The sequence g(n) is a geometric sequence with an explicit formula of g(n) = (2/3)^n * 900 grams.
Explanation:The sequence g(n) represents the amount of contaminants (in grams) that remains at the beginning of the nth hour. Each hour, a third of the contaminants is filtered out. To determine whether g(n) is an arithmetic or geometric sequence, we need to examine the change in the amount of contaminants from one hour to the next.
Let's look at the first few terms of the sequence:
g(1) = 900 grams (initial amount)g(2) = 2/3 * g(1) = 2/3 * 900 gramsg(3) = 2/3 * g(2) = 2/3 * (2/3 * 900 grams)From the pattern, we can see that each term of g(n) is obtained by multiplying the previous term by 2/3. Therefore, g(n) is a geometric sequence.
The explicit formula for the sequence g(n) can be written as g(n) = (2/3)^n * 900 grams.
What is 5 times 6 minus 3
Answer:
27
Step-by-step explanation:
5 × 6 = 30
30 - 3 = 27
Answer:
27
Step-by-step explanation:
(5) 6 -3 In PEMDAS you Multiply first because M is before S
30 - 3
27
¿Cuál es el area de un círculo con un diámetro de 5 pulgadas a la décima más cercana ?
Answer:
19.6 o 2.5π
Step-by-step explanation:
la fórmula para el área del círculo es A = πr ^ 2
WILL GIVE BRAINIEST
What is the Magnitude of A?
a) 4
b) −4
c) 3
d) −3
Graph:
Answer:
c) 3
Step-by-step explanation:
The magnitude of a vector is its length, ignoring its direction.
Vector a goes from 0 to -3, so its length is 3.
Answer:
c) 3
Step-by-step explanation:
Vector A: < -3, 0 >
Magnitude:
sqrt[(-3)² + 0²]
sqrt(9)
3
The Smiths spend 10% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $2,450 on entertainment. What was their total budget last year?
Answer:
$22500
Step-by-step explanation:
First, we have to find the total budget for this year.
They spend 10% on entertainment and $2450 will be spent on entertainment this year.
Let the total budget this year be x. Therefore:
[tex]\frac{10}{100} * x = 2450[/tex]
Simplifying:
[tex]10x = 2450 * 100 \\\\10x = 245000\\\\x = 245000 / 10[/tex]
=> x = $24500
Their total budget of this year is $24500.
Since they will spend $2000 more this year than last year, we have to deduct $2000 from this year's budget to find last year's.
This means that their budget last year was:
$24500 - $2000 = $22500
Their budget last year was $22500.
In the right triangle shown, mZA = 30° and BC = 6/2.
How long is AC?
Answer:
x = 18
Step-by-step explanation:
Since 30-60-90 triangles have a side ratio of y : y√3 : 2y.
Since 2y, here, is 12√3, then y is 6√3.
This means that the side x, is 6√3 * √3, which is:
x = 6√3 * √3
= 6 * 3
x = 18
Add the polynomials:
6a - 4b+cand 4a + 4b+c
Step-by-step explanation:
6a - 4b + c + 4a + 4b + c
Solving like terms
10a + 2c
Because - 4b + 4b = 0
10.6771 to the nearest tenth
Bonnie had 1 one-dollar bill, 2 five-dollar bills, and 2 ten-dollar bills in her pocket. She randomly took 3 bills from her pocket. How much money could Bonnie have taken from her pocket?
Answer:
There are 5 different outcomes, $30, $21, $20, $16 and $11.
Step-by-step explanation:
Bonnie has a total of 6 bills in her pocket. If she takes 3 random bills, this means that there are 20 different possibilities but the five dollar bills and ten dollar bills are not indistinctive so the number is not 20 for this example.
She can take the 1 dollar bill and the two 5 dollar bills which would make 11 dollars.
She can take the 1 dollar bill and the two 10 dollar bills which would make 21 dollars.
She can take the 1 dollar bill, one 5 dollar bill and one 10 dollar bills which would make 16 dollars.
She can take two 5 dollar bills and one 10 dollar bill which would make 20 dollars.
