The volume of a gas is inversely proportional to the pressure. If a pressure of 21 pounds per square inch corresponds to a volume of 20 cubic feet, what pressure is needed to produce a volume of 30 cubic feet

The educational researcher will need a sample size of at least 385 community college students to estimate the mean score on the math part of the SAT with a margin of error of 10 and 95% confidence.

To calculate the sample size required to estimate the mean score on the math part of the SAT of all community college students in the state, we can use the following formula:

n = (Zα/2 × σ / E) ^ 2

where:

n = sample size

Zα/2 = the z-score corresponding to the desired level of confidence (in this case, 95% confidence corresponds to a z-score of 1.96)

σ = the standard deviation of the population (given as 100)

E = the desired margin of error (given as 10)

Substituting the given values into the formula, we get:

n = (1.96 × 100 / 10) ^ 2

n = 384.16

Rounding up to the nearest integer, we get a sample size of 385. Therefore, the educational researcher will need a sample size of at least 385 community college students to estimate the mean score on the math part of the SAT with a margin of error of 10 and 95% confidence.

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Answer: 9.01 is the answer

Step-by-step explanation: Because when you add the number in the square you can split the number you add to the nearest sum to the number you get in the outcum.

The  integer coordinates will be strictly inside the rectangular region is 80.

We can find the dimensions of the rectangle by taking the absolute value of the difference between the x-coordinates and y-coordinates of two adjacent vertices. In this case, the dimensions are |5 - (-5)| = 10 and |4 - (-4)| = 8.

To find the number of integer coordinates strictly inside the rectangle, we can count the number of lattice points (points with integer coordinates) inside the rectangle using Pick's theorem. Pick's theorem states that the area of a lattice polygon (a polygon whose vertices have integer coordinates) can be found using the formula A = I + {B}\{2} - 1, where A is the area of the polygon, I is the number of lattice points strictly inside the polygon, and B is the number of lattice points on the boundary of the polygon.

In this case, the area of the rectangle is 10 \times 8 = 80. The boundary of the rectangle consists of 10 lattice points on the top and bottom sides and 8 lattice points on the left and right sides, for a total of 36 lattice points on the boundary.

Using Pick's theorem, we can solve for I:

80 = I + {36}÷{2} - 1

80 = I + 18 - 1

I = 63

Therefore, there are 63 lattice points strictly inside the rectangle.

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The relationship between chocolate sales and student happiness can be tested using the mean difference.

Specifically, a statistical test such as a correlation analysis or regression analysis can be used to examine the relationship between the amount of chocolate sales and the level of student happiness.

The mean difference refers to the difference in the average level of student happiness between two groups, such as those who consume more chocolate and those who consume less chocolate. This can help determine if there is a significant association between chocolate consumption and student happiness.

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Answer: the answer is 2 I believe

Step-by-step explanation:as you look at “stem” and go down to the number 4. You count below that. So 8, and 6. That’s 2 numbers :) hope this helps!

The stem and leaf plot shows the ages of people at the library. 2 people are under the age of 40.

The duration of a being's or thing's existence; the length of its existence or life up until the moment being discussed or alluded to age. A time frame for humans that begins at birth and is measured in years.

This time frame is typically characterised by a specific stage or level of physical or mental development as well as the potential for legal responsibility. The stem and leaf plot shows the ages of people at the library. 2 people are under the age of 40.

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To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3. Thus, the 75th term of the sequence is $111$.

To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3, we can use the base-3 (ternary) numeral system. The 75th term can be represented as the 74th number in base-3 without a digit 2 (as it will require subtraction to form distinct powers of 3).

The 74th number in base-10 is represented as $74_{10}$, which when converted to base-3 is $2202_3$. Since we need to avoid the digit 2, we can carry out the operation similar to addition with carry-over: $2202_3 + 1111_3 = 10310_3$.

