A mouse pushes a block of cheese across the floor with 4 N of force. How many meters did the mouse travel if she did 16 J of work?

The statistical evidence available is insufficient to conclude that the education improved the nutrition behavior of the students.

The value of the t-test to be used is the option d

d. 1.29

A t-test is a test that is used to compare the means of two groups to find out if the effectiveness of a treatment or process on a population or if there is a difference between the two groups. A t-test assumes that the data is normally distributed.

The null hypothesis is H₀; μ = 2.9 (The population of patients have the same mean score as before the education)

Alternative hypothesis, Hₐ; μ > 2.9 (There is an increase in the mean score of the population of patients)

The sample mean, [tex]\overline{x}[/tex] = 3.3

Sample standard deviation, s = 1.2

Sample size, n = 15

The t-statistic is; t = ([tex]\overline{x}[/tex] - μ)/(s/√(n))

Therefore; t = (3.3 - 2.9)/(1.2/√(15)) ≈ 1.29

The df value is; df = 15 - 1 = 14

The critical value for a one tailed t-test at 5% significance level and df value of 14 is 1.761, therefore;

The t-value (1.29) is less than the critical t-value at 5% significant level, and we fail to reject the null hypothesis, and therefore;

There is insufficient statistical evidence to conclude that the education improved the nutrition behavior of the patients at the regional hospital

The t-test to be used has a value; d. 1.29

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Answer:

x=9/2

Step-by-step explanation:

The answer is C. The LCM is the same as the least common multiple for two odd integers.

The least common multiple (LCM) of two even integers a and b can be found by dividing both a and b by 2 until they become odd integers. Then, the LCM can be found using the same method as for two odd integers.

For example, let's say a=12 and b=16. Dividing both by 2, we get a=6 and b=8. Dividing again, we get a=3 and b=4, which are both odd.

The LCM of 3 and 4 is 12, so the LCM of 12 and 16 is also 12.

Therefore, the answer is C. The LCM is the same as the least common multiple for two odd integers.

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Answer:

Factor by grouping, (5n+4)(n+3), or alternatively, (n+3)(5n+4)

Answer:

(n +3)(5n + 4)

Step-by-step explanation:

5n^2 + 19n + 12

= 5n^2 + 15n + 4n + 12

= 5n(n + 3) + 4(n + 3)

= (n +3)(5n + 4)

Hence Factorized.

The number of different collections of 60 coins that can be chosen is:

(60+4-1) choose (4-1) = 63 choose 3 = 22,275

If there are at least 60 of each kind of coin, we can assume that we have four different types of coins, such as quarters, dimes, nickels, and pennies. Let's assume we have x quarters, y dimes, z nickels, and w pennies.

We know that we need to choose a total of 60 coins. Therefore, we have the following equation:

x + y + z + w = 60

We want to find the number of different collections of coins that can be chosen. This is equivalent to finding the number of non-negative integer solutions to the equation above.

Using the stars and bars formula, the number of non-negative integer solutions to this equation is:

(n+k-1) choose (k-1)

where n is the total number of objects (60 in this case) and k is the number of groups we want to divide them into (4 in this case).

So, the number of different collections of 60 coins that can be chosen is:

(60+4-1) choose (4-1) = 63 choose 3 = 22,275

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The critical value of t is  1.303

What is confidence interval?

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.

Given:

n = 38 , C = 80% = 0.80 ,

α = 1-0.80 = 0.20

Degree of freedom :

Df = n - 1

    = 38-1

    = 37

From the t-table,

t value corresponding to  α =  0.20 and  Df =  37 is

t* = 1.303

The critical value of t is  1.303

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Answer:44

Step-by-step explanation:

The derivative the function f(x) = √(x²+ 13x)/√x³ is given by = (x-1)/(2x²√(x+13)).

We know that the divide rule of derivative of a function with respect to 'x' is given by,

d/dx (u/v) = (v*(du/dx) - u*(dv/dx))/v²

where u and v are the functions of independent variable x.

