336. chegg use a computer algebraic system (cas) and stokes' theorem to approximate line integral C(ydx+zdy+xdz), where c is the intersection of plane x+y=2

Answer:

a) 2/5

b) 1/10

Step-by-step explanation:

There are 20 people total.

a is that the chosen child is a girl.

2 + 6 = 8, --> there are 8 girls --> simplify

8/20 = 4/10 = 2/5

b is the probability that the chosen child is a left-handed girl, --> there are 2 left-handed girls --> 2/20 --> simplify to 1/10

And thus, we have our answers.

Answer:

A) 2/5

B) 1/10

Step-by-step explanation:

A) Total Girls = 8

Total Children = 19

Probability = \(\frac{NumberOfFavourableOutcomes}{Total No.OfOutcomes}\)

Probability = 8/20 = 4/10 = 2/5

B) Left-handed girls = 2

Total left handed children = 20

=> Probability = \(\frac{NumberOfFavourableOutcomes}{Total No.OfOutcomes}\)

=> Probability = 1/10

Answer: θ = 11.94 degrees

Step-by-step explanation:

You must find the blue angle. We will use Trigonometry. In a right angled triangle, the tangent of an angle is: The length of the side opposite the angle divided by the length of the adjacent side. The abbreviation is tan. tan(θ) = opposite / adjacent.

\(tan(\theta ) = opposite / adjacent\\tan(\theta ) = 5.5 / 26\\\theta=arctan( 5.5 / 26)\\\theta =11.94\)

Answer:

x = 12    x= -12

Step-by-step explanation:

x^2-144=0

This is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(x-12) (x+12) =0

Using the zero product property

x-12= 0  x+12 =0

x = 12    x= -12

Answer:

x = 12 or x = -12

A) Serial correlation is often present in time series data because it arises from the inherent nature of the data

B) The presence of serial correlation in the residual is a problem because it violates one of the assumptions of linear regression analysis, which is the assumption of independent and identically distributed (IID) errors.

I. Serial correlation is often present in time series data because it arises from the inherent nature of the data. Time series data refers to observations collected over time, where each observation is dependent on previous observations. This dependence can result in a pattern of correlation or relationship between consecutive data points.

One common reason for serial correlation in time series data is seasonality. Seasonality refers to the repetitive pattern or trend that occurs within a specific time period. For example, sales of ice cream may increase during the summer months and decrease during the winter months. This pattern of seasonality can create a correlation between consecutive observations within the same season.

Another reason for serial correlation is autocorrelation. Autocorrelation occurs when there is a correlation between an observation and its lagged values, meaning the previous observations. For example, if the stock price of a company is increasing over time, it is likely to exhibit positive serial correlation as each observation is influenced by the previous price.

II. The presence of serial correlation in the residual is a problem because it violates one of the assumptions of linear regression analysis, which is the assumption of independent and identically distributed (IID) errors. In linear regression, the residuals represent the unexplained variation in the dependent variable after accounting for the effects of the independent variables.

When serial correlation exists in the residuals, it means that the errors in the model are not independent and are related to each other. This violates the IID assumption and can lead to biased and inefficient estimates of the regression coefficients. In other words, the estimated coefficients may not accurately represent the true relationship between the independent and dependent variables.

Additionally, serial correlation in the residuals can affect the statistical significance of the regression model. If the residuals are serially correlated, the standard errors of the regression coefficients may be underestimated, leading to inflated t-values and p-values. As a result, variables that are actually not significant may appear to be significant in the presence of serial correlation.

To address the problem of serial correlation in the residuals, various techniques can be applied, such as transforming the data, including lagged variables in the model, or using time series analysis methods. These techniques aim to account for the dependence structure in the data and produce reliable estimates of the regression coefficients.

In summary, serial correlation is often present in time series data due to the inherent dependence between consecutive observations. However, its presence in the residuals of a regression model can be problematic as it violates the assumption of IID errors and can lead to biased estimates and incorrect statistical inferences. Proper techniques should be employed to address serial correlation and ensure the validity of the regression analysis.

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Answer:

m<DBC = 109

Step-by-step explanation:

8x-27=6x+7

8x=6x+34

2x=34

x=17

8(17)-27= 109

Answer: 109

Step-by-step explanation:

i'm not entirely sure of this answer as its been a while since ive done problems like this, however, i think the steps to solve are setting (8x-27) equal to (6x+7). Once you do that, you can solve for x. Substitute x into angle DBC to find the answer.

The correct option that represent the box plot is

B. 41, 42, 43, 43, 43, 45, 47, 48, 50, 50

Statistical data based on the minimum, first quartile, median, third quartile, and maximum are shown graphically in a box plot.

