Consider a regular surface S given by a map x: R2 R3 (u, v) (u +0,- v, uv) For a point p= (0,0,0) in S, Compute N.(p), N. (p)

Answers

Answer 1

N(p) = 1/√2 (-1,0,1) and  N.(p) = (0,0,0) . (1/√2) (-1,0,1) = 0.

Given a regular surface S given by a map x:

R2 ⟶ R3(u, v) ⟼ (u + 0, - v, uv).

For a point p = (0,0,0) in S, we are required to compute N . (p), N. (p)

We have, x(u,v) = (u + 0, -v, uv)

∴ x1 = 1, x2 = -1, x3 = v

N(p) = 1/√(1+u²+v²) [ux1 × vx2 + ux2 × vx3 + ux3 × vx1]

Here, u = 0, v = 0

∴ x(0,0) = (0,0,0)

∴ x1(0,0) = 1, x2(0,0) = -1, x3(0,0) = 0

Now, x1 × x2 = 1 × (-1) - 0 = -1, x2 × x3 = (-1) × 0 - 0 = 0, x3 × x1 = 0 × 1 - (-1) = 1

Hence, N(p) = 1/√2 (-1,0,1)

Also, N.(p) = (0,0,0) . (1/√2) (-1,0,1) = 0.

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Related Questions

A dress needs 3.65m of clothe. A tailor makes six dresses. How much cloth does the tailor need? a. 21.9m b. 36.9m c. 45.9m d. 63.9m e. Other:

Answers

Answer:

21.9 m

Step-by-step explanation:

Take the amount for one dress and multiply by 6

3.65*6 =21.9 m

Answer:

21.9m

Step-by-step explanation:

3.65m*6=21.9m

that is how to solve it because one clothe is 3.65m so therfore six clothe will be 3.65*6=21.9m

What is 1000 more than 4,590?

Answers

Answer:

5,590

Step-by-step explanation:

4,590 +1,000

does anyone know how to answer 18 - 16/5

does anyone know how to answer 18 - 16/5

Answers

18- 16/5 = 14.8

If that’s what you’re asking

Answer:

5.8 or 29/5

Step-by-step explanation:

you have a typo mistake it's 61 not 16

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the followinWhat percentage of people has an IQ score greater than 120?

Answers

Answer:

Percentage of people with IQ greater than 120 is 84.134%

Step-by-step explanation:

First thing we do here is to calculate the

z-score

Mathematically;

z-score = (x-mean)/SD

here, x = 120, mean = 100 while SD = standard deviation = 20

z-score = (120-100)/20 = 20/20 = 1

The probability we want to calculate is;

P(x > 120) or P(z >1)

we proceed to use the standard score table to get this;

From the standard score table ;

P(z >1) = 0.84134

which is in percentage = 84.134%

two birds are flying in the air. bird A is currently 500 feet in the air and is decending at a constant rate of 75 ceet per minute. bird b who is originally 100 feet in the air begins to increse in altitude at a constant rate of 25 feet per minute. bird a begins to asend in the air at the same time bird b begins to desend in the air


Questions:

What is bird A’s height above the ground?

What is bird B’s height above the ground?

After how many minutes did the two birds reach the same height?

When is bird A above bird B?

When is bird B above bird A?

after 1 minute what is the difference in height between the birds?

Answers

The difference between the two high altitudes is therefore 300 feet.

How to solve

Let 't' denote the time in minutes when both birds are at the same height. If both of these fowls are traveling, one descending and the latter ascending, then we obtain a formulaic value for t using the equations below.

Distance descended by bird A = 75tDistance ascended by bird B = 25tOriginal altitude-distance difference = 500 - 100 = 400 feet

Therefore, if we solve: 75t - 25t = 400, it follows that 50t = 400 and t = 8 minutes.

Given this information, after 8 minutes, the two birds reach the same height.

Consequently, before the 8-minute interval, bird A is situated at a higher level than bird B since the prior's rate of descent is less than the current bird's ascent.

Once they have reached the shared altitude, bird B is above bird A given its continuous upward elevation, contrasting against bird A's descending course.

Their heights after only 1 minute has elapsed; the Height of bird A after 1 minute is calculated to be 425 feet - (500 - 75(1)) and for bird B it is 125 feet - (100 + 25(1)).

The difference between the two high altitudes is therefore 300 feet.

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4) Your drawer contains 9
white shirts, 4 blue shirts,
and 7 red shirts. You place 3
shirts (one at a time) at
random into your bag for a
weekend trip. What is the
probabilty that all three
shirts you put in your bag
are white? Express your
answer as a decimal
rounded to the nearest
hundredth (two places past
the decimal).

