[SCREENSHOT INCLUDED] If f(x) = sqrt(2x+1) then f '(4) =

[SCREENSHOT INCLUDED] If F(x) = Sqrt(2x+1) Then F '(4) =

Answers

Answer 1

Using the definition,

\(f'(4) = \displaystyle \lim_{x\to4} \frac{f(x)-f(4)}{x-4}\)

The numerator in the difference quotient is

\(f(x) - f(4) = \sqrt{2x+1} - \sqrt{2\cdot4+1} = \sqrt{2x+1}-3\)

Multiply the numerator and denominator by the conjugate of this expression,

\(\displaystyle \frac{\sqrt{2x+1}-3}{x-4} \cdot \dfrac{\sqrt{2x+1}+3}{\sqrt{2x+1}+3}\)

The modified numerator reduces to a difference of squares,

\(\displaystyle \frac{\left(\sqrt{2x+1}\right)^2-3^2}{(x-4)\left(\sqrt{2x+1}+3\right)}\)

Simplify this to get

\(\displaystyle \frac{2x+1-9}{(x-4)\left(\sqrt{2x+1}+3\right)} = \frac{2(x-4)}{(x-4)\left(\sqrt{2x+1}+3\right)}\)

Since x is approaching 4, it never actually takes on the value of 4, so (x - 4)/(x - 4) reduces to 1. Then the limit is equivalent to

\(f'(4) = \displaystyle \lim_{x\to4} \frac{f(x)-f(4)}{x-4} = \lim_{x\to4}\frac2{\sqrt{2x+1}+3}\)

and the remaining limand is continuous at x = 4, so that

\(f'(4) = \dfrac2{\sqrt{2\cdot4+1}+3} = \dfrac26 = \boxed{\dfrac13}\)


Related Questions

The cost of a gym membership is a onetime fee of $140, plus a monthly fee of $40. Brendan wrote a $500
check to pay his gym membership for a certain number of months, including the onetime fee. How many
months of membership did he pay for?

Answers

Answer: he payed for 9 months

Step-by-step explanation:

500-140= 360      and 360 divided by 40 is 9

Write an equation in slope intercept form for the line perpendicular to y = 2x - 3 that passes through the point (-3, -3)

Answers

Answer:

y=-1/2x-9/2

Step-by-step explanation:

check picture

Write an equation in slope intercept form for the line perpendicular to y = 2x - 3 that passes through

The equation of the line perpendicular to y = 2x - 3 that passes through the point (-3, -3) is y = (-1/2)x - 9/2 in slope-intercept form.

To find the equation of a line perpendicular to y = 2x - 3, we need to determine the slope of the original line and then find the negative reciprocal of that slope.

The original line has a slope of 2. The negative reciprocal of 2 is -1/2.

Now, we have the slope (-1/2) and the point (-3, -3) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values:

y - (-3) = (-1/2)(x - (-3))

y + 3 = (-1/2)(x + 3)

Expanding and simplifying:

y + 3 = (-1/2)x - 3/2

y = (-1/2)x - 3/2 - 3

y = (-1/2)x - 3/2 - 6/2

y = (-1/2)x - 9/2

Therefore, the equation of the line perpendicular to y = 2x - 3 that passes through the point (-3, -3) is y = (-1/2)x - 9/2 in slope-intercept form.

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a) Write an equation for the line of best fit.


Y=-0.007x+13.713


5. The data below shows the population of a city,


In millions of people, since 1950.


Year Population


1950 1.75


1960 1.68


1970


1.52


1980


1.16


TO


b) Estimate the population of the city in 2020.


1990


1.04


2000


0.98

Answers

Answer  

Step-by-step explanation:

In millions of people, since 1950

there are two important properties of probabilities. 1) individual probabilities will always have values between and . 2) the sum of the probabilities of all individual outcomes must equal to .

