Consider a small shop with only one checkout counter. The arrivals of customers are distributed throughout the day such that a line rarely forms at the counter. Suppose the arrival times of customers at the counter follows the Exponential Distribution: X Exp(0.4). 0.4 0.3 0.2 0.1 0.0 0.0 2.5 5.0 7.5 10.0 12.5 15.0 х a. What is the mean time (in minutes) between customers? u = b. Determine the following probability. P(2 < X < 10) Suppose X ~ Exp(0.25). Determine the following probabilities. (Include four decimal places.) Note: This is a challenging problem. a. P(X > 5) = b. P(X < 3) = C. P(X > 7X > 5) = Suppose X ~ U(2, 7). Determine P(X > 6 | X > 5). Note: This is a very challenging problem.

The rate of decrease of volume of the sphere when its diameter is 6 cm is -96π cubic cm/min.

Given that the snowball is a sphere, we can use the formula for the volume of a sphere.

The formula for the volume of a sphere is

V = 4/3 πr³

We need to find out the rate of decrease of volume when the diameter is 6 cm.

To find the rate of decrease of volume, we need to differentiate the above formula. Differentiating the above formula w.r.t. time, we get

dV/dt = 4/3 π(3r²)(dr/dt)

Where r is the radius of the sphere and dr/dt is the rate of change of the radius.

Let d be the diameter of the sphere. Then we can write,r = d/2

Also, given that dr/dt = -2cm/min

Substituting the values in the equation for the rate of decrease of volume,

dV/dt = 4/3 π(3(d/2)²)(-2) = -8π/3 d²

As the diameter of the sphere is 6 cm, d = 6 cm.Substituting the value in the equation above, we get

dV/dt = -8π/3 (6)² = -96π cubic cm/min

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Answer:

The answer rounded is 6.10, but the actual answer would be 6.095

Step-by-step explanation:

5.75 X 0.06 = 0.345 || 0.345+5.75 = 6.095

A 6.10

According to the laws of stuff a calculate of 5.75 to the percentage of 6 is 6.10

Answer:

3.33 minutes

Step-by-step explanation:

first know that the escalator can move 30 people in 1 minute.

then, we can write in a mathematical expression as:

30 people = 1 minute

100 people = ? minutes.

cross multiply, i.e. 30×? = 100×1

therefore, ? = 100/30

? = 3.33 minutes.

therefore, it's going to take 3.33 minutes for the escalorr to take 100 people.

The probability density function (PDF) is a mathematical function that describes the probability of a random variable taking a certain value. It is a measure of the probability of a given outcome within a given range.

Probability is a branch of mathematics used to quantify the likelihood of an event occurring. It is used to calculate the chances of a certain outcome or a combination of outcomes in a given situation. Probability is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. Probability is used to make predictions, analyze data, and understand the complexity of the world around us.

b. The probability of generating a random number between 0.25 and 0.85 (to 1 decimal place) is 0.6.

c. The probability of generating a random number with a value less than or equal to 0.4 (to 1 decimal place) is 0.4.

d. The probability of generating a random number with a value greater than 0.6 (to 1 decimal place) is 0.4.

e. The mean of the given set of 50 random numbers is 0.527084 and the standard deviation is 0.307766.

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A mathematical function known as the probability density function (PDF) calculates the likelihood that a random variable will have a particular value. It is a measurement of the likelihood of a specific outcome within a specific range.

What is probability?

Mathematics' branch of probability is used to determine how likely an event is to occur. It is employed to determine the probabilities of a specific outcome or a mixture of outcomes in a particular circumstance. A number between 0 and 1 is used to represent probability, with 1 denoting a certain event and 0 denoting an impossibility. To generate predictions, examine data, and comprehend how complicated the world is around us, probability is used.

b. The probability of generating a random number between 0.25 and 0.85 (to 1 decimal place) is 0.6.

c. The probability of generating a random number with a value less than or equal to 0.4 (to 1 decimal place) is 0.4.

d. The probability of generating a random number with a value greater than 0.6 (to 1 decimal place) is 0.4.

e. The mean of the given set of 50 random numbers is 0.527084 and the standard deviation is 0.307766.

