If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30 ?

Answer:

time series

Step-by-step explanation:

A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time.

After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa. Thus mom gave $ 320 to each girl

Solution:

Given that Lily and Elsa are both college students

Before mom gave them this months allowance lily had $750 and Elsa had &215

Amount (in dollars) with Lily and Elsa already is given as:

amount with Lily = $ 750

amount with Elsa = $ 215

After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa

Let "x" be the equal amount of money which mom gave to Lily and Elsa

Now amount with Lily and Elsa after mom gave equal amount is:

amount with Lily = amount with Lily already + x

amount with Lily = 750 + x

amount with Elsa = amount with Elsa already + x

amount with Elsa = 215 + x

Given that lily had twice as much money as Elsa

Amount with lily = 2(amount with elsa)

750 + x = 2(215 + x)

750 + x = 430 + 2ax

2x - x = 750 - 430

x = 320

Therefore mom gave $ 320 to each girl

Answer:

Each DVD cost for Hector at $17.80.

Step-by-step explanation:

Total Money Spent = $36.75

Number of DVD to buy = 2

Sales tax = $2.15

Amount of Coupon to be used = $1.00

We need to find the cost of each DVD.

Let the Cost of each DVD be 'x'.

Now We can say that Total Money spent on DVD's is equal to Number of DVD to buy multiplied by Cost of each DVD plus Sales Tax minus Amount Coupon used.

Framing in equation form we get;

[tex]2x+2.15-1=36.75[/tex]

Solving the equation to find the value of x we get;

[tex]2x+1.15=36.75\\\\2x=36.75-1.15\\\\2x= 35.6\\\\x=\frac{35.6}{2}= \$17.8[/tex]

Hence Each DVD cost for Hector at $17.80.

Answer:

12

Step-by-step explanation:

3x + 7 = 5x - 17

5x - 3x = 7 + 17

2x = 24

x = 12

Answer:

The first option is the correct one, the area of the shaded portion of the circle is

[/tex](5 \pi -11.6)ft^2[/tex]

Step-by-step explanation:

Let us first consider the triangle + the shadow.

The full area of the circle is the radius squared times pi, so

A=[tex](5 ft)^2 \cdot \pi \\25 ft^2 \cdot \pi[/tex]

Since [tex]\frac{72^{\circ}}{360^{\circ}}=\frac{1}{5}[/tex], the area of the triangle + the shaded area is one fifth of the area of the whole circle, thus

[tex]A_1=\frac{1}{5}25 ft^2 \cdot \pi\\ =5 ft^2 \cdot \pi[/tex]

If we want to know the area of the shaded part of the circle, we must subtract the area of the triangle from [tex]A_1[/tex].

The area of the triangle is given by

[tex]A_{triangle}=\frac{1}{2}\cdot (2.9+2.9)ft \cdot 4 ft\\= 11.6 ft^2[/tex]

Thus the area of the shaded portion of the circle is

[tex]A_1-A_{triangle}=5 \pi ft^2-11.6ft^2\\= (5 \pi -11.6)ft^2[/tex]

Answer:

A

Step-by-step explanation: i did the test and review

Answer:

The answer is option is (4) y ≤ 14

Step-by-step explanation:

The given function, y = - 0.5[tex](x + 10)^{2} + 14[/tex]

We have to find the range of this function. If we take the first part of the function alone we can see that it is always negative or zero. So the maximum value of the function is 14.

This happens when we make the first part zero and for that we put x = -10.

So the maximum value of the function occurs at x = -10 and that value is y = 14.

Hence the range is y ≤ 14.

The answer is option is (4) y ≤ 14

Answer:

Step-by-step explanation:

All the masses here are based on the main mass of the sand.  So we will call sand "x".  If there is two times as much cement as sand, then cement is 2x; if there is three times as much stone as sand, then stone is 3x.  All of these added together equal a mass of 600 kg:

x + 2x + 3x = 600 so

6x = 600 and

x = 100 kg

There are 100 kg of sand.  That means that there is 200 kg of cement and 300 kg of stone

Answer:

200 kg

Step-by-step explanation:

Total weight of the mixture = 600kg

Let the weight of the cement in the mixture be x kg.

