5. Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the x-axis of the graph off(x) = -(x+3)^2 - 2. Write a rule for g.

u in the plane in set of real numbers rℝcubed3 spanned by the columns, then the one solution matrix is,   \(\left[\begin{array}{ccc}x_{1} &\\x_{2} &\\\end{array}\right]\) = \(\left[\begin{array}{ccc}2&\\6.66&\\\end{array}\right]\)

Given data,

Let u [-16 18 10] and A [2 -3 1 -4 5 1]

u in the plane in set of real numbers rℝcubed3 spanned by the columns of A,

So,

We can write,

u = \(\left[\begin{array}{ccc}-16&\\18&\\10&\end{array}\right]\) and A = \(\left[\begin{array}{ccc}2&-3\\1&-4\\5&1\end{array}\right]\)

Then,

AX = b

w = \(\left[\begin{array}{ccc}2&-3&-16\\1&-4&18\\5&1&10\end{array}\right]\)

A = \(\left[\begin{array}{ccc}2&-3\\1&-4\\5&1\end{array}\right]\)

null A = \(\left[\begin{array}{ccc}x_{1} &\\x_{2} &\\\end{array}\right]\)

\(\left[\begin{array}{ccc}2&-3\\1&-4\\5&1\end{array}\right]\)    \(\left[\begin{array}{ccc}x_{1} &\\x_{2} &\\\end{array}\right]\)= \(\left[\begin{array}{ccc}0&\\0&\\0&\end{array}\right]\)

2\(x_{1}\) - 3\(x_{2}\) = 0

\(x_{1}\) - 4\(x_{2}\) = 0

5\(x_{1}\) + 1\(x_{2}\) = 0

We can solve the equations,

2\(x_{1}\) - 3\(x_{2}\) = 0

\(x_{1}\) - 4\(x_{2}\) = 0

-----------------------

\(x_{1}\) - 7\(x_{2}\) = 0

\(x_{1}\) = 7\(x_{2}\)

We can substitute \(x_{1}\) values,

2\(x_{1}\) - 3\(x_{2}\) = 0

2*7\(x_{2}\) - 3\(x_{2}\) = 0

\(14x_{2}\) - 3\(x_{2}\) = 0

11\(x_{2}\) = 0

\(x_{2}\) = 0

\(\left[\begin{array}{ccc}2&-3\\1&-4\\5&1\end{array}\right]\)    \(\left[\begin{array}{ccc}x_{1} &\\x_{2} &\\\end{array}\right]\)= = \(\left[\begin{array}{ccc}-16&\\18&\\10&\end{array}\right]\)

2\(x_{1}\) - 3\(x_{2}\) = -16

\(x_{1}\) - 4\(x_{2}\) = 18

5\(x_{1}\) + 1\(x_{2}\) = 10

We can solve the matrix equations,

2\(x_{1}\) - 3\(x_{2}\) = -16

\(x_{1}\) - 4\(x_{2}\) = 18

--------------------------

\(x_{1}\) - 7\(x_{2}\) = 2

\(x_{1}\) = 2 + 7\(x_{2}\)

\(x_{1}\) = 2 + 7(0)

\(x_{1}\) = 2

2\(x_{1}\) - 3\(x_{2}\) = -16

2*2 - 3\(x_{2}\) = -16

4 - 3\(x_{2}\) = -16

- 3\(x_{2}\) = -16 - 4

- 3\(x_{2}\) = -20

3\(x_{2}\) = 20

\(x_{2}\) = 20/3

\(x_{2}\) = 6.66

Therefore,

u in the plane in set of real numbers rℝcubed3 spanned by the columns, then the one solution matrix is,   \(\left[\begin{array}{ccc}x_{1} &\\x_{2} &\\\end{array}\right]\) = \(\left[\begin{array}{ccc}2&\\6.66&\\\end{array}\right]\)

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The average speed of the tip of the second hand is π/30 cm/s.

The average speed of the tip of the second hand is π/30 cm/s. This is because the second hand rotates in a full circle of 2π radians in 60 seconds, which means its angular velocity is 2π/60 = π/30 radians per second.

The length of the second hand is 1 cm, so the linear velocity of the tip of the second hand is equal to the product of its length and angular velocity, which is (1 cm) x (π/30 rad/s) = π/30 cm/s. Therefore, the average speed of the tip of the second hand over the full 60-second cycle is π/30 cm/s.