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Check the picture below.

The direction of the resulting force upon the piling is approximately 298.85 degrees

We can use vector addition to find the direction of the resulting force. Let's call the force exerted by the first bulldozer F1, and the force exerted by the second bulldozer F2. We can represent each force as a vector with a magnitude and direction.

F1 has a magnitude of 1850 pounds and points in a westerly direction. We can represent it as a vector (-1850, 0).

F2 has a magnitude of 3250 pounds and points in a northerly direction. We can represent it as a vector (0, 3250).

To find the resulting force, we need to add these two vectors. We can do this by adding the x-components and the y-components separately.

The x-component of the resulting force is -1850 (from F1) plus 0 (from F2), which is -1850.

The y-component of the resulting force is 0 (from F1) plus 3250 (from F2), which is 3250.

So the resulting force is a vector with components (-1850, 3250). We can find the direction of this vector by taking the inverse tangent of the ratio of the y-component to the x-component.

tan(theta) = (3250) / (-1850)

theta = -61.15 degrees

The negative sign indicates that the resulting force points to the southwest. To get the angle in the range of 0 to 360 degrees, we can add 360 degrees to the angle if it is negative.

theta = 360 - 61.15

theta = 298.85 degrees

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The density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams.

The density of a material is defined as its mass in line with unit volume, generally expressed in grams in line with cubical centimeter( g/ cm ³). To compute the density of the presented wax, we need to divide its mass by applying its volume.

Presented that the volume of the wax is2.5 cm ³ and its mass is 4.5 g, we will compute its density as

Density = Mass/ volume = 4.5 g/2.5 cm ³ = 1.8 g/ cm ³

Thus, the density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams. knowing the density of a fabric can help in relating the cloth or in predicting its deportment in distinct qualifications.

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Answer:

Below

Step-by-step explanation:

Area of a parallelogram is given by:    base * height

   base =  6 m    height = 8 m

     area = 6* 8 = 48 m^2

Janella recognizes a gain of $36,000 and her basis in the distributed property is $54,000.

Janella's basis in her partnership interest is $120,000, which includes her share of partnership debt. When the partnership pays off its debts and liquidates, Janella receives a proportionate liquidating distribution consisting of $42,000 cash and inventory valued at $24,000 (adjusted basis to the partnership = $20,000).

To calculate Janella's recognized gain or loss, we need to compare her basis in the partnership interest to the fair market value of the distributed assets.

The fair market value of the distributed assets is $42,000 (cash) + $24,000 (inventory) = $66,000.

The amount of the loss is the excess of her basis over the fair market value of the distributed assets, which is $120,000 - $66,000 = $54,000.

To determine Janella's basis in the distributed property, we need to adjust her basis in the partnership interest by the amount of the liquidating distribution she received.

Janella received a total liquidating distribution of $42,000 cash + $24,000 inventory = $66,000. Her share of partnership debt was $150,000, and the partnership paid off all its debts, so she no longer has any debt basis.

Janella's distribution of $66,000 exceeds her adjusted basis of $30,000 by $36,000. She recognizes a gain of $36,000. Therefore, Janella's new basis in the distributed property is $120,000 - $66,000 (liquidating distribution) = $54,000.

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The probability a male's growth plate will fuse before age 17 is 0.1112, for this we have to learn probability.

Probability of an event is a number that shows what is the possibility of an event occur.

we have to take entire area under the standardized curve from and including the left tail up to the z-score for 17.

[tex]= \frac{(17 - 18.6 years)}{1.308333 years}[/tex]

[tex]= \frac{(-1.6) }{1.308333}[/tex]

[tex]= -1.22293[/tex]

[tex]= approx. 1.22.[/tex]

The area from the mean to +ve or -ve 1.22 is .3888

We have to subtract .3888 from area from the tail to the mean (.5000) to get area from the tail to 1.22.

