A large quantity of waste material contains metal. At the successive passes through a recovery
process the mass of the metal recovered is:
32kg at the first pass,
24kg at the second pass;
18kg at the third pass;
13,5kg at the fourth pass, and so on, to form a geometric sequence,
1. How much metal would be recovered at the eighth pass?
(Round off the answer to TWO decimal places)
Answer:
The amount of metal recovered at the eight pass is approximately 4.27 kg
Step-by-step explanation:
The mass of metal recovered formed the following geometric sequence;
32 kg, 24 kg, 18 kg, 13.5 kg
∴ The first term, a = 32 kg
The common ratio in the geometric sequence is found as follows;
r = a·r/a = 24 kg/(32 kg) = 0.75
r = a·r²/a·r = 18 kg/(24 kg) = 0.75
r = a·r³/a·r² = 13.5 kg/(18 kg) = 0.75
The mass of the metal recovered in the eight pass will be the 8th term of the geometric series given as follows;
nth term = a·rⁿ⁻¹
a = 32, r = 0.75, n = 8
∴ 8th term = 32·(0.75)⁸⁻¹ = 32·0.75⁷ = 2187/512 ≈ 4.27
The amount of metal recovered at the eight pass ≈ 4.27 kg.
The eight term of the geometric sequence is 4.27.
Geometric sequenceA geometric sequence is in the form:
aₙ = ar⁽ⁿ⁻¹⁾
where aₙ is the nth term, a is the first term and r is the common difference.
Given that a = 32, r = 24/32 = 0.75
The eight term is a₈ = 32(0.75)⁸⁻¹ = 4.27
The eight term of the geometric sequence is 4.27.
Find out more on Geometric sequence at: https://brainly.com/question/9300199
Solve and
graph this
inequality.
-3x>15
Answer:
x > -5
Step-by-step explanation:
-3x > 15
divide by -3
x > -5
Answer: x<-5
Step-by-step explanation:
First, we must isolate x in order to graph the inequality properly. To solve for x, you must divide each side by -3. Because you are dividing by a negative number, you must switch the side around. So, the inequality would be [tex]x<-5[/tex]t.To graph this, you must put a veritcal dotted line (since the equation has a less than symbol) and shade to the left (this shows all the possiblilties of what x could be. Or, if you were to graph it on a number line, put an open circle on -5 and draw an arrow left from the dot. Hope this helps!
HELP PLEASE!!!!!!!!!!
Volunteers at Sam's school use same of the student council's savings for a special project. They buy 3 backpacks for $6 each and fill each backpack with paper and pens that cost $6. By how much did the students council's savings change because of this project?
I need help with this please I don't understand my kids work
The volume of the rectangular pyramid is ___ cubic units.
Answer:
600 cubic units.
Step-by-step explanation:
The formula for a rectangular pyramid is[tex]V=\frac{lwh}{3}[/tex] or volume is equal to length x width x height divided by 3. The length is 15, the width is 10, and the height is 12. This equals to 1800, then we divide it by three for the answer.
will mark the best awnser :)
Answer:
15 square feet
Step-by-step explanation:
Which statement is true about the expression 4 (9+6)?
A: the expression has two factors
B: the expression has three coefficients
C: the expression has one variable
D: the expression has two variable terms
(YOULL BE MARKED BRAINLIST PLSSSS HELP)
don’t answer if you don’t know
i need help due asap
Step-by-step explanation
the third one
Step-by-step explanation:
Let's solve for y.
8x−3y>11
Step 1: Add -8x to both sides.
8x−3y+−8x>11 −8x −3y>−8x+11
Step 2: Divide both sides by -3.
−3y/−3 > −8x+11/−3
y<8/3x−11/3
Answer:
y<8/3x−11/3
Lincoln invested $2,800 in an account paying an interest rate of 5\tfrac{3}{8}5
8
3
% compounded continuously. Lily invested $2,800 in an account paying an interest rate of 5\tfrac{7}{8}5
8
7
% compounded quarterly. After 15 years, how much more money would Lily have in her account than Lincoln, to the nearest dollar?
Answer: 445
Step-by-step explanation:
Lincoln’s Final Amount:
Compounded Continuously: A=Pe^rt
P= 2800
r= 0.05375
t=15
A=2800e^0.05375(15)
A=2800e^0.80625
A=6270.5833
Lily’s final amount:
Compounded quarterly:
A=P(1+r/n)^nt
P=2800
r=0.05875
t=15
n=4
A=2800(1+ 0.05875/4)^4(15)
A=2800(1.0146875)^60
A=6715.7829
How much more money does Lily have?
6715.7829-6270.5835
=445.1994
The money would Lily have in her account than Lincoln, to the nearest dollar 445.
We have to determine the compound interest Lincoln’s final amount
Compounded Continuously
A=Pe^rt
P= 2800
r=0.05375
t=15
A=2800e^0.05375(15)
A=2800e^0.80625A=6270.5833
What is the formula for compound interest?
