g(x)=8x+2
g( ) = -62

Answer:

m∠ABC = 130°

Step-by-step explanation:

BD is the angle bisector of angle ABC .

Therefore, ∠ABD ≅ ∠DBC

Measure of angle DBC = 65°

Therefore, m∠ABD = m∠DBC = 65°

m∠ABC = m∠ABD + m∠DBC

              = 65° + 65°

              = 130°

Answer:

yes (B)

Step-by-step explanation:

the graph passes the vertical line test

To find the limit of the function (x^2 - 9x + 14) / (x - 7) as x approaches 7, we can substitute the value of x = 7 into the function and see if it yields a meaningful result or if it approaches a certain value.

Plugging in x = 7 into the function:

(7^2 - 9 * 7 + 14) / (7 - 7) = (49 - 63 + 14) / 0

We can see that the denominator becomes zero, which indicates an indeterminate form. In this case, we cannot directly evaluate the limit by substituting the value of x = 7.

To determine the limit in such cases, we can use algebraic techniques. Let's simplify the expression by factoring the numerator:

(49 - 63 + 14) / 0 = (7 - 7)(7 - 2) / 0

We can see that we have a factor of (7 - 7) in the numerator, which cancels out. We are left with:

(7 - 2) / 0

Now, we can see that the numerator is nonzero and the denominator is zero, which leads to an undefined value.

Therefore, the limit of the function as x approaches 7 is DNE (does not exist).

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Answer:

ASA

Step-by-step explanation:

hope it helps ;)

Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

Answer:

number 2? ok it's 43

Step-by-step explanation:

hope this is helpful! have an amazing day :) God Bless you

Answer:

A. He did not use a random sample, and he tried to show cause and effect with an observational study

Hope this helps! : D

Step-by-step explanation:

8.

(08.05 MC)

Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch TV while they do their homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV while doing homework will cause his grades to improve. What mistake has Augusto made? (6 points)

Answer:

6

Step-by-step explanation:

48/8=6

divide each side by 8

Answer:

x = 6

Step-by-step explanation:

If you divide both sides of the equation by 8, then you end up with x = 6.

The recursive formula for our sequence is the one in the first option.

aₙ = aₙ₋₁ + 6

With a₁ = 7

Here we have the following sequence:

7, 13, 19, 25, ...

This one seems to be an arithmetic sequence, to check this, let's take the difference between consecutive terms:

13 - 7 = 6

19 - 13 = 6

25 - 19 = 6

This means that the recursive formula for our sequence is "add 6 to the previous term" or:

aₙ = aₙ₋₁ + 6

With a₁ = 7

so the correct option is the first one.

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The first step in developing a competency-model is to gather background information and analyze the existing standards within the workplace.

The first-step involves conducting a thorough examination of the organization's goals, strategies, and the specific job roles or positions for which the competency-model will be developed.

By gathering background information, organizations can understand the context in which the competency-model will be applied.

Analyzing existing standards within the workplace involves assessing the current performance expectations, competencies, and criteria used for evaluating employees in their respective roles.

The purpose of this step is to identify any gaps or areas for improvement in the existing standards and to ensure that the development of the competency model aligns with the organization's overall objectives.

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The first step in developing a competency model is conducting a job analysis.

developing a competency model is a systematic process that helps organizations define the key competencies needed for their employees. The first step in this process is conducting a job analysis.

A job analysis involves gathering information about the job, such as its purpose, tasks, responsibilities, and required qualifications. This information can be collected through methods like interviews, observations, and surveys. By analyzing the job, organizations can identify the critical competencies that are necessary for effective job performance.

These competencies can then be used to guide various HR processes, including recruitment, selection, training, and performance management. By aligning the competencies with job requirements, organizations can ensure that they have the right people with the right skills in the right positions.

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Answer:

the absolute value is always the same number positive so the answer would just be 4

Step-by-step explanation:

Answer:

300ft

Step-by-step explanation:

The proof for each theorem is matched as;

<EFC is a right angle: Definition of a right angle

m<EFC = 90; Definition of a tangent line

m<EFC + m<FEC + m<ECF = 180 degrees; triangle sum theorem

90 + m<FEC + m<ECF = 180; substitution property of equality

m<FEC + m<ECF = 90; substitution property of equality

m<FEC + m<ECF = definition of complementary angles

To determine the values, we need to know the following;

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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John observed 133 people passing by his store, with 54 of them entering the store. Among those who entered, only 26 made a purchase.