Answers

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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Algebra 1 common assessment unit 2-1 SY23

Algebra 1 common assessment unit 2-1 SY23

Answers

Answer:

\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)

Use the diagram to complete the statements.
Segment AD must be congruent to segment
Segment BC must be congruent to segment

Answers

Answer:

DC and AB

Step-by-step explanation:

I just did it

Answer:

dc and ab

Step-by-step explanation:

hi there! this is a probability algebra 2 question

here is the question in text form and i’ll add the chart as an image

The following table represents the highest educational attainment of all adult residents in a certain town. If an adult is chosen randomly from the town, what is the probability that they have a high school degree or some college, but have no college degree? Round your answer to the nearest thousandth.

please answer asap

hi there! this is a probability algebra 2 question here is the question in text form and ill add the

Answers

The probability that they have a high school degree or some college, but have no college degree is 0 .622.

Given,

The highest educational attainment of all adult residents in a certain town.

If an adult is chosen randomly from the town ,

High school or some college = 3316 + 4399 = 7715

Total adults in town = 16819

Therefore we get,  

P(A)=7715/16819

P(A)=0.458

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Translate the shape by the vector
Y₁
9
8
7
6
5
4
3
2
1
O
1
2 3 4 5 6 7
5
89
X

Answers

Answer: Your welcome!

Step-by-step explanation:

14

13

12

11

10

9

8

7

6

O

6

7 8 9 10 11 12 13

10

1415

The answer is 14, 13, 12, 11, 10, 9, 8, 7, 6, O, 6, 7, 8, 9, 10, 11, 12, 13, 10, 14, 15. This is the result of translating the shape by the vector (5, 4). The original shape was shifted 5 units to the right and 4 units down, resulting in the new shape.

[ ] divided by 8 = 3
What number makes the equation true?

Answers

The answer is : 24

You must do 3 x 8 to get your answer

Solve for x.
9x3x36
0-6
O-4
O
4
6

Solve for x.9x3x360-6O-4O46

Answers

Answer:

\(9x = 3x - 36 \\ 6x = - 36 \\ x = - 6\)

hopefully this will u...^⁠_⁠^

a square is inscribed in a circle. how fast is the area of the square changing when the circel is increasing at 1 in/min

Answers

The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.

Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.


2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s

Substituting r² = s²/2,

\(ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)\)

Now, substituting r² = s²/2,

dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)

Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),

dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute

Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.

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Which line from "Harriet Tubman" highlights how much Tubman cared for others?
"Harriet Tubman didn't take no stutt
**Farewell'she sang to her friends one night"
"And she kept on going till she got to the North
"To save Black sisters and brothers" HELPPP

Which line from "Harriet Tubman" highlights how much Tubman cared for others?"Harriet Tubman didn't take

Answers

Answer:

He did not take anything

Step-by-step explanation:

Answer:

Hi there!

Your answer is;

A) her bravery

Explanation:

Using background knowledge of the bravery & courage that Harriet Tubman had to have will help us answer this

Step-by-step explanation:

Use The Following Function f(x)=-2(x-3)^2 +2, to find:a. vertexb.the directions of the parabola. c. the width of the parabola.d.the axis of symmetrye.the x-interceptsf.the y-interceptsg.the number of solutions.h.the standard form of the equation

Answers

\(\begin{gathered} \\ f(x)=-2(x-3)^2+2 \end{gathered}\)

Required:

a. vertex

b.the directions of the parabola.

c. the width of the parabola.

d.the axis of symmetry

e.the x-intercepts

f.the y-intercepts

g.the number of solutions.

h.the standard form of the equation​

Solution:

The vertex form of the equation of a parabola is

\((y-k)=4p(x-h)^2\)

where h and k are the coordinates of the vertex.

a) Manipulating this function to the vertex form:

\(\begin{gathered} y=-2(x-3)^2+2 \\ (y-2)=-2(x-3)^2 \end{gathered}\)

Here, h = 3 and k = 2 . Thus the vertex is at V ( 3, 2 )

b) If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If a is negative, it opens down or to the left.

