The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7.

What is the common difference of the arithmetic sequence?

Answer:

Step-by-step explanation:

You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.

David's solution is correct up to Step 4.

At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...

  Step 4: (5 -3)x -4 = 2x -4

David's incorrect solution should have been 2x -4.

Given that the area of the region bounded by the curve f(x) and x-axis from x=4 to x=10 is 13/5, the average value of the negative-valued function y=f(x) over the interval [4,10] is -13/30.

The average value of a function f(x) over an interval [a,b] is given by:

average value = (1/(b-a)) * integral from a to b of f(x) dx

In this case, we are given that the function y=f(x) is negative-valued, and the area of the region bounded by the curve and x-axis from x=4 to x=10 is 13/5. This means that the integral of f(x) over the interval [4,10] is equal to -13/5:

\(\int\limits^{10}_4 \, f(x) dx\) = -13/5

To find the average value of f(x) over this interval, we divide this integral by the length of the interval:

average value = (1/(10-4)) * \(\int\limits^{10}_4 \, f(x) dx\)

             = (1/6) * (-13/5)

             = -13/30

Therefore, the average value of the negative-valued function y=f(x) over the interval [4,10] is -13/30. This means that if we were to draw a horizontal line at the height of -13/30 over the interval [4,10], the area between this line and the x-axis would be equal to the area of the region bounded by the curve f(x) and x-axis over the same interval.

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The 36th derivative of f(x) = cos(2x) is \(2^{17}\)* cos(2x).

To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).

Let's start by finding the first few derivatives of f(x) = cos(2x):

f'(x) = -2sin(2x)

f''(x) = -4cos(2x)

f'''(x) = 8sin(2x)

f''''(x) = 16cos(2x)

We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.

Based on this pattern, we can see that the 36th derivative will be:

f^(36)(x) =\((-1)^{17} * 2^{17} *\) cos(2x)

Simplifying this expression, we have:

f^(36)(x) = \(2^{17} * cos(2x)\)

Therefore, the 36th derivative of f(x) = cos(2x) is\(2^{17\) * cos(2x).

It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.

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Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

Answer:

x - 9 = -1

Step-by-step explanation:

When you see less than you switch the numbers. So, for instance, it says 9 less than x means x-9

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

Dividing fractions and dividing mixed numbers can be similar, as mixed numbers can be represented as fractions.

For example, the mixed number 3 1/2 can be represented as the fraction 7/2, which you can then divide by the divisor in your problem:

(3 1/2) / (1/2) = (7/2) / (1/2) = 7

-------

Another way to look at dividing mixed numbers compared to fractions is like this: dividing a mixed number takes imagining how many of your divisor-fractions (like (1/2) above) the whole-number part of the mixed number (like 3 above) can hold:

The 3 in (3 1/2) can hold 6 (1/2)'s because (1/2) x 6 = (1/2) x (6/1) = (6/2) = 3

There is no difference between dividing fractions and dividing mixed numbers

Note that there are different types of fractions:

All the types of fractions can be converted from one form to another

As explained above, mixed numbers are also examples of fractions, and ways of dividing fraction are the same

\(\frac{2}{3} \div \frac{3}{5} \\\\\frac{2}{3} \times \frac{3}{5}\\\\= \frac{2}{5}\)

If the two numbers to be divided are mixed fractions, they can be converted to improper fractions before the division operation is carried out

We can therefore conclude that there is no difference between dividing fractions and dividing mixed numbers

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Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.

But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.

So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.

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The number of candies each bag would contain is given by the inequality relation 3 < A < 4 , where A is the number of candies

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Now , the total number of candies with Tom = 14 candies

The number of bags = 4 bags

So , the number of candies each bag = total number of candies with Tom / number of bags

On simplifying , we get

The number of candies each bag A = 14 / 4 = 3.5 candies

Now , the value 3.5 lies between the whole numbers 3 and 4

Hence , the inequality is 3 < A < 4

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Answer:

25%

Step-by-step explanation:

add both kinds of tickets first to get the total

24 early admission + 72 regular = 96 total tickets

then divide 24 early tickets by 96 total tickets to get the decimal, then multiply by 100 to get percent

\(\frac{24}{96} = 0.25 * 100 = 25\)%

Answer:

D

Step-by-step explanation:

5x-2+2x+1

5x+2x+1-2

7x-1

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

What is banquet?

A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.

To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.

Let's define the variables:

Let x be the number of adult guests.

Let y be the number of student guests.

Now, let's write the system of inequalities representing the constraints of the situation:

The total number of guests cannot exceed 125: x + y ≤ 125

The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375

To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.

The boundary lines of each inequality are:

x + y = 125 (the line that connects the points (0, 125) and (125, 0))

45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))

To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.