So, the growth plates will fuse before age 17 [tex]= .5000-.3888 = 0.1112[/tex]

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The prοbabilities fοr all pοssible values οf the randοm variable x are:

P(x) = 0.1785 P(x) = 0.3911 P(x) = 0.3462 P(x) = 0.1124 P(x) = 0.0118.

The jοint prοbability is the likelihοοd οf twο (οr mοre) events. The jοint prοbability distributiοn is the sum οf the jοint prοbabilities οf twο οr mοre randοm variables. Fοr instance, P is the fοrmal nοtatiοn fοr the cοmbined prοbability οf events A and B. (A and B)

We can use the fοllοwing fοrmula tο find the prοbabilities fοr all pοssible values οf the randοm variable, x, in a binοmial situatiοn where n = 4 and = 0.35:

P(x) = (n chοοse x)[tex]* \pi ^x * (1-\pi)^{(n-x)[/tex]

where "n select x" is the binοmial cοefficient, which equals n! / (x! * (n-x)!).

Then, fοr x = 0, 1, 2, 3, and 4, we can cοmpute P(x) as fοllοws:

P(x=0) = (4 chοοse 0) [tex]* 0.35^0 * 0.65^4 = 0.1785[/tex]

P(x=1) = (4 chοοse 1) [tex]* 0.35^1 * 0.65^3 = 0.3911[/tex]

P(x=2) = (4 chοοse 2) [tex]* 0.35^2 * 0.65^2 = 0.3462[/tex]

P(x=3) = (4 chοοse 3) [tex]* 0.35^3 * 0.65^1 = 0.1124[/tex]

P(x=4) = (4 chοοse 4) [tex]* 0.35^4 * 0.65^0 = 0.0118[/tex]

When we rοund these numbers tο fοur decimal places, we get:

P(x=0) = 0.1785

P(x=1) = 0.3911

P(x=2) = 0.3462

P(x=3) = 0.1124

P(x=4) = 0.0118

As a result, the prοbabilities fοr all pοssible values οf the randοm variable x are as fοllοws:

P(x=0) = 0.1785

P(x=1) = 0.3911

P(x=2) = 0.3462

P(x=3) = 0.1124

P(x=4) = 0.0118

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Therefore , the solution of the given problem of angle comes out to be the smaller angle will therefore rotate through one unit angle each time.

In Euclidean mathematics, a tilt is a shape consisting of two sides, or cylindrical faces, that separate at the wall's centre and its apex. Two rays may come together at their intersections to create an angle. Another result of two things interacting is an angle. They are characterized as dihedral angles. Two line beams can be arranged in different ways at their extremities to produce a two-dimensional curve.

Here,

A small pattern block is a geometric structure made up of six congruent isosceles triangles organised around a regular hexagon with six equal-length sides.

Two of the angles in an isosceles triangle are identical in size, while the third angle varies.

We need to first create a frame of reference in order to determine how many unit angles the smaller angle of a small pattern block turns through.

Assume that we begin by placing the little pattern block in its initial location with one of its sides vertically aligned.

This results in one of the isosceles triangles being vertically aligned after turning the block.

The smaller angle will therefore rotate through one unit angle each time if we continue to rotate the small pattern block anticlockwise by one-sixth of a complete revolution for each subsequent turn.

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Case 1: The value of the vector B is equal to [tex]\overrightarrow {B} = (7, - 20)[/tex].

Case 2: The values of variables m and n from vector operations are - 5 and - 4, respectively.