According to the problem statement, there is twice as much cement as sand, therefore the weight of sand relative to cement will be 1/2, i.e.

sand weight = 1/2x =0.5x

Similarly, weight of stone will be three times as much as sand.

Meaning, stone weight = 3*0.5x=1.5x

Total weight of all the components will be

cement weight + sand weight  + stone weight  =

x + 0.5x + 1.5x = 3x

But 3x = 600,

x = 600/3= 200 kg

Answer:

Step-by-step explanation:

[tex]E=\frac{1}{2}mv^2[/tex]

All the variables on the right are being multiplied together then the whole mess is being divided by 2.  Let's get rid of the 2 first.  The undoing of division is multiplication, so we will begin by multiplying both sides by 2 to get

[tex]2E=mv^2[/tex]

Next we will move the m. The undoing of multiplication is division.  So we divide both sides by m to get

[tex]\frac{2E}{m}=v^2[/tex]

The undoing of a square is to take the square root, so we will do that to both sides giving us, finally

[tex]\sqrt{\frac{2E}{m} }=v[/tex]

Answer:

d

Step-by-step explanation:

Answer:

a) A response of 8.9 represents the 92nd ​percentile.

b) A response of 6.6 represents the 62nd ​percentile.

c) A response of 4.4 represents the first ​quartile.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5.9

Standard Deviation, σ = 2.2

We assume that the distribution of response is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) We have to find the value of x such that the probability is 0.92

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.92[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(z<1.405) = 0.92[/tex]

[tex]\displaystyle\frac{x - 5.9}{2.2} = 1.405\\x = 8.991 \approx 8.9[/tex]

A response of 8.9 represents the 92nd ​percentile.

b) We have to find the value of x such that the probability is 0.62

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.62[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(z<0.305) = 0.92[/tex]

[tex]\displaystyle\frac{x - 5.9}{2.2} = 0.305\\x = 6.571 \approx 6.6[/tex]

A response of 6.6 represents the 62nd ​percentile.

c) We have to find the value of x such that the probability is 0.25

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.25[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(z<0.305) = -0.674[/tex]

[tex]\displaystyle\frac{x - 5.9}{2.2} = -0.674\\x = 4.4172 \approx 4.4[/tex]

A response of 4.4 represents the first ​quartile.

Answer:

187 eggs

Step-by-step explanation:

Correct Question:

After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs left over. Each carton holds 12 eggs. How many eggs did Dale collect?

Dale filled up each carton with 12 eggs (that's the full capacity.

Dale filled up 15 full cartons.

So, the eggs he collected in carton:

15 * 12 = 180 eggs

He still had 7 left over, so total number of eggs that Dale collected is:

180 + 7 = 187 eggs

Answer: [tex]\$1.99[/tex]

Step-by-step explanation:

The missing figure is attached.

For this exercise you need to analize the information provided.

You can observe in the picture attached that the cost of a package of wrapping paper is $3.76 and each bow costs $1.05.

Since Inez bought 1 package of wrapping paper and 4 bows, you get that the total amount of money she spent was:

[tex]Total=\$3.76+4(\$1.05)\\\\Total=\$7.96[/tex]

According to the data given in the exercise, Inez wrapped 4 identical gifts.  So, let be "x" the cost for wrapping each gift.

This is:

[tex]x=\frac{\$7.96}{4}\\\\x=\$1.99[/tex]

1.99

Step-by-step explanation:

Answer: The outbound trip is 18 miles per hour

Step-by-step explanation:

Let x represent the speed of the plane.

An aircraft carrier made a trip. Let us assume that this trip was outbound. The trip there took 5 hours.

Distance = speed × time. Therefore

Distance = 5x

The trip back took 6 hours. It averaged 3 mph faster on the trip there then on the return trip. This means that the speed on the trip back is x - 3 mph.

