What is the coefficient of x8y9 in the expansion of (3x + 2y)17? Answer in terms of a whole number.
Answers
The coefficient of x^8y^9 in the expansion of (3x + 2y)^17 is 5314410.
How we know the coefficient of x8y9 in the expansion of (3x + 2y)17?The coefficient of x^8y^9 in the expansion of (3x + 2y)^17 can be found using the binomial theorem:
The general term in the expansion of (3x + 2y)^17 is given by:
T(r+1) = (17Cr)(3x)^(17-r)(2y)^rwhere r is the index of the term, and C(r) is the binomial coefficient.
To find the coefficient of x^8y^9, we need to find the value of r such that:
(17-r) = 8 and r = 9Solving these equations, we get:
r = 8 and r = 9Therefore, the coefficient of x^8y^9 in the expansion of (3x + 2y)^17 is given by:
T(9) = (17C9)(3x)^8(2y)^9We can simplify the expression further by evaluating the binomial coefficient:
(17C9) = 17!/(9!8!) = (1716151413121110)/(87654321) = 24310Substituting this value into the expression for T(9), we get:
T(9) = 24310*(3x)^8*(2y)^9= 243103^8x^82^9y^9= 5314410x^8y^9Learn more about Coefficient
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Related Questions
Clare follows the same workout cycle each time she goes to the gym. First, she runs for
1
3
of an hour. Then, she lifts weights for
1
6
of an hour. If Clare has 1
1
2
hours to spend at the gym, how many times can she go through her workout cycle?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Answers
Answer:
3 times.
Step-by-step explanation:
She has 1 1/2 hour to spend in the gym.
1 hr = 60 minutes.
1/2 of an hour= 1/2 * 60= 30 minutes.
In total, she spends 90 minutes in the gym.
If 1/3 of an hour is meant in running, it translates into: 1/3 * 60 = 20 minutes.
If 1/6 of an hour is spent in weight-lifting, it translates into: 1/6 * 60 = 10 minutes.
In total, she spends, 20 minutes + 10 minutes = 30 minutes for both activities.
To obtain the number of times she would perform both activities, we divide the total amount of time spent in the gym by the amount of time spent for both activities.
90 minutes/30 minutes= 3 times for each cycle.
In mrs. Wilson’s math class, the ratio of girls to boys is 5 to 8. If there are 24 total students, how many boys are in the class
Answers
find the 4th term in the expansion of the expression of (2r-7)^5
Answers
The 4th term in the expansion of $(2r - 7)^5$ is $-123480$.
What is expansion ?Expansion refers to the process of writing a mathematical expression in a more detailed and expanded form. One common type of expansion is a polynomial expansion, where a polynomial expression is written as a sum of terms, each term consisting of a coefficient multiplied by a variable raised to a power.
The general term in the expansion of $(2r - 7)^5$ is given by:
$T_r = \binom{5}{r}(2r)^{5-r}(-7)^r$
To find the 4th term, we need to substitute $r=3$:
$T_3 = \binom{5}{3}(2\cdot3)^{5-3}(-7)^3$
Simplifying:
$T_3 = \binom{5}{3}(2\cdot3)^2(-343)$
$T_3 = 10 \cdot 36 \cdot (-343)$
$T_3 = -123480$
Therefore, the 4th term in the expansion of $(2r - 7)^5$ is $-123480$.
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What is the scale factor of the dilation of ABCD centered at the origin?
Answers
Step by step
Measure sides of pre image ABCD and image A’B’C’D’ lines from graph
Measure of
Pre Image line AD = 8 units
Image Line A’D’ = 4 units
Divide image by pre image
4/8 = 1/2 scale factor
Pre image line BC = 4 units
Image line B’C’ = 2 units
Divide image by pre image
2/4 = 1/2 scale factor
Keep in mind your pre image is bigger and your image is smaller so your scale factor will be less than one, or a fraction.
On Friday night, the Morrison family set up camp in
the Ocala National Forest. On Saturday morning they hiked to a wilderness area 3 miles due north and 4 miles due east of their campsite. The elevation of the wilderness area is the same as the elevation of the campsite. To the nearest 0.1 mile, what is the straight line distance from the wilderness area to the Morrisons' campsite?
