The probability of drawing a king, a king or queen, a diamond, or a black card from a deck of 52 cards is 1/52, 4/52, 13/52, and 26/52, respectively.
(a) The probability that a king is drawn is 1/52, since there is only one king in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king is 1/52.
(b) The probability that a king or a queen is drawn is 4/52, since there are four kings and queens in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king or queen is 4/52.
(c) The probability that a diamond is drawn is 13/52, since there are 13 diamonds in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a diamond is 13/52.
(d) The probability that a black card is drawn is 26/52, since there are 26 black cards in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a black card is 26/52.
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If x varies directly as y, find x when y = 8 a) x = 6 when y = 32 b) x = 14 when y = -2
a) The value of x is 42.6 when k =16/3 is directly proportional to y.
b) The value of x is -56 when k is -7 is directly proportional to y.
What kind of variation is one where x and y are directly proportional?
If x = ky for some constant k can be used to indicate the relationship between the variables y and x, then we may say that y varies directly with y or that x is directly proportional to y.x varies directly as y
x α y
x = ky
a) x=6 ; y = 32
x = ky
6 = k(32)
k = 16/3
if y = 8
then,
x = (16/3) * 8
= 128/3
x = 42.6
Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.
b) x= 14 and y = -2
x = ky
14 = k(-2)
k = -7
if y = 8
then,
x = ky
x= (-7) 8
x = -56
Hence, the value of x is -56 when k is -7 is directly proportional to y.
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Does anyone know the answer for this?
The Venn diagram has been drawn and the product of LCM and GCF are the same as 24 x 36.
What is a Venn diagram?A Venn diagram is a pictorial representation of data represented in a circle.
The intersection parts of the circle represent the commonality of both sets.
As per the given, 24 and 36
The factors of 24 are as 2³ × 3
The factors of 36 are as 2² × 3²
The common factors 2² × 3
The LCM of 24 and 36 is 72 and the GCF is 12.
LCM x GCF = 24 x 12
72 x 12 = 24 x 12
864 = 864
Hence "After drawing a Venn diagram, it was discovered that the LCM and GCF product equals 24 x 36.".
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A circle with center w is shown in the figure below.
Radius = TW
Diameter = TX
Chord = UV
The length of TX is 6 units.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as πr².
We have,
From the figure:
Diameter = TX
Radius = TW or WX or WY
Chord = UV
WY = 3 units
TX = TW + WX = 3 + 3 = 6 units.
Thus,
TX is 6 units.
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The price of one gallon of milk has increased from $3.24 to $4.05. What is the percentage increase?
Answer:
the price of one gallon of milk has increased by 25%.
Step-by-step explanation:
The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:
(0.81 / 3.24) * 100% = 25%
Therefore, the price of one gallon of milk has increased by 25%.
The solution is 25 %
The percentage increase in the price of one gallon of milk is given by the equation P = 25 %
What is Percentage Error?
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage error is the difference between the measured value and the true value , as a percentage of the true value
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100
Given data ,
Let the original price of the milk be A = $ 3.24
Let the increased price of the milk be B = $ 4.05
Let the percentage increase in the price be = P
Now , the equation will be
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100
Substituting the values in the equation , we get
Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100
On simplifying the equation , we get
Percentage increase P = ( 0.81 / 3.24 ) x 100
Percentage increase P = 0.25 x 100
Percentage increase P = 25 %
Therefore , the value of P is 25 %
Hence , the percentage increase is 25 %
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Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Use a significance level of alpha = 0.1 The degree of freedom is The test statistic is Determine the rejection region for the test of The final conclusion is
Final conclusion would be that the difference between the means of the two samples is not statistically significant.
What is Null Hypothesis?
The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
It is not possible to test the claim that the two samples come from populations with the same mean without more information about the samples themselves. In order to test this claim, you need to have the sample data, the sample sizes, and the standard deviations of the samples. You can then use a t-test for independent samples to determine whether the difference between the means of the two samples is statistically significant.
The t-test is a statistical test that is used to compare the means of two samples. The test statistic for the t-test is the difference between the means of the two samples divided by the standard error of the difference. The degree of freedom for the t-test is the sum of the sample sizes minus 2. The significance level, alpha, is the probability of making a type I error, which is the probability of rejecting the null hypothesis when it is true. The rejection region for the t-test is the set of values of the test statistic for which the null hypothesis is rejected.