The given function is,

f(x) = √(x²+ 13x)/√x³

Simplifying the function we get,

f(x) = √((x² + 13x)/x³) = √((x(x + 13)/x³) = √(x+13)/√x² = √(x+13)/x

differentiating the above function with respect to 'x' we get,

f'(x) = (x*(d/dx(√(x+13))) - √(x+13)*(d/dx(x)))/x²

      = ((x/(2√(x+13)) - 1/(2√(x+13)))/x²

      = (x-1)/(2x²√(x+13))

Hence the derivative is (x-1)/(2x²√(x+13)).

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Answer:

  (b)  (g∘f)(x) = (x +1)²

Step-by-step explanation:

Given that f(x) = x +1 and g(x) = x², you want to know the meaning of (g∘f)(x).

The ring operator (∘) is used to form a composition of functions. The composition is evaluated right to left:

  (g∘f)(x) = g(f(x))

That is, f(x) is evaluated first, and the result is used as the argument for function g.

  g(f(x)) = g(x +1) = (x +1)²

Then ...

  (g∘f)(x) = (x +1)²

A graph of Krypton's proportional relationship is shown below.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

In order to have a proportional relationship, the variables representing the mass (grams) and the volume (liters) must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 30/8

Constant of proportionality, k = 3.75.

Therefore, the required linear equation is given by;

y = kx

y = 3.75x

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For the random sample of 45 and mean 51mph the correct claim is given by,

Option 1. At 0.10 level of significance there is enough evidence to support claim that mean speed is less than 50 mph.

Random sample size = 45

Mean = 51mph

Population standard deviation = 5 mph

Test whether the mean speed of westbound traffic during morning peak hours is less than 50 mph,

The null and alternative hypotheses are,

Null hypothesis is μ >= 50

Alternative hypothesis is μ < 50

where μ is the population mean speed.

Since n > 30

For the population standard deviation, use a z-test.

The test statistic is ,

z = (X - μ) / (σ / √(n))

where X is the sample mean,

σ is the population standard deviation,

and n is the sample size.

Substituting the given values, we get,

z = (51 - 50) / (5 / √(45))

  =1.34

Using a attached standard normal distribution calculator value  ,

The p-value for this test is 0.00901.

At a significance level of 0.10, the p-value is less than the significance level.

Reject the null hypothesis.

Conclude that there is enough evidence.

To support the claim that the mean speed of westbound traffic during morning peak hours is less than 50 mph.

Therefore, for given random sample and mean correct option is 1. At 0.10 level of significance there is enough evidence to support claim that mean speed is less than 50 mph.

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The value of the integral I₁ is (1/2)π.

To evaluate the integral I₁ = ∫(1 to 0) √(1-x²) dx, we can use known areas of geometric shapes. Specifically, we can use the fact that the integral represents the area of the upper half of a unit circle centered at the origin, and we can use this to express the integral in terms of a known area formula.

The area of a unit circle is given by A = πr² = π(1)² = π. Since the integral I₁ represents the area of the upper half of the unit circle, we can express I₁ as half the area of the entire circle:

I₁ = (1/2)π

Therefore, the value of the integral I₁ is (1/2)π.

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The total cost of the purchases is $144. 8. So, the cost of the case of air fresheners is $33.97.

Let's start by calculating the total cost of the buckets, brushes, and towels.

The cost of 5 buckets is

5 buckets x $2.89/bucket = $14.45

The cost of 10 brushes is

10 brushes x $7.91/brush = $79.10

The cost of 48 towels is

48 towels x $0.36/towel = $17.28

So the total cost of the buckets, brushes, and towels is

$14.45 + $79.10 + $17.28 = $110.83

We know that the total cost of all the purchases, including the case of air fresheners, is $144.8. Therefore, we can calculate the cost of the case of air fresheners by subtracting the total cost of the buckets, brushes, and towels from the total cost of all the purchases

$144.8 - $110.83 = $33.97

So $33.97 is the cost of the case of air fresheners.

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The area between the curve is 3,295.525 square unit.

We have

Curve: y= -2x³+ 21x² -45x

The curve meet at x axis, y=0

-2x³+ 21x² -45x= 0

2x² - 21x + 45 = 0

x= 7.5 or x=3

Now, The curve lies above the x-axis between x= 3 or x=2 and x= 7.5 or x=6.

