is the cost function and p(x) = 1700-7x is the demand function, find the production level that will maximize profit. Show more. Solutions.

The expression equivalent to [tex](x + 3)/(x^2 - 2x - 3)[/tex]divided by [tex](x^2 + 2x - 3)/(x + 1)[/tex] is option (d) x + 3/(x + 1).

To simplify the given expression, we need to divide the numerator of the first fraction by the denominator of the second fraction and vice versa.

The expression [tex](x + 3)/(x^2 - 2x - 3)[/tex] divided by [tex](x^2 + 2x - 3)/(x + 1)[/tex] can be rewritten as[tex](x + 3)/(x^2 - 2x - 3)[/tex]multiplied by[tex](x + 1)/(x^2 + 2x - 3).[/tex]

Now, let's simplify the individual fractions:

The numerator (x + 3) and denominator [tex](x^2 + 2x - 3)[/tex])in the first fraction cannot be further simplified.

The numerator (x + 1) and denominator[tex](x^2 + 2x - 3)[/tex] in the second fraction can also not be simplified.

When we multiply the fractions, the resulting expression is (x + 3)(x + [tex]1)/(x^2 - 2x - 3)(x^2 + 2x - 3).[/tex]

By multiplying the numerator and denominator, we get [tex](x^2 + 4x + 3)/(x^4 - 4x^2 + 9).[/tex]

However, this expression is not equivalent to any of the given options. It seems that none of the provided options match the simplified expression.

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The closest coordinate plane to the point (6, 2, 7) is the xy-plane.

To determine which coordinate plane is closest to a given point, we look at the value of the coordinate that is perpendicular to each plane. The xy-plane is defined by the equation z = 0, which means that the z-coordinate is always 0 on this plane.

In the given point (6, 2, 7), the z-coordinate is 7. Since it is not equal to 0, the point does not lie on the xy-plane. However, we can compare the absolute values of the z-coordinate with the absolute values of the coordinates on the other planes.

The absolute value of 7 is smaller than the absolute values of 6 and 2, indicating that the point (6, 2, 7) is closer to the xy-plane than the other coordinate planes.

Regarding the equation of the sphere with center (6, 2, 7) that just touches the xy-plane at one point, we need additional information to determine the radius of the sphere or the coordinates of the point of tangency. Without this information, we cannot provide a specific equation for the sphere.

Therefore, the xy-plane is the coordinate plane closest to the point (6, 2, 7), indicating that the z-coordinate is further away from zero compared to the other coordinates.

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Whyte Clinic records an amount of $ 434100 as the cost for the land.

To purchase a land Whyte Clinic did costs:

Cost of Land is given by = $ 420000

Amount of property taxes due on the land is given by = $ 4500

The total fees for title and attorney is given by = $ 3000

The cost to grade the land is given by = $ 6600

So the total cost for the land recorded by the Whyte Clinic is given by

= $ (420000 + 4500 + 3000 + 6600)

= $ 434100

Hence Whyte Clinic records an amount of $ 434100 as the cost for the land.

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The number of electrons flowing per second is known as as electric current, Option (c) is correct.

The Current represents the flow of electric charge in a circuit and is measured in Amperes (A). It is a fundamental quantity that indicates the rate at which electrons pass through a specific point in a conductor.

The Voltage (potential difference), is the driving force that pushes the electrons through the circuit. The Resistance, on the other hand, opposes the flow of current. Power, measured in Watts (W), is the rate at which electrical energy is consumed or produced in a circuit.

Therefore, the correct option is (c).

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Answer:

2x - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

(6x-1) / 3

First, we split the fraction into 2 fractions.

[tex]\frac{6x}{3}[/tex] + [tex]\frac{-1}{3}[/tex]

Cancel the common factor of 6 and 3.

2x + [tex]\frac{-1}{3}[/tex]

Move the negative in front of the fraction.

2x - [tex]\frac{1}{3}[/tex]

So, the answer is 2x - [tex]\frac{1}{3}[/tex]

[tex]\sf Hello!\\\\\\\sf \dfrac{6x-1}{3} \\\\\\= \dfrac{6x}{3} - \dfrac{1}{3} \\\\\\ \boxed{= \sf2x - \dfrac{1}{3}}[/tex]

The other substance formed during the chemical reaction between iron, oxygen, and water is hydrogen gas (H2).