In this function x is squared and a is equal to -2 . Therefore, the parabola opens downward.

c) The focal width of the parabola is equivalent to 4p. From the vertex form of the equation, we can tell that 4p is 2. Thus, the width of the parabola is 2 units

\((y-2)=-2(x-3)^2\)

h) THE STANDARD FORM OF THE EQUATION

\(\begin{gathered} y=-2(x-3)^2+2 \\ y=-2(x^2-6x+9)+2 \\ y=-2x^2+12x-18+2 \\ y=-2x^2+12x-16 \\ \end{gathered}\)

d) The axis of symmetry is given by x = -b / 2a

In the above equation of the parabola, a = -2 and b = 12. Thus x = -b / 2a = - (12) / 2 ( -2 ) = -12 / - 4 = 3

The axis of symmetry is x = 3

THE INTERCEPT FORM y = a(x - r)(x - s), where r and s are the x-intercepts on the graph. It tell us if there are two x-intercepts, one x-intercept or no x-intercepts.

\(\begin{gathered} y=-2x^2+12x-16 \\ y=-2(x^2-6x+8) \\ y=-2\lbrack(x-4)(x-2)\rbrack \end{gathered}\)

e) From the intercept form of the equation of the parabola, we can tell that r = + 4 and s = + 2. Therefore , the x - intercepts of the parabola are at x = 4 and x = 2

f) The y -intercept is the point at which the parabola crosses the y -axis where x is zero. In the given funxction , if we let x be equal to zero then y is :

\(\begin{gathered} y=-2x^2+12x-16 \\ y=-2(0)^2+12(0)-16 \\ y=-16 \end{gathered}\)

The y -intercept of the parabola is y = -16 .

g) A parabola can have one, two, or no solutions. The solution of a parabola refers to the points where the graph does intersect with the x-axis. In the given function , there are two points where the parabola intersects the x-axis ( refer to e ) at x = 4 and x = 2. Therefore, the given parabola has two solution.

h) The standard equation of a parabola is

\(y=ax^2+bx+c\)

The standard form of the given function is : ( refer to the deriviation above, after c )

\(y=-2x^2+12x-16\)

Answers:

a) V ( 3, 2 )

b) The parabola opens downward

c) The width of the parabola is 2 units

d) The axis of symmetry is x = 3

e) The x - intercepts of the parabola are at x = 4 and x = 2

f) The y -intercept of the parabola is y = -16

g) The given parabola has two solutions.

h) The standard form of the given function is

\(y=-2x^2+12x-16\)

Use The Following Function f(x)=-2(x-3)^2 +2, to find:a. vertexb.the directions of the parabola. c. the

family went on two vacations. the first trip took 3 2/3 hours to drive to Indiana and the second trip took 4 1/2 hours to drive to Michigan. how much longer did it take to drive to Michigan than Indiana?

Answers

SOLUTION

From the question given, it means that the trip to Indiana took

\(3\frac{2}{3}\text{ hours }\)

While that of Michigan took

\(4\frac{1}{2}\text{ hours }\)

To find how much longer it took to drive to Michigan than Indiana, we simply subtract. This becomes

\(4\frac{1}{2}-3\frac{2}{3}\)

Changing the mix frac

Tennis balls must have a high rebound, or bounce, that is approved by the International Tennis Federation. Rebound is measured by dropping a ball from a height of 100 inches and measuring how high it bounces. Approved balls must bounce back up 53 to 58 inches. A tennis coach tested 50 tennis balls and found that the mean bounce was 56.2 inches and the standard deviation was 1.8 inches The z-score of a ball that bounces 56.2 inches is This ball has a bounce that is the mean.​

Answers

Answer:

0.0 and equals to :)

Step-by-step explanation: just got it right on edg

Answer:

The person above is right, and deserves brainliest.

0.0

equal to

ED2021

Which of the following causes changes in the CPI to overstate the true inflation rate?
a. new product bias
b. substitution bias
c. increase in quality bias
d. all of the above

Answers

Answer:

Step-by-step explanation:

The correct answer is d. All of the above causes changes in the CPI to overstate the true inflation rate.

Which best describes the 3 dimensional figure obtained from rotating the figure's 360 degrees around the vertical axis?​

Which best describes the 3 dimensional figure obtained from rotating the figure's 360 degrees around

Answers

Check the picture below.

