Answer:
a) Neither,b) t(n) = (n - 4)²--------------------------------------
We observe that, the sequence is symmetric and all the terms are perfect squares:
16, 9, 4, 1, 0, 1, 4 ⇒ 4², 3², 2², 1², 0², 1², 2²This is neither arithmetic nor geometric.
The zero term is 16 and the fourth term is 0 so the nth term would be:
t(n) = (n - 4)²Answer:
a) Neither
b) t(n) = n² - 8n + 16
Step-by-step explanation:
An Arithmetic Sequence has a constant difference between each consecutive term.
A Geometric Sequence has a constant ratio (multiplier) between each consecutive term.
Part (a)As the sequence has neither a constant difference or a constant ratio, the sequence is neither arithmetic or geometric.
Part (b)Work out the differences between the terms until the differences are the same:
First differences
[tex]16 \underset{-7}{\longrightarrow} 9 \underset{-5}{\longrightarrow} 4 \underset{-3}{\longrightarrow} 1 \underset{-1}{\longrightarrow} 0 \underset{+1}{\longrightarrow} 1 \underset{+3}{\longrightarrow} 4[/tex]
Second differences
[tex]-7 \underset{+2}{\longrightarrow} -5 \underset{+2}{\longrightarrow} -3\underset{+2}{\longrightarrow} -1\underset{+2}{\longrightarrow} 1\underset{+2}{\longrightarrow} 3[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² = 1.
Write out the numbers in the sequence n² and determine the operation that takes n² to the given sequence:
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-8} n&0& 1& 2&3 &4 &5 &6 \\\cline{1-8}n^2 &0& 1& 4& 9&16 & 25&36 \\\cline{1-8} \sf operation&+16& +8&+0&-8&-16&-24&-32\\\cline{1-8} \sf sequence & 16&9 &4 & 1& 0& 1& 4\\\cline{1-8}\end{array}[/tex]
As the operation is not constant, work out the differences between the operations:
[tex]16\underset{-8}{\longrightarrow} 8\underset{-8}{\longrightarrow} 0\underset{-8}{\longrightarrow} -8\underset{-8}{\longrightarrow} -16\underset{-8}{\longrightarrow} -24\underset{-8}{\longrightarrow} -32[/tex]
As the differences are the same, the second operation in the sequence is -8n. Write out the numbers in the sequence with both operations and and determine the operation that takes (n² - 8n) to the given sequence:
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-8} n&0& 1& 2&3 &4 &5 &6 \\\cline{1-8}n^2 -8n&-0&-7&-12&-15&-16&-15&-12\\\cline{1-8}\sf operation &+16&+16&+16&+16&+16&+16&+16\\\cline{1-8} \sf sequence & 16&9 &4 & 1& 0& 1& 4\\\cline{1-8}\end{array}[/tex]
As the operation is constant, the final operation in the sequence is +16.
So the equation for the nth term is:
[tex]\implies t(n)=n^2-8n+16[/tex]
If (y + 1) varies directly as square root of x and y =14 when x = 27, find the value of y when
x = 64 without finding the variation constant.
Answer:
22.1 or 22
Step-by-step explanation:
Y + 1 varies√x
Y + 1 = K√x ( k is costant)
so we solve for K
given: 14 + 1 = K√27
15 = K√27
divide both sides by √27
15/√27 = K
to find the value of y
y + 1 = 15/√27 (8) : substitute K for 15/√27
Y + 1 = 120/√27
i.e Y = 120/√27 - 1
Y = 23.1 - 1
Y = 22.1 or 22
Which set of numbers below DO NOT make a triangle?
7,7,7
6, 3, 3
3,4,5
5, 11,7
Answer:
6, 3, 3 (B)
Step-by-step explanation:
Two sides of a triangle must be greater than the remaining side
A way to think about this is like this:
The two shortest sides of a triangle must be greater than the final side
Go through this process for each option and find the B does not work
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f. f(x) = ; g(x) =
Answer:
Di ko alam
Step-by-step explanation:
Hirap niyan eh
Given f(x) = -(x - 5)^2 + 1, what is the value of h?
