if S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.
You can try to show this by induction:
• According to the given closed form, we have [tex]S_1=3\times2^{1-1}+2(-1)^1=3-2=1[/tex], which agrees with the initial value S₁ = 1.
• Assume the closed form is correct for all n up to n = k. In particular, we assume
[tex]S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}[/tex]
and
[tex]S_k=3\times2^{k-1}+2(-1)^k[/tex]
We want to then use this assumption to show the closed form is correct for n = k + 1, or
[tex]S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}[/tex]
From the given recurrence, we know
[tex]S_{k+1}=S_k+2S_{k-1}[/tex]
so that
[tex]S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)[/tex]
[tex]S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}[/tex]
[tex]S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)[/tex]
[tex]S_{k+1}=3\times2^k-2(-1)^k[/tex]
[tex]S_{k+1}=3\times2^k+2(-1)(-1)^k[/tex]
[tex]\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}[/tex]
which is what we needed. QED
David used exactly 8 cups of flour to make 6 bread. How much can he make with 12 cups?
Answer:
9 Loaves of Bread
Through dividing 6(total bread) by 8(total cups) you get 3/4C per bread
So you multiply 12 by 3/4 or 0.75 to get 9
which figure is described below?
the locus of points in a plane equidistant between ( -1 , 4 ) and ( 3 , 4 )
Answer:
D. lineStep-by-step explanation:
A child has toy blocks that contain the numbers 1 through 80. What is the probability that the will pick up a number that is
not a multiple of 11?
• Give your answer in fraction form. Reduce the fraction if necessary.
Answer:
73/80
Step-by-step explanation:
multiples of 11 between 1 and 80 are 11,22,33,44,55,66,77
number of terms=7
P(multiple of 11)=7/80
P(not a multiple of 11)=1-7/80=73/80
Someone answer this please coreectly!!
Answer:
7 and 8
Step-by-step explanation:
[tex]7^{2} =49\\\\8^{2} =64[/tex]
plz help will give crown
Answer:
choice D) d ≥ 5
Step-by-step explanation:
What is the measure of B ?
Answer: if you add then all up you get 75 so it could be A or D I don't know if it want the volume and the volume is 75 hope this helped
Step-by-step explanation:
pleas make brainly
What is the median of the given set of data? 1. 1. 5. 4. 3. 7. 2.9. 4, 8
Answer:
4
Step-by-step explanation:
Arrange in order
1,1,2,3,4,4,5,7,8,9
Cross off each number from each side little by little
1,2,3,4,4,5,7,8
2,3,4,4,5,7
3,4,4,5
4,4
There are two numbers left so we would find whats between them. But, since it is the same number, you just write the same one as the median.
median= 4
to make 20 pancakes you must use 7 eggs. How many eggs are needed to make 54 pancakes?
Answer:
18.9 eggs
Step-by-step explanation:
54÷20= 2.7
2.7 ×7=18.9
Ms. Larsen is buying 2 delivery vans for her business. The price of the first van
is shown below.
$16,257
The digit 2 in the price of the second van is 10 times the value of the digit 2 in the price of the first van. Which amount could be the price of the second van?
Answer:
18057
Step-by-step explanation:
uh just 200 x 10 = 200 add that to the 6 to make 18057$ which is the price of the second van.
$72 for 7 1/2 hours. Find the unit rate
Answer:
$9.60 for 1 hour
The unit rate is $9.60
Step-by-step explanation:
40% of the students in a school are boys. lf there are 240 boys, how many student are therein the school?
please help me i font understand not alink please i need it now
9514 1404 393
Answer:
25 km/h
Step-by-step explanation:
The relation between speed, time, and distance is ...
speed = distance/time
distance = speed × time
__
The distance relation is used to find the distance on the first line of the table. The problem statement tells you all of the distances are the same.
The speed relation is used to find the speed on the remaining lines of the table. For the average speed, the total distance and total time are used in the computation.
The average speed is 25 km/h.
plz help will give crown
Given the figure below, find the values x of and z.
Answer:
x=7
z=79
Step-by-step explanation:
13x+10=101
13x=91
x=7
180-101=79
Gio weighed five boxes before he shipped them. The weights were: 52, 48, 48, 54, and 50 Which statement is true?
Answer:The mode is equal to the minimum
Step-by-step explanation:
Answer: The mode is equal to the minimum
Step-by-step explanation:
What is the answer to 420 + 69 =
Answer:
420 + 69 = 489
Step-by-step explanation:
HOPE THIS HELPS
brainliest pls :)
Answer:
489
Step-by-step explanation:
420 + 69 = 489
What is the answer to 8/12 = ?/3
Answer:
? = 3×8/12 = 24/12 = 2
Step-by-step explanation:
Here it is, it is correct.
Answer: (2) /3
Step-by-step explanation:
#1 Way: Solve by a proportion
Let x be the unknown number
Given
8/12=x/3
Cross-multiply
12x=24
x=2
Ans: (2)/3
----------------------------------------------------------
#2 Way: Look at the product between numbers
Given
8/12=?/3
From this, we can see the difference (quotient) between the known value 3 and 12 is 4, meaning 12÷3=4.
Applying the same factor, 8÷4=2
Ans: (2)/3
Hope this helps!! :)
Please let me know if you have any questions
The vertex of the function is (6, -8)
Answer: I did a screen shot of the answer
Step-by-step explanation:
James bought a new DVD player with a 30% coupon. If James paid $87.00, what was the original price?
A. $113.10
B. $124.29
C. $147.90
D. $290.00
Answer:
$113.1
Step-by-step explanation:
: you add the 30% + the 87 bucks. Hope it helps friend! Please mark the brainliest. A.
