The hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in, rounded to the nearest tenth. This is calculated by using the Pythagorean Theorem, which states that a2 + b2 = c2 and plugging in the values for a and b.
The hypotenuse of a right triangle is the longest side of the triangle and is always opposite of the right angle. To calculate the length of the hypotenuse, you need to use the Pythagorean Theorem. The theorem states that a2 + b2 = c2, where a and b are the legs of the triangle and c is the hypotenuse. In this case, a is 18 inches and b is 26 inches, so the equation would be 182 + 262 = c2. Plugging in the values, we get 324 + 676 = c2, which simplifies to 1000 = c2. To find the length of the hypotenuse, we need to take the square root of 1000, which is 31.6 inches. Rounded to the nearest tenth, the hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in.
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오
NK=(12
If the quadrilateral below is a rhombus, find the missing
measures. MK = 24, JL = 20, and m/MJL = 50°. Round to 1
decimal place.
NL=10
ML=(68
JM=(68
m&KNL=(
), m&KJL=(
m_MLK=
), m/JKM=(
The measures of angles of a rhombus are ∠KNL = 90° , ∠KJL = 50° , ∠MLK = 100° and ∠JKM = 40°
What is the perimeter of Rhombus?A Rhombus has four sides of the same length, its perimeter can be determined using the formula Perimeter = 4a, where "a" stands for the side's length.
When the two diagonals of a rhombus are known,
The perimeter = 2√p² + q²
where 'p' and 'q' are the diagonals.
Given data ,
Let the rhombus be represented as JKLM
where MK and JL are the diagonals and N is the midpoint of intersection
The measure of MK = 24
The measure of JL = 20
The measure of NK = 12
The measure of ∠MJL = 50°
Now , the diagonals of a rhombus bisect each other , so
NK = MK/2 = 12
And , NL = JL / 2 = 10
Now , to calculate the measure of ML ,
In triangle MNL, ∠N = 90°
MN = NK = 12 , NL = 10
Using Pythagorean theorem of triangles , we get
ML² = MN² + NL²
ML² = 12² + 10²
ML² = 244
ML = √244
On simplifying the equation , we get
ML = 2√61 = 15.62
The measure of ML = measure of JM = 15.62 ( all sides are equal )
The measure of ∠KNL = 90° ( diagonals of a rhombus are perpendicular bisectors )
∠KJL = ∠MJL (diagonals bisect angles)
The measure of ∠KJL = 50°
∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°
∠MJK = ∠MLK (opposite angles are equal)
The measure of ∠MLK = 100°
∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)
50 + 90 + ∠JKM = 180
The measure of ∠JKM = 40°
∠JKL = 2 x ∠JKM (diagonal bisect angle)
The measure of ∠JKL = 2 x 40
The measure of ∠JKL = 80°
∠JKL = ∠JML (opposite angles are equal)
The measure of ∠JML = 80°
Hence , the measures of rhombus is solved
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Write 60.9% as a decimal.
A.0.0609
B.0.609
C.0.00609
D.6.0900
To convert a percentage to a decimal, divide the percentage by 100, The correct answer is B. 0.609.
What is Decimal number?When the decimal places in the factors are tallied together, they equal the number of decimal places in the product. A decimal number is one with a whole and a fraction part separated by a decimal point.
A base-10 representation of numeric values is used in the decimal numbering system. The system is widely used in daily life to complete routine tasks like grocery shopping, stock trading, keeping track of football scores, or scrolling through cable channels. Decimal numbers include 7, 28, 199, and 532.11.
To convert a percentage to a decimal, divide the percentage by 100.
So, 60.9% as a decimal would be:
60.9 / 100 = 0.609
Therefore, The correct answer is B. 0.609.
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Is 96 the lowest common multiple of 4 and 24?
no
4x6=24
24x1=24
hence 24 is the lowest common multiple , i hope this helped xx
cover all material from the lessons but will hopefully remind you of key points. To be prepared,
you must study all packets from Unit 1.
A salesman tracks the number of cars he sells through the model c, where c(m) is number of cars sold
and m is the month for 0 ≤ m ≤ 24.
1. What does c(10) represent?
2. What does
c(16)-c(8)
16-8
represent? 3. What does
represent?
c(7)-c(6.999)
7-6.999
a. It should be noted that c(10) represents the number of cars sold in the 10th month.
b. c(16) - c(8) represents the number of cars sold in the 16th month minus the number of cars sold in the 8th month. This difference could represent the net change in the number of cars sold between those two months.
