Using the alternate form of the definition of the derivative, Compute f'(c) for f(x) = x+4/x, c=4

Answer:

\(8 \ feet\)

Step-by-step explanation:

In this situation, one is given the following information. A ladder is leaning against a wall and has a measure of (17) feet. The bottom of the ladder is (15) feet away from the wall. One can infer that the wall forms a right angle with the ground. Thus, the triangle formed between the ground, ladder, and wall is a right triangle. Therefore, one can use the Pythagorean theorem. The Pythagorean theorem states the following,

\(a^2+b^2=c^2\)

Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle. The parameter (c) represents the hypotenuse or the side opposite the right angle. In this case, the legs are the ground and wall, and the hypotenuse is the ladder. Substitute this into the formula a solve for the height of the wall.

\(a^2+b^2=c^2\)

Substitute,

\((ground)^2+(wall)^2=(ladder)^2\\\\(15)^2+(wall)^2=(17)^2\\\)

Simplify,

\((15)^2+(wall)^2=(17)^2\\\\225+(wall)^2=289\)

Inverse operations,

\(225+(wall)^2=289\\\\(wall)^2=64\\\\wall=8\)

Consequently, the measurement between points AA and BB is roughly 14092.3 feet, rounded to the closest hundredth of a foot.

A pair of rays (half-lines) with such a shared termination are combined to form an angle. The latter is referred to as the angle's vertex, and the beams are sometimes referred to as the angle's legs and other times as its limbs.

Let's call the distance from point AA to the lighthouse/beacon light as "d" and the distance from point BB to the lighthouse/beacon light as "x".

We can use the tangent function to relate the angles of elevation to these distances:

tan(14°) = h/d, where h is the height of the lighthouse/beacon light above sea level

tan(5°) = h/x

We can eliminate h from these equations by solving for it in terms of d and x. Rearranging the first equation, we get:

h = d tan(14°)

This is what we get when we enter it into the second equation:

tan(5°) = (d tan(14°))/x

Solving for x, we get:

x = d tan(14°)/tan(5°)

Substituting the given value of d (1246 feet), we get:

x = 1246 tan(14°)/tan(5°) ≈ 14092.3 feet

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There were no fewer than 1 fruit snacks in the bag.

From the question, we have the following parameters that can be used in our computation:

x + 3 >= 4

Subtract 3 from both sides of the inequality

So, we have the following representation

x + 3 - 3 >= 4 - 3

When the like terms are evaluated, we have

x >= 1

This means that that were at least 1 fruit snack in the bag.

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200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, \(\frac{50.00}{0.25}\)= 200 pounds.

The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.

The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.

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Answer:

a. \(B+S = 1 \)

\(0.06B+0.1S \geq 0.075 \)

\(B \geq 0.3 \)

Objective function:

\(R=0.06B+0.1S\)

b) See Attached picture

30% in bonds and 70% in stocks

Step-by-step explanation:

a.

In order to solve the first part of the problem we need to take into account that the problem wants us to determine the percentage that should be allocated to each of the possible investment alternatives. In that case, the sum of the percentages must be equal to 1 (which means that we will have 100 of the trust fund)

so that gives us our first restriction for the problem.

B+S=1

Next, the problem tells us that the projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. It also states that he wants to select a mix that will enable him to obtain a total return of at least 7.5%, so we can take this information and get the second restriction from it:

\(0.06B+0.1S \geq 0.075 \)

Next, the problem tells us that whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund, so that's where the last restriction comes from:

\(B \geq 0.3 \)

now, the idea is to optimize the investment, this is get the greatest amount of money out of the trust fund, so the objective function is:

\(R=0.06B+0.1S\)

which represents the return on the investment.

b)

For part b we can start by graphing each of the restrictions:

\(B+S = 1 \)

This will be a single line, you can draw the line by setting B=0 first so you get:

0+S=1

S=1

So the first point to plot will be (0,1)

next, we can set s=0 to get:

B+0=1

B=1

so the second point to plot will be (1,0)

so you can plot the two points and connect them with a straight line. This is the green line on the uploaded graph.