Now, we can convert $10310_3$ back to base-10: $(1 \times 3^4) + (0 \times 3^3) + (3 \times 3^2) + (1 \times 3^1) + (0 \times 3^0) = 81 + 0 + 27 + 3 + 0 = 111$.

Thus, the 75th term of the sequence is $111$.

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Therefore, there were 75 downloads of the standard version with total size downloaded is 75 MB + 3(25 MB) = 150 MB.

To solve this problem, we can use a system of equations. Let x be the number of downloads for the standard version and y be the number of downloads for the high-quality version.

From the problem, we know that:
- The size of the standard version is x MB
- The size of the high-quality version is 3y MB
- The total size downloaded for the two versions was x + 3y MB

Putting these equations together, we get:

x + 3y = 150

We also know that the size of the standard version is smaller than the high-quality version, so we can assume that the standard version was downloaded more times than the high-quality version:

x > y

Now we have two equations and two unknowns. We can solve for x and y by substitution or elimination.

Let's use substitution:

From the second equation, we can isolate y:

y = x/3

Substitute this into the first equation:

x + 3(x/3) = 150

Simplify:

x + x = 150

2x = 150

x = 75

So there were 75 downloads of the standard version.

To check our answer, we can find the number of downloads for the high-quality version:

y = x/3 = 75/3 = 25

And verify that the total size downloaded is 75 MB + 3(25 MB) = 150 MB.

Therefore, there were 75 downloads of the standard version.

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We need a sample size of at least 876 adults to estimate the percentage of adults.

To find the sample size needed for estimating the percentage of adults who have consulted fortune-tellers with a 0.04 margin of error and a 99% confidence level, we can use the following formula:

n = (Z² * p * (1 - p)) / E²

where:

n = sample size

Z = Z-score associated with the confidence level (in this case, 2.58 for a 99% confidence level)

p = the expected proportion of adults who have consulted fortune-tellers (in this case, 0.18 based on the prior reliable poll)

E = the margin of error (in this case, 0.04)

Plugging in the values, we get:

n = (2.58² * 0.18 * (1 - 0.18)) / 0.04²

n ≈ 875.85

Rounding up to the nearest whole number, we need a sample size of at least 876 adults to estimate the percentage of adults who have consulted fortune-tellers with a 0.04 margin of error and a 99% confidence level, assuming the prior reliable poll suggested that 18% of adults have consulted fortune-tellers.

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To find the time required for more than 200 cars to have entered the parking lot with a probability of 0.9, we need to use the properties of the Poisson distribution and its cumulative distribution function (CDF).

Given:

- Poisson distribution rate (λ) = 100 cars per hour

- Desired probability (P(X > 200)) = 0.9

The Poisson distribution probability mass function (PMF) is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

To find the time required, we need to determine the value of λt (λ multiplied by time) that corresponds to the desired probability.

Using the CDF of the Poisson distribution, we can express the desired probability as:

P(X > 200) = 1 - P(X ≤ 200)

Since the CDF is a cumulative probability, we want to find the time (t) at which P(X ≤ 200) is less than or equal to 0.1. We can incrementally increase t until we reach the desired probability.

Step 1: Calculate the rate parameter for the desired time:

λt = λ * t

100 * t = λt

Step 2: Calculate the cumulative probability P(X ≤ 200) using the Poisson CDF:

P(X ≤ 200) = ∑[k=0 to 200] (e^(-λt) * (λt)^k) / k!

Step 3: Incrementally increase t until P(X ≤ 200) ≤ 0.1:

Start with t = 0, and increase it until P(X ≤ 200) ≤ 0.1 is achieved. This can be done using numerical methods or a Poisson distribution calculator.

The specific value of time required can vary based on the precise probability calculation and numerical approximation used. To obtain an accurate and precise result, it is recommended to use specialized software, statistical calculators, or programming languages with built-in functions for Poisson distributions.

