Answer:
$132.74
Step-by-step explanation:
First: divide the sales price by 100
6.75 ÷ 100 = 0.0675
Second: multiply the answer from the first step by the original price
0.0675 x 124.35 = 8.393625
round to the hundredths place
8.393625
8.39
Third: add the original price with the answer from the second step
124.35 + 8.39 = 132.74
A recent survey by the American Automobile Association showed that a family of two adults and two children on vacation in the United States will pay an average of $247 per day for food and lodging with a standard deviation of $60 per day. You can compute the mean food and lodging cost of a 10-day vacation by multiplying the per-day mean by 10. The standard deviation for the 10-day vacation can be found by multiplying by 10 also.
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).
a. What is the mean for food and lodging for a 10-day vacation? _______
b. What is the standard deviation of the distribution for the 10-day vacation? ______
c. What is the variance of the distribution for the 10-day vacation? ______
The statistical measures for the 10-day vacation are given as follows:
a) Mean: $2470.
b) Standard deviation: $189.74.
c) Variance: $²36,001.
What is the mean for the 10-day distribution?To find the mean for n days, we take the mean amount in a single day and multiply by n.
Hence:
247 x 10 = $2470.
What is the standard deviation for the 10-day distribution?To find the standard deviation for n days, we take the standard deviation for a single day and multiply by the square root n.
Hence:
60 x sqrt(10) = $189.74.
What is the variance for the 10-day distribution?The variance is the square of the standard deviation, hence:
($189.74) = $²36,001.
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Is x = -14 a solution to 9x - 7 = -7?
Answer:
since x=-14
9(-14)-7
-126-7=-133.
6.48 x 10 5
-------------------------
(2.4 x 10 4) (1.8 x 10 -2)
Answer:
1.5×10³
Step-by-step explanation:
You want to know the value of the expression given with numbers in scientific notation.
EvaluationThe usual rules of arithmetic and exponents apply. Your calculator or spreadsheet can use and display the numbers in scientific notation for you.
[tex]\dfrac{6.48\times10^5}{(2.4\times10^4)(1.8\times10^{-2})}=\dfrac{6.48}{2.4\times1.8}\times10^{5-4-(-2)}=\boxed{1.5\times10^3}[/tex]
Write the decimal as a fraction.
8.33 = 10F
- 0.83 = -F
[?]
=
Hint: Subtract the first equation from this new
equation to eliminate the repeating decimal.
Enter the decimal value
the fraction form of the number will be 5 / 18.
We are given the decimal number as:
0.83(bar on 3) = F ...(1)
Now, we need to convert this into fraction.
For this, we will first multiply both the sides by 10
Do, we get that:
8.33 ( bar on 3) = 10 F ...(2)
Now, we will Subract (1) from (2), we get that:
9 F = 8.33 (bar on 3) - 0.83 (bar on 3)
9 F = 7.5
F = 7.5 / 9
F = 2.5 / 9
F = 25 / 90
Reducing the fraction into simplest form:
F = 5 / 18.
Therefore, we get that the fraction form of the number will be 5 / 18.
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Can someone help me I will mark u brilliant
Answer: R'=(-4, -3)
S'=(-4, -10)
T'=(-8, -10)
U'=(-8, -3)
Step-by-step explanation:
When rotated around the origin by 180 degrees, the rectangle will have all its coordinates' x and y values negated.
R=(4,3) ==> R'=(-4, -3)
S=(4,10) ==> S'=(-4, -10)
T=(8,10) ==> T'=(-8, -10)
U=(8,3) ==> U'=(-8, -3)
|x-2|=|4+x|
How can I find the value of X?
Answer:
x = -1
Step-by-step explanation:
You want to find the value(s) of x that satisfy the equation |x-2| = |4+x|.
DomainsThe behavior of each absolute value function changes at the point where its argument is zero. For this equation, that will be two points:
x -2 = 0 ⇒ x = 2
x +4 = 0 ⇒ x = -4
These two points on the number line divide the domain of the equation into three parts:
x < -4-4 ≤ x < 22 ≤ x.The behavior of the equation will be different in those three domains.
x < -4In this domain, both absolute value functions negate their arguments. That means the equation is equivalent to ...
-(x -2) = -(4 +x)
2 = -4 . . . . . . . . . . add x to both sides
This has no solutions: there are no values of x that will make this true.
-4 ≤ x < 2In this domain, the absolute value function on the left negates its argument, so the equation is equivalent to ...