Next we can graph the second restriction:

\(0.06B+0.1S \geq 0.075 \)

we can use the same procedure we used for the previous graph, in this case the points would be:

(0 , 0.75) and (1.25, 0)

and again connect the two points with a straight line. Next we need to decide which region of the graph to shade for which we can pick two arbitrary points on each side of the line, for example we can pick:

(0,0) and (2,2) and see which one makes the inequality true:

for (0,0) we get:

\(0.06B+0.1S \geq 0.075 \)

\(0.06(0)+0.1(0) \geq 0.075 \)

\(0 \geq 0.075 \)

Which is false, therefore we need to shade the other region of the graph:

for (2,2) we get:

\(0.06B+0.1S \geq 0.075 \)

\(0.06(2)+0.1(2) \geq 0.075 \)

\(0.32 \geq 0.075 \)

Which is true, so we shade the region of the graph that contains that point. (see red graph)

now we graph the third restriction:

\(B \geq 0.3 \)

In order to graph this third restriction we just need to draw a vertical line at B=0.3 and shade everything to the right of that line. (Blue graph)

Now, we can analyze the graph, in this case we need to locate the points where the green line crosses the red and the blue line which gives us the following coordinates:

(0.3, 0.7) and (0.625, 0.375)

these two points can be found by setting the first restriction equal to each of the other two restrictions if you are to do it algebraically. If you are using a graphing device, you can directly read them from the graphs.

So once we got those points, we can see which one gives us the greatest percentage of return.

let's test the first point (0.3, 0.7)

\(R=0.06B+0.1S\)

\(R=0.06(0.3)+0.1(0.7)\)

R=0.088

so this distribution gives us 8.8% in return, let's test the second point:

(0.625, 0.375)

\(R=0.06B+0.1S\)

\(R=0.06(0.625)+0.1(0.375)\)

R=0.075

so this distribution gives us 7.5% in return.

In this case the best distribution for us is 30% in bonds and 70% in the stock fund to get a return of 8.8%

The number of infected students after 5 days = 694

The number of infected students  with respiratory virus is modeled by an exponential function f(t) = 25000 /1+332e^(-0.45t) where time t, is measured in days.

We need to find the number of students infected with the virus after 5 days.

For t = 5,

f(5) = 25000 /1+332e^(-0.45 * 5)

f(5) = 25000 /(1+332*0.1054)

f(5) =  25000 /35.9928

f(5) = 694.58

f(5) ≈  694

Therefore, the number of students infected with the virus after 5 days = 694

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The complete question is:

75 students are currently infected with respiratory virus- that is spreading through a population of college students_ The number of infected students is modeled by f(t) = 25000 /1+332e^(-0.45t) where time; t, is measured in days. How many students are predicted to be infected with the virus after 5 days? Round your answer to the nearest whole number.

Millimeter is the best unit to define the radius of the pencil.

The distance from a circle's centre to any point on its periphery is known as the radius. The radius of a circle is also known as the distance separating any two points on the circle from its centre. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

The smallest unit of measurement is the millimetre. There are a thousand millimetres in a metre, and a dime is somewhat thicker than a millimetre. When measuring anything's length in metric units, you'll be working with meters and variants on meters, including millimeters.

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we are given the following expression:

we are asked to plug in the following constants, b = -9 and k = 4, to do that, we will replace the values given for b and k in the expression, like this:

Now we will solve the multiplications inside the parenthesis, like this:

Now we will solve the operation inside the parenthesis, we get:

Now we solve the multiplication:

therefore, the final answer after pluging in b and k is -792.

Recall that a system of equations can be represented by graphs of various functions, those systems have solutions at the points where the graphs intercept each other, therefore, if the graph do not intercept each other there are no solutions to the system of equations.

Answer: First and last graphs.

Answer:

  (d)  480 minutes, and 6 hours

Step-by-step explanation:

An hour is 60 minutes, so you have ...

  3 hours = 180 minutes . . . . . adding 10 minutes gives 190 minutes

  4 hours = 240 minutes

  5 hours = 300 minutes . . . . . adding 50 minutes gives 350 minutes

  6 hours = 360 minutes

__

  480 minutes is 8 hours, not 6 hours.

  480 min ≠ 6 h

There is insufficient information so the joint probability mass function of X and Y.

given that

there are three bowls they are a red bowl , a green bowl and a blue bowl  are on the kitchen table

alan places one egg into a randomly selected bowl.

X = # of eggs placed into the red bowl

Y = # of empty bowls at the end of the experiment.

the joint probability mass function of X and Y

1. Not sufficient

R=5

let us consider when G = 2 , B = 1 => P(G) = 2/8

when G=1, B=2 => P(G) = 1/8

2. Not Sufficient

P(B) = 1/3 = x/3x

But this doesn't tell us anything about B or total because P(B) = 1/3 , but it could also be 2/6 or 3/9 so on..

