consider the circle

The average value of f(x) over [2, 6] is given by the definite integral,

[tex]\displaystyle f_{\rm ave[2,6]} = \frac1{6-2} \int_2^6 3\ln(2+x^3)\cos(x) \, dx[/tex]

and is approximately -1.67284.

The approximate average value of the function in the closed interval [2,6] is -1.628.

It is given that the f is the function given by:  [tex]\rm f(x) = 3ln(2+x^2)cosx[/tex]

It is required to find the average value of f in the closed interval [2,6]

It is defined as the mathematical approach to calculating the smaller parts or components.

We have function f:

[tex]\rm f(x) = 3ln(2+x^2)cosx[/tex]

For the average value in [2,6]

We integrate the function with lower limit 2 and higher limit 6.

[tex]\rm \int_{2}^{6}f(x) =\int_{2}^{6}( 3ln(2+x^2)cosx)\\[/tex]

The average value of the above function:

[tex]\rm =\frac{1}{6-2} \int_{2}^{6}( 3ln(2+x^2)cosx)\\[/tex]

Further solving:

[tex]\rm =\frac{3}{4} \int_{2}^{6}( ln(2+x^2)cosx)\\[/tex]

Further solving and applying limits we get:

[tex]=\frac{3}{4}\times-2.2304[/tex]

= -1.628

Thus, the approximate value of the function in the closed interval [2,6]

is -1.628.

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Answer/Step-by-step explanation:

The graph of the equation y = 1/2x on the coordinate plane is plotted below

The given equation is:

y = 1/2x

The equation is of the form:

y  =  mx  +  c

where m represents the slope

and c represents the y-intercept

Comparing the equation y = 1/2x  with y = mx + c

The slope, m = 1/2

The y-intercept, c = 0

The line graph with slope, m = 1/2, and y-intercept, c = 0 is plotted below

[RevyBreeze]

Take 2 points

Slope:-

[tex]\\ \rm\hookrightarrow m=\dfrac{6-4}{2+7}[/tex]

[tex]\\ \rm\hookrightarrow m=\dfrac{2}{9}[/tex]

[tex]\\ \rm\hookrightarrow m=0.2[/tex]

The PDF for the wait time (denoted by the random variable X) is

[tex]f_X(x) = \begin{cases}\lambda e^{-\lambda x} & \text{if }x \ge 0 \\ 0 &\text{otherwise}\end{cases}[/tex]

where λ = 1/75. We want to find Pr[X > 70 | X ≥ 40]. Pierre has already been waiting for 40 min, so if he waits another 30 min he will have waited for a total of 70 min.

By definition of conditional probability,

Pr[X > 70 | X ≥ 40] = Pr[X > 70 and X ≥ 40] / Pr[X ≥ 40]

If X > 70, then automatically X ≥ 40 is satisified, so the right side reduces to

Pr[X > 70 | X ≥ 40] = Pr[X > 70] / Pr[X ≥ 40]

Use the PDF or CDF to find the remaining probabilities. For instance, using the PDF,

[tex]\mathrm{Pr}[X > 70] = \displaystyle \int_{-\infty}^{70} f_X(x) \, dx = \int_0^{70} f_X(x) \, dx \approx 0.3932[/tex]

Or, using the CDF,

[tex]F_X(x) = \displaystyle \int_{-\infty}^x f_X(t) \, dt = \begin{cases}0&\text{if }x<0 \\ 1-e^{-\lambda x} & \text{if }x \ge 0\end{cases}[/tex]

[tex]\implies \mathrm{Pr}[X > 70] = 1 - \mathrm{Pr}[X \le 70] = 1 - F_X(70) \approx 0.3932[/tex]

Similarly, you'll find that Pr[X ≥ 40] ≈ 0.5866.

It follows that

Pr[X > 70 | X ≥ 40] ≈ 0.3932 / 0.5866 ≈ 0.6703

Answer:

-1, 0, 1, 2, 3, 4, 5 are the values greater than -2

Step-by-step explanation:

Let's imagine a number line.

Numbers that are bigger are on the right side of the number line.

The numbers to the right of -2 are:

And so on...

Numbers that would be less than -2 will be on the left side

etc...

-Chetan K

Answer:

-1,0,1,2,3,4,5

ep-by-step explanation:

think of it on a number line

Answer:

We want to use time so we will say

The time it takes to finish a jog, t, at the speed of s.

Step-by-step explanation:

The dependent variable we know depends on the independent variable.

Our independent variable is speed because it represents itself where time depends on speed. The reason it depends on speed is that the time to finish a jog depends on your speed.

