The sampling distribution for the variance estimator in ANOVA is chi-square regarless of the assumptions of the data

Answer:

[tex]volume\ = \pi \frac{625^2}{6}[/tex]

Step-by-step explanation:

See the attached figure.

y₁ = 25x  and  y₂ =x²

The intersection between y₁ and y₂

25x = x²

x² - 25x = 0

x(x-25) = 0

x = 0 or x =25

y = 0 or y =25² = 625

The points of intersection (0,0) and (25,625)

To find the volume of the solid obtained by rotating about the y-axis the region bounded by y₁ and y₂

y₁ = 25x ⇒ x₁ = y/25 ⇒ x₁² = y²/625

y₂ =x² ⇒ x₂ = √y ⇒ x₂² = y

v = ∫A(y) dy = π ∫ (x₂² - x₁²) dy

∴ V =

[tex]\pi \int\limits^{625}_0 {y-\frac{y^2}{625} } \, dy =\pi( \frac{y^2}{2} -\frac{y^3}{3*625} ) =\pi (\frac{625^2}{2} -\frac{625^3}{3*625}) =\pi ( \frac{625^2}{2}-\frac{625^2}{3}) =\pi \frac{625^2}{6}[/tex]

To find the volume of the solid formed by rotating the region bounded by y = 25x and y = x²25 about the y-axis, one needs to calculate the area of a typical slice, then integrate this area over the range of x-values.

To find the volume V of the solid obtained by rotating the region bounded by y = 25x and y = x225 about the y-axis, we can apply the method of slicing.

First, we need to find the area A(x) of a typical slice perpendicular to the x-axis. Here we have two functions, finding the x- values where these functions intersect gives the bounds on the integral for the volume.

We can find the area A(x) = pi*(outer radius)2 - pi*(inner radius)2 = pi[(25x)ˆ2 - (xˆ2 * 25)ˆ2].

To find V, we integrate A(x) over the interval of x-values. This will give us the exact volume of the solid.

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Answer:

0.8749

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 0, \sigma = 1[/tex]

The probability that Z is less than 1.15 is:

This is the pvalue of Z = 1.15, which is 0.8749.

The probability that Z is less than 1.15: P(Z < 1.15) = Φ(1.15) ≈ 0.8749 or 87.49%

For a standard normal distribution with a mean of 0 and a standard deviation of 1, the probability that the random variable Z is less than 1.15 can be calculated using the standard normal cumulative distribution function (CDF).

The standard normal CDF gives the probability that a standard normal random variable takes a value less than or equal to a given value. We can use a standard normal distribution table or a calculator/software to find the value of the CDF at the desired point.

Let's denote the CDF of the standard normal distribution as Φ(z). Then, the probability that Z is less than 1.15 is given by:

P(Z < 1.15) = Φ(1.15)

Using a standard normal distribution table or calculator, we find that Φ(1.15) ≈ 0.8749.

Therefore, the probability that Z is less than 1.15 is approximately 0.8749 or 87.49%.

Answer:

Step-by-step explanation:

The diagram consists of different boxes if the same sizes. Each box is a square with sides measuring 1 cm. The area of each box would be

1 × 1 = 1cm^2

The area of the parallelogram is the total number of squares that it contains. To determine this, the first step is to count the total number of complete squares. Looking at the diagram, there are 11 complete squares. This means

11 × 1 = 11 square units.

The next step is to count the number of incomplete squares and divide by 2. The number of incomplete squares are 8

8/2 = 4

4 × 1 = 4 square units

The area of the parallelogram would be

11 + 4 = 15 square units

Answer:

$12,400

Step-by-step explanation:

Given:

Week earning + 9% commission = $1,916

Weekly Earning = $800

Commission for the Week = $1,916 - $800 = $1,116

Let total sales for the week = x

Therefore, x = ($1,116 * 100)/9

x = $12,400

Answer:

$12400

Step-by-step explanation:

Wages = Basic pay + Commission

1916 = 800 + 9%A

Let A be the total sales

9%A = 1916 - 800

9%A = 1116

A = $12400

The rate of change is A. constant, B. linear

Step-by-step explanation:

Rate of change is the ratio of change in value of y with corresponding value of x

Rate of change=Δy/Δx

Rate of change=5-2/4-1 =3/3=1

The rate of change is constant in the given interval and linear with a positive slope.