When iron (Fe) reacts with oxygen (O2) and water (H2O), a chemical reaction occurs. The iron undergoes oxidation, combining with oxygen to form iron oxide, commonly known as rust (Fe2O3). The balanced chemical equation for this reaction is:

4Fe + 3O2 + 6H2O → 2Fe2O3 + 6H2

In this equation, the coefficient of water (H2O) indicates that six molecules of water are required for the reaction to take place. As a result, along with the formation of rust (Fe2O3), six molecules of water break down into hydrogen gas (H2) and oxygen gas (O2). However, since the reaction takes place in the presence of excess water, the hydrogen gas easily escapes as a gaseous product, leaving behind rust as the visible product of the reaction.

Therefore, in addition to rust (iron oxide), the chemical reaction involving iron, oxygen, and water also produces hydrogen gas (H2) as another substance.

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During the chemical reaction, when iron reacts with oxygen and water, rust (iron oxide) and another substance are produced. What is the identity of the other substance formed during this reaction?

The null hypothesis of the given problem is: H₀: p = 0.75

A null hypothesis is defined as a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes it is simply referred to as the "null," and is represented as H₀.

We are told that Reynolds claims the proportion of free throws made for their team is 75%. Since Roberson thinks this value is higher than the true proportion, then we can say that the null hypothesis is expressed as: H₀: p = 0.75

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Complete question is:
Reynolds claims the proportion of free throws made for their team is 75%. Roberson thinks this value is higher than the true proportion. What is a null hypothesis for this scenario?

The expression "root(7, 3)" is equivalent to "7^(1/3)" and represents the cube root of 7.

We have,

"root(7, 3)":

This notation represents the nth root of a number, where 7 is the radicand (the number under the root symbol) and 3 is the index or the degree of the root.

In this case, the index is 3, so we are finding the cube root of 7.

"7^(1/3)":

This notation represents the same mathematical operation but in exponential form.

The base is 7, and the exponent is 1/3, which is equivalent to taking the cube root of 7.

Both "root(7, 3)" and "7^(1/3)" express the same idea of finding the number that, when raised to the power of 3, gives us 7.

The cube root of 7 is the value that, when multiplied by itself three times, equals 7.

Thus,

The expression "root(7, 3)" is equivalent to "7^(1/3)" and represents the cube root of 7.

Both notations indicate the same mathematical operation of finding the number that, when raised to the power of 3, results in 7.

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Answer:

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

Given function:

Find its inverse in steps below.

1) Substitute x with y and f(x) with x:

2) Solve for y:

Hence the inverse function is:

The matching choice is C.

The standard unemployment rate can be calculated based on the labor force and the number of unemployed individuals. In this case, with a labor force of 152 million and 13 million unemployed, we can determine the standard unemployment rate.

The standard unemployment rate is a widely used measure to assess the health of an economy's labor market. It is calculated by dividing the number of unemployed individuals by the labor force and multiplying by 100 to express it as a percentage.

The labor force is given as 152 million and the number of unemployed individuals is 13 million. To calculate the standard unemployment rate, we divide the number of unemployed by the labor force and multiply by 100:

Standard Unemployment Rate = (Number of Unemployed / Labor Force) * 100

Plugging in the given values:

Standard Unemployment Rate = (13 million / 152 million) * 100

Calculating this expression, we find that the standard unemployment rate is approximately 8.55%. This means that 8.55% of the labor force is currently unemployed. It is important to note that the standard unemployment rate provides an overview of the current unemployment situation but may not capture the full complexity of the labor market dynamics.

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Victor is currently 11 years old, and his father is currently 44 years old.

Let's assume Victor's current age is represented by V, and his father's current age is represented by F.

According to the given information, Victor is a quarter of his father's age, so we can write the equation:

V = (1/4)F

In 10 years, Victor's age will be V + 10, and his father's age will be F + 10. The sum of their ages in 10 years is given as 75:

(V + 10) + (F + 10) = 75

Substituting V = (1/4)F into the equation:

((1/4)F + 10) + (F + 10) = 75

Simplifying the equation:

(1/4)F + 10 + F + 10 = 75

(5/4)F + 20 = 75

(5/4)F = 55

Multiplying both sides by 4/5 to solve for F:

F = (55 x 4) / 5

F = 44

Substituting F = 44 into V = (1/4)F:

V = (1/4) x 44

V = 11

Therefore, Victor is currently 11 years old, and his father is currently 44 years old.