Answers
The straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.
To find the straight-line distance from the wilderness area to the Morrisons' campsite, we can use the Pythagorean theorem.
Let's consider the campsite as the origin (0, 0) on a coordinate plane. The wilderness area is located 3 miles due north and 4 miles due east from the campsite. Therefore, its coordinates are (4, 3).
Using the Pythagorean theorem, the straight-line distance d is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the coordinates of the campsite (0, 0) and the wilderness area (4, 3) into the formula, we get:
d = √((4 - 0)² + (3 - 0)²)
= √(4² + 3²)
= √(16 + 9)
= √25
= 5
Therefore, the straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.
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1 Consider the sequence of composite numbers4,6,8,9,10,12,14,15,16,……
Find: a. S3
b. S5
c. S12
Answers
If the sequence of composite numbers4,6,8,9,10,12,14,15,1
a. S3 = 8
b. S5 = 16
c. S12 = 60
The sequence given is a sequence of composite numbers, which are numbers that can be divided by a number other than 1 or itself. In this sequence, each number is one greater than the previous number. To find the answers for a. S3, b. S5 and c. S12, we will add all of the numbers up to the corresponding term.
a. S3 = 4 + 6 + 8 = 18
b. S5 = 4 + 6 + 8 + 9 + 10 = 37
c. S12 = 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 = 60
Therefore, the answers are:
a. S3 = 8
b. S5 = 16
c. S12 = 60
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A single-server service facility has unlimited amount of waiting space. The customer interarrival times are exponentially distributed with mean 2.2 minutes (i.e. f(x) = De-/2.2). The customer service times in minutes) follow the following discrete distribution: 1 2 3 PTS .3 .3 (a) What is the mean and variance of the service times? (b) What is the traffic intensity? (e) What is the system throughput? (a) What is the long-run average waiting time (excluding service time) for each customer? (e) What is the long-run average number of customers in the system?
Answers
(a) To find the mean and variance of the service times, we can use the given discrete distribution.
The mean can be calculated by taking the weighted average of the service times: Mean = (1 * 0.3) + (2 * 0.3) + (3 * 0.4) = 0.3 + 0.6 + 1.2 = 2.1 minutes
To find the variance, we need to calculate the squared deviations from the mean and then take the weighted average: Variance = [(1 - 2.1)^2 * 0.3] + [(2 - 2.1)^2 * 0.3] + [(3 - 2.1)^2 * 0.4]
= [(-1.1)^2 * 0.3] + [(-0.1)^2 * 0.3] + [(0.9)^2 * 0.4]
= 0.363 + 0.003 + 0.324
= 0.69
(b) The traffic intensity (ρ) is the ratio of the mean service time to the mean interarrival time. In this case, the mean service time is 2.1 minutes, and the mean interarrival time is given as 2.2 minutes. Therefore:
Traffic Intensity (ρ) = Mean Service Time / Mean Interarrival Time
= 2.1 / 2.2
= 0.9545
(e) The system throughput is the average number of customers served per unit of time. Since the interarrival times are exponentially distributed, the system throughput can be calculated as the reciprocal of the mean interarrival time:
System Throughput = 1 / Mean Interarrival Time
= 1 / 2.2
≈ 0.4545 customers per minute
(a) The long-run average waiting time (excluding service time) for each customer can be calculated using Little's Law. Little's Law states that the long-run average number of customers in a stable system is equal to the product of the long-run average arrival rate and the long-run average waiting time. Since the system is single-server, the arrival rate is the same as the throughput. Therefore:
Long-run Average Waiting Time = Average Number of Customers / Throughput
= 1 / System Throughput
≈ 1 / 0.4545
≈ 2.2 minutes
(e) The long-run average number of customers in the system can also be calculated using Little's Law. It is equal to the product of the long-run average arrival rate and the long-run average time a customer spends in the system. Since the arrival rate is the same as the throughput, and the service time includes both waiting time and service time, we can subtract the waiting time from the total service time to find the time spent in the system:
Long-run Average Number of Customers = Throughput * (Mean Service Time - Waiting Time)
≈ 0.4545 * (2.1 - 2.2)
≈ -0.0454
The negative value indicates that, on average, there are no customers in the system, which suggests that the system is underutilized or not operating at its full potential.
