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That’s a fact.

The value of both methods is the same.Therefore, the Divergence Theorem is verified.

The given function is:F(x, y, z) = 2xi − 2yj + z²kSurface S: Cylinder x² + y² = 16, 0 ≤ z ≤ 6. Hence, we have to verify the Divergence Theorem by evaluating as a surface integral and as a triple integral.We know that,

As the surface is a cylinder, the unit normal vector is given by (x/4, y/4, 0).

Thus, we haveF . dS = (2x, -2y, z²) . (x/4, y/4, 0) dS= (x² + y²)/8 dS

As the surface is a cylinder with the radius of 4 and the height of 6, by using the cylindrical coordinate system for evaluating the flux integral, we get:

∫∫S F . dS= ∫(0 to 6) ∫(0 to 2π) (r²/8) rdrdθ= ∫(0 to 6) [r³/24] (0 to 2π) dθ= 3

Triple Integral Calculation:Let the cylinder be taken as E, whose upper and lower limits are 0 and 6, respectively.

The volume element can be expressed as dV = r dr dθ dz.

For F(x, y, z) = 2xi − 2yj + z²k,

we have to compute ∇ . F.∇ . F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z= 2 - 2 + 2z= 2z

From Divergence Theorem, we know that

∫∫S F . dS = ∫∫∫E ∇ . F dV= 2∫∫∫E z dV

Now, we will calculate the triple integral as:

∫∫∫E zdV = ∫(0 to 6) ∫(0 to 2π) ∫(0 to 4) z r dz dθ dr= 32π

Therefore, the value of both methods is the same.Therefore, the Divergence Theorem is verified.

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The amount of yellow paint Curt and Melanie should use is 0.45 quarts so that they can make 1.5 quarts bucket of seafoam green paint.We can use per cent equation.

Given that to make 1.5 quarts bucket of seafoam green paint Curt and Melanie have to mix 70 parts blue paint and 30 parts yellow paint.If 100 percent represent total paint then for 1.5 quarts we have to find the proportion of yellow paint.Let it be x.

30%  / 100% =30 / 100 = x / 1.5 quarts.

We can reduce the equation further,

0.3  = x / 1.5.

0.3 * 1.5 = x

x = 0.45

We can also find blue paint proportion similar by substituting 30 per cent to 70 per cent.

As a result of our calculation, we found the amount of yellow paint to be 0.45 quarts.

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The true statements about the random variable is:

1. P(X > 17) - P(X < 17)

2. P(X < 21) - P(Z < 1)

1. P(X > 17) - P(X < 17): Since X follows a normal distribution with a mean (µ) of 17 and a standard deviation (σ) of 4, the probability of X being greater than 17 is equal to the probability of X being less than 17 (i.e., P(X > 17) = P(X < 17)). Therefore, the difference between these probabilities is zero.

2. P(X < 21) - P(Z < 1):

To compute P(X < 21), we need to calculate the area under the normal distribution curve to the left of 21. Similarly, to compute P(Z < 1), we need to calculate the area under the standard normal distribution curve to the left of 1.

As X follows a normal distribution with mean 17 and standard deviation 4, we can convert X to a standard normal random variable Z using the formula Z = (X - µ) / σ. So, Z = (21 - 17) / 4 = 1. P(Z < 1) represents the probability of Z being less than 1, which is approximately 0.8413. Thus, P(X < 21) - P(Z < 1) is equal to the probability of X being less than 21 minus 0.8413.

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the complete question is:

consider a random variable, x, where x~n(17, 4). which of the following statements are true? select all that apply.

P(X>17)-P(X <17)

P(X<21)-P(Z<1)

P(X<11) = P(X<3)

P(X<21) P(Z<2)

Answer:

x² + y² = 4

Step-by-step explanation:

We need to write the standard equation of circle with , centre (0,0) and radius 2 unit . The Standard equation of the circle ⭕ is ,

=> ( x - h)² + (y -k)² = r²

=> ( x -0)² + (y-0)² = 2²

=> x² + y² = 4 .

The value of cos (x + pi) is -✓3/2, based on the stated information and known trigonometric values.

As per the known fact, the value of x wil be 30° as it is the specific value whose cosine or cos is ✓3/2. Now, we also know that π represents 180°. Also, the formula for cos (a + b) is cos A cos B - sin A sin B.

So, cos (x + pi) will be -

cos x cos pi - sin x sin pi

Keeping the values and solving -

cos (x + pi) = cos 30 cos 180 - sin 30 sin 180

cos (x + pi) = (✓3/2 × -1) - (1/2 × 0)

cos (x + pi) = -✓3/2

Hence, the value of cos (x + pi) is -✓3/2.