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Answer:

The accrued value after 5 years is $1,605.95.

The accrued value after 10 years is $1,672.9.

The accrued value after 15 years is $1,739.85.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex].

In this problem, we have that:

[tex]P = 1539, I = 0.01[/tex]

Accrued value after 5 years

This T when t = 5. So

[tex]E = P*I*t[/tex]

[tex]E = 1339*0.01*5 = 66.95[/tex]

The total is

[tex]T = E + P = 66.95 + 1539 = 1605.95[/tex]

The accrued value after 5 years is $1,605.95.

Accrued value after 10 years

This T when t = 10. So

[tex]E = P*I*t[/tex]

[tex]E = 1339*0.01*10 = 133.9[/tex]

The total is

[tex]T = E + P = 133.9 + 1539 = 1672.9[/tex]

The accrued value after 10 years is $1,672.9.

Accrued value after 15 years

This T when t = 15. So

[tex]E = P*I*t[/tex]

[tex]E = 1339*0.01*15 = 200.85[/tex]

The total is

[tex]T = E + P = 200.85 + 1539 = 1739.85[/tex]

The accrued value after 15 years is $1,739.85.

Answer:

27m²

Step-by-step explanation:

surface area is area of all sides

these is two triangles and a rectangle

area of triangle = (base x height) /2 = (3 x 4)/2= 12/2 =6

area of rectangle = length x breadth = 5x3 = 15

surface area = area of triangle + area of triangle + area of rectangle

6 + 6 + 15 = 27m²

Step-by-step explanation:

You need to find six combinations of a and b such that a² + b² = 7.

a = 1, b = √6

a = √2, b = √5

a = √3, b = 2

a = 2, b = √3

a = √5, b = √2

a = √6, b = 1

Answer:

Solution of the system is (2,1).                                                          

Step-by-step explanation:

We are given the following system of equation:

[tex]3x+4y=10\\x - y = 1[/tex]

We would use the elimination method to solve the following system of equation.

Multiplying the second equation by 4 and adding the two equation we gwt:

[tex]3x + 4y = 10\\4\times (x-y = 1)\\\Rightarrow 4x - 4y = 4\\\text{Adding equations}\\3x + 4y + (4x-4y) = 10 + 4\\7x = 14\\\Rightarrow x = 2\\\text{Substituting value of x in second equation}\\2 - y = 1\\\Rightarrow y = 1[/tex]

Solution of the system is (2,1).

Answer: the solution is (2, 1)

Step-by-step explanation:

The given system of simultaneous equations is given as

3x+4y=10 - - - - - - - - - - - - -1

x−y=1 - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 1 an equation 2 by 3. It becomes

3x + 4y = 10

3x - 3y = 3

Subtracting, it becomes

7y = 7

Dividing the left hand side and the right hand side of the equation by 7, it becomes

7y/7 = 7/7

y = 1

Substituting y = 1 into equation 2, it becomes

x - 1 = 1

Adding 1 to the left hand side and the right hand side of the equation, it becomes

x - 1 + 1= 1 + 1

x = 2

Answer:

Step-by-step explanation:

The first step is to rearrange the given quadratic equation so that it will take the form of the standard quadratic equation which is expressed as

ax² + bx + c = 0

The given quadratic equation is expressed as

2 = - x + x² - 4

Rearranging it, we would subtract 2 from the left hand side and the right hand side of the equation. It becomes

2 - 2 = - x + x² - 4 - 2

- x + x² - 6 = 0

x² - x - 6

a = 1

b = - 1

c = - 6

Substituting into the quadratic formula, it becomes

x = [- (- 1) ± √(- 1)² - 4(1)(- 6)] /2(1)

Answer:

10 roses

Step-by-step explanation:

To find the number of roses in the blue vase, we double the number of roses in the red vase. Since the red vase has 5 roses, the blue vase contains 10 roses.