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Translation =

Victor is a quarter of his father's age and in 10 years their ages will add up to 75. How old is each?

The tax basis of the advance at the end of this year is $60,000.

To determine the tax basis of the advance at the end of this year, we need to take into account the $100,000 advance received from the publisher and the $40,000 income taxes already paid on the advance.

The tax basis represents the amount on which future taxes will be calculated. In this case, since the textbook will not be finished until next year, the tax basis at the end of this year will be adjusted to account for the income taxes already paid.

Tax basis of the advance = Advance received - Income taxes paid

Tax basis of the advance = $100,000 - $40,000

Tax basis of the advance = $60,000

Therefore, the tax basis of the advance at the end of this year is $60,000. This amount will be used to determine any future tax obligations related to the textbook advance.

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p(x,y): x > 0 ∧ y > 0; q(x,y): x² + y² = z², The code has a precondition that x and y must be greater than zero. The postcondition verifies the correctness of the code by ensuring that the sum of the squares of x and y is equal to the square of z, adhering to the Pythagorean theorem for a right-angled triangle.

The code in option C has a precondition p(x,y): x > 0 ∧ y > 0, which means that both x and y should be greater than zero. The postcondition q(x,y): x² + y² = z² verifies the correctness of the code.

After executing the code, it ensures that the sum of the squares of x and y is equal to the square of z. This condition is consistent with the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (z) is equal to the sum of the squares of the other two sides (x and y).

By checking that the postcondition holds true, we can confirm that the code correctly calculates the square of the hypotenuse in a right-angled triangle, given the lengths of the other two sides.

Therefore, the code requires x and y to be positive. The postcondition checks if the sum of the squares of x and y is equal to the square of z, aligning with the Pythagorean theorem for a right-angled triangle.

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The manga is worth $54 after 3 years. Hence, the correct answer is A) 54.

To find the worth of the manga after 3 years using the given function:

[tex]y = 250(0.6)^x[/tex]

We substitute x = 3 into the equation:

[tex]y = 250(0.6)^3[/tex]

Now, we calculate:

y = 250 × 0.6 × 0.6 × 0.6

y = 250 × 0.216

y = 54

Therefore, the manga is worth $54 after 3 years.

Hence, the correct answer is A) 54.

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If a=4, b=6, and sina=3/5 in triangle abc, then sin b equals: 9/10

To find sin(b) in triangle ABC, we can use the sine function in a right angle and the given information.

Given:

a = 4

b = 6

sin(a) = 3/5

We know that the sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle ABC, let's label the side opposite angle a as side c and the hypotenuse as side h.

sin(a) = c / h

Substituting the given values:

3/5 = 4 / h

To solve for h, we can cross-multiply:

3h = 5 * 4

3h = 20

h = 20 / 3

Now, we can use the sine function to find sin(b):

sin(b) = side opposite angle b / hypotenuse

sin(b) = 6 / (20 / 3)

sin(b) = 6 * (3 / 20)

sin(b) = 18 / 20

sin(b) = 9 / 10

Therefore, sin(b) equals 9/10.

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The notation B(500, 5) indicates that X follows a binomial distribution with n = 500 and p = 0.01.

What is binomial distribution?

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials. It models situations where there are two possible outcomes, often referred to as "success" and "failure," and the probability of success remains constant for each trial.

The distribution of X, the number of students from a high school class that get full scholarships to four-year schools, would follow the binomial distribution with parameters n and p.

The correct distribution for X would be B(500, 5), where B represents the binomial distribution.

In this case, n = 500, which represents the number of trials (number of students in the high school class), and p = 5/500 = 0.01, which represents the probability of success (probability that a student gets a full scholarship).

The notation B(500, 5) indicates that X follows a binomial distribution with n = 500 and p = 0.01.

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After considering the given data we conclude that the total number of red buttons should be added is 7, under the given condition that the probability of drawing a green button is 40%.