-(x -2) = (4 +x)
-2 = 2x . . . . . . . . . add x-4 to both sides
-1 = x . . . . . . . . . divide by 2
This value of x is in the domain, so represents a solution to the equation.
x = -1
2 ≤ xIn this domain, neither absolute value function negates its argument, so the equation is equivalent to ...
x -2 = 4 +x
-2 = 4 . . . . . . . subtract x
This has no solutions: there are no values of x that will make this true.
The given equation has one solution: x = -1.
__
Additional comment
When solving an equation like this graphically, it is often useful to put it in the form f(x) = 0. We can obtain that form by defining ...
f(x) = |x -2| -|4 +x|
The graph of this is attached. The only solution is where f(x) = 0, at x = -1.
Note that the function is parallel to the x-axis outside of the middle domain, so will not have any x-intercepts in those regions.
What is that converted to Celcius?
degrees Celcius
Answer:
32° degree Fahrenheit is converted to celcius
Answer:
use 273k that is if is changing from celcius to Kelvin
A contract was made to be completed in 40 days and 24 men were put to work. After 28 days, 11 more men were engaged and the work was completed just in time. if not extra men engaged, how many days would the work have taken.
If no extra men were engaged then the work would have been completed in 45.5 days.
What is work?In physics, work is a measure of energy transfer that occurs when an object is moved over a distance by an external force, at least a portion of which is applied in the direction of displacement.So,
= (24 × 28) + (24 + 11) × 12= 672 + 420= 1092The time required by 24 men to complete their work is:
= 1092/24= 45.5Therefore, if no extra men were engaged then the work would have been completed in 45.5 days.
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A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?
31 students
40 students
41 students
66 students
Answer:
40 students
Step-by-step explanation:
I think it is 40 students because 60 + 40= 100 then 100 x 40 = 4,000
then the SCHOOL has to pay a $30 cleaning fee so that will add up to $4,030! I hope this helps everybody!
40 students will be going on the trip
How to calculate the number of students that will be going on the trip ?Each student will pay $60 for food and lodging
Each student will also pay $40 for the bus
Total amount of fee that will be paid by each student is
= 60 +40
= 100
The school will pay $30 cleaning fee for the bus, it's only the school that will be paying this fee, the students are not included. This will will be subtracted from the total cost which is $4,030 leaving us with $4,000
Therefore the number of students going on the trip can be calculated as follows
= 4,000/100
= 40
Hence 40 students will be going on the trip
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Solving Advanced Linear Equations: Mastery Test
Select the correct answer from each drop-down menu.
Consider the equation below.
The equation was solved using the following steps.
Step 1:
Step 2:
Step 3:
Step 4:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
-2 to 5x and 8.
6.x
✓16.
-2(5z + 8) = 14 + 6z
-16.
-10z <- 16
-16z
Reset
-
16 = 14
-16z =
30
= 14 + 6z
H
=
H =
Next
30656
-18
Submit T
The solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8
How to complete the steps to solve the equation?The equation is given as
-2(5z + 8) = 14 + 6z
Open the bracket
So, we have
-10z - 16 = 14 + 6z
Collect the like terms
So, we have
-10z - 6z = 14 + 16
Evaluate the like terms
So, we have
-16z = 30
Divide both sides of the equation by 16
So, we have
z = -15/8
Hence, the solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8
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Write two expressions
that represent the volume of the cube, one with
exponents and one without.
The two expressions for the volume of a cube with a side length of S are:
V = S^3
V = S*S*S
How to express the volume of the cube?A cube is a rectangular prism where the 3 dimensions have the same measure, which we will call the side-length of the cube.
So, if S is the sidelength of the cube, the volume will be given by the product between the product between the dimensions of the cube, and the 3 dimensions measure the same thing, which is S, then:
V = S*S*S
That is the expression without exponents, and the expression with an exponent is really trivial, we have S multiplied by itself 3 times, so we get:
V = S^3
These are the two expressions for the volume.
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Challenge: A scuba diver has 30 cubic feet of air in his tank and dives under the water at
3:15pm. When he resurfaced at 3:30pm, he had 12 cubic feet of air left. How many cubic
feet of air per minute did he use?
The cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
Unit rateQuantity of air in his tank = 30 cubic feetTime he dives in = 3:15pmTime he resurfaced = 3:30pmQuantity of air remaining in the tank = 12 cubic feetCubic feet of air used per minute = Difference in quantity of air in his tank / difference in time
= (30 - 12) / (3:30pm - 3:15pm)
= 18 / 15
= 1.2 cubic feet of air per minute
Therefore, the cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
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Use the multiplier method to decrease £56 by 14%
You must show your working.
- 7.84 is actual difference of percentage by multiplier method to decrease.
