The solution is Option D.
The sum of the arithmetic sequence is 5,490
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the sum of the arithmetic progression be represented as S
Now , the number of terms n = 60
Let the first term be a₁ = 3n , when n = 1
a₁ = 3
Now , the second term a₂ = 3n , when n = 2
a₂ = 6
So , the common difference of the arithmetic sequence d = second term - first term
d = 6 - 3
d = 3
Now , the sum of the first n terms of the sequence is
Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Substituting the values in the equation , we get
S₆₀ = ( 60/2 ) [ 2 ( 3 ) + ( 60 - 1 ) ( 3 ) ]
On simplifying the equation , we get
S₆₀ = 30 [ 6 + 59 ( 3 ) ]
S₆₀ = 30 [ 6 + 177 ]
S₆₀ = 30 ( 183 )
S₆₀ = 5490
Therefore , the value of S is 5,490
Hence , the sum of the arithmetic sequence is 5,490
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Malik, who is 5 feet tall, stands 15 feet from a mirror. In
the mirror, he can see the reflection of the top of a tree,
which he measures to be 92 feet away from the mirror. round your answer to the nearest hundredth
An interior designer made a scale model of a room. Each 1 inch in the model represented 12 feet in the actual 1 room. If the length of a hall was 2 inches in the model, what was the actual length of the hall?
Answer:
Step-by-step explanation:
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16x³-128y³
pls answer fast
Answer:
16x³-128y³
2((2x)³-(4y)³)
2(2x-4y)(4x²+8xy+16y²)
2×2×4(x-2y)(x²+2xy+4y²)
16(x-2y)(x²+2xy+4y²)
is your answer in factor form.
The required factor is given by 16(x-2y)(x²+2xy+4y²)
factors can be defined as the the numbers that multiply to give that number.
Factorization
It follow the
a^3-b^3 = (a-b)(a^2+ab+b^2)
[tex]16x^3-128y^3\\16(x^3-(2y)^3)\\16(x-2y)(x^2+2xy+4y^2)[/tex]
Thus the required factor is given by 16(x-2y)(x²+2xy+4y²).
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HELP ME ASAP I NEED HELP NOW
Zeros:
x = -2
x = 6
Smaller zero: -2
A light bulb manufacturer randomly checks light bulbs. Of 1,000 light bulbs checked, 30 light bulbs are defective. How many light bulbs will most likely be defective in a batch of 3,500?
A. 60
B. 105
C. 120
D. 180
Answer:
105
Step-by-step explanation:
(30/1000) * 3500 = 105
help please! if it’s correct ill give brainliest
Answer:
[tex]radius = \sqrt{ {15}^{2} + {36}^{2} } = 39 \\ area = 4 \times {39}^{2} \times \pi = 19103.76[/tex]
Help !!!!!!!!! !!!!!!!!!!!!
Answer:
28
Step-by-step explanation:
Add up the angles of the ones given so
40 + 112 = 152 and then subtract by 180 to get the missing angle: 180 - 152 = 28
I hope this helped!
Answer:
28°
Step-by-step explanation:
40° + 112 ° + angleCBA =180
152°+ angleCBA= 180
angle CBA=180° - 152°
angle CBA= 28°
what's the answer dhdhdizdjskxi
Answer:
138 ft for the area in the proposed design of the green section.
To find the area of the whole shape, you gotta divide it into polygons. So, you find the area of the big rectangle at the bottom first: 18 x 7 = 126. That's the area of the big rectangle.
Then, you find the area of the little square on top. 4 x 4 - 16, that's the area. Then, you gotta add those two together: 126 + 16. The total area is 142 square feet.
1001 divided by 7
( long division )
Answer: 143
Step-by-step explanation: hope this helps :)
cual es el resultado de 5-4(6-12)
Answer:
29
Step-by-step explanation:
5-(4*(6-12))=29
Answer:
La respuesta es 29, espero que esto ayude.
Determine if the sequence below is arithmetic or geometric and
determine the common difference / ratio in simplest form.
1,3,5...
This is
sequence and the
is equal to
Answer:
arithmetic
Step-by-step explanation:
geometric sequences grow really fast in a short amount of time while arithmetic sequences have a steady growth over any period of time
Answer:
This is an arithmetic sequence and the common difference is equal to 2.
3. Simplify:
a) 4a - 3b + a - 2b
Answer:
4a-3b+a-2b
5a-3b-2b
5a-3b-2b
5a-5b
solution: 5a-5b
Price of bread was increased by 5% to a retail price of $3.57. What was the original price ?
Answer:
3.39
Step-by-step explanation:
In ΔXYZ, ∠Y=90° and ∠X=40°. ∠ZWY=51° and XW=600. Find the length of ZY to the nearest integer.
The image of the triangle is missing so i have attached it.
Answer:
ZY ≈ 391
Step-by-step explanation:
From the attached image, ∠WZY = 180 - (51 + 90) = 39°. Because ΔWYZ is a right angle triangle and sum of angle in a triangle = 180°
Now, similarly ∠XZY = 180 - (40 + 90) = 50°
Using sine rule, we can find WZ;
WZ/sin 40 = XW/sin 50
We are given XW = 600
Thus;
WZ = (600 × sin 40)/sin 50
WZ = 503.5
Now, ZY can be found using trigonometric ratios;
ZY/WZ = sin 51°
Thus;
ZY = 503.5 × sin 51
ZY ≈ 391
What is 7.936 rounded to the hundredths place
Answer:
7.94 is your answer
Step-by-step explanation:
......
