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.
Whats 5-5-5-5-5-5x5757575
Answer:
-28787890
Step-by-step explanation:
f(x)=x-5 is the function linear quadratic exponential or neither
Answer:
Linear
Step-by-step explanation:
It is a first-degree function, the variable "x" has power 1
when graphed, a straight line results in
Hope this helps
The round temperature dial on a thermostat has a diameter of 26 millimeters. What is the dial's circumference?
C = 2 x pi x r = pi x d
so
C = 3,14 x 26 = 81,64 mm
a thousand dollars is left in a bank savings account drawing 7% interest, compounded quarterly for 10 years. what is the balance at the end of that time
Work Shown:
A = P*(1+r/n)^(n*t)
A = 1000*(1+0.07/4)^(4*10)
A = 2001.59734318603
A = 2001.60
This assumes that you do not withdraw any of the money over the course of the 10 years. Also, the interest rate must stay the same at 7%.
Given that a= 6 cm and b = 5 cm, work out the area of the triangle.
Answer:
15cm²
Step-by-step explanation:
Area of a triangle: 1/2*b*h
a = height (6cm)
b = base (5cm)
A = 1/2* b * h
A = 1/2 * 5 * 6
A = 1/2 * 30
A = 15cm² <== final answer
Hope this helps!
You roll two number cubes
Let event A = You roll an even number on the first cube.
Let event B = You roll a 2 on the second cube.
Are the events independent or dependent? Why?
O A. Dependent, because both cubes have six sides.
O B. Independent, because the outcome of the first roll doesn't affect
the outcome of the second roll.
O C. Independent, because they have no outcomes in common.
D. Dependent, because 2 is an even number.
Answer: B: Independent, because the outcome of the first roll doesn't affect the outcome of the second roll.
Step-by-step explanation:
Events are independent when the outcome of one does not effect the other. Rolling dice for example: If you roll an even number on your first cube, there is no way that it will effect the roll on the second cube, hence the two events are independent.
Below is the graph of a polynomial function with real coet
of the function are shown in the graph.
m
27
Use the graph to answer the following questions.
(a) Over which intervals is the function increasing? Choose all that apply.
o(-00,-5) o (-5, -2) 0 (-2,2) 0 (2,6) o(-2,6) o (6,00)
(b) At which x-values does the function have local maxima? If there is more than
one value, separate them with commas.
(c) What is the sign of the function's leading coefficient?
(Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all
that apply.
5
06
08 09
04
07
This question is about Polynomial Functions. The reading below is done using the attached graph.
a) Over which intervals is the function increasing?The function is increasing over the following intervals:
(2,6) Option D; and (-2,6) Option E.b) Yes, the points on the x-axis that has local maxima are:
Point -2, and Point 6.
c) The leading coefficient is negative. The sign is given as:
f(x) → -∞
as x → + ∞
d) The possible degree of the function is:
06- (Option B).
Learn more about Polynomial Functions at:
https://brainly.com/question/2833285
George wanted to measure the angle of a water slide at the lake. He used a sheet of folded paper that formed a 20° angle. He measured and found that three of the folded paper angles would fit in the angle made by the slide and the ground.
Which of the following was the angle of the water slide?
The angle of the water slide is 60 degrees.
The equation that models his work is 3 × 20 = 60 degrees.
How to find the sum of angles of a figure/object?
He wants to measure the angle of a water slide at the lake.
He used a sheet of folded paper that formed 20 degrees to measure the angle of the the water slide at the lake.
He noticed three folded paper angle fits in the angle made by the slide and the ground.
Since each angle is equals to 20 degrees, and the three fits into the angle made by the slide and the ground, the angle of the water slide is as follows:
20 × 3 = 60 degrees
learn more on angles here: https://brainly.com/question/16746032
Carlos is saving for a new bike. he is paid $6.60 an hour and works 10 hours per week at his after-school job. If he saves 75% of the money he earns, how much does he save each week?
Answer:
16.50 per week
Step-by-step explanation:
6.60 times 10 equals 66 minus 75% equals 16.50
write a quadratic function f whose only zero is 11
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here's the solution ~
To write a quadrilatic function, we have to use its roots, like we have to subtract the roots from x and multiply them ~ then we will get our required function !
Since our only root is 11 here, we have to do t double
[tex]\qquad \sf \dashrightarrow \:(x - 11)(x - 11)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 11x - 11x + 121 [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 22x + 121[/tex]
That's our required function ~ I hope you understood the whole thing !
What number (X) comes next in the series (17, 9, 18, 7, 19, 5, 20, X)
3
4
16
21
23
Answer:
17, 9, 18, 7, 19, 5, 20, X
Bold: 17, 18, 19, 20, .....
