Answer:
[tex]S_{1893} =5632.98[/tex]
Step-by-step explanation:
The correct form of the question is:
[tex]S = 1.001^{1892} + ... + 1.001^2 + 1.001 + 1[/tex]
Required
Solve for Sum of the sequence
The above sequence represents sum of Geometric Sequence and will be solved using:
[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]
But first, we need to get the number of terms in the sequence using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = First\ Term[/tex]
[tex]a = 1.001^{1892}[/tex]
[tex]r = common\ ratio[/tex]
[tex]r = \frac{1}{1.001}[/tex]
[tex]T_n = Last\ Term[/tex]
[tex]T_n = 1[/tex]
So, we have:
[tex]T_n = ar^{n-1}[/tex]
[tex]1 = 1.001^{1892} * (\frac{1}{1.001})^{n-1}[/tex]
Apply law of indices:
[tex]1 = 1.001^{1892} * (1.001^{-1})^{n-1}[/tex]
[tex]1 = 1.001^{1892} * (1.001)^{-n+1}[/tex]
Apply law of indices:
[tex]1 = 1.001^{1892-n+1}[/tex]
[tex]1 = 1.001^{1892+1-n}[/tex]
[tex]1 = 1.001^{1893-n}[/tex]
Represent 1 as [tex]1.001^0[/tex]
[tex]1.001^0 = 1.001^{1893-n}[/tex]
They have the same base:
So, we have
[tex]0 = 1893-n[/tex]
Solve for n
[tex]n = 1893[/tex]
So, there are 1893 terms in the sequence given.
Solving further:
[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]
Where
[tex]a = 1.001^{1892}[/tex]
[tex]r = \frac{1}{1.001}[/tex]
[tex]n = 1893[/tex]
So, we have:
[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{1 -\frac{1}{1.001} }[/tex]
[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{1.001 -1}{1.001} }[/tex]
[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{0.001}{1.001} }[/tex]
[tex]S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001^{1893}})}{\frac{0.001}{1.001} }[/tex]
Simplify the numerator
[tex]S_{1893} =\frac{1.001^{1892} -\frac{1.001^{1892}}{1.001^{1893}}}{\frac{0.001}{1.001} }[/tex]
[tex]S_{1893} =\frac{1.001^{1892} -1.001^{1892-1893}}{\frac{0.001}{1.001} }[/tex]
[tex]S_{1893} =\frac{1.001^{1892} -1.001^{-1}}{\frac{0.001}{1.001} }[/tex]
[tex]S_{1893} =(1.001^{1892} -1.001^{-1})/({\frac{0.001}{1.001} })[/tex]
[tex]S_{1893} =(1.001^{1892} -1.001^{-1})*{\frac{1.001}{0.001}}[/tex]
[tex]S_{1893} =\frac{(1.001^{1892} -1.001^{-1}) * 1.001}{0.001}[/tex]
Open Bracket
[tex]S_{1893} =\frac{1.001^{1892}* 1.001 -1.001^{-1}* 1.001 }{0.001}[/tex]
[tex]S_{1893} =\frac{1.001^{1892+1} -1.001^{-1+1}}{0.001}[/tex]
[tex]S_{1893} =\frac{1.001^{1893} -1.001^{0}}{0.001}[/tex]
[tex]S_{1893} =\frac{1.001^{1893} -1}{0.001}[/tex]
[tex]S_{1893} =5632.97970294[/tex]
Hence, the sum of the sequence is:
[tex]S_{1893} =5632.98[/tex] ----- approximated
Ann started reading a book that is 300 pages long. She reads 40 pages a day. Which function shows how many pages Ann has left after d days?
a) f(d) = 300 − 40d
b) f(d) = 300 + 40d
c) f(d) =300d − 40
Answer:
A should be the answer
Step-by-step explanation:
6.6.PS-11
Find the whole.,
155% of what number is 31?
155% of is 31.
(Type a whole number.)
plz help ASAP
Answer:
20
Step-by-step explanation:
31 ÷ 155% =
31 ÷ (155 ÷ 100) =
(100 × 31) ÷ 155 =
3,100 ÷ 155 =
20
please help me with this equation
Answer:
Option A, 1.7
Step-by-step explanation:
Step 1: Figure out the base
The base of an exponent is the number on the bottom. For example, if the given choice was [tex]50^{2}[/tex], then the base would be 50. However, since we are given [tex]1.7^{3}[/tex], then the was would be 1.7
100 PTS NEED HELP ASAP NO GUESSING NO COMING FOR POINTS IF YOU COMING FOR POINTS THATS FINE I JUST NEED THIS HELP!!!
Answer:
it’s A, because it’s an actually x and y equation that’s functional
Step-by-step explanation:
Ok have a great day
what is the product of 25 and (6/5n +31/4)
Answer:
30n + 193.75
Step-by-step explanation:
Product means multiplication so 25([tex]\frac{6}{5}n +\frac{31}{4}[/tex])
The first step is distribution of 25 to all numbers in ( ).
25([tex]\frac{6}{5}n[/tex]) is 30 and 25([tex]\frac{31}{4}[/tex]) is 193.75
Now we have the equation 30n + 193.75 which cannot be simplified further since the two variables are not like terms.
PLEASE HELP 50 POINTS AND BRAINLIEST FOR WHOEVER ANSWERS CORRECTLY!!! PLEASE HELP FAST!
1. Sharon and Geordi both worked hard over the summer. Together they earned a total of $525. Geordi earned $75 more than Sharon.
(a) Write a system of equations for the situation. Use s for the amount Sharon earned and g for the amount Geordi earned.
(b) Graph the equations of the system on the graph provided
Answer:
s + g = 575
g = 75 + s
g = 325
s = 250
Step-by-step explanation:
Given that :
Total amount earned by Sharon and Geordi = $525
Also, Geordi earned $75 more than Sharon
Let amount earned by Sharon = s
Amount earned by Geordi = g
Equations :
s + g = 575 - - - equation 1
g = 75 + s - - - equation 2
Put g = 75 + s in equation 1
s + 75 + s = 575
2s + 75 = 575
2s = 575 - 75
2s = 500
s = 250
g = 75 + s
g = 75 + 250
g = 325
when adding two rational numbers tell what the sign of the sum will be if one rational number is positive and one is negative
The sum of four and seven times a number is -31. What is the number?
Answer:
The number is -5
Step-by-step explanation:
Let x be the number
Write it out as an algebraic expression: 7x + 4 = -31Subtract 4 from each side, so it now looks like this: 7x = -35Divide each side by 7 to cancel out the 7 next to x. It should now look like this: x = -5I hope this helps!
Answer:
The number is -1.107142857142857
Step-by-step explanation:
I just used a calculator
pls help me
calculate the slope of the line that passes through (3,2) and (-7,4) in a fraction
Answer:
-1/5
Step-by-step explanation:
slope can be found with the equation found in the image.
assign each coordinate with the according variable
x1 = 3 x2 = -7 y1 = 2 y2 = 4
and input the values accordingly.
4 - 2 / -7 - 3 PEMDAS (order of operations)
= 2/ -10 Simplify
= 1/ -5
=-1/5
PLEASE HELP REALLY QUICK
Jose starts a savings account with $80. At the end of 6 months, the
account has $350. Assuming there is a constant rate, how much did Jose
save per month?
A $270
B $72
C $60
$45
Answer:
D $45
Step-by-step explanation:
you would take the $350 and divide it by 80 an you get 4.375 than you round that to the nearest 5th
Determine the value of y, if x is – 7.
y= x2 - 9
Answer:
y= -23
Step-by-step explanation:
10 bags of chips and 8 soda cans cost $15. 5 bags of chips and 5 soda cans cost $8. How much does a bag of chips cost? How much does a can of soda cost?
Answer:
One bag of chips costs $1.10
One can of soda costs $0.50
Step-by-step explanation:
1. Create a system of equations (b = bags of chips | s = soda)
10b + 8b = 15
5b + 5s = 8
2. Use the Elimination method by multiplying 5b+5s=8 by -2
10b + 8b = 15
-2(5b + 5s = 8)
=
10b + 8b = 15
- 10b - 10s = -16
(10b and -10b will cancel out, so you will only have s left)
=
-2s = -1
Divide by 2
Soda = 1/2, or $0.50
3. Plug in S (0.50) into an equation above and get B by itself
5b + 5(0.50) = 8
=
5b + 2.5 = 8
- 2.5 -2.5
5b = 5.5
Bag of Chips = $1.10
20% of 80 = 40% of ________ ?
Answer: 160
Step-by-step explanation:
[IMAGE] is this linear or not and why? if it is what’s the equation?
Answer:
Linear, equation: y = -2x + 1
In what time will a sum of money double itself at 10%?
ease answer this please I need helppp....
Answer:
8 generations
Step-by-step explanation:
Start with $1 and add 10% per generation until you reach $2. (Multiply by 1.1).
$1
$1.10
$1.21
$1.33
$1.46
$1.61
$1.76
$1.94
$2.12
Matthew mixes 1/2 cup of yellow paint for every 1/5 cup of blue paint to make green paint. how many cups of yellow paint are needed for 1 cup of blue paint.
Answer: He needs 2 1/2 cups of yellow paint
For every cup of milk, we use 4 cups of flour. Write a linear equation to represent the relationship.
Your class collected money to buy turkeys and hams for
the local food shelter. After the collection, your class
had exactly enough money to buy 11 hams and 9
turkeys. If you raised a total of $316, and each turkey
cost $18, how much is one ham?
Answer: $14.00
Step-by-step explanation:
9 turkeys costed a total amount of $162.00
We need to subtract that from the total cost, $316.00, to find out how much money was spent on 11 hams.
316 - 162 = 154
So, 11 hams costed 154.
We then need to find the unit rate of 11 turkeys for 154 dollars.
To do that, we must divide 154 ÷ 11
That gives us 14.
Therefore, your answer is: $14.00 per ham.
A pickup truck that can hold up to 3000 pounds is carrying a big machine that is 300 pounds and a few smaller ones that each weigh 60 pounds
At least how many small machines can you fit so that it will not exceed the weight limit of the truck?
A) no more than 50
B) no less than 50
C) no less than 45
D) no more than 45
Answer:
no more than 45
Step-by-step explanation:
3k-300 leaves u with 2700/60 and you get 45
Answer:
D. no more of 45
Step-by-step explanation:
i took the quick check
Which expression is equal to (1.5)3? Select all that apply. A. 5.0625 B. 3.375 C. 4.5 D. 2.25 × 1.5 E. 2.5 × 1.25
Answer:
c
Step-by-step explanation:
points equal to y = - 1/2x + 5
Answer:
x= (-10,0)
y= (0,5)
Step-by-step explanation:
Find the x-intercepts.
Tap for more steps...
x-intercept(s):
(-10,0)
y-intercept(s):
(0,5)
how do I solve this
Answer:
15 degrees
Step-by-step explanation:
7x - 15 = 90
+15. +15
7x = 105
divide both sides by 7
x = 105/7 = 15
Malika has a credit card balance of $321. Her available credit on this card is $4,679. What is her credit line
on this card?
Answer: 5,000
Step-by-step explanation:
4679 + 321=5000
If Malika has a credit card balance of $321. Her available credit on this card is $4,679. Then $5000 is her credit line on this card
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Malika has a credit card balance of $321
Available credit on this card is $4,679.
We need to find her credit line on credit card
To find this we just need to add $321 and $4,679.
Three hundred twenty one plus four thousand six hundred seventy nine
$321+$4,679.
We get five thousand
$5000
Hence, $5000 is her credit line on this card
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
what’s the answer i need help plssss!!!
Answer:
wouldent that be 8 x 3 lol????
Step-by-step explanation:
Answer:
follow the steps
Step-by-step explanation:
a²+b²=c²
8²+8²=c²
64+64=c²
find the square root of 128
whoever answers correctly gets brainliest
Answer:
it is C 64.8 do you need explanation?
What is the value of (32 + 1)">
Answer:
yes
Step-by-step explanation:
Answer:
i have gotten 160.5
Step-by-step explanation:
Probability of rolling a composite number on a dice and the coin landing on tails
Answer choices are 1/8, 2/3 and 5/6
This is 7th grade math btw
Answer:
5/6.
Step-by-step explanation:
The only composite numbers on a die are 4 and 6, so the probability of landing on them is 2/6 or 1/3. The probability of landing on tails on a coin is 1/2. Add them together (1/3 + 1/2) and you get the total probability of 5/6.
I hope this helps.
I don’t understand number 1 and I need help solving it?
Answer:
1/4 cup more
Step-by-step explanation:
1/2 + x = 3/4 ===> 0.5 + x = 0.75
-0.5 -0.5
x = 0.25
0.25 = 25/100 = 1/4 cup
There are 15 male teachers in the school. There are 35 female teachers in the school. Fill in the table
to show the relationship between the female and male teachers.
When ringing up a customer, a cashier needs 7 seconds to process payment as well as 1 second to scan each item being purchased.If it takes 21 second storing up a customer, how many items are being purchased?
Answer:
14 items
Step-by-step explanation:
21-7=14
