The third term of a geometric progression is 63/4 and the sixth term is 1701/32. Find the sum of the first 12 terms of the sequence.
Answer:
The sum of the first 12 terms of the sequence is 2703.673096
Step-by-step explanation:
The nth term of a geometric progression is a(n) = [tex]ar^{n-1}[/tex], where
a is the first termr is the common ratio between each two consecutive termsThe sum of n terms of the geometric progression is s(n) = [tex]\frac{a(r^{n}-1)}{r-1}[/tex]
∵ The third term of a geometric progression is [tex]\frac{63}{4}[/tex]
∴ a(3) = [tex]\frac{63}{4}[/tex]
∵ a(3) = ar²
→ Equate its two right sides
∴ ar² = [tex]\frac{63}{4}[/tex] ⇒ (1)
∵ The sixth term is [tex]\frac{1701}{32}[/tex]
∴ a(6) = [tex]\frac{1701}{32}[/tex]
∵ a(6) = a[tex]r^{5}[/tex]
→ Equate its two right sides
∴ a[tex]r^{5}[/tex] = [tex]\frac{1701}{32}[/tex] ⇒ (2)
→ Divide (2) by (1)
∴ r³ = [tex]\frac{27}{8}[/tex]
→ Take ∛ for both sides
∴ r = [tex]\frac{3}{2}[/tex] = 1.5
→ Substitute the value of r in (1) to find a
∵ a(1.5) = [tex]\frac{63}{4}[/tex]
∴ 1.5a = 15.75
→ Divide both sides by 1.5
∴ a = 10.5
→ Let us find the sum of the first 12 terms
∵ n = 12, a = 10.5, and r = 1.5
→ Substitute them in the rule of the sum above
∵ s(12) = [tex]\frac{10.5(1.5^{12}-1)}{1.5-1}[/tex]
∴ s(12) = 2703.673096
∴ The sum of the first 12 terms of the sequence is 2703.673096
(f- g)(x) =
what is the answer?
Answer:
(f- g)(x) =fx−gx
Step-by-step explanation:
The measure of one side of a square is (s - 3) inches long. Which pair of expressions both represent the perimeter of this square?
a) 2s + 3 and (s + 3) + (s + 3)
b)2(s + 3) and (s + 3) + (s + 3)
c) 4s + 3 and (s + 3) + (s + 3) + (s + 3) + (s + 3)
d) 4( + 3) and (s + 3) + (s + 3) + (s + 3) + (s + 3)
The measure of one side of a square is (s + 3) inches long. The pair of expressions which both represents the perimeter of this square is:
d) 4( s + 3 ) and (s + 3) + (s + 3) + (s + 3) + (s + 3)
simiply the following (-4)⁶÷(-4)³.i will mark as brainlest
can someone help me like ion get it
Answer:
D is the correct answer.
algebra 1- pls help! (I messed up previous question so I’m retyping it-)
Solve for x
-8x+14 ≥60 OR -4x+50 -2
B.) x ≤ -23/4
C.) x>-2
D.) There are no solutions
There are 3 boys for every 4 girls in a class. If there are 16 girls, how many boys are there?
If there are 3 boys for every 4 girls in a class, there would be 12 boys because 16 ÷4 us 4, and 4×3 is 13.
Read the proof.
Given: AB ∥ DE
Prove: △ABC ~ △EDC
Triangles A B C and E D C connect at point C. Sides A B and D E are parallel.
Statement Reason
1. AB ∥ DE 1. given
2. ∠ACB and ∠ECD are vert. ∠s 2. definition of vertical angles
3. ∠ACB ≅ ∠DCE 3. vertical angles are congruent
4. ∠BDE and ∠DBA are alt. int. ∠s 4. definition of alternate interior angles
5. ∠BDE ≅ ∠DBA 5. alternate interior angles are congruent
6. △ABC ~ △EDC 6. ?
AA similarity theorem
ASA similarity theorem
AAS similarity theorem
SAS similarity theorem
Answer:
Its AA similarity theorem
Step-by-step explanation:
correct on edge 2021
The triangles ABC and EDC are similar by AA similarity theorem.
What is similarity in triangles?Two triangles are said to be similar if their corresponding sides are in equal ratio and corresponding angles are congruent.
Given is a proof of showing △ ABC ~ △ EDC
The proof is as follows :-
Statement Reason
AB ∥ DE Given
∠ ACB = ∠ ECD definition of vertical angles
∠ BDE ≅ ∠ DBA alternate interior angles are congruent
△ ABC ~ △ EDC AA similarity theorem
AA similarity theorem :-
AA similarity theorem states that when two corresponding angles of two triangles are found congruent then the triangles are similar by AA similarity theorem.