Now to evaluate this problem, we can apply the formula for probability of an event:
[tex]P(event) = number of favorable outcomes / total number of outcomes[/tex]
Let us consider we apply summation with regards to x red buttons to the bag. Then the total number of buttons in the bag will be 5 + 8 + x = 13 + x.
The probability of drawing a green button is given as 40%. Therefore, the probability of drawing a blue button is also 40% since there are only two colors in the bag.
Applying the formula above, we can write:
[tex]P(drawing a green button) = number of green buttons / total number of buttons[/tex]
0.4 = 8 / (13 + x)
Solving for x, we get:
x = 7
Hence, we need to add 7 red buttons to the bag so that the probability of drawing a green button is 40%.
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Women who have experienced pelvic inflammatory disease (PID), even if treated successfully, may have long-term health problems. These health problems can include various complications and consequences related to reproductive health and overall well-being.

PID is an infection of the female reproductive organs, typically caused by sexually transmitted infections such as chlamydia or gonorrhea. If left untreated or inadequately treated, PID can lead to serious complications. Even with successful treatment, some women may experience long-term effects

Some of the potential long-term health problems associated with PID include: Chronic pelvic pain: PID can cause inflammation and scarring in the pelvic organs, leading to ongoing pain in the lower abdomen or pelvis. Infertility: The scarring and damage caused by PID can obstruct or damage the fallopian tubes, making it difficult for an egg to travel from the ovary to the uterus, resulting in infertility.

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The measure of <B is 61 degree.

length of arc CD = 20.859 unit and length of are BD =​ 22.4118 unit.

First, using Angle sum property in triangle DCB

<D + <C + <B = 180

49 + 70 + <B= 180

<B = 180 - 119

<B = 61 degree

Now, using sine law

CB / sin 49 = BD / sin 70

18 / 0.75470958022 = BD / 0.93969262078

BD = 22.4118

and, 18 / 0.75470958022 = CD / 0.87461970713

CD = 20.859

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The term "microbiome" refers to all the microorganisms that inhabit a particular location, including their functional genes and metabolites.

The microbiome encompasses the entire collection of microorganisms, including bacteria, viruses, fungi, and other microbes, that reside in a specific environment such as the human gut, soil, or ocean. It extends beyond just the microorganisms themselves to include their collective genetic material (genes) and the products of their metabolism (metabolites). The microbiome is highly diverse and dynamic, playing crucial roles in various biological processes and contributing to the overall health and functioning of the ecosystem it inhabits.

The concept of the microbiome emphasizes the interconnectedness between an organism and its symbiotic microorganisms. For example, the human microbiome refers to the diverse microbial communities that reside within and on the human body, interacting with the host organism in complex ways. These microorganisms not only impact human health but also provide essential functions such as digestion, immune system modulation, and nutrient production. Understanding the composition, diversity, and functional potential of the microbiome is a rapidly evolving field of research, with significant implications for human health, agriculture, and environmental sustainability.

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In the consolidated financial statements, the intercompany sales between Perez, Inc. and Senior, Inc. need to be eliminated to avoid double counting of the profits.

When Perez, Inc. sells goods to Senior, Inc., the intercompany sales should be eliminated in the consolidated financial statements. This means that the revenue and cost of goods sold related to these transactions should be removed from both companies' individual income statements.

Since Perez, Inc. sold goods with a 40% gross profit to Senior, Inc., the gross profit on these intercompany sales needs to be eliminated. This adjustment ensures that the consolidated financial statements reflect only the external sales and expenses of the group as a whole.

Furthermore, as Perez, Inc. owns 80% of Senior, Inc., the consolidated income statement should also reflect the portion of Senior, Inc.'s income that belongs to the non-controlling interest (20% ownership not held by Perez, Inc.). This adjustment ensures that the consolidated financial statements accurately reflect the economic interest of both the parent company (Perez, Inc.) and the non-controlling interest (the remaining 20% ownership in Senior, Inc.).

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erez, Inc., owns 80% of Senior, Inc. During the year just ended, Perez sold goods with a 40% gross profit to Senior. Senior sold all of these goods during the year. In its consolidated financial statements for the year, how should the summation of Perez and Senior income statement items be adjusted?

In the first month's payment for a $180,000 mortgage with a 5.5 percent, 30-year loan, a portion will go towards the principal. The exact amount can be determined using an amortization schedule.

