Helpppppppppppppppppppppppppppp

Answer:

4x - 5y = 30

4x - 5(0) = 30

x1 = 7.5 y1 = 0

Find y-intercept

The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.

4x - 5y = 30

4(0) - 5y = 30

y2 = -6 x2 = 0

(x1,y1) and (x2,y2)

(7.5,0) and (0,-6)

Solve for x

To solve for x, we solve the equation so the variable x is by itself on the left side:

4x - 5y = 30

x = 1.25y + 7.5

Solve for y

To solve for y, we solve the equation so the variable y is by itself on the left side:

4x - 5y = 30

y = 0.8x - 6

The statement that It is sufficient to test an analogy by asking what are its relevant similarities is false.

Analogy refers to the process of comparison of two or more items such that it explains some idea, or classification or familiarity and representativeness. Studying the analogies helps in enhancing, strengthening and reinforcing the skills in areas such as reading comprehension, homophones, deductive reasoning and logic.

Testing an analogy only by relevant similarities will produce partial results which might not be suitable to fully explain the reason. Hence, both relevant similarities and differences are to be considered for more detailed review. Different kind of analogies used to explain the differences or similarities are synonym and antonym, symbol and reference, degree of differences.

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Answer:

Domain is the set of all x values, the independent quantity, for which the function f(x) exists or is defined.

Step-by-step explanation:

i just graphed it

Answer:

Domain:

\(x\in\mathbb{R}\)

Range:

\(y\geq -5\)

Step-by-step explanation:

The domain is the span of x-values covered by the graph, and the range is the span of y-values covered by the graph.

From the graph, we can see that the x-values covered by the graph will extend infinitely in both directions. Therefore, the domain of the graph is all real numbers.

We can't write this as an inequality, but we can write:

\(x\in\mathbb{R}\)

For the range, we can see from the graph that the lowest y-value is y=-5. The graph doesn't go any lower than that. However, the graph will also cover all values greater than -5. Therefore, the range of the graph is all values greater than or equal to -5. In an inequality, this is:

\(y\geq -5\)

No function exists in this relation. No, since there isn't always a single output for every input.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.

We have to show the relation between a function.

The x-values are entered into the function machine. The function machine generates the y-values after its operations are complete. Any internal function is possible.

A mapping diagram with arrows pointing from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5, as well as two circles with the numbers 0, and labels for the x and y values, respectively

but according to the definition of y, it should give only one value

Hence, it is not a function.

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Answer:

2

Step-by-step explanation:

Performing these calculations using the provided data will yield the estimated average gross revenue of movies whose top two stars earn $5.0 million, along with the 95% confidence interval.

The mean of your estimate plus and minus the range of that estimate makes up a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

To estimate the average gross revenue of movies whose top two stars earn $5.0 million, we can use a confidence interval. Here's how we can calculate it:

Step 1: Calculate the sample mean (\(\bar{x}\)) and the sample standard deviation (\(s\)) of the gross revenue for movies where the top two stars earn $5.0 million.

Step 2: Determine the sample size (\(n\)) of the movies where the top two stars earn $5.0 million.

Step 3: Calculate the standard error (\(SE\)) of the sample mean using the formula \(SE = \frac{s}{\sqrt{n}}\).

Step 4: Determine the critical value (\(t^*\)) for a 95% confidence level. Since the sample size is relatively small (\(n < 30\)), we use the t-distribution. The degrees of freedom (\(df\)) for this calculation would be \(n - 1\).

Step 5: Calculate the margin of error by multiplying the standard error (\(SE\)) by the critical value (\(t^*\)): \(ME = t^* \times SE\).

Step 6: Construct the confidence interval by subtracting and adding the margin of error to the sample mean: \(\bar{x} - ME\) to \(\bar{x} + ME\).

Let's perform these calculations using the given data:

Movie Cost of Two   Highest Paid Performers \(($mil)\)     Gross Revenue \(($mil)\)

1                                            5.3                                              48

2                                           7.2                                              65

3                                            1.3                                              18

4                                            1.8                                              20

5                                            3.5                                             31

6                                            2.6                                             26

7                                               8                                              73

8                                            2.4                                             23

9                                            4.5                                             39

10                                          6.7                                              58

Step 1: Calculate the sample mean \((\(\bar{x}\))\) and the sample standard deviation ((s)) of the gross revenue for movies where the top two stars earn $5.0 million.

