The division of a polynomial is illustrated below.
What is a polynomial?It should be noted that a polynomial simply means an expression that consist of variables which involves the operation of addition, subtraction, etc.
The way to divide the polynomial will be:
Set up the division problem.
Determine the first term of the quotient.
Multiply the answer by the divisor.
Write it below the like terms of the dividend.
Subtract the bottom binomial from the term above it.
Bring it down and repeat the steps until you reach the last term.
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Five years ago, you invested $475 in corporate stock. You received dividends of $10 at the end of each quarter for two years. You then received quarterly dividends of $15 for the following three years. You just sold the stock for $1,700, immediately after receiving your 20th quarterly dividend check. What is your rate of return?
Group of answer choices
32.43%
31.03%
93.09%
9.73%
The rate of return earned on the investment of $475 five years ago in the corporate stock is 312.63%.
What is the rate of return?The rate of return is the net gain or loss of an investment expressed as a percentage of the investment's initial cost.
It is given by the formula, R= {Vf - Vi}/{Vi} x 100.
Where:
R = Rate of return
Vf = final value, including dividends and interest
Vi = initial value
Data and Calculations:Investment cost = $475
Dividends received:
1st two years = $80 ($10 x 8)
Three years = $180 ($15 x 12)
Total dividends received = $260 ($80 + $180)
Total revenue from sale = $1,700
Total proceeds = $1,960 ($1,700 + $260)
Total return = $1,485 ($1,960 - $475)
Rate of return = 312.63% ($1,485/$475 x 100)
Thus, the rate of return is 312.63%.
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The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $310.
a. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost between $1000 and $1250?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
b. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost which exceeds $1250?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
c. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost below $1220?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
Using the normal distribution, it is found that the probabilities are given as follows:
a) 0.8871 = 88.71%.
b) 0.0778 = 7.78%.
c) 0.8485 = 84.85%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters in this problem are given as follows:
[tex]\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5[/tex]
Item a:
The probability is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000, hence:
X = 1250:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1250 - 1140}{77.5}[/tex]
Z = 1.42
Z = 1.42 has a p-value of 0.9222.
X = 1000:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1000 - 1140}{77.5}[/tex]
Z = -1.81
Z = -1.81 has a p-value of 0.0351.
0.9222 - 0.0351 = 0.8871 = 88.71% probability.
Item b:
The probability is one subtracted by the p-value of Z when X = 1250, hence:
1 - 0.9222 = 0.0778 = 7.78%.
Item c:
The probability is the p-value of Z when X = 1220, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1220 - 1140}{77.5}[/tex]
Z = 1.03
Z = 1.03 has a p-value of 0.8485.
0.8485 = 84.85% probability.
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The value of y varies inversely with x. What is the value of k when y=12.7 and x=8
Answer: 101.6
Step-by-step explanation:
y∝(1/x)
this implies that
y=k/x eq(*)
when y=12.7 and x=8
12.7=k/8
(12.7)(8)=k
101.6 =k
I need help with number 7 and 8 and 9!
Answer:
in the 8 is ADB, in the 7 I'm not sure about you need to do sorry, or maybe you need to classify what triangle it is think is a scalene triangle because has a different measurements
Find the surface area
Answer:
17038.94mm
Step-by-step explanation:
Solve the following equation by first writing the equation in the form ax² = c
²-49-0
a.
b.
C.
d.