Answers

Answer:

7.37%

Step-by-step explanation:

9/20 x 8/19 x 7/18 = 7/95 (simplified) which is 7.37%

I support her no matter how she feels I’m still gonna love her congrats queen so happy for u ok

Answers

Answer:

As you should

Step-by-step explanation:

Answer:

PURRIOD

Step-by-step explanation:

Just a random question for points.

Would you rather get a 21/50 or a 23/33
Do the math and see where the decimals take you, then answer.

Answers

I would rather get a 23/33

Answer:

0.42

Explanation:

21/50= 0.42

22/33=0.667766,7

Therefore, 0.42 is the less equaled answer

Please give A 5.0 score and braniest!

Hopefully this helps!

a jet travels 1128 miles against a jetstream in 2 hours and 1368 miles with the jetstream in the same amount of time. what is the rate of the jet in still air and what is the rate of the jetstream?

Answers

Given the distance covered by a jet in the air, and the distance covered with the jetstream, we have to find the rate of the jet in still air, and the rate of the jetstream.

Let the rate of the jet in still air be x, and the rate of the jetstream be y. Since the jet travels 1128 miles against the jetstream in 2 hours, we have:
1128 = (x - y) × 2 ---------------- (1)
Similarly, since the jet travels 1368 miles with the jetstream in 2 hours, we have:
1368 = (x + y) × 2 ---------------- (2)
Now, we need to solve these two equations to find the values of x and y. Let's first solve equation (1) for y:
y = x/2 - 564
Plugging in this value of y in equation (2), we get:
1368 = (x + x/2 - 564) × 21368 = (3x/2 - 564) × 21368 = 3x/2 × 2 - 564 × 2
Simplifying, we get:2736 = 3x - 1128
Solving for x, we get:
x = 1288Therefore, the rate of the jet in still air is 1288 mph. Plugging this value of x in equation (1), we get:
y = 1288/2 - 564y = 60
Therefore, the rate of the jetstream is 60 mph. Hence, the required values are:x = 1288 mph and y = 60 mph.

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6x+7y=4x+4y6, x, plus, 7, y, equals, 4, x, plus, 4, y complete the missing value in the solution to the equation.

Answers

The missing value is 6.

As per the question, y = -4. Keeping the value of y in the equations to find the value of x.

6x + 7(-4) = 4x + 4(-4)

Performing multiplication on each side of the equation

6x - 28 = 4x - 16

Rewriting the equation with identical values on each side of the equation

6x - 4x = 28 - 16

Performing subtraction on each side of the equation to find the value of x

2x = 12

Shifting 2 to Right Hand Side of the equation

x = 12 ÷ 2

Performing division on Right Hand Side of the equation

x = 6

Hence, the value of x is 6.

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The complete question is -

6x+7y=4x+4y

Complete the missing value in the solution to the equation.

(__,-4)

To what degree is this polynomial function?

A) second
B) third
C) fourth
D) fifth

To what degree is this polynomial function?A) second B) thirdC) fourth D) fifth

Answers

The fourth

Don’t be upset if it’s wrong

What is the perimeter of the shape?
12 ft
14 ft
26 ft
38 ft

What is the perimeter of the shape?12 ft 14 ft 26 ft38 ft

Answers

Answer:

38

Step-by-step explanation:

4+10+9+3=26

9-4=5

10-3=7

26+5=31

31+7=38

Hope this helps! Have a great day ahead. Tell me if im wrong :) Stay Safe <3

Make X the
subject of m=n+x/p

Answers

Answer:

x = pm - pn

Step-by-step explanation:

m = n + \(\frac{x}{p}\)  Subtract n from both sides

m - n = n - n + \(\frac{x}{p}\)

m-n = \(\frac{x}{p}\)   Multiply both sides by p

p(m - n) = (\(\frac{p}{1}\)) \(\frac{x}{p}\)          \(\frac{p}{1}\) means the same as p

pm - pn = x             Distribute the p

x = pm - pn

If the errors of a time series forecast are: 5, -3, 0 and -2,
compute the MAD and MSE.
Group of answer choices
0 and 2.5
2.5 and 9.5
0 and 9.5
None of the above

Answers

Absolute Deviation (MAD):Mean Absolute Deviation (MAD) is the average of the absolute values of the errors. The formula to calculate the MAD is:

MAD = (|5| + |-3| + |0| + |-2|)

/4= 10/4= 2.5Hence, the MAD of the given time series forecast is 2.5.Mean Squared Error (MSE):Mean Squared Error (MSE) is the mean of the squared errors. The formula to calculate the MSE is:

MSE = [(5^2 + (-3)^2 + 0^2 + (-2)

^2)/4]= (25 + 9 + 0 + 4)

/4= 38/4= 9.5Hence, the MSE of the given time series forecast is 9.5.Therefore, the answer is option B: 2.5 and 9.5.

