YEsStep-by-step explanation:
The recursive formula for a geometric sequence is given below.
f(1) = 5
(n) = 3 . f(n − 1), for n > 2
What is the 7th term in the sequence?
Answer:
3645
Step-by-step explanation:
f(1)=5
f(2)=3*5=15.
f(3)=45, basically it's a geometric sequence with formula an=5*(3)^(n-1). The 7th term is 5*(3)^6=3645
If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as
V=5000 (1-1/50*t)^2 0⤠t ⤠50.
1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)
a. 5 min
b. 10 min
c. 20 min
d. 50 min
2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?
Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation
answer:
1) a) -180 gallons/minute ,
b) -160 gallons/minute
c) -120 gallons/minute
d) 0
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins
Step-by-step explanation:
Volume of tank = 5000 gallons
Time to drain = 50 minutes
Volume of water remaining after t minutes by Torricelli's law
V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )
1) Determine the rate at which water is draining from the tank
First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank
V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]
a) After t = 5minutes
V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]
= -180 gallons/minute
b) After t = 10 minutes
V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]
= - 160 gallons/minute
c) After t = 20 minutes
V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]
= -120 gallons/minute
d) After t = 50 minutes
V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]
= 0 gallons/minute
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins because no water flows out after 50 minutes
if my savings of $x grows 10 percent each year, how much will i have in 2 years?
Answer:
$240
Step-by-step explanation:
A year has 12 month in it so lets multiply the 10 by 12 which is $120,Mean a year is $120 so 2years will be $120×2 which is $240
Answer:
x+1/5x
Step-by-step explanation:
Because the eqaution would be x+10%=x+1/10+10%=1/5+x
Then the equation equals x+1/5
Which behavior would best describe someone who has good communication skills with customers ? a) Following up with some customers b) Talking to customers more than listening to them c) Repeating back what the customer says d) Interrupting customers frequently
Answer:
C. repeating back what the customer says
Michael is 4 times as old as Brandon and is also 27 years older than Brandon.
How old is Brandon?
Answer:
9
Step-by-step explanation:
b = Brandon
4b=b+27
-b -b
-------------
3b = 27
---- ----
3 3
b = 9
Brandon is 9 years old.
if x, y, and z are positive integers and 2^x * 3^y * 5^z = 54,000, what is the value of x + y + z
Given:
If x, y, and z are positive integers, then
[tex]2^x\times 3^y\times 5^z=54000[/tex]
To find:
The value of [tex]x+y+z[/tex].
Solution:
First we need to find the prime factors of 54000.
[tex]54000=2\times 2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5[/tex]
[tex]54000=2^4\times 3^3\times 5^3[/tex] ...(i)
We have,
[tex]54000=2^x\times 3^y\times 5^z[/tex] ...(ii)
On comparing (i) and (ii), we get [tex]x=4,y=3,z=3[/tex].
The sum of [tex]x,y,z[/tex] is:
[tex]x+y+z=4+3+3[/tex]
[tex]x+y+z=10[/tex]
Therefore, the value of [tex]x+y+z[/tex] is 10.
[18].Simplify (TTE): x(2x+y+5) - 2(x²+xy+5) + y(x + y)
Answer:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
Step-by-step explanation:
Given
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Required
Simplify
We have:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Open brackets
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]
Collect like terms
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
35 + 3 x n with n = 7
From September 1991 to September 1994 the enrollment at a particular school declined by 20 percent. If the number of students enrolled at that school in September 1994 was 720, what was the enrollment in September 1991
Answer:
900
Step-by-step explanation:
Given that :
Enrollment declined by 20% from between September 1991 to September 1994
This means there was a reduction in enrollment ;
Enrollment in September 1994 = 720
Enrollment in September 1991 = x
Hence,
Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991
720 = (1 - 20%) * x
720 = (1 - 0.2) * x
720 = 0.8x
720 / 0.8 = 0.8x/0.8
900 = x
Hence, Enrollment in September 1991 = 900 enrollments
A coin is tossed and a die is rolled. Find the probability of getting a head and a number greater than 1.
___.
(Type an integer or a simplified fraction.)
Answer:
5/12
Step-by-step explanation:
Heads: 1/2
Number greater than 1
A dice has 6 sides. 5 are greater than 1
The probability is 5/6
P(heads and a die greater than 1) = 1/2 * 5/6 = 5/12 or a little less than 1/2
Find the value of [(33.7)² - (15.3)²]^½ leaving your answer correct to 4 significant figures
Answer:
30.03
Step-by-step explanation:
[(33.7)² - (15.3)²]^½
= [1135.69 - 234.09]^½
= [901.6]^½
= 30.02665483
= 30.03 (4sf)
A package contains 12 resistors, 3 of which are defective. If 4 are selected, find the probability of getting
Answer:
Incomplete question, but I gave a primer on the hypergeometric distribution, which is used to solve this question, so just the formula has to be applied to find the desired probabilities.
Step-by-step explanation:
The resistors are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
12 resistors, which means that [tex]N = 12[/tex]
3 defective, which means that [tex]k = 3[/tex]
4 are selected, which means that [tex]n = 4[/tex]
To find an specific probability, that is, of x defectives:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = x) = h(x,12,4,3) = \frac{C_{3,x}*C_{9,4-x}}{C_{12,4}}[/tex]
Conan puts tennis balls into tubes after gym class. There are 17 tennis balls, and each tube holds 3 balls. How many tubes does Conan completely fill? How many tennis balls are left?