Based on the information you provided, it seems that John runs a computer software store. Yesterday, he counted a total of 133 people who walked by the store. Out of those 133, 54 of them actually came into the store. Lastly, out of the 54 people who entered the store, only 26 of them made a purchase.

In summary, John observed 133 people passing by his store, with 54 of them entering the store. Among those who entered, only 26 made a purchase.

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Answer:

A: 49500 km

B:

9.57

⋅

10

−

6

Step-by-step explanation:

Answer:

5/8 or 0.625

Step-by-step explanation:

number of students in class=40

Boys=15

Girls = 40-15

40-15=25

25/40=5/8 or 0.625

Answer: b = (−ah+2a)/h

Step-by-step explanation:

Step 1: Flip the equation.

Step 2: Add (-1)/2ah to both sides.

Step 3: Divide both sides by h/2.

Given differential equation is : \($y''+xy'+x^2y=0$\)To find series solution we assume : $y(x)=\sum_{n=0}^{\infty} a_n x^n$ Differentiate $y(x)$ with respect to x: $y'(x)=\sum_{n=1}^{\infty} na_n x^{n-1}$Differentiate $y'(x)$ with respect to \(x: $y''(x)=\sum_{n=2}^{\infty} n(n-1) a_n x^{n-2}$.\)

Substitute $y(x)$, $y'(x)$ and $y''(x)$ in the given differential equation and collect coefficients of $x^n$, then set them to 0:$$\begin\({aligned}n^2 a_n+(n+1)a_{n+1}+a_{n-1}=0\\a_1=0\\a_0=1\end{aligned}$$\)The recurrence relation is : $a_{n+1}=\frac{-1}{n+1} a_{n-1} -\frac{1}{n^2}a_n$.

Now, we will find the first few coefficients of the series expansion using the recurrence relation:  \($$\begin{aligned}a_0&=1\\a_1&=0\\a_2&=-\frac{1}{2}\\a_3&=0\\a_4&=\frac{-1}{2\cdot4}\\a_5&=0\\a_6&=\frac{-1}{2\cdot4\cdot6}\\&\quad \vdots\end{aligned}$$\).

The series solution is given by:  \($$y(x)=\sum_{n=0}^{\infty} a_n x^n = 1-\frac{1}{2}x^2+\frac{-1}{2\cdot4}x^4+\frac{-1}{2\cdot4\cdot6}x^6+ \cdots$$.\)

Thus, the series solution of $y''+xy'+x^2y=0$ is $y(x)=1-\frac{1}{2}x^2+\frac{-1}{2\cdot4}x^4+\frac{-1}{2\cdot4\cdot6}x^6+ \cdots$ which is in the form of a Maclaurin series.

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The series solution of the differential equation y(x) = a₀ - 1/3x²a₀ + 1/45xa₀ - 2/945x⁶a₀ + ....

You should knows than the series solution is used to seek a power series solution to certain differential equations.

In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.

The differential equation y′′+xy′+x²y=0 is a second-order homogeneous differential equation with variable coefficients.

The function y(x) can be expressed as a power series of x

y(x) = ∑(n=0 to ∞) aₙxⁿ

Differentiate y(x)

y′(x) = ∑(n = 1 to ∞) n aₙxⁿ ⁻ ¹

y′′(x) = ∑(n = 2 to ∞) n(n - 1) aₙxⁿ ⁻ ²

By Substituting these expressions into the differential equation

\(\sum\limits^{\infty}_2 n(n-1) a_n x^{n-2} + \sum\limits^{\infty}_1 a_n x^n + x^2 \sum\limits^{\infty}_0 a_n x^n = 0\)

By simplifying the expression by shifting the indices of the first sum, we get

\(\sum\limits^{\infty}_0 (n+2)(n+1) a_{n+2} x^n + \sum\limits^{\infty}_0 a_n x^n + \sum\limits^{\infty}_0 a_n x^{n+2} = 0\)

Equating the coefficients of like powers of x to zero gives us a recurrence relation for the coefficients aₙ in terms of aₙ₋₂.

y(x) = a₀ - 1/3x²a₀ + 1/45xa₀ - 2/945x⁶a₀ + ...,

where a₀ is an arbitrary constant.