Can someone answer this
Answer:
54
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 3, 4 ] , then
f(b) = f(4) = 81 ← value of y from table for x = 4
f(a) = f(3) = 27 ← value of y from table for x = 3
average rate of change = [tex]\frac{81-27}{4-3}[/tex] = 54
What is the area, in square feet, of the shaded part of the rectangle below?
===============================================
Work Shown:
A = area of the rectangle
A = length*width
A = 16*17
A = 272 sq ft
B = area of triangle
B = base*height/2
B = 16*8/2 ..... note that 17-9 = 8
B = 16*4
B = 64 sq ft
C = area of shaded trapezoid
C = A - B
C = 272 - 64
C = 208 sq ft
--------------------
Alternative Method:
Apply the trapezoid area formula
b1 = 17 and b2 = 9 are the parallel bases
h = 16 is the height perpendicular to either base
A = h*(b1+b2)/2
A = 16*(17+9)/2
A = 16*(26)/2
A = 16*13
A = 208 sq ft
Finding probability
Answer:
6/8??
Step-by-step explanation:
I am a little confused with the question but i believe its 6/8
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
Solve for X
Answer:
[tex]AD/ED=AB/CB[/tex][tex]15/x=9/3[/tex][tex]45/9=9x/9[/tex][tex]x=5[/tex]----------------------
hope it helps...
have a great day!!
Answer:
x=5
Step-by-step explanation:
2) determine the length of the hypotenuse from the picture
A) 21 cm
B) 28 cm
C) 35 cm
D) 49 cm
Dont put the answer
In a link
Solve for X please help
Answer:
x = 10
Step-by-step explanation:
First square both sides of the equation...
[tex]2\sqrt{x + 8} = 3\sqrt{x - 2} \\(2\sqrt{x + 8})^{2} = (3\sqrt{x - 2})^{2} \\ 4(x + 8) = 9(x - 2)\\4x + 32 = 9x - 18\\-5x = -50\\x = 10[/tex]
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answer:
The answers are A and D
Step-by-step explanation:
2/6 simplified is 1/3 and none of the other choices are equal to 1/3, so the answers are A and D.
6x - 4y = 38
x + y = 5
Answer: y= -4/5 and x= 29/5
Step-by-step explanation:
From eqn2 , x= 5-y. Thus substituting in eqn1 will give
6(5-y)-4y=38
30-6y-4y=38
30-10y=38
-10y=38-30
-10y= 8
y=8/-10---> y= -4/5
Substituting y in eqn2 we have
x+(-4/5)=5
x=5+4/5
x=29/5
Leigh-Mari walks 10 kilometres to a waterfall at an
average speed of 3 kilometres per hour.
(a) Write down, in terms of r, the time taken in hours.
(b) Leigh-Mari returns from the waterfall but this time she
walks the 10 kilometres at an average speed of (x+1)
kilometres per hour. The time of the return journey is
30 minutes less than the time of the first journey. Write
an equation in x and show that it simplifies to
2 + 1 - 20 = 0.
(c) Solve the equation x2 + - 20 = 0.
(d) Find the time Leigh-Mari takes to walk to the waterfall,
Answer:
immma send you the link friend me on hereStep-by-step explanation:
Gabrielle's age is three times Mikhail's age. The sum of their ages is 80. What is Mikhail's age?
Answer:
Mikhail is 20 years old
Step-by-step explanation:
80 = Mikhail + Gabrielle
Gabrielle is 60 years old
Mikhail is 20 years old
20 * 3 = 60
20 + 60 = 80
I really need help! is my answer correct ?
expand and simplify (3x+4)(2x+3)
Answer:
answer is 6x^2+17x+12
Step-by-step explanation:
3x(2x+3)+4(2x+3)=6x^2+9x+8x+12=6x^2+17x+12
find the volume of the prism
Answer: 4,218,750
Step by explanation:
50 POINTS!!!!
A rectangular garden has length twice as great as its width. A second rectangular garden has the same length as the first garden and width that is 4 meters greater than the width of the first garden. The second garden has area of 120 square meters. What is the length of the two gardens? Enter your answer in the box. m=
Answer:
24 meters
Step-by-step explanation:
First we need to show width and length as variables.
let width of garden 1 = W
let length of garden 1 = L
let width of garden 2 = w
let length of garden 2 = l
Now make equations that are explained in the question
L = 2W
l = L
w = W + 4
l × w = 120
Now with that we can find l and w.
Now by looking at the factors of 120, find the factors that work throughout the question.
That is 12 and 10.
l=12
w=10
This means that...
L=12
W=6
Now the answer is 24 meters
Answer:
12m
Step-by-step explanation:
just took the test
IF you add 6 tens of thousands, 5 thousands and 3 hundreds together what is the value of the largest digit of the answer?
Answer:
ten thousands place
Step-by-step explanation:
6 tens of thousands = 60,000
5 thousands= 5,000
3 hundreds= 300
60,000
+ 5,000
+ 300
65,300