What percentage means?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.56 - Percentage decrease =
56 - (14% × 56) =
56 - 14% × 56 =
(1 - 14%) × 56 =
(100% - 14%) × 56 =
86% × 56 =
86 ÷ 100 × 56 =
86 × 56 ÷ 100 =
4,816 ÷ 100 =
48.16
56 decreased by 14% = 48.16
Absolute change (actual difference):
48.16 - 56 = - 7.84
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An architect charges $1800 for a first draft of a three-bedroom house. If the work takes longer than 8
hours, the architect charges $105 for each additional hour. What would be the total cost for a first draft
that took 14 hours to complete?
The total cost for a first draft that took 14 hours to complete is $2430.
How to illustrate the expression?It should be noted that when the work takes longer than 8 hours, the architect charges $105 for each additional hour. For 14 hours, the additional hours will be:
= 14 - 8
= 6 hours
Therefore, the total cost will be:
= 1800 + (105 × 6)
= 1800 + 630
= 2430
Therefore, the total cost for a first draft that took 14 hours to complete is $2430.
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Determine the end behavior of each function.
(a)
p(x) = a(x + b)5(x − c)3
, where a, b, and c are constants and
a < 0
.
p(x) → as x → −∞
p(x) → as x → ∞
(b)
f(x) =
9x2 − 11x + 2
8x2 − 6
f(x) → as x → −∞
f(x) → as x → ∞
(c)
g(x) = 9 + e−6x
g(x) → as x → −∞
g(x) → as x → ∞
Step-by-step explanation:
(a)
a, b, c are constants and play no role with their value when it goes relative to enormous numbers and to infinity.
but the sign is important.
a < 0, so, it will stay < 0 for all eternity/infinity.
(x + b)⁵ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (the exponent 5 is odd, so a negative value put to an odd power will create a negative result value).
(x - c)³ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (for the same reasons - 3 is an odd number).
x going to -infinity,
p(x) = -×-infinity×-infinity = -infinity
x going to infinity,
p(x) = -×infinity×infinity = -infinity
(b)
the x² terms drown out all other terms with lower x exponent (so, incl. -11x or any constants).
what remains for very, very large x is
9x²/8x² = 9/8 = 1.125
since we have x² terms, it does not matter, if x is positive or negative, the result is always positive.
so, x going to infinity or to -infinity, p(x) is the same again :
p(x) = 9/8 = 1.125
(c)
finally, we have a different result for x going to -infinity or to infinity.
x going to -infinity :
the exponent of e is then -6×-infinity = infinity. and e to the power of infinity is infinity.
p(x) = 9 + infinity = infinity
x going to infinity :
the exponent of e is then -6×infinity = -infinity. and e to the power of -infinity is 1/e to the power of infinity.
and that is 1/infinity. the limit for that is 0.
p(x) = 9 + 0 = 9
helpppppppppppppppppppp...................................
Answer: Its quadrant 3
Step-by-step explanation:
Hope this helps!
Answer:
Quadrant 3
Step-by-step explanation:
Lets have an example
Lets say we are plotting the point (-4,-4)
so, we would go left on the x-axis, to -4. So we will be in either Quadrant 2 or Quadrant 3
Now we go down 4, so we end up in Quadrant 3
Hence, The answer is Quadrant 3
Hope this helps!^^
To make five cups of lemonade you mix three cups of water with two cups of lemon
juice. If there are sixteen cups in a gallon, how many cups of lemon juice are needed to
make ten gallons of lemonade?
A: 16
B: 32
C: 40
D: 48
E: 64
(I know the answer is E but I don't know how to get it)
Use your knowledge of angle relationships to solve
for x in the diagram. Leave your answer as an exact
decimal.
The nearest decimal which is the approximate value of x is 18°..
The two slanting lines given in the diagram are parallel.
Furthermore, the horizontal line crosses both parallel lines given above.
Then the measure of the angles marked in the question is equal.
Therefore, we have 5x + 7° = 9x - 63°.
⇒ 63° + 7° = 9x - 5x
⇒ 70° = 4x
⇒ x = 70°÷ 4 = 17.5° ≈ 18°(approximate to the nearest decimal)
Therefore, x = 18°
Let us now compute the magnitude of each angle.
5x + 7 = 5 × 18 + 7 = 90 + 7 = 97
9x - 63 = 9 × 18 - 63 = 162 - 63 = 99
The measurement of these two angles differs by two degrees.. Because the value of x is not exact. We used the approximated value.
Let us recalculate the angle measurements using the exact value 17.5.