Answer:

1) [tex]\dfrac78[/tex]

2) [tex]\dfrac{17}{12} = 1 \frac{5}{12}[/tex]

3) [tex]\dfrac{53}{12}=4 \frac{5}{12}[/tex]

Step-by-step explanation:

1)

[tex]\dfrac38+\dfrac12=\dfrac38+\dfrac{1 \times4}{2 \times 4}=\dfrac38+\dfrac48=\dfrac78[/tex]

2)

[tex]\dfrac23+\dfrac34=\dfrac{2 \times 4}{3 \times 4}+\dfrac{3 \times3}{4 \times3}=\dfrac8{12}+\dfrac{9}{12}=\dfrac{17}{12}=1 \frac{5}{12}[/tex]

3)

First convert mixed number into improper fraction:

[tex]4 \frac23=\dfrac{3\times4+2}{3}=\dfrac{14}{3}[/tex]

[tex]\implies 4 \frac23-\dfrac{3}{12}=\dfrac{14}{3}-\dfrac{3}{12}=\dfrac{14\times4}{3\times4}-\dfrac{3}{12}=\dfrac{56}{12}-\dfrac{3}{12}=\dfrac{53}{12}=4 \frac{5}{12}[/tex]

The given properties of one pair of parallel sides in the four sided

quadrilateral, indicates that the shape is a trapezium.

Response:

Given that the side with length 6 is parallel to the side with length 8, we

and that the figure is four sided, we have;

The given figure is a trapezium;

Where;

a and b = The lengths of the parallel sides

h = The height of the figure = 5

Which gives;

[tex]Area = \dfrac{6 + 8 }{2} \times 5 = \mathbf{35}[/tex]

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Answer:35 sq units

Step-by-step explanation:

Answer:

The volume of the rectangular prism is 352 ft. The total surface area is 328 ft.

Step-by-step explanation:

Volume:

V = whl

V = 8 x 4 x 11

V = 352 ft

For finding surface area you have to find the lateral surface area: 152 ft, top surface area: 88 ft, and the bottom surface area: 88 ft. Add all that up and you get 328 ft.

Answer:

x=-55

Step-by-step explanation:

(2)(4)+(11)(3)+(13)(2)+2x−8=x+4

Simplify both sides of the equation.

8+33+26+2x+−8=x+4

Combine like terms

(2x)+(8+33+26+−8)=x+4

2x+59=x+4

2x+59=x+4

Subtract from both sides

2x+59−x=x+4−x

x+59=4

Subtract 59 from both sides

x+59−59=4−59

x=−55

Answer:

Todo terreno+ caballo+caminado=distancia ; (2/5)d+(1/3)d+80=d

Step-by-step explanation:

The expression which has the greatest value is; Choice B: f(g(-2))

The value of g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3 is; 586

Question 1;

From the information given;

Hence, from the options given; upon substitution, it follows that the expression with the greatest value is;

Question 2;

From the task content;

Hence, upon substitution of -4 into the function;

Read more on functions of functions;

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Answer:

8.5

Step-by-step explanation:

For inverse variation of (x, y), x*y = constant

so 4*17 = 8*y

y = 4*17/8 = 17/2 = 8.5

Answer:

y > 4x + 1.

Step-by-step explanation:

The other person that listed their answer was also correct.

In order to make an equation as such, we need to find the slope of this line and the y-intercept. The y-intercept is the "+b" in y=mx+b. The slope is mx. So, to identify the slope we need to calculate rise over run on the graph, which is 4. So:

y __ 4x + __.

On the y-intercept, the y crosses and meets at the point (0,1) on the x-intercept exactly, so we don't need to worry about there being any fractions right now. So:

y __ 4x + 1.

Now, because this line has a positive slope, the inequality symbol is "chomping" at the y, like this:

y > 4x + 1.

I hope that this helps.

The answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign is y = -2x + 3

The inequality symbol is less than (<). This means that all points below the line y = -2x + 3 satisfy the inequality.

To understand why this is the case, let's consider a few points on the line y = -2x + 3. For example, the point (0, 3) is on the line. If we plug these coordinates into the inequality, we get:

y = -2x + 3

3 = -2(0) + 3

3 = 3

This is a true statement, so we know that the point (0, 3) satisfies the inequality.

Now, let's consider a point that is below the line y = -2x + 3. For example, the point (1, 1) is below the line. If we plug these coordinates into the inequality, we get:

y = -2x + 3

1 = -2(1) + 3

1 = 1

This is also a true statement, so we know that the point (1, 1) satisfies the inequality.