For the given data, the sample mean is:

\(\(\bar{x} = \frac{\sum \text{Gross Revenue}}{n} = \frac{48 + 65 + 18 + 20 + 31 + 26 + 73 + 23 + 39 + 58}{10}\)\)

The sample mean \(\(\bar{x}\)\) is the average of the gross revenue for the given movies.

Step 2: Determine the sample size ((n)) of the movies where the top two stars earn $5.0 million.

In this case, (n = 10) since there are 10 movies in the given data.

Step 3: Calculate the standard error ((SE)) of the sample mean using the formula \(\(SE = \frac{s}{\sqrt{n}}\)\).

To calculate (s), we need to find the sample variance. The sample variance \((\(s^2\))\) is calculated as:

\(\(s^2 = \frac{\sum (\text{Gross Revenue} - \bar{x})^2}{n-1}\)\)

Once we have \(\(s^2\)\), we can calculate (s) by taking the square root:\(\(s = \sqrt{s^2}\)\).

Finally, we can calculate (SE) using the formula above.

Step 4: Determine the critical value ((t*)) for a 95% confidence level.

To find the critical value, we need to determine the degrees of freedom ((df)) which is (n - 1). Using the degrees of freedom, we can find the critical value from the t-distribution table or using statistical software. For a 95% confidence level, the critical value is \(\(t^*\)\).

Step 5: Calculate the margin of error by multiplying the standard error ((SE)) by the critical value \((\(t^*\)): \(ME = t^* \times SE\)\).

Step 6: Construct the confidence interval by subtracting and adding the margin of error to the sample mean: \(\(\bar{x} - ME\) to \(\bar{x} + ME\)\).

Performing these calculations using the provided data will yield the estimated average gross revenue of movies whose top two stars earn $5.0 million, along with the 95% confidence interval.

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The maximum number of major ideas that can be included in a specific purpose statement depends on several factors, but it is generally recommended that the statement include one to three major ideas. This helps the speaker to focus their ideas and organize their content in a way that effectively communicates their message to the audience

A specific purpose statement is a statement that defines the main objective or goal of a speech or presentation. It serves as a guide for the speaker, helping them to focus their ideas and organize their content in a way that effectively communicates their message to the audience.

The number of major ideas that can be included in a specific purpose statement depends on several factors, including the length of the speech or presentation, the complexity of the topic, and the speaker's ability to effectively communicate their message.

In general, it is recommended that a specific purpose statement include only one to three major ideas. This allows the speaker to focus their attention on a limited number of key points and ensures that the audience is not overwhelmed with too much information. Additionally, having a limited number of major ideas makes it easier for the speaker to organize their content and for the audience to understand and retain the information.

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A specific purpose statement should include one or two major ideas that are focused and directly relevant to the topic at hand.

Including too many ideas can make the statement confusing and difficult for the audience to understand, so it's important to be selective about which ideas to include.

The goal is to create a specific purpose statement that is clear, concise, and easy for the audience to understand, while effectively conveying the key ideas of the communication.

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The probability that the difference between the two numbers that appear will be less than 3 is 6/36 or 1/6.

There are 36 possible outcomes when two balanced dice are rolled, and 6 of those outcomes have a difference of less than 3. Thus, the probability of the difference between the two numbers being less than 3 is 6/36 or 1/6.

The probability of the difference between two numbers appearing when two balanced dice are rolled is determined by the number of possible outcomes that have a difference less than 3. Out of the 36 possible outcomes, 6 of them have a difference of less than 3, so the probability of the difference being less than 3 is 6/36 or 1/6.