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The coordinates of a point is the location of the point in a plane.

The coordinates of the centers of holes are: (48.5, 28) and (28, 48.5)

Given

\(\theta_1 = \theta_2 = \theta_3 = 30^o\)

\(R = 60\)

\(r = 56\)

I've added an attachment as an illustration

Considering \((x_1,y_1)\)

To solve for x1, we make use of cosine ratio.

So, we have:

\(\cos(\theta_1) =\frac{x}{r}\)

Make x the subject

\(x_1 = r \times \cos(\theta_1)\)

\(x_1 = 56 \times \cos(30^o)\)

\(x_1 = 48.5\)

To solve for y1, we make use of sine ratio.

So, we have:

\(\sin(\theta_1) =\frac{y_1}{r}\)

Make y the subject

\(y_1 = r \times \sin(\theta_1)\)

\(y_1 = 56 \times \sin(30^o)\)

\(y_1 = 28\)

So, we have:

\((x_1,y_1) = (48.5,28)\)

Considering \((x_2,y_2)\)

To solve for x2, we make use of cosine ratio.

So, we have:

\(\cos(\theta_1+\theta_2) =\frac{x_2}{r}\)

Make x the subject

\(x_2 = r \times \cos(\theta_1+\theta_2)\)

\(x_2 = 56 \times \cos(30+30)\)

\(x_2 = 56 \times \cos(60^o)\)

\(x_2 = 28\)

To solve for y1, we make use of sine ratio.

So, we have:

\(\sin(\theta_1+\theta_2) =\frac{y_2}{r}\)

Make y the subject

\(y_2 = r \times \sin(\theta_1+\theta_2)\)

\(y_2 = 56 \times \sin(30+30)\)

\(y_2 = 56 \times \sin(60)\)

\(y_2 = 48.5\)

So, we have:

\((x_2,y_2) = (28,48.5)\)

Hence, the coordinates of the centers of the holes are: (48.5, 28) and (28, 48.5)

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Answer:

C)

10(a + 10) = 12 2

Applying the secant-tangent segment theorem, the equation that will result using the figure given is: C. 10(a + 10) = 12².

The secant-tangent segment theorem states that if a tangent and a secant intersect at a point outside a circle, then the square of the measure of the products of the secant segment and its external secant segment equals the square of the measure of the tangent segment.

Thus, using the figure given, the equation that results from applying the secant-tangent segment theorem would be: C. 10(a + 10) = 12²

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The temperature went down 2 degrees on Saturday and then wen up 2 degrees on Sunday -2 £ 2 = 0 , which means the temperature in Sunday was the same temperature as it was on Friday.

82 degrees.

Answer:

y = x - 10

Step-by-step explanation:

10 less than x would be written as x - 10, and subtracting 10 from x would ensure y (the output) is always less than the number you put in for x

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The height of the tip of the minute hand of a wall clock is 9 ft. Then the correct option is C.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The height, h, in feet of the tip of the minute hand of a wall clock as a function of time, t, in minutes can be modeled by the equation

\(h =0.75 \cos \left ( \dfrac{\pi}{30(t-15)} \right ) + 8\\\)

When t = 0, then the value of the h will be

\(h =0.75 \cos \left ( \dfrac{\pi}{30(0-15)} \right ) + 8\\\\\\h =0.75 \cos \left ( \dfrac{\pi}{-450} \right ) + 8\\\\\\h =0.75 \cos \times 0.9999+ 8\\\\\\h = 0.74998+8\\\\\\h = 8.74889 \approx 9\)

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Answer:

9

Step-by-step explanation:

The answer above is correct.

Answer: The answer is speed.

Answer:

If f=5 pounds of pressure, l=5.4 feet long

Step-by-step explanation:

Force needed to break a board varies inversely with the length of the board

Let

Force to break the board=f

Length of the board=l

f=k/l

Where k is a constant

If f=9 pounds of pressure and l=3 feet long

f=k/l

9=k/3

Cross product

9*3=k

27=k

If k=27, f=5 pounds of pressure. Find l?

f=k/l

5=27/l

Cross product

5l=27

l=27/5

=5.4

l=5.4 feet long

Using proportions, it is found that the board that requires 5 pounds of pressure to break is 1.67 inches long.

The rule of three is:

9 pounds - 3 feet

5 pounds - x feet

Applying cross multiplication:

\(9x = 3(5)\)

\(x = \frac{15}{9}\)

\(x = 1.67\)

The board that requires 5 pounds of pressure to break is 1.67 inches long.