In this problem we find two cases of operations between two vectors. According to linear algebra, there are two fundamental operations:

Case 1:

The value if vector B can be found by following operation:

[tex]\overrightarrow{B} - \overrightarrow {A} = (5, - 5)[/tex]

[tex]\overrightarrow {B} = \overrightarrow {A} + (5, - 5)[/tex]

[tex]\overrightarrow{B} = (2, - 4) + (5, - 5)[/tex]

[tex]\overrightarrow{B} = (2 + 5, - 4 - 5)[/tex]

[tex]\overrightarrow {B} = (7, - 20)[/tex]

Case 2:

First, determine the expression for the given operator:

2 · a - 2 · b = 2 · (- 3, m) - 2 · (n, - 4)

2 · a - 2 · b = (- 6, 2 · m) + (- 2 · n, 8)

2 · a - 2 · b = (- 6 - 2 · n, 2 · m + 8)

Second, find the values of m and n:

(- 6 - 2 · n, 2 · m + 8) = (2, - 2)

- 6 - 2 · n = 2

- 3 - n = 1

n = - 4

2 · m + 8 = - 2

- m - 4 = 1

m = - 5

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The constraints as a system of linear inequalities include the following;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640

75x + 60y ≤ 12,900

The solution set for the system of linear inequalities is shown in the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640.

75x + 60y ≤ 12,900

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The total distance that Mishka covers on the trip is 265 miles.

Speed measures how fast an object is moving with respect to time. Speed is the ratio of total distance to total time.

Speed = distance / time

Distance = speed x time

Distance covered while driving on the highway = 75 x 3 = 225 miles

Distance covered while driving on the side road = 40 x 1 = 40 miles

Total distance covered = 225 miles + 40 miles = 265 miles

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Assuming that ∠1 and its adjacent angle form a straight line, we know that the sum of the angles on a straight line is 180°. Therefore, the measure of the adjacent angle is 180° - 39° = 141°.

we can also look at the other angles in the figure. From the diagram, we can see that ∠2 and ∠3 are acute angles, which means they are less than 90°. Additionally, we know that the sum of the angles in a triangle is 180°, so ∠2 + ∠3 + ∠4 = 180°.

Since ∠2 and ∠3 are acute, their sum must be less than 180°. Therefore, ∠4 must be an obtuse angle (greater than 90°) in order for the sum to be 180°. This makes sense, as an obtuse angle is required to form a triangle with two acute angles.

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The lifetime cost of the model is $765.

Kate is re-modelling her kitchen.

She is going shopping for a refrigerator.

The model price is $405, and the estimated energy cost per year is $36.

If the model has an estimated lifetime of 10 years,

Lifetime cost of the model:

The lifetime cost of the model is $765

Explanation: Given, The model price is $405

Estimated energy cost per year is $36.

The model has an estimated lifetime of 10 years.

Lifetime cost of the model can be calculated as follows:

Total lifetime cost = Initial cost + (Estimated energy cost per year × Estimated lifetime)

Initial cost = $405

Estimated energy cost per year = $36

Estimated lifetime = 10 years

Total lifetime cost = $405 + ($36 × 10)

Total lifetime cost = $405 + $360

Total lifetime cost = $765

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The simplest form of the given radical expression as required to be determined is; -3³√2a.

As evident form the task content; the given expression whose simplified form is to be determined is;

3 ³√2a - 6 ³√2a

Since; 3³√2a is common to both terms of the expression; Hence, by factorisation; we have;

3³√2a (1 - 2)

= 3³√2a • -1

= -3³√2a

Ultimately, the simplified form of the radical expression is; -3³√2a.

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Answer:

250 ml

Step-by-step explanation:

300ml + 250ml =550ml

550ml - 200ml=350ml

350ml - 150ml + 100ml=300ml

300ml - 50ml=250ml

The circumference of the circle with diameter 4 is 12.56 units using 3.14 as the value of π.

The circumference of a circle is given by the formula C = πd, where d is the diameter of the circle. If the diameter of the circle is given as 4, then we can substitute it into the formula to get:

C = πd

C = π(4)

Since we are given to use 3.14 for π, we can substitute it into the formula to get:

C = 3.14(4)

C = 12.56

It's important to note that the circumference of a circle is the distance around the edge or perimeter of the circle.

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Answer:

343 cubic meters.

Step-by-step explanation:

To find the volume of a cube given its surface area, we need to first find the length of one of its sides.