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
write your answer in simplest radical form
Answer:
z = √3
Step-by-step explanation:
sin (30°) = z / 2√3
z = sin (30°) 2√3
z = √3
ALGEBRA 2 SIMPLIFY THE EXPRESSION
Step-by-step explanation:
here's the answer to your question
(x/4) + (2x/7 =135 solve it
Answer:
the ans is 252................
Solve for x
-1/2x + 3 = -x + 7
Answer:
8
Step-by-step explanation:
If you add x to the left side of the equation you get positive 1/2x +3=7
you then would subtract 3 from 7 to get 4
this would leave you with 1/2x=4
if you divide 4 by 1/2 you get 8 as the answer.
e movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. How could you correctly rewrite the equation 4(10+5) = 6(12 - 2) using the distributive property
9514 1404 393
Answer:
4·10 +4·5 = 6·12 -6·2
Step-by-step explanation:
Each outside factor multiplies each inside term.
4(10 +5) = 6(12 -2)
4·10 +4·5 = 6·12 -6·2
A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?
Answer:
dv = surface area * dh
so
dv/dt = surface area * dh/dt
width at surface = 40 + (80-40)(30/40)
= 40 + 30 = 70 cm = 0.70 m
so
surface area = 9 * .7 = 6.3 m^2
so
.3 m^3/min = 6.3 m^2 * dh/dt
and
dh/dt = .047 meters/min or 4.7 cm/min
Step-by-step explanation:
PLZ ANSWER QUESTION IN PICTURE
Answer: y = 3x + 6
Step-by-step explanation:
(x-intercept of -2: (-2,0))
(slope = m)
y = mx + b, (-2,0), m = 3
[tex]y=mx+b\\0=3(-2)+b\\0=-6+b\\b=6\\y=3x+6[/tex]
A car which was advertised for sale for 95000, was ultimately sold for 83600. Find the percent reduction in the price?
Answer: 12%
Step-by-step explanation:
95,000-83,600=11,400
(11,400/95000)(100) = 12%
The percentage reduction in the price of the car is 12%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Original price of car=95000 and Selling price=83600
Thus the reduction in price= 95000-83600
=11400
Thus percentage reduction in the price of the car is
= 11400/95000 × 100
=12%
Hence, The percentage reduction in the price of the car is 12%
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ2
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 70% salt. She wants to obtain 30 ounces of a mixture that is 60% salt. How many ounces of each solution should she use?
Answer:
Let x = the number of ounces of Solution A
Let y = the number of ounces of Solution B
x + y = 180 y = 180 - x
.60x + .85y = .75(180)
.60x + .85y = 135 Multiply both sides of the equation by 100 to remove the decimal points.
60x + 85y = 13500
60x + 85(180 - x) = 13500
60x + 15300 - 85x = 13500
-25x = -1800
x = 72ounces
y = 180 - 72
y = 108 ounces
Step-by-step explanation:
Wyzant (ask an expert) solution on their website.
Find the missing side of the triangle
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Pytago:
x[tex]x^{2} +7^{2} = 9^{2} \\\\x = \sqrt{9^{2} - 7^{2} } x = 4\sqrt{2}[/tex]
I am struggling and I would be so happy if any of you helped me. Can someone help me with the last two red boxes please? The rest of the question is for reference to help solve the problem. Thank you for your time!
Answer:
I think you can go with:
The margin of error is equal to half the width of the entire confidence interval.
so try .74 ± = [ .724 , .756] as the confidence interval
Step-by-step explanation:
the guys is wrong i checked
Step-by-step explanation:
the guys is wrong i checked
PLEASE HELP THIS IS DUE ASAP!!!!!!!!!!!!!!
the answer is 1/12
the first rolling a 4 has a 1/6 chance of happening and half of the numbers on the die are odd, so 1/6*1/2=1/12
4) The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center, find the total mass of the given rod and the center of the mass
Answer:
a. 16 slug b. 3.2 ft
Step-by-step explanation:
a. Total mass of the rod
Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x
So, λ ∝ x³
λ = kx³
Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,
k = λ/x³ = λ/(L/2)³ = 8λ/L³
substituting the values of the variables into the equation, we have
k = 8λ/L³
k = 8 × 2/4³
k = 16/64
k = 1/4
So, λ = kx³ = x³/4
The mass of a small length element of the rod dx is dm = λdx
So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft
M = ∫₀⁴dm
= ∫₀⁴λdx
= ∫₀⁴(x³/4)dx
= (1/4)∫₀⁴x³dx
= (1/4)[x⁴/4]₀⁴
= (1/16)[4⁴ - 0⁴]
= (256 - 0)/16
= 256/16
= 16 slug
b. The center of mass of the rod
Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm = λxdx = (x³/4)xdx = (x⁴/4)dx.
We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft
The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod
= (1/4)∫₀⁴x⁴dx/M
= (1/4)[x⁵/5]₀⁴/M
= (1/20)[x⁵]₀⁴/M
= (1/20)[4⁵ - 0⁵]/M
= (1/20)[1024 - 0]/M
= (1/20)[1024]/M
Since M = 16, we have
x' = (1/20)[1024]/16
x' = 64/20
x' = 3.2 ft
Use the order of operations to simplify 3/4+8(2.50-0.5).
Answer:
16[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Find the area of a triangle as a mixed number.
Answer:
I believe the answer is 4 37/50!
