Carly will need to buy 27.05 gallons of gas for the trip, which will cost her $7.28.
To calculate the total cost of the road trip, we need to find out how many gallons of gas Carly will need and then multiply that by the cost per gallon.
First, we need to convert the distance from miles to gallons, using the truck's fuel efficiency of 21 miles per gallon
568 miles ÷ 21 miles per gallon = 27.05 gallons
So Carly will need approximately 27.05 gallons of gas for the trip.
Next, we need to convert the cost of gas from liters to gallons. There are 3.79 liters in 1 gallon, so the cost of gas is:
$1.02 per liter ÷ 3.79 liters per gallon = $0.269 per gallon
Finally, we can calculate the total cost of the road trip by multiplying the number of gallons of gas by the cost per gallon
27.05 gallons × $0.269 per gallon = $7.28
Therefore, the road trip will cost Carly approximately $7.28.
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What is the length of the hypotenuse of the triangle below?
A 7-foot-high rectangular door needs 2 lengths of trim that make an X on the door.
If the door width is 3 feet, what is the length of the diagonal in feet?
10
�
�
10
ft
21
�
�
21
ft
40
�
�
40
ft
58
�
�
58
ft
The length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.
Length of triangle calculation.
The lengths of the trim pieces that make an X on the door form the legs of a right triangle, and the diagonal of the door forms the hypotenuse of the right triangle. Using the Pythagorean theorem, we can find the length of the hypotenuse:
a^2 + b^2 = c^2
where a and b are the lengths of the trim pieces and c is the length of the hypotenuse.
Each trim piece forms a right triangle with the height of the door (7 feet) and one half of the width of the door (1.5 feet). Using the Pythagorean theorem, we can find the length of each trim piece:
a^2 + b^2 = c^2
where a = 7 feet and b = 1.5 feet
c = sqrt(a^2 + b^2) = sqrt((7 feet)^2 + (1.5 feet)^2) = sqrt(49 + 2.25) = sqrt(51.25) ≈ 7.154 feet
The length of each trim piece is approximately 7.154 feet. Since there are two trim pieces that intersect at the center of the door, the length of the hypotenuse is twice this length:
2 * 7.154 feet ≈ 14.308 feet
Therefore, the length of the diagonal of the door is approximately 14.308 feet. Rounding to the nearest whole number, the answer is 14 feet.
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What is the area of this figure? 10 mi 17 mi 3 mi 4 mi 4 mi 6 mi 4 mi 18 mi
The area of the figure is 197 square miles
How to find the area of the figure.To find the area of the figure, we need to first identify the shape of the figure. From the given dimensions, it appears to be an irregular quadrilateral with a triangle on top.
We can divide the figure into two parts: a rectangle with dimensions 17 mi by 10 mi, and a triangle with base 18 mi and height 3 mi.
The area of the rectangle is:
Area of rectangle = length x width = 17 mi x 10 mi = 170 mi^2
The area of the triangle is:
Area of triangle = (base x height) / 2 = (18 mi x 3 mi) / 2 = 27 mi^2
Therefore, the total area of the figure is the sum of the areas of the rectangle and triangle:
Total area = 170 mi^2 + 27 mi^2 = 197 mi^2
So the area of the figure is 197 square miles.
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can someone help me pls!!!! Imma give u brainliest
Answer:
sin0= 9/15
cos0= 12/15
tan0 = 9/12
What number should be written in the penultimate line of the script instead of -1 for the function f to be linear? justify
For the function f to be linear, the number that should be written in the penultimate line of the script should be 0 because a linear function has a constant slope and no term with a power higher than 1.
In the general form of a linear function
y = mx + b
where m is the slope and b is the y-intercept.
Since the function f is defined as
f(x) = x² + mx + b
we can see that it is a quadratic function.
Therefore, to make it linear, we need to eliminate the x² term.
To eliminate the x² term, we can set the coefficient of x² to 0. Since the coefficient of x² is 1, we can subtract x² from both sides of the equation
f(x) = x² + mx + b
f(x) - x² = mx + b
Now, we have a linear function since the term with x² has been eliminated. Thus, the number that should be written in the penultimate line of the script is 0, which will make the coefficient of x² equal to 0 and eliminate the quadratic term.
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Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. a. (2xy2 − 3xy3)(2xy2 + 3xy3) b. (2xy2 − 3xy3)(2xy2 − 3xy3) c. (4xy2 + 9xy3)(xy2 − xy3) d. (4xy2 − 9xy3)(xy2 − xy3)
Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. (2xy2 − 3xy3)(2xy2 + 3xy3). So, correct answer is A.