Thus, the required Area

= [tex]\int\limits^3_2 {2x^3 + 21x^2 - 45x} \, dx[/tex] + [tex]\int\limits^6_3 {2x^3 + 21x^2 - 45x} \, dx[/tex] + [tex]\int\limits^6_{7.5} {2x^3 + 21x^2 - 45x} \, dx[/tex]

= [[tex]x^4[/tex]/2 + 7x³ - 45x²/2[tex]|_2^3[/tex] +  [[tex]x^4[/tex]/2 + 7x³ - 45x²/2[tex]|_3^6[/tex]  +  [[tex]x^4[/tex]/2 + 7x³ - 45x²/2[tex]|_6 ^{7.5[/tex]

= [  40.5 + 189 - 202.5 - 8 - 56 + 90 + 1,512 + 648 - 810 - 40.5-189+202.5

+ 1,582.031 + 2,953.12- 1,265.625 -1512-648+810]

= 3,295.525

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The value of the 5 that has 1/10 of the value of the 5 in 345.217 is 0.5 ones, hence the answer to the provided question based on values.

The worth or usefulness of something is referred to as its value. It is a way to gauge how important or significant something is to a person or organisation. A variable's or function's assigned numerical value is referred to as a value. Value can have many meanings depending on the situation it is employed in.

The value of the number 5 in 345.217 is 5 units, or 5 ones.

We may divide the value of the first five by ten to get the value of the remaining five that is one-tenth that of the first five:

5 units ÷ 10 = 0.5 units

So the value of the other 5 is 0.5 units or 0.5 ones.

Therefore, the value of the 5 that has 1/10 of the value of the 5 in 345.217 is 0.5 ones.

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The derivative for the function f(x) = [tex]\frac{1 + sec(x^2)}{(1 - tan(x^2))}[/tex] is f'(x) = [tex]\frac{[2x(sec(x^2) - tan(x^2) sec^2(x^2))]}{ (1 - tan(x^2))^2}[/tex]

To find the derivative of the given function, we can use the quotient rule of differentiation.
Let f(x) = [tex]1 + sec(x^2) / (1 - tan(x^2))[/tex]
Then, f'(x) = [tex][(1 - tan(x^2)) d/dx(sec(x^2)) - sec(x^2) d/dx(tan(x^2))] / (1 - tan(x^2))^2[/tex]
Now, we need to find [tex]d/dx(sec(x^2))[/tex] and [tex]d/dx(tan(x^2)).[/tex]
[tex]d/dx(sec(x^2)) = sec(x^2) tan(x^2) (2x)[/tex]
[tex]d/dx(tan(x^2)) = sec^2(x^2) (2x)[/tex]
Substituting these values back in the derivative equation, we get:
f'(x) = [tex][(1 - tan(x^2)) (sec(x^2) tan(x^2) (2x)) - sec(x^2) (sec^2(x^2) (2x))] / (1 - tan(x^2))^2[/tex]
Simplifying further, we get:
f'(x) = [tex][2x(sec(x^2) - tan(x^2) sec^2(x^2))] / (1 - tan(x^2))^2[/tex]
Therefore, the derivative of the given function f(x) = [tex]1 + sec(x^2) / (1 - tan(x^2)) is f'(x) = [2x(sec(x^2) - tan(x^2) sec^2(x^2))] / (1 - tan(x^2))^2.[/tex]

The complete question is:-

Q.1 Find the derivative for the following functions: a. 1+sec x2 f(x)= [tex]\frac{1+sec x^2}{1- tan x^2}[/tex]

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Using regression analysis requires that our data meets the following criteria:
1) there is a pattern to our data,
2) the errors (residuals) of our regression analysis don't have a pattern,
3) most of the errors are small. Therefore, all of these criteria must be met in order to use regression analysis effectively.