Which best describes the 3 dimensional figure obtained from rotating the figure's 360 degrees around

x^2 - 81y^2

can someone please answer this ?​

Answers

Answer:

Since both terms are perfect squares, factor using the difference of squares formula.

(x+9y)(x−9y)

Answer:

Step-by-step explanation:

x^2-81y^2

=(x)^2-(9y)^2

=(x-9y)(x+9y)

Patrick has a credit card with an APR of 15. 40% and a billing cycle of 30 days. The following table shows Patrick’s credit card transactions in the month of August. Date Amount ($) Transaction 8/1 1,466. 22 Beginning balance 8/6 28. 48 Purchase 8/9 150. 00 Payment 8/17 115. 75 Payment 8/20 40. 00 Purchase 8/22 31. 76 Purchase How much greater will Patrick’s August finance charge be if his credit card company computes finance charges using the previous balance method than if it computes finance charges using the adjusted balance method? a. $2. 44 b. $3. 41 c. $2. 13 d. $4. 69.

Answers

Patrick’s August finance charge will be $0.6717 more if it is calculated using the previous balance method.

What is the difference between the previous balance method and the adjusted balance method?

Previous balance method: Interest charges are based on the amount owed at the beginning of the previous month's billing cycle.

Adjusted balance method: Based on finance charges on the amount(s) owed at the end of the current billing cycle after credits and payments have been posted.

The total amount on which interest will be applied using the previous balance method is;

\(= 1,466.22+28.48+40.00+31.76\\\\ = 1566.46\)

So, interest levied on this is;

\(= 1566.46 \times 15.40 \times \dfrac{30}{360} \times \dfrac{1}{100}\\\\=20.10\)

Now, the total amount on which interest will be applied using the adjusted balance method is;

\(= 1566.46-150.00-115.75\\\\=1300.71\)

So, interest levied on this is;

\(= 1300.71 \times 15.40 \times \dfrac{30}{360} \times \dfrac{1}{100}\\\\=16.69\)

The difference between charges by previous balance method and adjusted balance method is;

= 20.10 - 16.69 = 3.41

Hence, Patrick’s August finance charge will be $0.6717 more if it is calculated using the previous balance method.

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PLS HELP
Identify the area of a regular hexagon with side length 17 in. rounded to the nearest tenth.

Answers

750.8 square inches

Answer:

750.8in squared

Step-by-step explanation:

The area of a regular polygon is one-half times the length of the apothem times the perimeter.

Notice that the formula combines the areas for the six triangles that fit inside the hexagon.

The perimeter is equal to the sum of the six triangle bases and the apothem is the height of each triangle.

The interior angles of the hexagon have a measure of 120°

, so the angles at the base of the triangle (and the third angle) have measure 60°

.The height forms a 30°−60°−90°

triangle, which has one leg equal to half of the hexagon side, or 8.5 in.

, and the other leg equal to 8.53–√ in

The figure shows a regular hexagon. Each angle of the hexagon measures 120 degrees. There is a triangle inside the hexagon. The base of the triangle coincides with one of the sides of the hexagon and one of the vertices of the triangle is the center of the hexagon. The length of the apothem is 8.5 times square root of 3 inches. The angles at the base of the triangle measure 60 degrees. The angle between the apothem and the side of the triangle measures 30 degrees. The apothem divides the base of the triangle into two parts. One of the parts is 8.5 inches long.

Find the perimeter of the hexagon.

P=6(17)

Simplify.

P=102in.

The formula for the area is A=12aP

. Substitute the known values and simplify.

A=12(8.53–√)(102)

=433.53–√in2

Round to the nearest tenth as 750.8 in

Therefore, the area of the regular hexagon with side length 17in.

is A≈7508. in2

.

Solve the system of equations 5x - 6y = 33 and 2x +y = -14 by combining the
equations.

Answers

Answer:

look at the picture i have sent

Solve the system of equations 5x - 6y = 33 and 2x +y = -14 by combining theequations.

19u=2,527. Solve the equation

Answers

Answer:

=133

Step-by-step explanation:

1. Divide both sides of the equation by the same term

19=2527

2. Simplify

If you divide numbers you will get:

=133

And that's the answer

I hope this helps     :)

Nina bought 3. 45 pounds of walnuts and 1. 83 pounds of almonds. How many more pounds of walnuts did she buy than almonds?.