To multiply two binomials, we use the FOIL method which stands for First, Outer, Inner, Last. For option A, using the FOIL method, we get
(2xy² - 3xy³)(2xy² + 3xy³) = (2xy²)² - (3xy³)² = 4x²y⁴ - 9x²y⁶
This is the given polynomial, so option A is correct.
For other option, we have two identical binomials multiplied together, which would give us a trinomial with three terms, so it cannot be a product of two binomials.
Option C is also incorrect because when we multiply the two binomials, we do not get the given polynomial. Option D is incorrect as well because the signs are incorrect and we would get a different polynomial when we multiply the two binomials.
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--The given question is incomplete, the complete question is given
" Given the polynomial 4x²y⁴ − 9x²y⁶, rewrite as a product of polynomials. a. (2xy² − 3xy³)(2xy² + 3xy³) b. (2xy² − 3xy³)(2xy² − 3xy³) c. (4xy² + 9xy³)(xy² − xy³) d. (4xy² − 9xy³)(xy² − xy³)"--
11. Phyllis ran in a 5-kilometer race to help raise money for the school. How many meters long is the race?
Answer:5000 meters
Step-by-step explanation:1km=1000m
5. Find the perimeter and area
*Triangle- based prism*
Step-by-step explanation:
for the perimeter you have to say two brackets live plus height plus with plastic
wo random samples of earnings of professional golfers were selected. one sample was taken from the professional golfers association, and the other was taken from the ladies professional golfers association. at , is there a difference in the means? the data are in thousands of dollars. use the critical value method with tables. pga lpga
in general, to perform a hypothesis test comparing the means of two independent samples using the critical value method, you would follow these steps:
State the null and alternative hypotheses. For example, the null hypothesis could be that there is no difference in means between the two populations (i.e., H0: µ1 - µ2 = 0), and the alternative hypothesis could be that there is a significant difference in means (i.e., Ha: µ1 - µ2 ≠ 0).
Determine the level of significance, α, which represents the probability of rejecting the null hypothesis when it is actually true. For example, if α = 0.05, then there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).
Calculate the test statistic. The most common test statistic for comparing the means of two independent samples is the t-test. The formula for the t-test is:
t = (x1 - x2) / [s^2pooled/n1 + s^2pooled/n2]^0.5
where x1 and x2 are the sample means, s^2pooled is the pooled variance (calculated using the two sample variances and sample sizes), and n1 and n2 are the sample sizes.
Determine the critical value(s) from the t-distribution table based on the degrees of freedom (df) and level of significance (α). The degrees of freedom for a two-sample t-test is calculated as:
df = n1 + n2 - 2
Compare the test statistic to the critical value(s). If the absolute value of the test statistic is greater than the critical value(s), then reject the null hypothesis; otherwise, fail to reject the null hypothesis.
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Help on both problems pls
Answer:
DE = √21
x = 10
Step-by-step explanation:
4)
AC is bisected by BX
AC/2 = 8/2 = 4 = AB
BX² + AB² = AX²
3² + 4² = AX²
AX = 5 = radius of the circle
DE² = DX² - EX²
DE² = 5² - 2² = 25 - 4 = 21
DE = √21
6)
x² = (11-5)² + 8² = 36 + 64 = 100
x = √100 = 10
x = 10
What is the area of a right triangle with a height of ten and one-half feet and a base of 33 feet?
twenty-one and three-fourths ft2
forty-three and one-half ft2
one hundred seventy-three and one-fourth ft2
three hundred forty-six and one-half ft2
The area of the right triangle is 173.25 square feet.
What is the area of the right triangle?The formula for the area of a right triangle is:
A = (1/2)bh
where A is the area, b is the base, and h is the height.
We are given that the height of the right triangle is ten and one-half feet (10.5 ft) and the base is 33 feet.
Substituting the given values into the formula, we get:
A = (1/2)(33)(10.5)
Simplifying the expression on the right side, we get:
A = 173.25
Therefore, the area of the right triangle is 173.25 square feet.
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What is the value of the quadratic equation: y=4x^2+8x+7
The value of quadratic equation with the help of hit and trial method is 39
what is quadratic equation ?A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable (usually x) in the equation is 2. It is in the form:
ax^2 + bx + c = 0
where a, b, and c are constants and a is not equal to zero.
According to given informationthe value of given quadratic equation is
given
y=4x²+8x+7
using hit and trial method:
The value of the quadratic equation y = 4x² + 8x + 7 depends on the value of x.
To find the value of y for a specific value of x, simply substitute that value of x into the equation and solve for y.
