I need the answers to this question

In matrix form, the system is given by

[tex]\begin{bmatrix} -1 & 1 & -1 \\ 2 & -1 & 1 \\ 3 & 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -20 \\ 29 \\ 29 \end{bmatrix}[/tex]

I'll use G-J elimination. Consider the augmented matrix

[tex]\left[ \begin{array}{ccc|c} -1 & 1 & -1 & -20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right][/tex]

• Multiply through row 1 by -1.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right][/tex]

• Eliminate the entries in the first column of the second and third rows. Combine -2 (row 1) with row 2, and -3 (row 1) with row 3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 5 & -2 & -31 \end{array} \right][/tex]

• Eliminate the entry in the second column of the third row. Combine -5 (row 2) with row 3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 3 & 24 \end{array} \right][/tex]

• Multiply row 3 by 1/3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

• Eliminate the entry in the third column of the second row. Combine row 2 with row 3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

• Eliminate the entries in the second and third columns of the first row. Combine row 1 with row 2 and -1 (row 3).

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 9 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

Then the solution to the system is

[tex]\boxed{x=9, y=-3, z=8}[/tex]

If you want to use G elimination and substitution, you'd stop at the step with the augmented matrix

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

The third row tells us that [tex]z=8[/tex]. Then in the second row,

[tex]y-z = -11 \implies y=-11 + 8 = -3[/tex]

and in the first row,

[tex]x-y+z=20 \implies x=20 + (-3) - 8 = 9[/tex]

Considering the definition of probability, 12 of the 48 students surveyed were in favor of the new dress code.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)=number of favorable events÷ number of total events

In this case, you know:

Replacing in the definition of probability:

P(A)=225 students÷ 900 students

Solving:

P(A)= 0.25

Expressed as a percentage:

P(A)= 25%

In this case, you know:

Replacing in the definition of probability:

0.25=students in favor of the new dress code÷ 48 students

Solving:

students in favor of the new dress code= 0.25×48 students

students in favor of the new dress code= 12 students

Finally, 12 of the 48 students surveyed were in favor of the new dress code.

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Answer:

1 +-3i

Step-by-step explanation:

Answer:

answer is 1) x=±3i

Step-by-step explanation:

Answer:

Step-by-step explanation:

8 adults means 48 children

11 adults means 66 children

15 adults means 120 children

Answer: 60

Step-by-step explanation:

Almost everything in this picture is irrelevant to finding the measure of x.

x = 180 - 90 - 30 = 60

The relationship between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e include:

These are usually formed when two straight lines meet at a common endpoint or vertex.

Angles 3 and 4 are equal due to them being alternative interior angles and other relationships are mentioned above.

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The following statements are considered to be propositions:

Deductive reasoning can be defined as a type of logical reasoning that typically involves drawing conclusions based on a given set of rules and conditions or from one or more premises (factual statements) that are assumed to be generally (universally) true.

A proposition can be defined as a type of statement (assertion) that is typically used to express an opinion or a judgement, with either a true or false answer.

This ultimately implies that, a proposition refers to a type of statement (assertion) that is either a true or false.

In this context, we can infer and logically deduce that the following statements are considered to be propositions:

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The left hand derivative of the given function comes out to be 3a² + 3ah + h².

Deducing the Left Derivative:

The given function is,

f(x) = x³ + 2

⇒ f(a) = a³ + 2

The left hand limit is the definition of the left-hand derivative of f: f′⁻(x) = [tex]lim_{h- > 0}[/tex]f(x+h)f(x)h. F is said to be left-hand differentiable at x if the left-hand derivative exists.

Now, the formula for the left derivative of a function is given as,

f'(a)⁻ = [ f(a+h) - f(a) ] / [ (a+h) - a]

f'(a)⁻ = [ ((a+h)³ + 2) - (a³+2) ] / h

f'(a)⁻ = (a³ + 3a²h + 3ah² + h³ + 2 - a³ - 2) / h

f'(a)⁻ = (3a²h + 3ah² + h³) / h

f'(a)⁻ = h(3a² + 3ah + h²) / h

f'(a)⁻ = 3a² + 3ah + h²

Hence, the left derivative is 3a² + 3ah + h².

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Given the width and length of Teresa's new desktop computer, the length of the diagonal of the desktop screen is approximately 22.8 inches.