The formula for the surface area of a cube is:

SA = 6s^2

where SA is the surface area and s is the length of one of the cube's sides.

We are given that the surface area is 294 square meters, so we can set up the equation:

294 = 6s^2

Simplifying, we get:

49 = s^2

Taking the square root of both sides, we get:

s = 7

So the length of one of the cube's sides is 7 meters.

To find the volume of the cube, we use the formula:

V = s^3

Substituting in 7 for s, we get:

V = 7^3 = 343

Therefore, the volume of the cube is 343 cubic meters.

Answer:

343m³

Step-by-step explanation:

Surface area of a cube is A = 6a²

6a² = 294

Divide both sides by 6

a² = 49

Square root of both sides

a =7

Substitute the value of a into volume

Volume of Cube V = a³

V = 7x 7x7

V = 343m³

Answer:

The error in Amanda's calculation is in line 2, where she incorrectly subtracted 6x instead of adding 6x, as well as incorrectly subtracting 24 instead of adding 24.  Amanda also omitted the addition sign in line 3 of her calculations.

Step-by-step explanation:

To factor a quadratic polynomial in the form ax² + bx + c, find two numbers that multiply to ac and sum to b.

Therefore, for the given polynomial 4x² + 22x + 24:

⇒ ac = 4 · 24 = 96

⇒ b = 22

The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

Therefore, the factor pair that sums to 22 is 16 and 6.

Rewrite b as the sum of these two numbers:

⇒ 4x² + 22x + 24

⇒ 4x² + (16 + 6)x + 24

⇒ 4x² + 16x + 6x + 24

Therefore, the error in Amanda's calculation is in line 2, where she incorrectly subtracted 6x instead of adding 6x, as well as incorrectly subtracting 24 instead of adding 24.  Amanda also omitted the addition sign in line 3 of her calculations.

The correct calculation is as follows:

   4x² + 22x + 24

⇒ 4x² + 16x + 6x + 24

⇒ 4x(x + 4) + 6(x + 4)

⇒ (4x + 6)(x + 4)

Given :-

To find:-

Answer:-

Given polynomial to us is ,

[tex]\implies 4x^2 + 22x + 24 \\[/tex]

With respect to the standard form of polynomial ax² + bx + c , we have;

Step 1 :- Split the middle term into two parts p and q such that p × q = a × c and p + q = b

Such two numbers are 16 and 6 .

Hence, we can rewrite it as ,

[tex]\implies 4x^2 + 16x + 6x + 24 \\[/tex]

But Amanda wrote [tex] 4x^2+16x - 6x + 24[/tex] , so she made a mistake here by writing +6x as -6x .

Step 2:- Factor out the common terms .

[tex]\implies 4x( x + 4) + 6(x+4) \\[/tex]

Step 3 :- Take out [tex] x+4[/tex] as common.

[tex]\implies (x+4)(4x+6) \\[/tex]

This is our required factored form .

Hence we can see that Amanda made a mistake only in splitting the term term .

and we are done!

Answer:

2,3,4,10

Step-by-step explanation:

DIVIDE METERS BY 1000 SINCE KILO MEANS 1000

Answer:2000m=2km

3000m=3km

4000m=4km

10000m=10

Step-by-step explanation:

1kilometers is equal to 1000 meters. So, we divide meters with 1000 in order to find kilometers.

The solution to the inequality expression given as x + 2 < 5 is x < 3

Inequality expressions refer to statements in mathematics that use symbols like <, >, ≤, or ≥ to compare two values.

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

x + 2 < 5

Subtract 2 from both sides of the inequality expression

So, we have the expression below

x + 2 < 5 - 2

Evalaute the like terms

x < 3

This means that, the solution is x < 3

The graph of the inequality is added as an attachment

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The experimental probability of not selecting a peppermint candy is 77.78%, so the correct option is the third one.

We want to find the experimental probability of selecting a candy that is not peppermint.

