The sequence {an} converges to 1.
To determine if the sequence {an} converges, we can use the limit definition of convergence. Taking the limit as n approaches infinity of an, we have:
lim(n→∞) an = lim(n→∞) (1 − 1/6n) ^5n
Using the limit law for exponents, we can rewrite this as:
lim(n→∞) (1 − 1/6n) ^5n = [lim(n→∞) (1 − 1/6n)]^5n
Now we can use the limit law for products to separate the limit into two parts:
lim(n→∞) (1 − 1/6n) ^5n = [lim(n→∞) (1 − 1/6n)]^ [lim(n→∞) 5n]
The limit of (1 − 1/6n) as n approaches infinity is 1, so the first part simplifies to:
lim(n→∞) (1 − 1/6n) ^5n = 1^ [lim(n→∞) 5n]
The limit of 5n as n approaches infinity is infinity, so the second part is:
lim(n→∞) (1 − 1/6n) ^5n = 1^∞
This is an indeterminate form, so we need to use another method to find the limit. Taking the logarithm of both sides, we have:
ln(lim(n→∞) (1 − 1/6n) ^5n) = ln(1^∞)
Using the limit law for logarithms, we can rewrite this as:
lim(n→∞) 5n ln(1 − 1/6n) = ln(1)
The limit of ln(1 − 1/6n) as n approaches infinity is 0, so the left-hand side simplifies to:
lim(n→∞) 5n ln(1 − 1/6n) = 0
This means that the limit of the sequence {an} is 1, since:
lim(n→∞) an = lim(n→∞) (1 − 1/6n) ^5n = 1^∞ = e^0 = 1
Therefore, the sequence {an} converges to 1.
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Express two-thirds of age gap in terms of y if the age gap between a father and a daughter is y years
Answer:
(2/3)y
Step-by-step explanation:
Given that :
Age gap between father and daughter = y
2/3 of the difference in their ages expressed as in terms of y ;
2/ 3 * y
(2/3)y
Can someone please help me!!! Ill mark brainliest!!
Answer: 252 ft
Find the area of the whole thing, then find the area of the green rectangle, then subtract to find the answer.
What do these circles have in common?
Answer:
They are all circles? I dont really know how to explain it so that is all I got to say
Step-by-step explanation:
what is slope of (12.-18) and (-15.-18).
Answer:
3
Step-by-step explanation:
What number goes in the blank? (-3)(?)=36 *
Answer:
-12
Step-by-step explanation:
-3x=36
x=36/-3
x=-12
Answer:
-12
Because (-3)(-12)=36
any negative number multiplied by another = positive number :3
In the system of equations, which variable would it be easiest to solve for?
2 x + 4 y = 26. 3 x + y = 9.
The easiest to solve for is x in the first equation.
The easiest to solve for is y in the first equation.
The easiest to solve for is x in the second equation.
The easiest to solve for is y in the second equation.
Answer:
The easiest way of solving this is to eliminate one of the variables. If you multiply each of the equations by a number so you can add the equations together and have only one variable left, you can solve the single variable equation. Try multiplying the first equation by 11, the second by -10 and adding them, thus eliminating the y variable. After this, substitute that value you have for x and solve for y. I hope this helps.
Step-by-step explanation:
D Itś D DDDDDD DDDDDDDDDDDDDDDDDD
Find the value of 200 + 9 + 0.3 +0.001.
Answer:
209.301
Step-by-step explanation:
Pepper has 7.5 bags to clear 12 yd squared to distribute evenly among the beds . About how many bags will she need to use for each square yard?
Answer:
5/8 bags
Step-by-step explanation:
Pepper ha 7.5 bags
These bags are needed to clear 12 yards squared equally
Therefore the number of bags required for each square yard can be calculated as follows
= 7.5/12
= 0.625
0.625 to fraction is 5/8
Hence 5/8 bags is needed for each square yard
Enter 2/5 and 1/3 as a pair of equivalent fractions with the least common denominator between the two fractions.
Answer:
2/5 = 6/15
1/3 = 5/15
Step-by-step explanation:
LCD of 5 and 3 is 15.
So 2/5 = 2*3/15 = 6/15
and
1/3 = 5*1 / 15 = 5/15
please help me on this will give you brainliest
Answer:
The answer is really simple. Add 33 and 67 then subtract it from 180 and the answer is 80.
Answer:
x=80 degrees
Step-by-step explanation:
upper right corner angle =67 degrees because it is a corresponding congruent angle.
The sum of all the inside angles of all triangles is 180 degrees.