If the test statistic does not fall in the rejection region, you cannot reject the null hypothesis, and you must conclude that the difference between the means of the two samples is not statistically significant.
Final conclusion would be that the difference between the means of the two samples is not statistically significant.
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Question 12 options:
Nick determines the remainder of
, using the remainder theorem.
How does she proceed to the correct answer?
Fill in the blanks from the work bank below: (do not enter spaces)
x = 1 x = -1 x = 0 -23 -19 -15 -29
Nick evaluates the numerator of the rational expression when
. He concludes that the remainder of the division is
The input value for the expression is 1 and the remainder is -15.
What is the remainder theorem?The Remainder Theorem begins with an unnamed polynomial p(x), where "p(x)" simply means "some polynomial p with variable x". The Theorem then discusses dividing that polynomial by some linear factor x a, where an is simply a number.
Given polynomial is 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19 and is divided by x + 1. Find the value of the polynomial at 1 and then calculate the remainder by synthetic solution.
F(x) = 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19
F(1) = 5 - 3 + 2 - 19
F(1) = -19 + 4
F(1) = -15
The remainder will be calculated by synthetic calculation,
1 __5 ___-3___2_____-19
|
| ______5___ 2______4
5 2 4 -15
The remainder of the given expression is -15.
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Find the Derivative of 1/x+2
Answer: 2x+1
x
Step-by-step explanation:
Assume that a company makes only one product, maintains no beginning or ending inventories, and uses a standard costing system. The standard cost card for that product is shown below:
Standard Quantity or Hours Standard Price or Rate Standard Cost
Direct materials 3 pounds $ 13.00 per pound $ 39.00
Direct labor 2 hours $ 16.00 per hour $ 32.00
Fixed manufacturing overhead 2 hours $ 8.00 per hour $ 16.00
The company purchased 22,000 pounds of direct materials from its supplier at a cost of $12.50 per pound. The company used 22,000 pounds of direct material to start and complete 7,800 units of finished goods during the period. Its direct laborers worked 16,000 hours and were paid a total of $248,000. Based on this information, the total increase recorded in the Work in Process account related to direct labor would be:
Garrison 17e Rechecks 2020-09-29
Multiple Choice
$241,800.
$256,000.
$248,000.
$249,600.
Group Ends
Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor.
How to calculate labor cost ?To determine the total increase recorded in the Work in Process account related to direct labor, we need to first calculate the total standard cost of direct labor for the period and then compare it to the actual cost of direct labor.
According to the standard cost card, each unit of the product requires 2 hours of direct labor at a rate of $16.00 per hour.
This means that the total standard cost of direct labor for the period is 2 * $16.00 * 7,800 = $248,000.
Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor. Therefore, the total increase recorded in the Work in Process account related to direct labor would be $0.
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How to set up the following question in the image below?
The expected number of students that pick soda is 80
How to determine the expected number of students that pick Soda?From the bar graph, we have the following parameters that can be used in our computation:
Ice cream = 40
Soda = 20
popsicle = 10
This means that the proportion of soda is
Soda = 20/(40 + 20 + 10)
Evaluate the sum
Soda = 20/70
So, we have
Soda = 2/7
For a group of 280 students, we have
Soda = 2/7 *280
Evaluate
Soda = 80
Hence, the number of students is 80
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The length of a rectangle is 3 meters less than
twice its width. The area of the rectangle is
104 m²2. Find the dimensions of the rectangle.
Therefore, the length of a rectangle is 13m and width is 8m
What is area?A region's size on a planar or curved surface is described mathematically as its area. In contrast to a plane region or plane's area, which refers to a form or planar lamina, a surface area is the size of an open surface or the edge of a three-dimensional object.
Here,
width=x
length=2x-3
Area =l x w
104=(2x-3)(x)
104=2x^2-3x
52=x^2-3/2(x)
52+9/16=x^2-3/2(x)+9/16
841/16=(x-3/4)^2
29/4=x-3/4
x=32/4
x= 8m
Thus width = 8m
length = 2(8)-3 = 13m
Therefore the length of a rectangle is 13m and width is 8m
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My sister is 8 years older than I am. The sum of our ages is 28. Find our ages.
I am years old. My sister is years old.
Answer:
My sister is
18
years old.