-49
- 149
= 7
:= ±7
The solution to the given equation is x = ±7. The correct option is d. x = ±7
Solving quadratic equationsFrom the question, we are to determine the solution to the given equation
The given equation is
x²-49 = 0
NOTE: I assumed the variable is x
Solving the equation
x²-49 = 0
Writing in the form ax²= c
x² = 49
∴ x = ±√49
x = ±7
Hence, the solution to the given equation is x = ±7
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Solve 7x2(x + 1) = 6x + 14
Ox=-12
Ox = 12
Ox= -16
Ox = 16
[tex]\large\displaystyle\text{$\begin{gathered}\sf 7x-2(x+1)=6x+4 \end{gathered}$}[/tex]
Use the distributive property to multiply −2 by x+1.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 7x-2x-2=6x+14 \end{gathered}$}[/tex]Combine 7x and −2x to get 5x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-2=6x+14 \end{gathered}$}[/tex]Subtract 6x on both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-2-6x=14 \end{gathered}$}[/tex]Combine 5x and −6x to get −x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -x-2=14 \end{gathered}$}[/tex]Add 2 to both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -x=14+2 \end{gathered}$}[/tex]Add 14 and 2 to get 16.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -x=16 \end{gathered}$}[/tex]Multiply both sides by −1.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-16 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]{ Pisces04 }[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{7x - 2(x + 1) = 6x + 14}[/tex]
[tex]\huge\textbf{DISTRIBUTE 2 WITHIN the}\\\\\huge\textbf{PARENTHESES:}[/tex]
[tex]\mathsf{7x - 2(x) + 2(1) = 6x + 14}[/tex]
[tex]\mathsf{7x - 2x - 2 = 6x + 14}[/tex]
[tex]\huge\textbf{COMBINE the LIKE TERMS (if you}\\\\\huge\textbf{have any):}[/tex]
[tex]\mathsf{(7x - 2x) - 2 = 6x + 14}[/tex]
[tex]\mathsf{5x - 2 = 6x + 14}[/tex]
[tex]\huge\textbf{ADD 2 to BOTH SIDES:}[/tex]
[tex]\mathsf{5x - 2 + 2 = 6x + 14 + 2}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{5x = 6x + 16}[/tex]
[tex]\huge\textbf{SUBTRACT 6x to BOTH SIDES}[/tex]
[tex]\mathsf{5x - 6x = 6x + 16 - 6x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{-x = 16}[/tex]
[tex]\mathsf{-1x = 16}[/tex]
[tex]\huge\textbf{DIVIDE -1 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{-1x}{-1} = \dfrac{16}{-1}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{x = \dfrac{16}{-1}}[/tex]
[tex]\mathsf{x = -16}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Describe how the graph of each function can be obtained from the graph of y = f(x). Make sure you use full sentences to explain the transformation of the new function.
a) y=3f(x)–2
(b) y=f(x-1)–4
(c) y=f(1⁄2x)+5
Using translation concepts, the changes are described as follows:
a) The function is vertically stretched by a factor of 3, and shifted down 2 units.
b) The function is shifted 1 unit right and 4 units down.
c) The function is horizontally compressed by a factor of 2 and shifted up 5 units.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Item a:
The changes are as follows:
y -> 3y, hence the function is vertically stretched by a factor of 3.y -> y - 2, hence the function is shifted down 2 units.Item b:
The changes are as follows:
x -> x - 1, hence the function is shifted right 1 unit.y -> y - 4, hence the function is shifted down 4 units.Item c:
The changes are as follows:
x -> 0.5x, hence the function is horizontally compressed by a factor of 2.y -> y + 5, hence the function is shifted up 4 units.More can be learned about translation concepts at https://brainly.com/question/4521517
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You plan to borrow $36,500 at a 7.7% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?
The amount of interest you would be paying in Year 2 is: $2,492.62.
InterestFirst step is to calculate the Equal Monthly Payment
Equal Monthly Payment=P×r×(1+r)^t/(1+r)^t-1
Where:
P=Principal=$36,500
r=Rate=7.7%
t=Time=7 years
Equal Monthly Payment=36,500×0.077×(1+0.077)^7÷(1+0.077)^7-1
Equal Monthly Payment=36,500×0.077×(1.077)^7÷(1.077)^7-1
Equal Monthly Payment=36,500×0.077×1.6807763÷1.6807763-1
Equal Monthly Payment=4,723.82/0.6807763
Equal Monthly Payment=$6,938.875
Second step is to calculate Year 1 Closing balance
Year 1 Closing balance = Beginning balance + Interest - EMI Payment
Year 1 Closing balance= $36,500 +($36,500×7.7%) - $6,938.875
Year 1 Closing balance= $36,500 + $2,810.5 -$6,938.875
Year 1 Closing balance = $32,371.625
Third step is to calculate year 2 interest
Year 2 Interest= $32,371.625×7.7%
Year 2 Interest=$2,492.62
Therefore the amount of interest you would be paying in Year 2 is: $2,492.62.