The student's question is about determining the number of roses in the blue vase given certain conditions about the number of flowers in vases. We know that each vase has 12 flowers, the red vase has 7 tulips, and thus 5 roses because the total is 12. The blue vase has twice as many roses as the red vase, so we need to double the number of roses in the red vase to find that number.

Since the red vase has 5 roses, the blue vase will have twice as many, which is 10 roses.

Here's the calculation step by step:

Answer:

Step-by-step explanation:

answer to Step 1

Households with unlisted numbers or without telephones.

answer to Step 2

2.People without the extra income to keep a phone line will largely comprise the population without a phone line.

3.Very busy people or those interested in maintaining privacy will largely comprise those with unlisted numbers.

Answer: C. If he passes the class, she will pay $100.

A. If she ended up paying $100, he must have passed the class.

Step-by-step explanation:

For a statement to be true, one assumption might imply the other assumption. In this case, A and C fulfills it.

Final answer:

The mathematician's statement makes passing the class a necessary condition for her son to receive $100. If he received the money, he must have passed the class, but not receiving the money does not conclusively prove he did not pass. The statement does not make passing the class a sufficient condition, as there could be other requirements.

Explanation:

The statement made by the mathematician to her son is a classic example of a conditional statement in logic, particularly looking at necessary and sufficient conditions. To analyze the truth of the given statements, we must understand the relationship between passing the class and receiving the $100.

Answer:

1) The production canister welds have consistently lower burst strengths than the test nozze welds.

2) The production canister weids have much more variable burst strengths.

3) The test nozzle welds data contain 2 outliers.

4) Test nozzle welds have much more variable burst strengths.

5) The production canister welds have much higher burst strengths.

6) The production canister welds data contain 2 outiers.

Step-by-step explanation:

Hello!

The boxplots summarize the information of test nozzle closure welds and production canister nozzle welds.

The boxplot for the test nozzle closure welds shows that the first quartile and second quartile are close to each other but the third quartile is more separated to them, meaning that the data contained in the box is asymmetric, the data seems to have less variability between C₁ and C₂ and more between C₂ and C₃, the box is right-skewed.

The left whisker is larger than the right one, there are no outliers in the sample, due to most of the data being comprehended below C₁, the overall distribution of the data set is left-skewed, with large variability.

The boxplot for production cannister nozzle welds shows that the box is small (the variability of the data set is low) and symmetric, with C₂ in the middle of it and C₁ and C₃ are equidistant to the second quartile.

The whiskers of the box are small but they have almost the same length, showing that there is the same amount of data in them, this adds to the overall symmetry of the data set.

Finally, this data set shows two outliers, these values are far from the box, meaning that they are relatively extreme unusual values in regards to the rest of the sample but their distance to the box seems to be equal wich adds to the conclusion of the symmetrical distribution, with low variability of the data set.

I hope it helps!

Answer:

[tex]P = \left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right][/tex]

[tex]Q = \left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right][/tex]

Step-by-step explanation:

[tex]P*\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}y\\z\\x\end{array}\right][/tex]

[tex]Q*\left[\begin{array}{c}y\\z\\x\end{array}\right]=\left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right] \left[\begin{array}{c}y\\z\\x\end{array}\right] = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]

Answer:

Step-by-step explanation:

Triangle QRS is a right angle triangle.

From the given right angle triangle

RS represents the hypotenuse of the right angle triangle.

With 30 degrees as the reference angle,

QR represents the adjacent side of the right angle triangle.

QS represents the opposite side of the right angle triangle.

