which expression is equivalent to

1) The net area between the two functions is 2.

2) The net area between the two functions is 4/3.

3) The net area between the two functions is 17/6.

4) The net area between the two functions is approximately 1.218.

5) The net area between the two functions is 1/2.

The area between the two curves is determined by definite integrals for a interval between two values of x. A general formula for the definite integral is presented below:

[tex]A = \int\limits^{b}_{a} {[f(x) - g(x)]} \, dx[/tex]   (1)

Where:

Now we proceed to solve each integral:

The lower and upper limits between the two functions are 0 and 1, respectively. The definite integral is described below:

[tex]A = \int\limits^1_0 {x^{0.5}} \, dx - \int\limits^1_0 {x^{2}} \, dx[/tex]

[tex]A = 2\cdot (1^{1.5}-0^{1.5})-\frac{1}{3}\cdot (1^{3}-0^{3})[/tex]

[tex]A = 2[/tex]

The net area between the two functions is 2. [tex]\blacksquare[/tex]

The lower and upper limits between the two functions are -3 and -1, respectively. The definite integral is described below:

[tex]A = - 4 \int\limits^{-1}_{-3} {x} \, dx - \int\limits^{-1}_{-3} {x^{2}} \, dx - 3 \int\limits^{-1}_{-3}\, dx[/tex]

[tex]A = -2\cdot [(-1)^{2}-(-3)^{2}]-\frac{1}{3}\cdot [(-1)^{3}-(-3)^{3}] -3\cdot [(-1)-(-3)][/tex]

[tex]A = \frac{4}{3}[/tex]

The net area between the two functions is 4/3. [tex]\blacksquare[/tex]

The definite integral is described below:

[tex]A = \int\limits^{1}_{0} {x^{2}} \, dx + 2\int\limits^{1}_{0}\, dx + \int\limits^{1}_{0} {x} \, dx[/tex]

[tex]A = \frac{1}{3}\cdot (1^{3}-0^{3}) + 2\cdot (1-0) +\frac{1}{2}\cdot (1^{2}-0^{2})[/tex]

[tex]A = \frac{17}{6}[/tex]

The net area between the two functions is 17/6. [tex]\blacksquare[/tex]

The definite integral is described below:

[tex]A = \int\limits^{0}_{-1} {e^{-x}} \, dx+ \int\limits^{0}_{-1} {x} \, dx[/tex]

[tex]A = -(e^{0}-e^{1}) + \frac{1}{2}\cdot [0^{2}-(-1)^{2}][/tex]

[tex]A \approx 1.218[/tex]

The net area between the two functions is approximately 1.218. [tex]\blacksquare[/tex]

This case requires a combination of definite integrals, as f(x) may be higher that g(x) in some subintervals. The combination of definite integrals is:

[tex]A = \int\limits^{\frac{\pi}{3} }_0 {\sin 2x} \, dx - \int\limits^{\frac{\pi}{3} }_{0} {\sin x} \, dx + \int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin x} \, dx -\int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin 2x} \, dx[/tex]

[tex]A = -\frac{1}{2}\cdot (\cos \frac{2\pi}{3}-\cos 0)+(\cos \frac{\pi}{3}-\cos 0 ) -(\cos \frac{\pi}{2}-\cos \frac{\pi}{3} )+\frac{1}{2}\cdot (\cos \pi-\cos \frac{2\pi}{3} )[/tex]

[tex]A = \frac{1}{2}[/tex]

The net area between the two functions is 1/2. [tex]\blacksquare[/tex]

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Answer:

50, 30 and 20

Step-by-step explanation:

Check out the attached photo

Answer:

random sampling is more accurate

Answer:

-1

Step-by-step explanation:

we plug in p = -3 in the equation to get the answer.

f(p) = -1

Answer:

x = ± 2i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

x² = - 12 ( take square root of both sides )

x = ± [tex]\sqrt{-12}[/tex] = ± [tex]\sqrt{4(3)(-1)}[/tex] = ± 2i[tex]\sqrt{3}[/tex]

Answer:

coke red

Step-by-step explanation:

correct me if im wrong

Answer:

Step-by-step explanation:

1 pound = 16 ounces

16 ounces = $7.99

1 ounce = $0.50 (about)

Answer:

not sure if the 4 is seperate but if it is then (30+26)+(6-33)

Step-by-step explanation:

Lets see

Left:-

Not left anything

Answer:

18/1

Step-by-step explanation:

Answer:

1/2. I think if I'm wrong I'm sorry

Answer:

0.9952076759

Step-by-step explanation:

Probability that all three survive

= 0.9984 × 0.9984 × 0.9984

= 0.9952076759

Step-by-step explanation: please see attached to PDF document.

