The brightness of illumination, l, of an object varies inversely as the square of its distance , d, from the source of illumination, if l = 18 luxes when d= 4m, find l if d =3m

Cameron will drink 98 liters of water in seven weeks.

Unit conversion is the process of converting a measurement expressed in one unit to an equivalent measurement expressed in another unit.

To find the answer in Liters we need to convert the daily amount of water from milliliters to liters.

This involves using a conversion factor (1 liter = 1000 milliliters) to convert the units from milliliters to liters.

Here we have

Cameron drinks 2,000 milliliters of water every day  

Let's convert the daily amount of water Cameron drinks from milliliters to liters by dividing by 1000:

2000 milliliters / 1000 = 2 liters

So, Cameron drinks 2 liters of water every day.

To find out how many liters he will drink in seven weeks, we need to multiply his daily intake by the number of days in seven weeks.

There are 7 days in a week, so:

7 weeks x 7 days =  49 days

The amount of water taken by Cameron can be

2 liters/day x 49 days = 98 liters

Therefore,

Cameron will drink 98 liters of water in seven weeks.

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The probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison is 0.7552.

The coefficient of variation of the number of inmates who were unemployed when they entered prison is 0.5477.

We have,

A)

We can approach this problem using the binomial probability formula since each inmate can either be unemployed or employed when they entered prison, and the probability of being unemployed is 0.4.

The probability of exactly k successes in n trials with probability of success p is given by the binomial probability formula:

P(k) = ( [tex]^nC_k[/tex]) [tex]p^k (1 - p)^{n - k}[/tex]

where [tex]^nC_k[/tex] is the binomial coefficient, which can be calculated as

n! / (k! (n - k)!).

For this problem, we want to find the probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison:

P(2 or more inmates were unemployed) = P(2) + P(3) + P(4) + P(5)

P(2) = ([tex]^5C_2[/tex])  x 0.4² x 0.6³ = 0.2304

P(3) = ([tex]^5C_3[/tex]) x  0.4³x  0.6² = 0.3456

P(4) = ([tex]^5C_4[/tex]) x [tex]0.4^4[/tex] x 0.6 = 0.1536

P(5) = ([tex]^5C_5[/tex]) x [tex]0.4^5[/tex] * 0.6^0 = 0.0256

Therefore, P(2 or more inmates were unemployed).

= 0.2304 + 0.3456 + 0.1536 + 0.0256

= 0.7552.

The probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison is 0.7552.

B)

The coefficient of variation (CV) is a measure of relative variability that is defined as the standard deviation divided by the mean.

In this case, we are interested in the number of inmates who were unemployed when they entered prison.

Let X be the number of inmates who were unemployed when they entered prison, and let mu and sigma be the mean and standard deviation of X, respectively.

From the problem statement, we know that the probability of an inmate being unemployed when they entered prison is 0.4, so the expected value of X is:

mu = E(X) = n x p = 5 x 0.4 = 2

To find the standard deviation of X, we can use the formula:

σ = √(np(1 - p))

σ = √(5 x 0.4 x 0.6) = 1.0954

Now,

The coefficient of variation of the number of inmates who were unemployed when they entered prison is:

CV = σ/μ = 1.0954 / 2 = 0.5477

Thus,

The probability of selecting exactly 2, 3, 4, or 5 inmates who were unemployed when they entered prison is 0.7552.

The coefficient of variation of the number of inmates who were unemployed when they entered prison is 0.5477.

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The  points lies on the line y-2=3(x-4) is (D) (0, -1)

The equation y - 2 = 3(x - 4) represents a line in point-slope form, where the slope of the line is 3 and the y-intercept is -10.

To determine which of the following points lies on this line, we can substitute the x and y coordinates of each point into the equation and see if the equation is true.

Substituting the coordinates of point A into the equation, we get:

5 - 2 = 3(1 - 4)

3 = -9

This equation is not true, so point A does not lie on the line.

Substituting the coordinates of point B into the equation, we get:

-6 - 2 = 3(4 - 4)

-8 = 0

This equation is not true, so point B does not lie on the line.