Answers

Answer:

The answer is 1.62 or 1.6 more lbs of walnuts than almonds

Step-by-step explanation:

You subtract 1.83 from 3.45 and you'll get 1.62 or 1.6 if you're rounding.

i’m not able to solve this question

im not able to solve this question

Answers

Y=my+b is the first step to your question so it’s 3x+20

Jenny is solving the equation 3 x + 5 = 4 x + 2 using algebra tiles. She cannot decide if she should add 3 negative x-tiles or add 2 negative unit tiles to both sides first. Which explains which Jenny should do first?

A.She should add 3 negative x-tiles first because that is the only way to isolate the variable.

B.She should add 2 negative unit tiles first because that is the only way to get to the correct solution.

C.She can do either one first because zero pairs will be created to isolate the variable either way.

D.She should do neither one first because the first step is to add 4 negative tiles to both sides.

Answers

Answer:

Step-by-step explanation:

A

Answer:

A She should add 3 negative x-tiles first because that is the only way to isolate the variable. Is the correct answer

Step-by-step explanation:

Hope this helps! :)

Can someone please explain I’ll mark brainlest

Can someone please explain Ill mark brainlest

Answers

Answer:

TriangleJXP = Triangle HCD

Side XJ = side HC

Side CD = side JP

Side PX = HD

Step-by-step explanation:

Looking at both of the triangles you use the lines on “top” of the side. These lines represent congruence meaning that they are similar to each other.

So looking at side JP u can see that there are two lines meaning that this is the second side that is congruent to another side, side CD.

Hope this helps.

i am doing home
work and need help due day

i am doing homework and need help due day

Answers

A=a2 there's your answer bro ✔️✔️✔️✔️✔️✔️✔️✔️✅✅✅✅✅✅✅✅✅

express the following equation in the form y=mx+c and identify the gradient:
2y=7x-5
5x-3y=4
10-2x+3y=0​

Answers

Answer:

y = 7/2x - 5/2 ; gradient is 7/2

y = 5/3x - 4/3 ; gradient is 5/3

y = -2/3x - 10/3; gradient is -2/3

Step-by-step explanation:

2y = 7x-5

2y/2 = (7x - 5)/2 y = 7/2x - 5/2

5x - 3y=4

(5x-3y) -5x = 4 -5x -3y = -5x + 4-3y/-3 = (-5x+4)/-3 y= 5/3x - 4/3

10 - 2x+3y = 0

(10-2x+3y) -10 = 0 - 10-2x + 3y = -10(-2x + 3y) + 2x = -10 + 2x 3y = 2x -10 3y/3 = (2x - 10)/3 y = 2/3x -10/3

NOTE: The gradient is the slope

Determine the average rate of return for a project that is
estimated to yield total income of $382,000 over four years, cost
$695,000, and has a $69,000 residual value.
_ %

Answers

The average rate of return for a project that is estimated to yield a total income of $382,000 over four years, cost $695,000, and has a $69,000 residual value is 4.5% .

Here's how to solve for the average rate of return:

Total income = $382,000

Residual value = $69,000

Total cost = $695,000

Total profit = Total income + Residual value - Total cost

Total profit = $382,000 + $69,000 - $695,000

Total profit = -$244,000

The total profit is negative, meaning the project is not generating a profit. We will use the negative number to find the average rate of return.

Average rate of return = Total profit / Total investment x 100

Average rate of return = -$244,000 / $695,000 x 100

Average rate of return = -0.3518 x 100

Average rate of return = -35.18%

Rounded to one decimal place, the average rate of return is 35.2%. However, since the average rate of return is negative, it does not make sense in this context. So, we will use the absolute value of the rate of return to make it positive.

Average rate of return = Absolute value of (-35.18%)

Average rate of return = 35.18%Rounded to one decimal place, the average rate of return for the project is 4.5%.

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suppose you obtain a chi-square statistic of 3.86. are your results statistically significant if the critical value obtained from the distribution of chi-square is 6.63 with an alpha level of .01?

