from this year to ten years later, the number of people employed as physician assistants in the country is expected to increase by 47%. the number of people employed as physician assistants today is 69,000. Find the predicted number of physician assistants after ten years

The value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.

Mean value theorem is the theorem which is used to find the behavior of a function.

The function given as,

[tex]f(x) = 6x^2 - 4x + 2[/tex]

The value of function at 0,

[tex]f(0) = 6(0)^2 - 4(0) + 2\\f(0)=2[/tex]

Differentiate the given equation,

[tex]f(x)' = 6\times2x - 4\times1 + 0\\f(x)' = 12x - 4\\f(x)' = 12x -4[/tex]

If the constant c between 1 and 9 such that the average value of the function f(x) on the interval (1,9], then,

[tex]f(c)'=12c-4[/tex]

Using Lagrange's mean value theorem,

[tex]f(c)'=\dfrac{f(9)-f(1)}{9-1}\\12c-4=\dfrac{452-4}{9-1}\\12c=54+4\\c=\dfrac{60}{12}\\c=5[/tex]

Thus, the value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.

Learn more about the mean value theorem here;

https://brainly.com/question/15115079

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Answer:

5.5402

Step-by-step explanation:

First you need to find the average value of the function, you can use a calculator to do that, which you will find is 164.

The questions asks you to find a number between 1 and 9 so that f(c) (which is just f(x)) equals the average value of the function.

Since you already know the average value (164), you can set the equation equal to 164 and solve for x, which should give you 5.5402.

If you want more information: the function equals the average value, which is 164=6x^2-4x+2, is the equation you want to set up and solve for x.

You may get two answers and I can't explain why because I don't understand it that well, just use the one that is in the 1 to 9 range.

The second answer should be negative which is out of the 1 to 9 range, which leaves you with the other number that rounds up to 5.5402

I hope this helps any other struggling students

Answer:

    6000 in the 6th year    39000 total

Step-by-step explanation:

depreciates 200 per year

7000   6800   6600   6400   6200   6000  

Answer:

The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?

The vertex of the graph of g is 1.5 units to the left of

the vertex of the graph of f.

B

The y-intercept of the graph of g is 1.5 units above the

y-intercept of the graph of f.

The graph of g is a reflection of the graph of f across

the y-axis.

The graph of g is a reflection of the graph of f across

the x-axis.

Step-by-step explanation:

Answer:

it is a to my calculation

Step by step

Answer:

The anser is B

Step-by-step explanation:

There are twice as many silver cars as blue cars

12 x 2 = 24       24 / 12 = 2

[tex]\large\bold{{Question :}}[/tex]

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm find the radius of the circle.

[tex]\large\bold\red{\underline{Solution :-}}[/tex]

Here, O is the center of the circle.

⟼ Given :

⟼ To Find : We have to find the radius OP.

Since QP is tangent, OP perpendicular to QP.

(Since, Tangent is Perpendicular to Radius ⠀⠀⠀⠀⠀⠀⠀at the point of contact)

So, ∠OPQ=90°

⟼ By Applying Pythagoras Theorem :

OP² + RQ² = OQ²

OP² + (24)² = (25)²

OP² = 625 - 576

OP² = 49

OP = √49

OP = 7 cm

Hence, The Radius is 7 cm

⠀⠀

⠀

Here after drawing the diagram for the question we came to knew that the length of line OQ is 25 cm and length of line PQ is 24 cm.

So line OQ is hypotenuse , line OP is perpendicular , line PQ is base.

Let us simply apply the concept of Pythagoras theorem to find out the length of line OP.

[tex]: \: \implies \: \sf{(Hypotenuse) {}^{2} \: = \: (Base) {}^{2} \: + \: (Perpendicular) {}^{2} } \\ \\ : \: \implies \: \sf{(OQ) {}^{2} \: = \: (OP) {}^{2} \: + \: (PQ) {}^{2} } \\ \\ : \: \implies \: \sf{(25) {}^{2} \: = \: (OP) {}^{2} \: + \: (24) {}^{2} } \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25) {}^{2} - \: (24) {}^{2}} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25 \times 25) - \: (24 \times 24)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (625) - \: (576)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 625 - \: 576} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 49} \\ \\ : \: \implies \: \sf{OP \: = \: \sqrt{49} } \\ \\ : \: \implies \: \red{\bf{OP \: = \: 7}}[/tex]

★ Therefore,

Answer:

circumference of a circle formula is C=2*pi*r

Step-by-step explanation:

then  

141.3 = 2*pi * r

solve for r

141.3/ (2*pi) = r

22.48859 feet

diameter is  2*r

2*22.48859= 44.9771 feet

divide by 3 because there are 3 feet in one yard

44.9771/3= 14.99239 yds.  

it doesn't say to round off, but I would call this 15 yds.

Diameter is 15 yards   ± .008 yds  That's just about 1/4 of an inch

it is 2

Step-by-step explanation:

Answer:

the most appropriate answer will Be 2

Step-by-step explanation:

be happy

Answer:addaddition

Step-by-step explanation:

just adddd all

Answer:

4.4%

Step-by-step explanation:

The overall probability is the product of the individual probabilities.