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Answer:

7.5 mL

Step-by-step explanation:

If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.

On average, there is only 1 letter that will go into the right envelope.

It is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

There are three main types of average: mean, median and mode. Each of these techniques works slightly differently and often results in slightly different typical values. The mean is the most commonly used average. To get the mean value, you add up all the values and divide this total by the number of values.

To find Average, we add up all the values and then divide this total by the number of values.

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​

Answer:

y= -x

or

y= -1x

Step-by-step explanation:

hope it helps :)

The correct statement is: 3. The median number of organisms found in Northeastern streams is larger than the median for Southeastern streams.

The Southeastern plot is skewed to the right:

Looking at the Southeastern stemplot, we can see that the values are concentrated towards the left side with a longer tail on the right side. This indicates that the distribution is skewed to the right. Therefore, statement 1 is correct.

The Northeastern plot is nearly symmetric:

Examining the Northeastern stemplot, we observe that the values are distributed relatively evenly on both sides of the stem. There is no evident skewness in either direction, suggesting a nearly symmetric distribution. Hence, statement 2 is incorrect.

The median number of organisms found in Northeastern streams is larger than the median for Southeastern streams:

To determine the median, we need to consider the middle value(s) of the datasets. In the Southeastern plot, the median is represented by the value "5." In the Northeastern plot, the median is represented by the value "7." Since 7 is greater than 5, it implies that the median number of organisms found in Northeastern streams is larger than the median for Southeastern streams. Thus, statement 3 is correct.

Based on the analysis of the stemplots, we can conclude that the correct statement is statement 3: The median number of organisms found in Northeastern streams is larger than the median for Southeastern streams.

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The weight is less on the moon than on the Earth due to the force of gravity being less on the moon.

Weight can be defined as the force with which the center of the Earth, or even the center of a satellite planet such as Earth attracts a body towards its center. This is determined by:

This makes your weight to be less in the moon as the force of gravity there is also less.

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The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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y = (-1/8)x^2 is a downward opening parabola with vertex = the origin (0,0) relatively flat.

Parabola points horizontally  left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.  

what is parabola?

Focus and directrix are equidistant from the vertex.

Focus has an x coordinate = 0 and y coordinate <0 axis of symmetry is the y axis or x=0.

Find one more point on the parabola, go horizontally from the focus to the parabola, that distance equals the distance from the parabola at that point to the directrix. its x coordinate = -2 times its y coordinate. it helps to graph a rough sketch of the parabola.

y = (-1/8)x^2

y = (-1/8)(-2y)^2

y = -4y^2/8 = -y^2/2

2y = -y^2

2 =- y

x=-2y = -2(-2) = 4

plug that point (4,-2) into y =(-1/8)x^2

-2 = (-1/8)(4)^2 = -16/8 = -2 = the y coordinate of the vertex,

x coordinate = 0

the focus = (0,-2)

distance from the focus to the vertex = 2

distance from the directrix to the vertex = 2

the latus rectum = distance from the parabola points horizontally  left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.   "Latus rectum" is the math term for that distance.

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y = (-1/8)x² is a downward opening parabola with vertex = the origin (0,0) relatively flat. Parabola points horizontally  left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.  

What is a parabola?

A parabola is a U-shaped plane curve. Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line.

The topic of conic sections includes a parabola, and all of its principles are discussed here.

Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms.

Several examples of parabolas in real life The wheel stance in yoga resembles a parabola.

The Banana's shape is beginning to resemble a parabola. A parabola is emerging from the Rainbow.

A series of points in a plane that are evenly spaced off from a straight line is referred to as a parabola.

Focus and directrix are equidistant from the vertex.

Focus has an x coordinate = 0 and y coordinate <0 axis of symmetry is the y axis or x=0.

Find one more point on the parabola, and go horizontally from the focus to the parabola, that distance equals the distance from the parabola at that point to the directrix. its x coordinate = -2 times its y coordinate. it helps to graph a rough sketch of the parabola.

y = (-1/8)x²

y = (-1/8)(-2y)²

y = -4y²/8 = -y²/2

2y = -y²

2 =- y

x=-2y = -2(-2) = 4

plug that point (4,-2) into y =(-1/8)x²

-2 = (-1/8)(4)² = -16/8 = -2 = the y coordinate of the vertex,

x coordinate = 0

the focus = (0,-2)

distance from the focus to the vertex = 2

distance from the directrix to the vertex = 2

the latus rectum = distance from the parabola points horizontally left and right of the focus = from (4,-2) to (-4,-2) = 2(4) = 8.   "Latus rectum" is the math term for that distance.