To calculate how much of the first month's payment goes towards the principal, we can follow these steps:

Step 1: Determine the monthly interest rate: Divide the annual interest rate by 12 to obtain the monthly interest rate. In this case, 5.5 percent divided by 12 equals 0.004583 (approx).

Step 2: Calculate the monthly payment: Use a loan payment formula or a mortgage calculator to determine the monthly payment amount. For a $180,000 mortgage with a 30-year loan term and a 5.5 percent interest rate, the monthly payment would be approximately $1,019.32 (approx).

Step 3: Create an amortization schedule: An amortization schedule shows the breakdown of each monthly payment, indicating the amount allocated to interest and principal. Using the loan details, create an amortization schedule or use an online tool to generate one.

Step 4: Locate the first month on the schedule: Find the first month's entry on the amortization schedule to determine the amount allocated to principal. This amount will vary depending on the specific terms of the loan. Locate the principal portion of the payment, which represents the reduction of the loan balance.

By following these steps and referencing the amortization schedule, you can determine the exact amount of the first month's payment that goes towards the principal of the $180,000 mortgage.

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The test statistic from the calculator output, rounding to two decimal places, is t = 1.63.

What is test statistic?

A test statistic is a numerical value calculated from sample data in hypothesis testing. It quantifies the difference or relationship between the sample data and the null hypothesis. The test statistic is used to assess the strength of evidence against the null hypothesis and make a decision about its validity.

To test whether the true mean age of the store's shoppers is significantly higher than 21, a t-test can be used. The ages of the first 10 people surveyed are given as follows: 24, 20, 36, 19, 22, 29, 24, 18, 19, and 25. We can calculate the sample mean and sample standard deviation of these ages.

Sample mean: 23.6

Sample standard deviation: 5.65

Sample size: 10

Hypothesized mean: 21

To calculate the test statistic (t-value):

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

t = (23.6 - 21) / (5.65 / √10)

t ≈ 1.63 (rounded to two decimal places)

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Exhibit Corp. would recognize a $6,000 gain on disposal if it sells the equipment for $12,000 cash.

To determine the gain or loss on disposal of equipment, we need to compare the selling price with the net book value of the equipment. The net book value is the cost of the equipment minus its accumulated depreciation.

In this case, the cost of the equipment is $22,000, and the accumulated depreciation is $18,000. Therefore, the net book value is $22,000 - $18,000 = $4,000.

If the equipment is sold for $12,000, which is higher than its net book value of $4,000, there is a gain on disposal. The gain is calculated by subtracting the net book value from the selling price: $12,000 - $4,000 = $8,000.

Since the question asks for the gain or loss, we consider the sign of the amount. A gain is positive, so the correct answer is c. a $6,000 gain on disposal.

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The statement "according to company records, the probability that a washing machine will need repairs during an eleven-year period is 0.12" can be classified as an example of empirical probability.

What is probability?

Probability is a branch of mathematics that deals with quantifying the likelihood or chance of an event occurring.

Reasoning:

Empirical probability, also known as experimental probability, is based on observed data or evidence from past events or experiments. In this case, the probability of a washing machine needing repairs during an eleven-year period is derived from company records, which implies that it is based on actual observations or data collected over time.

The probability value of 0.12 is obtained from the analysis of historical records, indicating the proportion of washing machines that required repairs out of the total number of washing machines observed during the eleven-year period. This observed frequency serves as the basis for calculating the empirical probability.

Unlike classical probability, which assumes equal likelihood for all outcomes, empirical probability is specific to the observed data or sample. It reflects the relative frequency of an event based on real-world observations and is applicable when historical data or empirical evidence is available.

Hence, the statement provided represents an example of empirical probability as it relies on company records and observed data to estimate the likelihood of washing machines needing repairs during an eleven-year period.

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The identical rates of silent and replacement changes in pseudogenes support the neutral theory of evolution. Pseudogenes, being non-functional and not subject to selective constraints.

The observation that the rate of silent and replacement changes is identical in pseudogenes, as determined by the start codon ,explained in the light of the neutral theory of evolution proposed by . According to the neutral theory, most genetic variation that accumulates over time is due to random genetic drift rather than natural selection.                                                                                                                                                                                                                            

In pseudogenes, the mutations that occur are generally selectively                                                                                                                                                                            neutral, meaning they do not confer any advantage or disadvantage to the organism. Pseudogenes are non-functional copies of genes that have lost their protein-coding ability due to various mutations, such as insertions, deletions, or premature stop codons. Since pseudogenes are not under functional constraints, mutations in these regions are generally not subject to purifying selection, which eliminates deleterious changes.