Hence, the missing reason is AA similarity theorem.
For more references on AA similarity theorem, click;
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Hello :) pls help thank you very much!
......................
Answer:
Given: That's exactly what we've been givenCombine Like TermsSubtraction property of equality: We subtract 12 from both sides of the equation.GIVING BRAINLIEST I ONLY NEED A SENTENCE!
During a chemical reaction, how do the substances that form differ from the substances that react?
Answer:
The substances that form are a combination of the two reactants.
Step-by-step explanation:
Help me pleaseeeeeeeeeeeeeeeeeeeee
Answer:
its the 4/7x 28
Step-by-step explanation:
you count by 2 and then you look for the numbers
Answer:
THE OTHER PERSON IS WRONG DO NOT LISTEN YOUNG ONE
Step-by-step explanation:
THE ANSWER IS D, 2/7 x 28
can someone help me ASAP??? 49 POINTS!!!!!!!!!
John has 600 marbles and he is giving to his friends. he gives 1/5 of them to bob, 8% to pat, and 75 to matt. How many marbles does John have left?
Answer:
John has 357 marbles left.
Step-by-step explanation:
120 marbles went to Bob
48 went to Pat
and 75 to Matt.
A company can produce 60 million chocolate candies within a 24-hour period.
Part A
Using this rate, create an equation to represent the number of chocolate candies,
c
, in millions, the company can produce in
h
hours.
Answer:
f(x)=60c * 24h
Step-by-step explanation:
Hope this helped!
During one day in a hardware store, 37 people came in and made a purchase, and 13 people looked around but didn’t purchase anything. Express the following in ratios:
a. Purchasers to nonpurchasers
b. Nonpurchasers to purchasers
c. Purchasers to total customers
d. Nonpurchasers to total customers
HELP WHATS THE ANSWER
Answer:
13.5
Step-by-step explanation:
what is the sum of 3 8 added to 1 3
Answer:
37
Step-by-step explanation:
First multiply 3 by 8 (24)
then add 13
An artifact is four times 4 times older than an antiuqe book. In 200 years the artifact will be 3 times older than the book. How old is the artifact now?
Answer:
The present age of the artifact is 1,600 years
Step-by-step explanation:
let the present age of the artifact = x
let the present age of the book, = y
x = 4y ---- equation (1)
x + 200 = 3(y + 200) ------equation (2)
x + 200 = 3y + 600
substitute in the value of x into the equation;
4y + 200 = 3y + 600
4y - 3y = 600 - 200
y = 400
Then, x = 4 x 400
x = 1,600 years
Therefore, the present age of the artifact is 1,600 years
Answer:
The present age of the artifact is 1,600 years
Step-by-step explanation:
let the present age of the artifact = x
let the present age of the book, = y
x = 4y ---- equation (1)
x + 200 = 3(y + 200) ------equation (2)
x + 200 = 3y + 600
substitute in the value of x into the equation;
4y + 200 = 3y + 600
4y - 3y = 600 - 200
y = 400
Then, x = 4 x 400
x = 1,600 years
Which best describes the relationship between the successive terms in the sequence shown?
2.4, –4.8, 9.6, –19.2
(A)The common difference is –7.2.
(B) The common difference is –2.4.
(C)The common ratio is –2.0.
(D)The common ratio is –0.5.
Answer:
(C)The common ratio is –2.0Step-by-step explanation:
Given sequence:
2.4, –4.8, 9.6, –19.2This is not AP as the difference in terms is not common
This is GP with the common ratio of -2 as:
-19.2/9.6 = 9.6/ -4/8 = -4.8/2.4 = -2Correct choice is (C)
The image of the point (7,-4) under a translation is (12,-5). Find the coordinates
of the image of the point (-8, -3) under the same translation.
Which values of a, b, and c correctly represent the answer in simplest form? 3 =a O a=38.0= 14.0=1 a=1.0= 14.C = 38 O a= 1.5=7.C= 19 O a = 19.0= 7.0= 1
Answer:
The answer could be A) or D) because the zero acts as a place holder. Its a little easier to derive it if you have a bigger decimal
Step-by-step explanation:
Use the coefficient of variation to determine
which data set varies the most.
on
Data Set 1: 2 = 12 and s = = 7
Data Set 2: 2
0.12 and s
= 0.3.