Total number of marbles: 15

Original number of blue marbles: 6

First drawing (6 blue and 15 total):

p(blue) = 6/15 = 2/5

Second drawing (5 blue and 14 total):

p(blue) = 5/14

Third drawing (4 blue and 13 total):

p(blue) = 4/13

p(blue followed by blue followed by blue) = 2/5 × 5/14 × 4/13 = 40/910 = 4/91

p(blue followed by blue followed by blue) = 4/91 = 0.043956... = 4.4%

Answer:

answer is ‘see analysis’

Step-by-step explanation:

f(x)=x^2−2x+1

Yw and pls mark me brainiest

Answer:

-infty<xinfty

Step-by-step explanation:

Let g(t) denote the inner integral. By the fundamental theorem of calculus, the first derivative is

[tex]\displaystyle \frac{d}{dx} \int_0^x g(t) \, dt = g(x)[/tex]

Then using the FTC again, differentiating g gives

[tex]\displaystyle \frac{dg}{dx} = \frac{d}{dx} \int_1^{\sin(x)} \sqrt{1+u^4} \, du = \boxed{\cos(x) \sqrt{1+\sin^4(x)}}[/tex]

Answer: hii

Step-by-step explanation:

"a horizontal line written above a mathematical symbol to give it some special meaning."

" The vinculum can indicate a repeating decimal value: When it is not possible to format the number so that the overline is over the digit(s) that repeat, one overline character is placed to the left of the digit(s) that repeat: ‾"

Hopefully this helps you!

- Matthew

Answer:

c > 9

Step by Step explanation

Answer:

H. 36 sq inches

Step-by-step explanation:

area of rectangle

= 4 x 6

= 24

area of triangle

= 1/2 x (10-6) x (4+2)

= 12

total shaded area

= 24 + 12

= 36 sq inches

so answer is H

hope this helps!

Answer:

i think The final answer would be $3512.58

Step-by-step explanation:

Answer:

centre = (- 1, - 3 ) , radius = 6

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² + 2x + 6y = 26 ( collect x and y terms )

x² + 2x + y² + 6y = 26

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(1)x + 1 + y² + 2(3)y + 9 = 26 + 1 + 9

(x + 1)² + (y + 3)² = 36 ← in standard form

with centre = (- 1, - 3 ) and r = [tex]\sqrt{36}[/tex] = 6

[tex](x {}^{2} + 2x + 1) - 1 = (x + 1) {}^{2} - 1[/tex]

[tex](y {}^{2} + 6y + 9) - 9 = (y + 3) {}^{2} - 9[/tex]

[tex](x + 1) {}^{2} - 1 + (y + 3) {}^{2} - 9 = 26[/tex]

[tex](x + 1) {}^{2} + (y + 3) {}^{2} = 26 + 10[/tex]

[tex](x + 1) {}^{2} + (y + 3) {}^{2} = 36[/tex]

[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]

[tex]r {}^{2} = 36[/tex]

[tex]r = \sqrt{36} = 6[/tex]

Answer:

See answer(s) below

Step-by-step explanation:

$ 176.98   to nearest cent is  $ 176.98

176.98 cents rounded to the nearest cent is 177 cents

Step 6. Check the answer in the problem and make sure it makes sense.

Yes, 75+0.25\left(500\right)=200.

Step 7. Write a sentence that answers the question. Sergio and Lizeth can travel 500 miles and still stay on budget.

Taleisha’s phone plan costs her ?28.80 a month plus ?0.20 per text message. How many text messages can she use and keep her monthly phone bill no more than ?50?

Answer:

Length: 8 m

Explanation:

                                     square area: length²

As length is positive, length = +8

Answer:

A) 13.5 Hours

B) 27 Hours

Step-by-step explanation:

So the total journey was 54 hours.

5/8 of that would be 33 and 3/4 hours or how long the airplane journey was.

1/4 would be 13 and a half hours or how long the train journey was

And the remaing amount was the 6 3/4 hours which was the bus journey

So the answers are Fu Da spent 13 and a half hours on the train journey and he spent 27 more hours on the plane than the bus

answer: 5 miles

Step-by-step explanation:

use the distance formula to solve this problem. plug in the two coordinates to solve this problem.

Step-by-step explanation:

Take the natural log of both sides:

[tex]ln ({x}^{y} ) = ln ({y}^{x} )[/tex]

Logarithm rules allow you to bring down the exponents:

[tex]yln(x) = xln(y)[/tex]

Now differentiate. We will have to implicitly differentiate 'y' since it is a function of 'x'. Both sides require the product rule:

[tex] \frac{dy}{dx} ln(x) + \frac{y}{x} = ln(y) + \frac{x}{y} \frac{dy}{dx} [/tex]

Isolate the terms that have y' since that is what we want:

[tex] \frac{dy}{dx} ln(x) - \frac{x}{y} \frac{dy}{dx}= ln(y) - \frac{y}{x} [/tex]

Factor out y' to get:

[tex] \frac{dy}{dx}( ln(x) - \frac{x}{y})= ln(y) - \frac{y}{x} [/tex]

Therefore:

[tex] \frac{dy}{dx} = \frac{ln(y) - \frac{y}{x} }{ln(x) - \frac{x}{y} } [/tex]

f(x) = 1/x and its derivative f '(x) = -1/x² are discontinuous only at x = 0; everywhere else it is defined and behaves nicely in the sense that f is

• continuous on the closed interval [1, 3], and

• differentiable on the open interval (1, 3)

and the MVT holds.

The theorem says there is some real number c between 1 and 3 such that

[tex]f'(c) = \dfrac{f(3) - f(1)}{3 - 1}[/tex]

Solve for this c :

[tex]-\dfrac1{c^2} = \dfrac{\frac13-\frac11}{3 - 1} \implies c^2 = 3 \implies \boxed{c = \sqrt3}[/tex]

Domain are the x values

{-4,-2,0,2}

Answer:

{-4, -2, 0, 2]

Step-by-step explanation:

THIS IS THE SET OF X-VALUES:

Domain is {-4, -2, 0, 2]

Answer

the answer is 105

Step-by-step explanation:

multiply 5 and 21

answer is 105

Step-by-step explanation:

multiply 5x21