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The width of a confidence interval for the population mean depends on the sample size, standard deviation, and the desired level of confidence. Generally, for a greater confidence level, the width of the confidence interval will be wider.

This is because a higher confidence level means that we want to be more certain that the true population mean falls within the interval. To achieve this higher level of certainty, we need to widen the interval to include a larger range of possible values for the population mean.

However, it's important to note that the increase in width may not be proportional to the increase in confidence level. In fact, the width of the confidence interval increases at a decreasing rate as the confidence level increases.

This means that the increase in width from a 90% confidence interval to a 95% confidence interval will be less than the increase in width from an 80% confidence interval to a 85% confidence interval, even though both involve a 5% increase in the level of confidence.

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Answer:

2 days

Step-by-step explanation:

The probability of choosing 6 people at random from the group and having all of them be left-handed is approximately 0.00002599 or 0.0026%.

We can approach this problem using the binomial distribution, which models the probability of a certain number of successes (in this case, choosing left-handed people) in a fixed number of trials (choosing 6 people).

Let p be the probability of choosing a left-handed person, which is given as 15% or 0.15. Then, the probability of choosing all 6 people to be left-handed can be calculated as:

P(6 left-handed) = (0.15[tex])^6[/tex] * (1 - 0.15)[tex]^(6 - 6) * C(6, 6)[/tex]

where C(6, 6) represents the number of ways to choose 6 items from a set of 6, which is equal to 1.

Plugging in the values, we get:

P(6 left-handed) = (0.15[tex])^6[/tex] * (0.85)^0 * 1

= 0.00002599

Therefore, the probability of choosing 6 people at random from the group and having all of them be left-handed is approximately 0.00002599 or 0.0026%.

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The null and alternative hypotheses are H₀ = μ ≥ 6 and H₁ = μ < 6.

Given that, the mean GPA of students in colleges is different from 2.0 (out of 4.0).

H₀: μ = 2.0 and H₁: μ ≠ 2.0

So,

We test the likelihood of the statement being true in order to decide whether to accept or reject our alternative hypothesis. Since, the question wants to test if the college student take less than six years to graduate on average, then we take, H₀ = μ ≥ 6.

And,

WE determine whether to accept or reject based on the likelihood of the null hypotheses being true, so we then take H₁ = μ < 6.

Hence, the null and alternative hypotheses are H₀ = μ ≥ 6 and H₁ = μ < 6.

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To determine the probabilities, we need to use the standard normal distribution table or a calculator that has this function. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

(a) P(−0.79 ≤ z ≤ −0.57) = We need to find the area under the standard normal distribution curve between z = -0.79 and z = -0.57. Using a standard normal distribution table or calculator, we find this probability to be 0.0767.
(b) P(z > 1) = We need to find the area under the standard normal distribution curve to the right of z = 1. Using a standard normal distribution table or calculator, we find this probability to be 0.1587.

(c) P(z ≥ −3.36) = We need to find the area under the standard normal distribution curve to the right of z = -3.36 (or the area to the left of z = 3.36, which is the same thing since the standard normal distribution is symmetrical). Using a standard normal distribution table or calculator, we find this probability to be 1.

(d) P(z < 4.96) = We need to find the area under the standard normal distribution curve to the left of z = 4.96. Since this value is greater than any z-score on the standard normal distribution table, we can say that this probability is extremely close to 1 (or practically 1).


To find the probabilities for a standard normal distribution, you can use a z-table or an online calculator based on the given intervals, rounding to four decimal places:

(a) P(-0.79 ≤ z ≤ -0.57) = P(z ≤ -0.57) - P(z ≤ -0.79) = 0.2843 - 0.2148 = 0.0695
(b) P(z > 1) = 1 - P(z ≤ 1) = 1 - 0.8413 = 0.1587
(c) P(z ≥ -3.36) = 1 - P(z < -3.36) = 1 - 0.0004 = 0.9996
(d) P(z < 4.96) = 0.9999 (since the probability of z > 4.96 is extremely small)

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From the perimeter of rectangle painting with frame, the width of the frame, i.e., x is equals to the three inches.