Step-by-step explanation:
s = m + 8 Eq. 1
s + m = 28 Eq. 2
s = my sister age
m = my age
Replacing Eq. 1 in Eq. 2:
(m+8) + m = 28
2m + 8 = 28
2m = 28 - 8
2m = 20
m = 20/2
m = 10
From Eq. 1:
s = m + 8
s = 10 + 8
s = 18
Check:
from Eq. 2:
s + m = 28
18 + 10 = 28
is melissa correct that m(
Answer:
no melissa isn't correct she has made 3 mistakes
Step-by-step explanation:
which statement describes the solutions of this equation? x/x+2 + 1/x = 1
Answer:
[tex]\frac{x}{x+2}+\frac1x=1\\\rightarrow \frac{x^2+(x+2)}{(x^2+2x}=1\\\rightarrowx^2+x+2=x^2+2x\\\rightarrowx+2=2x\\\rightarrow x=\boxed2[/tex]
Only one solution, which is two. The answer should be C. You could obviously see that if there is no squaring then there will be no extraneous solutions.
what does
QR=
PR=
M
We need to use Right Angled Triangle Properties.
PR≈15 and QR≈12 is the length of the sides.
What is a Right Angled Triangle?
According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of its angles is a right angle (90o). Triangle PQR is a right triangle in the illustration, and its components are its base, height, and hypotenuse. Here, QR is the base, PQ is the height, and PR is the hypotenuse. The essential side of a right triangle is its hypotenuse, which is also its largest side and sits across from the triangle's right angle.
In a right triangle we have: (Hypotenuse)2 = (Base)2 + (Altitude)2
Area of a right triangle = (1/2 × base × height) square units.
Calculation:PR is the Hypotenuse of the Triangle.
PQ=9
Angle ∡PQR=37° and Angle ∡RPQ=53°
So Sin(theta)=opposite side/Hypotenuse
⇒Sin(37°)=9/Hypotenuse
⇒Hypotenuse=9/0.6018
⇒Hypotenuse=14.955
PR⇒14.955
We know that (Hypotenuse)2 = (Base)2 + (Altitude)2
⇒(14.955)2=(9)2+(QR)2
QR=11.9438
PR≈15 and QR≈12
We need to use Right Angled Triangle Properties.
PR≈15 and QR≈12 is the length of the sides.
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Sample Response: First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller.
Which did you include in your answer?
Check all that apply.
Write the ratios as fractions.
Find a common denominator.
Compare the numerators to see that 4:10 is the smaller ratio.
In the aforementioned scenario, the choice you must include in your response is to find a common denominator.
In the simplest terms, what is fraction?One can refer to a fraction as being in its lowest term or in its simple form when the numerator and denominator are known to have no common factors besides 1. In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech.
The common denominator will be between 10 and 20, and there is a common numerator as well. The common denominator will be 20 because both can divide it and 10 is less than 20.
Finding a common denominator is the solution you should choose in the scenario mentioned above.
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Convert the measurement. 28.4 grams ≈ ounces
Answer: 1.0017805194 ounces
Step-by-step explanation:
To change 28.4 g to oz divide the mass in grams by 28.349523125. The 28.4 grams to ounces formula is [oz] = [28.4] / 28.349523125. Thus, we get (all results rounded to 2 decimals):
28.4 g to oz = about 1 oz
28.4 g to ounces = about 1 ounces
28.4 grams to ounces = about 1 oz
Twenty-eight point four grams to ounces equal 1 international avoirdupois ounces, the unit used to measure grocery products (mass) in retail stores in the United States for example.
HOPE THIS HELPS 189328 :)!If (x+2) is a factor of
Answer: a=3 and b=1
Step-by-step explanation:
Let p(x)=x 2 +ax+2b
If x+2 is a factor of p(x)
Then by factor theorem
p(−2)=0
⇒(−2)
2
+a(−2)+2b=0
⇒4−2a+2b=0
⇒a−b=2 ---(i)
Also given that a+b=4 ---(ii)
Adiing (i) and (ii) we get
2a=6
⇒a=3
putting a=3 in (i) we get
a−b=2
⇒3−b=2
⇒b=1
Therefore we get a=3 and b=1
Clarks Inc., a shoe retailer, sells boots in different styles. In early November the company starts selling “SunBoots” to customers for $70 per pair. When a customer purchases a pair of SunBoots, Clarks also gives the customer a 30% discount coupon for any additional future purchases made in the next 30 days. Customers can’t obtain the discount coupon otherwise. Clarks anticipates that approximately 20% of customers will utilize the coupon, and that on average those customers will purchase additional goods that normally sell for $100. Required: 1. How many performance obligations are in a contract to buy a pair of SunBoots? 2. Assume Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon. Prepare a journal entry to record revenue for the sale of 1,000 pairs of SunBoots.