For example, if x = 2, then:
y = 4(2)² + 8(2) + 7
y = 16 + 16 + 7
y = 39
So the value of the quadratic equation y = 4x^2 + 8x + 7 when x = 2 is 39.
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4.a) Increase £75 by 5%
Please help me and explain this to me.
Answer:
£78.75
Step-by-step explanation:
An easy way step but longer way to do this is
10% of 75 is 7.5 ((75/10= 7.5))
divide by 2 on both sides
5% = 3.75
then just add it, its increasing 75 by 5%
so 75 + 3.75 = 78.75
What is the volume of the composite shape?
17. Corina makes $27 for every 2 hours that she works. If she worked 36
hours this week, how much money did she make?
If she worked 36 hours this week, then Corina made $486 this week.
From the question, we have the following parameters that can be used in our computation:
Corina makes $27 for every 2 hours that she works.
So she makes:
27/2 = $13.50 per hour
If she worked 36 hours this week, she would make:
36 hours x $13.50 per hour = $486
Therefore, Corina made $486 this week.
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a textile manufacturing process finds that on average, two flaws occur per every 50 yards of material produced. a. what is the probability of exactly two flaws in a 50-yard piece of material? b. what is the probability of no more than two flaws in a 50-yard piece of material? c. what is the probability of no flaws in a 25-yard piece of material?
a. The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.
b. The probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.
c. The probability of no flaws in a 25-yard piece of material is approximately 0.3679.
To find the probability of exactly two flaws in a 50-yard piece of material, we can use the Poisson distribution. Let λ be the average number of flaws per 50 yards of material, which is 2. Then, the probability of exactly k flaws occurring in a 50-yard piece of material is given by
P(k flaws) = (e^(-λ) × λ^k) / k!
So, for k=2, we have
P(2 flaws) = (e^(-2) × 2^2) / 2! ≈ 0.2707
Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.
b. To find the probability of no more than two flaws in a 50-yard piece of material, we need to sum the probabilities of having 0, 1, or 2 flaws. So, we have
P(no more than 2 flaws) = P(0 flaws) + P(1 flaw) + P(2 flaws)
We already know P(2 flaws) from part (a). To find P(1 flaw), we can use the same formula as before with λ=2 and k=1
P(1 flaw) = (e^(-2) × 2^1) / 1! ≈ 0.2707
To find P(0 flaws), we use the same formula with λ=2 and k=0
P(0 flaws) = (e^(-2) × 2^0) / 0! ≈ 0.1353
Therefore, we have:
P(no more than 2 flaws) = 0.2707 + 0.2707 + 0.1353 ≈ 0.6767
So, the probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.
c. To find the probability of no flaws in a 25-yard piece of material, we can again use the Poisson distribution, but with a different value of λ. Since the average number of flaws per 50 yards is 2, the average number of flaws per 25 yards is 1. So, we have:
P(0 flaws) = (e^(-1) × 1^0) / 0! ≈ 0.3679
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Mr ade plans to spend his monthly salary as fellow
food-20%
children-25%
parents-20%
car-10%
entertainment-10%
saving-2½
miscellenceous-2½
if the amount of saving kept for saving is Ghc 250.00. calculate his
a) monthly salary
b) total amount spent on his parent
a) His monthly salary is, 555.6
b) Total amount spent on his parent is, 111.1
Given that;
Mr. Ade plans to spend his monthly salary as follows
food-20%
children-25%
parents-20%
car-10%
entertainment-10%
saving-2½
miscellenceous-2½
And, the amount of saving kept for saving is Ghc 250.00.
Hence, We get;
Monthly salary is,
Since, We have;
Percent of savings = 100% - 20% - 10% - 10% - 12.5% - 2.5%
= 45%
Hence, We get;
45% of salary = 250
45/100 x salary = 250
Monthly salary = 25000 / 45
Monthly salary = 555.6
And, Money spent on parents;
20% of 555.6
20/100 x 555.6
111.1
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what is the number of permutations of the letters in the word indis- tinguishable such that the strings git, tin, and nab do not appear in the permutation?
The number of permutations of the letters in the word indistinguishable such that the strings git, tin, and nab do not appear in the permutation is
3,172,973,824,000
Let A be the set of stages that contain the string "git",
B be the set of changes that contain the string "tin", and
C be the set of stages that contain the string "nab".
We need to discover the number of stages that don't contain any of these strings, which is the same as finding the measure of the set (A∪B∪C)'.
Utilizing the guideline of inclusion-exclusion, we have:
|A∪B∪C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|
We need to discover |(A∪B∪C)'|, which is the complement of the set A∪B∪C. In this manner:
|(A∪B∪C)'| = n! - |A∪B∪C|
Now we have to discover the measure of the sets A, B, and C, and their convergences.