The resulting graph should look like this:

The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

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TRUE

Point D represents a number less than the number Point C represents

Point E represents the smallest number of all the numbers represented by points.

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer:

5/8 in simplest form is 5/8

Step-by-step explanation:

Answer:

5/8 is in the simplest form already.

Step-by-step explanation:

It cant be lowered anymore, due to 5 not being divisible by 4, 2, or 8, which is what 8 is divisible by.

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.

To model this relationship, we can use the inverse variation equation, which can be expressed as:

y = k/x

Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.

Let's examine the data given in the table to find the value of k:

Number of Photos (x) Cost per Photo (y)

10 10

25 4

50 2

100 1

We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):

2 = k/50

Solving for k:

k = 2 * 50 = 100

Now that we have the value of k, we can write the function that models the data:

y = 100/x

Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Answer:

solve for V= pier^/3

solve for R=Square root3Vpie over pie

Step-by-step explanation:

V=multiply 1/3(pier^2)

R= Take root of both sides and solve

Answer:

dividing by a fraction (1/3) is equivalent to multiplying by its inverse (3)

3+%2A+v+%2F+%28pi+%2A+r%5E2%29 = h

Step-by-step explanation:

Answer:

There are 10 credits per semester.

Step-by-step explanation:

Given that: A college student takes the same number of credits each semester.

They had 8 credits when they started, and after 5 semesters, they had total 58 credits.

Now, In which rate they are earning credits per semester,

for that use the formula:

\(rate=\frac{change of credits}{total no of semeters}\)

rate=50/5

The change in credits is 58-8 = 50, since the

student earned 50 credits in 5 semesters.

So the rate at which they are earning credits per semester is:

Rate = 10 credits per semester.

Hence, there are 10 credits per semester.

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The expected values of the raffle ticket for you are given as follows:

For the PTO, the expected values are given as follows:

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For you, the distribution is given as follows:

Hence the expected value for one ticket is given as follows:

E(X) = 62/280 - 4 x 279/280

E(X) = -$3.76.

For twelve tickets, the expected value is given as follows:

12 x -3.76 = -$45.12.

For the PTO, we use the inverse signals, as the distribution is the inverse, that is:

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So, the codomain of the function is the set of all real numbers: codomain = R.

In mathematics, a function is a rule that maps a set of inputs (domain) to a set of outputs (codomain) in such a way that each input is associated with exactly one output. A function can be represented using various notations, including equations, graphs, and tables. A function can be thought of as a machine that takes an input and produces an output. The input is usually represented by the variable x, and the output is represented by the variable y. The relationship between the input and output is defined by the function rule. Functions are used in many areas of mathematics, science, and engineering to describe various phenomena, such as motion, growth, and decay. They are also used to model and analyze data in statistics and economics, and to design and control systems in engineering and computer science.

Here,

The codomain is the set of all possible output values of a function.

For the given function, f(x) = x² - 4, we can see that the output values are obtained by squaring the input value, subtracting 4, and therefore can be any real number.

To find the codomain of the function f(x) = x² - 4, we need to determine the range of the function, which is the set of all possible output values.

Let y = f(x) = x² - 4.

To find the range, we need to solve for y:

y = x² - 4

y + 4 = x²

Taking the square root of both sides, we get:

x = ±√(y + 4)

Therefore, the range of the function is the set of all real numbers greater than or equal to -4, since y + 4 must be non-negative for real values of y:

range = {y | y + 4 ≥ 0} = {y | y ≥ -4}

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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Angle 1 = 55 degrees ( corresponding angles are eqaul)

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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Answer:

1)

A) \(\frac{}{X}\) ~ N(8.5;0.108)

B) P(\(\frac{}{X}\) > 9)= 0.0552

C) P(X> 9)= 0.36317

D) IQR= 0.4422

2)

A) \(\frac{}{X}\) ~ N(30;2.5)

B) P( \(\frac{}{X}\)<30)= 0.50

C) P₉₅= 32.60

D) P( \(\frac{}{X}\)>36)= 0

E) Q₃: 31.0586

Step-by-step explanation:

Hello!

1)

The variable of interest is

X: pollutants found in waterways near a large city. (ppm)

This variable has a normal distribution:

X~N(μ;σ²)

μ= 8.5 ppm

σ= 1.4 ppm

A sample of 18 large cities were studied.

A) The sample mean is also a random variable and it has the same distribution as the population of origin with exception that it's variance is affected by the sample size:

\(\frac{}{X}\) ~ N(μ;σ²/n)

The population mean is the same as the mean of the variable

μ= 8.5 ppm

The standard deviation is

σ/√n= 1.4/√18= 0.329= 0.33 ⇒σ²/n= 0.33²= 0.108

So: \(\frac{}{X}\) ~ N(8.5;0.108)

B)

P(\(\frac{}{X}\) > 9)= 1 - P(\(\frac{}{X}\) ≤ 9)

To calculate this probability you have to standardize the value of the sample mean and then use the Z-tables to reach the corresponding value of probability.

