a rectangular page is to contain 30 square inches of print hte margins one ach side are 1 inch find the idmensions of hte page such that ht eleast amount of pape ris used

Answers

Answer 1

The length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

Now, According to the question:

The area of a rectangular page can be calculated using the area of a rectangle which is just the product of the length and the width of the page.

                                                         A = lw

Here, l represents the length of the page and w represents the width of the page.

Determine the dimensions of a page given that the printed area is [tex]30in^2[/tex]

and the page has margins on each side, each having a width of 1in.

We will first set up an equation using the details that we know. We know that the printed area is  [tex]30in^2[/tex] We can let x be the length of the printed area and y be the width of the printed area. Assuming that the printed area is rectangular, the area is

[tex]A_p=xy[/tex]

30 = xy

[tex]y = \frac{30}{x}[/tex]

Now, we want to minimize the amount of paper used. The length of the entire page would be x + 2 since we have to consider the 1-in margins at the top and the bottom. Similarly, the width would be y+ 2  since we have to consider the margins at the sides. The area of the page is as follows.

A = (x+2)(y + 2)

We can substitute the value of y in terms of x.

A(x) = (x + 2)([tex]\frac{30}{x} +2[/tex])

A(x) = x ([tex]\frac{30}{x}[/tex]) + 2x + 2[tex](\frac{30}{x} )[/tex] + 4

A(x) = 30 + 2x + [tex]\frac{60}{x}[/tex] + 4

A(x) = 34 + 2x + [tex]\frac{60}{x}[/tex]

We want to minimize this area, so we will apply differentiation to this function. By finding its derivative and equating it to zero, we can find the value/s of x that will minimize the area.

A'(x) = [tex]2-\frac{60}{x^2}[/tex]

0  = [tex]2-\frac{60}{x^2}[/tex]

[tex]2 =\frac{60}{x^2}[/tex]

[tex]2x^2=60\\\\x^{2} =\frac{60}{2}\\ \\x^{2} =30\\\\x =[/tex]±[tex]\sqrt{30}[/tex]

Since we are dealing with dimensions, we can only choose the positive value, x =√30. Now, to determine if this would really minimize the area of the page, we can substitute it into the second derivative of the function. If the result is positive, the value of x would give the minimum area.

A"(x) = [tex]\frac{120}{x^3}[/tex]

[tex]A"(\sqrt{30} )=\frac{120}{(\sqrt{30})^3 }[/tex]

[tex]A"(\sqrt{30} )=0.73[/tex]

We can now use the value of x to find the dimensions of the page. Take note that the dimensions of the page are x + 2 and y + 2

x + 2 = √30 + 2

y + 2 = [tex]\frac{30}{x}[/tex] + 2

y +2  = [tex]\frac{30}{\sqrt{30} }[/tex] + 2

y + 2 = [tex]\sqrt{30}+2[/tex]

Therefore, the length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

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Related Questions

Please help me with this question.

Answers

The solution to the system of equations in this problem is given as follows:

X = [28571

      14286].

How to solve the system of equations?

The system is defined by the following equation:

X = DX + E.

The matrices D and E are known, while X = [A; B] is the output matrix. Applying the multiplication of matrices, the system of equations is defined as follows:

0.2A + 0.3B = 10000.0.5A + 0.4B = 20000.

Inserting this system into a calculator, the solution is given as follows:

A = 28571.B = 14286.

Hence the matrix X is given as follows:

X = [28571

      14286].

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Traveling 120km total, 1st 59km are 90km P/h. Remaining km are 50km P/h. How long does the trip take total?

Answers

The total trip took a total of 1.87 hours.

What is the speed of an object?

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: Total distance=120 km and 59 km at 90 km/hr and the remaining distance at 50 km/hr

Remaining distance= 120-59

                                 =61 km

Thus for the first 59 km the time it took was

Time= Distance/ Speed

       = 59/90

       =0.65 hr

Similarly time taken for the second part of the journey is = 61/50

                                                                                               =1.22

Hence, total time taken for the trip is 1.22+0.65=1.87 hr.

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someone help !!
geometry: find the value of x

Answers

Answer:

x = 18

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the 5 interior angles and equate to 540

3x + 23 + 95 + 7x - 4 + 90 + 9x - 6 = 540

19x + 198 = 540 ( subtract 198 from both sides )

19x = 342 ( divide both sides by 19 )

x = 18

In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothing and carry‑on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not normally distributed, especially when the population includes both men and women, but they are not very non‑Normal. A commuter plane carries 22 passengers. What is the approximate probability P that the total weight of the passengers exceeds 4500 pounds? Use the four‑step process to guide your work. Give your answer as a percentage precise to two decimal places. P=___?