To determine QR, we would apply trigonometric ratio

Cos θ = adjacent side/hypotenuse side. Therefore,

Cos 30 = QR/14

√3/2 = QR/14

QR = 14 × √3/2

QR = 14√3/2 = 7√3/2

Answer:

a) Figure attached

b) For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j

And the final position vector can be calculated adding the 3 vectors like this:

[tex] s = A +B+C[/tex]

[tex] s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j[/tex]

We can find the magnitude of s like this:

[tex] |s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983[/tex]

And then we can find the angle with this formula:

[tex] \theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44 [/tex]

The other possibility is [tex] \theta = 50.44+180 =230.44[/tex]

And since they want the angle measured from East the correct angle would be [tex] \theta = 230.44[/tex]

Step-by-step explanation:

Part a

On the figure attached we have the vectors for the pattern described.

Part b

For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j

And the final position vector can be calculated adding the 3 vectors like this:

[tex] s = A +B+C[/tex]

[tex] s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j[/tex]

We can find the magnitude of s like this:

[tex] |s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983[/tex]

And then we can find the angle with this formula:

[tex] \theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44 [/tex]

The other possibility is [tex] \theta = 50.44+180 =230.44[/tex]

And since they want the angle measured from East the correct angle would be [tex] \theta = 230.44[/tex]

Answer:

cos 38 = 17/c

Step-by-step explanation:

cos 38 = 17/c is the correct statement

Answer:

[tex]14\frac{1}{3}[/tex]

Step-by-step explanation:

Let's write this out as an equation. Let the unknown quantity be x:

[tex]x+\frac{2}{3} - \frac{1}{3} (x+\frac{2}{3}) = 10\\\\3x+2-x -\frac{2}{3} = 30\\\\9x+6-3x-2=90\\\\6x= 86\\\\x = \frac{86}{6} =\frac{43}{3} =14\frac{1}{3} \\[/tex]

Answer: the quantity is 9

Step-by-step explanation:

Let x represent the quantity.

A quantity and its 2/3 are added together. The 2/3 of the number is 2/3 × x = 2x/3

The sum of the quantity and its 2/3 would be

x + 2x/3 = (3x + 2x)/3 = 5x/3

From the sum, 1/3 of the sum is subtracted. 1/3 of the sum would be

1/3 × 5x/3 = 5x/9

Subtracting 1/3 of the sum from the sum, it becomes

5x/3 - 5x/9 = (15x - 5x)/9 = 10x/9

If the remainder is 10, it means that

10x/9 = 10

Crossmultiplying

10x = 9 × 10 = 90

x = 90/10

x = 9

SR =sin (angle) = opposite leg/ hypotenuse

sin(52) = SR/ 7.6

SR = 7.6 x sin(52)

SR = 5.988 ( round answer as needed.)

QR = cos(angle) = adjacent leg / hypotenuse

Cos(52) = QR/ 7.6

QR = 7.6 x cos(52)

QR = 4.679. ( round answer as needed).

Angle S = 180 - 90 -52 = 38 degrees

Answer: lowering

Step-by-step explanation:

Statins are drugs that are administered in order to help reduce cholesterol level in the body. Statins achieves this by making it impossible for the body to have access to substances that helps to produce cholesterol. This drug reduces cholesterol up to 50% and are taken once every day. Examples includes rosuvastatin, pitavastatin, simvastatin.

(a) Growth Rate Constants: 6

(b) Carrying Capacity Constants: 0

Interaction Constants: 3

The species compete since the interaction constant is positive, indicating competition for resources between the two species.

For the given system:

[tex]\[ x' = 6x \][/tex]

[tex]\[ S_{xy} = 32y^2 - 8y - 8 + 3xy - 31 \][/tex]

(a) Growth Rate Constants: The growth rate constant for species [tex]\(x\)[/tex] is [tex]\(6\)[/tex].

(b) Carrying Capacity Constants: There is no explicit term indicating a carrying capacity for either species in the given equations, so the carrying capacity constants are both [tex]\(0\)[/tex].

Interaction Constants: The interaction constant between the two species can be identified from the term [tex]\(S_{xy}\)[/tex], which is [tex]\(3\)[/tex] in this case.

So, the answers are:

(a) Growth Rate Constants: [tex]\(6\)[/tex]

(b) Carrying Capacity Constants: [tex]\(0\)[/tex]

Interaction Constants: [tex]\(3\)[/tex]

The species compete since the interaction constant is positive.