A=P(1+r/n)^nt
P=2800
r=0.05875
t=15
n=4
A=2800(1+ 0.05875/4)^4(15)
A=2800(1.0146875)^60
A=6715.7829
=6715.7829-6270.5835
=445.1994
Therefore money would Lily have in her account than Lincoln, to the nearest dollar 445.
To learn more about the interest visit:
https://brainly.com/question/2151013#SPJ2
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***WILL MARK BRAINLEST***
Find the y-intercept for the parabola defined by this equation: y = -x^2 - 2x + 3 separate the values with a comma
Answer:
y-intercept is (0, 3)
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y.
Help plz, just give me the points on the graph thanksss <33
melanie is using the spinner to play a card game. the spinner has six sections of equal size. What is the probability that melanie will have to take cards when she spins the spinner. A.1/6. B.1/4. C. 1/3. D.2/3. E.3/4
Answer:
The answer is very clear is 2/3
Step-by-step explanation:
5) Does the graph show a function? *
Answer:
yes
Step-by-step explanation:
I think
Is 14 19 23 a right triangle
Answer:no
Step-by-step explanation: because it is an acute triangle
I NEED HELP WIT DIS ASSIGNMENT ASAP
Factorise by using the product-sum method: x² + 11x + 24 *
Answer:
(x+3)(x+8)
Step-by-step explanation:
x² + 11x + 24 = (x+3)(x+8)
Can someone help? Will mark Brainliest
Answer: The answer is the 3rd one
Step-by-step explanation:
9514 1404 393
Answer:
(d) AE = (32√6)/3
Step-by-step explanation:
The side length ratios in a 30-60-90 triangle are 1 : √3 : 2. In a 45-45-90 triangle, they are 1 : 1 : √2.
So, we have the side length ratios ...
CE : CD = 2 : √3
BE : CE = √2 : 1
AE : BE = 2 : √3
Then the ratio AE : CE is ...
[tex]\dfrac{AE}{CD}=\dfrac{2}{\sqrt{3}}\cdot\dfrac{\sqrt{2}}{1}\cdot\dfrac{2}{\sqrt{3}}=\dfrac{4\sqrt{2}}{3}[/tex]
Multiplying by the length of CD, we have ...
AE = (8√3)(4√2)/3
AE = (32√6)/3 . . . . . matches the last choice
Find the missing sides of the triangle. Leave your answers in simplest radical form.
Answer5
34
Step-by-step explanation: 45
screenshot attached on the bottom
Answer: 1st circle 0.42n
Step-by-step explanation:
Answer:
p=0.42n
Step-by-step explanation:
Im not sure but if you do 2.52 divided by 6 you get 0.42 so my answer is A (p=0.42n)
Inez has $72 to buy video games each game costs $9 how many video games can Inez buy
Answer:
8
Step-by-step explanation:
1 video game = 9
? = 72
72/9=8
Answer:
8
Step-by-step explanation:
evaluate - |-7+3| please
Help
ASAP
Answer:
-|-4|
any number when we out from abslute value becomes positive so
-(4)=-4
How do you find an exponential growth model
Answer:
When the line of the graph is going up
Step-by-step explanation:
When the line is going down that means its a exponential decay :)
lani used 2 3s cup of raisins,3 8s cup of cranberries, and 3 4s cup of oatmeal to bake cookies. Which ingredient did lani use least amount of?
Answer:
Step-by-step explanation:
To compare the fractions, give them a common denominator.
⅔ = 16/24
⅜ = 9/24
¾ = 18/24
⅜ < ⅔ < ¾
Last one for today. Please help
Answer:
D) (-2,0)
Step-by-step explanation:
(-2,0)
(-2-2)²+(y+3)²=25
16+9=25
25=25
what is a decimal that is equivalent to the fraction 9/100
Answer:
0.09
Step-by-step explanation:
9/100 as a decimal is 0.09.
Answer:
0.09!
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
0.09 is your answer!
Hope this helped.
Signed ~Jaz~
Anyone know the correct answer to this?
Answer:
It should be y=4x-7
Step-by-step explanation:
M is the slope meaning Δx over Δy or rise over run
So if you look at (2,2) and count up to (3,6) the rise is 4 and the run is 1 meaning the slope is 4.
B is the y- intercept so then it would just be -7.
9514 1404 393Answer:
y=4x-6
Step-by-step explanation:
The line intersects the y-axis at y=-6, so that is the value of 'b' in the slope-intercept form.
The horizontal difference between marked points is 1 unit; the vertical difference is 4 units. That means the slope is . . .
m = rise/run = 4/1 = 4
Filling in these values (m=4, b=-6), we get ...
y = 4x -6
HURRY PLEASE I NEED THIS NOW
Find the time.
I = prt
Principal: $500
Rate: 5%
Interest earned: $25
Time: ?
Answer:
1 year
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year,
then, solving our equation
t = 25 / ( 500 × 0.05 ) = 1
t = 1 years
The time required to
accumulate simple interest of $ 25.00
from a principal of $ 500.00
at an interest rate of 5% per year
is 1 year.
What is the volume of a cylinder
Answer:
Step-by-step explanation:
i d k