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30,000 times 8 thank you for answering.
Answers
Answer:
240,000
Step-by-step explanation:
have a nice day
Someone help pls......
Answers
Answer:
f(- 1) = - 5
Step-by-step explanation:
f( - 1) has x = - 1 in the interval - 5 < x ≤ 0 , thus
f(x) = | - 3x + 2 | - 10 , so
f(- 1) = | - 3(- 1) + 2 | - 10 = | 3 + 2 | - 10 = | 5| - 10 = 5 - 10 = - 5
please show work
Max has a collection of 99 dimes and pennies worth $4.41. How many pennies does he have?
Answers
Answer:
61 pennies
Step-by-step explanation:
d + p = 99
0.1d + 0.01p = 4.41
d = 99 - p
0.1(99 - p) + 0.01p = 4.41
9.9 - 0.1p + 0.01p = 4.41
-0.09p = -5.49
p = 61
Answer: 61 pennies
10 marbles what is the probability of drawing 2 blue marbles if the first marble is placed back in the bag before the second draw
Answers
Complete Question:
There are 10 marbles. What is the probability of drawing 2 blue marbles if the first marble is NOT placed back in the bag before the second draw.
2 yellow, 3 pink, 5 blue
Answer:
\(P(B_1\ and\ B_2) = \frac{2}{9}\)
Step-by-step explanation:
Given
\(Blue = 5\)
\(Pink = 3\)
\(Yellow = 2\)
\(Total = 10\)
When the first blue marble is selected, the probability is:
\(P(B_1) = \frac{n(Blue)}{Total}\)
\(P(B_1) = \frac{5}{10}\)
Since the first marble is not returned, we have the following marbles left
\(Blue = 4\)
\(Pink = 3\)
\(Yellow = 2\)
\(Total = 9\)
The probability of picking a second blue marble is:
\(P(B_2) = \frac{n(Blue)}{Total}\)
\(P(B_1) = \frac{4}{9}\)
So, the required probability is:
\(P(B_1\ and\ B_2) = P(B_1) * P(B_2)\)
\(P(B_1\ and\ B_2) = \frac{5}{10} * \frac{4}{9}\)
\(P(B_1\ and\ B_2) = \frac{5*4}{10*9}\)
\(P(B_1\ and\ B_2) = \frac{20}{90}\)
\(P(B_1\ and\ B_2) = \frac{2}{9}\)
Alina flipped a nickel 10 times. It landed on heads 7 times and tails 3 times. If she flips the coin again, what is the probability of getting tails?
Answers
Answer:
Probability=number of chances/total possible outcome
P=3/10
Does this graph represent a function? Why are why not?
Answers
No, because it fails vertical line test.
What is vertical line test?
Vertical line test is defined as a method used to find if the given equation or graph represents a function or not. The vertical line test states that a vertical line needs to cuts the graph of a function (equation) at only one point, for it to represent a function.
Hence, in the given graph, the function intercepts the y- axis at two points, therefore, it fails vertical line test.
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Classify each angle.
Answers
Answer:
∠MDP = 90° = Right angle
∠MDP = 180° = Straight angle
∠ODM = 90° = Right angle
∠OND = Not an angle
∠NDO = 90° = Right angle
∠NDM = 180° = Straight angle
∠PMN = Not an angle
∠PDO = 180° = Straight angle
∠PDN = 90° = Right angle
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If 7 toothpaste tubes cost $40.50, how much does one tube cost?
Answers
Answer:
40.5/7=(answer)
In 1980, James planted a tree that was 1 foot tall. In 1996, that same tree was 51 feet tall. James finds that the height of the tree can be modeled by the
radical function H (t) = v kt + 1 where H (t) is the height of the tree in feet, t, is the number of years since 1980, and k is a specific constant. What
is the value of k?
Answers
Value of the specific constant 'k' for the given function will be 3.125.
Simplification of a function for the value of variables used: If a function modeling the height of a tree in 't' years is.