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Answer:

See Explanation

Step-by-step explanation:

Given

\(1\ can = 2.2m^2\)

Required

Determine the number of cans for the wall

The dimension of the wall is not given. So, I will use the following assumed values:

\(Length=20m\)

\(Width = 44m\)

First, calculate the area of the wall

\(Area = Length * Width\)

\(Area = 20m * 44m\)

\(Area = 880m^2\)

If \(1\ can = 2.2m^2\)

Then \(x = 880m^2\)

Cross Multiply:

\(x * 2.2m^2 = 1 * 880m^2\)

\(x * 2.2m^2 = 880m^2\)

\(x * 2.2 = 880\)

Make x the subject

\(x = \frac{880}{2.2}\)

\(x = 400\)

400 cans using the assume dimensions.

So, all you need to to is, get the original values and follow the same steps

To find and sketch the domain of the function f(x, y) = ln(9 - x^2 - 9y^2), follow these steps:

1. Identify the function: f(x, y) = ln(9 - x^2 - 9y^2).
2. Determine the domain: The natural logarithm, ln, is defined only for positive input values. Therefore, we need to find the values of x and y that make the expression inside the logarithm positive: 9 - x^2 - 9y^2 > 0.
3. Rearrange the inequality: x^2 + 9y^2 < 9.
4. Divide by 9: (x^2)/9 + y^2 < 1.

The inequality (x^2)/9 + y^2 < 1 represents the region inside an ellipse with major axis length 2√9 = 6 and minor axis length 2√1 = 2. The center of the ellipse is at the origin (0, 0).

To sketch the domain:

1. Draw the x and y axes.
2. Sketch the ellipse with the given axes lengths and centered at the origin.
3. Shade the region inside the ellipse to represent the domain.

The domain of the function f(x, y) = ln(9 - x^2 - 9y^2) is the set of points (x, y) inside the ellipse (x^2)/9 + y^2 < 1, which has been sketched as described.

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Answer:

14.49

Step-by-step explanation:

a)

Solution,

According to fuel gauge,the petrol left is exactly between 1/2 and 3/4 part of the 40 litres.

i.e. Left fuel = (1/2 + 3/4)/2 litres

Here,

1/2 of 40l = 1/2×40l

= 20l

3/4 of 40l = 3/4×40l

= 30l

Then,

Left fuel = (20l + 30l)/2

= 50l/2

= 25l

Consumed fuel = 40l - 25l

= 15l

Therefore,15 litres of petrol is used to travel 240km

b)

Solution,

Consumed fuel = 15l

Distance covered = 240km

Then,

Fuel consumption rate = 240km/15 l

= 16km/l

Therefore,the rate of petrol consumption is 16km/l of his car for this journey

a.  4 is an extraneous root. , b. 0 is an extraneous root. , c. -3 is an extraneous root. , d. -13.21 is an extraneous root. , e. 9.22 is an extraneous root.

To solve the equation, we can begin by finding a common denominator for the fractions on the left-hand side. The common denominator is (x + 3)(x - 4). We can then rewrite the equation as follows:

[4x(x - 4) + 3(x + 3)] / [(x + 3)(x - 4)] = 5

Expanding and simplifying the numerator, we have:

[4x^2 - 16x + 3x + 9] / [(x + 3)(x - 4)] = 5

Combining like terms, we obtain:

(4x^2 - 13x + 9) / [(x + 3)(x - 4)] = 5

To eliminate the fraction, we can cross-multiply:

4x^2 - 13x + 9 = 5[(x + 3)(x - 4)]

Expanding the right-hand side, we get:

4x^2 - 13x + 9 = 5(x^2 - x - 12)

Simplifying further:

4x^2 - 13x + 9 = 5x^2 - 5x - 60

Rearranging the equation and setting it equal to zero, we have:

x^2 - 8x - 69 = 0

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation may not yield rational roots, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 8x - 69 = 0, we have a = 1, b = -8, and c = -69. Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)^2 - 4(1)(-69))) / (2(1))

= (8 ± √(64 + 276)) / 2

= (8 ± √340) / 2

= (8 ± 2√85) / 2

= 4 ± √85

So, the possible solutions for x are x = 4 + √85 and x = 4 - √85.