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Answer:

Step-by-step explanation:

3

The probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

To calculate the probability of rolling all six numbers at least once when rolling a six-sided die 12 times, we can use the concept of permutations.

The total number of possible outcomes when rolling a six-sided die 12 times is 6^12 since each roll has six possible outcomes. This represents the denominator of our probability calculation.

Now, let's calculate the numerator, which represents the number of favorable outcomes where we get all six numbers at least once. We can use the concept of derangements (or the principle of inclusion-exclusion) to determine this.

A derangement is a permutation in which none of the elements appear in their original position. In our case, we want to find the number of derangements for a set of six elements (the six numbers on the die).

The formula to calculate the number of derangements for a set of n elements is given by n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).

Using this formula, we can calculate the number of derangements for six elements:

Number of derangements = 6! * (1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!) = 265

Therefore, the numerator of our probability calculation is 265.

Finally, we can calculate the probability by dividing the numerator by the denominator:

Probability = Number of favorable outcomes / Total number of possible outcomes = 265 / 6^12

Calculating this value:

Probability ≈ 0.0263

So, the probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

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Sam spent two-fifth of his work day by answering email. He works for 9 hours.

Steps to translate and solve a word problem using algebraic expressions:

- Assign the unknowns to variables

- Translate the word into operators plus, less, multiply, or division

- Isolate the unknown

In the given problem, let p is the variable to express the total hours Sam worked yesterday.

He spent two-fifth of hi work day by answering email = 2/5 p

He spent 3.6 hours answering email yesterday, means:

2/5 p = 3.6

p = 5 x 3.6/2 = 9 hours

Hence, Sam worked for 9 hours.

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Answer:

B) 68 cm²

Step-by-step explanation:

Answer:

rational numbers are perfect squares irrational numbers are non terminating/go on forever

Step-by-step explanation:

Answer:the one going in a positive direction. so up lIke this /

Answer:

the bottom left choice,

positive graphs show the points going from bottom left of the graph to the upper right of it

negative correlation shows the opposite, points from the upper left to the lower right

Step-by-step explanation:

Answer:

2^16 or 65,536

Step-by-step explanation:

First, you'll find the answers to 2^6 and 2^10

2^6=64 while 2^10=1024, then you multiply 1024 by 64 which gives you 65,536.

**or, the easier way is to just add the two exponents together since you see that the bases are the same.

The algebraic expression that can be represented by the statement is -5x/2 = 10

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

The negation of the product of five times a number divided by two is ten

Represent the variable with y

So, we have the following representation

The negation of the product of five times x divided by two is ten

Express the product as an actual product

So, we have the following representation

The negation of 5x divided by two is ten

Express the quotient as an actual quotient

So, we have the following representation

The negation of the 5x/2 is ten

Lastly, we have

-5x/2 = 10

Hence, the expression is -5x/2 = 10

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Answer:

x = 3

Step-by-step explanation:

the tangent- tangent angle is half the difference of the measures of the intercepted arcs, that is

8x + 1 = \(\frac{1}{2}\) ( 39x - (24x - 5) )

8x + 1 = \(\frac{1}{2}\) (39x - 24x + 5) ← multiply both sides by 2 to clear the fraction

16x + 2 = 39x - 24x + 5

16x + 2 = 15x + 5 ( subtract 15x from both sides )

x + 2 = 5 ( subtract 2 from both sides )

x = 3

a - 1/a =5

take squaring both side

(a - 1/a )^2 = (5)^2

a^2 +1/a^2 -2.a.1/a =25

a^2+1/a^2 -2 =25

a^2+1/a^2 =27 (answer)

Answer:

\(a^2+\frac{1}{a^2}=23\)

Step-by-step explanation:

\(a+\frac{1}{a}=5\\squaring\\a^2+(\frac{1}{a})^2+2\times a \times \frac{1}{a}=5^2\\a^2+\frac{1}{a^2} +2=25\\a^2+\frac{1}{a^2}=25-2=23\)

Answer:

false

Step-by-step explanation:

because

-3(x-5)

-3x+15