Using regression analysis requires that our data meets the following criteria:
1) there is a pattern to our data,
2) the errors (residuals) of our regression analysis don't have a pattern,
3) most of the errors are small. Therefore, all of these criteria must be met in order to use regression analysis effectively.
Using regression analysis requires that our data meets the following criteria: there is a pattern to the data, the errors (residuals) of the regression analysis don't have a pattern, most of the errors are small, and all of these conditions must be satisfied for an effective analysis.

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The correlation coefficient between weight and height for these 9 individuals is approximately -0.73. So  the answer is (a) -0.73.

The correlation coefficient between weight and height can be estimated by using a statistical software or a calculator. Using a calculator, the correlation coefficient is calculated as follows:

- Enter the weight and height data into two separate lists (e.g. L1 and L2).
- Press the STAT button, then select CALC, and then select option 4: LinReg(ax+b).
- Enter L1 and L2 as the Xlist and Ylist, respectively.
- Make sure that the option "Calculate" is set to "r", which stands for the correlation coefficient.
- Press ENTER to calculate the correlation coefficient.

Using this method, the correlation coefficient between weight and height for these 9 individuals is approximately -0.73. Therefore, the answer is (a) -0.73.

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The 95% confidence interval for the population mean μ is approximately 29.64 hg < μ < 31.36 hg.

To construct a confidence interval estimate of the mean weight of newborn girls, we can use the formula:

CI = x ± t*s/√n

where CI is the confidence interval, x is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-value from the t-distribution table for the given confidence level and degrees of freedom (df = n-1).

For a 95% confidence level with df = 234, the t-value is 1.97. Plugging in the values given in the question, we get:

CI = 30.5 ± 1.97*(6.7/√235) = (29.6, 31.4)

This means we are 95% confident that the true mean weight of newborn girls falls within the interval (29.6, 31.4) hg.

Comparing this with the previous confidence interval of 28.9 hg < μ < 31.9 hg with only 12 sample values, x=30.4 hg, and s=2.3 hg, we can see that the new confidence interval is slightly wider but overlaps with the previous interval. This suggests that the two sets of results are not very different.

Therefore, the confidence interval for the population mean μ is (29.6, 31.4) hg.

Using the provided statistics for newborn girls' weights (n=235, x=30.5 hg, s=6.7 hg), we can construct a 95% confidence interval for the population mean (μ) using the formula:

CI = x ± (t * s/√n)

Here, x is the sample mean, s is the sample standard deviation, and n is the sample size.

For a 95% confidence level and degrees of freedom (df) = n - 1, the t-value is approximately 1.96.

CI = 30.5 ± (1.96 * 6.7/√235) = 30.5 ± 0.86



Comparing this to the confidence interval 28.9 hg < μ < 31.9 hg with 12 sample values, x=30.4 hg, and s=2.3 hg, the results are not significantly different as both intervals overlap and include similar values.

However, the interval based on 235 samples is narrower, indicating a higher precision in the estimate.

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The probability that a premium paid this year by a randomly selected worker is between $3331 and $4453 is approximately 0.7054 - 0.0934 = 0.6120.

a) To find the probability that a premium paid this year by a randomly selected worker is less than $3331, we need to standardize the value of $3331 using the mean and standard deviation of the population, and then find the corresponding probability using a standard normal distribution table or calculator.

Z-score = (x - μ) / σ = (3331 - 4129) / 600 = -1.32

Using a standard normal distribution table or calculator, we find that the probability of a standard normal random variable being less than -1.32 is approximately 0.0934.

Therefore, the probability that a premium paid this year by a randomly selected worker is less than $3331 is approximately 0.0934.

b) To find the probability that a premium paid this year by a randomly selected worker is greater than $4453, we need to standardize the value of $4453 using the mean and standard deviation of the population, and then find the corresponding probability using a standard normal distribution table or calculator.

Z-score = (x - μ) / σ = (4453 - 4129) / 600 = 0.54

Using a standard normal distribution table or calculator, we find that the probability of a standard normal random variable being greater than 0.54 is approximately 0.2946.

Therefore, the probability that a premium paid this year by a randomly selected worker is greater than $4453 is approximately 0.2946.

c) To find the probability that a premium paid this year by a randomly selected worker is between $3331 and $4453, we need to standardize these values using the mean and standard deviation of the population, and then find the corresponding probabilities and subtract them.