What is a function about?The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. The process of evaluating a function is typically straightforward when we have the function in the form of a formula.
In this case, c(10) represents the number of cars sold in the 10th month.
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help pls i’m stuck!!
Step-by-step explanation:
inscribed angles subtended by the same arc are equal.
the angle FGH is "based" on the same arc (FH) as the angle FJH.
so, FGH = FJH = 56°.
Please Help Me! I really need this question answered. I am behind in my work!!!!!
Answer:
The flagpole is 15 ft tall.
Step-by-step explanation:
In this problem, we are asked to create a proportion of similar triangles to solve for the height of a flagpole.
1) Setting up the ProportionWe are given an equation with the proportion:
[tex]\dfrac{h}{6\text{ft}}=\dfrac{\square}{\square}[/tex]
We can fill in the blanks as follows:
[tex]\dfrac{h}{6\text{ft}}=\dfrac{25 \text{ft}}{10 \text{ft}}[/tex]
Notice that the heights of the triangles compared are both in the numerator, and the lengths of both triangles are in the denominator.
2) Solving the ProportionThen, to solve for the height of the flagpole, we can isolate the variable h in the proportion.
[tex]\dfrac{h}{6}=\dfrac{25}{10}[/tex]
↓ multiply both sides by 6
[tex]h = \dfrac{150}{10}[/tex]
↓ simplify the fraction
[tex]h = 15 \text{ ft}[/tex]
So, the flagpole is 15 ft tall.
Como puedo resolver esto?
- x - y = 4
The points on the graph of the equation represent the solution set to the equation.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the equation as -
- x - y = 4
The given equation is -
- x - y = 4
x + y = 4
The graph of the given equation will represent a straight line. All the points on the line represent the solution set to the equation.
Therefore, the points on the graph of the equation represent the solution set to the equation.
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{Question in english -
How can i solve this?
- x - y = 4}
a significance test about a proportion is conducted using a significance level of . the test statistic equals . the p-value is . a. if were true, for what probability of a type i error was the test designed? b. if this test resulted in a decision error, what type of error was it?
a) The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.
A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.
In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.
If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.
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The complete question is:
A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.
a) What chance of a Type I error was the test designed for, if H0 were true?
b) What judgement would you draw on this test (reject or fail to reject)?
c) What kind of error, if any, was there as a result of this test?
What is the solution to 3 (2k + 3) = 6 - (3k - 5)?
Move the correct answer to each box. Not all answers will be used.
k
-8 -2 2
3 8
9
Answer: 22k
Step-by-step explanation:
The solution to the equation is k = 2/9
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
3 ( 2k + 3 ) = 6 - ( 3k - 5 ) be equation (1)
On simplifying , we get
3 ( 2k ) + 9 = 6 - 3k + 5
6k + 9 = 11 - 3k
Adding 3k on both sides , we get
9k + 9 = 11
Subtracting 9 on both sides , we get
9k = 2
Divide by 9 on both sides , we get
k = 2/9
Therefore , the value of k is 2/9
Hence , the solution is k = 2/9
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___ % of 20 is 3.2?
- 15%
-16%
- 18%
- 20%
−2x+y = 0 - −7x+3y = 2
To solve this system of linear equations, we need to find the values of x and y that make both equations true at the same time. One method to solve this is to use elimination or substitution.
First, let's rearrange the first equation:
y = 2x
Next, we can substitute y = 2x into the second equation:
-7x + 3y = 2
-7x + 3(2x) = 2
-7x + 6x = 2
-x = -2
So, x = 2.
Finally, we can use the first equation to find y:
y = 2x
y = 2 * 2
y = 4
So, the solution to the system of equations is (x, y) = (2, 4).
Your school is going to start offering afterschool clubs they will be nine clubs to choose from to have clubs at least 23 students we will need to sign up for each one what is the least number of students that must sign up to have all nine clubs
At least number of students who must have signed up to have all nine clubs is equal to 207.
Number of clubs school going to start after school = 9 clubs
At least number of students need to sign up in each one of the club is equal to 23 students.