Substituting the coordinates of point C into the equation, we get:

-8 - 2 = 3(-2 - 4)

-10 = -18

This equation is not true, so point C does not lie on the line.

Substituting the coordinates of point D into the equation, we get:

-1 - 2 = 3(0 - 4)

-3 = -12

This equation is true, so point D lies on the line.

Therefore, the answer is (D) (0, -1).

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The question is incomplete. the complete question is:

Which of the following points lies on the line y-2=3(x-4)

The points are:

A) (1, 5)

B) (4, -6)

C) (-2, -8)

D) (0, -1)

The required quadratic equation is s² - 25 = 0 and length of sides  be 5 cm.

Given that

Number of square pieces of wood = 8

Length of side of each piece = s cm

Area of 8 pieces of wood = 200 cm²

We know the equation A = s²,

Where s is the side length, determines the area of a square.

Then total area of all the pieces can be written as:

 8s² = 200

⇒ s² = 25

⇒ s² - 25 = 0

or s = 5 cm

Hence quadratic equation ⇒ s² - 25 = 0 and side = 5 cm

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Answer:

the answer is 6 trust. poopoo

Answer:

1/2, 5/8, 3/4, 7/16, 3/8, 5/16

Answer:

7/16, 5/16, 5/8, 3/8, 3/4, 1/2

Step-by-step explanation:

you see the biggest numbers mean the more times its been split so the smaller each peice would be so therefor the biggest number would be the smallest tool and vice versa

The answers are:

B. The graph of f(x) is shifted up 50 units

E. The graph of f(x) is shifted right 10 units

F. The graph of f(x) is reflected over the x-axis

The given function is f(x) = x²

This is an upward-facing vertical parabola.

The vertex is the smallest.

The vertex's origin is at (0, 0).

g(x) = –5x² + 100x – 450

This is an open downhill vertical parabola.

The vertex is the greatest

The first thing to notice is that fx) opens up whereas g(x) opens down, indicating that a reflection across the x-axis was used.

Find the g(x) vertex.

change the form to vertex

g(x) = –5x² + 100x – 450

Complete the square

g(x) = -5(x² - 20x) - 450

g(x) = -5(x² - 20x + 100) - 450 + 500

g(x) = -5(x² - 20x + 100) + 50

g(x) = -5( x - 10)² + 50

The vertex is located at (10, 50).

To the vertex from (0,0) to (10,50)

The translational principle is

(x,y) ------> (x+10,y+50)

This implies ----> The translation is 50 units up and 10 units to the right.

The adjustments are

The f(x) graph is moved forward by 50 units.

The f(x) graph is 10 units to the right.

Over the x-axis is a reflection of the f(x) graph.

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The complete question is,

Which transformations have been applied to the graph of f(x) = x² to produce the graph of g(x) = –5x² + 100x – 450? Check all that apply.

A.The graph of f(x) = x² is shifted up 25 units.

B.The graph of f(x) = x² is shifted up 50 units.

C.The graph of f(x) = x² is shifted down 950 units.

D.The graph of f(x) = x² is shifted left 10 units.

E.The graph of f(x) = x² is shifted right 10 units.

F.The graph of f(x) = x² is reflected over the x-axis.

The part number for a 6" elbow connector is: A. J44564

Based on the given details, it appears that the elbow is labeled as J44564 while its corresponding key is marked K2778. In regard to your request for a 6" elbow connector, the matching key that is meant for a pipe fitting of similar size has been located.

Specifically, K2531. Despite the change in key, it's worth noting that the elbow part number remains consistent (J44564). Therefore, our answer ultimately reads as A. J44564.

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Setting is essential to the growth of a tale because it establishes the period of time, location, and environment in which the action of the story occurs.

The entire meaning of the story can be shaped by the environment through establishing the atmosphere, tone, and topic.

The characters' actions and choices might be influenced by the setting's physical environment, which can also present challenges or opportunities for the characters.

For instance, characters in a tale set in a post-apocalyptic world with few resources may be forced to make morally challenging decisions and fight for survival, but characters in a story set in a beautiful house may be more interested in social dynamics and power conflicts.