She can take two 10 dollar bills and one 5 dollar bill which would make 30 dollars.
So there are 5 different outcomes, $30, $21, $20, $16 and $11.
I hope this answer helps.
Final answer:
Bonnie could have possibly drawn $11, $21, $20, or $25 by selecting any 3 bills out of 1 one-dollar bill, 2 five-dollar bills, and 2 ten-dollar bills.
Explanation:
The question concerns the amount of money Bonnie could have taken from her pocket after randomly selecting 3 bills. To answer this, let's consider her initial set of bills: 1 one-dollar bill, 2 five-dollar bills, and 2 ten-dollar bills.
Here are the possible combinations of 3 bills she could draw:
1 one-dollar bill and 2 five-dollar bills: $1 + $5 + $5 = $11
1 one-dollar bill and 2 ten-dollar bills: $1 + $10 + $10 = $21
2 five-dollar bills and 1 ten-dollar bill: $5 + $5 + $10 = $20
1 five-dollar bill and 2 ten-dollar bills: $5 + $10 + $10 = $25
Therefore, the amounts of money Bonnie could have drawn are $11, $21, $20, and $25.
how many meters longer is 3 meters than 3 yards
Answer:
0.2568 mStep-by-step explanation:
How many meters longer is 3 meters than 3 yards?
Yard to meter
1 yard = 0.9144 mThe difference:
3 meters - 3 yards = 3*( 1 - 0.9144) m =0.2568 mAnswer:
0.279
Step-by-step explanation:
3 meters = 3.279 yards
~Subtract to find the difference
3.279 - 3 = 0.279
As you can see, 3 meters if larger than 3 yards.
Best of Luck!
Find the zeros: 5w=35
Answer:
w=7
Step-by-step explanation:
Answer:
I want brainliest
Step-by-step explanation:
5w=35
w=7
Solve the equation 1 4 (16 + 12x) = 28 by first using the distributive property. The equivalent equation is found by distributing the One-fourth to get . The first step is . The second step is . The answer is .
Answer:
The equivalent equation is found by distributing the 1/4 to get 4 + 3x = 28
The first step is subtract 4 to both sides.
The second step is divide both sides by 3.
The answer is x = 8.
Step-by-step explanation:
Answer:
Divide by 1/4
Subtract
Divide
8
Step-by-step explanation:
a bullet fired from a gun traveled 3,600 m south in 6.0 seconds. What was its velocity in (a) m/sec and (b) km/hour?
Step-by-step explanation:
Velocity = Displacement/Time
a) Velocity in m/s = 3600m/6s
= 600m/s
b) (Converting m into km)
1000m = 1km
3600m = ?
3600/1000 = 3.6km
(Converting secs to hours)
1mins = 60secs
60mins = ?
60 * 60 = 3600 secs
This means there are 3600 secs in 1 hour
3600secs = 1hour
6.0 secs = ?
6.0/3600 = 0.00167 hours (approximately)
Velocity in km/h = 3.6km/0.00167h
= 2155.69km/h (approximately)
In summary...
a) 600m/s
b) 2155.69km/h
The bullet's velocity is 600 meters per second (m/s) and also 2,160 kilometers per hour (km/h), calculated by dividing the distance traveled by the time taken and converting the units accordingly.
To find out the bullet's velocity in meters per second (m/s), you'll need to use the formula for velocity which is distance traveled divided by the time taken. Here, the bullet traveled 3,600 meters in 6.0 seconds.
Velocity in m/s = Distance / Time
Velocity in m/s = [tex]\frac{3600}{6}[/tex]
Velocity in m/s = 600 m/s
For velocity in kilometers per hour (km/h), first convert meters to kilometers by dividing by 1,000 and then convert seconds to hours by dividing by 3,600 (the number of seconds in an hour).
Velocity in km/h =[tex]\frac{ (Velocity in m/s x 3,600) }{1000}[/tex]
Velocity in km/h = [tex]\frac{(600 m/s x 3,600) }{1000}[/tex]
Velocity in km/h = 2,160,000 / 1,000
Velocity in km/h = 2,160 km/h
Therefore, the bullet's velocity is 600 m/s and 2,160 km/h.