Please help me solving part A
Answer:
Solution is at the image
Step-by-step explanation:
3. A lemonade recipe calls for 1 cup each of sugar and lemon juice and 8 cups of water
Answer:
what exactly are we solving
Step-by-step explanation:
Given P = 2 (l + b) when l = 15 and P = 50,
find b
Answer:
b = 10
Step-by-step explanation:
P = 2 (l + b)
l = 15
P = 50
Substitute
50 = 2 (15 + b)
multiply
50 = 30 + 2b
subtract
20 = 2b
divide
b = 10
P = 2 (l + b) when l = 15 and P = 50
To Find:-To find b
Solution:-P = 2 (l + b) [Given]
Putting the value of P = 50 and l = 15 we get,
50 = 2(15 + b)
[tex] \frac{50}{2} [/tex] = 15 + b
25 = 15 + b
25 - 15 = b
10 = b
So, b = 10
Value of b is 10. [Answer]
Q. Find the value of x.
I need help
Answer:
9
Step-by-step explanation:
Which graph represents the inequality x ≥ 23?
Answer:
D
Step-by-step explanation: A filled bubble means that it is equal to and whichever way the arrow is point represents whether the answer is greater than or less than.
The graph representing the inequality x ≥ 23 is shown on the number line begining from 23 with a closed and shaded circle.
What is an inequality?An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
A number line can be used to represent numbers placed on regular intervals. A number line can be used to represent an inequality.
The graph representing the inequality x ≥ 23 is shown on the number line begining from 23 with a closed and shaded circle.
Find out more on inequality at: https://brainly.com/question/24372553
7 2/3 + 8 1/2 + 4 1/6 =
Answer:
20 1/3 or 61/3
Here you go, have a nice day!!
A company sells their product in Canada and the United States. They wonder if people in both countries will respond similarly to a new advertisement for the product. They show the ad to a sample of 202020 Canadians and a separate sample of 202020 Americans. Here is a summary of the responses in each sample and the results from a chi-squared test:
Chi-square test: Response vs. country
Canada US
Positive 11 5
Expected 8.0 8.0
Neutral 6 5
Expected 5.5 5.5
Negative 3 10
Expected 6.5 6.5
x = 6.110, DF = 2, P-value = 0.047
Assume that all conditions for inference were met. At the a=0.05 significance level, what is the most appropriate conclusion to draw from this test?
Answer:
This is convincing evidence that the responses differ between these countries.
Step-by-step explanation:
The data in this study came from separate samples, so a test for homogeneity is appropriate. Since the P-value is less than the significance level, we should reject the null hypothesis that the distribution of responses is the same in both countries.
The most appropriate conclusion to draw from the test is an evidence of a significant association between the country of origin and the responses to the new advertisement
What is chi squared statistic?
The chi-squared statistic (often denoted as χ^2) is a measure of the discrepancy between the observed frequencies and the expected frequencies in a categorical data set. It is commonly used in statistical hypothesis tests to assess whether there is a significant association or relationship between categorical variables.
The formula for calculating the chi-squared statistic depends on the type of data and the specific hypothesis being tested. In general, it involves computing the sum of squared differences between the observed and expected frequencies, divided by the expected frequencies.
The chi-squared statistic follows a chi-squared distribution, and its value can be compared to critical values or used to calculate a p-value to determine the statistical significance of the association.
Given data ,
Based on the given summary and the results of the chi-squared test, we can draw the following conclusion:
At the significance level of α = 0.05, we have enough evidence to reject the null hypothesis and conclude that there is a statistically significant difference in the responses to the new advertisement between Canadians and Americans.
The chi-squared statistic (x) of 6.110 with 2 degrees of freedom (DF) produces a p-value of 0.047, which is less than the significance level of 0.05.
This indicates that the observed differences in the responses between the two countries are unlikely to occur by chance alone, and there is evidence of a significant association between the country of origin and the responses to the new advertisement.
Hence , the chi-squared statistic is solved
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A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases? (a) 20% of all adult Americans support the changes (b) 25% of all adult Americans support the changes
Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
What is proportionality ?In mathematics, proportionality is the connection between two factors that maintains a fixed ratio called scale factor. Or, to put it another way, if one variable is increased or divided by a specific number, the second variable will also be doubled or divided by that identical number, maintaining their proportionality. Calculus, algebra, and geometry are three areas of mathematics where this idea is frequently applied.
given
(a) If 20% of adult Americans favour the suggested reforms, the sample size needed at the very least is:
n = [(zα/2)² * p * (1-p)] / E²
where z/2 is the standard normal distribution's critical value for the chosen degree of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.2 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.2 * (1-0.2)] / 0.05²
n = 1536.64
Thus, the study would require at least 1537 more adult Americans to be sampled.
(b) The minimal sample size needed if the proposed modifications are
supported by 25% of all adult Americans is:
n = [(zα/2)² * p * (1-p)] / E²
where:
The standard normal distribution's critical value, z/2, depends on the desired level of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.25 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.25 * (1-0.25)] / 0.05² \sn = 384.16
Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
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Can y’all actually answer my question instead of those linking those links cause I don’t
Know what to do on there please & thank youu :)
Answer:
no
Step-by-step explanation:
the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4 the sum of 3 and 5, divided by 4
The side lengths of a triangle are 12.5 inches, 4.4 inches, and 11.7 inches. Which statement best describes the triangle formed using these side lengths?
A.) The triangle is an acute triangle
B.) The triangle is a right triangle
C.) A triangle cannot be formed using these measurements
D.) It is impossible to determine the type of triangle
Answer:
The triangle is a right triangle
Step-by-step explanation:
a4.4 x b11.7=c12.5 a4.4=19.36 b11.7=136.89 12.5=156.25 if you add a squared and b squared you get 156.26 which means its an right triangle