Now, let's check which of the given options (a, b, c, d, e) are extraneous roots by substituting them into the original equation:

a. 4: Substitute x = 4 into the equation: 4(4)/(4 + 3) + 3/(4 - 4) = 5. This results in a division by zero, which is undefined. Therefore, 4 is an extraneous root.

b. 0: Substitute x = 0 into the equation: 4(0)/(0 + 3) + 3/(0 - 4) = 5. This also results in a division by zero, which is undefined. Therefore, 0 is an extraneous root.

c. -3: Substitute x = -3 into the equation: 4(-3)/(-3 + 3) + 3/(-3 - 4) = 5. Again, we have a division by zero, which is undefined. Therefore, -3 is an extraneous root.

d. -13.21: Substitute x = -13.21 into the equation and evaluate both sides. If the equation does not hold true, -13.21 is an extraneous root.

e. 9.22: Substitute x = 9.22 into the equation and evaluate both sides. If the equation does not hold true, 9.22 is an extraneous root.

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Answer:

Is a or c

Step-by-step explanation:

step- by- step explanation

The maximum value of y(t) on the interval [0, 4] is y(1) = 1/3 and the minimum value is y(4) = 16/3.

To discover the most extreme and least values ​​of y(t) over the interim [0, 4], we must begin with discovering the basic points of y(t) and after that calculate y(t) at the basic points. 

To find the critical point, we need to find where the derivative of y(t) is zero or undefined. So we start by finding the derivative of y(t).

\(y'(t) = 2t^2 - 10t + 8\)

Setting y'(t) = 0 to find the location equal to zero gives:

\(2t^2 - 10t + 8 = 0\)

Simplified, it looks like this:

\(t^2 - 5t + 4 = 0\)

There is factoring:

(t - 1)(t - 4) = 0

So the critical points are t = 1 and t = 4.

Then evaluate y(t) at the critical points and the endpoints of the interval [0, 4].

y(0) = 0

y(1) = 1/3

y(4) = 16/3

A second derivative test can be used to determine if a value is the maximum or minimum. The second derivative of y(t) is

y''(t) = 4t - 10

At t = 0, y''(t) = -10, which is negative. This means that y(t) has a local maximum at t = 0.

At t = 1, y''(t) = -6, which is also negative. This means that y(t) has a local maximum at t = 1.

At t = 4, y''(t) = 6, which is positive. This means that y(t) has a local minimum at t = 4. Therefore, the maximum value of y(t) on the interval [0, 4] is y(1) = 1/3 and the minimum value is y(4) = 16/3.  

The correct question is

A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=2/3t^3−5t^2+8t. Over the time interval 0<t<5, for what values of t is the speed of the particle increasing?

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Answer:

bro I can’t do it TvT

Below steps provide a general approach to assess the approximation of a normal curve using a histogram.

As an AI text-based model, I don't have access to the specific table or image you mentioned. However, I can provide you with some general guidance on determining whether a histogram approximates a normal curve.

To assess whether a histogram approximates a normal curve, you need to consider the shape and characteristics of the data distribution. Here are a few steps to help you evaluate the histogram:

1. Plot the histogram: Start by creating a histogram based on the recorded data for the number of tornadoes in 2008. The histogram should have the number of tornadoes on the vertical axis (y-axis) and a range of values (e.g., number of tornadoes) on the horizontal axis (x-axis).

2. Evaluate symmetry: Look at the shape of the histogram. A normal distribution is symmetric, meaning that the left and right sides of the histogram are mirror images of each other. If the histogram is symmetric, it suggests that the data may follow a normal distribution.

3. Check for bell-shaped curve: A normal distribution typically exhibits a bell-shaped curve, with the highest frequency of values near the center and decreasing frequencies towards the tails. Examine whether the histogram resembles a bell-shaped curve. Keep in mind that it doesn't have to be a perfect match, but a rough resemblance is indicative.

4. Assess skewness and kurtosis: Skewness refers to the asymmetry of the distribution, while kurtosis measures the shape of the tails relative to a normal distribution. A normal distribution has zero skewness and kurtosis. Calculate these statistics or use statistical software to determine if the skewness and kurtosis values deviate significantly from zero. If they are close to zero, it suggests a closer approximation to a normal curve.