The rate of silent changes (synonymous substitutions) refers to nucleotide changes that do not alter the amino acid sequence of the protein encoded by a gene. These changes occur in the third position of the codon, where the genetic code is degenerate, allowing multiple codons to encode the same amino acid. Silent changes are often considered selectively neutral because they do not affect the phenotype of the organism.

The rate of replacement changes (non-synonymous substitutions), on the other hand, refers to nucleotide changes that result in a different amino acid being incorporated into the protein sequence. These changes can potentially affect the structure and function of the protein and may be subject to selective pressure.

In pseudogenes, both silent and replacement changes occur at a similar rate because the majority of mutations in pseudogenes are selectively neutral. Since pseudogenes are non-functional, there is no selection pressure to maintain the protein-coding sequence.

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To produce 1 ATP molecule, approximately 3 H ions must be moved into the matrix.

ATP synthesis in cells occurs through a process called oxidative phosphorylation, which takes place in the mitochondria.

During oxidative phosphorylation, a series of protein complexes, known as the electron transport chain, transfer electrons from electron donors to electron acceptors.

As electrons are transferred, protons (H ions) are pumped from the matrix to the intermembrane space, creating an electrochemical gradient.

The electrochemical gradient created by the movement of protons (H ions) across the inner mitochondrial membrane is harnessed by an enzyme called ATP synthase.

ATP synthase acts as a molecular turbine, utilizing the energy from the movement of H ions to produce ATP.

The exact number of H ions required to synthesize one ATP molecule can vary slightly depending on the specific cellular conditions.

However, on average, it is estimated that around 3 H ions need to move back into the matrix through ATP synthase for the synthesis of 1 ATP molecule.

This process, known as chemiosmosis, is essential for the generation of ATP, which serves as the primary energy currency in cells.

By utilizing the energy derived from the movement of H ions down the electrochemical gradient, cells are able to produce ATP efficiently and meet their energy demands for various cellular processes.

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Carson Kelly is expected to hit approximately 31 home runs in 2024.

To find how many home runs Carson Kelly is expected to hit in 2024, we can use the formula for compound interest, where the initial amount is the number of home runs he hit in 2019, and the interest rate is the expected growth rate of his home run hitting ability, which is 12 percent or 0.12 as a decimal.

Let H be the number of home runs hit in 2019, and H(n) be the number of home runs hit in year n, then we can write:

H(n) = H * (1 + r)^n

Where r is the growth rate, and n is the number of years into the future.

If we plug in the given values, we can find the number of home runs Carson Kelly is expected to hit in 2024, which is 5 years after 2019.

H = 18 (number of home runs in 2019)

r = 0.12 (growth rate)

n = 5 (number of years into the future)

H(5) = 18 * (1 + 0.12)^5

H(5) = 18 * 1.7623

H(5) = 31.9214

It's important to note that this is simply an estimate based on the given growth rate, and the actual number of home runs he hits in 2024 may vary based on many factors, including injuries, team support, and the skill of opposing pitchers, among others.

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The mileage that is within a z-score of 1.5 is approximately 34.4 miles.

To determine which mileage is within a z-score of 1.5, we need to use the mean (x) and standard deviation (s) values provided. The formula to calculate the z-score is:

[tex]z = (x - \mu) / \sigma[/tex]

Where:

z is the z-score,

x is the value we want to compare,

[tex]\mu[/tex] is the mean,

[tex]\sigma[/tex]is the standard deviation.

In this case, the mean ([tex]\mu[/tex]) is given as x = 29, and the standard deviation ([tex]\sigma[/tex]) is given as s = 3.6.

We can rearrange the formula to solve for x:

[tex]x = z * \sigma + \mu[/tex]

Substituting z = 1.5, [tex]\sigma[/tex] = 3.6, and [tex]\mu[/tex] = 29 into the formula, we can calculate the mileage:

x = 1.5 * 3.6 + 29

x = 5.4 + 29

x = 34.4

Therefore, the mileage that is within a z-score of 1.5 is approximately 34.4 miles.

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