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The polynomial for this problem is given as follows:

y = x³ - 2x² - 11x + 52.

The zeros of the polynomial are given as follows:

Then the linear factors of the polynomial are:

By the Factor Theorem, the polynomial is defined as a product of it's linear factors, as follows:

y = (x + 4)(x - 3 + 2i)(x - 3 - 2i)

y = (x + 4)(x² - 6x + 9 - 4i²)

y = (x + 4)(x² - 6x + 13) -> as i² = -1.

y = x³ - 2x² - 11x + 52.

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The cost of each shirt and each pair of pants will be $11 and $12 respectively.

Let

s  = cost of a shirt

p = cost of a pair of pants

From the problem, we know that:

2s + 3p = 58 (Equation 1)

1s + 2p = 35 (Equation 2)

We can solve for s and p by using a method called substitution. We can rearrange Equation 2 to solve for s in terms of p:

s = 35 - 2p

We can then substitute this expression for s into Equation 1 and simplify:

2(35 - 2p) + 3p = 58

Distributing the 2, we get:

70 - 4p + 3p = 58

Combining like terms, we get:

70 - p = 58

Subtracting 70 from both sides, we get:

-p = -12

Dividing both sides by -1, we get:

p = 12

So a pair of pants costs $12.

We can now use this value to solve for the cost of a shirt.

Substituting p = 12 into Equation 2, we get:

s + 2(12) = 35

Simplifying, we get:

s = 11

So a shirt costs $11.

Therefore, each shirt costs $11 and each pair of pants costs $12.

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Answer: cos 20​ = -√3/2

Step-by-step explanation:

Since sin 2015 = 0 and 20° is in the second quadrant, we know that the reference angle for 20° is 20° - 180° = -160°. So we need to find the value of cos(-160°).

We can use the fact that cos(-θ) = cos(θ) to find the value of cos(-160°) as follows:

cos(-160°) = cos(160°)

To find the cosine of 160°, we can use the identity cos(180° - θ) = -cos(θ) as follows:

cos(160°) = cos(180° - 20°) = -cos(20°)

Now, we need to determine the sign of cos(20°) in the second quadrant. Since 30°, 45° and 60° are angles in the first quadrant with exact values of √3/2 and 90° - 60° = 30°, 90° - 45° = 45°, 90° - 30° = 60° are their respective corresponding angles in the second quadrant, we can use the fact that cosine is a decreasing function in the second quadrant to conclude that:

1 > cos(20°) > √3/2

Therefore, since sin 2015 = 0, we know that cos(-160°) = -cos(20°) = 0, which implies that cos(20°) = 0.

Therefore, cos 20​ = -√3/2.

The two chords of the circle are same and x = 3

Given data ,

Let the circle be represented as C

Now , the length of the two chords of the circle are

The length of chord JK = 52 units

The length of chord LM = 18x - 2

Now , the two arcs subtended by the chords are the same , so

The lengths of the chords are same

Now , JK = LM

On simplifying , we get

52 = 18x - 2

Adding 2 on both sides , we get

18x = 54

Divide by 18 on both sides , we get

x = 54/18

x = 3

Hence , the chords are solved and x = 3

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Answer:

153.86 units²

Step-by-step explanation:

 You need to find the area of a circle, given that its radius is 7.

I am going to apply the formula:

A = πr²

whereas -

here's a diagram for reference -

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 7\ cm}\end{picture}[/tex]

--

Plug all the data into the formula:

A = 3.14 * 7^2

A = 3.14 * 49

A = 153.86

[tex]\bigstar[/tex] Therefore, the area is 153.86 units²

Answer: leaves

Step-by-step explanation:

Joey should carefully observe the leaves of the plants during his experiment. Photosynthesis primarily occurs in the leaves, where chlorophyll, the pigment responsible for capturing sunlight, is located. The process of photosynthesis converts sunlight, carbon dioxide, and water into glucose and oxygen. Polluted air can negatively impact photosynthesis by reducing the availability of carbon dioxide or by damaging the chlorophyll and other components involved in the process.