If y = 3x squared + 4 find the value of y when x = 2
Answer:
The value of y is 16.
Step-by-step explanation:
You have to substitute x = 2 into the equation :
[tex]y = {3x}^{2} + 4[/tex]
Let x = 2,
[tex]y = 3( {2)}^{2} + 4[/tex]
[tex]y = 3(4) + 4[/tex]
[tex]y = 12 + 4[/tex]
[tex]y = 16[/tex]
Answer:
y = 16
Step-by-step explanation:
Let's solve your equation together
3x^2 + 4
We have been given that x = 2
So first we must replace x by 2.
y = 3(2)^2 + 4
Now we solve the equation
2^2 = 4
y = 3(4) + 4
3 * 4 = 12
y = 12 + 4
12 + 4 = 16
y = 16
Hope this helps :)
California has a land area of 163,676 mi2 and a population of 39.51 million people. Find the population density of California to the nearest tenth
answer choices
241.4 people per mi2
4142.6 people per mi2
24.1 people per mi2
0.004 people per mi2
Answer:
(A)241.4 people per mi²
Step-by-step explanation:
California's Population=39.51 million=39,510,000
California's Land Area=163,676 mi²
Population Density=Population ÷Area
=39,510,000÷163,676
=241.39
≈241.4 people per mi² (correct to the nearest tenth)
Is 600,000,25 greater than 62,500
Answer:
Yes
Step-by-step explanation:
Yes, 600,000,25 is greater than 62,500.
What is 2.85 to the nearest hundredth I ready
Answer: 2.85
Rounded to the nearest 0.01
2.85 rounded to the nearest hundredth is 2.85
Answer:
2.9
Step-by-step explanation:
An item is regularly priced at $85. Juan bought it on sale for 55% off the regular price. How much did Juan pay?
What is the radius and diameter of the following circle?
7.5 cm
Radius =
cm
Diameter
=
cm
Answer:
radius=7.5cm
diameter=15cm
Step-by-step explanation:
diameter=2radius
=2×7.5
=15
Write the system of equations corresponding to the augmented matrix shown below ⎡⎣⎢⎢−8−2150−9−6−11−21−1⎤⎦⎥⎥ Note: Write an equation in each answer field and do not solve the system.
the system of equations corresponding to the augmented matrix is:
-8x - 2y - 1z = -15 ,0x - 9y - 6z = -11 ,-2x + 1y - 21z = -1
what is augmented matrix ?
An augmented matrix is a way of representing a system of linear equations in a matrix form. It consists of a rectangular array of numbers, where the coefficients of the variables in each equation are placed in one part of the matrix
In the given question,
To write the system of equations corresponding to the augmented matrix, we need to represent the coefficients and constants of the variables.
The given augmented matrix corresponds to the following system of linear equations:
-8x - 2y - 1z = -15
0x - 9y - 6z = -11
-2x + 1y - 21z = -1
where x, y, and z are variables.
Therefore, the system of equations corresponding to the augmented matrix is:
-8x - 2y - 1z = -15
0x - 9y - 6z = -11
-2x + 1y - 21z = -1
To know more about augmented matrix, visit:
https://brainly.com/question/16796667
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Objects in free fall are constantly picking up speed as they fall back to Earth (prior to reaching terminal velocity).
Answer:
i think true but im not sure
Step-by-step explanation:
let f(x) = 4x - 5 ; g(x) = 6x - 3
find 2f(x) + 3g(x)
select the correct response:
1. 8x - 13
2. 10x + 1
3. 26x - 19
4. -24x -21
Answer:
the answer is 3: 26x-19
Step-by-step explanation:
f(x)=4x-5 g(x)=6x-3
2f(x)+3g(x)
=2*(4x-5)+3*(6x-3)
=8x-10+18x-9
26x-19
help Evaluate: -18 + 4(6 ÷ 2)^2
Answer:
18
Step-by-step explanation:
6 divided by 2 is 3, 3 to the power of 2 is 9, 9 times 4 is 36, 36 plus -18 is 18.
