The formula for the sequence is an = [tex]2^n[/tex], where n is a positive integer. This formula is proven correct using mathematical induction.
To find a formula for the sequence defined by a1 = 1 and ak = 2ak-1, we can use mathematical induction to establish a pattern and then derive the formula. Here's how we can solve it step by step:
Step 1: Base case:
For k = 1, we have a1 = 1.
Step 2: Assume the formula holds for some positive integer n, where n ≥ 1.
Assume that an = [tex]2^{n-1[/tex] for some positive integer n.
Step 3: Use the assumption to prove the formula for the next term.
Now, let's prove that an+1 = [tex]2^n[/tex] holds.
Using the recursive formula ak = 2ak-1, we have:
an+1 = 2an
Substituting the assumed formula an = [tex]2^{n-1[/tex], we get:
an+1 = 2([tex]2^{n-1[/tex])
To simplify, we have:
an+1 = [tex]2^n[/tex]
Step 4: Conclusion:
Based on the assumption and the proof for the next term, we can conclude that the formula an = [tex]2^n[/tex] holds for all positive integers n ≥ 1.
Therefore, the formula for the sequence defined by a1 = 1 and ak = 2ak-1 is an = [tex]2^n[/tex].
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Software can generate samples from (almost) exactly Normal distributions.
Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2:
6.47 7.51 10.10 13.63 9.91
These data match the conditions for a z test better than real data will: the population is very close to Normal and has known standard deviation s = 2, and the population mean is µ = 10.
Test the hypotheses
H0 : µ = 8
Ha : µ ? 8
In Exercise 15.41 (given above), a sample from a Normal population with mean µ = 10 and standard deviation s = 2 failed to reject the null hypothesis H0 : µ = 8 at the a = 0.05 significance level.
Enter the information from this example into the Power of a Test applet.
(Don't forget that the alternative hypothesis is two-sided.)
What is the power of the test against the alternative µ = 10?
The power of the test against the alternative µ = 10 is 1.
Given: A sample from a Normal population with mean µ = 10 and standard deviation s = 2 failed to reject the null hypothesis
H0: µ = 8 at the a = 0.05 significance level.
To find :
The power of the test against the alternative µ = 10.
Step 1: We have
H0 : µ = 8
Ha: µ ≠ 8α
= 0.05
Sample size n = 5
Population Standard deviation s = 2
Population means µ = 10
The alternative hypothesis is two-sided.
Hence α/2 = 0.025.
Using a normal table, the critical values for a two-tailed test at the 0.05 level of significance are -1.96 and +1.96 respectively.
Step 2: We know that
[tex]\[z=\frac{\overline{x}-\mu }{\frac{s}{\sqrt[]{n}}}\][/tex]
where [tex]\[\overline{x}\][/tex] = sample mean,
µ = Population mean,
s = Population Standard deviation and
n = sample size.
By using the given data, z can be calculated as below:
[tex]\[z=\frac{10-8}{\frac{2}{\sqrt[]{5}}}[/tex]
=[tex]4.47[/tex]
The value of z falls in the critical region if it is less than -1.96 or greater than +1.96.
Since 4.47 is greater than +1.96, the null hypothesis is rejected.
Since the null hypothesis is rejected, it is logical to expect that the power of the test will be high.
Hence, the power of the test against the alternative µ = 10 is 1 (100%).
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the temperature is -2c if the temputure rises to 15c , what is the new temputure
Answer:
13c
Step-by-step explanation:
-2 + 12 = 13
A: x>106
B: x<106
C: x=106
Which one is it?
Answer:
x is equal to 106
Step-by-step explanation:
when x is on the opposite side of 2 intersecting lines, it will be the same angle as the angle opposite to it
John is 30 years old. He will receive two payments of $2500 each. The first payment will be an unknown number of years in the future. The second payment will be five years after the first payment. At an annual effective interest rate of I=5%, the present value of the two payments is $2606. Determine at what age John will receive the second payment.