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A cyclist is biking a certain amount of distance in 25 minutes
How long will it take for a pedestrian to walk the same amount of distance when it’s speed is 2 2/5 times slower than the cyclist

Answers

the time it would take for the pedestrian to walk the same distance as the cyclist is 5/3 times the time it takes for the cyclist.

Let's assume that the distance the cyclist is biking is "d", and the speed of the cyclist is "s". We are given that the cyclist covers this distance in 25 minutes, which can be written as:

d = s x 25

Now, let's assume that the speed of the pedestrian is "p". We are given that the speed of the pedestrian is 2 2/5 times slower than the speed of the cyclist. This can be written as:

p = (3/5) x s

Note that we converted 2 2/5 to an improper fraction of 12/5, and then subtracted it from 3 to get 3/5. This gives us the speed of the pedestrian in terms of the speed of the cyclist.

Now, we want to find out how long it would take for the pedestrian to walk the same distance "d". We can use the formula:

time = distance / speed

For the cyclist, we have:

time for cyclist = d / s

For the pedestrian, we have:

time for pedestrian = d / p

Substituting the expressions for "d", "s", and "p" that we obtained earlier, we get:

time for cyclist = d / s = d / (25s/25) = d / (s x 25/1)

time for pedestrian = d / p = d / [(3/5) x s] = d / (3s/5) = d / (s x 3/5)

We can simplify these expressions by multiplying and dividing by appropriate factors, as follows:

time for cyclist = d / (s x 25/1) = d / s x 1/25

time for pedestrian = d / (s x 3/5) = d / s x 5/3

So, the time it would take for the pedestrian to walk the same distance "d" is:

time for pedestrian = (d / s) x (5/3) = (time for cyclist) x (5/3)

Therefore, the time it would take for the pedestrian to walk the same distance as the cyclist is 5/3 times the time it takes for the cyclist.

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helppp i don’t know how to solve will make right answer brianlyist

helppp i dont know how to solve will make right answer brianlyist

Answers

Answer:

MARK ME BRAINLIEST OR ELSE .....

nothing lol.

Step-by-step explanation:

helppp i dont know how to solve will make right answer brianlyist

a tank in the shape of a hemisphere has a radius of 2 feet. if the liquid that fills the tank has a density of 85.8 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Answers

Answer: 1438

Step-by-step explanation:

I just did it

Thus,  the total weight of the liquid in the tank is approximately 1808 pounds.

To find the total weight of the liquid in the tank, we need to first find the volume of the hemisphere and then multiply it by the density of the liquid.

The formula for the volume of a hemisphere is (2/3)πr^3, where r is the radius. Given that the radius is 2 feet, the volume can be calculated as:

Volume = (2/3)π(2)^3 = (2/3)π(8) = 16π/3 cubic feet

Next, we need to multiply the volume by the density of the liquid, which is 85.8 pounds per cubic foot:

Weight = Volume × Density = (16π/3) × 85.8 = (16π × 85.8) / 3 ≈ 1807.6 pounds

Rounded to the nearest full pound, the total weight of the liquid in the tank is approximately 1808 pounds.

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50 points! Which expressions are equivalent to (see image)? Select three

50 points! Which expressions are equivalent to (see image)? Select three

Answers

Answer:

Option 4

Step-by-step explanation:

\(5( \frac{1}{3} x + 7) - 3( \frac{1}{2} x - 4)\)

\( \frac{5}{3} x + 35 - \frac{3}{2} x + 12\)

\( \frac{5}{3} x - \frac{3}{2} x + 35 + 12\)

\(2 \times 5x - 3 \times 3x \div 3 \times 2 + 47\)

\( \frac{10x - 9x}{6} + 47\)

\( \frac{x}{6} + 47\)

Answer:

Solution given:

5(⅓x+7)-3(½x-4)

distribute it

\( \frac{5}{3} x+35-\frac{3}{2}x+12\)

\( \frac{5}{3} x-\frac{3}{2}x+35+12\)

\( \frac{5*2-3*3}{3*2} x+47\)

\( \frac{1}{6} x+47\) is a required answer.