If a diagonal line cuts through a rectangle, it forms two equal right triangles. the side lengths of this triangle can be easily determined using Pythagoras theorem. Pythagoras theorem is expressed as;

c² = a² + b²

Where c is the hypotenuse or diagonal, a is base length and b is perpendicular height.

Given the data in the question;

We substitute into the equation above.

c² = a² + b²

c² = (18in)² + (14in)²

c² = 324in² + 196in²

c² = 520in²

c = √( 520in² )

c = 22.8in

Given the width and length of Teresa's new desktop computer, the length of the diagonal of the desktop screen is approximately 22.8 inches.

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The volume of the rectangular prism aquarium = 17 1/16 ft.

Volume of a rectangular prism = (l)(w)(h), where:

The aquarium is a rectangular prism. Its dimensions are given as:

Length (l) = 3 1/4 ft

Width (w) = 3 ft

Height (h) = 1 3/4 ft

Substitute

Volume of the rectangular prism aquarium = (3 1/4)(3)(1 3/4)

Volume of the rectangular prism aquarium = (13/4)(3)(7/4)

Volume of the rectangular prism aquarium = (13 × 3 × 7)/(4 × 4)

Volume of the rectangular prism aquarium = (273)/(16)

Volume of the rectangular prism aquarium = 17 1/16 ft.

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The height of the container be so as to minimize cost will be 1.20. inches.

The volume of the box will be:

= 2x × 3x × h

= 6x²h

Volume = 6x²h

12 = 6x²h

h = 2x²

The cost function will be:

C = 2.60(2)(6x²) + 4.30(12x)h

C = 31.2x² + 51.6xh

Taking the derivative

62.4x + 51.6h

h = 1.20

Therefore, the height of the container be so as to minimize cost will be 1.20 inches.

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We can write the integration domain as

[tex]D = \left\{(x,y) \mid -1 \le y \le 1 \text{ and } 2y-2 \le x \le -y+1\right\}[/tex]

so that the integral is

[tex]\displaystyle \iint_D -\sin(y+x) \, dA = \int_{-1}^1 \int_{2y-2}^{-y+1} -\sin(y+x) \, dx \, dy[/tex]

Compute the integral with respect to [tex]x[/tex].

[tex]\displaystyle \int_{2y-2}^{-y+1} -\sin(y+x) \, dx = \cos(y+x)\bigg|_{x=2y-2}^{x=-y+1} \\\\ ~~~~~~~~ = \cos(y+(2y-2)) - \cos(y+(-y+1)) \\\\ ~~~~~~~~ = \cos(3y-2) - \cos(1)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_{-1}^1 (\cos(3y-2) - \cos(1)) \, dy = \left(\frac13 \sin(3y-2) - \cos(1) y\right) \bigg|_{y=-1}^{y=1} \\\\ ~~~~~~~~ = \left(\frac13 \sin(3-2) - \cos(1)\right) - \left(\frac13 \sin(-3-2) + \cos(1)\right) \\\\ ~~~~~~~~ = \boxed{\frac13 \sin(1) - 2 \cos(1) + \frac13 \sin(5)}[/tex]

Answer:

Most you can do is factor out the x and turn it into   x (3x + 7)

roots would be x = 0 and x = -7/3

Answer:  x(3x+7)

Step-by-step explanation:

You would factor the x out of both of your values and put on the outside of the parenthesis. And you put the two numbers that you have left inside of the parenthesis. And that is as far down as this function can be factored.

Answer:

To know the final result we have to make 30% of 56 dollars and add the result to the 56 dollars to know the original price.

Operations:

30% de 56 = (30x56)/100= 16,8 dollars.

56+16,8= 72,8 dollars (final result)

A pair of shoes is reduced by 30% down to a price of £56 then the original price of the pair of shoes was £80.

To find the original price of a pair of shoes using a mathematical approach. We are given that the shoes were reduced by 30% and their final price is £56. We will use algebraic equations to determine the original price of the shoes.

Let's denote the original price of the shoes as "P". Since the shoes were reduced by 30%, we can express this reduction as a decimal, which is 0.30 (30% = 30/100 = 0.30).

The amount of reduction is then given by 0.30 multiplied by the original price, which is 0.30P.