Answer:
16 years
Step-by-step explanation:
Let us assume that he would received the first payment after t years
So
The following formula should be used
PV = P ÷ (1 + r)^t + P ÷ (1 + r)^t+5
$2,606 = $2,500 ÷ (1 + 0.05)^t + $2,500 ÷ (1 + 0.05)^t + 5
$2,606 = $2,500 ÷ 1.05^t (1 + 1 ÷ (1.05)^5)
1.05^t = $2,500 ÷ $2,606 (1.7835) = 1.71098
t = ln(1.71098) ÷ ln(1.05)
= 11
Therefore he would be received the second payment after
= 11 + 5
= 16 years
solve the problem. determine if the lower bound theorem identifies -4 as a lower bound for the real zeros of f(x). f (x) = 3x3 2x2 - 9x 4 select one: a. yes b. no
The correct answer is: a. yes. To determine if the lower bound theorem identifies -4 as a lower bound we need to analyze the behavior of the function as x approaches negative infinity.
The lower bound theorem states that if a polynomial function has a negative leading coefficient (in this case, 3), then any lower bound M must have the property that f(M) is either negative or zero.
Let's evaluate f(-4) to see if it is negative or zero: f(-4) = 3(-4)^3 + 2(-4)^2 - 9(-4) + 4= 3(-64) + 2(16) + 36 + 4= -192 + 32 + 36 + 4= -120. Since f(-4) = -120 is negative, the lower bound theorem identifies -4 as a lower bound for the real zeros of f(x).Therefore, the correct answer is: a. yes
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Arthur wrote that 15 – 14.7 = 3.
Use the drop-down menus to explain why 3 is incorrect.
the point is supposed to be in front of the three
.3
Answer:
the answer is 0.3
Step-by-step explanation:
I hoped this helped
Cari’s Bakery, Inc., began operations in October. The owner contributed cash of $14,400 and a delivery truck with fair value of $19,200 to the company.
Which of the following describes how these transactions would affect the company’s equity accounts?
A) Increase contributed capital by $33,600
B) Increase earned capital by $33,600
C) Increase contributed capital by $14,400 and earned capital by $19,200
D) Increase earned capital by $14,400 and contributed capital by $19,200
E) None of these are correct.
The transaction would affect the company's equity accounts by increasing contributed capital by $14,400 and earned capital by $19,200. The correct answer is option C.
Equity accounts are a component of the balance sheet that represents the net worth of a business. The equity accounts include contributed capital and earned capital. Contributed capital, also referred to as paid-in capital, is the value of cash or other assets contributed to a company by investors in exchange for shares of ownership in the company. Contributed capital represents the long-term financial interests of owners in the business.
Earned capital is the amount of money that a business earns through its operations. It is also referred to as retained earnings. The difference between a business's assets and liabilities is its equity. It represents the total value of the assets that a company owns after all liabilities have been settled. According to the question, the owner contributed cash of $14,400 and a delivery truck with a fair value of $19,200 to the company. This transaction will increase contributed capital by $14,400 (the cash contribution) and increase earned capital by $19,200 (the delivery truck contribution).Therefore, option C: Increase contributed capital by $14,400 and earned capital by $19,200 is the correct answer.
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I need help fast and for real no bots
Answer: d. 201.06
Step-by-step explanation:
To find area of a circle we use the equation 2pi(r) or in this case 2*pi(16)= 804.25in^2 but since we are looking for the shaded region which is 1/4 or one-fourth of the circle so divide 804.25/4 to get 201 or specifically 201.06
Drag and drop all methods of showing Triangle Similarity or Triangle Congruence into the appropriate box. SAS, SSS, ASA, AAS, CPOCTAC, HL, AA
Similar Triangle Justifications Congruent Triangle Justifications
Answer:
hi
Step-by-step explanation:
by
Given the figure below, find the values of x and z.
Answer:
x = 12
z = 101
Step-by-step explanation:
Hello There!
First lets find z
Well the angle that has a measure of 79 degrees and angle z are supplementary angles meaning that the sum of the two is 180
So we can find the missing angle by subtract the given angle (79 in this case) from 180
180 - 79 = 101 so z = 101
Now lets find x
The angle that has a measure of 79 degrees and the angle labeled (6x+7) are vertical angles
If you didn't know vertical angles are congruent
That being said lets create an equation to solve for x
79 = 6x + 7
now we solve for x
step 1 subtract 7 from each side by
7 - 7 cancels out
79 - 7 = 72
now we have 72 = 6x
step 2 divide each side by 6
72/6=12
6x/6=x
we're left with x = 12
Find the value of x for which / || m
Answer:
Step-by-step explanation:
i need to find the area and circumference for each circle
Answer:
Step-by-step explanation:
5
A rectangular prism with a length of 5 inches a width of 4 inches and a height of 3 inches is how many square inches
Answer:
20
Step-by-step explanation:
length x width = area
4 x 5 = 20
(not 100% sure, but I hope this helps)
This pattern follows the rule multiply by 2. What other feature do you observe? 4, 8, 16, 32, 64, 128
Answer:
Each number is 2 to the power some integers.