.) how many ways are there to place testing dummies into the rollercoaster? b.) how many ways are there to place dummies into the roller coaster if the front car must have 3 or fewer testing dummies in it? c.) how many ways are there to place dummies into the roller coaster if the back car must be empty? d.) how many ways are there to place dummies into the roller coaster if the neither the front or back car can be

Answers

(a) There are 2²⁸ = 268,435,456 ways to place testing dummies into the rollercoaster

(b) There are 15 × 2²⁴ = 402,653,184 ways to place dummies into the rollercoaster if the front car must have 3 or fewer testing dummies.

(c) There is only 1 × 2²⁴ = 16,777,216 way to place dummies into the rollercoaster if the back car must be empty.

(d) There are 15 × 2²⁰ = 15,728,640 ways to place dummies into the rollercoaster if neither the front nor the back car can be full.

a) There are 7 cars and each car has 4 seats, there are a total of 7 × 4 = 28 seats. Each seat can either be occupied by a testing dummy or left empty.

For each seat, there are two possibilities (dummy or empty). Since each seat can be treated independently, the total number of ways to place the testing dummies is 2²⁸.

2²⁸ = 268,435,456

b) If the front car must have 3 or fewer testing dummies,

The front car can have 0, 1, 2, or 3 testing dummies.

There are C(4, 0) + C(4, 1) + C(4, 2) + C(4, 3) = 1 + 4 + 6 + 4 = 15 ways to select the number of dummies for the front car.

The remaining 6 cars can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2⁴ possibilities for each of the 6 remaining cars.

Total number of ways = 15 × (2⁴)⁶ = 15 × 2²⁴.

15 × 2²⁴ = 402,653,184

c) If the back car must be empty, we can calculate the number of arrangements by considering the possibilities for the back car and then multiplying it by the remaining possibilities for the other cars.

The back car can have 0 dummies. There is only 1 possibility for the back car.

The remaining 6 cars can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2^4 possibilities for each of the 6 remaining cars.

Total number of ways = 1 × (2⁴)⁶ = 1 × 224.

1 × 2²⁴ = 16,777,216

d) If neither the front nor back car can be full, we can calculate the number of arrangements by considering the possibilities for both the front and back cars and then multiplying it by the remaining possibilities for the other cars.

The front car can have 0, 1, 2, or 3 testing dummies. There are C(4, 0) + C(4, 1) + C(4, 2) + C(4, 3) = 1 + 4 + 6 + 4 = 15 ways to select the number of dummies for the front car.

The back car can have 0 dummies. There is only 1 possibility for the back car.

The remaining 5 cars (excluding the front and back cars) can have any number of dummies between 0 and 4. Each car has 4 seats, and each seat can be occupied by a dummy or left empty. So, there are 2^4 possibilities for each of the 5 remaining cars.

Total number of ways = 15 × 1 × (2⁴)⁵ = 15 × 2²⁰.

15 × 2²⁰ = 15,728,640

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The question is incomplete the complete question is :

an amusement park is testing a roller coaster ride for safety. the roller coaster has 7 distinguishable cars, each of which contains 4 distinguishable seats. each seat can either be occupied by a testing dummy or left empty. the dummies are indistinguishable from one another, and there are enough to fill every car. for all sub-problems below, you are allowed to leave the entire ride empty, fill every seat in the ride, or anything in between. (update 2/17/23: the cars cannot be rearranged. they are fixed in one order.) a.) how many ways are there to place testing dummies into the rollercoaster? b.) how many ways are there to place dummies into the roller coaster if the front car must have 3 or fewer testing dummies in it? c.) how many ways are there to place dummies into the roller coaster if the back car must be empty? d.) how many ways are there to place dummies into the roller coaster if the neither the front or back car can be full?

help me please, i need an answer asap

help me please, i need an answer asap

Answers

Answer:

answer is A - library books by genre and by Adult or Child

Step-by-step explanation:

your column on the left will have different genre of books

your top column will have children or adults

help me please, i need an answer asap

Mila is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day. Let



P represent Mila's total pay on a day on which she sells



x dollars worth of computers. The table below has select values showing the linear relationship between



x and



.

P. Determine how much money Mila would be paid on a day in which she sold $1000 worth of computers.

Mila is a salesperson who sells computers at an electronics store. She makes a base pay amount each day

Answers

The equation that represent Mila's total pay on a day on which she sells x dollars is P = 0.01x + 65

What is an equation?

An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.

A linear equation is in the form:

y = mx + b

Where m is the slope (rate), b is the y intercept

Let P represent Mila's total pay on a day on which she sells x dollars worth of computers.