Answer:
It began after the stock market crash of October 1929, which sent Wall Street into a panic and wiped out millions of investors. Over the next several years, consumer spending and investment dropped, causing steep declines in industrial output and employment as failing companies laid off workers.
consider the two functions. which statement is true?
Answer:
The right answer is D
Step-by-step explanation:
The slope of the first function is 2.5, the slope of the second function is 3, so function 2 has a greater rate of change by [tex]\frac{1}{2}[/tex].
Adrienne’s lunch cost $13.16. She hands the cashier $20. About how much change does Adrienne receive?
Answer:
Use long subtraction to evaluate.
6.84
Step-by-step explanation:
In the diagram, JK is congruent to GI. Solve for x if HJ = 3x, HK = 2x, KI = 6x, and JG = 18 units.
Plz help! I don’t know how to do these!
4. x= 40
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Answer:
x = 3 && y = - 1
Step-by-step explanation:
Just solving the two equations
the first equation
y = 4/3 x +3
y - 4/3 x = 3 ..............................................(1)
the second equation
y = -2/3x -3
y + 2/3 x = -3 ..............................................(2)
by substracting 2 from 1
-4/3x - 2/3x = -6
divide by -1
4/3x +2/3x = 6
6/3x = 6
2x = 6
x= 3
then subsititute by value x in any of given eqautions
pls help 100 points helphelp
Answer:
Some kind of evadence
Step-by-step explanation:
Answer:
Im pretty sure it would be C.
Step-by-step explanation:
Sine a signature, photograph and quotes are all pieces of evidence, you can rule them out and infer that c would be the most reliable answer.
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
-1
Step-by-step explanation:
If you multiply x by -1 you will get the y value to be the negative of that number.
Hope this helps!!
Answer:
so first find what y equals then put the negative in front of it lol there is a pattern positive and negative
3,-3
4,-4
5,-5
6,-6
y,-y
Step-by-step explanation:
suppose that rectangle ABCD is dilated to A'B'C'D using the origin as the center and a mangnitude of 2. What are the coordinates of C'?
Answer:
-8,-8
Step-by-step explanation:
Hope u get it right! :D
One end of a ramp is raised to the back of a truck 5 feet above the ground. 1 point
If the length of the ramp is 8 feet, what is the approximate measure of the
angle the ramp makes with the ground? Round your answer to the nearest
tenth of a degree.
38.7°
58.0°
32.0
51.3
Answer:
38.7°
Step-by-step explanation:
You are basically looking at a triangle with a 90° angle (check picture).
Since we are looking for the ramp's angle and are given the length of the opposite and the hypothenuse, we have to solve the following equation:
[tex]sin (\alpha) = opposite / hypothenuse= 5 ft/8ft[/tex]
which is equivalent to
[tex]\alpha = sin^{-1}(5/8)\approx 38.7\deg[/tex]
Imagine you are a financial analyst at an investment bank. According to your research of publicly-traded companies, 60% of the companies that increased their share price by more than 5% in the last three years replaced their CEOs during the period. At the same time, only 35% of the companies that did not increase their share price by more than 5% in the same period replaced their CEOs. Knowing that the probability that the stock prices grow by more than 5% is 4%, find the probability that the shares of a company that fires its CEO will increase by more than 5%.
Answer:
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this problem:
Event A: Company fires the CEO
Event B: Shares increase by more than 5%.
Probability of a company firing it's CEO:
35% of 100 - 4 = 96%(shares did not increase by more than 5%).
60% of 4%(shared did increase by more than 5%).