Answer:

a) 6

b) 1/3

c) 2

Step-by-step explanation:

a) 3 ( x + 1 ) - x = 15. expand the bracket

3x + 3 - x = 15

2x + 3 = 15. collect the like terms

2x = 15 - 3.

2x = 12.

x = 12/2 = 6

b) 5 ( x + 2 ) - 2x = 11. expand the bracket

5x + 10 - 2x = 11

3x + 10 = 11. collect the like terms

3x = 11 - 10

3x = 1

x = 1/3

c) 6 ( 1 - 2x ) = - 4 - 7x. expand the bracket

6 - 12x = -4 -7x. collect the like terms

6 + 4 = -7x + 12x

10 = 5x

or

5x =. 10

x = 10/5 = 2

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Answer: a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold

Step-by-step explanation:

Answer:

Answer: a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

equal both using corresponding law

Answer:

I know 3 h(x)=4sin(2x+pi)+3  is the correct option.

Step-by-step explanation:

I don't exactly know why but based on examples in this class I made this conclusion.

Answer:

all are -3

Step-by-step explanation:

substitue 0

Answer:

81 [ft].

Step-by-step explanation:

1) the basic formula is: h=gt²/2, where g - acceleration due to gravity, t - elapsed time;

2) if the final velocity is 72, g=32, then it is possible to calculate elapsed time:

[tex]t=\frac{V}{g}=\frac{72}{32}=\frac{9}{4} [sec].[/tex]

3) if g=32, t=9/4, then the required height is:

[tex]h=\frac{32*(\frac{9}{4} )^{2} }{2}=\frac{16*81}{16}=81[ft].[/tex]

The height of the building comes to be 81 feet.

Initial velocity u= 0 feet/sec

Final velocity v= 72 feet/sec

The acceleration due to gravity g =32ft /sec²

Height of the building h= suppose h

The equation of a motion is:

[tex]v^{2} =u^{2} +2gh[/tex]

Where u and v are the initial and final velocities.

[tex]72^{2} =0+2*32*h\\144 = 64h\\h=81[/tex]

So, the height of the building = 81 feet.

Therefore, the height of the building comes to be 81 feet.

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Step-by-step explanation:

I only understand English i am sorry

The probability that the selected number is even, multiple of 4 and prime are 7/15, 1/5 and 2/5 respectively

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Given the following set

S=​{1, ​2, 3,​ 4,..., 15}

n(S) = 15

If the selected number is even

E = {2, 4, 6, 8, 10, 12, 14}

n(E) = 7

Pr(selecting even number) = n(E)/n(S)

Pr(selecting even number) = 7/15

If the selected number is a multiple of 4

E = {4, 8, 12}

n(E) = 3

Pr(multiple of 4) = n(E)/n(S)

Pr(multiple of 4) = 3/15 = 1/5

If the selected number is a prime number

E = {2, 3, 5, 7, 11, 13}

n(E) = 6

Pr(prime number) = n(E)/n(S)

Pr(prime number) = 6/15 = 2/5

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x=2

Step-by-step explanation:

y=7-2x -------(1)

6y=9x

y=9x/6 = 3x/2------(2)

Now,

Equation equation 1 and 2

7-2x= 3x /2

2(7-2x)=3x

14-4x=3x

14=4x+3x

14=7x

14/7=x

x=2

Answer:

126x - 42x²

Step-by-step explanation:

Finding the necessary information

Area

Answer:

Step-by-step explanation:

18+x=24 and 6x+3 fail distributive property, while 3(6+x)=72 is not the same as 3(6+x)=24

Answer:

D (1;3).

Step-by-step explanation:

1) the condition 'across the X-axis' means the x-coordinate is not changed, the y-coordinate is changed to positive value. Then

2) the required coordinates of point D are (1; 3).

note, the suggested option is not the only one.