The final price of the shoes after the reduction is £56. We can set up an equation to represent this:

P - 0.30P = 56

Now, let's simplify the equation:

0.70P = 56

Next, we need to isolate "P" on one side of the equation. To do this, we divide both sides by 0.70:

[tex]\[ \frac{{0.70P}}{{0.70}} = \frac{{56}}{{0.70}} \][/tex]

This simplifies to:[tex]\[ P = \frac{{56}}{{0.70}} \][/tex]

Now, let's calculate the value of "P":

[tex]\[ P = \frac{{56}}{{0.70}} = 80 \][/tex]

So, the original price of the pair of shoes was £80.

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Answer: 16

Step-by-step explanation:

1.5x = 24

24/1.5 = 16 students.

Answer:

4x + 3 just take away rhe values

The value of the probability is 0.30

Using the table of values, we have:

P(x <= -3) = P(x = -5) + P(x = -3)

From the table of values, we have:

P(x = -5) = 0.17

P(x = -3) = 0.13

Substitute the known values in the above equation

P(x <= -3) = 0.17 + 0.13

Evaluate the sum

P(x <= -3) = 0.30

Hence, the value of the probability is 0.30

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Combining the above inequalities, we get :

[tex]\qquad❖ \: \sf \:0.2 < 0.8 < 0.801 < 0.9[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

The length of the rectangular section of the roof is 25 m

From the question, we are to determine the length of the section of the roof

From the given information,

The area of the rectangular section = 180 m²

The width of the rectangular section = 7 1/5 m = 7.2 m

Using the formula for area of a rectangle

A = l × w

Where A is the area

l is the length

and w is the width

Then,

180 = l × 7.2

l = 180/7.2

l = 25 m

Hence, the length of the rectangular section of the roof is 25 m

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Answer:

25

Step-by-step explanation:

Just did it on Khan Academy.

The area below the mean compares to the area above the mean in a normal distribution as the areas are always equal regardless of the mean. Option A This is further explained below.

Generally, The normal distribution, also known as the Gaussian distribution, is a kind of probability distribution that is symmetric around the mean. This means that it demonstrates that data that are closer to the mean are more likely to occur than data that are farther away from the mean. When represented graphically, the normal distribution takes the shape of a "bell curve."

In conclusion, In a normal distribution, the area below the mean is compared to the area above the mean since the areas are always equal regardless of the mean. This is true even if the mean is different.

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Complete Question

How does the area below the mean compare to the area above the mean in a normal distribution?

A. the areas are always equal regardless of the mean

B. the areas are sometimes equal depending upon the standard deviation of the distribution

C. the area above the mean is larger since the values are larger as you move above the mean

D. the areas are sometimes equal depending upon the value of the mean

Answer:

  (f•g)(x) = 4x² -7x -11

Step-by-step explanation:

The product of the two functions is the product of their respective definitions.

(f•g)(x) = f(x)•g(x) = (x+1)•(4x -11)

  = x(4x -11) +1(4x -11) . . . . . use the distributive property

  = 4x² -11x +4x -11 . . . . . . . and again

(f•g)(x) = 4x² -7x -11 . . . . . collect terms

The answers to the questions are:

1. The confidence level is 99 percent.

2. We have to conclude that there is no sufficient evidence available to support this claim because the Confidence interval contains 75 sec.

1. The confidence level here should be

1- 0.01 = 0.99

= 99 percent

Given that, 99% confidence interval for population mean (μ) is (-34.1 sec u< u < 264.1 ) seconds.

We are to test  the claim that the population mean is greater than 75 sec.

2.

The given confidence interval contains the value of 75 sec, so there is not sufficient evidence to support the claim that the mean is greater than 75 sec.

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Answer:

z = [tex]\sqrt{30}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )

z = [tex]\sqrt{30}[/tex]

Answer:

  279/1640

Step-by-step explanation:

The relations between the various trig functions can be used to find the necessary function values.

Solving for cos(θ), we have ...

  41 cos(θ) = 9

  cos(θ) = 9/41 . . . . . divide by 41

The Pythagorean relation tells you ...

  sin²(θ) +cos²(θ) = 1   ⇒   sin(θ) = √(1 -cos²(θ))

  sin(θ) = √(1 -(9/41)²) = (√(41² -9²))/41 = 40/41

The tangent relation is ...

  tan(θ) = sin(θ)/cos(θ) = (40/41)/(9/41) = 40/9

The value of the given expression is ...

  (sin(θ) -cos(θ))/tan(θ) = (40/41 -9/41)/(40/9) = (31/41)(9/40) = 279/1640

__

Additional comment

This can also be figured by a suitable calculator or spreadsheet. Output formatted as a fraction is often an option. Here, the result is rational.