5. Apply statistical tests: You can also employ statistical tests, such as the Shapiro-Wilk test or the Anderson-Darling test, to formally assess the normality of the data distribution. These tests provide a p-value that indicates the likelihood of the data being drawn from a normal distribution. Lower p-values suggest less normality.

Remember that these steps provide a general approach to assess the approximation of a normal curve using a histogram. It's essential to consider the context of your specific data and apply appropriate statistical techniques if necessary.

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Answer:

B

Step-by-step explanation:

55.85 divided by 7.25 is 7. something sooooo if pants cost 7 dolars more thats 14

The cost of a shirt is $7 and the cost of a pant is $14.

The answer is option B.

Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?

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Their present age are:

Vikas 's age = 15 years, Mother's age = 42 years  and

Grandmother's age = 64 years.

Let that present age of Vikash is x yrs.

So, his Mother's age= (x+27) yrs

Grandmother's age = (x+27+22) i.e., (x+49) yrs.

According to question,

   x+ (x+27)+ (x+49) = 121

⇒ 3x+ 76 = 121

⇒ 3x = 121-76

⇒ x= 45/3

⇒ x = 15

Therefore,

x = 15

Which means the age of Vikas is 15 years.

Now

So, mother's age will be = 15+27

                                        = 42 years.

And,

Grandmother's age = 15+49

                                = 64 years.

Hence, age of Vikash, his Mother and his Grandmother are 15 yrs, 42 yrs, and 64 yrs respectively.

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The equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

What is Equation in Spherical Coordinates?

A mathematical equation that is represented in terms of the spherical coordinates of a point is known as an equation in spherical coordinates. A three-dimensional coordinate system known as spherical coordinates makes use of two angles, typically represented by symbols and a radial distance (r), and a coordinate system to find points in space.

\($r^2 = 81$\)

To represent the equation in spherical coordinates, we substitute the Cartesian coordinates \($x = r\sin(\phi)\cos(\theta)$, $y = r\sin(\phi)\sin(\theta)$, and $z = r\cos(\phi)$\) into the equation. After substitution and simplification, we have:

\($r^2\sin^2(\phi)\cos^2(\theta) + r^2\sin^2(\phi)\sin^2(\theta) + r^2\cos^2(\phi) = 81$\)

Since \(r^2 = 81,\) we can substitute it into the equation:

\($81\sin^2(\phi)\cos^2(\theta) + 81\sin^2(\phi)\sin^2(\theta) + 81\cos^2(\phi) = 81$\)

Finally, we divide the equation by 81 to simplify:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

So, the equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

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The value of the expression is -44 and thus does not depend on the value of x

An algebraic expression can be described as a mathematical expression made up of variables, terms, factors, coefficients and constants.

They are also made up of mathematical or arithmetic operations, which includes;

From the information given, we have that;

(x-5)(x+8)-(x+4)(x-1)

expand the bracket

x² + 8x - 5x - 40 - (x² -x + 4x - 4)

x² + 8x - 5x - 40 - x² + x - 4x + 4

collect like terms

3x - 3x - 40 - 4

add or subtract like terms

0 - 44

Hence, the expression does not depend o x

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Answer:

g(4) = 5

Step-by-step explanation:

Substitute 4 for each occurrence of x in the given function:

g(4) = 2(4) - 3 = 8 - 3 = 5

g(4) = 5

Answer:

2 percent

Step-by-step explanation:

We can use two separate fractions, one representing the amount of physics majors expected and the amount of seniors expected in physics majors by the university.

\(\frac{400x}{66} = \frac{400}{3600}\)

Now cross multiply.

\(\frac{66*400}{400x * 3600}\)

x will be removed.

\(\frac{26400}{1320000}\)

Simplifying this fraction will get you \(\frac{1}{50}\), which in percentage form, will be 2 percent.

Answer:

Sixty-three percent is the statistic and 39% is the parameter.

Step-by-step explanation:

Answer:

1 1/2 inches on a map is 18 miles in real life.

Step-by-step explanation:

1 in. = 12 miles

1 1/2 in. = X

1 1/2 x 12 = 18

1 1/2 inches on a map is 18 miles in real life.