Hence, the distance from the focus to the vertex is 2 and the distance from the directrix to the vertex is 2 of the parabola y=-1/8x².

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Answer: y=(√x)/13 for x>0)

Step-by-step explanation: Y is f^-1(x) btw

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

x =  ± \(\frac{4}{3}\)

Step-by-step explanation:

9x² − 16 = 0

9x² = 16

x² = \(\frac{16}{9}\)

x = ± √\(\frac{16}{9}\)

x =  ± \(\frac{4}{3}\)

So, the answer is:  x = \(\frac{4}{3}\) , - \(\frac{4}{3}\)

Answer:

16.4 TRUST ME

Step-by-step explanation:

Mark as brainliest

By using testing of hypothesis, it can be concluded that-

The correct set of hypotheses is

\(H_0 : \mu \geq 85\)

\(H_a : \mu < 85\)

What is testing of hypothesis?

Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.

A student believes that the average grade on the final examination in statistics is at least 85.

The null hypothesis is \(\mu \geq 85\)

The alternative hypothesis is \(\mu < 85\)

So, the correct set of hypotheses is

\(H_0 : \mu \geq 85\)

\(H_a : \mu < 85\)

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Answer:

1/6 or 16

Step-by-step explanation:

I hope this is the correct answer

Answer:

(x-24)(x-1)

Step-by-step explanation:

common sense + practice

kinda did it in my head

If the function f (x) = 3 logx and g(x) \(=\) x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

In the question ,

it is given that ,

the function f(x) is

f(x) \(=\) 3logx

and the function g(x) is

g(x) \(=\) x² + 1 ,

the value of the composite function g[f(x)] will be

g[f(x)] = g(f(x))

Substituting the value of f(x) = 3logx , we get

g(f(x)) = g(3logx)

Substituting the value of 3logx in the place of x in the function  g(x) = x² + 1 ,

we get ,

= (3logx)² \(+\) 1

Therefore , If the function f (x) = 3 logx and g(x) = x² + 1 , then the value of composite function g[f(x)] is (3logx)² + 1 , the correct option is (a) .

The given question is incomplete , the complete question is

If f ( x ) = 3 log x and g( x ) = x² + 1 , find the value of composite function g[ f ( x )] .

(a) (3logx)² + 1

(b) 3log(x² + 1)

(c) 3(x² + 1)logx

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Answer:

78

Step-by-step explanation:

Answer:

1. 29.52

2. 69.39

Step-by-step explanation:

1. 9.4*3.14=29.52

2. 4.7*4.7=22.09

22.09*3.14= 69.39

Answer: 8n^2

Step-by-step explanation:

I did test and got 100

answer: they spend $27.92 on goodie bags

the hourly rate is $37.5

they spend $177.92 in total

Answer:

y=1/2x+4

Step-by-step explanation:

The point of intersection is 4, and it goes up one, right 2 so the rise over run is 1/2

An inequality is a mathematical statement that uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to compare two quantities. In real life, we can use inequalities to describe a wide range of situations. For example, let's say you are buying groceries and you have a budget of $50. You could use the inequality  total cost of groceries < $50 to describe your situation. This inequality states that the total cost of the groceries must be less than $50, or you will exceed your budget.

In another real life situation, let's say you are training for a race and you want to run a certain distance in a specific amount of time. You could use the inequality distance > speed × time to describe your goal. This inequality states that the distance you run must be greater than the product of your speed and the time it takes you to complete the race. Inequality statements can also be used in social science and economics. For example, we can use an inequality to describe the income distribution in a society. We could say that the top 10% of earners have an income greater than the bottom 90% of earners, using the inequality top 10% income > bottom 90% income.

In summary, inequalities can be used to describe real life situations by comparing two quantities using symbols such as <, >, ≤, or ≥. We can use inequalities to describe a wide range of situations, from grocery shopping to income distribution.

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There are 11 letters in the word mathematics. The probability of selecting the letter "e" first is 1/11, which is approximately 0.091 in decimal form when rounded to the nearest thousandth.

This is because there is only one "e" in the word mathematics, and we are selecting one letter out of the 11 total letters.