For set A, able to settle the string "git" in its put in 3! ways, and after that permute the remaining 14 letters in 14! ways. In this manner, |A| = 3!×14!.
Essentially, we will discover |B| = 3!×14! and |C| = 3!×14!.
For the convergences, we are able to settle the comparing strings in their places and permute the remaining 11 letters in 11! ways. In this manner,
|A∩B| = 2!×11!,
|A∩C| = 2!×11!,
and |B∩C| = 2!×11!.
At long last, we have |A∩B∩C| = 1!×11! since we are able to settle all three strings in their places and permute the remaining 11 letters in 11! ways.
Substituting these values into the inclusion-exclusion equation, we get:
|A∪B∪C| = 3(3!×14!) - 3(2!×11!) + 1!×11!
|A∪B∪C| = 13608000
Subsequently:
|(A∪B∪C)'| = 17! - 13608000
|(A∪B∪C)'| = 3172973824000
So there are 3,172,973,824,000 permutations of the letters within the word "indistinguishable" such that the strings "git", "tin", and "nab" don't show up within the stage.
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Mrs. Dundee wants to sell the rights to her new Cajun cookbook, and she has two offers. The first publisher has offered to pay $80,000 up front and a $3 royalty for every book sold. The second publisher has offered to pay $30,000 up front and $5 for every book sold. Over what range of sales will Mrs. Dundee make more from the second publisher than from the first?
Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.
What is the rate?In mathematics, rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.
According to the given information:Let's represent the number of books sold as "x". Then, the total amount of money that Mrs. Dundee will make from the first publisher is:
Total from first publisher = $80,000 + ($3 x x) = $3x + $80,000
Similarly, the total amount of money that she will make from the second publisher is:
Total from second publisher = $30,000 + ($5 x x) = $5x + $30,000
We want to find the range of values of x for which the total amount from the second publisher is greater than the total amount from the first publisher. In other words, we want to find the range of values of x for which,
$5x + $30,000 > $3x + $80,000
Simplifying this inequality, we get:
$2x > $50,000
x > $25,000
Therefore, Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.
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The vertices of a figure are given. Rotate the figure as described. Find the coordinates of the image.
E(−4, 1), F(−3, 3), G(−2, 3), H(−1, 1)
180°
about the origin
what is the side length of a square with the area of 1/16 sq
The side length of the square that has the given area would be = 1/4
How to calculate the side length of a given square?To calculate the side length of a given square the formula for the area of a square should be used. That is;
Area of a square = a²
where;
a = length = ?
area = 1/16
That is = 1/16 = a²
a = √1/16
= 1/4
Therefore the side of the square whose area is given should have the length of 1/4
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The hypotenuse of a right triangle measures 16 cm and one of its legs measures 9 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Simplify (2x3y)(3x4y2).
5x7y3
6x7y2
6x7y3
6x12y2 -------------------------------- (69 points ill follow you thank the question and
account if its right)
The expression[tex](2x^3y)(3x^4y^2)[/tex] simplifies to [tex]6x^7y^3[/tex]. The coefficients are multiplied, and the variables are combined by adding their exponents. Option C.
To simplify the expression [tex](2x^3y)(3x^4y^2),[/tex] we can multiply the coefficients and combine the variables with the same base by adding their exponents.
Multiplying the coefficients, we have:
2 * 3 = 6
For the variables, we multiply the x terms by adding their exponents (3 + 4 = 7), and the y terms by adding their exponents (1 + 2 = 3).
Therefore, simplifying the expression [tex](2x^3y)(3x^4y^2)[/tex] gives us:
[tex]6x^7y^3[/tex]
Hence, the simplified form of[tex](2x^3y)(3x^4y^2)[/tex] is[tex]6x^7y^3[/tex]. Option c is correct.
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Answer:
C:6x7y3
Step-by-step explanation:
i took the test and got it right
Which quadratic inequality best describes the graph?
Answer: parabolic curve
Step-by-step explanation:
Answer: parabolic curve
Step-by-step explanation:
A number line going from negative 2 to positive 1. What is the correct order of the fractions from least to greatest? Point A: −11 3 Point B: −2 3 Point C: 1 3 Point D: −12 3 The correct order for the fractions is .
Answer:
D, A, B, C
Step-by-step explanation:
-12/3, or -4, is lowest
-11/3, or -3.6, is 0.3 more, therefore closer to 0.
-2/3, or -0.6, is much closer to 0, precisely 3 units closer.
1/3, or 0.3, is the only positive number, so it is the most amount.
PLEASE HELP I'LL GIVE THE BRAINLIEST!