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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\( ab = \sqrt{ {12 }^{2} + { (- 5)}^{2} } \\ \ \\ = 13\)

\(bc = \sqrt{ {3}^{2} + { (- 4)}^{2} } \\ = 5\)

Answer:

The domain of \(f(x)\) is \(Dom \{f(x)\} = \mathbb{R}-\{1\}\).

Step-by-step explanation:

Let \(f(5\cdot x ) = \frac{x-5}{5\cdot x-1}\), which is rearranged by algebraic means:

1) \(f(5\cdot x ) = \frac{x-5}{5\cdot x-1}\)  Given

2) \(f(5\cdot x) = \frac{x\cdot 1 - 5}{5\cdot x -1}\) Modulative property

3) \(f(5\cdot x) = \frac{5^{-1}\cdot (5\cdot x)-5}{5\cdot x -1}\) Existence of multiplicative inverse/Associative and commutative properties.

4) \(f(x) = \frac{5^{-1}\cdot x - 5}{x-1}\) Composition of functions.

5) \(f(x) = \frac{(5^{-1}\cdot x-5)\cdot (5\cdot 5^{-1})}{x-1}\) Existence of multiplicative inverse/Associative property.

6) \(f(x) = \frac{(x-25)\cdot 5^{-1}}{x-1}\)  Commutative, associative and distributive properties/\(a\cdot (-b) =-a\cdot b\)/Definition of subtraction

7) \(f(x) = (x-25)\cdot [5^{-1}\cdot (x-1)^{-1}]\) Definition of division/Associative property

8) \(f(x) = (x-25)\cdot (5\cdot x -5)^{-1}\)  \(a^{c}\cdot b^{c} = (a\cdot b)^{c}\)/Distributive property/\(a\cdot (-b) =-a\cdot b\)/Definition of subtraction

9) \(f(x) = \frac{x-25}{5\cdot x - 5}\) Definition of division/Result

The domain of a polynomial-based rational function consists in all values of the real set except values where denominator equals zero. The value of \(x\) such that rational function becomes undefined is:

1) \(5\cdot x - 5 = 0\)  Given

2) \(5\cdot (x-1) = 0\) Distributive property

3) \([5\cdot (x-1)]\cdot 5^{-1} = 0\cdot 5^{-1}\) Compatibility with multiplication

4) \((x-1)\cdot (5\cdot 5^{-1}) = 0\) Commutative and associative properties/\(a\cdot 0 = 0\)

5) \(x-1 = 0\) Existence of multiplicative inverse/Modulative property

6) \(x+[1+(-1)] = 1+0\) Compatibility with addition/Commutative and associative properties

7) \(x = 1\) Existence of additive inverse/Modulative property/Result

Hence, the domain of \(f(x)\) is \(Dom \{f(x)\} = \mathbb{R}-\{1\}\).

Part a: The probability that a given battery will last between 2.3 and 3.6 years is 80.41%.

Part b: The probability that a given battery will last longer than 24 months is 97.72%.

For the given question,

The data for the storage battery are-

Part a: The probability that a given battery will last between 2.3 and 3.6 years.

Find z score for x = 2.3 years.

z(2.3) = (x - μ )/σ

Put the values,

z(2.3) = (2.3 - 3.0)/0.5

z(2.3) = -1.4

Use negative z score table;

P(z = -1.4) = 0.0808

Similarly, for x = 3.6

z = (3.6 - 3)/0.5

z = 1.2

Use positive z table;

z = 0.8849

P(2.3<x<3.6) = 0.8849 - 0.0808

P(2.3<x<3.6) = 0.8041

Thus, the probability that a given battery will last between 2.3 and 3.6 years is 80.41%.

Part b: The probability that a given battery will last longer than 24 months = 2 years.

x = 2 years

z (2) = ( 2 - 3.0 )/ 0.5

z = 2

P(x > 2) = 0.9772

Thus, the probability that a given battery will last longer than 24 months is 97.72%.

To know more about the normal distribution, here

https://brainly.com/question/23418254

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