Answer:

42

Step-by-step explanation:

The stock price according to the constant growth dividend model is $71.57.

What is percent?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%

We can use the constant growth dividend model to calculate the stock price:

Next Dividend / (Required Rate of Return - Growth Rate) Stock Price

Since the problem only provides the last dividend, we need to calculate the next dividend first. We can use the growth rate to find the next dividend:

Next Dividend = Last Dividend × (1 + Growth Rate) = $5.95 × (1+0.0314) = $6.14

Stock Price $6.14 / (0.1188 -0.0314) $71.57

Therefore, the stock price according to the

constant growth dividend model is $71.57.

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Answer:

50 ft. × 50 ft.

Step-by-step explanation:

Let's assume that the rectangular exhibit has a length of 'L' and a width of 'W'. The area of the exhibit is given as 2500 square feet, so we have:

L × W = 2500

We want to change the dimensions of the exhibit to minimize the amount of fencing needed while keeping the same area. The amount of fencing needed is directly proportional to the perimeter of the exhibit. The perimeter of a rectangular exhibit is given as:

P = 2L + 2W

We want to minimize P while keeping the area constant. One way to do this is to use the area formula to express one of the variables in terms of the other and then substitute it in the perimeter formula.

From the area formula, we have:

L × W = 2500

W = 2500 / L

Substituting W in the perimeter formula, we get:

P = 2L + 2(2500 / L)

Simplifying, we get:

P = 2L + 5000/L

To minimize P, we can take the derivative of P with respect to L and set it to zero:

dP/dL = 2 - 5000/L² = 0

Solving for L, we get:

L² = 2500

L = 50

Substituting L in the equation for W, we get:

W = 2500 / L = 50

Therefore, the new dimensions of the rectangular giraffe exhibit should be 50 feet by 50 feet to minimize the amount of fencing needed while keeping the same area.

The length of string of the kite is 13 m.

Question :-

A boy is flying a kite which is 12 m high from the ground the horizontal distance of the boy from the kite is 5 m, find the length of string of the kite?

Solution :-

The scenario is setting up a picture of a right triangle, where the horizontal distance of the boy from the kite is the base and the height of the kite from the ground is the height of triangle, and the length of the string is acting as a hypotenuse,

So, using the Pythagoras theorem,

12² + 5² = x²

x = √144+25

x = √169

x = 13 m

Hence, the length of string of the kite is 13 m.

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The correct Newton-Raphson formula is [tex]x_i + 1 = x_i - (x_i^2 - a/ 2x_i)[/tex]. Option A

The Newton-Raphson method is an iterative approach for determining the root of a real-valued function.

The Newton-Raphson formulal is gotten from linear formula for f(x)  from the point x_i

= x_i - f(x_i) / f'(x_i)

In this situation, we are trying to see that f(x) = 0

given f(x) = x^2 - a

f'(x) = 2x

If we add this to the above to the newton Raphson method, it should be

[tex]x_i + 1 = x_i - (x_i^2 - a/ 2x_i)[/tex]

This formula is employed iteratively, beginning with a guess x_0. The value of x converges to the square root of a with each iteration. The procedure is repeated until the appropriate level of precision is obtained.

The above answer is based on the full question below as seen in the picture;

Root Finding - Newton Raphson Method: which of the following is the Newton-Raphson formula to compute the square root of a > 0

a. x_i + 1 = x_i - (x_i^2 - a/ 2x_i) which is [tex]x_i + 1 = x_i - (x_i^2 - a/ 2x_i)[/tex]

b. x_i + 1 = x_i - (x_i^2 + a/ 2x_i) which is [tex]x_i + 1 = x_i - (x_i^2 + a/ 2x_i)[/tex]

c. x_i + 1 = x_i + (x_i^2 - a/ 2x_i) which is [tex]x_i + 1 = x_i + (x_i^2 - a/ 2x_i)[/tex]

d. x_i + 1 = x_i - (x_i^2 + a/ 2x_i) which is [tex]x_i + 1 = x_i - (x_i^2 + a/ 2x_i)[/tex]

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Answer:

B) 3/4

Step-by-step explanation:

longest length is 1 7/8

Shortest is 1 1/8

1 7/8 — 1 1/8 = 6/8

6 / 2 = 3

8 / 2 = 4

6/8 = 3/4

In order to achieve market equilibrium is; The monthly supply of milk must increase by 8 billion gallons. Option D is correct.