We have a rectangular painting measures 13 inches by 14 inches. Also, it contains a frame of uniform width around the four edges. Let the uniform width of frame be 'x inches'. See the above figure of painting, it is a rectangle.

Length of rectangular painting = 14 inches

Width of rectangle= 13 inches

The perimeter of the rectangle formed by the painting and its frame = 70 inches

We have to determine width of the frame.

Length of rectangle painting with frame = (14+ 2x) in

Width of rectangle painting with frame = (13+ 2x) in

As we know perimeter is sum of boundary lengths of a shape or geometry. So, the perimeter of rectangle= 2 ( l + w)

Substitute values of length, width and perimeter for painting with frame, 70 = 2( 14 + 2x + 13 + 2x )

Simplify the expression, 70 = 28 + 4x + 26 + 4x

=> 70 = 8x + 54

=> 8x = 70 - 54 = 24

=> x = 3 inches

Hence, required value is 3 inches.

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Complete question:

A rectangular painting measures 13 inches by 14 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 70 inches. Determine the width of the frame What is the width of the frame? inches

Thus,  there are 720 different Loco Mocos that can be ordered if we consider all six protein options, but this number can vary depending on individual preferences and availability.

A Loco Moco is a popular Hawaiian dish that usually consists of a base of white rice topped with a hamburger patty, a fried egg, and brown gravy.

However, it can be customized by adding different types of proteins such as Portuguese sausage, bacon, turkey, hot dog, salmon, or mahi. So, how many different Loco Mocos can be ordered?

If we consider all six proteins listed in the question, we have six options for the first protein, and then five options left for the second protein (since one has already been used), four options for the third protein, three for the fourth, two for the fifth, and one for the sixth.

Using the multiplication principle, we can calculate the total number of different Loco Mocos as follows:

6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore, there are 720 different Loco Mocos that can be ordered if we consider all six proteins. However, this number can vary depending on the number of protein options available at a particular restaurant or if a customer chooses to only add one or two proteins to their Loco Moco.

In conclusion,  there are 720 different Loco Mocos that can be ordered if we consider all six protein options, but this number can vary depending on individual preferences and availability.

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1 gallon contains 231 cubic inches. A rectangular container has dimensions of 32 in. by 16 in. by 28 in. A comparable container is one-quarter the size. Larger container holds 61.1 more gallons.

To solve this question, we have to find the volume of both the containers. First, we will find the volume of the container whose sides are 32 in. by 16 in. by 28 in.

Volume = multiplication of sides

= 32 × 16 × 28 in

= 14,336 inches cube

Now, we will find the sides of the smaller container which is scale factor of 1/4

Side 1 of small container = 1/4 × 32 = 8 in

Side 2 of small container = 1/4 × 16 = 4 in

Side 3 of small container = 1/4 × 28 = 7 in

Volume of container which is small = 8 × 4 × 7 = 224 cu in

Now, we will calculate the difference of volume to find the difference in capacity of containers.

Larger container holds more = 14,336 cu in - 224 cu in

= 14,112 cu in

Now, we will convert it into galloons.

231 cu in = 1 galloon

14,112 cu in = 14,112 / 231 galloons

= 61.1 galloons

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Therefore,  Selecting a five from a deck of 52 playing cards is not a simple event. This is due to the multiple outcomes (one for each suit).

whether selecting a five from a standard deck of 52 playing cards is a simple event, and you would like the main answer in the last two lines.
To determine if this event is a simple event, we must first define a simple event. A simple event is an event that consists of only one outcome or one possible result. In a standard deck of 52 playing cards, there are 4 fives (one in each suit: hearts, diamonds, clubs, and spades).
Since there are 4 fives in the deck, selecting a five is not considered a simple event because there are multiple outcomes (one for each suit).