Answers

The chi-square statistic of 3.86 is not statistically significant if the critical value obtained from the distribution of chi-square is 6.63 with an alpha level of .01.

To determine if the obtained chi-square statistic of 3.86 is statistically significant or not, we need to compare it to the critical value obtained from the distribution of chi-square, which is 6.63, at a significance level of 0.01.

In this case, the obtained chi-square value is less than the critical value, indicating that we fail to reject the null hypothesis. This means that the observed frequencies in the sample are not significantly different from the expected frequencies based on the null hypothesis. The alpha level of 0.01 indicates that we are willing to accept a 1% chance of making a Type I error, which is rejecting the null hypothesis when it is actually true. Since the obtained chi-square value is not greater than the critical value, we do not have sufficient evidence to reject the null hypothesis.

In summary, the results are not statistically significant at the 0.01 significance level, based on the obtained chi-square statistic of 3.86 and the critical value of 6.63. This means that there is no significant difference between the observed and expected frequencies, based on the null hypothesis.

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Find the point on the planex y + z= 9that is closest to the point(3, 4, 6).(x, y, z)=? In which equation is y a linear function of x?A. y = 4x - 8B. y = 4x^2 - 8C. y = 4xy - 8D. y = 4/x - 8 which of the following is characteristic of a bailment? a. there is a separation of ownership and possession b. a bailment must be a contract c. it must last for an indefinite time d. it must be for the benefit of both parties. A 54kg female athlete participating in heaving training requires a minimum of how much protein daily O 108g O 92g O 432g O 549 Gina has 7 2/6 feet of silver ribbon and 2 4/6 of gold ribbon how much more silver ribbon does Gina have than gold ribbon ? The Earth's biosphere is consists of A(only the water on Earth that is in its solid form.B(all of the Earth's water, including surface water, groundwater, snowcover, ice, and water in the atmosphere.C(the part of the earth and its atmosphere in which living organisms exist or that is capable of supporting life.D(the solid part of the earth consisting of the crust and outer mantle. A(n)serves as a place for people to share stories and photos on the Internet. Given The Cost Formula ,=12000+6x Total Cost At An Activity Level Of 9,000 Units Would Be: What is the value of x? before achieving territorial status and statehood, the great majority of present-day nevada was part of which territory? and adults and complain of knee pain he is diagnosed with osgood schlatter disease. What assessment finding is 4. Write a C++ program as follows: 1. write the function void replace( stringk s ) that replaces the letters abcABC of a string s with a pound symbol # 2. write the main function with a while loop where (a) ask the user Enter a string: (b) use the function above to print the string with letters replaced. 5. Write a C++ program as follows: 1. write the function bool is.binary( const string& s ) which returns true if the strings consists of only '0or '1'; for example "101100" is a binary string. 2. write the main() function with a while loop where (a) ask the user Enter a binary string: (b) use the function above to determine whether the string is binary. Which implementation mode of BranchCache has no designated server to store the data, and each client at a remote site has its own local cache for data it downloads?a. Hosted Modeb. Cache Modec. Distributed Cache Moded. Branch Mode The mother calls the nurse to report that her toddler just been burned on the arm. The nurse should advise the mother to first:A. pack the arm in ice, and then take the child to the closest emergency department.B. rub the burned area with an antibacterial ointment, and then call the child's health care provider (HCP).C. run cool water over the burned area, and then wrap it in a clean cloth.D. call the child's health care provider (HCP) immediately, and then wrap the arm in a clean cloth. A company had a tractor destroyed by fire. The tractor originally cost $137,000 with accumulated depreciation of $70,800. The proceeds from the insurance company were $32,000. The company should recognize: 13. Simplify the expression.-(10)-2 Cost of Bikes ($) at Bike Shop312, 352, 480, 392, 368, 352, 416, 640a. meanThe mean is? carols buys 3 gallons of juice for a party. What is greatest number of cups of juice he can Surve an 8in by 12in picture has a frame of uniform width around it the area of the frame is equal to the area of the picture. what is the width of the frame 4+82-23 what would we do first a 4+8 b82 c2-2 d23