The journal entry is given in answer part b
What is Discount coupon?A discount coupon is defined as a certificate that entitles the customer to avail of a reduction in the invoice price if the terms mentioned on it are met. It is a technique applied by the sellers to expand sales.
Given that, Clarks Inc., a shoe retailer, sells boots in different styles. In early November, the company starts selling “SunBoots” to customers for $70 per pair. When a customer purchases a pair of SunBoots, Clarks also gives the customer a 30% discount coupon for any additional future purchases made in the next 30 days. Customers can’t obtain the discount coupon otherwise. Clarks anticipates that approximately 20% of customers will utilize the coupon, and that on average those customers will purchase additional goods that normally sell for $100.
a) Two performance obligations are associated with contract. The first one is related to the sun boots, and the other one is associated with discount coupon provided. The discount coupon would be considered a separate obligation because it gives a certain right to the customers that they would not have received if the sale was not made to them.
b) Journal entry =
Account title and explanation Debit ($) Credit ($)
Cash (1000×$70) $70000
Sales Revenue ($70,000-$6000) $64000
Deferred Revenue $6000
Now,
Computation of the deferred revenue:
Deferred revenue = pairs sold × Average purchase price × Discount × Redemption of coupon
= 1000 × 100 × 30% × 20%
= $6000
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Write an equation to match this graph.
The equation that matches the graph is 7x-30y=-275
How to find the equation of a line?We should know that an equation is a mathematical expression in which two sides are equal.
The equation of a line is the equation formed with the slope of the straight line
The slope of the of the is determined taking the points
[tex]M=\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]
Slope=(7-1)÷(35-5)
m=1/5
The equation of the line is
1/5 = (y-1)÷(x-35)
Cross multiplying the equation
7x-245=30y-30
Rearrange,
7x-30y=-30-245
7x-30y=-275
In conclusion the equation to match the graph is 7x-30y=-275
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AOB is a sector of a circle, centre O and radius 12 cm. The length of arc AB is 15 cm. Find the area of the sector.
The formula to find the arc length of a circle = θ/360 ×2××r
The formula to find the area of a sector= θ/360××r²
The only thing missing is "θ"
The arc length is given to be 15cm so basically θ/360×2×3.14×12 = 15
θ= 360×15 ÷ 2×3.14×12 = 5400÷ 75.36= 71.65
now that we found "θ" we just continue with the formula to find the area of a sector (θ/360×r²)
=71.65×3.14×12²= 90cm
(it's a bit complicated but i hope this helped i tried to simplify it as much as i could)
You buy 9 granola bars for a camping trip. Each bar costs $0.95. What
is the total cost of 9 granola bars before tax?
Answer:
Step-by-step explanation: 9 multiplied by .95 = $8.55 before tax
Alex biked a 48-mile trail in 4 hours. For the first half of the time, he biked twice as fast as he did the second half of the time. What speed did Alex bike the first half?
Alex's speed in the first half of the time is 12 miles per hour
How t find the speed of bikingInformation from the problem include:
For the first half of the time, Alex biked a 48-mile trail in 4 hours.
he biked twice as fast as he did the second half of the time.
Average speed is calculated using the ratio of distance to time spent
this is represented by the formula
= distance / time
The speed for the first half is solved as below
= 48 mile / 4 hours
= 12 mile / hours
= 12 mph
speed for the first half is 12 mph
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Review the graph. Given z = -1 - i, which letter represents z3?
Answer:
C
Step-by-step explanation:
Multiply z times itself. Then multiply z times that first answer, to get z^3.
There's a formula for cubing a binomial but even if you don't remember it (like me) you can still find z^3.
But remember that i^2 = -1
This is related to sqrt(-1)= i, a definition for the imaginary number.
On the graph, go left or right for the real part and up or down for the imaginary part.
see image.
Which expression can be used to represent the volume of this prism?
Responses
3 × 9 × 9 units³
2 × 3 × 3 units³
2 × 3 × 9 units³
3 × 3 × 18 units³
The expression that represents the volume of the prism is
2 × 3 × 9 units³. That is option C.
What is a prism?Prism is defined as the type of polyhedron that has two polygonal faces lying in parallel planes and with the other faces parallelograms.