Therefore, we can conclude that all points below the line y = -2x + 3 satisfy the inequality y < -2x + 3.

Here is a graph of the inequality y < -2x + 3.

As you can see from the graph, all points below the line y = -2x + 3 satisfy the inequality y < -2x + 3.

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#SPJ2

1. Observe question

2. Employ Point-Slope formula

(y2 - y1)/(x2 - x1 )=

(-10-9)/(-6-9) =

-19/-15=

19/15

Slope: 19/15

Answer:[tex]\frac{19}{15}[/tex] or 1.26667

Step-by-step explanation:

m=rise over run=Δy over Δx

m=y2−y1x2−x1

m=−10−9−6−9

m=−19−15

m=19/15

Answer:

you didnt attach the picture or assignment

Answer:

2.5

Step-by-step explanation:

y=ax+b

9= -2a+b <=> b= 9+2a

34=8a+b = 8a+9+2a = 10a + 9

a = (34-9)/10 = 2.5

Answer:

Step-by-step explanation:

Use the slope formula:

Answer:

15 cm

Step-by-step explanation:

540cm squared= 36 · b

540 ÷36= b

b= 15 cm

Answer:

y = - 7/4 x + 1 1 / 4

Step-by-step explanation:

Answer:

y = 66

Step-by-step explanation:

y=3x+45

putting the value of x in equation which is 7 .

=> y = 3(7)+45

=> y = 21+45

=> y = 66

Answer:

16 dollars

Step-by-step explanation:

The price includes the price of an empty bag B and the price of popcorn that is proportional to x (the number of ounces). Let each popcorn cost A$. Then the price of bag y = Ax + B

Given x = 10, y = 6, so 6 = 10A + B    (1)

Given x = 20, y = 8, so 8 = 20x + B   (2)

(2) - (1): 2 = 10A, so A = 2/10 = 0.2

Sub it into (1), 6 = 10*0.2 + B = 2 + B, so B = 6 - 2 = 4

We got y = 0.2x + 4

Check: x = 35, y = 0.2*35 + 4 = 11 (right)

x = 48, y = 0.2*48 + 4 = 13.6 (right)

Now find y when x = 60

y = 0.2*60 + 4 = 16 dollars

Answer:

63x + 18

Step-by-step explanation:

9 multiply 7x to give 63x

and 9 multiplies 2 to give 18

Answer:

Option C. 63x +18 is correct.

Step-by-step explanation:

7x ×9= 63x

2×9=18

=63x + 18

Hope it helps.......

Let's proof

PQ is the perpendicular bisector Hence

Now apply Pythagorean theorem

[tex]\\ \tt\hookrightarrow PQ^2+QD^2=PD^2[/tex]--(1)

[tex]\\ \tt\hookrightarrow PQ^2+CQ^2=PC^2[/tex]

As QD=CD

[tex]\\ \tt\hookrightarrow PQ^2+QD^2=PC^2[/tex]--(2)

From (1) and (2)

[tex]\\ \tt\hookrightarrow PC^2=PD^2[/tex]

[tex]\\ \tt\hookrightarrow PC=PD[/tex]

Answer:

Given [tex]\overline{\rm PQ}[/tex] is the [tex]\perp[/tex] bisector of [tex]\overline{\rm CD}[/tex]

⇒  [tex]\overline{\rm CQ}=\overline{\rm CD}[/tex]

⇒ ΔPQD ≅ ΔPQC

⇒ CP = PD

Step-by-step explanation:

Given [tex]\overline{\rm PQ}[/tex] is the [tex]\perp[/tex] bisector of [tex]\overline{\rm CD}[/tex]

⇒  [tex]\overline{\rm CQ}=\overline{\rm CD}[/tex]

⇒ ΔPQD ≅ ΔPQC

⇒ CP = PD

Answer:

  GPA ≈ 2.67

Step-by-step explanation:

Grade points are weighted by credit hours:

  GPA = ∑(grade points×credit hours) / ∑(credit hours)

  GPA = (3×2 +2×4 +4×3 +2×3)/(2 +4 +3 +3)

  = (6 +8 +12 +6)/12 = 32/12 = 2 2/3

  GPA ≈ 2.67

Answer:

Lynn's gross pay for the week is $29.12

Step-by-step explanation:

Lynn gets paid $2.08 for each usable machine part she makes. Out of the 440 parts she made this week, only 14 parts were usable.

Therefore, use the equation:

$2.08 x 14 = $29.12

Answer:

A:61°

B:72°

C:47°

Explanation:

I took the test and it was correct