180-33-67=x
x=80 degrees
please help and be correct please :( have a explanation also
Answer:
Part A: 3 bowls Part B: See Below
Step-by-step explanation:
Part A: If he uses 1/6 to make ONE bowl, 3/6 is one half so he can make THREE bowls.
Part B: Just draw the fact of 1/2 being equal to 3/6 there for making 3 bowls and you'll be good! :)
Hope this Helped! ^ - ^
PLEASE HELP
7x+3y=20 and -4x-6y=11 find the value of 3x-3y
Answer:
im pretty sure the answer is A 6
Step-by-step explanation:
45 is 3% of what number?
quick I need an answer!
hurry pls!
Answer:
stop rushing brat
Step-by-step explanation:
Step-by-step explanation:
Steps to solve "45 is 3 percent of what number?"
We have, 3% × x = 45
or,
3
100
× x = 45
Multiplying both sides by 100 and dividing both sides by 3,
we have x = 45 ×
100
3
x = 1500
If you are using a calculator, simply enter 45×100÷3, which will give you the answer.
Geometry help, please!!!
provide the missing reasons for the proof.
Given:
Prove: ΔABC ~ ΔDBE
_____________________________________________
picture provided below
Answer:
1: Given
2: Verical angles are always congruent
3: Angle Angle theorem
You conduct a simulation regarding students scores on a physics test. Your null hypothesis is
that the mean score on the test is less than or equal to 80 points. Your alternative hypothesis is
that the mean score is greater than 80 points.
You determine that the results of your simulation have a p-value of 0.06. What does this mean?
Under the tested hypothesis, the outcome of the simulation has a probability of 6%. With a significance level of 5%, you should FAIL to reject the null hypothesis.
The p-value is the probability of getting true null hypothesis.
What is Null Hypothesis and Alternative Hypothesis?Null hypothesis is a hypothesis of a test which assumes that there is no statistical relationship between two variables. This is the hypothesis which is being testes.
Alternative hypothesis assumes that there is a relationship between two variables.
Given that,
You conduct a simulation regarding students scores on a physics test.
Null hypothesis is that the mean score on the test is less than or equal to 80 points.
Alternative hypothesis is that the mean score is greater than 80 points.
p value = 0.06 = 6%
This means that there is only a 6% that the null hypothesis of yours is true.
So the p value tells you the probability of getting a true null hypothesis.
Hence the p value is the probability of getting true null hypothesis.
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A snail is moving along a path that is 4 meters long. The snail moves at an average rate of 3 3/10 inches per minute. Question 1 Part A Find the length of the path to the nearest inch. (Hint: 1 in.≈2.54 cm) Enter the correct answer in the box.
Answer: The length of the path = 157 inches { approx}
Step-by-step explanation:
Given: The length of the path = 4 meters
1 meter = 100 centimeters
So 4 meters = 400 centimeters
Also 1 in. ≈ 2.54 cm
[tex]\Rightarrow\ 1 cm = \dfrac{1}{2.54}\ in.[/tex]
Now, [tex]\text{ 400 centimeters}=400\times\dfrac{1}{2.54}\text{ inches}[/tex]
[tex]=157.480314961\approx 157 \ \ \ \ \ \text{ [Rounded to the nearest inch.]}[/tex]
Hence, the length of the path = 157 inches { approx}
Question Progress
Solve the inequality 5y + 4 < 3y + 17
Answer:
y < [tex]\frac{13}{2}[/tex]
Step-by-step explanation:
Given
5y + 4 < 3y + 17 ( subtract 3y from both sides )
2y + 4 < 17 ( subtract 4 from both sides )
2y < 13 ( divide both sides by 2 )
y < [tex]\frac{13}{2}[/tex]
Answer:
y < 13/2
Step-by-step explanation:
(9r^2+4r-7)+(3r^2-3r)
Answer:
12r2+r−7
Step-by-step explanation:
hope it helped
Solve for y. 1 y – 1 3y + 7 10 y E
Answer:
[tex]y = \frac{17}{7}[/tex]
Step-by-step explanation:
1) To solve this question easily, cross multiply first. Multiply the denominator of the first fraction by the numerator of the second fraction, and multiply the denominator of the second fraction by the numerator of the first fraction:
[tex]\frac{y-1}{3y+7}=\frac{1}{10}\\1(3y+7) = 10(y-1)\\3y + 7 = 10y-10[/tex]
2) Now, solve like you would and isolate y. Subtract both sides by 10y.
[tex]3y + 7 = 10y-10\\-7y + 7 = -10[/tex]
3) Then, subtract both sides by 7.
[tex]-7y + 7 = -10\\-7y = -17\\[/tex]
4) Finally, divide both sides by -7 to receive the answer.
[tex]-7y = -17\\y = \frac{-17}{-7} \\y = \frac{17}{7}[/tex]
i really need help with this
Answer:
A+6+A = 20
A = 7
Step-by-step explanation:
J = number of problems Juana completed
A = number of problems Andy completed
J+A=20
J = A + 6
Replace J with A+6 in the first equation
A+6+A = 20
2A +6 = 20
Subtract 6 from each side
2A +6-6 = 20-6
2A =14
Divide by 2
2A/2 = 14/2
A = 7
Answer:
7
Step-by-step explanation:
set up your two equations.
j + a = 20. equation 1
j = a + 6. equation 2
since you know that j = a + 6, you can substitute a + 6 into the place of j. this is because you want to isolate a in order to find out how many problems andy completed.
j + a = 20
a + 6 + a = 20
now solve.
2a + 6 = 20
2a = 14
a = 7
andy has completed 7 problems. if juana completed 6 more than andy, then she has completed 13. 13 + 7 = 20.
how does (46)(4) = 56 please tell me
Answer:
ok, so 46 times 4 is 184.
Step-by-step explanation:
46
x 4
-------
184
So 6 times 4 is 24 and then you carry over the 2. 4 times 4 is 16. You add 2 to 16 and you get 18. So the total would be 184.
It's kinda hard to explain over brainly
Answer:
impossible
Step-by-step explanation:
46x4= 276
please mark me as brainlist
HELPPP. i need help with this i have trouble with ordered pairs
Garrett needs 3 3 gallons of fruit juice to make punch. He already has 56 5 6 gallon of grape juice and 23 2 3 gallon of orange juice. Drag amounts of juice that he can add to the juice he already has to make exactly 3 3 gallons. Juice Garrett has. Grape juice is labeled five-sixths gallon. Orange juice is labeled two-thirds gallon. CLEAR CHECK Orange juice labeled one-third gallon. Green juice is labeled one-sixth gallon. Juice Needed
Answer:
no por que ella no te ama lo siento
(help) Evaluate the expression 9y - 4(4) + y3 when y = 2.
Answer:
9y - 4(4) + y³= 18-16+8=10
Drew has more than 4 times as many baseball cards as mark. Katie has fewer than half as many cards as mark. Mark has m baseball cards
Answer:
Cards with Mark = 30
Cards with Drew = 120
Cards with Katie = 12
Step-by-step explanation:
The complete question is
Drew has 4 times as many baseball cards as Mark. Katie has 3 fewer than than half as many cards as Mark. In all they have 162 baseball cards. How many does each have?
Solution -
Let the number of cards with Mark be "X"
Number of cards with Drew = 4 *X = 4X
Number of Cards with Katies = 0.5 X -3
Sum of all the cards is equal to 162
X+4X + 0.5 X -3 = 162
5.5 X = 165
X = 30
Cards with Mark = 30
Cards with Drew = 4 * 30 = 120
Cards with Katei = 15-3 = 12
please hurry! I'm so confused
Answer:
Step-by-step explanation:
The general equation is
y = 2.49x + 24.99
The number of cones bought is x
The cake cost is 24.99
The total cost is y
===========
So the meaning of (5,37.44) is that she bought 5 cones and 1 cake. Let's just check that out.
Check
y = 2.49*5 + 24.99
y = 12.45 + 24.99
y = 37.44
So the total cost (y) of 5 cones (2.49 each) and 1 cake ($24.99) is 37.44
what do you observe about the form of the equation of any circle whose center is at the point of origin
Ce clasă ești sa văd daca te pot ajuta
Han's family got a solar panel. Each month they get a credit to their account for the electricity that is generated by the solar panel. The credit they receive varies based on how sunny it is. In January they used $83.56 worth of electricity and generated $6.75 worth of electricity. Here is their electricity bill from January. Current charges: $83.56 Solar Credit: -$6.75 Amount due: $76.81 1) In July they were traveling away from home and only used $19.24 worth of electricity. Their solar panel generated $22.75 worth of electricity. What was their amount due in July?
Answer:
-$3.51
Step-by-step explanation:
Given that :
Current charges:
$83.56 Solar Credit: -$6.75
Amount due: $76.81
July they were traveling away from home and only used $19.24 worth of electricity. Their solar panel generated $22.75 worth of electricity. What was their amount due in July
Worth of electricity used in July = $19.24
Worth of electricity generated by solar = - $22.75
Electricity used in July + solar credit charge
$19.24 - $22.75
= -$3.51
2x x 5z x y
simplify the equation
Answer: The simplified form of 2x · 5z · y is 10xzy.
Step-by-step explanation:
1/3 + 3/8 =?? wich method can sole the number sentence