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Part II: Describe the pattern of the following sequence. (2 points)
1 subract 6
2 add 8
3 add 11
4 subract 5
5 add 10
A baker buys 10 apples from a farmer for $.25/each. the baker uses the 10 apples to make an apple pie that they sell in their bakery for $7.99. what is the total contribution to gdp?
The total contribution to the GDP is $5.49.
How to find the total contribution to GDP?GDP, the gross domestic product is the sum of all final goods and services produced in an economy within a given period.
When calculating GDP, only the value added of final goods and services are included. Intermediate goods are not added.
Therefore,
Total contribution to GDP = 7.99 - (10 X 0.25) = $5.49.
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You want to be able to withdraw $45,000 each year for 20 years. Your account earns 6% interest. a) How much do you need in your account at the beginning? $ b) How much total money will you pull out of the account? $ c) How much of that money is interest?
Step-by-step explanation:
gd seek is sssa eh uiiio if fsssw we to i if i jobs sss
3) How many whole 3s are there inside of 4½?
Answer:
1
Step-by-step explanation:
There is one whole 3 inside of 4 1/2 or 4.5.
Multiples of 3 are 3x1=3 3x2=6....
Only a single whole 3 can be inside of 4.5.
Answer:
One
Step-by-step explanation:
ONE
4.5 ÷ 3 = 1 . 5 <=====so there is one and a half 3's in 4.5
The simple interest on a certain sum of money for 2 years at 5% per annum is Rs 320. What will be the compound interest on the same sum for the same time at the same rate, the interest being calculated yearly? D 1800 cimple interest in 10 years. Find the The simple interest on a certain sum of money for 2 years at 5 % per annum is Rs 320. What will be the compound interest on the same sum for the same time at the same rate , the interest being calculated yearly ? D 1800 cimple interest in 10 years . Find the
Answer:
Rs 328
Step-by-step explanation:
Find the principal amount invested.
Simple Interest Formula
I = Prt
where:
I = interest earnedP = principalr = interest rate (in decimal form)t = time (in years)Given:
I = Rs 320r = 5% = 0.05t = 2 yearsSubstitute the given values into the formula and solve for P:
⇒ 320 = P(0.05)(2)
⇒ 320 = P(0.1)
⇒ P = 3200
Compound Interest Formula
[tex]\large \text{$ \sf I=P\left(1+\frac{r}{n}\right)^{nt} -P$}[/tex]
where:
I = interest earnedP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = 3200r = 5% = 0.05n = 1 (annually)t = 2 yearsSubstitute the given values into the formula and solve for I:
[tex]\implies \sf I=3200\left(1+\frac{0.05}{1}\right)^{2} -3200[/tex]
[tex]\implies \sf I=3200\left(1.05\right)^{2} -3200[/tex]
[tex]\implies \sf I=3200\left(1.1025\right) -3200[/tex]
[tex]\implies \sf I=3528-3200[/tex]
[tex]\implies \sf I=328[/tex]
Therefore, the compound interest on the same sum for the same time at the same rate is Rs 328.
Identify the factors of x² - 4x - 12.
(x+4)(x-3)
(x-4)(x+3)
(x-2)(x + 6)
(x + 2)(x-6)
Answer:
Step-by-step explanation:
ali picks three numbers out of a hat the lowest number was 11 the range was 13 and the median was 17 what was the three numbers
Answer:
11 , 17 , 24
Step-by-step explanation:
• Since the Lowest number is 11 and the range is 13 then
The greatest number is 11 + 13 = 24
• Therefore the three numbers are 11 , 17 and 24
because the median of the set 11 , 17 , 24 is 17
Problem
(a) Expand and simplify [tex](x^2+2)^2[/tex].