The graph's appearance as a rectangle with lines extending from the top and bottom gave rise to the phrase box plot.

How to read a box plot:

Read the minimum value at the bottom of the first line. = 41

Read the maximum value after the final line. = 50

Read the bottom quartile, which is at the box's beginning. = 43

Read the top quartile, which is towards the box's edge. = 48

Read the median that coincides with the box's inside line. = 44

The option B fit this

median = 43 + 45 / 2 = 44

first quartile = 43

third quartile = 48

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Answer:

i belive that x= -7

Step-by-step explanation:

.......

Answer:

The average speed of the plain was 800 miles/h

Step-by-step explanation:

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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Answer:

14

Step-by-step explanation:

3*6=18

18-4=14

Answer:

14

Step-by-step explanation:

I got it right on the test

Answer:  \(\frac{8x^3}{27y^6}\)

This is the fraction 8x^3 all over 27y^6

On a keyboard, we can write it as (8x^3)/(27y^6)

===========================================================

Explanation:

The exponent tells you how many copies of the base to multiply with itself.

We'll have three copies of \(\left(\frac{2x}{3y^2}\right)\) multiplied with itself due to the cube exponent on the outside.

So,

\(\left(\frac{2x}{3y^2}\right)^3 = \left(\frac{2x}{3y^2}\right)*\left(\frac{2x}{3y^2}\right)*\left(\frac{2x}{3y^2}\right)\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{2x*2x*2x}{(3y^2)*(3y^2)*(3y^2)}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{(2*2*2)*(x*x*x)}{(3*3*3)*(y^2*y^2*y^2)}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{8x^3}{9y^6}\\\\\)

-------------------

Or another approach you could take is to cube each component of the fraction. The rule I'm referring to is \(\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}\)

Applying that rule will lead to:

\(\left(\frac{2x}{3y^2}\right)^3 = \frac{(2x)^3}{(3y^2)^3}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{2^3*x^3}{3^3*(y^2)^3}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{8x^3}{27y^{2*3}}\\\\\left(\frac{2x}{3y^2}\right)^3 = \frac{8x^3}{27y^6}\\\\\)

Either way you should get 8x^3 all over 27y^6 as one fraction.

Answer:

four billion two hundred fifty-eight million one hundred forty-five thousand three hundred ninety-seven

Step-by-step explanation:

Answer:

Word form-

four billion, two hundred fifty-eight million, one hundred forty-five thousand, three hundred ninety-seven.

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

Distance = x = 5 km

Step-by-step explanation:

Let the distance be x

one hour and 20 minutes can be written in fraction = 1 1/3 = 4/3

Now we wil develop the equation

\(x/6+x/10=4/3\\\)

30 is the common multiple and can be multiplied on both sides for simplification.

equation will be reduced to

\(5x+3x=40\)

Solving for x

\(8x=40\\x=5\)

Answer:

13.3 ft

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\\\end{minipage}}\)  \(\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)

The surface area of a square-based pyramid is made up of:

Given:

Find the area of the square base and the area of one of the triangles by substituting the given values into the formulas:

\(\textsf{Area of the square base} = 5^2 = 25\; \sf ft^2\)

\(\textsf{Area of one of the side triangles} = \dfrac{1}{2} \cdot 5 \cdot l= 2.5l \; \sf ft^2\)

Substitute these values along with the given total surface area into the formula and solve for l:

\(\begin{aligned}\textsf{Total Surface Area}&=\sf square+4\;triangles\\\implies 158&=25+4\left(2.5l)\\158&=25+10l\\133&=10l\\l&=\dfrac{133}{10}\\l&=13.3\; \sf ft\end{aligned}\)

Therefore, the missing length is 13.3 feet.

Answer:

Correct choices: 2 and 4

Step-by-step explanation:

These two line segments have a positive slope.

Answer:

Choice B and D!

Step-by-step explanation:

Interval 2 goes up after going at a constant rate and interval 4 goes up from decreasing

The probability that x < y is 1/8 or 0.25 .

What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .

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Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

Answer:

difference = \(x^2-12x\)

Step-by-step explanation:

hope this helps :)

Answer:

Number of week same amount of money (W) = 5 week

Step-by-step explanation:

Given:

Amount Tyler have = $60

Amount Tyler's sister have = $135

Amount of allowances get = $5 per week

Amount sister spent per week = $10

Find:

Number of week same amount of money (W)

Computation:

Amount Tyler have in W week = 60 + 5(W)

Amount Tyler's sister have in W week = 135 -10(W)

So,

60 + 5W = 135 - 10W

15W = 75

W = 5

Number of week same amount of money (W) = 5 week

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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The equation of the circle, obtained by applying the completing the square method to the specified equation indicates that the center and radius of the circle are;