Distance = 6(x-3) = 6x - 18

Since the distance is the same,

5x = 6x - 18

6x - 5x = 18

x = 18

The speed on return or inbound trip would be 18 - 3 = 15 mph

Answer:

Only one.

Step-by-step explanation:

Given that there are 25 cookie of the same type in a cookie jar.

We have to select 4 cookies from these 25.

Since they are all the same type, they are identical.

The question is

How many ways can you choose 4 cookies from a cookie jar containing 25 cookies of all the same type?

There is no difference if we take any four cookies from these 25.

Hence no of different ways = 1

Only one is the answer.

Answer:

Step-by-step explanation:

25 P4=25×24×23×22=303600

Answer:

  no

Step-by-step explanation:

The ratio is ...

  boys : girls = 42 : 56 = (14·3) : (14·4) = 3 : 4 . . . . not 5:6

Emma is not correct.

Answer:

2 + (13/4)x = 1/2 + (11/2)y

Step-by-step explanation:

Let each jar of paint used by Liam be x

Let each jar of paint used by Evan be y.

Liam uses 2 quarts of yellow paints and adds 3 1/4 jars of blue paint. so we have

2 + 3 1/4x

= 2 + (13/4)x

Since Evan also uses 1/2 quarts of yellow paints and add 5 1/2 jar of red paint, we have

1/2 + 5 1/2y

= 1/2 + (11/2)y

Since they end up with the same volume of paint, we have

2 + (13/4)x = 1/2 + (11/2)y

Final answer:

The equation to show that Liam and Evan end up with the same volume of paint, considering all quantities are in quarts, is 2 + 3.25 = 0.5 + 5.5.

Explanation:

To solve the problem where Liam and Evan end up with the same volume of paint, we can write an equation that sets the total volume of paint used by each person equal to each other. Since Liam uses 2 quarts of yellow paint and adds 3 1/4 (which is equivalent to 3.25) jars of blue paint and Evan uses 1/2 quart of yellow paint and adds 5 1/2 (equal to 5.5) jars of red paint, the equation comparing their total amounts of paint in quarts can be written as:

2 + 3.25 = 0.5 + 5.5

Before writing this equation, we need to ensure that both expressions represent quantities in the same unit. We confirm that all the amounts are given in quarts, so there is no need to convert units in this case. The equation illustrates that the total volume of paint used by Liam and Evan is equal.

Answer:

[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]

So for this case the best answer would be:

d. 218’

Step-by-step explanation:

Previous concepts

Foot front : "Is a foot measured along the front of a piece of property".

Solution to the problem

For this case we need to begin finding the number of frontage feet, with the following formula:

[tex]Frontage fronts=\frac{Amount paid}{Unitary price}[/tex]

And for this case if we replace the values given we got:

[tex]Frontage fronts=\frac{100000}{250}=400 fromtage foot[/tex]

Now we need to convert the area to square feet. And we know that:

[tex] 1 acre= 43560 ft^2[/tex]

And converting we got: [tex]2 acre *\frac{43560 ft^2}{1 acre}=87120 ft^2[/tex]

Now we can divide the total area by the total of frontage feer and we got:

[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]

So for this case the best answer would be:

d. 218’

Answer:

The answer to your question is letter A

Step-by-step explanation:

Process

1.- Find two points of the line

A (1, 4)    B ( -1, 5)

2.- Find the slope of the line

     [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

     [tex]m = \frac{-5 - 4}{-1 - 1}[/tex]

     [tex]m = \frac{-9}{-2} = \frac{9}{2}[/tex]

3.- Find the equation of the line

     y - y1 = m(x - x1)

    y - 4 = 9/2(x - 1)

    2y - 8 = 9x - 9

    9x - 2y = - 9 + 8

    9x - 2y = - 1

4.- Convert the equation to a inequality,

    9x - 2y ≤ -1

Answer:

60 lines can be typed in the page

Step-by-step explanation:

Given:

Length of the page  = 17 inches

Length of the margin = 0.5-inch

length of one line  = 4/15

To Find:

The number of lines that can be typed on a page

Solution:

Let the number of line  that can be typed be  n

then

n <= [tex]n \leq \frac{\text { total length of the page}-\text {top margin} - \text{ bottom margin}}{\text{size of each line }}[/tex]

the top and bottom margins are 0.5 inches each

so we will be having

=> [tex]n \leq \frac{17 -0.5-0.5}{\frac{4}{15}}[/tex]

=>[tex]n \leq \frac{16}{\frac{4}{15}}[/tex]

=>[tex]n \leq \frac{16\times 15}{4}[/tex]

=>[tex]n \leq\frac{240}{4}[/tex]

=> [tex]n \leq 60[/tex]

Answer:

Step-by-step explanation:

1. ∠PQR is an alternate interior angle with the one marked 40°, so it has the measure 40°.

∠PRQ is an alternate interior angle with the one marked 60°, so it has the measure 60°.

Among the answer choices, the one describing ∠PQR as 40° is the only correct one.

__

2. ∠BAD = 2×∠BAE

  130 = 2(9x + 2) . . . substitute the given expressions

  65 = 9x + 2 . . . . . divide by 2

  63 = 9x . . . . . . . . .subtract 2

  7 = x . . . . . . . . . . . .divide by 9

__

3. Think again. Anything being rotated follows a circular path. Circular paths with different radii and the same center are concentric circles.

Straight lines connecting the pre-image and image points will be parallel (and different lengths), but the question is concerned with paths, not endpoints.

Why the path is described as "concentric circles," we're not sure. The path for a 90° rotation will be a 90° arc. It is perfectly reasonable to describe the paths of the two points as concentric arcs, rather than concentric circles. See the attachment.

__

4. Correct. The triangle inequality requires the sum of the two shortest side lengths exceed the longest side length. Here, that means 2+5 > 5 (true). The "toothpicks" meet the requirements of the triangle inequality, so will make a triangle.

The "triangle sum theorem" has to do with angles, not side lengths.

Answer:

(c) [tex]\left\ ({{4} \atop {1}} )\right.[/tex] [tex]0.25^{1} 0.75^{3}[/tex]

Step-by-step explanation:

As given in the statement, we have:

Out of 4 games pieces, 1 is winner.

Probability to win =p= [tex]\frac{1}{4}[/tex]

Jeff has game pieces = n = sample size = 4

As we need to find the probability that he wins exactly 1 prize, we will use binomial probability here :

[tex]P (X = k) = \left\ ({{n} \atop {k}} )\right. p^{k} (1-p)^{n-k} \\[/tex]

Evaluating at k=1, (k=1 as we need to find probability for exactly 1 prize won)

put n = 4, p =[tex]\frac{1}{4}[/tex]

P (X = 1) =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (1-0.25)^{4-1}[/tex]

P =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (0.75)^{3}[/tex]

Which is the probability that he wins exactly 1 prize and is option c.

Probability (Jeff wins 1 price in 4 game pieces) = C] [tex](4 c 1)(0.25)^1(0.75)^3[/tex]

Important Information : Probability (Winning a price) = 1 / 4 = 0.25

Probability (Not winning price) = 1 - Pr (Winning Price) = 1 - 0.25 = 0.75

Using Binomial Probability : Pr (X = r) = [tex]N c r . P^r . Q^(n-r)[/tex] .

Here N = number of trials (4 game pieces here) , P = Probability of Success (of winning price = 0.25) , R = Number of Success (1 price) , Q = Probability of failure (of not winning price = 0.75) ,

So, Probability = [tex]4 c 1 (0.25)^1 (0.75)^3[/tex]

To learn more about Probability, refer https://brainly.com/question/13609688?referrer=searchResults

Final answer:

To find the probability that A.J. and M.J. finish their jobs within a certain time, we need to calculate the z-score for the given values and use a standard normal distribution table or a calculator to find the probability.

Explanation:

(a) To find the probability that A.J. finishes in less than 900 minutes, we need to calculate the z-score (standard score) for the value 900 using the formula: z = (x - mean) / standard deviation. In this case, x = 900, mean = 50 minutes, and standard deviation = 10 minutes. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability.