\(H(t)=\sqrt{kt} + 1\)
[where, k = constant , t = Number of years]
And we have to find the value of 'k', simplify the function in terms of 'k'.
H(t) - 1 = √kt
[H(t) - 1]² = kt
k = \(\frac{[H(t)-1]^2}{t}\)
Given in the question,
James planted a tree of height 1 feet in 1980. Same tree was 51 feet tall in 1996.Number of years between 1980 and 1996 (t) = 16
H16) = 51 feet
Substitute the values in the expression,
\(k=\frac{[51-1]^2}{16}\)
\(k=\frac{50}{16}\)
\(k=3.125\)
Therefore, value of the constant 'k' will be 3.125.
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So far, Keiko has burned 475.7 calories. She wants to burn a total of 900 calories. How many more calories must Keiko burn?
please add the steps like if you are supposed to add or subtract
Answers
Answer:
900 - 475.7 = 424.3 calories she has to burn
Part a: use absolute values to calculate the distance in units from nina's house to her school. show your work. (4 points) part b: is the total distance from nina's house to the school to the grocery store greater than the total distance from nina's house to the school to the community center? justify your answer. (6 points)
Answers
The total distance from Nina's house to the school to the community center (20 units) is greater than the total distance from Nina's house to the school to the grocery store (18 units).
Part a: To calculate the distance in units from Nina's house to her school using absolute values, we need the coordinates of both locations. Let's assume Nina's house is located at point A (x1, y1) and her school is located at point B (x2, y2). The distance between these two points can be calculated using the distance formula:
Distance = |x2 - x1| + |y2 - y1|
Let's say Nina's house is at coordinates (3, 5) and her school is at coordinates (-2, -1). Plugging these values into the formula:
Distance = |(-2) - 3| + |(-1) - 5|
= |-5| + |-6|
= 5 + 6
= 11 units
Therefore, the distance from Nina's house to her school is 11 units.
Part b: To determine whether the total distance from Nina's house to the school to the grocery store is greater than the total distance from Nina's house to the school to the community center, we need the distances between these locations. Let's assume Nina's house is point A, her school is point B, the grocery store is point C, and the community center is point D.
Let's say the distance from Nina's house to the school is 11 units, the distance from the school to the grocery store is 7 units, and the distance from the school to the community center is 9 units.
Total distance from Nina's house to the school to the grocery store = 11 + 7 = 18 units
Total distance from Nina's house to the school to the community center = 11 + 9 = 20 units
Therefore, the total distance from Nina's house to the school to the community center (20 units) is greater than the total distance from Nina's house to the school to the grocery store (18 units).
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-3x + 4y – 5xy ; x= -3, y = 2
Need help ASAP plz
Answers
Answer:
47
Step-by-step explanation:
First, plug in the numbers.
x = -3 and y = 2.
-3(-3) + 4(2) - 5(-3)(2)
Simplify by multiplying.
-3 * -3 = 9
4 * 2 = 8
-5 * -3 * 2 = 30
Your new equation is:
9 + 8 + 30 = ?
Simplify by adding. 9 + 8 + 30 = 47
Answer:
47
Step-by-step explanation:
-3(-3) + 4(2) - 5(-3)(2)
9 + 8 + 30 = 47
4. the highest point on the graph of the normal density curve is located at a) an inflection point b) its mean c) μ σ d) μ 3σ
Answers
The highest point on the graph of the normal density curve is located at its mean represented by μ.
The highest point on the graph of the normal density curve is located at its mean. The normal density curve or the normal distribution is a bell-shaped curve that is symmetric about its mean. The mean of a normal distribution is the measure of the central location of its data and it is represented by μ. It is also the balancing point of the distribution. In a normal distribution, the standard deviation (σ) is the measure of how spread out the data is from its mean.
It is the square root of the variance and it determines the shape of the normal distribution. The normal distribution is an important probability distribution used in statistics because of its properties. It is commonly used to represent real-life variables such as height, weight, IQ scores, and test scores.