To find the probability that the first letter is "e" in the word "mathematics," follow these steps:

1. Count the total number of letters in the word: There are 11 letters in "mathematics."

2. Count the occurrences of the letter "e": There is 1 "e" in "mathematics."

3. Calculate the probability: Divide the occurrences of "e" by the total number of letters.

Probability = (Occurrences of "e") / (Total number of letters) = 1 / 11

In decimal form and rounded to the nearest thousandth, the probability that the first letter is "e" in the word "mathematics" when arranged randomly is approximately 0.091.

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Specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.

What is a Variable?

A variable is a quantity that can change in the context of a mathematical problem or experiment. We usually use one letter to represent a variable. The letters x, y, and z are common general symbols used for variables.

The procedure for identifying or indicating the value of cases on a variable is commonly known as data coding or data labeling. It involves assigning specific numerical or categorical values ​​to represent different categories or levels of a variable.

Here is the general procedure for encoding variables:

Define the variable: Start by clearly defining the variable you want to code. Understand its nature (eg nominal, ordinal, interval or ratio) and the categories or levels it covers.

Determine the encoding scheme: Decide on the encoding scheme you will use to represent the variable. For nominal variables (categories without their own order), you can assign numbers or labels to each category. For ordinal variables (categories with a meaningful order), you can assign numbers or labels that reflect the order. For interval or ratio variables, the numerical values ​​themselves can indicate the value of the variable.

Assign Codes: Assign specific codes or labels to represent each category or level of the variable. These codes can be numbers, letters, or any other symbol you choose. Make sure the codes are unique and do not overlap.

Apply Coding: Apply assigned codes to matching cases or observations in your dataset. Depending on the software or tool you are using, there are different ways to do this. You can manually enter codes, use syntax or programming commands, or use data transformation functions.

Verify your coding: Double-check your coding to ensure accuracy. Review a sample of the coded cases to ensure they match the intended coding scheme. This step is essential to avoid errors and inconsistencies in your data.

It is important to note that specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.

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The power to which a number or expression is raised is called the exponent.

1. An exponent is a mathematical notation that represents the power to which a number or expression is raised. It is written as a superscript number or variable placed above and to the right of the base number or expression.

2. The base number or expression is the number or expression that is being multiplied repeatedly by itself, raised to the power of the exponent.

3. The exponent tells us how many times the base number or expression should be multiplied by itself. For example, in the expression \(2^3\), the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself three times: 2 * 2 * 2 = 8.

4. The exponent can be a positive whole number, a negative number, zero, or a fraction. Each of these cases has different interpretations:

  - Positive exponent: Indicates repeated multiplication. For example, \(2^4\)means 2 multiplied by itself four times.

  - Negative exponent: Indicates the reciprocal of the base raised to the positive exponent. For example, \(2^{-3\) means 1 divided by \(2^3\).

  - Zero exponent: Always equals 1. For example, \(2^0\) = 1.

  - Fractional exponent: Represents a root. For example, \(4^{(1/2)\)represents the square root of 4.

5. Exponents follow certain mathematical properties, such as the product rule \((a^m * a^n = a^{(m+n)})\), the quotient rule \((a^m / a^n = a^{(m-n)})\), and the power rule \(((a^m)^n = a^{(m*n)})\).

Remember to use these rules and definitions to correctly interpret and evaluate expressions involving exponents.

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Answer:

d) 5

Step-by-step explanation:

we can observe that the x-value 5 appears twice in the relation. However, in a function or a relation, each x-value should only have one corresponding y-value. Therefore, the repetition of (5, 1) and (5, 2) indicates an inconsistency or ambiguity in the relation. As a result, 5 is not a valid x-value in the domain.

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer:

d = \(-\frac{43}{3}\)

Step-by-step explanation:

Step 1: we will simplify both sides of the equation

16d + 2/3 = (14)(d) + (14)(−2)

16d + 2/3 = 14d + −28

16d + 2/3 = 14d - 28

Step 2: we need to subtract 14d on both sides

16d + 2/3 - 14d = 14d - 28 - 14d

2d + 2/3 = -28vide both

Step 3: we will subtract 2/3 from both sides

2d + 2/3 - 2/3 = -28 - 2/3

2d = -86/3

Step 4: Divide both side by 2

2d/2 = d

-86/3/2 = -43/3

d = -43/3