of y depends on the value of x. The constant term -11 does not affect the fact that y is a function of x.

For any given value of x, the expression 3/x will yield a specific value, and subtracting 11 will further modify that value. So, each input value of x produces a unique output value of y, satisfying the definition of a function.

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If  your hotel is stories tall and the average story is feet high, the distance is  69 feet.

We can solve this problem using similar triangles. Let's call the distance between you and your hotel "x".

First, we need to determine the height of the building in front of you. Since we know it is five stories tall, and the average story is 10 feet high, its total height is 5 * 10 = 50 feet.

Now, we can use the similar triangles formed by the buildings and your line of sight to set up a proportion:

x / (h + 50) = 60 / h

where "h" is the height of the five-story building, and "h + 50" is the total height of the building and its billboard.

We can cross-multiply to get:

x * h = 60 * (h + 50)

Expanding the right side, we get:

x * h = 60h + 3000

Subtracting 60h from both sides, we get:

x * h - 60h = 3000

Factoring out the h, we get:

h * (x - 60) = 3000

Dividing both sides by h, we get:

x - 60 = 3000 / h

Substituting in the known values, we get:

x - 60 = 3000 / (10 * 32)

Simplifying, we get:

x - 60 = 9.375

Adding 60 to both sides, we get:

x = 69.375

x = 69 feet

Therefore, you are approximately 69 feet away from your hotel.

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The complete question is:

you are standing 60 feet away from a five-story building in los angeles, looking up at its rooftop. your eyes are approximately five feet above the ground. in the distance you can see the billboard on top of your hotel, but the hotel building is completely obscured by the building in front of you. if your hotel is 32 stories tall and the average story is 10 feet high, how far away from your hotel are you?