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Kayla Greene is a team lead for an environmental group for a certain region. She is investigating whether the population mean monthly number of kilowatt hours (kWh) used per residential customer in the region has changed from 2006 to 2017. She is concerned that changes such as more efficient lighting and the increased use of electronics and air conditioners are affecting the population mean monthly number of kilowatt hours consumed per residential customer. Kayla investigates the data and assumes the population standard deviation for 2006 and 2017 using the data that were provided to her by local utility companies. Using data that were collected by h company, Kayla selects a random sample of residential customers who were active for all of 2006 nd a separate sample of residential customers who were active for all of 2017. The population standard deviations and the results from the samples are provided in the accompanying table. Let A be the population mean monthly number of kilowatt hours consumed per residential customer in 2006 and jug be the population mean monthly number of kilowatt hours consumed per residential customer in 2017. What type of test is this hypothesis test? 2006 1 894.7kWh 1 361 σ,-193. 1 kWh 2017 910.2kWh n424 | σ2-182.9 kWh Select the correct answer below: O This is a left-tailed test because the alternative hypothesis is H,: Ha 0. O This is a left-tailed test because the alternative hypothesis is H. μ. μ2 < 0. O This is a two-tailed test because the alte 0 This is a right-tailed test because the alternative hypothesis is H.: μ' μ'>0. O This is a right-tailed test because the alternative hypothesis is H, rnative hypothesis is Ha : μ. 142 /0
Answers
This is a right-tailed test because the alternative hypothesis is H.: μ' > 0. Therefore, the correct option is H.: μ' > 0..
The hypothesis test conducted by Kayla Greene is a right-tailed test because the alternative hypothesis is H.: μ' > 0 is the correct option.
The null hypothesis in this test is H0: μ1 = μ2.
Alternative hypothesis in this test is
Ha: μ1 < μ2 (left-tailed),
μ1 ≠ μ2 (two-tailed),
μ1 > μ2 (right-tailed)
since Kayla wants to know if the population mean monthly number of kilowatt hours used per residential customer in 2017 has increased compared to that in 2006.
The population standard deviations and the results from the samples are provided in the accompanying table.
Therefore, the correct option is H.: μ' > 0..
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hey! please help i’ll give brainliest
Answers
Answer:
I think A is the answer
hope this helps
have a good day :)
Step-by-step explanation:
The carousel at an amusement park has 20 horses spaced evenly around its circumference. The horses are numbered consecutively from 1 to 20. The carousel completes one rotation about its axis every 40 seconds.
a. What is the central angle, in degrees, formed by horse #1 and horse #8?
b. What is the speed of the carousel in rotations per minute?
c. What is the speed of the carousel in radians per minute?
d. A child rides the carousel for 6 minutes. Through how many radians will the child pass in the course of the carousel ride?
Answers
The child passes through 18π radians in the course of the carousel ride.
To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.
Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.
Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.
To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.
6 minutes is equal to 360 seconds,
so the child passes through π/20 x 360 = 18π radians during the ride.
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if sat scores are normally distributed with a mean of 500 and standard deviation of 100, what is minimum score is needed to ensure that you are ni the top 7
Answers
To determine the minimum score needed to ensure that you are in the top 7%, we need to find the z-score associated with the top 7% and then convert it back to the raw score.
The top 7% corresponds to an area of 0.07 under the standard normal distribution curve. To find the z-score associated with this area, we can use a standard normal distribution table or a calculator.
Using a standard normal distribution table or calculator, we find that the z-score corresponding to an area of 0.07 is approximately 1.4051.
To convert this z-score back to the raw score, we can use the formula:
x = z * standard deviation + mean
Substituting the values into the formula, we get:
x = 1.4051 * 100 + 500
x ≈ 140.51 + 500
x ≈ 640.51
Therefore, the minimum score needed to ensure that you are in the top 7% is approximately 640.51.
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American General offers a 9-year annuity with a guaranteed rate of 6.28% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $1500 annually over the 9 year period? How much should a customer pay for this annuity? (Round to the nearest cent)
Answers
You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.
To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.