Therefore,  Selecting a five from a deck of 52 playing cards is not a simple event. This is due to the multiple outcomes (one for each suit).

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Each team member should run 9073.6 miles in the race on Course B.

Let's break down the problem step by step:

1. First, we need to find the length of Course B. We know that Course B is 212 times as long as Course A, and Course A is 214 miles. So, to find the length of Course B, we multiply:
  Course B length = 212 × 214 miles

2. Calculate the length of Course B:
  Course B length = 45368 miles

3. Now, we need to determine the distance each team member should run. There are 5 members on the team, and they need to run an equal distance on Course B. To find the distance for each member, we divide the total length of Course B by the number of team members:
  Distance per member = Course B length / number of members

4. Calculate the distance per team member:
  Distance per member = 45368 miles / 5

5. Finally, we find the distance each team member should run:
  Distance per member = 9073.6 miles

So, each team member should run 9073.6 miles in the race on Course B.

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The probability of both the socks and the t-shirt being white is 21/44.

The probability of selecting a white pair of socks from the drawer is 6/11. The probability of selecting a white t-shirt from the drawer is 7/8. To find the probability of both events occurring together, we multiply the two probabilities:
P(white socks and white t-shirt) = (6/11) * (7/8) = 0.4773
Therefore, the probability of randomly selecting one pair of white socks and one white t-shirt from the drawer is approximately 0.4773 or 47.73%.
Hi there! To find the probability that both the socks and the t-shirt you randomly select are white, you'll need to multiply the individual probabilities for each item being white.
For the socks, there are 6 white pairs out of a total of 11 pairs. So, the probability of selecting a white pair is 6/11.
For the t-shirts, there are 7 white ones out of a total of 8. So, the probability of selecting a white t-shirt is 7/8.
Now, multiply these probabilities together: (6/11) * (7/8) = 42/88. Simplify the fraction to get 21/44.
So, the probability of both the socks and the t-shirt being white is 21/44.

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Note that where the above qualities of a right triangle are given the value of BC in it's simples radical is 11√2.

Here we simply applied the trigonometric rule.

BC = a / Sin (Ф)

Where a = 11 and
Ф = 45

So

BC = 15.55635 = 11√2

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Strengths Finder 2.0 is a valuable tool that can help individuals identify and develop their unique strengths. By leveraging these strengths, individuals can achieve greater success in their personal and professional lives, and organizations can create a more positive and productive work environment.

Strengths Finder 2.0 is a popular survey tool that helps individuals identify their unique strengths and talents. The survey has been completed by 10 million people to date and has been adopted by many universities and organizations to assist individuals in identifying their strengths.

The survey consists of a series of questions designed to assess an individual's natural talents and abilities. The results are then used to provide personalized feedback and coaching on how to leverage those strengths in their personal and professional lives.

The use of Strengths Finder 2.0 has become increasingly popular in recent years as individuals and organizations recognize the importance of focusing on strengths rather than weaknesses. By identifying and developing their strengths, individuals can improve their performance, increase their engagement and job satisfaction, and achieve greater success in their careers.

Organizations that use Strengths Finder 2.0 have reported increased productivity, employee engagement, and retention rates. By providing employees with the tools and resources to develop their strengths, organizations can create a more positive and fulfilling work environment.

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The equation to represent the relationship is x - 3y + 9 = 0.

We have the table

Input (x)     Output (y)

      3              4

      6              5

      9              6

     12              7

     15              8

So, the equation can be formed as

(y - 4) = (5-4)/ (6-3) (x-3)

y - 4 = 1/3 (x -3)

3y - 12 = x - 3

x - 3y - 3 + 12 =0

x - 3y + 9 = 0

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The displacement and distance traveled depend on the given time interval.

To find the displacement, we need to integrate the velocity function from 0 to 5 or 0 to 5π, depending on the given time interval.