Other: 9, 7, 5, 3, 1 ....
I think the answer is 3
By finding the pattern, we conclude that the next number in the sequence is 3.
What number comes next in the series?
We have the sequence:
17, 9, 18, 7, 19, 5, 20, x.
Here the pattern is kinda simple.
First, we have a two-digit number which increases by one unit (on the odd positions). Then we have a single-digit number that decreases by two (on the even positions).
Then we will have:
x = 5 - 2 = 3
We conclude that the next number in the sequence is 3, we get:
17, 9, 18, 7, 19, 5, 20, 3.
If you want to learn more about sequences:
https://brainly.com/question/6561461
#SPJ2
If 15 percent of cars are blue and an observer's observation is 80 percent accurate, what is the probability that a car is, in fact, blue when the witness reports it as blue
The probability that a car is blue is the likelihood of the car being blue
The probability that a car is, in fact, blue when the witness reports it as blue is 12%
How to determine the probability?The given parameters are:
P(Blue) = 15%
P(Accurate) = 80%
The probability that a car is blue, and the observation is accurate is calculated as:
P(Blue and Accurate) = P(Blue) * P(Accurate)
This gives
P(Blue and Accurate) = 15% * 80%
Evaluate the product
P(Blue and Accurate) = 12%
Hence, the probability that a car is, in fact, blue when the witness reports it as blue is 12%
Read more about probability at:
https://brainly.com/question/25870256
Help picture below please
Answer:
B. NRS
Step-by-step explanation:
You have to put the letters left to right.
A painter bought 14 gallons of paint just enough to cover 2 room
7
Step-by-step explanation:
[tex]Based\ on\ the\ given\ conditions,\ formulate:[/tex]
[tex]14\div 2[/tex]
[tex]\frac{14}{2}[/tex]
Creoss out the common factor
[tex]7[/tex]
I hope this helps you
:)
helpppppppppppppppppppppppppp walk me thru
Answer:
i think its a trapazoid
Step-by-step explanation:
After 2 years, a certain car is worth $16600. When it is 9 years old, the same car is then worth
$9950.
Find the equation of the line in this situation.
Identify the slope for this situation and interpret it.
Identify the y - intercept for this situation and interpret it.
Identify the x - intercept for this situation and interpret it.
The linear function that describes the situation is:
y = -950x + 18500.
The slope of -950 means that the price of the car decays $950 per year.The y-intercept of 18500 means that the initial value of the car is of $18,500.The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, in 7 years, the price of the car decays by $6,650, hence the slope is given by:
m = -6650/7 = -950.
The slope of -950 means that the price of the car decays $950 per year.
Then, the equation is:
y = -950x + b.
After 2 years, a certain car is worth $16600, hence when x = 2, y = 16600, and:
16600 = -950(2) + b
b = 18500.
The equation is:
y = -950x + 18500.
The y-intercept of 18500 means that the initial value of the car is of $18,500.
The x-intercept is found when y = 0, hence:
-950x + 18500 = 0.
x = 18500/950
x = 19.47.
The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.
More can be learned about linear functions at https://brainly.com/question/24808124
These numbers are common multiples of ________.
15, 30, 45, 60
A) 2 and 3
B) 3 and 5
C) 4 and 5
D) 3 and 4
Answer:
The answer is B.
Step-by-step explanation:
15÷3=5 15÷5=3
30÷3=10 30÷5=6
45÷3=15 45÷5=9
60÷3=20 60÷5=12
Chapter 1 Test
What is the simplified form of the expression 3 + 8x - 2y - x + 1 + 4y? Enter your answers in the boxes.
X +
ly+
Answer:
7x+4+2y is your answer
F(4g2-9)=n i need to solve for f
Answer:
Step-by-step explanation:
It takes 7 hours and 12 minutes to fly
from Singapore to Tokyo, Japan. You have
to arrive at the airport 45 minutes before
departure. It is a 17 minute taxi ride from
your hotel. By what time would you need
to leave the hotel if the flight lands
at 3:23 p.m.?
The time I would need to leave the hotel if the flight lands at 3:23 p.m is 7 : 09 am
What time should I leave the hotel?The first step is to add the total hours of the flight to the time of the tax ride and the time you need to get to the airport.
7h + 12 min + 45 + 17 = 8 hours 14 minutes
Now subtact 8 hours 14 minutes form 3: 23
(12 + 3:23) - 8 hours 14 minutes =7 : 09 am
To learn more about how to calculate time, please check: https://brainly.com/question/26290873
A recipe calls for 4 cups of pecans for every 5 cups of walnuts. How many cups of pecans should be added to 8 cups of walnuts?