To get this, we need to get the difference between 1 and the probability of getting a peppermint candy, then we will get:

p = 1 - 2/9

p = 7/9

Now we want to express this as a percentage, so we need to multiply this by 100%

p = (7/9)*100%

p = 77.78%

We can see that the experimental probability is the one in the third option.

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The given inequality is true when w is greater than 5: w > 5. (option 4)

To solve the inequality, we can simplify the expression inside the absolute value brackets by distributing the negative sign and combining like terms:

Now we can split the inequality into two cases: 14w - 2 > 7 and -(14w - 2) > 7. Solving each case for w gives:

14w - 2 > 7

14w > 9

w > 9/14

-(14w - 2) > 7

-14w + 2 > 7

-14w > 5

w < -5/14

So the solution to the inequality is w > 9/14 or w < -5/14. However, we are given that w is greater than 5, so the only valid solution is w > 5.

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Complete Question:

Which inequality is true when the value of w is 13?

Tom is working two jobs to save money for prom, walking a neighbor's dog for $6.50 an hour and washing cars for $7 an hour, to make at least $91.

Tom is working to put money aside for the prom.. His mother has instructed him that in order to keep up with his schoolwork, he may only work a maximum of 15 hours each week. Tom has made the decision to wash cars for $7 per hour and walk his neighbor's dog for $6.50 per hour in order to achieve this aim. For his prom expenditures, he will need to earn at least $91. He must put in a maximum of 13.2 hours of work to earn $91. This implies he can stroll a dog for 8.4 hours and wash vehicles for 4.8 hours. He can also decide to simply perform one job; but, in order to earn the appropriate amount, he would need to walk his neighbor's dog for 12 hours.

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Therefore , the solution of the given problem of unitary method comes out to be the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).

By applying what was acquired and bringing this variable tactic into practise, along with all supporting information from two people who used a particular tactic, the work can be finished. In other words, if the wanted expression result occurs, either the entity specified in the formula will also be discovered, or both crucial processes will actually ignore the colour. A refundable fee of Rupees ($1.01) may be necessary for forty pencils.

Here,

The water bottle is currently 3/5 full and contains 24 1/4 ounces of water.

By dividing the bottle's capacity by the percentage that indicates how filled it is, we can determine how much water is inside:

=> 24 1/4 × 3/5 = (97/4) × (3/5)

=> 291/20 = 14 11/20

Therefore, there are 14 11/20 ounces of water in the water container.

We want to fill three cups, each of which needs five ounces of water, so we will need:

=>  5 x 3 = 15 ounces

There isn't enough water in the bottle to fill three glasses with 5 ounces each because the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).

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The total area of gray sections of the target is  1017 square inches. The correct option is (D).

To find the total area of the gray sections of the target, we need to first find the areas of the gray rings. We can do this by subtracting the area of the smaller circle from the area of the larger circle for each ring.

The area of a circle is given by the formula A = πr^2, where r is the radius.

For the outer gray ring, the radius is 1.5 feet. So, the area of the gray ring is:

A_gray_outer = π(1.5)^2 - π(1)^2

= 7.06858 - 3.14159

= 3.92699 square feet

For the middle gray ring, the radius is 1 foot. So, the area of the gray ring is:

A_gray_middle = π(1)^2 - π(0.5)^2

= 3.14159 - 0.78540

= 2.35619 square feet

For the inner gray ring, the radius is 0.5 feet. So, the area of the gray ring is:

A_gray_inner = π(0.5)^2 - 0

= 0.78540 square feet

The total area of the gray sections of the target is the sum of these three areas:

A_total_gray = A_gray_outer + A_gray_middle + A_gray_inner

= 3.92699 + 2.35619 + 0.78540

= 7.06858 square feet

To convert this to square inches, we multiply by the conversion factor (12 inches/foot)^2:

A_total_gray = 7.06858 * (12)^2

= 1016.7048 square inches

Rounding this to the nearest square inch gives:

A_total_gray ≈ 1017 square inches

So the correct answer is (D). 1017 square inches.

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