If the time interval is [0,5], we have:

Displacement = ∫[0,5] v(t) dt
Displacement = ∫[0,5] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5
Displacement = 6sin(5) - 6sin(0)
Displacement ≈ 2.785 meters

If the time interval is [0,5π], we have:

Displacement = ∫[0,5π] v(t) dt
Displacement = ∫[0,5π] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5π
Displacement = 0 - 6sin(0)
Displacement = 0 meters

To find the distance traveled, we need to integrate the absolute value of the velocity function over the given time interval.

If the time interval is [0,5], we have:

Distance = ∫[0,5] |v(t)| dt
Distance = ∫[0,5] |6cos(t)| dt
Distance = ∫[0,π/2] 6cos(t) dt + ∫[π/2,5] -6cos(t) dt
Distance = [6sin(t)] from 0 to π/2 + [-6sin(t)] from π/2 to 5
Distance = 6 - 6sin(5) ≈ 2.215 meters

If the time interval is [0,5π], we have:

Distance = ∫[0,5π] |v(t)| dt
Distance = ∫[0,5π] |6cos(t)| dt
Distance = ∫[0,π] 6cos(t) dt + ∫[π,2π] -6cos(t) dt + ∫[2π,3π] 6cos(t) dt + ∫[3π,4π] -6cos(t) dt + ∫[4π,5π] 6cos(t) dt
Distance = [6sin(t)] from 0 to π + [-6sin(t)] from π to 2π + [6sin(t)] from 2π to 3π + [-6sin(t)] from 3π to 4π + [6sin(t)] from 4π to 5π
Distance = 0 meters

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The measure of length of x from the similar triangles is x = 10

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔACD

Now , AC is the common side of the triangle

And , they are similar triangles

So , the corresponding sides are in the same ratio

And , x / 5 = 20 / x

On cross multiplying , we get

x² = 100

Taking square roots on both sides , we get

x = 10

Hence , the length of side is x = 10

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The correct option is b. judgmental sampling; convenience sampling.  

Judgmental sampling was used in Mexico to ensure a representative sample of target respondents, while convenience sampling with the snowball procedure was employed in Saudi Arabia due to the absence of sampling frames and social customs prohibiting personal interviews.

The question is about the different sampling techniques used for the same consumer research study in Mexico and Saudi Arabia. In Mexico, judgmental sampling was used by having experts identify neighborhoods where the target respondents lived; homes were then randomly selected for interviews.

In Saudi Arabia, convenience sampling employing the snowball procedure was used because there were no lists from which sampling frames could be drawn and social customs prohibited spontaneous personal interviews.

Judgmental sampling, also known as expert sampling or purposive sampling, is a non-probability sampling technique where the researcher selects participants based on their expertise or knowledge about the population being studied.

In the case of Mexico, experts identified neighborhoods where target respondents lived, and homes were randomly selected for interviews. This technique helped ensure that the sample was representative of the target population.

On the other hand, convenience sampling is another non-probability sampling technique where participants are selected based on their availability and ease of access.

In Saudi Arabia, due to the absence of lists for sampling frames and social customs prohibiting spontaneous personal interviews, the snowball procedure was used. Snowball sampling is a type of convenience sampling where existing participants recruit additional participants from their network. This process continues until the desired sample size is achieved.

Therefore, the correct answer is b. judgmental sampling; convenience sampling.

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The revolutions the wheel will have to make before the car comes to a complete stop are approximately 25.5 revolutions.

To find out how many revolutions the wheel will have to make before the car comes to a complete stop, we need to use the information provided about the distance and diameter of the wheel.

First, we need to convert the diameter from centimeters to meters: 61 centimeters = 0.61 meters.

Next, we can use the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter.

So the circumference of the wheel is: C = π(0.61m) = 1.92m.