Data Set 1 CV ~
% (Round to the
nearest percent)
Data Set 2 CV =
%
Answer:
Dataset 2
Step-by-step explanation:
The Coefficient of variation is the ratio of the standard deviation and the population mean.
Data Set 1: 2 = 12 and s = = 7
Data Set 2: 2
0.12 and s
= 0.3.
Coefficient of variation = (standard deviation / mean) * 100%
Dataset 1:
Standard deviation = 7 ; mean = 12
Coefficient of variation = (7 / 12 ) * 100% = 0.5833 = 58%
Dataset 2:
Standard deviation = 0.3 ; mean = 0.12
Coefficient of variation = (0.3 / 0.12) * 100% = 2.5 * 100% = 250
Hence dataset 2 varies the most with a greater value of variation Coefficient.
Which of the following is an example of discrete data?
Temperature (in Fahrenheit) of teh Pacific Ocean at Huntington Beach
Lifetime (in hours) of 35 fluorescent light bulbs
Amount of caffeine (in milligrams) for 8 ounces of popular drinks
Number of hamburgers sold each day at Hamburger Mary's
Weight of dogs (in pounds) at the Seal Beach Animal Care Center
Answer:
Number of hamburgers sold each day at Hamburger Mary's because it's counting a number of something, not measuring a quantity with respect to a variable like temperature or weight. If this is still unclear let me know what I need to clarify. Have a nice night.
In the diagram, Triangle ABC ~ Triangle ACD. If AD = 12 and DB = 15, What is AC?
Answer:
9
Step-by-step explanation:
DB^2=AD^2+AC^2
15^2=12^2+AC^2
AC^2=225-144
AC^2=81
AC=√81
AC=9
Target is having black Friday deals Alma enLG 50 TV cost $330 and it is on sale for 30% off what is the sale price of the TB after the discount in excluding tax
The last answer choice is 53 please answer
Answer:
Step-by-step explanation:
Chen is 44 inches tall
I Four men can dig
a pit in 5 days,
men can do the same job
in 2 days
How many
Answer:
7?
Step-by-step explanation :
yo creo que si
m(x)=x2+4x n(x)=x
(mn)(x)=
A.) x2+4x(x)
B.) (x2+4x)(x)
Answer:
b is correct
Step-by-step explanation:
The product of the functions M(x) and n(x) is x³+ 4x².
To find the product of the two functions, M(x) = x² + 4x and n(x) = x, we need to multiply them together.
So, (mn)(x) = M(x) × n(x)
Substituting the given functions:
(mn)(x) = (x² + 4x) × x
Now, we can simplify the expression by applying the distributive property of multiplication:
(mn)(x) = x × x² + x × 4x
Simplifying further:
(mn)(x) = x³ + 4x²
Therefore, the product of the functions M(x) and n(x) is x³+ 4x².
Learn more about Polynomial here:
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Suppose scientists compared the wind speeds and barometric pressure readings of two severe storms over the Atlantic Ocean. For one of the storms, the barometric pressure was 1,000 mb (millibars), and the maximum wind speed was 100 kmh (kilometers per hour). The second had a barometric pressure of 960 mb and maximum wind speeds of 180 kmh. (a) Develop a rule that you could use to predict the wind speed given any barometric pressure.
Answer:
So i found the teacher notes after hours of looking here are the exact answers so i would recommend changing the wording.
Part A: Ordered pairs in the form (mb, kmh): (1,000, 100) and (960,180) Let X be the barometric pressure and Y be the wind speed.
Slope= (180-100)
---------------- = -2
(960-1000)
Formula: y=-2(x-1000)+100
Part B: y=-2(980-1000)+100=140
140 kmh is reasonable. Because 980 mb is halfway between 960 mb and 1000 mb, we should expect a wind speed halfway between 180 kmh and 100 kmh.
Part C: The wind speed intercept is (0,2100) [or (2100,0) if written that way.] This means that when brometric pressure is 0 mb, then the wind speed would be 2100 kmh. However in the context of real weather, this is an impossible situation.
Part D: The slope means that every decrease of 2 kmh in wind speed corresponds to a 1 mb increase in barometric pressure.
hoped this helped :)
What is the answer to -4 x ( -6 )
Answer:
24x
Step-by-step explanation:
Multiply − 6 by − 4 .
Answer:
24
Step-by-step explanation:
you multiply negative 4 by negative 6
15 quarts=_cups how many cups???