Answer: 7 1/16  and 1 9/16

Step-by-step explanation:  1 3/8 x 1.5 is 1 3/8 x 1 5/10  11/8 x 15/10 which is 165/80. We divide it by 5/5 to get 33/16. This as a mixed number is 2 1/16.  We add 5 to get 7 1/16.

5/8 divided by 0.4 is 5/8 divided by 2/5. We divide this by first finding the reciprocal of 2/5 which is 5/2. 5/8 x 5/2 = 25/16. This as a mixed number is 1 9/16.

Considering the definition of combination, if no meal is repeated, 210 different meal arrangements are possible.

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.

To calculate the number of combinations, the following formula is applied:

[tex]C=\frac{m!}{n!(m-n)!}[/tex]

The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.

Joseph is planning dinners for the next 4 nights. There are 10 meals to choose from and no meal is repeated.

So, you know that:

Replacing in the definition of combination:

[tex]C=\frac{10!}{4!(10-4)!}[/tex]

Solving:

[tex]C=\frac{10!}{4!6!}[/tex]

[tex]C=\frac{3,628,800}{24x720}[/tex]

[tex]C=\frac{3,628,800}{17,280}[/tex]

C= 210

Finally, if no meal is repeated, 210 different meal arrangements are possible.

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The option that is a proportion is: B. 4/6 = 2/3.

A proportion can be defined as an equation whereby two ratios are set equal to each other, in such a way that the ratio on one side equals the ratio on the other side of the equation when simplified.

First Option is not a proportion because:

5/7 ≠ 10/12 (10/12 can be simplified further as 5/6, which is not equal to 5/7).

Second option is a proportion because:

4/6 = 2/3

8/12 = 2/3

Thus, 4/6 = 8/12.

Third Option is not a proportion because:

14/21 = 2/3

9/12 = 3/4

Therefore, 14/21 ≠ 9/12.

Fourth Option is not a proportion because:

9/15 = 3/5

12/18 = 2/3

Therefore, 9/15 ≠ 12/18.

In conclusion, the option that is a proportion is: B. 4/6 = 2/3.

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Answer:

7/18

Step-by-step explanation:

P(sophomore girl) is 7 out of a total 30.

P(girl) is 18 out of 30.

(7/30) / (18/30) = 7/18

If you just look at the girls column you can see this immediately. A given is that we're looking for a girl (18 girls), then what is the chance that it's a sophomore. That is 7 out of 18.

Answer:

The answer would be 7 over 18 in fraction form fill in 7 then 18

Step-by-step explanation:

7/18

0.1 or 10%

The numbers between 1 and 50 that end in 6 are as follows:

6, 16, 26, 36, 46

There are therefore 5 numbers between 1 and 50 that end in 6.

This means there are 5 out of 50, or 5/50.

5/50 is 0.1 as a decimal, or 10% in percentage form.

The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let [tex]$&\overline{A B} \cong \overline{D E} \\[/tex] and [tex]$&\overline{A C} \cong \overline{D F}[/tex]

Angle between [tex]$\overline{A B}$[/tex] and [tex]$\overline{A C}$[/tex] exists [tex]$\angle A$[/tex].

Angle between [tex]$\overline{D E}$[/tex] and [tex]$\overline{D F}$[/tex] exists [tex]$\angle D$[/tex].

Therefore, [tex]$\triangle A B C \cong \triangle D E F$[/tex] by SAS, if [tex]$\angle A \cong \angle D$$[/tex].

Given:

[tex]$&\overline{A B} \cong \overline{D E} \\[/tex] and

[tex]$&\overline{A C} \cong \overline{D F}[/tex]

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let [tex]$&\overline{A B} \cong \overline{D E} \\[/tex] and [tex]$&\overline{A C} \cong \overline{D F}[/tex]

Angle between [tex]$\overline{A B}$[/tex] and [tex]$\overline{A C}$[/tex] exists [tex]$\angle A$[/tex].

Angle between [tex]$\overline{D E}$[/tex] and [tex]$\overline{D F}$[/tex] exists [tex]$\angle D$[/tex].

Therefore, [tex]$\triangle A B C \cong \triangle D E F$[/tex] by SAS, if [tex]$\angle A \cong \angle D$$[/tex].

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