Complete Question :

Population models for two species can report either competition for resources (an rise in one species recede the growth rate in the other) or cooperation for asset (an rise in one species rise the growth rate in the other). For the systems below, identify the boundary as growth rates, carrying capacities, and measures of interconnection between species. Determine if the species compete or cooperate. x' = 6x Sxy = 32y^2 - 8y - 8 + 3xy - 31 (a) Growth Rate Constants: (b) Carrying Capacity Constants: interconnection Constants: Note: Your answers must be numbers (which may include 0). If there is more than one answer, different your answers with commas. Choose One: - The Species Do Not Interact - One species take part, the other Cooperates - Help Both Species Cooperate - Both Species Compete.

Answer:

Given:

Length of the garden is represented by :

[tex]3y+5[/tex]

The length is increased by 50%.

To find the new length.

Solution:

1) The original length = [tex]3y+5[/tex]

The increase in length will be = [tex]50%[/tex] of [tex]3y+5[/tex]

⇒ [tex]\frac{50}{100}(3y+5)[/tex]

⇒ [tex]\frac{1}{2}(3y+5)[/tex]

The new length  = Original length + Increased length = [tex](3y+5)+ \frac{1}{2}(3y+5)[/tex]

2) Let the original length = 100%

Increase percent of length = 50%

Total percent of length = [tex]100\%+50\%=150\%[/tex]

New length = [tex]150%[/tex] of [tex]3y+5[/tex]

⇒ [tex]\frac{150}{100}(3y+5)[/tex]

⇒ [tex]1.5(3y+5)[/tex]

Thus,  the new length of the garden can be represented by both expression :

[tex](3y+5)+ \frac{1}{2}(3y+5)[/tex] or [tex]1.5(3y+5)[/tex]

Answer:

A) The actual error |f(0.5) - P3(0.5)| is 0.0340735. The error using Taylor's error formula R₃(0.5) is 0.2917.

B) Te error in the interval [0.5,1.5] is 0.0340735.

C) The approximate integral using P₃(x) is 1/12

D) The real error between the two integrals is 4.687·10^(-3) while the error using \int_{0.5}^{1.5}|R_{3}(x)dx| is 0.018595

Step-by-step explanation:

A) To determine the error we first have to write the third grade Taylor polynomial P3(x):

[tex]P_n(x)=\displaystyle\sum_{k=0}^N \frac{f^{k}(a)}{k!}(x-a)[/tex] with N=3

[tex]P_3(x)=\displaystyle\sum_{k=0}^3 \frac{f^{k}(1)}{k!}(x-1)=(x-1)^2-\frac{1}{2} (x-1)^3[/tex]

The error for the third grade Taylor polynomial R₃(x) is represented as the next term non-written in the polynomial expression near to the point x:

[tex]R_3(x)=\displaystyle \frac{f^{4}(x)}{4!}(x-a)=\frac{1}{24} (\frac{2}{x^3}+\frac{6}{x^4})(x-1)^4[/tex]

Therefore the real error is:

[tex]Err(0.5)=|f(0.5)-P_3(0.5)|=0.0340735[/tex]

The error of the Taylor polynomial R₃(0.5) is:

[tex]R_3(0.5)=\displaystyle \frac{1}{24} (\frac{2}{0.5^3}+\frac{6}{0.5^4})(0.5-1)^4=0.2917[/tex]

B) The error in the interval [0.5,1.5] is the maximum error in that interval.

This is found in the extremes of the intervals. We analyze what happens in X=1.5:

[tex]Err(1.5)=|f(1.5)-P_3(1.5)|=0.01523[/tex]

[tex]R_3(1.5)=\displaystyle \frac{1}{24} (\frac{2}{1.5^3}+\frac{6}{1.5^4})(1.5-1)^4=\frac{1}{216}=4.63\cdot 10^{-3}[/tex]

Both of these errors are smaller than Err(0.5) and R₃(0.5). Therefore the error in this interval is Err[0.5,1.5] is Err(0.5).

