Sequences:
See the following attached image, where you can see sets of circles, which follow a certain pattern:
Number of circles in next row 6: 21 circles, and row 7: 28 circles
1) Determine the number of circles in the nth pile (general term)
2) What is the number of circles when n tends to infinity?
Answers
Answer:
The sequence is
1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, ...Each term is the sum of the consecutive numbers from 1 to that number.
The nth term is the sum of the first n numbers:
aₙ = 1 + 2 + 3 + ... + naₙ = 1/2n(1 + n) (formula for sum of the n terms of arithmetic progression with the first term of 1 and common difference of 1)aₙ = n(n + 1)/21) The number of circles in the nth pile is n(n + 1)/2
2) When n tends to infinity the number of circles tends to infinity
Related Questions
Mona has a bag containing 4 red marbles, 12 green marbles, and 8 black marbles. Without looking, she pulls out one marble from the bag and places it in an empty jar. She then pulls a second marble from the bag and places it in the jar. WHat is the probability that she will have 2 green marbles in the jar?
A. 12/24 x 11/23
B. 12/24 x 12/24
C. 1/12 x 1/11
D. 12/24 x 12/23
Answers
Please help soon- The weight of oranges growing in an orchard is normally distributed with a mean
weight of 6 oz. and a standard deviation of 1 oz. From a batch of 2500 oranges, how
many would be expected to weight less than 4 oz., to the nearest whole number?
Answers
A recipe uses 1 ¼ cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be made using 2 gallons of milk?
Answers
Answer:
128 is your answer
Step-by-step explanation:
1 gallon of milk will make 128 servings.
100% Correct hope this helps ツ
Answer:
25
Step-by-step explanation:
16 cups = 1 gallon
1 1/4 * 12 = 15 (12 cups)
15 * 2 = 30 (24 cups)
30 + 1 1/4 = 31 1/4 (25 cups)
Brainliest please UwU
Can someone please help?
Answers
Answer:
it's the top right box
Step-by-step explanation:
start from the first box and count how many units was added
Use systems of linear equations solve x+2y=4
Must include;
Step to solve problem
Answers
Answer: y=2-2x
Step-by-step explanation:
Volume answer rn djdjd
Answers
Answer:
133.7π cm^3 or approximately 418.77430072 cm^3.
Step-by-step explanation:
For the cylinder half, use the formula: π*r^2*h, or pi times radius squared times height.
Since the diameter is 8, which means the radius is 4, and the height is 6, the volume of the cylinder would be 96π or 301.59289474...
For the cone on top, use the formula 1/3 (π*r^2*h), or one third pi times radius squared times height. Don't forget to calcuate the part in parentheses before dividing it by three.
Because the overall height was 13, you can subtract the 6 from the cylinder to get the cone's height. It has a height of 7 and a radius of 4 just like the cylinder. The volume of the cone is 112π/3 or 37.3π.
Now add both volumes together to get 133.7π cm^3 or approximately 418.77430072 cm^3.
Identify a second of transformations that maps triangle ABC onto triangle A"B"C in the image below.
Answers
Answer: The answer is B because the triangle rotated a 90 degrees counterclockwise then got a reduction.
Step-by-step explanation:
5th grade math. correct answer will be marked brainliest
Answers
Answer:
4ft, 7 inches
Step-by-step explanation:
4 ft (48 inches), 7 inches
What is 8% of 200?
4
16
25
Done
Answers
Answer:
16
Step-by-step explanation:
8% of 200 is 16
Answer: 16
Explanation: That's an i-Ready Diagnostic!! Heh...
3 (a - 1) + 31 - 11a = 4 ( 2a + 3)
Answers
Answer:
-⅖
Step-by-step explanation:
We need to simplify the given equation and find out the value of a , as ,
=> 3(a-1)+31-11a = 4(2a+3)
=> 3a -3+31-11a = 8a + 12
=> -8a -28 = 8a + 12
=> 16a = -28-12
=> 16a = -40
=> a = -2/5
• Hence the value of a is -⅖ .3 ( a - 1 ) + 31 - 11a = 4 ( 2a + 3 )
____________________Solution :-Given Information :-Equation ➢ 3 ( a - 1 ) + 31 - 11a = 4 ( 2a + 3 )To Find :-The value of 'a'Calculation :-⇒ 3 ( a - 1 ) + 31 - 11a = 4 ( 2a + 3 )
Opening the brackets and multiplying the terms, We get,
⇒ 3a - 3 + 31 - 11a = 8a + 12
⇒ -8a + 28 = 8a + 12
⇒ 8a + 8a = - 28 - 12
⇒ 16a = 40
Transposing 16 to Right Hand Side, We get,
⇒ a = [tex] \sf \frac{40}{16} [/tex]
⇒ a = [tex] \sf \frac{-2}{5} [/tex]
____________________Final Answer :-The value of 'a' is [tex] \bf \frac{-2}{5} [/tex]____________________What is the expanded form of 8,609?
