3 Select the correct answer. What is the solution to this system of equations? 2.1 + y + z = 2 4r + 2y + 2z = 4 -61 – 3y – 3z = -6 O A. no solution OB. Infinite solutions OC. (2,0,2) OD. (0,1,1) Reset Next 2021 Edmentum. All rights reserved

We integrate over the surface S to obtain the result. The specific integration limits and method depend on the parameterization or representation of the surface S, which is not provided in the question.

To evaluate the integral ∫∫S curl F · dS using Stokes' Theorem, we need to calculate the curl of the vector field F and find the outwardly oriented surface integral over the surface S.

Given \(F(x, y, z) = xyz i + xy j + x^2yz k\), we first need to find the curl of F:

curl\(F = (∂Fz/∂y - ∂Fy/∂z) i + (∂Fx/∂z - ∂Fz/∂x) j + (∂Fy/∂x - ∂Fx/∂y) k\)

Taking partial derivatives, we get:

curl \(F = (xz - xy) i + (yz - y) j + (xy - 2xyz) k\)

Now, let's consider the surface S, which consists of the top and four sides (but not the bottom) of the cube with vertices (±4,±4,±4). Since S is oriented outward, we need to find the normal vector for each face and the top.

The normal vector for each face is either ±i, ±j, or ±k, depending on the face's orientation. For the top face, the normal vector is k.

Now, we can evaluate the surface integral using Stokes' Theorem:

∫∫S curl F · dS = ∫∫S (curl F) · n dS

Since the normal vector is constant and the magnitude of the normal vectors for each face is 1, we can simplify the integral as follows:

∫∫S curl F · dS = ∫∫S (curl F) · k dS

Now, we need to evaluate the surface integral over S using the normal vector k:

\(∫∫S curl F · dS = ∫∫S (xy - 2xyz) dS\)

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The absolute maximum and minimum values of the function over the indicated interval and indicate the x-values at which they occur f(x) = x² - 4x - 9; [0, 5],

we need to follow the steps given below:

Step 1: Differentiate the given function to find the critical points and intervals where the function increases and decreases.

f(x) = x² - 4x - 9f'(x)

= 2x - 4= 0

⇒ 2x = 4

⇒ x = 2

Thus, we get a critical point at x = 2.

Now, we will find the intervals where the function increases and decreases using the test point method:

f'(x) = 2x - 4> 0 for x > 2

∴ f(x) is increasing for x > 2.f'(x) = 2x - 4< 0 for x < 2

∴ f(x) is decreasing for x < 2.

Step 2: Check the function values at the critical points and the end points of the interval.

f(0) = (0)² - 4(0) - 9

= -9f(2) = (2)² - 4(2) - 9

= -13f(5) = (5)² - 4(5) - 9

= -19

Step 3: Now, we can identify the absolute maximum and minimum values of the function over the indicated interval

[0, 5].

Absolute maximum value of the function:

The absolute maximum value of the function over the interval [0, 5] is -9 and it occurs at x = 0.

Absolute minimum value of the function:

The absolute minimum value of the function over the interval [0, 5] is -19 and it occurs at x = 5.

Therefore, the absolute maximum and minimum values of the function over the indicated interval [0, 5] and the x-values at which they occur are as follows.

Absolute maximum value = -9 at x = 0

Absolute minimum value = -19 at x = 5

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Answer:

-28

Step-by-step explanation:

-16 +(-12)

= -16 - 12

adding both of them,

= - 28

Answer:

unmarked angle = 45

side opposite unmarked angle = 5√8

hypotenuse = 20

Step-by-step explanation:

The unmarked angle is 180 - 90 - 45 = 45

The side opposite this new 45 degree angle is also 5√8

The hypotenuse is

a^2 + b^2 = c^2

a = b = 5√8

a^2 = b^2 = 25*8 = 200

200 + 200 = c^2

c^2 = 400

sqrt(c^2) = sqrt(400)

c = 20

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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X is equal to 8 and Y is equal to 3.

A pair that has two values stated in a certain sequence between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate). For greater visual comprehension, it helps to locate a point on the Cartesian plane.

Each domain element should have exactly one picture for the function, therefore the newest element in the column of x shouldn't be 6,3,9,7. Thus, we have two options for x = 8 or 12

Taking 8 will allow us to add another to the column on y, making y equal to 3.

thus, x = 8 and y = 3.