Answers

The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than [tex]$\frac{4500}{22}[/tex]=204.545

[tex]$$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$[/tex]

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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my’s Annual Expenditures

Rent $ 8,580.00

Utilities $ 3,480.00

Internet & Phone $ 1,896.00

Entertainment $ 2,232.00

Student Loan Payment $ 4,116.00

Home & Auto Insurance $ 1,164.00

Food $ 6,000.00

Car Payment & Gas $ 2,820.00

Travel $ 1,200.00

Savings $ 1,200.00

Personal Expenses $ 1,847.00

Pet Expenses $ 965.00

Business Expenses $ 4,800.00
Q1. Amy’s day job is as a secretary at a law firm. After taxes and health insurance, she nets $1550 bi- weekly. How much does Amy net in a year from her day job?
Q2. Based on her net income and annual expenditures summary, by how much did Amy over or under spend this year?

Answers

Part a: Amy's net amount in a year from her day job is found as $40411.

Part b: Amy under spend this year by amount $8331.

Define the term annual expenditure?Just before annual contribution margin, all expense items in the profit and loss statement, including operating costs including finance charges, are referred to as annual expenditure.

Part a:

The calculation is done bi- weekly.

Total days = 2*7 = 14.

Net amount = $1550.

Net amount for the year = (1550/ 14)*365

Net amount for the year = $40411

Thus, Amy's net in a year from her day job is found as $40411.

Part b:

Total amount spend : Sum of all expenditures.

Total amount spend : $32,080

Difference =  $40,411 - $32,080

Difference =  $8331

Thus, based on her net income as well as annual expenditures summary,

Amy under spend this year by amount $8331.

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Find the value of M and N​

Answers

Answer: n=110, m=110

Step-by-step explanation: I think m=110 because of vertical angles. m might also equal 70.

if monique wanted to run 7/8 mile and she went to the school track which was one quater of a mile long how lany laps would she have to run

Which of the following questions could I use to find the answer check all that apply.

A. L x 1/4=7/8. YES OR NO

B. 7/8 x 1/4 = L. YES OR NO

C. 7/8 X 4=L. YES Or NO

D. L/ 7/8 = 1/4. YES OR NO


hURRY

Answers

if Monique wanted to run 7/8 mile and she went to the school track which was one quarter of a mile long. The number of lap Monique will complete is

C. 7/8 X 4 = L.

What is a lap in race?

One complete lap around a track or across a pool, from one end to the other: The track has 400 meters or approximately 25 mile per lap.

A lap is end to end of a track and in the problem a lap is 1/4 mile and Monique wants to complete 7/8 miles'. the comparison is as follows

assuming the number of laps is L

1 lap = 1/4 mile

L laps = 7/8 miles

cross multiplying

1 * 7/8 = L * 1/4

multiplying by 4 for each side

1 * 7/8 * 4 = L * 1/4 * 4

1 * 7/8 * 4 = L * 1

7/8 * 4 = L

hence option C is correct

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show that if xt x is not invertible, then at least one column of x is a linear combination of the others. this implies that there is only one way in which problem with invertibility of xt x may arise'

Answers

If the matrix xt x is not invertible, then its determinant is equal to 0. A determinant of 0 implies that the matrix is singular, meaning that its columns are linearly dependent.

This means that one of the columns of x can be expressed as a linear combination of the other columns, which implies that there is only one way in which the invertibility problem may arise: when the columns of the matrix x are linearly dependent.

If the determinant of xt x is equal to 0, then at least one column of x can be expressed as a linear combination of the others. For example, if column c can be expressed as a linear combination of columns a and b, then we can write:

c = k1a + k2b

where k1 and k2 are constants. This means that the information in column c is already represented in columns a and b, and so it is redundant.

This is the only way in which the invertibility problem of xt x may arise. If the columns of the matrix are linearly independent, then the determinant of xt x will be non-zero, and the matrix will be invertible.