So
[tex]P(A) = 0.35*0.96 + 0.6*0.04 = 0.36[/tex]
Intersection of events A and B:
Fires the CEO and shared increased by more than 5%, is 60% of 4%. So
[tex]P(A \cap B) = 0.6*0.04 = 0.024[/tex]
Probability that the shares of a company that fires its CEO will increase by more than 5%.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.024}{0.36} = 0.0667[/tex]
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.
Please help with this area
Answer:
L = 7 W= 12
Step-by-step explanation:
Ok so we already know that a rectangle is not even so the numbers will have to be 2 diff numbers.
The length is 5 feet less then width
w*l= 84
1* 84 2* 41 3*28 4*21 6*14 7*12
84-1 41-2 28-3 21-4 14-6 12-7
83 39 25 19 8 5
So,
your equation would be l*w = 7*12
Solve for m.
m
2
= 13
Answer:
m=6.5
Step-by-step explanation:
13 divided by 2= 6.5
5(y+25)=-13 i need help explaining
Answer:
y=-138/5=-27 3/5 = -27.6
Step-by-step explanation:
5(y+25)=−13
Divide both sides by 5.
y+25=-13/5
Subtract 25 from both sides.
y=-13/5−25
Convert 25 to fraction 125/5
y=-13/5-125/5
Since -13/5 and 125/5 have the same denominator, subtract them by subtracting their numerators.
y=-13 - 125/5
Subtract 125 from −13 to get −138.
y=-138/5
Geometric mean of 45 and 15
Answer:
30
Step-by-step explanation:
[tex]\frac{45+15}{2}[/tex] equals 30.
Answer:
45 + 15 = 60 divided by 2 is 30
(-40) divided by (_)= (-8) what is the missing number?
Answer:
5!
Step-by-step explanation:
-40÷5 = -8
Help pleaseeeeee!!!!!!!!
Answer:
2hklakkskamkaoaiaikanwkaisosossosooaolalao
b.1=(-2x2)+5
or you say x=2 and y=1
Step-by-step explanation:
bro bit a no answer ok
please mark me as brainlist
Anna needs to purchase some new clothes. for each pair of jeans she will buy three sweaters. how many sweaters can she purchase if she has $255?
jeans cost: $40 each
sweaters cost: $15 each
use elimination method for solving systems of equations.
Answer:
3
Step-by-step explanation:
each time Anna purchased a pair of jeans she spends 40+15(3)=40+45=$85, including the sweaters. to find how many jeans and sweaters she buys $255÷$85=3
Help me I’m stuck and please can someone explain this to me
Answer:
84 degrees
Step-by-step explanation:
3x = 4x - 28. Reason: Alternate Exterior Angle are congruent
X=28 Reason: Algebra
Y+4x-28= 180 Reason: Straight angles = 180 degrees
Y=84. Reason: Algebra
In a survey, 150 seventh graders said that they had been to a foreign country. That number represented 20% of the students who were surveyed. How many students were surveyed?
Answer:
750
Step-by-step explanation:
150/2=7.5
7.5*100=750
750*0.2=150
I ready volume with fractional length
Answer:
im here to help.
Step-by-step explanation:
yup
Among two congruent angles ,one has measure 69⁰,then the measure of other angle is
Answer:
Your answer is
Congruent means similar.
Other angle is 69°
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Can you show me the steps that you took to get the answer for this question?
SOLVE the EXPRESSION
Evaluate 6s - 3t If s=4 and t=-2
Answer:
30
Step-by-step explanation:
6(4) - 3(-2) =
24 + 6 =
30
Su is baking 5 batches each of cookies and cupcakes. The cookies use 2 cups of sugar per batch and the cupcakes use 3 cups of sugar per batch. Write two equivalent expressions using the Distributive Property. Then find how many total cups of sugar are needed.
I know the answer is 25 but how would I write the expression.
Answer:x=25 divided by 5
Step-by-step explanation:
absolute value of x=5
what is x
Answer:
5
Step-by-step explanation:
5 = 5
Common ratio of 1/2,1,2,4,8
Step-by-step explanation:
common ratio (r) = second term÷first term