5x + 7 = 5 × 17.5 + 7 = 87.5 + 7 = 94.5
9x - 63 = 9 × 17.5 - 63 = 157.5 - 63 = 94.5
So, the exact value of x is 17.5°.
Hence, The nearly value of x to the nearest decimal is 18°.
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Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training.
Week Time (s)
28.8
27.6
27.1
How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent
Randy's percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.
The percentage change will be calculated by the relation -
Percentage change = change in timing ÷ original time × 100
Calculating percentage change between Week 1 and Week 2
Change = 28.8 - 27.6
Change = 1.2 seconds
Percentage = (1.2 ÷ 28.8) × 100
Percentage = 4.17%
Calculating percentage change between Week 2 and Week 3
Change = 27.6 - 27.1
Change = 0.5 seconds
Percentage = (0.5 ÷ 27.6) × 100
Percentage = 1.8%
So, percent of change from Week 1 to Week 2 than from Week 2 to Week 3 was = 4.17 - 1.8
Percentage change = 2.37%
Therefore, the percentage change from Week 1 to Week 2 was 2.37% greater than Week 2 to Week 3.
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ayudaaaa c x 4=32 porfaaa :vvv
Answer:C=8
Step-by-step explanation:
32 divided by 4 = 8
What value of x makes this proportion true?
25/20 = x/4
A. 6
B. 9
C. 20
D. 5
desperate need in help
Answer: 8x^10
Step-by-step explanation:i guessed but when you multiply exponents you just add them so the exponent is 10 and then 2 cubed is 8
Which of the following facts, if true, is enough information for you to prove that lines l and m are parallel? Write yes or no for each.
m<2 + m<4 = 180 degrees ______
m<1 = m<7 _______
m<2 = m<6 _______
m<6 + m<3 = 180 degrees ______
m<1 = m<8 _______
(Click document to see image.)
Adding yes or no to the information that is enough to proof lines l and m are parallel
m<2 + m<4 = 180 degrees no
m<1 = m<7 no
m<2 = m<6 yes
m<6 + m<3 = 180 degrees no
m<1 = m<8 yes
What are parallel lines?This is a term used in geometry to refer to lines that will never intersect. The concept of parallel lines is used to find angles that are related or equal to each other by the following theorems:
Vertical angles theoremCorresponding angles theoremAlternate interior angles theoremAlternate exterior angles theoremUsing the mentioned theorems we apply to the statements as follows: The first statement is correct but not used to prove parallel lines. The second statement is not correct.
The third statement is correct, it represents transitive property of equality angles, where m<2 equals m<3 by Vertical angles theorem and m<3 is equal to m<6 as by Alternate interior angles theorem.
m<6 + m<3 = 180 degree: the two angles are equal as earlier explained but their sum is not 180 degrees
m<1 = m<8: The equality of these two angles is shown by transitive property of equality angles, and it is enough to prove that line l and m are parallel lines
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A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 17 minutes, and then flies directly back to the hive at feet per second. It is away from the hive for a total of 19 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
Answer: (a) The equation is so called "time equation"
D/12 + 16*60 + D/8 = 19*60 seconds
(b) To determine the distance D, solve the equation
D/12 + D/8 = 19*60 - 16*60 = 3*60
multiply both sides by 24
2D + 3D = 3*60*24
5D =4320
D =4320/5 = 864 ft
Step-by-step explanation:
3 1/3 divided by 3/8
Enter your answer, as a mixed number in simplest form,in the boxes
The left and right page numbers of an open book are two
consecutive integers whose sum is 67. Find these page
numbers. Show your work (the steps)! Show the original
equation. Write a short summary of the result. Hint: Let x be the
first consecutive integer.
The original equation will be x + x + 1 = 67 and the left page will have 33 page number and the right one will have 34 page number.
Let x be the first consecutive integer.
So, x + 1 is the first consecutive integer.
Sum of the two integers = 67
⇒ x + x + 1 = 67 (This is the original equation)
Combining the like terms:
⇒ 2x + 1 = 67
Subtract 1 from both the sides:
⇒ 2x = 67 - 1
⇒ 2x = 66
Divide both sides by 2:
⇒ x = 66/2 = 33
Therefore, the original equation will be x + x + 1 = 67 and the left page will have 33 page number and the right one will have 34 page number.