From the table, using the point (5000, 115) and (7000, 135):

P - 115 = [(135 - 115)/(7000 - 5000)](x - 5000)

P = 0.01x + 65

The equation is P = 0.01x + 65

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Làm tính nhanh
2x. ( X² - 7x -3 )

Answers

Answer:

Step-by-step explanation:

2x.(x²-7x-2x-3)=

2x.x² -2x.7x -2x.3=

2x³-14x²-6x

At Sunday’s Best Ice Cream in New Orleans, the price of Ice Cream was $4.00 for a large sundae. Due to the holidays, they are decreasing their price by 12%. What is the new price for the large sundae?

Answers

the answer is $3.88

Step-by-step explanation:

because the ice cream was $4.00 and they subtracted it by 12% which would be $4.00 minus .12 which would give you $3.88

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?

Answers

Answer:

\(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).

Step-by-step explanation:

According to the Rational Root Theorem, the potential roots of a polynomial are

\(x=\pm\dfrac{p}{q}\)  

where, p is a factor of constant and q is a factor of leading term.

The given polynomial is

\(f(x)=9x^8+9x^6-12x+7\)

Here, 9 is the leading term and 7 is constant.

Factors of 9 are ±1, ±3, ±9.

Factors of 7 are ±1, ±7.

Using rational root theorem, the rational or potential roots are

\(x=\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\)

Therefore, the potential root of f(x) are \(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).  

Answer:

its D, 3/7.

Step-by-step explanation:

just did it egen2020

can someone help me I really need help with math

can someone help me I really need help with math

Answers

Answer:

21.     5g - f = 25 - f

22.     100 - 3b = 6b

23.    4 (14 + c) = A2

24. 8o = 52

25. 12f = 30

26. 21 + 2w = P

27. f - 32 (5 / 9) = C

28. D = m / v

29. prt = I

Better understanding...

24. Let "o" refer to the number of octaves

25. Let "f" refer to the number of flats

26. Let "p" represent the Perimeter, Let "l" represent the length, Let "w" represent the width

28. Let "d" represent the density, Let "m" represent the mass, Let "v" represent the volume

29. Let "i" represent the simple interest

Sorry, this took so long.. Hopefully this helps! Feel free to mark barinliest!

if 6 people share 31 apples equally, how many apples should each person get ?

Answers

Answer:

5 apples

Step-by-step explanation:

\(\frac{31}{6}=5.16666667\)

Since the problem asks for how many apples, you'll have to round down the number you get. 5.16666667 rounded down gives you 5 apples each.

-4×(-2)[2×(-6)+3×(2×6-4-4)]

Answers

\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

A frustum is made by removing a small cone from
a similar large cone.
Work out the volume of the frustum, below.
Give your answer in terms of x
3 cm
4.5 cm
6 cm
3 cm

A frustum is made by removing a small cone froma similar large cone.Work out the volume of the frustum,

Answers

The volume of the frustum, in terms of x, is (2.65π)x + 12π.

To find the volume of the frustum, we need to consider the volumes of the large cone and the small cone separately.

The large cone:

The radius of the base of the large cone is 6 cm, and its height is x + 3 cm (including the height of the small cone).

The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.

So, the volume of the large cone is V_l = (1/3) * π * (6^2) * (x + 3).

The small cone:

The radius of the base of the small cone is 4.5 cm, and its height is x cm.

Similarly, the volume of the small cone is V_s = (1/3) * π * (4.5^2) * x.

Now, the volume of the frustum is the difference between the volume of the large cone and the volume of the small cone:

V_frustum = V_l - V_s

= (1/3) * π * (6^2) * (x + 3) - (1/3) * π * (4.5^2) * x

= (1/3) * π * (36) * (x + 3) - (1/3) * π * (20.25) * x

= (12π/3) * (x + 3) - (4.05π/3) * x

= 4π(x + 3) - (1.35π)x

= 4πx + 12π - 1.35πx

= (4 - 1.35)πx + 12π

= (2.65π)x + 12π

Therefore, the volume of the frustum, in terms of x, is (2.65π)x + 12π.

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Brandon asked some friends how much they pay in rent. The results are shown on the graph below. What is the mean of his friends' rents?

Answers

Answer: $690

Step-by-step explanation: I added all the numbers together and then I divided it by five and got $690

800+700+500+700+750=690

Which table represents a function?
х
-3
0
-2
8
y
-1
0
-1
1
х
-5
0
-5
6
у
-5
O
5
-6

Which table represents a function?-30-28y-10-11-50-56-5O5-6

Answers

Answer:

d

Step-by-step explanation:

sorry if i am wrong

Other Questions
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