A. 1.6 cups
B. 2.5 cups
C. 6.4 cups
D. 10 cups
I really need help with the answers
Answer:
Part A: 512 ft²
Part B: 3 cans
Step-by-step explanation:
Part A:
We can divide the shape into 2 areas or rectangles.
The top rectangle's area: 20 x 12 =240
The bottom: 34 x 8 = 272
add these 2 up, 240 +272, and you get 512, the area of this figure.
Part B:
We have to divide the number of feet covered by the area:
512/200 = 2.56
However, we half to round up, cause we cant buy part of a can, we have to buy a whole one.
So, we get 3 cans.
A case of glue weighs 24 pounds. A pallet loader can lift 3 tons. How many cases can a pallet loader lift?
Answer:
250 cases
Step-by-step explanation:
3 tons is 6000 pounds
you divide 6000 by 24 and get 250
that is your answer
Which transformation would create an image and a pre image that are similar figures?
The transformation which would create an image and pre image that are similar figures is dilation.
What is Similarity Transformation?Similarity transformations are transformations where there occurs a dilation with one or more transformations like rotation, reflection or translation.
This is called so because the triangles so formed will be similar figures.
Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
When the pre image is reflected, rotated or translated, it is not affecting the shape and the size. So the image and the pre image will be congruent.
Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Dilation enlarges or reduces the size, so they are similar figures.
Hence dilation is the similar transformation.
Learn more about Similarity Transformations here :
https://brainly.com/question/28993652
#SPJ2
Simplify (X-2)(x+3)(2x+1)
Answer:
Step-by-step explanation:
Use FOIL method.
(x -2)(x+3) = x*x + x*3 + (-2)*x + (-2)*3
= x² + 3x - 2x -6 {Combinelike terms}
= x² + x - 6
(x² + x -6)*(2x + 1) = x²*2x + x²*1 + x*2x +x*1 + (-6)*2x + (-6)*1
= 2x³ + x² + 2x² + x -12x - 6
= 2x³ + 3x² - 11x - 6
x – 5 ÷ 3 + b
6b + 15b ÷ 3
c - 2c × 4
PLEASE ANSWER ITS CONFUSING
Hey there!
Basically for all of your equations/questions you have to COMBINE the LIKE TERMS (if they are any in the particular equation you have)
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
QUESTION/EQUATION #1
x - 5 ÷ 3 + b
We pretty much CANNOT do anything to this equation because it doesn’t have that many like terms.
So, thus your answer will most likely be/
[b + x - 5 ÷ 3]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
QUESTION/EQUATION #2
6b + 15b ÷ 3
= 21b ÷ 3
= 7b
Thus, your answer is: [7b]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
QUESTION/EQUATION #3
c - 2c × 4
REWRITE
= 1c - 2c × 4
COMBINE the LIKE TERMS
= 1c - 7
= -7c
Thus, your answer is: [-7c]
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A rectangular parking lot has a length that is 9 yards greater than the width. The area of the parking lot is 360 square yards. Find the length and the width.
Answer: The width is 15 yards and the length is 24 yards
Step-by-step explanation:
Let x represent the width of the parking lot in yards
Let the length of the parking lost be (x + 9) as the length is 9 yards greater than the width
So, area = width * length
i.e. 360 = x(x + 9)
360 = x2 + 9x
x2 + 9x - 360 = 0
x2 + 24x - 15x - 360 = 0
x(x + 24) - 15(x + 24) = 0
(x + 24)(x - 15) = 0
Either x = -24 or, x = 15
But as width can not be negative, so we can not have, x = -24
So, we have, x = 15
Therefore, (x + 9) = (15 + 9) = 24
So, we have the following answers.
Width : 15 yards
Length : 24 yards
The average daily rainfall in Seattle for the month of June has a mean absolute deviation of 1.3 inches. What conclusion can you make about the average daily rainfall in Seattle for the month of June?
Using the mean absolute deviation, it can be concluded that the daily rainfall volume differs from the mean by an average of 1.3 inches.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.In this problem, the mean absolute deviation is of 1.3 inches, hence, it can be concluded that the daily rainfall volume differs from the mean by an average of 1.3 inches.
More can be learned about the mean absolute deviation at https://brainly.com/question/3250070
Answer:
Step-by-step explanation:
i need help please its due today
A passport consists of 2 letters followed by 2 digits. How many different passports can be formed?
67,600 different passwords can be formed.
26 x 26 x 10 x 10 = 67,600 (26 letters in the alphabet and 10 from 0-9)