the sum of the first six terms of a G.P is 9 times the sum of the first three terms . what is the first term ?
Without any more information, the first term can be any number.
Let a be the first term in the geometric progression, and let r be the common ratio between consecutive terms. Then
a + ar + ar ² + ar ³ + ar ⁴ + ar ⁵ = 9 (a + ar + ar ²)
ar ³ + ar ⁴ + ar ⁵ = 8 (a + ar + ar ²)
r ³ + r ⁴ + r ⁵ = 8 (1 + r + r ²)
r ³ (1 + r + r ²) = 8 (1 + r + r ²)
r ³ = 8
r = 2
Now with this ratio, the sum of the first six terms is
a (1 + r + r ² + r ³ + r ⁴ + r ⁵) = a (1 - r ⁶)/(1 - r) = 63a
while the sum of the first three terms is
a (1 + r + r ²) = a (1 - r ³)/(1 - r) = 7a
and of course 63a = 9 • 7a, and this is true for any a.
hii if you answer correctly i will give you brainliest pls as soon as possible
Answer:
x = 14 degrees
Step-by-step explanation:
There are a minimum of 4 triangles that this polygon can be divided into.
Hence, the total internal angle is (4*180) degrees = 720 degrees.
Therefore, 10x + (8x-16) + (12x-8) + (7x+2) + (9x+4) + (6x+10) = 720 degrees.
52x - 8 = 720 degrees
x = 728/52 degrees
x = 14 degrees
Hope this helped!
given that 3 feet equal 1 yard, how many yards equals 1 feet ?
Answer:
0.333333
Step-by-step explanation:
Hope this helps and have a great day!
If a +2<b+3 then ____.
a-b<1
a<b+1
a<b
b<a
Answer:
a<b+1
Step-by-step explanation:
a +2<b+3
a<b+3-2
a<b+1
Answer: a - b < 1 or a < b + 1
a + 2 < b + 3
⇔ a - b < 3 - 2
⇔ a - b < 1
Step-by-step explanation:
what is the answer to 5/6 times 4/3 =
Answer:
[tex]\frac{10}{9}[/tex]
Step-by-step explanation:
Answer: 10/9 or 1.111111111
Step-by-step explanation:
What is the common difference for this arithmetic sequence?
45, 39, 33, 27, 21, .
O A. 45
OB. 6
OC. 39
OD. -6
Answer:
Concept: Series
Start by taking the first and second An and finding the difference You can then prove your result by taking any ordinary An and subtracting it by An-1Hence 45-39= 6 To prove our result of 6; 39-33= 6 Hence the common difference is Rate brainlistA factory is able to make 99 televisions in 3 hours. What is the constant of proportionality?
Answer: 33 televisions in 1 hour
Step-by-step explanation:
99/3=33
Answer:
33 TVs IN 1 HR
Step-by-step explanation:
TRUST ME
Factor completely.
x3 + x2 – 25x – 25
what’s the answer
Answer:
(x+1)(x+5)(x-5)
Step-by-step explanation:
Please answer this as quick as you can
Answer:
Step-by-step explanation:
3 and 2 for what i see with the question i don't know if the blue is blocking a tick but i think its 2 and 3 tell me if there a tick on where the blue started so then i might change my answer
A bank manager is interested in the average length of time that customers are willing to wait in line before they give up and leave the bank. Match the vocabulary word with its corresponding example.
The average length of time that the 25 customers waited before leavingthe bank
The list of times for the 25 customers who left the bank
All of the bank's customers
The 25 customers that the manager observed leave
The length of time a customer waits before leaving the bank
The average length of time that all customers will wait before leaving the bank
a. Parameter
b. Variable
c. Sample
d. Population
e. Statistic
f. Data
Answer: The average length of time that the 25 customers waited before leaving the bank. e. Statistic
The list of times for the 25 customers who left the bank. f.Data
All of the bank's customers d. Population
The 25 customers that the manager observed leave. c. Sample
The length of time a customer waits before leaving the bank. a. Variable.