8. For brevity, let U = unemployed, E = employed, M = male, F = female. We're given that

P(M) = P(F) = 50/100 = 1/2

P(U) = 60/100 = 3/5

P(M | U) = 2/3

P(E) = 40/100 = 2/5

P(F | E) = 3/4

8a. This follows immediately from the given information. Specifically,

P(E) = 1 - P(U) = 1 - 3/5 = 2/5

8b. By definition of conditional probability,

P(A | B) = P(A and B) / P(B)   ⇒   P(A and B) = P(A | B) P(B)

It follows that

P(M and U) = P(M | U) P(U) = 2/3 • 3/5 = 2/5

8c. Using Bayes' rule/the definition of conditional probability,

P(U | F) = P(U and F) / P(F) =  P(F | U) P(U) / P(F)

Since F and M are mutually exclusive,

P(F | U) = 1 - P(M | U)

and so

P(U | F) = (1 - 2/3) • 3/5 / [(1 - 2/3) • 3/5 + 3/4 • 2/5] = 2/5

8d. Here we assume gender and employment status are independent, so for instance

P(F and E) = P(F) P(E)

We then have by the inclusion/exclusion principle that

P(F or U) = P(F) + P(U) - P(F and U) = P(F) + P(U) - P(F) P(U)

We also have by the law of total probability

P(F) = P(F and U) + P(F and E)

so

P(F or U) = P(F and U) + P(F and E) + P(U) - P(F) P(U)

By the assumed independence,

P(F or U) = P(F) P(U) + P(F) P(E) + P(U) - P(F) P(U)

P(F or U) = P(F) P(E) + P(U)

P(F or U) = 1/2 • 2/5 + 3/5 = 4/5

9.

a. This is mostly a matter of counting the ways a given type of stamp can fall out.

[tex]P(A) = \dfrac{\dbinom{20}3}{\dbinom{24}3} = \dfrac{285}{506}[/tex]

since there are 20 non-green stamps.

[tex]P(B) = \dfrac{\dbinom21 \dbinom{22}2}{\dbinom{24}3} = \dfrac{21}{92}[/tex]

since there are 2 red and unused stamps, 1 of which we want; the other 2 stamps come from the remaining 22 non-red-and-unused stamps.

[tex]P(A \cap B) = \dfrac{\dbinom21 \dbinom{18}2}{\dbinom{24}3} = \dfrac{153}{1012}[/tex]

since exactly 1 of the stamps must be red and unused, and the other 2 stamps that fall out can be neither green nor red and unused.

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{162}{253}[/tex]

which follows from the inclusion/exclusion principle.

b. There is a total of 10 used stamps, so the probability of at least 1 going missing is

[tex]P(C) = \dfrac{\dbinom{10}1\dbinom{14}2 + \dbinom{10}2\dbinom{14}1 + \dbinom{10}3}{\dbinom{24}3} = \dfrac{415}{506}[/tex]

By definition of conditional probability,

[tex]P(C \mid A) = \dfrac{P(C \cap A)}{P(A)}[/tex]

However, there are no used green stamps; any used stamp that goes missing must be red, blue or yellow. So the event A ∩ C is really just the event C, and

[tex]P(C \mid A) = P(C) = \dfrac{415}{506}[/tex]

c. A and C are independent if and only if

[tex]P(A \cap C) = P(A) P(C)[/tex]

We know

[tex]P(C \cap A) = P(C)[/tex]

so if A and C are independent, then

[tex]P(C) = P(A) P(C)[/tex]

but this would imply P(A) = 1, which is clearly not the case as we found in 9.a. So A and C are not independent.

Answer:

It will take 16 hours to earn $144.

Step-by-step explanation:

If Adam earns $36 in 4 hours,

36 = 4k

k = 9

Therefore, expression for total earnings will be,

y = 9x

a). For y = $144,    144 = 9x      x = 16 hours

Answer:

x = 1 ± [tex]\sqrt2[/tex]

Step-by-step explanation:

Hope this helped! Have a nice day!
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Answer:

0

Step-by-step explanation:

7-11=-4

-4+4=0

Answer:

9d^2(5d−2)

Step-by-step explanation:

Answer:

tan 70 times thirty gives you -1.70

Answer:

[tex]4x + 20[/tex]

Step-by-step explanation:

[tex]4(x + 3) + 8 = 4x + 12 + 8 = 4x + 20[/tex]

The residual plot regarding the depth of the water is the difference between the observed response and the fitted response values.

Your information is incomplete. Therefore, an overview of a residual plot will be given. A residual plot is a graph that shows the residual on the vertical axis while the independent variable is on the horizontal axis.

Here, the equation of the least-squares regression line is 9 = 13.0 -0.259x, where y is the depth of the water and x is the number of hours past midnight.

In this case, the residual plot regarding the depth of the water is the difference between the observed response and the fitted response values.

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Answer: C

Step-by-step explanation: Edge '23 Trust me