Answer:
Box A: 2 × 4.5 × 6 = 54 cubic inches
Box B: 6 × 2.5 × 3 = 45 cubic inches
Box C: 5 × 4.5 × 2.25 =
50.625 cubic inches
Box D: 2.5 × 2.25 × 3 = 16.875 cubic inches
From least to greatest, the order of the boxes' volumes is D, B, C, A.
A salesman's commission varies directly as his sales.If the commission is $10 for $100 in sales, find the commission for $150 in sales.
a. $12 b. $20 c. $15 d. $25
The commission for $150 in sales is $15. This corresponds to option (c) in the given answer choices.
We are told that the salesman's commission varies directly with his sales. This means that if the sales increase by a certain percentage, then the commission will also increase by the same percentage. We can set up a proportion to solve for the commission:
Commission/Sales = Commission Rate
We are given that the commission rate is $10 for every $100 in sales. We can use this information to set up a proportion:
Commission/150 = 10/100
To solve for the commission, we can cross-multiply and simplify:
Commission = (150 x 10)/100 = $15
In general, if we let x represent the sales amount, and c represent the commission, then we can use the formula:
c = (x/100) * 10
where 10 represents the commission rate of $10 per $100 in sales. We can use this formula to calculate the commission for any given sales amount.
Therefore, Correct option is C.
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DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!! 20 POINTS
Students in a high school mathematics class decided that their term project would be a study of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as “strict”. They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students.
1. Describe the parameter of interest and a statistic the students could use to estimate the parameter.
2. Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning.
3. The students quickly realized that, as there is no definition of “strict”, they could not simply ask a student, “Are your parents or guardians strict?” Write three questions that could provide objective data related to strictness.
4. Describe an appropriate method for obtaining a sample of 100 students, based on your answer in question 1.
The percentage of students at the school who describe their parents or guardians as "strict" is the key statistic. 2. A sample survey is the ideal research design for this project.
What is Proportion?Since it would be impractical to poll all 1000 kids at the school, the students intend to collect data from a sample of students in order to concentrate on the strict guardians, which is a population parameter.
The sample proportion could be used by the students as a statistic to determine this population proportion. They can ask a sample of pupils drawn at random from the school whether they think their parents or guardians are "strict". The percentage of sample kids who respond "yes" can be used to approximate the percentage of school-wide students who view their parents or guardians as "strict". A statistic that offers an estimate of the population parameter of interest is the sample proportion.
Random sampling would be a suitable technique for generating a sample of 100 pupils. Each kid in the school might be given a number, and the pupils could then use a random number generator to choose 100 numbers from the list. The chosen students might then be contacted and asked to take part in the study. This technique lessens the possibility of bias in the sample selection process and aids in ensuring that the sample is representative of the population.
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PLEASE HELP FASTTT LIKW IN LESS THAN 30 MINUTES PLSS IM GIVING BRAINLIEST
Answer:
Each student will have passed 17 tests; It will take 3 weeks.
Step-by-step explanation:
The explanation is in the picture.
y=3-x 3y+x=5 solve by substitution method
Answer:
x = 2
y = 1
Step-by-step explanation:
3y + x = 5 y = 3 - x
3(3 - x) + x = 5
9 - 3x + x = 5
9 - 2x = 5
-2x = -4
x = 2
Now put 2 in for x and solve for y
3y + x = 5
3y + 2 = 5
3y = 3
y = 1
Let's Check
1 = 3 - 2
1 = 1
So, x = 2 and y = 1 is the correct answer.
Write an expression for the apparent nth term an of the sequence. (Assume that n begins with 1.) 4, 5/3, 6/5, 1, 8/9
The nth term of the sequence as: an = { 4 (n - 1) if n is odd
1 if n is even and n ≠ 4 8/2n when n = 4
What is arithmetic progression and its formula ?
An arithmetic progression is a list of numbers where each term is obtained by adding a specific number to the previous term, except for the first term. The following formulas help solve arithmetic progression problems: AP common difference: d = an - an-1. AP nth term: an = a (n -1)d
Sum of n terms of AP: Sn = n/2 (2a (n - 1)d)
The given sequence is 4, 5/3, 6/5, 1, 8/9.
To find the expression for the nth term, we must observe the pattern of the sequence. We see that the numerators of the series fractions increase by 1 for each term, while the denominators increase by 2 for each term except the fourth term, which is 1. Therefore, we can write the nth term of the sequence as:
an = { 4 (n - 1) if n is odd
1 if n is even and n ≠ 4
8/2n when n = 4
where n is a positive integer representing the position of the term in the sequence.
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