The average length of time that all customers will wait before leaving the bank a. Parameter
Step-by-step explanation:
A data is a list of observations.
In statistics, a variable is an attribute that defines a person, place, thing, or thought.
A large group that have similar individuals as per the researcher's point of view is known as population, where its subset is known as sample.
The measure of certain characteristic in population is known as parameter, where for sample it is known as statistic.
The correct description of the given examples are:
The average length of time that the 25 customers waited before leaving the bank.
e. Statistic
The list of times for the 25 customers who left the bank.
f. Data
All of the bank's customers
d. Population
The 25 customers that the manager observed leave.
c. Sample
The length of time a customer waits before leaving the bank.
a. Variable.
The average length of time that all customers will wait before leaving the bank
a. ParameterWe can see that a bank manager is interested in finding out the average wait time which each customer has to wait and we can see that this is known as a parameter.
Read more about variables here:
https://brainly.com/question/3766847
Someone pls help me :((
Answer:
They are both correct.
Step-by-step explanation:
4(-7)(-1) equals 28. 4(7) is also equal to 28, meaning that Josh is correct. 2 negatives equals a positive, so (-28)(-1) will also be 28. This means Evangelina is also correct.
3
6x
21(x + 1) 21(x + 1 )
.
21(x+1)=21x+21?
3*6x=18x
The sum of 7 ⅓ and a number, n is 10 ⅜. What is the number?
Answer:
3 1/24
Step-by-step explanation:
to find the answer subtract ( 10 3/8 - 7 1/3 = 3 1/24 ).
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[tex]7 \frac{1}{3} + n = 10 \frac{3}{8} \\ [/tex]
[tex] \frac{21 + 1}{3} + n = \frac{80 + 3}{8} \\ [/tex]
[tex] \frac{22}{3} + n = \frac{83}{8} \\ [/tex]
Subtract sides 22 / 3
[tex] - \frac{22}{3} + \frac{22}{3} + n = - \frac{22}{3} + \frac{83}{8} \\ [/tex]
[tex]n = \frac{83}{8} - \frac{22}{3} \\ [/tex]
[tex]n = \frac{83 \times 3}{8 \times 3} - \frac{22 \times 8}{3 \times 8} \\ [/tex]
[tex]n = \frac{249}{24} - \frac{176}{24} \\ [/tex]
[tex]n = \frac{249 - 176}{24} \\ [/tex]
[tex]n = \frac{73}{24} \\ [/tex]
[tex]n = \frac{72 + 1}{24} \\ [/tex]
[tex]n = 3 \frac{1}{24} \\ [/tex]
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HELP IS FOR TODAY EXERCISE 2 SIMPLIFY FRACTIONS
Answer:
Do u have English version?
Step-by-step explanation:
Please help these are two different questions !
Answer:
120 Girls
Step-by-step explanation:
First, you have to combine the dark shade girls and the light shade girls together to get 7.
Then, you should divide 210 by 7, to get 30
Finally, using 30 as your multiplier,
you go and multiply 30 x 4 to get 120 girls :D
f(-5) if(x) - 4x + 2
Answer:
22
Step-by-step explanation:
-4(-5)+2
20+2
22
Find the Lateral Area
A triangular prism and its dimensions are shown in the diagram.
5 cm
5 cm
8 cm
6 cm
What is the lateral surface area of this triangular prism in square centimeters?
Answer:
? please explain
Step-by-step explanation:
Answer:128 I think is the answer
Step-by-step explanation:
A full 335 ml can of Coca-Cola is filtered at a rate
of 5 ml per minute into an empty can. How long
will it take for the two cans to have the same
amount, a, of Coca-Cola?
Mm
9514 1404 393
Answer:
33.5 minutes
Step-by-step explanation:
There are many ways you can look at this problem. One is to write equations for the amount in each can, and solve for the time that makes those amounts equal. Another is to consider how much time it takes to reduce the volume by half.
Using the first method, we have ...
335 -5t = 5t
335 = 10t
335/10 = 33.5 = t
It takes 33.5 minutes for the cans to have the same amount.