Center (0, 6) and radius 7.5

The general form of the equation of a circle is; (x - h)² + (y - k)² = r², where;

(h, k) = The coordinates of the center of the circle

r = The measure of the length of the radius

The possible equation obtained from a similar question on the internet can be presented as follows;

x² + y² - 12·y - 20.25 = 0

The above equation can be evaluated using the completing the square method and excluding the x² term as follows;

y² - 12·y - 20.25 = 0

y² - 12·y = 20.25

y² - 12·y + (-12/2)² = 20.25 + (-12/2)²

y² - 12·y + (-6)² = 20.25 + (-6)² = 56.25

(y - 6)² = 56.25

Therefore;

y - 6 = √(56.25) = ±7.5

The possible equation of the circle obtained by plugging in the x² term therefore is; (x - 0)² + (y - 6)² = 7.5²

The center of the circle is therefore;

(h, k) = (0, 6)

The radius of the circle, r = 7.5

The possible correction is therefore, option (a), where the 5 is a typing error

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The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

The values using Law of Sines are:

∠ B = 62∘; b = 11.58 and c = 16.40.

The relationship between a triangle's sides and angles is demonstrated using the sine rule. It is specified as:

A/Sin(A) = B/Sin(B) = C/Sin(C)

Where A, B, and C are indeed the angles and A, B, and C are the angles' opposing sides.

∠ A = 43 ∘ , ∠ C = 75 ∘ , b = 15 ;

Part a:

∠ B = 180 -  ∠ A  -  ∠ C

∠ B = 180 - 43 ∘  - 75∘

∠ B = 62∘

Part b: the value of a.

a/Sin(A) = b/Sin(B)

a =  b/Sin(B) * Sin(A)

a = 15/Sin(62) * Sin(43)

b = 11.58

Part c: the value of c

b/Sin(B) = c/Sin(C)

c = b/Sin(B) * Sin(C)

c = 15/Sin(62) * Sin(75)

c = 16.40

Thus, the values using Law of Sines are obtained.

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(a) In a seating arrangement with 12 people, there are 12! (factorial of 12) possible seating arrangements. The outcome is fully detailed about the seating. 2 people can be seated in 2! Ways. There are 10 people left to seat and there are 10! Ways to seat them. So, we get the following:(2! × 10!)/(12!) = 1/6. Therefore, the probability that Tyrion and Cersei are sitting next to each other is 1/6.

(b) In this smaller sample space, we will only focus on Tyrion and Cersei. There are only 2 possible ways they can sit next to each other:

1. Tyrion can sit to the left of Cersei

2. Tyrion can sit to the right of CerseiIn each case, the other 10 people can be seated in 10! Ways.

So, the probability that Tyrion and Cersei are sitting next to each other in this smaller sample space is:(2 × 10!)/(12!) = 1/6, which is the same probability we got using the larger sample space.

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Answer:

\(\Huge \boxed{\mathrm{B. \ 6}}\)

Step-by-step explanation:

We can apply the Intersecting Secant-Tangent Theorem.

TV is the secant.

VW is the tangent.

VW² = VT × VU

(x+6)² = (5+x+4) × (x+4)

Combine the terms in bracket.

(x+6)² = (x+9)(x+4)

Expand brackets on both sides of the equation.

x²+12x+36=x²+13x+36

Subtract x² from both sides.

12x+36=13x+36

Subtract 12x from both sides.

36=x+36

Subtract 36 from both sides.

0=x

WV = x+6

x=0

WV = 0+6 = 6

The measure of the tangent WV is 6.

The best fit line for the scatter plot is shown in the graph second option second is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}\)

m and c are the slope of and y-intercept of the line of best.

As we can see in the picture there are scatter plots are shown.

The equation of the best fit will be which passes or nears every dot.

In the scatter plot second the line is very close to every point.

Thus, the best fit line for the scatter plot is shown in the graph second option second is correct.

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The answer is Option C) 7th graders in her school.

In order to ascertain the suitability of a candidate for any popular position, his popularity can be assessed by taking a survey of the concerned sample.

Answer:

She should ask the 7th graders in  the school

Step-by-step explanation:

Because their opinion is important in electing the president.

Answer:

216

Step-by-step explanation:

4 × 63 - 4 - 32

= 252 - 4 - 32

= 252 - 36

= 216

So, 4 × 63 - 4 - 32 = 216 using the PEMDAS rule.

Answer:

the answer is 216 using the dmas rule

Answer:

see the images and explanation

Step-by-step explanation:

for the graph:

the domain 0 < x < 5

the range for each functions:

g(x) = 2x + 1

g(x) = y  ,   1 < y < 11

h(x) = 2x + 2 ,  2 < y < 12