The formula to calculate the present value of an annuity is:
PV = PMT × [1 - (1 + r)⁻ⁿ] / r
Where:
PV is the present value of the annuity (the amount you should pay initially)
PMT is the payment amount received annually ($1500 in this case)
r is the interest rate per period (6.28% or 0.0628)
n is the total number of periods (9 years)
Let's substitute the values into the formula:
PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628
Calculating this expression:
PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628
PV = $1500 × [1 - 0.575255] / 0.0628
PV = $1500 × 0.424745 / 0.0628
PV ≈ $10117.09
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the scores on a standardized test are normally distributed with a mean of 90 and standard deviation of 15. what test score is 0.1 standard deviations above the mean?
Answers
The test score is 91.5.
z-score:
A z-score is the number of standard deviations from the mean value of the reference population.
Here we have to find the test score.
Mean(μ) = 90
Standard deviation(б) = 15
z-score = 0.1
Formula for z-score:
z = X - μ / б
Now putting the values in the equation:
0.1 = X - 90 / 15
1.5 = X - 90
X = 91.5
Therefore the test score is 91.5.
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A builder wants to build a bridge whose cross section is 55ft 6in wide an equation to find the distance b in feet between each beam Is...
Answers
An equation is used to represent expressions with equal values. The equation to find the value of b is: \(55.5ft = 5b + 10.5ft\)
Given that:
\(Width = 55ft\ 6in\)
To get the value of distance b, we simply add up the length of every item that makes up the cross-section.
So, we have:
\(Width = 3ft + \frac 34 ft +b+ \frac 34 ft +b+ \frac 34 ft +b+ \frac 34 ft +b+ \frac 34 ft +b + \frac 34 ft +3ft\)
Collect like terms
\(Width = b + b + b + b + b + 3ft + \frac 34 ft + \frac 34 ft + \frac 34 ft + \frac 34 ft + \frac 34 ft + \frac 34 ft +3ft\)
\(Width = 5b + 10\frac 12 ft\)
Substitute \(Width = 55ft\ 6in\)
\(55ft\ 6in = 5b + 10\frac 12 ft\)
\(5ft\ 6in = 5b + 10.5ft\)
Convert inches to feet
\(55ft + \frac{6}{12}ft = 5b + 10.5ft\)
\(55ft + 0.5ft = 5b + 10.5ft\)
\(55.5ft = 5b + 10.5ft\)
Collect like terms
\(5b = 55.5ft -10.5ft\)
\(5b = 45ft\)
Divide both sides by 5
\(b = 9ft\)
Hence:
An equation to find the value of b is: \(55.5ft = 5b + 10.5ft\).And the value of b is 9 ftRead more about equations at:
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Y=x^3, y=-1, x=2 square cross section perpendicular to the y-axis
Answers
The required answer is a square cross-section with a side length of 3.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
The cross-section we are interested in is a square that lies in the plane y=-1. To find this square, we need to find the value of x where the curve y=x³ intersects the plane y=-1.
y=x³ and y=-1 intersect when,
x = (-1)^(1/3)
x = -1, since (-1)³ = -1.
The curve y=x³ intersects the plane y=-1 again when x=2, since 2³=8 and -1<8. Therefore, the square cross-section perpendicular to the y-axis that we are looking for has a side length 2-(-1)=3.
Hence, the answer is a square with a side length of 3.
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find an explicit formula for the nth term of the sequence whose first several terms are {0,3,8,15,24,35,48,63,80,99,...}
Answers
The explicit formula for the nth term of the given sequence is:
an = 3n - 3
How to find the explicit formula for nth term?
To find the explicit formula for the nth term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
To apply this formula, we need to find the values of a1 and d for the given sequence.
From the first two terms of the sequence, we can find the common difference:
d = 3 - 0 = 3
Using the value of the first term and the common difference, we can find the value of a1:
a1 = 0
Now we can substitute these values into the formula for the nth term:
an = 0 + (n - 1)3
Simplifying, we get:
an = 3n - 3
Therefore, the explicit formula for the nth term of the given sequence is:
an = 3n - 3
So the 10th term of the sequence is:
a10 = 3(10) - 3 = 27
and the 20th term of the sequence is:
a20 = 3(20) - 3 = 57
and so on.
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At a sale, dresses were sold for $22 each. This price was 55% of a dress original price. How much did a dress originally cost?
Answers
Answer:
40
Step-by-step explanation:
Divide: 55/22 = 0.4
Multiply: 0.4 * 100 = 40.