At least number of students need to sign up to have all in nine clubs is equal to :
At least number of student in 1 club > 23
⇒ At least number of student in 9 club > 23 × 9
At least number of student in 9 club > 207
Therefore, at least number of students need to signed up to have in all nine given clubs are 207 students.
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If Sullivan got 32 pieces of candy, how many did Carter get? Answer
Sullivan received half as many candy as Carter did, or half as many candies as Sullivan received.
What is an amount?aggregate means the complete amount or quantity. attempting to estimate the time required. the amount on hand or being considered. mutable noun How much of something there is, how much you possess, require, or receive, is known as its amount. He is dependent on that sum of money to get by.Therefore, a number only refers to things that we can count. Contrarily, quantity relates to how much of something there is, such as how much liquid, resistance, or stimulation. In actuality, the term "amount" refers to amounts that we can measure but not count individually." Amount is defined as the representation of total quantity of given object."
According to the question,
Number of candies Sullivan got = s
Number of candies Carter got = 2s
Compare the given amount of data we get,
Number of candies Carter got = 2(Number of candies Sullivan got )
This shows Carter got twice number of candies comparison to Sullivan.
or
Number of candies Sullivan got = 1/2 (Number of candies Carter got)
Sullivan got half number of candies compare to Carter.
Hence, we conclude Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.
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can solve the question in the picture and solve both parts
Answer:
zeroparallel to the x-axisStep-by-step explanation:
You want to know the slope of the line segment between (-4, -3) and (3, -3), and its relation to the x-axis.
SlopeThe slope of a line between two points (x1, y1) and (x2, y2) is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For the given points, the slope is ...
m = (-3 -(-3))/(3 -(-4)) = 0/7 = 0
The slope of the line segment is zero.
The line segment has the same slope as the x-axis. It is parallel to the x-axis.
__
Additional comment
The equation of the line segment is ...
y = -3 . . . for -4 ≤ x ≤ 3
The equation of the x-axis is ...
y = 0
rk
d not
4 Fill in the gaps in the following paragraphs to summarise the
information about the learners' masses.
4.1
The boys' masses range from a minimum of ..... to a maximum
of ..... kg.
4.2
The girls' masses range from a minimum of ..... to a maximum
of ..... kg.
5 Organise the data into the following frequency table.
Mass interval Tally
Tally
Number of female
learners who have a
mass in this interval
40 - 49,9 kg
50 - 59,9 kg
60 - 69,9 kg
70-79,9 kg
80 - 89,9 kg
Number of male
learners who have a
mass in this interval
6 Compare the frequencies for the female and male learners and
describe any differences that you notice.
4.1. The boys' masses range from a minimum of 32 kg to a maximum of 82 kg.
4.2. The girls' masses range from a minimum of 35 kg to a maximum of 67 kg.
What are the responses to other questions?5: To create the frequency table, we need to tally the number of male and female learners in each mass interval. Here are the tallies:
Mass interval Tally
40 - 49,9 kg |||| (4 females)
50 - 59,9 kg ||||||| (7 females)
60 - 69,9 kg ||||| (5 females)
70-79,9 kg || (2 males)
80 - 89,9 kg || (2 males)
Note: The vertical lines represent the tallies, with each line representing one learner.
6: By looking at the frequency table, we can compare the number of male and female learners in each mass interval. We can see that there are more female learners in the lower mass intervals (40-49.9 kg, 50-59.9 kg, and 60-69.9 kg) compared to male learners. On the other hand, there are more male learners in the higher mass intervals (70-79.9 kg and 80-89.9 kg) compared to female learners
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A trail map has a scale of 3 in. : 2 mi. On the map,
a trail is 5 in. long.
How long is the actual trail?
0 1/mi
O2 mi
O O
12
3-mi
O 07 mi
Answer:
Step-by-step explanation:
in: mi
3:2
5:x
3*1.6667=5
2*1.6667=3.3334/
becaus the first answer was rounded up, the last one needs to be rounded down.
so the answer, rounded up to the nearest hundredth is 3.34
(rounded up to the nearest whole number is 3)
Here are the hottest recorded temperatures (ln^ F) for eight cities throughout North America. Complete the grouped frequency distribution for the data. In the distribution, the frequency of a class is the number of temperatures that class. (Note that we are using a class width of 5.)
The frequency of each class interval 103 - 107, 108 - 112 and 113 - 117 are 2, 2 and 4 respectively.