So we can have different B . Thus we can have different G combinations.

Together - Not Sufficient

P(B) = x/(3x) , R = 5

P(G) = 1- P( not G )

= 1- P(R or B)

But we cannot calculate this with out knowing P(R) and P(B).

we cannot solve this problem because there is no proper information is given.

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Answer:

60 slices

Step-by-step explanation:

1 pizza = 10 slices

6 pizzas = 10 slices * 6 = 60 slices

Answer: 3.65 M

Step-by-step explanation:

14.6/4 = 3.65

Yes, the relationship is proportional and the slope is 1000/3. The unit rate is also 1000/3. So, slope is directly proportional to the unit rate. Since, slope=unit rate.

When the ratio is expressed as a quotient, the same number is provided for every pair of distinct points on the same line ("rise over run"). In a diagram that shows a roof or a road as a description or a plan, the line may be practical as determined by a road surveyor; on a falling line, there is a negative "rise."

The slope's absolute value can be used to estimate a line's steepness, incline, or grade. The slope of a line in the plane that includes the x and y axes is commonly represented by the letter m and is defined as the difference between the y coordinate and the equivalent difference in the x coordinate between two distinct points on the line.

The sales are directly proportional to the number of days

The slope of the lines is given by (3, 1000), (6, 2000)

Slope=(2000-1000)/(6-3)

Slope=1000/3

From the graph given,

$1000 is obtained on 3 days.

Therefore, the unit rate is 1000/3

Therefore, Slope=unit rate=1000/3

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If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.

Answer:

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Step-by-step explanation:

I clicked on the black picture. thought is was the box to enter the answer.

Answer:

Kindly check explanation

Step-by-step explanation:

________A___ B___ C___ Total

Male____ 9___13___ 6____ 28

Female_ 20__ 19___ 2____ 41

Total___ 29__ 32___ 8____ 69

If one student is chosen at random,

Find the probability that the student got a C:

P(getting C) = (number of C's) / total number

P(getting C) = 8 / 69

Find the probability that the student was female AND got a "C":

P(female and C):

(number of female who got C / total number)

= 2 / 69

Find the probability that the student was male OR got an "B":

P(male OR B) :

(Number of males or B) = (28 + 32) - 13 = 47

= 47 / 90

find the probability that the student got a 'C' GIVEN they are female:______.

P(C given they are female) :

This is the proportion of females who got C

Total Number of females = 41

Females who got C = 2

Hence,

P(C given they are female) = 2 / 41

The upper and lower interval estimate are often describe as associated with a specific level of confidence.

In statistics, interval estimate is the process of determining the interval, or range of values, within which a parameter—such as the mean (average) of a population—is most likely to fall.

The interval encompassing a population parameter is determined by computing the statistic from values obtained from a random sample chosen from the population and by using the understanding (derived from probability theory) of how accurately sample properties reflect those of the full population.

The possibility that the estimated confidence interval estimate will include the genuine population parameter is frequently referred to as the confidence level.

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Answer:

Step-by-step explanation:

sinθ = opp/hyp

ssin30 = 17 / y

y = 17 / sin30 = 17 /0.5 = 34

Multiply each side by 10, then simplify

Here, we want to know how to proceed with solving the equation

As we can see, we have the division sign between the terms on the left hand side of the equation

To solve the equation, we have to find the value for x by isolating it

What this mean here is that we will have to multiply both sides by 10; so that we can isolate x

Thus, the correct answer here is to multiply each side by 10, then simplify

Answer:

v=(-4w)/(-w+2)

Answer:

k=3.5, and y=3.5x is the equation of the line

Step-by-step explanation:

y and x are proportional means that y = kx for some constant k.

Thus, when y=7 and x=2, we have that 7 = k * 2, so that k = 7/2 = 3.5,

and the equation of the line is y = 3.5x

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

y=2/3

Step-by-step explanation:

2y+4y=6-3y

⇔ 2y+4y+3y=6

⇔ 9y=6

⇔ y=6/9=2/3

The answer is:

y = 2/3

Work/explanation:

For now, I focus on the left side and combine the like terms:

\(\bf{2y+4y=6-3y}\)

\(\bf{6y=6-3y}\)

Add 3y to each side

\(\bf{6y+3y=6}\)

Combine like terms

\(\bf{9y=6}\)

Divide each side by 9

\(\bf{y=\dfrac{6}{9}}\)

\(\bf{y=\dfrac{2}{3}}\)

Hence, the answer is 2/3.