find the domain of the following function below. f(x)=3x-5/2

Answer:

The graph given can be further simplified as follows:

[tex]g(x)=2x+2[/tex]

I have drawn and attached the graph with the answer.

Step-by-step explanation:

The graph given can be further simplified as follows:

[tex]g(x)=2x-1+3[/tex]

[tex]g(x)=2x+2[/tex]

Slope of the graph is 2 as x has a coefficient of 2 and intercept is 2.

To graph the above substitute several values to x and calculate the corresponding g(x) values.

[tex]g(1)=2*1+2\\g(1)=4[/tex]

So when x=1, g=4

[tex]g(3)=2*3+2\\g(3)=8[/tex]

So when, x=3, g=8

Calculate several values in the same way and then plot the values is a Cartesian plane, x values in x axis and take g(x) values as y axis.

Then you will get a few dots in a straight line, join those dots with a line and that is the graph.

I have drawn and attached the graph with the answer.

Answer:

The graph is shown below.

Step-by-step explanation:

The given function is

[tex]g(x)=2^{x-1}+3[/tex]

It is an exponential function.

The given exponential function is defined for all real numbers. So, the domain of given function is all real numbers.

Domain = { x | x ∈ R }

Domain = (-∞,∞)

We know that

[tex]2^{x-1}>0[/tex]

Add 3 on both sides.

[tex]2^{x-1}+3>0+3[/tex]

[tex]g(x)>3[/tex]

Range of the function is

Range = (3,∞)

Table of values is

x         y

0         3.5

1           4

2          5

Plot these point on a coordinate plane.

The graph of given function is shown below.

O.5 is the correct answer

Residual plots can indicate the appropriateness of a linear model by examining patterns and deviations of the residuals.

A residual plot is a graph that shows the difference between the observed and predicted values in a linear regression model. It helps to assess the appropriateness of the linear model by examining the patterns and deviations of the residuals. In the first graph, there seems to be a systematic pattern and non-randomness in the residuals, indicating that the linear model may not be appropriate. However, in the second graph, the residuals are randomly scattered around zero with no evident pattern, suggesting that the linear model is more appropriate.

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Final answer:

The land area of Australia is roughly 7.62 trillion square meters, calculated by multiplying the area in square miles (2,941,526) by the conversion factor of 2,590,000 square meters per square mile.

Explanation:

The student is asking for the conversion of Australia's land area from square miles to square meters. To convert square miles to square meters, we use the conversion factor that 1 square mile is equal to 2.59 square kilometers or 2,590,000 square meters. Therefore, the land area of Australia in square meters is calculated by multiplying the area in square miles by the conversion factor:

2,941,526 mi2 × 2,590,000 m2/mi2 = 7,619,652,340,000 m2

The land area of Australia is approximately 7.62 trillion square meters.

The confidence level for the interval x ± 2.88σ/√n is approximately 99.9%. The term 'confidence level' speaks to how frequently the true value of the parameter would be inside the interval for replicated experiments. Without additional information, we cannot compute the confidence level for just 'x'.

In statistics, a formula exists to find the confidence interval. For the interval x ± 2.88σ / √n, the confidence level is nearly 99.9%. We find this by referring to the z-table (standard normal table) with a z-score of 2.88. This leaves 0.05% in each tail of the distribution.

On the topic of confidence levels, a 95% confidence interval implies that if you were to take 100 random samples from your population, approximately 95 of those samples would capture the true population parameter.

For the other part of your question, when we talk about the interval x, it doesn't provide enough detail to calculate a confidence level. It needs to be stated in context of the standard deviation and the sample size.

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Answer:

80,000,000

Step-by-step explanation:

We can rewrite this expression as:

(4 x 10⁵) x (2 x 10²)

To solve this, we multiply first 4 x 2 = 8 and then we multiply the powers of ten using law of exponents:

10⁵x10²= 10₇.

Therefore, the answer is: 8 x 10⁷. If we write it in decimal form we would have:

80,000,000

Final answer:

The two numbers in question are 8 and 41.

Explanation:

Step-by-Step Solution to Find the Two Numbers

Let the smaller number be x. Thus, the larger number would be x + 33. According to the problem, the larger number divided by the smaller number gives a quotient of 5 and a remainder of 1. We can represent this information using the following equation:

(x + 33) = 5x + 1

This equation states that when the larger number is divided by the smaller number, we obtain a quotient of 5 and a remainder of 1.

Now, let's solve the equation for x:

Since we have found the smaller number to be 8, the larger number is:

8 + 33 = 41

Therefore, the two numbers are 8 and 41.

The modulus operator would confirm our solution since 41 % 8 does indeed yield a remainder of 1, as stated in the problem.

Combining like terms gives

9x−30=180. Adding 30 to both sides yields

9x=210. Dividing by 9, we find x=23.3333.

To solve the equation

4x+5x−30=180, we first combine like terms:

4x+5x=9x

So the equation becomes:

9x−30=180

Next, we isolate the variable

x by adding 30 to both sides:

9x=180+30

9x=210

Finally, we divide both sides by 9 to solve for

Answer:

94

Step-by-step explanation:

1 89

2321

33

214

The order of operations is the steps used to simplify any mathematical expression. Order of operations refers to which operations should be performed in what order and it is denoted by PEMDAS, This means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right). If parentheses are enclosed within other parentheses, work from the inside out.

[tex] (2+8)/2*9/3\\ Performing \; the \; operation\; in\; Parenthesis\; first\\ \\ 10/2 *9/3\\ Dividing \; 10/2\; from\; left\; to\; right\\ \\ 5*9/3\\ Multiply\; from\; left\; to\; right\\ \\ 45/3\\ Divide \; to\; get\; final\; answer\\ \\ 15 [/tex]

Conclusion:

The correct solution for the arithmetic expression (2+8)/2*9/3 using the order of operations is 15

The volume of the pyramid is πr³ cubic units. Then the correct option is A.

Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (A × H) / 3

V = (L × B × H) / 3

Where, A is the base area of the pyramid.

Let r be the radius of base circle of the cone.

The height of the pyramid in the diagram is three times the radius of the cone.

Then the height of the pyramid will be 3r.

The base area of the pyramid is the same as the base area of the cone.

Base area of pyramid = Base area of cone

Base area of pyramid = πr²

Then the volume of the pyramid will be

Volume of pyramid = (1/3) x  πr² x (3r)

Volume of pyramid = πr² x r

Volume of pyramid = πr³ cubic units

The volume of the pyramid is πr³ cubic units.

Then the correct option is A.

Complete question is attached below.

More about the volume of the pyramid link is given below.

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The formula f=11gh can be solved for h by dividing both sides of the equation by 11g. This will give h = f / (11g), where h is isolated on one side of the equation.

To solve the formula f=11gh for the variable h, we need to isolate h on one side of the formula. The current formula tells us that the value of f is equal to the result of 11 times g times h.

As our goal is to solve for h, we can do this by dividing both sides of the equation by 11g. In doing so, the 11g on the right side of the equation will cancel out, leaving us with just h on one side.

So the formula solved for h will look like this:
h = f / (11g).

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