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Can someone help me with this and show work please All the questions
The evaluation of the given angles are as follows;
A = 107.5° and B = 72.5°‹F = 18°, ‹E = 72°128° and 52°‹Q = 32°, ‹R = 58°45° and 135°33 s‹ABD = 47°, ‹DBC = 43°a = 8, b = 54a = 20m‹ADB = 25° , m‹BDC = 65°What are complementary and supplementary angles?Complementary angles sum up to 90°
Supplementary angles sum up to 180°
1. Let A and B represent the two angles, we have;
A + B = 180°
A - B = 35°
Which gives;
A + B + (A - B) = 180° + 35° =215°
A + B + (A - B) = A + A = 2•A
Which gives;
2•A = 125°
A = 215°/2 = 107.5°
A + B = 180°
B = 180° - A
Therefore;
B = 180° - 107.5° = 72.5°
The two angles are; A = 107.5° and B = 72.5°
2. ‹E + ‹F = 90° Definition of complementary angles.
‹E = ‹F + 54°
Which gives;
2•‹F + 54° = 90°
Therefore;
‹F = 18°
‹E = 72°
3. Let A represent the angle, we have;
A + A - 76° = 180°
A = 256°/2 = 128°
The measure of the angle is 128°
The measure of its supplement is 52°
4. ‹Q + ‹Q + 26 = 90
‹Q = (90-26)/2 = 32
‹Q = 32°
‹R = 32° + 26°= 58°
5. Let A represent the angle, we have;
A + 3•A = 180°
4•A = 180°
A = 180°/4
A = 45°
The measure of the supplement = 3 × 45° = 135°
6. Angle left = 90° - 35° = 55°
Speed= 35°/(21 s) = 5/3°/s
Time remaining for the bridge= 55°/(5/3°/s) = 33 s
7. 3•r + 5 + 5•r - 27 = 90
8•r - 22 = 90
r = 112/8 = 14
‹ABD = 3•r + 5 = 47°
‹DBC = 5•r - 27 = 43°
8. 4•a + 58 = 2•b - 18 = 90
a = 8
b = 54
9. a + 15 + a + 35 = 90
a = 40/2 = 20
10. 3•a + 10 + 13•a = 90
16•a = 80
a = 80/16 = 5
m‹ADB = 3•a + 10 = 25°
m‹BDC = 13•a = 65°
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4/z >= 3; z = 2
Please solve
The inequality expression 4/z >= 3 is false, when z = 2 because 2 is not greater than or equal to 3
How to evaluate the expression?The inequality expression is given as
4/z >= 3
The value of z is given as
z = 2
Substitute 2 for z in the inequality expression given as
4/z >= 3
So, we have:
4/2 >= 3
Evaluate the quotient
2 >= 3
The above inequality expression is false.
This is so because 2 is not greater than or equal to 3
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The diameter
of the Earth is 1.3 × 10 km.
The diameter of the Moon is 3.5 × 10 km.
The diameter of the Sun is 400 times greater
than the diameter of the Moon.
How many times smaller is the diameter of
the Earth than the diameter of the Sun
Earth's diameter is 0.0092 times less than the sun's diameter.
Ratio, in math, is a time period this is used to examine or greater numbers. It is used to indicate how large or small a sum is in comparison to another.In a ratio, portions are as compared the use of division. Here the dividend is referred to as the `antecedent' and the divisor is referred to as the 'consequent'. For example, in a collection of 30 people, 17 of them opt for to stroll within side the morning and thirteen of them favor to cycle. We use the ratio formulation whilst evaluating the connection among numbers or portions. The popular shape of representing a ratio of among portions say 'a' and 'b' is a: b, that's examine as 'a is to b'.The Diameter of Earth = 1.3 * 10⁴ km
The Diameter of Moon = 3.5 * 10³ km
Let the diameter of sun be x km
According to the question
The diameter of the sun is 400 times that of the moon.
x = 400 * 3.5 * 10³ km
= 14 * 10⁵ km
The Diameter of earth / diameter of sun
= 1.3 * 10⁴ / 14 * 10⁵
= 0.0092
Hence, The diameter of the Earth is 0.0092 times that of the Sun.
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Find the remainder when 2x^10 - 3ix^8 + (1 + i)x^2 - (3 + 2i)x + 1 is divided by (x - i)
Be sure to show your work.
Use the polynomial remainder theorem. The remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x-c[/tex] is exactly [tex]p(c)[/tex].
In this case,
[tex]p(x) = 2x^{10} - 3ix^8 + (1+i)x^2 - (3+2i)x + 1[/tex]
and [tex]c=i[/tex]. Then the remainder is
[tex]p(i) = 2i^{10} - 3i^9 + (1+i)i^2 - (3+2i)i + 1[/tex]
Since [tex]i^2=-1[/tex] and [tex]i^4=1[/tex],
[tex]p(i) = -2 - 3i - 1 - i - 3i + 2 + 1 = \boxed{-7i}[/tex]