(b) To find the probability that M.J. finishes in less than 900 minutes, we use a similar process as in part (a), but with different mean and standard deviation values. In this case, x = 900, mean = 52 minutes, and standard deviation = 15 minutes.

(c) To find the probability that A.J. finishes before M.J., we can compare the means of the two distributions. Since A.J.'s mean is lower than M.J.'s mean, the probability of A.J. finishing before M.J. is higher.

Answer

Cluster sampling. See explanation below.

Step-by-step explanation:

For this case they not use random sampling since we are selecting people from flights. Because we select just 5 random flights.

Is not stratified sampling since we don't have strata clearly defined on this case, and other important thing is that in order to apply this method we need homogeneous strata groups and that's not satisfied on this case.

Is not convenience sampling because they NOT use a non probability method in order to select the people from the flights.

So then the only possible method is cluster sampling since we have clusters clearly defined (Passengers from the airlines), and we satisfy the condition of homogeneous characteristics on the clusters and an equal chance of being a part of the sample, since we are selecting RANDOMLY, the 5 flights to take the information.

Answer:

The answer to your question is below

Step-by-step explanation:

1)  Given

2)  Subtraction property of equality (because we are subtracting the same quantity on both sides).

3) Simplification

4) Subtraction property of equality ( because we are subtracting the same quantity on both sides).

5) Simplification

6) Multiplication property of equality (because we are multiplying the same quantity on both sides).

7) Simplification

Answer:

-6 and -7 are the roots

Step-by-step explanation:

The quadratic equation given is:

[tex]x^{2}+13x=-42\\Taking\ -42\ to\ left\ hand\ side\ we\ get\\x^{2} +13x+42=0[/tex]

We can factorise the equation as:

[tex]x^{2}+6x+7x+42=0\\(x^{2}+6x)+(7x+42)=0\\[/tex]

Taking x common from the first bracket and 7 common from the second bracket we get:

[tex]x(x+6)+7(x+6)[/tex]

Taking (x+6) common from both terms we get:

[tex](x+6)(x+7)=0[/tex]

x= -6 or x=-7

Hence -6 and -7 are the roots of the given quadratic equation.

Answer:

Number of week day hours purchased  is 5

Step-by-step explanation:

Total number of Parking hours purchased = 26 parking hours

Parking cost on weekdays = $2 per hour

Parking costs on weekends = $10 per hour

Total amount spent on parking =  $220.

To Find:

Number of week days purchased = ?

Solution:

Let  

The number of week days purchased be x

The number of weekends purchased be  y

We know that the total hours purchased is 26

So,

x+y = 26

y = 26-x------------------------------------------------------(1)

Now the total cost is 220

(Total number of weekdays X cost per weekday ) +(Total number of weekends + cost per weekend) =220

Substituting the values

=>[tex]x\times 2 + y \times 10[/tex] = 220

=>[tex]x \times 2 + (26-x) \times 10 =220[/tex]

=>2x + 260 -10x =220

=>260 -8x = 220

=>260 -220 =8x

=>40 = 8x

=>x=[tex]\frac{40}{8}[/tex]

x= 5-------------------------------------------(2)

Now substituting (2) in (1) we get

y= 26-5

y= 21

Answer:

Bakery will sell  [tex]4w+6[/tex] loaves of bread next year.

Step-by-step explanation:

Given:

Number of loaves of bread sold last year = 'w'

Now Given:

This year, the bakery sold three more than twice the number of loaves of bread sold last year.

Framing in equation form we get

Number of loaves of bread sold this year = [tex]2w+3[/tex]

Also Given:

next year the bakery plans on selling twice the number of loaves of bread sold this year.

framing in equation form we get;

Number of loaves of bread bakery will sell next year = [tex]2(2w+3) = 4w+6[/tex]

Hence Bakery will sell  [tex]4w+6[/tex] loaves of bread next year.

The bakery expects to sell  4w + 6  loaves of bread next year.