C) The approximation of the integral and the real integral is:

[tex]I_f=\displaystyle\int_{0.5}^{1.5} f(x)\, dx=\int_{0.5}^{1.5} (x-1)ln(x)\, dx=0.08802039[/tex]

[tex]I_{p3}=\displaystyle\int_{0.5}^{1.5} P_3(x)\, dx=\int_{0.5}^{1.5} (x-1)^2-0.5(x-1)^3\, dx=1/12=0.0833333[/tex]

D) The error in the integrals is:

[tex]Errint=|I_f-I_{p3}|=4.687\cdot10^{-3}[/tex]

[tex]Errint(R_3)=\displaystyle\int_{0.5}^{1.5} R_3(x)\, dx=\int_{0.5}^{1.5} \frac{1}{24} (\frac{2}{x^3}+\frac{6}{x^4})(x-1)^4\, dx=0.018595[/tex]

Answer:

a. [tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex] . Set S × T has 9 elements.

b. [tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]. Set T × S has 9 elements.  

c. [tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex] . Set S × S has 9 elements.

d. [tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex] . Set T × T has 9 elements.

Step-by-step explanation:

The given sets are S={2,4,6} and T={1,3,5}.

We need to find the set-roster notation to write each of the following sets, and the number of elements that are in each set.

a.

[tex]S\times T=\{(s,t)|s\in S and t\in T\}[/tex]

[tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex]

Set S × T has 9 elements.

b.

[tex]T\times S=\{(t,s)|s\in S and t\in T\}[/tex]

[tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]

Set T × S has 9 elements.  

c.

[tex]S\times S=\{(s,s)|s\in S \}[/tex]

[tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex]

Set S × S has 9 elements.

d.

[tex]T\times T=\{(t,t)|t\in T\}[/tex]

[tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex]

Set T × T has 9 elements.

Using the set roster notation, the number of elements in each of the sets would be the product of the number of elements in each individual set, which is 9.

A.) S × T :

{2, 4, 6} × {1, 3, 5}

{(2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6, 5)}

Number is of elements = 9

B.) T × S :

{1, 3, 5} × {2, 4, 6}

{(1,2), (1,4), (1,6), (3,2), (3,4), (3, 6), (5, 2), (5,4), (5,6)}

Number is of elements = 9

C.) S × S :

{1, 3, 5} × {1, 3, 5}

{(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 3), (5, 1), (5, 3), (5, 5)}

Number is of elements = 9

D.) T × T :

{2, 4,6} × {2, 4, 6}

{(2,2), (2, 4), (2, 6), (4,2), (4, 4), (4, 6), (6,2), (6, 4), (6,6)}

Number is of elements = 9

Hence, the distribution of values of each set.

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Answer:

Yes

Step-by-step explanation:

A system in echelon form can have more variables than equations. ... Every linear system with free variables has infinitely many solutions. True, a free variable can take any value, and so there are infinitely many solutions. Any linear system with more variables than equations cannot have a unique solution.

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

The slope is given as 1/2 and the line passes through (2, - 3)

To determine the intercept, we would substitute x = 2, y = - 3 and m= 1/2 into y = mx + c

y = mx + c. It becomes

- 3 = 1/2 × 2 + c = 1 + c

c = - 3 - 1 = - 4

The equation becomes

y = x/2 - 4

Answer:

answer is AC^2

Step-by-step explanation:

Answer: The change in the value of x would be : [tex]\Delta x=4.5 [/tex]    .

Step-by-step explanation:

We know that if y represents the value of some varying quantity, then as the value of y varies from p to q.

The change in the value of y is given by :-

[tex]\Delta y=q-p[/tex]     [Next value - previous value]

Given : x represents the value of some varying quantity.

So , As the value of x  varies from 3.5 to 8.

The change in the value of x is given by :-

[tex]\Delta x=8-3.5=4.5 [/tex]  

Hence, the change in the value of x would be : [tex]\Delta x=4.5 [/tex]