Z-score for $3331 = (3331 - 4129) / 600 = -1.32

Z-score for $4453 = (4453 - 4129) / 600 = 0.54

Using a standard normal distribution table or calculator, we find that the probability of a standard normal random variable being less than -1.32 is approximately 0.0934, and the probability of a standard normal random variable being less than 0.54 is approximately 0.7054.

Therefore, the probability that a premium paid this year by a randomly selected worker is between $3331 and $4453 is approximately 0.7054 - 0.0934 = 0.6120.

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We reject the null hypothesis that there is no significant difference between the means of the three groups.

We then calculate the mean square (MS) between groups and the mean square within groups. The MS between groups is the SS between divided by the df between, and the MS within groups is the SS within divided by the df within.

Finally, we calculate the F-statistic, which is the ratio of the MS between groups to the MS within groups. If the F-statistic is greater than the critical value at the chosen significance level (α), we reject the null hypothesis that there is no difference between the means of the groups.

In this problem, we have 12 people divided equally into three groups, with four people in each group. The mean score for each group is:

Group A: 1.0

Group B: 3.0

Group C: 7.0

The overall mean score is 3.67. The SS between groups is 70.67, and the SS within groups is 20.67. The df between groups is 2, and the df within groups is 9.

The MS between groups is 35.33, and the MS within groups is 2.30. The F-statistic is 15.39, which is greater than the critical value of 3.89 at the α level of .05.

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The probability that one toss will come up heads and the other will come up tails when you flip a coin two times is 50%.

Imagine you've got a coin, and you flip it two times. Once you flip a coin, it can either arrive on heads (the side with a confront) or tails (the side with the hawk, in the event that it's a US quarter).

On the off chance that you flip the coin two times, there are four distinctive conceivable ways the coin can arrive:

heads-heads (HH),

heads-tails (HT),

tails-heads (TH),

and tails-tails (TT).

Presently, out of these four conceivable results, the HT and TH results have one hurl(toss) that comes up heads and the other hurl that comes up tails. So, we're curious about the likelihood of getting either HT or TH.

Since there are four conceivable results and two of them are HT and TH, the likelihood of getting one hurl that comes up heads and the other that comes up tails is 2 out of 4, or 50%.

So, in the event that you flip a coin two times, there's a 50-50 chance that you'll get one hurl that comes up heads and the other that comes up tails

Hence, the likelihood that one hurl will come up heads and the other will come up tails after you flip a coin two times is 2 out of 4, or 50%. 

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The probability that a randomly chosen positive integer less than mn is not divisible by either m or n is (mn - m - n + 1) / (mn - 1).

We can start by finding the total number of positive integers less than mn. Since we are choosing a number less than mn, we have mn-1 possible choices.

Next, we can count the number of positive integers less than mn that are divisible by m or n. To do this, we can use the principle of inclusion-exclusion.

The number of positive integers less than mn that are divisible by m is (n-1) m, because there are n-1 multiples of m less than or equal to mn. Similarly, the number of positive integers less than mn that are divisible by n is (m-1) n.

However, if we simply add these two numbers together, we would be double-counting the numbers that are divisible by both m and n. Therefore, we need to subtract the number of multiples of mn. There is only one such multiple, which is mn itself.

So, the number of positive integers less than mn that are divisible by either m or n is:

(n-1) m + (m-1) n - 1

To find the probability that a randomly chosen positive integer less than mn is not divisible by either m or n, we can subtract this number from the total number of choices and divide by the total number of choices:

P(not divisible by m or n) = (mn-1 - [(n-1) m + (m-1) n - 1]) / (mn-1)

Simplifying this expression, we get:

P(not divisible by m or n) = (mn - m - n + 1) / (mn - 1)

This is the probability that we are looking for, in terms of m and n.

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Answer: 1485 dollars

Step-by-step explanation:

She earns 44 dollars per week and one additional dollar for each book that she sells. She sells 33 books.

First, you do 33x1=33 dollars for selling 33 books

Then you do 44+1=45 for the 1 additional dollar she gets for selling books.