(b) Hence fully factorise [tex]x^4 +4x+3[/tex].
a. [tex]x^4 + 4x^2 + 4[/tex]
b. x = ∛-1 and -3
How to expand the expressiona. Given
(x² + 2)²
First, we open up the bracket
[tex](x^2 + 2) (x^2 + 2)[/tex]
Multiply through
[tex]x^4 + 2x^2 + 2x^2 + 4[/tex]
Collect like terms
[tex]x^4 + 4x^2 + 4[/tex]
b. Let's factorize
[tex]x^4 + 4x + 3[/tex]
Find the factors of 3 that are products of 4, they are 3 and 1
Use it to replace 4x as 3x and x
[tex]x^4 + 3x + x + 3[/tex]
Let's make the expression two
[tex](x^4 + 3x) (x+ 3)[/tex]
Find the common factor
[tex]x^3(x + 3)+ 1(x+ 3)[/tex]
So,
[tex]x^3 + 1 = 0[/tex] and [tex]x + 3 = 0[/tex]
[tex]x = 3\sqrt{-1}[/tex] and x = -3
Thus, x = ∛-1 and -3
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REALLY need help on this question
The values of the composite functions can be derived from the given tables as follows;
(g•f)(0) = -2(g•f)(1) = 1The domain of f(x) are; -2, -1, 0, 1The range of g(x) are; 2, 0, 1, 5How can the composite functions be evaluated?By composite functions definition, we have;
(g•f)(0) = g(f(0))
From the given tables, we have;
f(0) = 1
g(1) = -2
Therefore;
(g•f)(0) = g(f(0)) = g(1) = -2Similarly, we have;
(g•f)(1) = g(f(1))
From the given tables, we have;
f(1) = 0
g(0) = 1
Therefore;
(g•f)(1) = g(f(1)) = g(0) = 1The domain of f(x) are the possible x-values of f(x).
From the given table the domain of f(x) is; -2, -1, 0, 1The range of g(x) are the possible y-values of g(x).
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What is the extraneous solution found in solving the equation log2 4x + log₂ (x + 1) = 3
Answer:
x = -2
Step-by-step explanation:
We are given the logarithmic base 2 equation of:
[tex]\displaystyle{\log_2 (4x) + \log_2 (x+1) = 3}[/tex]
Apply logarithm property of addition where:
[tex]\displaystyle{\log_a M + \log_a N = \log_a MN}[/tex]
Therefore, we will write new equation as:
[tex]\displaystyle{\log_2 [4x(x+1)] = 3}[/tex]
Apply logarithm to exponential form using:
[tex]\displaystyle{\log_a M = N \to a^N = M}[/tex]
Thus, another new rewritten equation is:
[tex]\displaystyle{2^3 = 4x(x+1)}\\\\\displaystyle{8 = 4x(x+1)}\\\\\displaystyle{2=x(x+1)}[/tex]
Expand the expression in and arrange the terms in quadratic expression:
[tex]\displaystyle{2=x^2+x}\\\\\displaystyle{0=x^2+x-2}\\\\\displaystyle{x^2+x-2=0}[/tex]
Solve for x:
[tex]\displaystyle{(x+2)(x-1)=0}\\\\\displaystyle{x=-2,1}[/tex]
These are potential solutions to the equation. To find extraneous solution, you’ll have to know the domain of logarithm function. We know that logarithm’s domain is defined to be greater than 0. Henceforth, anti-logarithm must be greater than 0.
( 1 ) 4x > 0, x > 0
( 2 ) x + 1 > 0, x > -1
Therefore, our anti-log must be greater than 0, so any solutions that are equal or less than 0 will be considered as extraneous solution.
Hence, x = -2 is the extraneous solution.
Find the value of Y to nearest tenth...
cos 64degrees = y/8
Step-by-step explanation:
what is the problem ? this is very straight forward with a calculator :
cos(64°) = y/8
y = 8×cos(64°) = 8×0.438371147... = 3.506969174... ≈
≈ 3.5
Trinity has 12 ounces of tea leaves. If
each cup of tea requires 3 ounce
of tea leaves, how many cups of tea
can Trinity make?
cups of tea
Answer:
4 cups of tea
Step-by-step explanation:
12 ounces ÷ 2/3 ounces = 18 cups of tea.
12/1 ÷ 2/3
12/1 x 3/2
= 36/2
=18
Answer:
4 cups of tea
Step-by-step explanation:
Given Trinity has 12 ounces of tea leaves, and 1 cup of tea requires 3 ounce of tea leaves,
No. of cups of tea = Total amount of tea leaves / Tea leaves required per cup of tea
= 12 / 3
= 4 cups of tea.
a group of 4 numbers have an average of 15, three of the numbers are 18,11 and 25. what is the other number??
