Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.
The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation
dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min
or, more succintly,
x' = -1/100 x
This equation is separable as
dx/x = -1/100 dt
Integrating both sides gives
∫ dx/x = -1/100 ∫ dt
ln|x| = -1/100 t + C
x = exp(-1/100 t + C )
x = C exp(-t/100)
(a) Using the initial condition x (0) = 18, we find
18 = C exp(0) ==> C = 18
so that
x(t) = 18 exp(-t/100)
(b) After 20 minutes, we have
x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74
so the tank contains approximately 14.74 kg of salt after this time.
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample? Make sure to give a whole number answer.
Answer:
The administrator should sample 968 students.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.88}{2} = 0.06[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.06 = 0.94[/tex], so Z = 1.555.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 300.
This means that [tex]n = 300[/tex]
If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 1.555\frac{300}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 300*1.555[/tex]
Dividing both sides by 15
[tex]\sqrt{n} = 20*1.555[/tex]
[tex](\sqrt{n})^2 = (20*1.555)^2[/tex]
[tex]n = 967.2[/tex]
Rounding up:
The administrator should sample 968 students.
Joe nas to take two quizzes tomorrow. He nas only enough time to study one of them. • The science quiz has 7 true-or-false questions. • The English quiz has 3 multiple-choice questions. Joe calculates the probability that he will get each question correct by guessing. ?
Answer:
C.
Step-by-step explanation:
Science questions are T/F. That's .5 or [tex]\frac{1}{2}[/tex] chance to get it right.
7 questions. Each with a [tex]\frac{1}{2}[/tex].
That's [tex](\frac{1}{2})^{7}[/tex]
[tex](\frac{1}{2})^{7}[/tex] = [tex]\frac{1}{128}[/tex] = .0078 = .008 rounded
English questions are multiple choice. 4 choices. That's .25 or [tex]\frac{1}{4}[/tex]
3 questions. Each [tex]\frac{1}{4}[/tex]
That's [tex](\frac{1}{4})^{3}[/tex]
[tex](\frac{1}{4})^{3}[/tex] = [tex]\frac{1}{64}[/tex] = .0156 = .016 rounded
The probability of getting all questions correct is 0.004 which is lower than for science (0.016).
Science questions are said to have a 6 out of 6 correct answer range and a 0.5 chance of being answered properly.
So, P(6) = 0.5⁶
P(6) = 0.016
We are informed that there are 4 out of 4 correct answers for English, with a 0.25 chance of getting it right.
Thus; P(4) = 0.25⁴ = 0.004
Thus, we conclude that they will have to study English.
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equation that passes 1,3 and slope of 2 in point slope form
Answer:
y-3 = 2(x-1)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-3 = 2(x-1)
Answer:
3=2x+1
Step-by-step explanation:
Use the equation y=mx+b
where y is the y component, x is the variable and b is the x intercept
resolver utilizando la regla de clamer
Answer:
pordondede donde eres?
Step-by-step explanation:
........................
Present value takes ____________.
A. Compounding rate.
B. Discounting rate.
C. Inflation rate.
D. Deflation rate
I need help answering this question asap
Answer:
Step-by-step explanation:
Abdul's gas tank is 1/3 full. After he buys 12 gallons of gas, it is 7/9 full. How many gallons can abdul's tank hold
Answer:
Abdul's tank can hold 27 gallons of gas.
Step-by-step explanation:
Given that Abdul's gas tank is 1/3 full, and after he buys 12 gallons of gas, it is 7/9 full, to determine how many gallons can Abdul's tank hold the following calculation must be performed:
1/3 = 0.3333
7/9 = 0.7777
0.777 - 0.333 = 0.444
0.444 = 12
1 = X
12 / 0.444 = X
27 = X
Therefore, Abdul's tank can hold 27 gallons of gas.
The lengths of two sides of the right triangle ABC shown in the illustration given
a= 7cm and b= 24cm
Answer:
25 cm.
Step-by-step explaination:
Given,
Two sides of a triangle:
a = 7cm
b = 24 cm
To find,
Third side:
c = ?
By Pythagorean Theorem;
a² + b² = c²
[where c is the longest side,hypotenuse]
Putting the value of a and b;
we get,
7² + 24² = c²
49 + 576 = c²
625 = c²
25² = c² (square root)
25 = c
c = 25
Therefore, the length of the third side will be equal to 25 cm.