What is meant by Grouped Frequency Distribution?A grouped frequency distribution is the distribution of data into various classes with equal width with the frequency being the number of outcomes in that class.
Given are the hottest recorded temperatures (in °F) for eight cities throughout North America.
113 110 108 104 117 116 113 103
The class intervals are 103 - 107, 108 - 112 and 113 - 117.
In the distribution, the frequency of a class is the number of temperatures that class.
The temperatures in the class 103 - 107 are 103 and 104.
Frequency of 103 - 107 = 2
The temperatures in the class 108 - 112 are 108 and 110.
Frequency of 108 - 112 = 2
The temperatures in the class 113 - 117 are 113, 113, 116 and 117.
Frequency of 113 - 117 = 4
Hence the frequency are 2, 2 and 4 for the intervals 103 - 107, 108 - 112 and 113 - 117 respectively.
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please this is so urgent
Select the correct answer.
What is the domain of the exponential function shown in the graph?
Answer: Choice D
Explanation:
The notation [tex]-\infty < \text{x} < \infty[/tex] says x is anything between negative infinity and positive infinity. Basically x is any real number. This is because the curve stretches forever to the left and right. Any number can be the x input.
Zoe ran a lemonade stand 5 times last summer. The numbers of lemons needed depended on
the number of customers each time
The standard deviation of the number of lemons used is equal to 14.7.
How to calculate the mean?Mathematically, the mean for these set of data would be calculated by using this formula:
Mean = [F(x)]/n
F(x) = 47 + 45 + 61 + 44 + 16
F(x) = 213.
Mean = 213/5
Mean = 42.6
Next, we would calculate the standard deviation of this data set by using this formula:
SD = √(1/n × ∑(xi - u₁)²)
SD = √(1/5 × (47 - 42.6)² + (45 - 42.6)² + (61 - 42.6)² + (44 - 42.6)² + (16 - 42.6)²)
Standard deviation, SD = √(1073.2/5)
Standard deviation, SD = 14.7.
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Lillian needed
2 bottle of glue to make 8 Halloween Decorations. How many can she make
10
with 1 bottle of glue?
which value could be the length of the side of the triangle the triangle is not drawn to scale 5 and 12 and x
The third side is between 7 and 17 inches long.
What is the theorem of triangle inequality?This theorem states that for any triangle, the sum of the lengths of the first two sides will always be greater than the length of the third side.
A triangle's two sides have lengths of 5 and 12 inches.
According to the triangle Inequality (theorem), any triangle's two sides must add up to more than its third side.
The length of the third side will be,
5 + 12 = 17 inches
It is to be noted that the difference between the two sides cannot be less on the third side.
The third side must be greater than,
12 – 5 = 7 inches.
As a result, the third side's length ranges from 7 to 17 inches.
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Somebody please look at this picture and help me pleaseeeeeee
Answer:
I think it's
Step-by-step explanation:
usually involves reading the pattern on the table while keeping in mind that x goes on top and y on
please help me with this
Answer: 1 [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Make it a mixed number then simplify if you can. I hope this helps.
Find the number that makes the ratio equivalent to 63:9.
7:
How much would $100 invested at 6% interest compounded monthly be
worth after 20 years? Round your answer to the nearest cent.
A (t) = P(1+r/n)^nt
Answer:
D
Step-by-step explanation:
[tex]100(1 + \frac{016}{12}) ^{12(20)}[/tex]
331.02
Answer:
D. $220.00
Explanation :
Pt(1+r/n) n
Ashwin helps paint a square mural in his classroom. Then he helps paint a mural in the hallway whose length is 7 feet longer and whose width is 3 feet shorter. Let x represent the side length of the mural in Ashwin's classroom. Write an expression that represents the two binomials you would multiply to find the area of the hallway mural. Use that expression to find the area of the hallway mural if each side of the classroom mural is 8 feet long.
A.
(x + 7)(x + 3); 165 square feet
B.
(x – 7)(x + 3); 11 square feet
C.
(x – 7)(x – 3); 5 square feet
D.
(x + 7)(x – 3); 75 square feet
Answer:
(x + 7)(x - 3) = 75 square feet.
Step-by-step explanation:
Given that x represents the side length of the mural in Ashwin's classroom, the hallway mural's length is x + 7 feet and its width is x - 3 feet. The area of the hallway mural can be found by multiplying these two binomials, (x + 7)(x - 3), to get x^2 + 4x - 21.