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Your question is incomplete, but most probably, the full question was:

Proof that [tex]X^{T} X[/tex] is not invertiblethen at least one column of x is a linear combination of the others. This implies that there is only one way in which a problem with the invertibility of xt x may arise

help it is for a grade tomorrow

Answers

Answer:

Step-by-step explanation:

customers: 6

minutes: 40

Express each of the following as the sum Of a whole number and a fraction 9/7

Answers

Answer:

1 + 2/7

Step-by-step explanation:

9/7 =

(7+2) / 7 =

7/7 + 2/7 =  ==> use distribution

1 + 2/7  ==> 7/7 = 1, so simplify the expression

3. A dilation is represented in the following table. Determine the scale factor for the dilation.
Express your answer in function notation (x,y) → (kx,ky).
Pre-Image
Image
I
(2,4)
(1, 2)
(1, 0)
(0.5, 0)
(-4,-1)
(-2,-0.5)

Answers

The scale factor of the dilation, expressed in function notation, (x, y) → (k·x, k·y), is (x, y) → (0.5·x, 0.5·y)

What is a dilation transformation?

A dilation transformation is a transformation in which the dimensions of the image are obtained by multiplying the dimensions of the pre-image by a value, known as a scale factor of the dilation.

The possible table, based on the similarities of the coordinate points can be presented as follows;

Pre-Image [tex]{}[/tex]    Image

(2, 4) [tex]{}[/tex]             (1, 2)

(1, 0)  [tex]{}[/tex]            (0.5, 0)

(-4, -1) [tex]{}[/tex]           (-2, -0.5

The specified formula for the image, following the dilation of the point (x, y) by a scale factor of k is; (x, y) → (k·x, k·y)

Therefore, we get;

k = k·x/x = k·y/y

The comparison of the points in the table with the points (x, y), and (k·x, k·y), indicates that we get;

When (x, y) = (2, 4) and (k·x, k·y) = (1, 2)

Therefore;

k = k·x/x = k·y/y = 1/2 = 2/4  = 0.5

The scale factor of the dilation , k = 0.5, therefore;

(x, y) → (0.5·x, 0.5·y)

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Gina is going to buy 100 stickers

Answers

Gina should buy from Stickers4u.

What is multiplication?

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Gina is going to buy 100 stickers.

If she buys from the shop - Stickers4u,

then the cost is,

= 100/25 x 2.15

= 4 x 2.15

= 8.6.

And if she buys from the World stationary,

then the cost is,

= (100 - 50)/10 x 1.65

= 5 x 1.65

= 8.25

Therefore, she should buy from Stickers4u.

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Every day, Patrick's orange juice stand uses 3/4 of a bag of oranges. How many days will 1 1/2 bags of oranges last?

Answers

Answer:

2 days

Step-by-step explanation:

We want to divide 1 1/2 by 3/4

1 1/2 ÷ 3/4

Change the mixed number into an improper fraction.

3/2 ÷ 3/4

Copy dot flip

3/2 * 4/3

Rewrite

3/3 * 4/2

1 * 2

2

It will last 2 days

Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
x-7=-2

Answers

The equation x - 7 = -2 can be solved for x by adding 7 to both sides:

x - 7 + 7 = -2 + 7
x = 5

This equation has a unique solution: x = 5. This means that there is exactly one value of x that satisfies the equation.

To support the conclusion that the equation has a unique solution, we can substitute x = 5 back into the equation and check that it is true:

5 - 7 = -2
-2 = -2

Since the left-hand side and the right-hand side are equal, the equation is true for x = 5, and it has a unique solution

If m


BAC is 48


, what is the measure of


GAE?

Answers

Answer:

132

Step-by-step explanation:

180 - 48 = 132   These angles are supplemental.  They add to 180

Answer:

<GAE = 48

Step-by-step explanation:

<BAC = 48

<BAC = <GAE

two letters without replacement from the three letters a b and c how many ways can this be done if the order of choice is taken into consideration how many ways can this be done if the order of the choices is not taken into consideration​

Answers

Answer:

If order is considered = 6

If order is not considered = 3

Step-by-step explanation:

If order is to be taken in consideration then the following values can be taken:

a, b

a, c

b, a

b, c

c, a

c, b

Total = 6 ways

If order is not taken in consideration then the following values can be taken:

a, b

a, c

b, c

Total = 3 ways

Evaluate the limit.

Answers

Refer to the attached image.

Point P is on line segment O Q . Given O Q = 11 OQ=11 and O P = 9 , OP=9, determine the length P Q ‾ . PQ ​

Answers

Answer: PQ is 9 units.

Step-by-step explanation:

The length of PQ can be found using the proportion of OQ and OP.