To achieve market equilibrium, the quantity supplied must equal the quantity demanded. In this case, the demand for milk is 18 billion gallons per month and the supply is 10 billion gallons per month, so there is a shortage of 8 billion gallons per month (18 - 10 = 8).

To eliminate the shortage and achieve equilibrium, the supply of milk must be increased by the same amount as the shortage, which is 8 billion gallons per month.

Therefore, the monthly supply of milk must increase by 8 billion gallons.

Hence, D. is the correct option.

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Answer:

The length of the hypotenuse of each right triangle is approximately 12.7 inches, rounded to the nearest tenth.

Step-by-step explanation:

Let's start by finding the length of one side of the square posterboard.

Since the perimeter is 36 inches, and a square has four equal sides, we can divide the perimeter by 4 to get the length of one side:

36 ÷ 4 = 9

So each side of the square posterboard is 9 inches long.

When Miranda cuts the posterboard along a diagonal, she forms two right triangles. Let's call the length of the hypotenuse of each right triangle "c".

We can use the Pythagorean theorem to find the length of "c":

a² + b² = c²

Since the posterboard is a square, each of the legs of the right triangle has a length of 9 inches.

9² + 9² = c²

81 + 81 = c²

162 = c²

c ≈ 12.7

So, the length of the hypotenuse of each right triangle is approximately 12.7 inches, rounded to the nearest tenth.

Answer:

  3√3 ≈ 5.20 square units

Step-by-step explanation:

You want the area of ∆ABC with centroid G such that ∆ABG is an equilateral triangle with side length 2.

The centroid of a triangle divides the median into two parts in the ratio 1:2, where the shorter part is the distance to the side being bisected, and the longer part is the distance to the vertex.

Here equilateral triangle ABG with side length 2 will have an altitude of √3, so the full length of CH is 3·√3.

The area of ∆ABC is ...

  A = 1/2bh

  A = 1/2(2)(3√3) = 3√3

The area of ∆ABC is 3√3 square units.

__

Additional comments

In the attached figure, GH is the median and altitude of ∆ABG. The figure is symmetrical about the line GH, so ∆ABC is isosceles and CH is its altitude and median.

We can find the length GH different ways. Perhaps the easiest is to refer to memory, where we find the side length ratios in ∆GAH are 1 : √3 : 2. This means for GA=2, GH=√3 and AH=1. We can also use trigonometry, which tells us GH/GA = sin(60°) = √3/2. Then GH=GA·√3/2 = √3.

Answer: 12.56

Step-by-step explanation: 3.14 x 1/2 of 4 x 2

The probability that they are both seniors nearest to two decimal places will be 0.29.

Given that:

The student council consists of 10 juniors and 12 seniors. If two members are voted to be officers.

The probability is given as,

P = (Favorable event) / (Total event)

The probability that they are both seniors will be given as,

P = ¹²C₂ / ²²C₂

P = 66 / 231

P = 2/7

P = 0.29

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The true or false statements are

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

Triangle fgh is rotated 90° clockwise around the origin to form triangle f’g’’h’.

This is a rigid transformation and as such the side lengths and angles would remain unchagned

So, we have

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The probability that the Islanders will win at most two out of five games in a series against the Rangers is 0.727.

The probability that the Islanders will win at most two out of five games in a series against the Rangers can be determined using the binomial probability formula:

where X is the number of games the Islanders win in the series.

Using the binomial probability formula, we can calculate:

P(X = 0) = (0.56)⁵ = 0.0772

P(X = 1) = 5C1 (0.44) (0.56)⁴ = 0.2807

P(X = 2) = 10C2 (0.44)² (0.56)³ = 0.3694

P(X ≤ 2) = 0.0772 + 0.2807 + 0.3694

P(X ≤ 2) = 0.7273

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