Z= \(\frac{\frac{}{X} - Mu}{\frac{Sigma}{\sqrt{n} } } = \frac{9-8.5}{0.33}= 1.51\)

Then using the Z table you'll find the probability of

P(Z≤1.51)= 0.93448

Then

1 - P(\(\frac{}{X}\) ≤ 9)= 1 - P(Z≤1.51)= 1 - 0.93448= 0.0552

C)

In this item, since only one city is chosen at random, instead of working with the distribution of the sample mean, you have to work with the distribution of the variable X:

P(X> 9)= 1 - P(X ≤ 9)

Z= (X-μ)/δ= (9-8.5)/1.44

Z= 0.347= 0.35

P(Z≤0.35)= 0.63683

Then

P(X> 9)= 1 - P(X ≤ 9)= 1 - P(Z≤0.35)= 1 - 0.63683= 0.36317

D)

The first quartile is the value of the distribution that separates the bottom 2% of the distribution from the top 75%, in this case it will be the value of the sample average that marks the bottom 25% symbolically:

Q₁: P(\(\frac{}{X}\)≤\(\frac{}{X}\)₁)= 0.25

Which is equivalent to the first quartile of the standard normal distribution. So first you have to identify the first quartile for the Z dist:

P(Z≤z₁)= 0.25

Using the table you have to identify the value of Z that accumulates 0.25 of probability:

z₁= -0.67

Now you have to translate the value of Z to a value of \(\frac{}{X}\):

z₁= (\(\frac{}{X}\)₁-μ)/(σ/√n)

z₁*(σ/√n)= (\(\frac{}{X}\)₁-μ)

\(\frac{}{X}\)₁= z₁*(σ/√n)+μ

\(\frac{}{X}\)₁= (-0.67*0.33)+8.5=  8.2789 ppm

The third quartile is the value that separates the bottom 75% of the distribution from the top 25%. For this distribution, it will be that value of the sample mean that accumulates 75%:

Q₃: P(\(\frac{}{X}\)≤\(\frac{}{X}\)₃)= 0.75

⇒ P(Z≤z₃)= 0.75

Using the table you have to identify the value of Z that accumulates 0.75 of probability:

z₃= 0.67

Now you have to translate the value of Z to a value of \(\frac{}{X}\):

z₃= (\(\frac{}{X}\)₃-μ)/(σ/√n)

z₃*(σ/√n)= (\(\frac{}{X}\)₃-μ)

\(\frac{}{X}\)₃= z₃*(σ/√n)+μ

\(\frac{}{X}\)₃= (0.67*0.33)+8.5=  8.7211 ppm

IQR= Q₃-Q₁= 8.7211-8.2789= 0.4422

2)

A)

X ~ N(30,10)

For n=4

\(\frac{}{X}\) ~ N(μ;σ²/n)

Population mean μ= 30

Population variance σ²/n= 10/4= 2.5

Population standard deviation σ/√n= √2.5= 1.58

\(\frac{}{X}\) ~ N(30;2.5)

B)

P( \(\frac{}{X}\)<30)

First you have to standardize the value and then look for the probability:

Z=  (\(\frac{}{X}\)-μ)/(σ/√n)= (30-30)/1.58= 0

P(Z<0)= 0.50

Then

P( \(\frac{}{X}\)<30)= 0.50

Which is no surprise since 30 y the value of the mean of the distribution.

C)

P( \(\frac{}{X}\)≤ \(\frac{}{X}\)₀)= 0.95

P( Z≤ z₀)= 0.95

z₀= 1.645

Now you have to reverse the standardization:

z₀= (\(\frac{}{X}\)₀-μ)/(σ/√n)

z₀*(σ/√n)= (\(\frac{}{X}\)₀-μ)

\(\frac{}{X}\)₀= z₀*(σ/√n)+μ

\(\frac{}{X}\)₀= (1.645*1.58)+30= 32.60

P₉₅= 32.60

D)

P( \(\frac{}{X}\)>36)= 1 - P( \(\frac{}{X}\)≤36)= 1 - P(Z≤(36-30)/1.58)= 1 - P(Z≤3.79)= 1 - 1 = 0

E)

Q₃: P(\(\frac{}{X}\)≤\(\frac{}{X}\)₃)= 0.75

⇒ P(Z≤z₃)= 0.75

z₃= 0.67

z₃= (\(\frac{}{X}\)₃-μ)/(σ/√n)

z₃*(σ/√n)= (\(\frac{}{X}\)₃-μ)

\(\frac{}{X}\)₃= z₃*(σ/√n)+μ

\(\frac{}{X}\)₃= (0.67*1.58)+30= 31.0586

Q₃: 31.0586