Step-by-step explanation:
The pattern is 4,8,16,32,64,128.
It follows the exponent of 2.
4=2*2 =[tex]2^{2}[/tex]
8=2*2*2=[tex]2^{3}[/tex]
16= [tex]2^{4}[/tex]
32 =[tex]2^{5}[/tex]
64=[tex]2^{6}[/tex]
128 =[tex]2^{7}[/tex]
so, it is 2 to the power integers.
Write an equation of the line perpendicular to the given line that contains P.
PLSS HELP IMMEDIATELY!!! i’ll give brainiest if u don’t leave a link!
Answer:
C
Step-by-step explanation:
The cost to place an ad in a weekly paper is $5.50 per line,i.The print set-up fee is $7.50.
Answer:
whats the question?
Step-by-step explanation:
How would I put this?
Answer:
10.35
Step-by-step explanation:
63,756 x 60 = 3825360
70 x 5,280 = 369600
3825360 ÷ 369600 = 10.35
What is the range of the function f = [0,00) + R, defined by the rule f(t) = -247 (a) (0,1) (c) R (b) (0,11 (d) (0,00)
The range of the function f = [0,00) + R, defined by the rule f(t) = -247 is {-247}. The correct option is d.
The range of a function is the set of all possible outputs or y-values. Here, the function is f(t) = -247 with the domain [0,00), which means that for any value of t between 0 and 00 (excluding 00), the function will always give the same output, -247. This is because the rule for the function is simply -247, and doesn't depend on the input value of t.
The range of the function f is simply {-247}, which is a singleton set containing only one element (-247). In other words, the only possible output or y-value for this function is -247, and there are no other possible values for f(t) for any value of t between 0 and 00 (excluding 00).
Thus, the correct option is d.
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Pls help, answer righhand I’ll mark brainly and you big smart!
Answer:
A. and C.
Step-by-step explanation:
Just remember that to find the roots, use the equation:
(-b +/- sqrt[b^2 - 4ac])/2a
I would appreciate Brainliest, but no worries.
During the summer John collected cans to recycle. In August he collected 718 cans bringing his total to 2,275 cans. How many cans did John collect before August?
Answer: 1557 cans
Step-by-step explanation:
Since we are informed that John collected 718 cans in August bringing his total number of cans to 2,275 cans, the number of cans that John collected before August will be:
= Total number of cans collected - Number of cans collected in August
= 2275 - 718
= 1557 cans
Quadratic Functions
Determine the value of y, if x is −9. y=x^2+8
Answer:nn
Step-by-step explanationn o:
Answer:
y = 89
Step-by-step explanation:
x = -9
y = x^2 + 8
y = (-9)^2 + 8
y = 81 + 8
y = 89
What is equivalent to 8?
A:2^3
B:3^-2
C:2^-3
D:3^2
Answer: A:2^3
Step-by-step explanation:
8=2*2*2=(2)^3
Choose the correct answer.
Between the years 1970 and 1976, what percentage change in the rate of exchange occurred in the German mark relative to the United States dollar (to the nearest percent)?
%
answer:
Between the years 1970 and 1976, what percentage change in the rate of exchange occurred in the German mark relative to the United States dollar (to the nearest percent)?