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It should be noted that a reflection is known as a flip and it's a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.

In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.

The reflection is attached.

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Answer:

12^2 + 43x + 35

Step-by-step explanation:

(3x+7)(4x+5)

=(3x+7)(4x+5)

=(3x)(4x)+(3x)(5)+(7)(4x)+(7)(5)

=12x2+15x+28x+35

=12x2+43x+35

Answer:

Would it be 25 that’s what I got

Step-by-step explanation:

Answer

2x - 7 = 4

Step-by-step explanation:

Answer:

2x-7=4

Step-by-step explanation:

seven less is a number minus 7 so __ - 7

a product of a number and 2 is multiplication so 2 * x or 2x therefore 2x-7

is 4 means equals 4 so 2x-7=4

voila

Answer:

-3/4

Step-by-step explanation:

2 1/2 = 5/2 = 10/4

1 3/4 = 7/4

when you subtract, you add and change the sign of the second term (add the opposite)

-10/4 + 7/4 = -3/4

In regression analysis, if the dependent variable is measured in dollars, the independent variable can be units.

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Answer:

1/3

Step-by-step explanation:

there are two numbers greater than 4, 5 and 6

so the probability is 2/6 or 1/3

Answer: There is an 1/3 chance of landing on a number greater than 4.

Step-by-step explanation: Divided into thirds to be made simpler 1/3 is 1-2, 2/3 is 3-4, and 3/3 (or the last third) is 5-6 (the number(s) greater than 4)

The t-test for a sample of size n = 16, with X = 58 and S = 8, testing the null hypothesis H0: μ = 50, has n - 1 = 15 degrees of freedom.

In a t-test, the degrees of freedom determine the shape of the t-distribution and are calculated based on the sample size. For an independent samples t-test, the degrees of freedom are calculated as n - 1, where n is the sample size.In this case, the sample size is n = 16. Therefore, the degrees of freedom for the t-test would be 16 - 1 = 15.

The degrees of freedom represent the number of independent pieces of information available to estimate the population parameters. In the t-test, they are used to calculate critical values and p-values associated with the t-distribution.

As the sample size increases, the t-distribution approaches the shape of a standard normal distribution. Having a larger sample size with more degrees of freedom provides more precision and accuracy in hypothesis testing and estimation.

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Answer:

23

Step-by-step explanation:

-3(-6)+5

18+5

23

Answer:

39

Step-by-step explanation:

G is the midpoint of the line FH, FH=2*GH. 9x+15=10x+8, x=7, FG=39

La razón que buscamos para los números de estudiantes es:

12:13

Sabemos que si de un numero N podemos separar 2 grupos, de tal forma que hay a elementos del grupo A y b elementos del grupo B, la razon de el grupo A al grupo B es a:b

En este caso sabemos que hay 25 estudiantes y hay 12 varones, entonces hay:

25 - 12 = 13 "hembras"

Entonces la razon que buscamos es:

12:13

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a) 1 gram=0.0022 pound

b) 7.897g=0.0174pounds

7g=0.0154pounds

In mathematics, a pound is a unit of measurement that represents how much mass an object has or how much matter it occupies. Pounds, in other terms, tell us how weighty a thing is. A soccer ball, for example, weighs approximately one pound. A pound is written as lb or lbs, where "lb" stands for libra.

A pound weighs 453.592 grams (g) or 0.4536 kilograms (kg) (there are 1000 grams in a kilogram). The term "pound" comes from the Roman unit of measurement Libra Pondo, which denoted one pound by weight. The English term pound was derived from the Latin second word pondo.

a) As we know that,

1 gram=0.0022 pound

b) For 7.897g,

7.897g=0.0174pounds

For 7g,

7g=0.0154pounds

Therefore, 7.897g=0.0174pounds

7g=0.0154pounds

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Answer:

$1.35

Step-by-step explanation:

8n = 10.80

Divide both sides by 8 to get n alone.

n = 10.80/8 = $1.35

In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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The answer is B part

As the requirement for the student is either a senior or one who studies maths or both.

So, just add the values within the two venn circles divide it by total no of values.

=> 240+40+110/240+40+110+840

=> 360/1200

Answer:

B

Step-by-step explanation:

840 people aren't senior or don't takes math.

210 + 40 = 250 are seniors

110 + 40 = 150 people take math

In this class has 840 + 210 + 40 + 110 = 1200 people => All

210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)

Probabilty that a randomly selected student is a senior or takes math =>\(\frac{P(S U M)}{All}\)

\(\frac{P(S U M)}{All} = \frac{360}{1200}\)

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