Let t= the amount Thomas earned. Thomas earned $ 49 or more
I NEED HELP ASAP PLS
Answer:
Pretty sure it's D. y=2/1x
Answer:
y= 2/1 x
Step-by-step explanation:
Start from (-2,-4) rise up 4 and over 2 which means 4/2 simplify to 2/1
a) What is the equation of line A?
b) What is the equation of line B?
Answer:
Line A is x = -3
Line B is y = 2.5
Step-by-step explanation:
Draw lines to match each fraction,
decimal, or percent on the right to an
equivalent number on the left.
Answer:
0.45 = 9/20
38% = 19/50
27/50 = 0.54
0.68 = 17/25
80% = 4/5
Step-by-step explanation:
Which equation represents a circle with a center at (-4,9) and a diameter of 10 units?
(x - 9)2 + (+ 4)2 = 25
(x + 4)2 + (- 9)2 = 25
(x - 9)2 + ( + 4)2 = 100
(x + 4)2 + (- 9)2 = 100
PLZ HELP!
The equation of circle with center at P ( -4 , 9 ) and diameter 10 units is given by ( x + 4 )² + ( y - 9 )² = 25
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the equation of circle be represented as A
Now , the value of A is
Let the center of the circle be P ( -4 , 9 )
Let the diameter of the circle be d = 10 units
So , the radius of the circle r = d/2 = 5 units
And , standard form of a circle is
( x - h )² + ( y - k )² = r²,
So , the equation of circle is
( x + 4 )² + ( y - 9 )² = 25
Hence , the equation of circle is ( x + 4 )² + ( y - 9 )² = 25
To learn more about equation of circle click :
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Esteban has $100 in bills. He has 22 bills total and each of them is either a $10 bill or a $2 bill. How many $10 bills does Esteban have?
Write 2 equations needed to solve this problem
Answer:
x = - 8, x = - 6
Step-by-step explanation:
Given
8 | x + 7 | - 3 = 5 ( add 3 to both sides )
8 | x + 7 | = 8 ( divide both sides by 8 )
| x + 7 | = 1
The expression inside the bars can be positive or negative, thus
x + 7 = 1 or - (x + 7) = 1 ← 2 equations to be solved
x + 7 = 1 ( subtract 7 from both sides )
x = - 6
or
-(x + 7) = 1
- x - 7 = 1 ( add 7 to both sides )
- x = 8 ( multiply both sides by - 1 )
x = - 8
the distance between two cities on a map is 3.5 centimeters the map uses a scale in which 1 centimeter represents 20 km what is the actual distance between these
two cities in kilometers
Answer:
1 cm = 20 km
so 3.5 cm would equal : 3.5 * 20 = 70 km
hope it helps ;)
Step-by-step explanation:
Help me out real fast pleaseeeeeeee
Answer:
25/6 = 4 1/6
Step-by-step explanation:
what you do is 5/6 times 5 i am pretty sure this is right
Answer:
B. 4 1/6
Step-by-step explanation:
1. Identify your key factors:
Terrance: 5
Brother: 5/6
2. Let's make them both fractions:
T: 30/6 B: 5/6
3. Now subtract the difference:
30/6-5/6
25/6
4. Simplify:
4 1/6
A construction company bought 673.718 kilograms of gravel and 140.91 kilograms of sand. How many kilograms of material did the company buy in all?
Answer:
814.628 kg
Step-by-step explanation:
We are finding the total number of kilograms, so we must add it all together.
673.718 + 140.91 = 814.628 kg in all
can anyone help me thanks
Answer:
grams
Step-by-step explanation:
kilometers is for length, milugrams are too small and millimeters dosent make sense
Luke works at a shoe store. He earns a 2% commission on all shoes he sells. If he sells $50 of shoes, how much money will he make with his commission?
Answer:
$1
Step-by-step explanation:
Commission earned on sale = 2%
Total sales made = $50
Commission earned for this sale :
Commission percent * worth of sales made
0.02 * $50
= $1