45 %
The percentage change in the rate of exchange occurred in the German mark relative to the United States dollar is 45%
How to determine the change in the rates?From the chart (table), we have the following rates in Germany:
Rate in 1970 = 27.42Rate in 1976 = 39.74The percentage change is then calculated using:
Percentage change= (Final - Initial)/Initial * 100%
This gives
Percentage change= (39.74 - 27.42)/27.42* 100%
Evaluate the quotient
Percentage change= 0.45* 100%
Evaluate the product
Percentage change= 45%
Hence, the percentage change in the rate of exchange occurred in the German mark relative to the United States dollar is 45%
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There is a sale on jeans where you will get 20% off the original price. If the jeans cost $65, how much will you SPEND on the jeans?
plzzzz answer
Use the SOR method with w = 1.2 to solve the following linear system with a tolerance TOL = 10-3 in the lo norm. - 4x1 + x2 – x3 + x4 = -2, X1 + 4x2 – X3 – X4 = -1, -X] – x2 + 5x3 + x4 = 0, X1 – x2 + x3 + 3x4 = 1.
Using the Successive Over-Relaxation (SOR) method with a relaxation factor of w = 1.2 and a tolerance of TOL = 10^-3 in the l2 norm, the linear system of equations can be solved iteratively. The solution will converge to the desired tolerance level.
The SOR method is an iterative technique used to solve linear systems of equations. It requires an initial guess for the solution and iteratively updates the values until the desired tolerance is reached.
To apply the SOR method, the given linear system can be rewritten as a matrix equation: AX = B, where A is the coefficient matrix, X is the solution vector, and B is the constant vector. The system can be solved by iterating through the equations and updating the values of X until convergence is achieved.
In this case, the SOR method is performed with a relaxation factor of w = 1.2, which helps to accelerate convergence. The tolerance is set to TOL = 10^-3, indicating the desired level of accuracy.
The SOR algorithm is then applied iteratively until the solution converges within the specified tolerance. The updated values of X are calculated using the SOR formula, and the process is repeated until the difference between consecutive iterations falls below the tolerance level.
By following this iterative process with the given parameters, the SOR method will yield the solution to the linear system of equations.
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OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME WHAT TO DRAW
Answer:
Step-by-step explanation:
Answer:
13107 employees
A. The picture
B. 10,972 + 2,135 = n
13107 = n
Step-by-step explanation:
10,972 + 2,135 = 13107
What should be drawn is in the photo.
Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!
Answer: n=4
Step-by-step explanation:
Given
3n-(2+n)=6
Expand Parenthesis (REMEMBER TO CHANGE SIGNS)
3n-2-n=6
Combine like terms
2n-2=6
Add 2 on both sides
2n-2+2=6+2
2n=8
Divide both sides by 2
2n/2=8/2
n=4
Hope this helps!! :)
Please let me know if you have any questions
Answer:
4
Step-by-step explanation:
4 Is the Answer because you have to multiply 4 to all the N's. Which means you have to multiply 4 by 3 which equals 12. Then 2+4=6. Then you would do 12-6=6. There's your answer. Here is the equation if it were like the problem: 12 - (2+4). I'm sure you can figure out the rest. Thanks. If you find any fault in my answer let me know! Have a good day!
find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. a(3, 4, 1), b(0, 6, 2), c(3, 5, 6)
The lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.
To find the lengths of the sides of the triangle with vertices A(3, 4, 1), B(0, 6, 2), and C(3, 5, 6), we can use the distance formula.
The distance formula between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in three-dimensional space is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
Let's calculate the lengths of the sides of the triangle:
Side AB:
d₁ = √((0 - 3)² + (6 - 4)² + (2 - 1)²)
= √((-3)² + 2² + 1²)
= √(9 + 4 + 1)
= √14
Side BC:
d₂ = √((3 - 0)² + (5 - 6)² + (6 - 2)²)
= √(3² + (-1)² + 4²)
= √(9 + 1 + 16)
= √26
Side AC:
d₃ = √((3 - 3)² + (5 - 4)² + (6 - 1)²)
= √(0² + 1² + 5²)
= √(0 + 1 + 25)
= √26
Now, let's analyze the triangle based on the lengths of its sides:
Since all three sides have different lengths (√14, √26, and √26), the triangle is neither an isosceles triangle (which has at least two sides of equal length) nor a right triangle (which satisfies the Pythagorean theorem).
In summary, the lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.
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the Median.)
Find quartile 2 using the data below:
23, 45, 52, 28, 42, 87, 56, 32, 48, 55, 24, 63, 68, 76, 67
Answer:
52
Step-by-step explanation:
if you put the numbers in order from least to greatest you'll see that 52 is in the middle