(PQ / OQ) = (OP / OQ)

PQ = (OP / OQ) * OQ

Substituting in the given values:

PQ = (9 / 11) * 11

PQ = 9

Therefore, the length of PQ is 9 units.

Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + [1/(32√2)] + [1/(243√3)] + [1/(1024√4)] + [1/(3125√5)] + ….
p = _____
A. converges B. diverges

Answers

The answer is B. diverges.

Theorem 9.11 states that if the sequence of positive terms (an) satisfies the condition 1/an^p converges, then the p-series ∑an converges if p > 1 and diverges if p ≤ 1. In this case, the positive terms of the sequence are given by [1/(n^(3/2))]. So, [1/an^p] = [1/(n^(3/2))^p] = [1/n^(3p/2)].

For the series to converge, we need [1/an^p] to converge, or [1/n^(3p/2)] to converge.

If 3p/2 > 1, then [1/n^(3p/2)] converges and the series converges.

If 3p/2 ≤ 1, then [1/n^(3p/2)] diverges and the series diverges.

So, to determine the value of p, we need to find the value of p such that 3p/2 = 1. Solving for p, we find that p = 2/3.

Since 2/3 ≤ 1, the series diverges. Therefore, the answer is B. diverges.

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i need help solving rhis problem please show your work​

Answers

The length of the GH is 4, when H is the midpoint of GI.

What is midpoint of a line?

An area of a line that connects two distinct locations is referred to as a line segment. It is the least path between two places that can be determined to have a length.

A line segment's midpoint is the point on the segment when it is divided into two similar segments. The point on a line segment that is equally spaced from the two terminating points is known as the midpoint of the segment.

Given that H is the midpoint of GI.

Then we can say that,

GI / 2 = GH

Substitute the equations of the length of GH and GI as given:

(9x - 19) / 2 = 3x - 5

9x - 19 = 2(3x - 5)

9x - 19 = 6x - 10

9x - 6x = -10 + 19

3x = 9

x = 3

Substitute the value of x in the equation of the length of the segment GH thus:

GH = 3x - 5

GH = (3)(3) - 5

GH = 4

Hence, the length of the GH is 4, when H is the midpoint of GI.

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Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.
[1 h 4
3 6 8]

Answers

The value of h can be any value other than 2.

Value of h for Consistent System

The augmented matrix of a consistent linear system must have a unique solution, which means the determinant of the coefficient matrix must be non-zero.

For the given matrix, the coefficient matrix is:

       [1 h

        3 6]

The determinant of this matrix is (1 * 6) - (3 * h) = 6 - 3h.

For the determinant to be non-zero and the system to be consistent, 6 - 3h must not be equal to zero, so h cannot be equal to 2.

Therefore, the value of h can be any value other than 2.

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please help me will give u extra points :)

Answers

From the graph, the compound inequality represented is x < -2 and x > 5

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequalities shows the non equal comparison of two or more numbers and variables. Compound inequality is an inequality that is composed of more than one inequality.

From the graph, the inequality is not a solid circle, so it is either > or < sign.

From the graph, the inequality shown is x < -2 and x > 5

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A 9 footbpiece of twine costs $8.64. What is the price per inch?

Answers

Answer: 0.08 dollars

Step-by-step explanation:

8.64 divided by 9 = 0.96

0.96 divided by 12 = 0.08

What is the volume of the cube shown?
WILL GIVE BRAINLEST​

Answers

Answer:

11.390625 in^3

Step-by-step explanation:

2.25^3 = 11.390625 in^3

Given the following diagram what can you conclude?

Answers

all of the above. the congruent marks help you to show that all of the answers are true

Answer:

YXZ=AXZ

because if you see the letters they form triangle

You roll two six-sided dice numbered from one through six. What is the probability that the maximum of the two dice is greater than or equal to six? Report your answer to three decimal places.

Answers

The probability that the maximum of the two dice is greater than or equal to six is 0.722.

What is probability?

Probability is a way of calculating how likely something is to happen. Probability can range from 0 to 1, with 0 indicating an impossibility and 1 indicating a certainty.

We are given that two six-sided dice numbered from one through six are rolled.

The sample space of the event is

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Probability that the maximum of the two dice is greater than or equal to six is

26 out of 36 i.e. 26/36

This is equal to 0.722.

Hence, the probability that the maximum of the two dice is greater than or equal to six is 0.722.

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how to solve that and what is the answer

Answers

The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Let 's' be the cost of the skirt. Then the equation is given as,

3/4(18 + s) = 31.50

The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.