The lengths of two sides of the right triangle ABC shown in the illustration given
a= 7cm and b= 24cm
Given,> a= 7cm
> b= 24cm
To find?Side c (third side)
Solution:-Using Pythagoras theorem,
▶️ a² + b² = c
▶️ 7cm ² + 24cm² = c²
▶️ 49cm + 576cm = c²
▶️ 625cm = c²
▶️ 25² = c² (25×25 = 625)
▶️ c = 25
The value of c is 25 cm.
if you run 250 ft of cable and lose rate 3.6 dB how much rate you lose at 100 ft
Answer:
99
Step-by-step explanation:
99
Marnie just finished setting herself up at a cozy spot at the airport. Her laptop is ready, phone within reach, and her papers are organized, but now, she's hungry. What should she do? a) Take her phone and laptop with her to get something to eat b) Leave her stuff, but get a snack really quickly O c) Put her coat over her laptop to hide it and go get a snack O d) Ask the person next to her to watch her stuff
Answer:
a) someone will steal her stuff in any other situation even if a stranger watches it
HELP OR IM GONNA FAIL pleasee!!!! Last one
What is the solution to the system of equations graphed below?
10
X= - x+2
y = 5x + 28
-10
Answer:
(-4,8)
Step-by-step explanation:
The solution to the system is where the lines intersect
The lines intersect at x=-4 , y = 8
(-4,8)
The entrance ticket for a carnival costs $89.97, which includes a royal meal
that costs $10.85, 1 play station game, and 3 water rides (Each water ride
costs the same price). The cost of a water ride is twice as that of a play
station game. Find the cost of a water ride. Estimate to the nearest tenths.
Subtract the meal:
89.97- 10.85 = 79.12
Let the play station game = x
A water ride is twice that so a water ride is 2x
There is 3 water rides : 3 x 2x =6x
The PlayStation game and water rides = 79.12
6x + x = 79.12
Simplify:
7x = 79.12
Divide both sides by 7:
X = 11.30
The PlayStation game is 11.30
The water ride = 2 x 11.30 = 22.60
What is the slope of the line that passes through the points (-9, 8) and (–21, 10)?
Write your answer in simplest form.
Answer:
-1/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 10-8)/(-21 - -9)
= ( 10-8)/(-21 +9)
= 2 /-12
= -1/6
Find the square root of (2-36i)/(2+3i)
Answer:
[tex]-8-6i[/tex]
Step-by-step explanation:
[tex]\frac{2-36i}{2+3i} * \frac{2-3 i}{2-3i}[/tex]
-104-78i /13
-8-6i
The square root of (2-36i)/(2+3i) is √(112-66i)/13.
The given expression is [tex]\frac{2-36i}{2+3i}[/tex].
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
Multiply both numerator and denominator by 2-3i.
Now, [tex]\frac{2-36i}{2+3i}\times\frac{2-3i}{2-3i}[/tex]
= [tex]\frac{(2-36i)(2-3i)}{(2+3i)(2-3i)}[/tex]
= [tex]\frac{(4-72i+6i-108i^2)}{4-9i^2}[/tex]
= [tex]\frac{(4-66i+108)}{4+9}[/tex]
= [tex]\frac{(112-66i)}{13}[/tex]
Now square root is √(112-66i)/13
Therefore, the square root of (2-36i)/(2+3i) is √(112-66i)/13.
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If the probability that an event occurs is 0.5 , the probability that the event does not occur is
Answer:
0.5
Step-by-step explanation:
P(that an event occurs) = 0.5
P(that an event does not occur) = 1 - P(that an event occurs)
= 1 - 0.5
= 0.5
Answer:
It is also 0.5
Step-by-step explanation:
From independent events:
[tex]{ \bf{p + q = 1}}[/tex]
p is probability for an event to occur (success).
q is probability for an event not to occur (failure).
[tex]{ \tt{0.5 + q = 1}} \\ { \tt{q = 1 - 0.5}} \\ { \tt{q = 0.5}}[/tex]
HELP PLS I DONT KNOW THIS ONE
Answer:
1
-------------
(x+2)(x-4)
Step-by-step explanation:
x+4 x+3
------------- * --------------
x^2+5x+6 x^2 -16
Factor
x+4 x+3
------------- * --------------
(x+3)(x+2) (x+4)(x-4)
Cancel like terms
1 1
------------- * --------------
(1)(x+2) (1)(x-4)
1
------------- x cannot equal -3, -4, -2, 4
(x+2)(x-4)
2x+3=60 thì x băng bao nhieu
Answer:
x=57/2
Step-by-step explanation:
2x+3=60
<=> 2x=57
=> x=57/2
Please find the missing ? Explanation need it
Answer:
the answer is 3.162
Step-by-step explanation:
Ryanair provides cheap flights in Europe but prides itself on their on-time record. Ryanair quotes a flight time of 2 hours, 5 minutes. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.
What is the expected flight time in minutes?