Let's break down the problem step by step:

1. Number of loaves sold this year:

  - Last year, the bakery sold  w  loaves of bread.

  - This year, the bakery sold three more than twice the number of loaves sold last year.

  - Therefore, the number of loaves sold this year is:

   [tex]\[ 2w + 3 \][/tex]

2. Number of loaves expected to be sold next year:

  - Next year, the bakery plans to sell twice the number of loaves sold this year.

  - Therefore, the number of loaves expected to be sold next year is:

   [tex]\[ 2 \times (2w + 3) \][/tex]

3. Simplify the expression:

  - Distribute the 2 in the expression:

  [tex]\[ 2 \times (2w + 3) = 2 \times 2w + 2 \times 3 = 4w + 6 \][/tex]

Therefore, the bakery expects to sell  4w + 6  loaves of bread next year.

Answer:

9.692%

Step-by-step explanation:

We have been given that a manufacturing process produces a critical part of average length 120 ​millimeters, with a standard deviation of 3 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected.

5 millimeters below mean would be [tex]115[/tex] and 5 millimeters above mean would be [tex]125[/tex].

Corresponding z values for 115 and 125 would be:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{115-120}{3}[/tex]

[tex]z=\frac{-5}{3}[/tex]

[tex]z=-\frac{5}{3}[/tex]

[tex]z=\frac{125-120}{3}[/tex]

[tex]z=\frac{5}{3}[/tex]

Now, we need to find [tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})[/tex] using normal distribution table.

[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=P(z<-1.66)+P(z>1.66)[/tex]

We know that [tex]P(z>1.66)=1-P(z<1.66)[/tex].

[tex]P(z>1.66)=1-0.95154 [/tex]

[tex]P(z>1.66)=0.04846[/tex]

[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.04846+0.04846[/tex]

[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.09692[/tex]

Now, we need to convert 0.09692 into percentage as:

[tex]0.09692\times 100\%=9.692\%[/tex]

Therefore, 9.692% of parts must be​ rejected on​ average.

About 0% of the parts would be​ rejected, on​ average.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where μ is the mean, x = raw score and σ is the standard deviation.

Given μ = 120, σ = 3. For z > 5:

P(z > 5) = 1 - P(z < -38.3) = 1 - 1 = 1 = 0%

About 0% of the parts would be​ rejected, on​ average.

Find out more on Z score at: https://brainly.com/question/25638875

Answer:

  ? = 47°

Step-by-step explanation:

The angle marked B at the intersection of the secants is half the difference of the arcs they intercept.

  ∠B = (DE -AC)/2 = (142° -48°)/2 = 47°

The unknown angle is 47°.

Answer:

x=4.8473 cups

Step-by-step explanation:

Concentration of Liquids

It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by

[tex]\displaystyle C=\frac{x}{y}[/tex]

It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.

Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is

x-1 cups of juice.

The new concentration is

[tex]\displaystyle \frac{x-1}{x}[/tex]

The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is

[tex]\displaystyle x-1-\frac{x-1}{x}[/tex] cups of juice.

Simplifying, the cups of juice are

[tex]\displaystyle \frac{\left (x-1\right)^2}{x}[/tex]

The new concentration is

[tex]\displaystyle \frac{\left (x-1\right)^2}{x^2}[/tex]

For the third time, we now have

[tex]\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}[/tex] cups of juice.

Simplifying, the final amount of juice is

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^2}[/tex]

And the final concentration is

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}[/tex]

According to the conditions of the question, this must be equal to 50% (0.5)

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5[/tex]

Taking cubic roots

[tex]\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}[/tex]

[tex]\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}[/tex]

Operating and joining like terms

[tex]\displaystyle x-\sqrt[3]{0.5}\ x=1[/tex]

Solving for x

[tex]\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}[/tex]

[tex]x=4.8473\ cups[/tex]

Let's test our result

Final concentration:

[tex]\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5[/tex]

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The correct option would be A. an = 3 + 4n

You may test my substituting values in:

3 + 4(1) = 7

3 + 4(2) = 11

etc

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Answer:

a

Step-by-step explanation: