Answer:
13
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
where a is the first term and r the common ratio
here a = 6 , r = [tex]\frac{12}{6}[/tex] = 2 and [tex]S_{n}[/tex] = 49146 , then
[tex]\frac{6(2^{n}-1) }{2-1}[/tex] = 49146
6([tex]2^{n}[/tex] - 1) = 49146 ( divide both sides by 6 )
[tex]2^{n}[/tex] - 1 = 8191 ( add 1 to both sides )
[tex]2^{n}[/tex] = 8192 ( take log of both sides )
log [tex]2^{n}[/tex] = log 8192 , that is
n log 2 = log 8192 ( divide both sides by log 2 )
n = [tex]\frac{log8192}{log2}[/tex] = 13
[tex]\red{ \underline { \boxed{ \sf{Common \: Ratio,r = \frac{any\:observed\:term}{previous\:term}}}}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf Common \: Ratio,r = \frac{12}{6} [/tex]
[tex]\quad \boxed{\sf {Common \:Ratio,r = 2 }}[/tex]
Now,
[tex]\green{ \underline { \boxed{ \sf{Sum\: of \: G.P. \: to\: n\:term,S_n = \frac{a(r^n-1)}{r-1}}}}}[/tex]
where
a = first termr = common Ration= number of termsPutting Values -
[tex]\begin{gathered}\\\implies\quad \sf 49146 = \frac{6(2^n-1)}{2-1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{\cancel{49146}}{\cancel{6}} = \frac{2^n-1}{1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 8191= \frac{2^n-1}{1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n-1 =8191 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =8191+1 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =8192 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =2^{13}\quad(8192= 2^{13}) \\\end{gathered} [/tex]
Comparing powers on both sides-
[tex]\begin{gathered}\\\implies\quad \boxed{\sf{ n = 13}}\\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Therefore, to get a sum of 49146 , 13 terms of this G.P. should be taken.
Find the volume of the prism.
Answer:
240 cm³
Step-by-step explanation:
Volume of prism= base area ×height
The base is a rectangle here, and its area has the formula of length ×breadth.
Given
length of base= 10 cm
breadth of base= 6 cm
height of prism= 4 cm
Base area
= 10(6)
= 60 cm²
Volume of prism
= 60(4)
= 240 cm³
Answer:
240 cm³
Step-by-step explanation:
Volume of a rectangular prism: l*w*h
L (length) : 10 cmW (width): 6 cmH (height): 4 cmV = l*w*h <== substitute the numbers (above) for the variables
V = 10*6*4
V = 60*4
V = 240 cm³ (cubed)
Hope this helps!
An assembly line consists of 21 tasks grouped into 5 workstations. The sum of the 21 task times is 90 minutes. The largest assigned cycle time is 20 minutes. What is the efficiency of this line?
Answer:
ok
Step-by-step explanation:
HELPPPPP PLEASE I DONT UNDERSTANDDDD
Answer:
Step-by-step explanation:
Solve for the equation equal to y
[tex]3x+4y=12\\4y=-3x+12\\y=\frac{-3}{4}+\frac{12}{4}[/tex]
The slope here is -3/4. The slope of a line perpendicular to the original has a negated and inverted slope. Therefore the slope is 4/3
What would you do if fear was not a factor and you could not fail?`
i know it's not a maths question but let's try
Answer:
Well, i would just say you just had to do your best in everything that you do. No pressure , no stress don't overwork yourself and simply take action. Then you will have a chance to get what you want because you tried your best to get to it. Although sometimes we don't get what we want, atleast we'll be closer. As they say, 'Aim for the sun to reach the moon"
Step-by-step explanation:
You're welcome
A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive substance. After 19 hours, 95 mg of the substance remains. How many milligrams will remain after 36 hours?
Answer:
51 milligrams
Step-by-step explanation:
Exponential growth or decay can be modeled by the equation ...
y = a·b^(x/c)
where 'a' is the initial value, 'b' is the "growth factor", and 'c' is the time period over which that growth factor applies. The time period units for 'c' and x need to be the same.
In this problem, we're told the initial value is a = 190 mg, and the value decays to 95 mg in 19 hours. This tells us the "growth factor" is ...
b = 95/190 = 1/2
c = 19 hours
Then, for x in hours the remaining amount can be modeled by ...
y = 190·(1/2)^(x/19)
__
After 36 hours, we have x=36, so the remaining amount is ...
y = 190·(1/2)^(36/19) ≈ 51.095 . . . . milligrams
About 51 mg will remain after 36 hours.
Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangles, as well as the perimeter and the area in each figure.
If tanθ= 2 find cotθ using identities. This is in quad. 1.
Answer: 1/2
Step-by-step explanation:
Margo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesMargo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inchesv
Find a solution to the linear equation 13x+y=26 by filling in the boxes with a valid value of x and y.
Answer:
y = -13x+26
Step-by-step explanation:
13x+y=26
y= -13x+26
Rewrite the expression x -3/11
in radical form.
Answer:
11x-3
11
Step-by-step explanation:
and that's the answer
Students from four classes are in talent show. A. There are 28 students in Ms. Fiona's class. The ratio of her student who are in the talent show to those who are not in the talent show is 2:5. How many of Ms. Fiona's students are in the talent show? B. Mr. Juan has 24 students in his class. Some of his students are also in the talent show. Explain why it is not possible for exactly 24% of the students in Mr. Juan's class to be in the talent show. C. The rest of the students in the talent show are from Mrs. Lee's class and Mr. Greg's class. • Mrs. Lee has 23 students in her class, and 7 of them are in the talent show. There are 4 more students from Mr. Greg's class than from Mr. Juan's class in the talent show. The number of students in the talent show from Mrs. Lee's class is greater than the number from Mr. Juan's class and fewer than the number from Mr. Greg's class. In all, 30% of the students in these three classes are in the talent show, Show or explain why there must be exactly 23 students in Mr. Greg's class. As part of the explanation, determine how many students from Mr. Greg's class are in the talent show
Answer:
B
Step-by-step explanation:
i had this question on my test
Find the LCM of 20, 35 & 50.
Answer:
Answer: LCM of 20,35 and 50 is 1400
Step-by-step explanation:
Write a qbasic progrsm to check pass or fail
Step-by-step explanation:
CLS
INPUT " Enter total marks "; M
IF M > 40 THEN
PRINT "You are passed "
ELSE
PRINT " You are failed "
END IF
END..
which list of fraction is in order from least to greatest value
A city that has an elevation of 15 meters is closer to sea level than a city that has an elevation of -10 meters.
Answer:
Step-by-step explanation: Your answer will be -10 because even though -10 is much lower than 15 it’s still closer to sea level.
A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.
How many employees took a break that lasted between 37 and 41 minutes?
Select from the drop-down menu to correctly complete the statement.
About (blank) employees took a break that lasted between 37 and 41 minutes.
36
90
120
180
Answer:
on k12 im pretty sure its 90
Step-by-step explanation:
there is 360 minutes and between the 37 and 41 (this took me a while ) then you should get 90!!!!! hope this helped
how many cubic inches of hot air would be needed to completely inflate a 12 in diameter beach ball
Answer:
904.78 cubic inches
Step-by-step explanation:
Since a beach ball is a sphere, use the formula for volume, V = 4/3 * pi * r^3 to find the volume of the beach ball, using 6 for radius since diameter is two times the radius and the diameter is 12 inches. 4/3 * pi * 6^3 = 904.78, so that many cubic inches of air would be needed to inflate the beach ball.
Hopefully this helps- let me know if you have any questions!
Joy's class voted on whether or not to do science fair projects in groups. Out of 24 votes, 18
were in favor of working in groups. What percentage of the votes were in favor of working in
groups
Write your answer using a percent sign (%).
Submit
Answer:
75%.
Step-by-step explanation:
That would be (18/24) * 100
= 3/4 * 100
= 75%
A consistent and dependent system is formed by the equations y = 3x + 9 and
6x – 2y = A, where A is a real number. Find the value of A.
-
Answer:
A = -18.
Step-by-step explanation:
We are given that y = 3x +9.
From this, we gather 3x - y = -9.
We then multiply both sides by 2 to get 6x – 2y = -18. Therefore, A = -18.
eometry Part 4 - Lesson 1 Assessment - EDCP.MA004.D
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2 3 4 5
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What is the area of a sector of a circle with a central angle of measure 180° and whose radius is 5
cm? Leave your answer in terms of I.
○
o
ле?
o com
35
O 2 cm
Answer: it would be 34
Step-by-step explanation:
250 gram as a percentage of 1 kg
Hey there!
Answer: 25%
[tex] \rightarrow \: (\sf{ \frac{250}{1000} ) \times 100}[/tex]
[tex] \rightarrow \: ( \sf{0.25) \times 100}[/tex]
[tex] \rightarrow \: \sf{ = 25\%}[/tex]
Answer:
25%
Step-by-step explanation:
the quantities must have the same units
1 Kg = 1000 grams
express the quantities as a fraction and multiply by 100%
[tex]\frac{250}{1000}[/tex] × 100% = 0.25 × 100% = 25%
I well give u brainliest
What are the x- and y-intercepts for the linear equation 2x – 4y = 8 ?
Question 6 options:
(4,0) and (0,-2)
(2,0) and (0,4)
(-2,0) and (4,0)
(-2,0) and (0,4)
The answer is a. (4,0) and (0,-2)
The difference is
Part B 287
Find the product of the expressions.
Answer:
12
Step-by-step explanation:
Ms. Gardner is thinking of a number
The number is even.
It is not divisible by 6
It is not divisible by 7
it is not greater than 81
It is not less than 64
Answer:
74
Step-by-step explanation: 74 is not divisible by 6 or 9not nor 7 and it's less than 81 and greater than 64
Find the volume. Please help! Thanks!
hehe
Volume of a Square Pyramid: 1/3 x length x width x height
Length = 2
Width = 2
Height = 3
Volume = 1/3 x 2 x 2 x 3
Volume = 1/3 x 4 x 3
Volume = 1/3 x 12
Volume = 4
Volume = 4 cm^3
Hope this helps!
A gas tank holds exactly 14 gallons of gas. If the tank is 2/3 empty, how many gallons remain in the tank?
2/3 empty would mean 1/3 of the total would remain:
14 gallons x 1/3 = 4 2/3 gallons are left in the tank
Solve for x
Can you pls help me?
Answer:
6x+50=92
Step-by-step explanation:
The x is for how much the classes cost plus the amount they charged her for the gear.
10+500000000 wats the answer
Answer:
500,000,010
Step-by-step explanation:
The 10 would be added to the last 2 digits (00) of the number. Therefore, the last 2 digits (00) plus 10 would be 10. The remainder of the number would remain the same, making the answer: 500,000,010
A team sells their jerseys for 40% more than it costs to have them made. What is the selling price of a jersey that cost the team $25.
Answer:
$35.
Step-by-step explanation:
SP = 25 + 0.40*25
= 25 + 10
= $35.
210 cartons is __% of 60 cartons
Answer:
should definitely be 28.56