When an ordered pair is used, the numbers do not repeat.

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Answer:

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.

Step-by-step explanation:

Given - A bag contains 10 blue marbles, 3 yellow marbles, and 12 orange marbles. If a blue marble is drawn you win $10. If a yellow marble is drawn you win $15. if an orange marble is drawn you lose $10. it cost $1 to play.

To find - Should you play the game?

Formula used -

Expected value , E[x] = ∑x p(x)

where p(x) is the probability.

Proof -

Given that,

Total blue marbles in a bag = 10

Total yellow marbles in a bag = 3

Total orange marbles in a bag = 12

So,

Total number of marbles in a bag = 10 + 3 + 12 = 25

Now,

Probability of getting blue marble = \(\frac{10}{25}\)

Probability of getting yellow marble = \(\frac{3}{25}\)

Probability of getting orange marble = \(\frac{12}{25}\)

So,

Expected value , E[x] = ∑x p(x)

                                   = (10)( \(\frac{10}{25}\)) + (15)(\(\frac{3}{25}\)) + (-10)(\(\frac{12}{25}\))

                                   = \(\frac{100}{25} + \frac{45}{25} - \frac{120}{25}\)

                                   = \(\frac{100 + 45 - 120}{25}\)

                                   = \(\frac{25}{25}\)

                                   = 1

So,

Expected value = 1

So,

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.

Answer:

1

Step-by-step explanation:

A) The volume of each dog compartment is 168,836 cm³.

To find the volume of each dog compartment, we multiply the length, width, and height of the compartment. Given that the length (l) is 38 cm, the width (w) is 97 cm, and the height (h) is 46 cm, the volume (V) can be calculated as follows:

V = l * w * h = 38 cm * 97 cm * 46 cm = 168,836 cm³

Therefore, the volume of each dog compartment is 168,836 cm³.

B)The volume of the dog box that is not used to hold dogs is 200,589 cm³.

To find the volume of the dog box that is not used to hold dogs, we need to subtract the volume of the dog compartments from the total volume of the dog box. The total volume of the dog box can be calculated by multiplying its length, width, and height. Given that the length (L) is 117 cm, the width (W) is 97 cm, and the height (H) is 61 cm, the total volume (V_total) can be calculated as follows:

V_total = L * W * H = 117 cm * 97 cm * 61 cm = 707,097 cm³

Since each dog compartment has a volume of 168,836 cm³, and there are three compartments, the total volume occupied by the dog compartments is:

V_dog_compartments = 168,836 cm³ * 3 = 506,508 cm³

To find the volume of the remaining space, we subtract the volume of the dog compartments from the total volume of the dog box:

V_remaining_space = V_total - V_dog_compartments = 707,097 cm³ - 506,508 cm³ = 200,589 cm³

Therefore, the volume of the dog box that is not used to hold dogs is 200,589 cm³.

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Answer:

3.5

Step-by-step explanation:

Answer:

x = 130°

Step-by-step explanation:

number of sides = 6

the sum of the total interior angles = (6 x 180) - 360 = 720°

x = 720 - 125 - 120 - 100 - 120 - 125 = 130°

Answer:

-84

Step-by-step explanation:

Plug in -5 for every value of x

-4(-5)^2 - 5(-5) -9

Answer:

-84

Step-by-step explanation:

When you see f(x) is the same as y but if x is replaced with a numerical value, X IS EQUAL TO IT. In this case, use x as -5.

So everytime you see x, replace it with -5 to get your answer.

\(-4(-5)^2-5(-5)-9=-84\)

f(x) = -84

Answer:

0.9798 + 0i

Step-by-step explanation:

Assuming that the square root symbol applies only to the number 0.04 and not the entire expression, we can write the complex number in standard form as:

√(1 - 0.04) = √0.96

Since √0.96 cannot be simplified further without using decimals, we can convert it to a decimal approximation using a calculator or by long division. One possible decimal approximation is:

√0.96 ≈ 0.9798

Therefore, the complex number in standard form is:

0.9798 + 0i

Where 0i represents the imaginary part, which is zero in this case since the complex number is a real number.