A 8,000+600+ 90
8,000+60+9
8,000 +900+ 6
8,000+600 +9
Answers
The last one 8,000 + 600 + 9
4+j3 amps and resistance of 5-j3 ohms what is the voltage of the circuit
Answers
Answer:
V = 29 + j3
Step-by-step explanation:
4+j3 amps and resistance of 5-j3 ohms what is the voltage of the circuit
V = IR I = 4+j3 amps R = 5-j3 ohms
V = 4+j3 × 5-j3
V = [4 × 5]+[j3 × -j3] + [4 × -j3] + [j3 × 5]
V = 20 + (-j²)9 + (-j12) + j15
V = 20 - 9 + j3 j3 × -j3 = 9 not -9 j = -1 j × j = -1 not 1 my mistake
V = 11 + j3 WRONG
my daughter's old TI 84 Plus Silver Edtion calculator got 29+j3
Find the area of each figure. Round to the nearest tenth. Use 3.14 or 22/7
a. 18.8
b.9.4
c. 113
d. 28.3
Answers
Answer:
d. 28.3
Step-by-step explanation:
Given
Radius ( r) = 3 m
Area of the circle
= π r²
= 3.14 * 3* 3
= 28.26
= 28.3 ft²
0.125,0.25,0.5,1 sequence
Answers
Answer:
1,2,4,8,16,32
Step-by-step explanation:
power of two sequence
Planes A and B intersect. Which describes the intersection of plane A and line m? Oline k B m Olinen À point X O point W X 3 k Y Z
Answers
The intersection of plane A and line m can be describes as line m .
What is reflectional symmetry?Let's a plane. Consider a design or shape on that plane. Now consider an axis.
If we think of that axis as a mirror, and on the opposite side of that axis create the image of the considered shape, then if the shape's image looks exactly as the shape itself, therrefore that shape is called to have a reflectional symmetry.
Given that Planes A and B intersect.
We can see the two walls as planes in geometry.
A plane can be thought of as a wall or a floor of a room also a flat surface that has no thickness.
When two planes intersect, their intersection is a line.
Learn more about symmetry here:
https://brainly.com/question/7783612
#SPJ7
which expression is equivalent to (4^-5 * 4^4) + (2^6/ 2^3)
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
can someone help me :(
Answers
Answer:
A is the correct answer
.......................
Answer:
A. y+116+30=180
Step-by-step explanation:
A straight angle is 180°.
all the given angles make up a straight angle, so they add to 180°.
The set of life spans of an appliance is normally distributed with a mean y = 48 months and a standard deviation or
8 months. What is the z-score of an appliance that stopped working at 64 months?
Answers
Answer:
The set of life spans of an appliance is normally distributed with a mean µ= 48 months and a standard deviation σ= 8 months. ... Thanh finds that his grade on the test has a z-score of -2.5. ... are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668.
Step-by-step explanation:
=============================================================
Explanation:
The raw score is x = 64, and we want to find its corresponding z score.
The mean and standard deviation are mu = 48 and sigma = 8 respectively.
The z score is...
z = (x-mu)/sigma
z = (64-48)/8
z = 16/8
z = 2
A z score of 2 means we're 2 standard deviations above the mean.
As the formula above implies, we find the difference from the raw score (x) to the mean (mu). Then we divide over sigma to find out how many sigma steps we have to take to go from mu to x.
A negative z score would indicate the raw score is below the mean.
What is the absolute value of a number?
Answers
Answer:
It is the distance from the zero on a number line. Also, it is never negative.
Step-by-step explanation:
Plz help ASAP plz help
Answers
Answer:
no solution for the answer
7/12 3/7 in simplest form
Answers
Answer:
Both fractions are in their simplest forms.
A circle has a diameter of 10 centimeters.
What is the best approximation of its area?
Use 3.14 to approximate for π.
15.7 cm²
31.4 cm²
78.5 cm²
314 cm²
Answers
Answer:
78.5 (please put brainliest)
Step-by-step explanation:
r = diameter / 2 = 5
area = π * r^2 = 25 * 3.14 = 78.5
Answer:
78.5 m^2
Step-by-step explanation:
PLEASE PLEASE HELP
what is the slope of the line
A. 0
B. 1
C. -2
D. no slope
Answers
Answer:
a.0
Step-by-step explanation:
The slope of any horizontal line is 0
Answer:
A, 0
Step-by-step explanation:
The slope of a line is Change in Y / Change in X. This line is parallel to X-axis, meaning the Y will always be the same. This means that the change in y is 0, meaning the slope is 0 / Change in X, which is 0.
Hank wants to rent a bike. Bike rentals cost $1.25 per hour plus a one-time
fee of $3. Which equation represents the relationship between the number
of hours h Hank rents the bike and the total cost c?
Answers
Answer:
c = 3 + (1.25 x h)
What is the distance between (2, 5) and (2, -7)?
Question 1 options:
2
5
12
14
Answers
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
A. 35
B. 96
C. 51
D. 80
Answers
Answer:
Its D
Step-by-step explanation:
Surface area of a solid figure can be found by multiplying the area of the base by the height of the figure.
True
O False
Answers
Answer:
Surface area of a solid figure can be found by multiplying the area of the base by the height of the figure.
it's false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Brenden spent 24 minutes playing a computer game. He stopped playing at 3:55 P.M. and went outside to ride his bike. What time did he start playing the computer game?
Answers
Answer:
3:31
Step-by-step explanation:
3 hours 55 minutes - 24 minutes = 3 hours 31 minutes
Answer:
3:31 PM
Step-by-step explanation:
55 - 24 = 31
So,
3:31 is the answer :)
Does anybody know the answer please.
Answers
Answer:
The sign of each y-coordinate changed.
Step-by-step explanation:
This was a reflection over the x-axis.
If you look at point F, it is (-5, -1) the corresponding point F' is (-5,1). Notice the numerical values of x and y are the same, but the sign of y flipped from negative to positive. The other four points all follow the same pattern.
What is the volume of a sphere with a radius of 3.1 cm, rounded to the nearest tenth
of a cubic centimeter?
Answers
Rounded to the nearest tenth It’s 124.8