Lastly, you do 45x33. If you break it down (45x30=1350) and (45x3=135). 1350+135= 1485 dollars

                                          Hope this helps!

Answer:

Step-by-step explanation:

16

According to the question, the information provided makes it impossible to assess the value of NC?

Tetrahedrons, also called triangle pyramids, are polyhedra with four trapezoidal faces, six edges that are level, and four vertex corners. The tetrahedron, which additionally happens to be the most straightforward of them all, is the only regular symmetric polygon with lower than five faces. The cylindrical structure at the base of the triangle is made of tetrahedra. If an object has four triangular-shaped faces, it is a tetrahedron. Regular Tetrahedrons are the ones that have equilateral triangle bases and isosceles triangle faces. A polyhedron has four sides.

Two comparable triangles, and ABC and AMN, are present in the given issue, because where "" indicates similarity.

The details are as follows:

AN = 8 AM = 6 MB = 4

We receive a request to determine NC's value.

The ratios of related sides are identical in similar triangles, which have proportionate sides. Using the equivalent ends of ABC and AMN, we can establish a ratio:

NC/AN = AB/AM

replacing the specified values:

AB/6 = NC/8

We can traverse-multiply and then use that result to solve for NC:

8 x AB 6 x NC 8 x AB 6 x NC

(Simplifying by dividing the two sides by 2) NC = (8AB)/6 NC = (4AB)/3

Since we do not have a specific value for AB or any additional information about the triangles, we cannot determine the exact value of NC. We can only express it in terms of AB, which is not provided in the given problem. Therefore, the value of NC cannot be determined with the information given.

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The given conditions justify testing a claim about a population mean p. Since the original population is normally distributed, and the sample size n = 22 is reasonably large, the Central Limit Theorem allows us to perform hypothesis testing for the population mean.

For the first question, the conditions justify testing a claim about a population mean as the sample size is greater than 30 (n=22), the sample mean (-5.77) is known, and the original population is normally distributed.

Yes, the given conditions justify testing a claim about a population mean. Although the original population is not normally distributed, the sample size n = 43 is large enough for the Central Limit Theorem to apply, which allows us to perform hypothesis testing for the population mean.

For the second question, the conditions do not justify testing a claim about a population mean as the sample size is greater than 30 (n=43), but the original population is not normally distributed. In this case, a non-parametric test or data transformation may be necessary.

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The points (x, y, z), (1, 1, 0), and (1, 2, 1) lie on a plane through the origin, then the determinant is zero

Since the plane passes through the root, any two vectors on the plane must be directly autonomous. In this manner, we will utilize the vectors (1, 1, 0) and (1, 2, 1) to discover the condition of the plane.

A vector opposite to the plane can be found by taking the cross item of the two vectors:

(1, 1, 0) × (1, 2, 1) = (-1, 1, 1)

The condition of the plane can be composed as:

x + y + z = d

where d may be steady to be decided. We are able to utilize one of the focuses on the plane, such as (1, 1, 0), to discover d:

1 + 1 + = d

d = 0

In this manner, the condition of the plane is:

x + y + z = 0

 To check that the point (x, y, z) = (1, 2, 1) lies on this plane, we will substitute these values into the condition over   

  1 + 2 + 1 = 0

 which is genuine, so the point lies on the plane.

To discover the determinant that is zero, we will utilize the three focuses (x, y, z), (1, 1, 0), and (1, 2, 1) to make a 3x3 lattice:

| x y z |

| 1 1 0 |

| 1 2 1 |

Growing the determinant along the primary push, we get:

x | 1  0 |

| 2 1 | = x(1 - 0) - y(1 - 0) + z(2 - 1) = x - y + z

Subsequently, the determinant is:

x - y + z

Since these three focuses lie on a plane through the root, they fulfill the condition:

x + y + z = 0

 Substituting z = -x + y into the expression for the determinant over, we get:

x - y + (-x + y) = 0

 Streamlining, we get:  

 0=0  

 Subsequently, the determinant is zero, as anticipated. 

To know more about determinants refer to this :

https://brainly.com/question/16981628

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