Answer:
18
Step-by-step explanation:
-18 + 4(6 ÷ 2)^2
PEMDAS says parentheses first
-18 + 4(3)^2
Then exponents
-18 + 4*9
Then multiply and divide
-18 +36
Then add and subtract
18
Find the limit of the sequence of partial sums whose general term is [tex]a_n=\frac{100^n}{n!}[/tex]
10
1
DNE
0
I am torn between the limit not existing and it being = 0.
Thank you so much.
Answer:
0
Step-by-step explanation:
If ∑aₙ converges, then lim(n→∞)aₙ = 0.
Using ratio test, we can determine if the series converges:
If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.
If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.
lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) / (100ⁿ / n!)|
lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) × (n! / 100ⁿ)|
lim(n→∞) |(100 / (n+1)|
0 < 1
The series converges. Therefore, lim(n→∞)aₙ = 0.
what is the area of a room that is 3 3/4 yards long and 3 1/3 yards wide
Answer:
12 1/2 yd^2
Step-by-step explanation:
The area is length times width
A = 3 3/4 * 3 1/3
Change to improper fractions
A = 15/4 * 10/3
Rewriting
A = 15/3 * 10/4
= 5 * 5/2
= 25/2
Changing back to a mixed number
= 12 1/2
Answer:
12½ yards²
Step-by-step explanation:
Area = length × width
Area = 3¾ × 3⅓
= 15/4 × 10/3
= 25/2
= 12½ yards²
when expanded 4x(3 Plus x)
Answer:
The answer is 12x + 4x².
Step-by-step explanation:
You have to expand it using Distributive Law :
[tex]4x(3 + x)[/tex]
[tex] = 4x(3) + 4x(x)[/tex]
[tex] = 12x + 4 {x}^{2} [/tex]
simplify 8x - 2y + x + x
Answer:
10x-2y
Step-by-step explanation:
the x's are really 1x
8x+1x+1x
=10x
the 2y stays the same so you end up with
10x-2y
Consider the expression 7x2 + 9 + 3x. Tell whether each statement is
True or False.
a. The expression has three terms.
b. The coefficient of x is 3.
c. The expression can be simplified to 10x2 + 9.
d. The constant term is 9.
Answer:
A is false
b is true
c is false
d is false
Step-by-step explanation:
Final answer:
In this response, the terms of the given algebraic expression are identified, coefficients are determined, and simplification possibilities are explored.
Explanation:
a. True: The expression 7x2 + 9 + 3x has three terms.
b. True: The coefficient of x is 3.
c. False: The expression cannot be simplified to 10x2 + 9. It remains as 7x2 + 9 + 3x.
d. True: The constant term in the expression is 9.
What are the solutions to the quadratic equation 3(x - 4)2 = 75?
O x= -9 and x = 1
x= -5 and x = 5
O x = -4 and x = 4
Ox= -1 and x = 9
OOO
Answer:
x = -1 and x = 9
Step-by-step explanation:
3(x-4)^2 = 75
(x-4)^2 = 75/3 = 25
(x-4)=[tex]\sqrt25[/tex]
(x-4)= 5 or (x-4)=-5
x=9 or x= -1
Final answer:
To solve the quadratic equation 3(x - 4)^2 = 75, we isolate the squared term, take the square root of both sides, and solve for x, which gives us the solutions x = -1 and x = 9.
Explanation:
The equation given is 3(x - 4)2 = 75. To solve for x, follow these steps:
Divide both sides of the equation by 3 to isolate the squared term: (x - 4)2 = 25.Take the square root of both sides of the equation to remove the exponent: x - 4 = ±5.Add 4 to both sides of the equation to solve for x: x = 4 ± 5.So, the solutions to the equation are x = -1 and x = 9.
what is first even number that is a multiple of 5 and 7?
Answer:
Step-by-step explanation:
5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60
Answer:
70
Step-by-step explanation:
the multiples of 5 are as follows -
5,10,15,20,25,30,35,40,45,50,55,60,65,70
the multiples of 7 are as follows -
7,14,21,28,35,42,49,56,63,70
from what is shown, 70 is the only first common multiple of the two numbers
i hope this helps! :)
please help me out on this!