Answer:
6
Step-by-step explanation:
The average of a set of numbers is their sum divided by their number. This fact lets us write an equation to find the missing number.
SetupLet x represent the missing number. The average of the 4 numbers is ...
(x +18 +11 +25)/4 = 15
SolutionMultiplying by 4 gives ...
x +54 = 60
Subtracting 54, we find the missing number:
x = 6
The other number is 6.
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe the below answers are correct. Thank you!
The problem proves that the distributor's claim is true and he has a right to complain.
But when the confidence interval is changed from 95% to 90% the distributor's claim proves to be false.
The Confidence Interval for 95% is 0.9687;0.98532
For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.
The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.
The Confidence Interval for 90% is 0.97156;0.982431
Here
μ = 0.977
s= σ= 0.03
95 % confidence interval is given by
x~± z∝/2 (s/√n)
Putting the values
0.977 ± 1.96 (0.03/√50)
=0.977 ± 0.008315
0.9687;0.98532
Part B:
x~+ 0.95= 0.977+0.95= 1.927
The critical region is Z ≥ 1.96 therefore the 1.927 lies in the acceptance region that the distributor's claim is true.
Part C:
For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.
Part D:
μ = 0.977
s= σ= 0.03
90 % confidence interval is given by
x~± z∝/2 (s/√n)
Putting the values
0.977 ± 1.28 (0.03/√50)
=0.977 ± 0.005431
0.97156;0.982431
Part D:
x~+ 0.90= 0.977+0.90= 1.877
The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.
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■.Given angle TUV and ray UW, if m/TUV = 89,
m/TUW = 22 +7x, and m/WUV = 41+ 6x, find m/WUV.
Assume that point W is on the interior of TUV
Giving brainliest
The measure of m<WUV is 53 degrees
Lines and angles
Given the following parameters
m<TUW = 22 +7x,
m<WUV = 41+ 6x
m<TUV. = 89
The related expression is given as:
m<TUV + m<WUV = m<TUV.
Substitute
22+7x+41+6x = 89
63 + 13x = 89
13x = 89 - 63
13x = 26
x = 2
Determine the measure of m<WUV
m<WUV = 41 + 6(2)
m<WUV = 41 + 12
m<WUV =53 degrees
Hence the measure of m<WUV is 53 degrees
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which liner equality will not have a shared solution set with the graphed liner inequality
The linear inequality wthat will not have a shared solution set with the graphed linear inequality is C. y > 5/3x + 2.
How to illustrate the information?It should be noted that the graph shows the shaded area as y < 5/3x + 1.. The slope of the line will be 5/3.
The two parallel lines are the same. The graph of the inequality is also attached.
The complete question is:
Which linear inequality will not have a shared solution set with the graphed linear inequality?
A. y < 5/3x – 2
B. y < -5/3x + 1
C. y > 5/3x + 2
D. y > -5/3x + 2
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pls solve...I will mark as BRAINLIST
Answer:
Here you go with your answer
Mark me as brainlist may your parents live long life
someone help me understand this
Answer:
Step-by-step explanation:
for reflection around x-axis.
(x,y)→(x,-y)
so P' is (-7,4)
given m∠J = 40° and HJ = 10, what is the length of GH
The required length of GH is 7.7.
Given, HJ = 10
m∠J = 40°
These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Let assume that there is right angle triangle GHJ.
Where HJ is base and GH is perpendicular.
Now,
cos40 = GH/HJ
GH = cos40 HJ
GH = 10 cos40
GH = 7.7
Thus, the required length of GH is 7.7.
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Write the nth term of the arithmetic sequence 2,6,18,54 find the 10th term of the sequence
Answer:
Step-by-step explanation:
Givens
t1 = 2
r = 3
n = 10
Formula
tn = a*r^(n -1) Substitute the givens into the this formula
Solution
t10 = 2 * 3^(10 - 1)
t10 = 2 * 3^9
t10 = 2 * 19683
t10 = 39366
Answer: 39366
What types of Functions will left endpoint lead to an under approximation and right endpoints lead to and over approximation?
What types of Functions will left endpoint lead to an over approximation and right endpoints lead to and under approximation?
The functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.
How to illustrate the function?It should be noted that function simply means the illustration that shows the relationship between the variables.
In this case, the functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.
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