A prism can be of a regular shape or of an irregular shape. The volume of a regular shapes prism can be calculated using the formula stated below
volume of a prism = l × b × h
Length (l) = 9 units
Breath = 2 units
Height (h) = 3 units.
Therefore, the volume of the given prism can be calculated as 2 × 3 × 9 units³.
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I need help
How do you find x:
2^(2x) + 2^(x+2) - 12 = 0
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
[tex]2^{2x}-2^2 2^x-12=0 \\ \\ (2^x)^2-4(2^x)-12=0[/tex]
Factoring the quadratic in [tex]2^x[/tex],
[tex](2^x+6)(2^x-2)=0 \\ \\ 2^x=-6,2 \\ \\ 2^x=2 \implies x=1 \\ \\ 2^x=-6 \implies x \notin \mathbb{R} \\ \\ \therefore x=\log_{2} (6)[/tex]
Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same
If you answer the visits, I will give branliest
The number or visits that Jim must make to make Plan A the cheaper option is more than 5 visits
How to illustrate the equation?An equation is the statement that illustrates the variables given. Jim has to choose between two gym membership plans.
For Plan A: $50 monthly membership fee and $10 per visit. This will be:
50 + 10v
Plan B: $25 one time membership fee and $15 per visit. This will be:
= 25 + 15v
Let v = number of visit
This will be illustrated as:
50 + 10v = 25 + 15v
Collect like terms
15v - 10v = 50 - 25
5v = 25
Divide
v = 25 / 5
v = 5
There will be more than 5 visits for a cheaper option.
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Can someone help me on this question?
Answer:
see below for the chart
64 pages in 1 hour
Step-by-step explanation:
You want to fill in the chart showing the analysis of the problem statement saying HP can read 16 pages in 1/4 hour. The problem statement is requesting the number of pages he can read in 1 hour.
ChartSee below for a filled-in chart.
SolutionAnalysis of the bottom line tells you that the right column is 4 times the middle column.
1 = 4 × 1/4
?? = 4 × 16 = 64
Harry Potter can read 64 pages in one hour.
i literally don’t know
∠U is congruent ∠S because all right angles are congruent.
Define congruent.If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence. When two sides and their included angle in one triangle are equal to two sides and their included angle in another, two triangles are said to be congruent. This concept of congruence appears to be based on the idea of a "rigid body," which may be moved without affecting the internal relationships between its components.
Given
∠U ≅ ∠S
All right angles are congruent.
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Find the area of a circle with radius 6 ft.
Answer:
The area of the circle is 113.04 square feet.
Step-by-step explanation:
Given;Radius (r) = 6 ftπ = 3.14Formula;A = πr²A = 3.14 × (6)² ft
A = 3.14 × 36 ft
A = 113.04 square feet.
Thus, The area of the circle is 113.04 square feet.
Answer:
28.274 square feet
Step-by-step explanation:
Multiply the radius by pi
Find the remainder term Rn in the nth order Taylor polynomial centered at a for the given function. Express the result for a general value of n. f(x)=e^-2x, a=2 Choose the correct answer below. O A. Rn (x) = (-2)^n e^-2c/(n+1)! (x- 2)^n for some c between x and 2. O B. Rn (x) = (-2)^n+1 e^-2c/(n+ 1)! for some c between x and 2. O C. (-2)1+1e 2c Rn(x)=?(n+1)!-(x-2)n + 1 for some c between x and 2. O D. n -2c OD. (x-2)"+1 for some c between x and 2.
The remainder term Rn is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2.
The remainder term Rn in the nth order Taylor polynomial centered at a for the given function f(x)=e^-2x, a=2 is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2. This remainder term represents the difference between the approximate value of the function given by the Taylor polynomial and the actual value of the function. By taking the limit as n approaches infinity, the remainder term can be used to determine the exact value of the function. The remainder term is an important concept in calculus as it is used to determine the accuracy of a given approximation.
For n=5, R5(x) = (-2)^5 e^-2c/(5+1)! (x-2)^5 for some c between x and 2.
Substituting n=5, x=7 and c=4, we have:
R5(7) = (-2)^5 e^-8/(6)! (7-2)^5
R5(7) = (-2)^5 e^-8/(720) (25)
R5(7) = (-2)^5 e^-8/18000
R5(7) = (-2)^5 e^-8/18000
R5(7) = -1.388888888 x 10^-9
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