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given the definitions

u= 1 2 3 4 5 6 7
a= 1 2 4 5
b= 1 3 5 7
how many elements are in A' u B?​

Answers

There should be 6

AUB

A jar contains 7 poker chips: 4 blue, 2 red and 1 white. You randomly select two chips from the jar. What is the probability that your selection includes two different colored chips? Report your answer to three decimal places.

Answers

The probability of selecting two different coloured chips is the fraction 14/49.

What is probability?

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

total possible outcome = 7

blue chips = 4

red chips = 2

white chips = 1

probability of selecting blue chips = 4/7

probability of selecting red chips = 2/7

probability of selecting white chips = 1/7

probability of selecting two coloured chips at random = 4/7 × 2/7 + 4/7 × 1/7 + 2/7 × 1/7

probability of selecting two coloured chips at random = 8/49 + 4/49 + 2/49

probability of selecting two coloured chips at random = 14/49

Therefore, the probability of selecting two different coloured chips is the fraction 14/49

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Kim has to prepare for a 16 miles race for 2/6 of the race Kim decides to walk preserve her energy she than sprints for 3/7 of the remaining time after she walked what is half of the race left

Answers

The half-distance left is 40/7 or 5.714 miles

How to find the distance?

Given that:

The total race is 16 miles long.

Kim walked for 2/6 of the race, which is (2/6) * 16 = 16/3 miles.

After walking 16/3 miles, there are 16 - 16/3 = 32/3 miles left in the race.

Kim then sprints for 3/7 of the remaining distance, which is (3/7) * 32/3 = 32/7 miles.

Half of the race is left after she finished sprinting and walking, which is

16 - 32/7 = 80/7 miles

Divide this by 2:

80/7 ÷2

= 40/7 miles are left.

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what is the crucial element in dealing with the audit of owner-managed businesses? This recursive function is operating on the array data structure. The method is to find the sum of a given array of integers, recursively. You are to write a simple public wrapper function that you pass the array into first, then call the recursive private helper method which takes in the array and an integer. Pseudo code is acceptable.An example is [3,5,1,7,9] ; begin at index 4 and add the value 9 to the recursive call at index 3, and repeat. 0 1 2 3 4Below are the method headers and Javadocs: please help me i'm desperate The fulfillment of advice such as that in the excerpt most directly contributed to which of the following in the late nineteenth century?The economic decline and depopulation of eastern citiesCompetition for resources among White settlers and American IndiansThe outbreak of war with Mexico over control of territoryRestrictions on immigration from eastern and southern Europe how can you ensure you give your customers exactly what they want? During the second half of the twentieth century, population trends in which of the following regions most strongly contrasted with the overall trends illustrated in the table? Please simplify the picture Give an example of a power shared by the state and national government in the US. what sorts of things would you like to do or accomplish in waterloo engineering and why? Assume that you graph lines f and g on the same coordinate plane and they intersect at point (4, 5). Which of the following statements is NOT true.1. (4,5) is on both lines2. if you plug 4 in for x and 5 in for y in each equation you will get true statements form both equations 3. (4,5) is the solution to the linear system4. other points that are on line f will also be solutions to the linear system5. None. all statements are true. a sample of gas is heated frtom 35 c to 70 c correctly describe what happens to the vo;lme which of these are considered factors that contribute to the spontaneity of a chemical reaction? in other words, which answer options tend to cause reactions to occur? select all that apply. Which of the following bonds undergoes stretching at the highest frequency?A. C-OB. C=OC. C=CD. C (triple bond) CE. C-H based on atmospheric stability considerations, do you think it would be best to burn agricultural debris in the early morning or the afternoon? El 19.8% de ___ es 720? Regarding emotional regulation, which of the following statements is NOT TRUE?By soothing an infant, the caregiver is helping the infant modulate their emotions.The soothing actions of a caregiver reduce the level of stress hormones of the infant.In order to develop good emotional regulation, an infant should be allowed to reach frequent intense, agitated states.The caregiver's actions influence the infant's neurobiological regulation of emotion. what is blood pressure answer choices A certain type of rocket sled is used to measure the effect of suddenacceleration. The sled at rest has a speed of 0.0 km/h, and then reaches atop speed of 320km/h in 0.18 seconds. What is the acceleration that takesplace in this time?HURRY PLEASEE How do the innate immune response and the complement system relate to one another? (This one requires thought on your part!) 8. Why do both HRP and fluorescein enter neighboring cells early, but not late at the two-cell stage?