If each side of the classroom mural is 8 feet long, the hallway mural would have sides of 15 feet and 5 feet, so its area would be 75 square feet, which is the answer.
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
11, 20, 29, ...
Find the 43rd term.
The given sequence appears to be an arithmetic sequence, as the difference between consecutive terms is 9. To find the 43rd term, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term (11 in this case), n is the term number (43 in this case), and d is the common difference (9 in this case).
Plugging in the values, we get:
a_43 = 11 + (43 - 1) * 9
a_43 = 11 + 42 * 9
a_43 = 11 + 378
a_43 = 389
So the 43rd term of the sequence is 389.
one way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. for example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. in this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. throughout the study, the health status of the participants is monitored closely. suppose that you are a researcher designing an experimental feeding trial. how would you set up your study and what limitations would you face? drag the labels onto the flow chart to identify the elements and limitations of your experimental design.
The steps to set up the study and the limitations that would be faced are explained below .
The Steps to setup the study are :
(i) Recruit a large and diverse group of participants who are willing to stick to the prescribed diets for the duration of the study.
(ii) Divide the participants randomly into two or more groups. One group would be given a diet high in trans fats, and the other group(s) would be given a diet low in trans fats.
(iii) Monitor the health status of the participants closely throughout the study .
(iv) At the end of the study, compare the health outcomes of the different groups of participants to determine whether there is a significant difference in health outcomes .
The Limitations of this type of study include :
⇒ the difficulty of controlling all aspects of participants' diets, since participants may consume other foods outside of what is provided to them.
⇒ the study may not be long enough to detect long-term effects of trans fats on health.
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The given question is incomplete , the complete question is
One way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. For example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. In this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. Throughout the study, the health status of the participants is monitored closely.
Suppose that you are a researcher designing an experimental feeding trial. How would you set up your study and what limitations would you face ?
Emma was ranked 54th in his graduating class of 296 students. At what percentile is Emma’s ranking?
Answer: 54 is 18.24% of 296
Step-by-step explanation:
54:296*100 =
(54*100):296 =
5400:296 = 18.24
Now we have: 54 is what percent of 296 = 18.24
Question: 54 is what percent of 296?
Percentage solution with steps:
Step 1: We make the assumption that 296 is 100% since it is our output value.
Step 2: We next represent the value we seek with x
Step 3: From step 1, it follows that 100% = 296
Step 4: In the same vein, x% = 54
Step 5: This gives us a pair of simple equations:
100% = 296 (1)
x% = 54 (2)
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left-hand side) of both equations have the same unit (%); we have
100% over x% = 296 over 54
Step 7: Taking the inverse (or reciprocal) of both sides yields
x% over 100% = 54 over 196
x=18.54
Binomial expansion
(a) Expand (1+e^x)+(e^3x) in ascending powers of x to the term x^2.
(b) If the coefficient of x^2 in the expansion [tex]\frac{(1+e^{x}-e^{3x})(1-3x)^{n}}{e^{3x} }[/tex] is [tex]\frac{433}{2}[/tex] , find n.
Answer:
Step-by-step explanation: (a) To expand (1 + e^x) + (e^3x) in ascending powers of x to the term x^2, we can use the Taylor series expansion.
The Taylor series expansion for e^x is given by:
e^x = 1 + x + x^2/2! + x^3/3! + ...
So,
e^x = 1 + x + x^2/2! + x^3/3! + ...
and
e^3x = 1 + 3x + 9x^2/2! + 27x^3/3! + ...
Now, we can substitute these expansions into the original equation to get:
(1 + e^x) + (e^3x) = 1 + (1 + x + x^2/2! + x^3/3! + ...) + (1 + 3x + 9x^2/2! + 27x^3/3! + ...)
Expanding, we get:
(1 + e^x) + (e^3x) = 2 + x + 4x + x^2/2! + 9x^2/2! + ...
So, to the term x^2, the expansion becomes:
(1 + e^x) + (e^3x) = 2 + x + 4x + (x^2/2! + 9x^2/2!) + ...
which simplifies to:
(1 + e^x) + (e^3x) = 2 + x + 4x + 11x^2/2! + ...
(b) The coefficient of x^2 in the expansion is 11/2!. So, n = 11/2! = 11/2.