Answer:

2 hours

Step-by-step explanation:

Answer:

2 hours

Step-by-step explanation:

Let x represent the time it takes together. Per hour the Equalizer

1/3hr + 1/8hr = 1/x  Multiplying each term by 24x so as all denominators = 1

8x + 3x = 24

11x = 24

x = 2.18 hrs, the time it takes them together

Answer:

-4,-3,-2,-1,1

Step-by-step explanation:

these numbers can be expressed in a fraction

According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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Answer:

y=1/5x+7

Step-by-step explanation:

i hope this helps :)

Answer:

2,2

Step-by-step explanation:

x=2 y=2 on the graph, simple.

The required value of the given function  f(a) = -2a^2 - 5a + 4 at a = -3 is 1

Function is characterized as a connection between a bunch of data sources having one result each. In straightforward words, a capability is a connection between inputs where each info is connected with precisely one result. Each Function has a domain and co-domain or range. A capability is by and large meant by f(x) where x is the information.

Function, f(a) = -2a^2 - 5a + 4

To find value of f(-3),

f(a) = -2a^2 - 5a + 4

Put a = -3 in th function

F(-3) = -2(-3)^2-5×-3+4

F(-3) = -18+15+4=1

F(-3) = 1

Thus, required value of f(-3) is 1

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Coorect Question:

What is f(-3) for the function f(a) = -2a2 - 5a + 4?

A = (2,5) E = (1,-3) I = (-4,4)

B = (4,4) F = (-2,-3) J = (-2,5)

C = (3,2) G = (-3,-1) K = (-1,4)

D = (3,-1) H = (-3,2) L = (1,4)

Answer:

im 100% sure that th ans is 2200

Step-by-step explanation:

261 is rounded to 300 and 757 is rounded to 800 and 1086 is rounded to 1100 all that added up is 2200

Answer:

1: (4,1) x=4 y=1

2: (1,10) x=1 y=10

3: (-25/4,5) x= -25/4 y=5

Step-by-step explanation:

It would be a lot to explain all three so if you really need it just ask

Answer:

1.3

Step-by-step explanation:

im not sure

Answer:

A

Step-by-step explanation:

If Kevin saved 46 dollars every 2 weeks, then he saved 46/2=23 dollars per week. Since Christy saved 26 dollars per week, she saved $3 per week more than Kevin. Therefore, the correct answer is choice A. Hope this helps!

The equation of the sine function is:

y = 2 sin((2π/47)(x + π)) - 4

The general equation for a sine function is:

y = A sin(B(x - C)) + D

where:

A = amplitude

B = 2π/period

C = horizontal phase shift

D = vertical displacement

Given the information in the problem, we can substitute the values and simplify:

A = 2 (amplitude)

period = 47, so B = 2π/47

horizontal phase shift = -π (shifted T units to the left)

vertical displacement = -4

Therefore, the equation of the sine function is:

y = 2 sin((2π/47)(x + π)) - 4

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The derivative of the given function using the Fundamental Theorem of Calculus, Part 1, is -2sinx * cosx.

In mathematics, the derivative of a function of a real variable measures the sensitivity to a change in the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

To find the derivative using the Fundamental Theorem of Calculus, Part 1, for the function \(d/dx(\int_{0}^{(sinx)} (1 - t^2) dt)\), proceed as follows:

1. Identify the function within the integral:

f(t) = 1 - t²
2. Take the derivative of the function with respect to t:

f'(t) = -2t
3. Replace the t variable with the upper limit of the integral, which is sinx:

f'(sinx) = -2sinx
4. Multiply the result by the derivative of the upper limit with respect to x:

d/dx(sinx) = cosx
5. Multiply the results from steps 3 and 4:

-2sinx * cosx

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Answer:

40.05

Step-by-step explanation:

The area of the tile which is trapezoid is  70 cm².

A trapezoid is a four-sided geometric shape with one pair of parallel sides.

The two non-parallel sides are usually referred to as the "legs" and the other two sides are the "bases".

A trapezoid can be either isosceles or non-isosceles depending on the angles of the legs.

A trapezoid can also be equilateral if all four sides have equal lengths.

The formula for the area of a trapezoid is (base 1 + base 2) x height/2.

In this case, the base 1 is 3 cm and the base 2 is 6 cm and the height is 4 cm.

Plugging these values into the equation

we get (3 cm + 6 cm) x 4 cm/2 = 70 cm².

Therefore, the area of the tile shown is 70 cm².

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