Now we can use the distance the car can stop in, 49 meters, to calculate the number of revolutions of the wheel:

49m ÷ 1.92m/rev ≈ 25.5 revolutions.

Therefore, the wheel will have to make approximately 25.5 revolutions before the car comes to a complete stop.

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The steps necessary to put he equation, x² - 3x + 27 = 8x - 3 in standard form is D. add 3 to both sides and subtract 8x from both sides

The standard form of quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number.

Hence, let's represent x² - 3x + 27 = 8x - 3 in standard form as follows:

x² - 3x + 27 = 8x - 3

Therefore, the two steps that are necessary to make the quadratic equation in standard form is add 3 to both sides and subtract 8x from both sides

Hence,

x² - 3x - 8x + 27 + 3 = 8x - 8x - 3 + 3

x² - 11x + 30 = 0

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In scientific notation, we write a number as a product of a number between 1 and 10 and a power of 10. The number before the multiplication sign is the significant figure, and the power of 10 indicates the magnitude of the number. To write a number to 3 significant figures, we only include one non-zero digit before the decimal point.

1. 2450: First, identify the non-zero digits (2, 4, and 5). Write the number as 2.45 and multiply it by 10 raised to the power of the number of places you moved the decimal point (3 in this case). So, the answer is 2.45 x 10^3.

2. 0.000326: Identify the non-zero digits (3, 2, and 6) and write the number as 3.26. Move the decimal point 4 places to the right, so multiply by 10 raised to the power of -4. The answer is 3.26 x 10^-4.

3. 0.000934: With non-zero digits 9, 3, and 4, write the number as 9.34. Move the decimal point 4 places to the right and multiply by 10^-4. The answer is 9.34 x 10^-4.

4. 685000: The non-zero digits are 6, 8, and 5, so write the number as 6.85. Move the decimal point 5 places to the left and multiply by 10^5. The answer is 6.85 x 10^5.

In summary:
2450 = 2.45 x 10^3
0.000326 = 3.26 x 10^-4
0.000934 = 9.34 x 10^-4
685000 = 6.85 x 10^5

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The  determinant of this matrix is -67/16.

To find the determinant of a matrix by row reduction to echelon form, we perform elementary row operations until the matrix is in echelon form, and then take the product of the diagonal entries. The determinant is the product of the pivots, with a factor of -1 for each row exchange.

Let's start with Exercise 5:

-1 -3  1
1  4  9
-1  0  5

We can start by adding the first row to the third row to eliminate the -1 in the (3,1) position:

-1 -3  1
1  4  9
0 -3  6

Next, we can multiply the third row by -1/3 to get a pivot in the (3,3) position:

-1 -3  1
1  4  9
0  1 -2

Then we add 3 times the second row to the third row to eliminate the 3 in the (3,2) position:

-1 -3  1
1  4  9
0  0  3

We now have an upper triangular matrix, which is in echelon form. The product of the diagonal entries is -1*4*3 = -12. Since we did not perform any row exchanges, there is no factor of -1. Therefore, the determinant of this matrix is -12.

Now let's move on to Exercise 6:

-1  0  5
3 -32  3
3  3  -1

We can start by adding 3 times the first row to the second row to eliminate the 3 in the (2,1) position:

-1  0   5
0 -32  18
3  3  -1

Then we can add the first row to the third row to eliminate the 3 in the (3,1) position:

-1  0   5
0 -32  18
0  3  4

Next, we can multiply the second row by -1/32 to get a pivot in the (2,2) position:

-1  0   5
0  1  -9/16
0  3   4

Then we add 9/16 times the second row to the third row to eliminate the -9/16 in the (3,2) position:

-1  0  5
0  1  -9/16
0  0  67/16

We now have an upper triangular matrix, which is in echelon form. The product of the diagonal entries is -1*1*67/16 = -67/16. Since we performed two row exchanges, there is a factor of (-1)^2 = 1. Therefore, the determinant of this matrix is -67/16.

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