Answer:
The expected flight time is 2 hours 10 minutes
Step-by-step explanation:
Given
[tex]a = 2\ hours[/tex]
[tex]b = 2\ hours\ 20\ mins[/tex]
Required
The expected flight time
To do this, we simply calculate the mean using:
[tex]Mean = \frac{a + b}{2}[/tex]
So, we have:
[tex]Mean = \frac{2\ hours + 2\ hours\ 20\ mins}{2}[/tex]
[tex]Mean = \frac{4\ hours\ 20\ mins}{2}[/tex]
[tex]Mean = 2\ hours\ 10\ mins[/tex]
Simplify |3 − 11| − (15 ÷ 3 + 2) 2
A number increased by 100% and decreased by 20% is x. what is the number ? NEEDED TODAY
Answer:
Let's assume the number be 100.
According to the problem , 100 is increased by 100%.
So, new number will be 100+100=200
Now 200 will decreased by 20%.
So, 20% of 200= 0.20*200= 40.
So, again the number has been changed into 200+40=240.
So, x=240
Step-by-step explanation:
9514 1404 393
Answer:
x/1.6
Step-by-step explanation:
Let n represent the number. When n is increased by 100%, its new value is ...
n(1 +100%) = n(1 +1) = 2n
When this value is decreased by 20%, its new value is ...
(2n)(1 -20%) = (2n)(0.8) = 1.6n
This value is x, so the number is ...
1.6n = x
n = x/1.6 . . . . . . . divide both sides by 1.6
is the sequence 1/6, 1/2, 3/2,9/2 arithmetic, or geometric
Answer:
geometric
Step-by-step explanation:
A physicist examines 10 water samples for iron concentration. The mean iron concentration for the sample data is 0.711 cc/cubic meter with a standard deviation of 0.0816. Determine the 90% confidence interval for the population mean iron concentration. Assume the population is approximately normal.
Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 2 of 2: Construct the 90% confidence interval. Round your answer to three decimal places. Lower endpoint? Upper endpoint?
Answer:
Poggers
Step-by-step explanation:
A student-faculty committee consisting of 6 members is to be chosen from a pool of candidates consisting of 5 students and 7 faculty members. The committee must have at least 2 student members and at least 1 faculty member. How many possibilities are there
Answer:
[tex]T=812[/tex]
Step-by-step explanation:
From the question we are told that:
No. Committee Members [tex]n=6[/tex]
Pool of : 5 students and 7 faculty members
At least 2 student members and at least 1 faculty member
Generally the committee is mathematically given by
The Total Events are
[tex]T=(^5C_2*^7C_4)+(^5C_3)*(^7C_3)+(^5C_4)*(^7C_2)+(^5C_5)*(^7C_1)[/tex]
[tex]T=350+350+105+7[/tex]
[tex]T=812[/tex]
Find the missing length indicated
Answer:
x = 960
Step-by-step explanation:
x=√{576×(576+1024)}
or, x = √(576×1600)
or, x = √576×√1600
or, x = 24×40
or, x = 960
Answered by GAUTHMATH
Answer:
Step-by-step explanation:
These two cones are similar. What is the value of x?
Answer:
A
Step-by-step explanation:
Given that the cones are similar then corresponding dimensions are in proportion, that is
[tex]\frac{12}{2}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )
12x = 6 ( divide both sides by 12 )
x = 0.5 → A
35 POINTS HELP in the figure above the circle has center O and radius 6 what is the length of arc acb
Answer:
9.425 or 3π
Step-by-step explanation:
arc length = 2πr(θ/360)
The angle is 90˚ as indicated by the square symbol.
ABC = 2π6(90/360) = 9.425 or 3π
Round to the nearest whole number.
6.4
Answer:
6
Step-by-step explanation:
Therefore, the number 6.4 rounded to the nearest whole number is 6. * If the number you are rounding off is followed by 0,1,2,3,4, round the number down. To find 6.4 rounded to the nearest whole number.
Please Mark me brainliest
Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 8282 times and recording the number the ball lands on.
Answer:
No, binomial distribution cannot be applied.
Step-by-step explanation:
We known that a Binomial Distribution depends on provided experiment , a binomial distribution have only 2 outcomes. For example, when we flip a coin in the air, then the possible outcomes are Head and Tail.
But in the context, an American roulette wheel has [tex]37[/tex] outcomes. It means when we spin the American Roulette wheel, ball may lend on any of the numbers between 0 to 36. So there are more than [tex]2[/tex] outcomes.
Therefore, binomial distribution can not be applied here.
Two angles of a triangle have the same measure.
If two sides have lengths 15 and 20, what is the
greatest possible value of the perimeter of the
triangle?
9514 1404 393
Answer:
55 units
Step-by-step explanation:
If two angles have the same measure, the triangle is isosceles. That means two sides have the same measure. Since the two given sides are different measures, the remaining side must be one of those. The perimeter will be greatest if the congruent sides are the longest. The greatest perimeter is ...
15 + 20 + 20 = 55 . . . units
