Answer:
s(t) = 160/3 ( 1 - e^(-3t / 200) )
Step-by-step explanation:
volume of pure water in tank = 1000 L
Brine contains 0.04kg of salt/L
Inflow rate of Brine containing 0.04kg of salt/L = 5L/min
Brine containing 0.06 kg of salt/L
Inflow rate of Brine containing 0.06 kg of salt/L = 10L/min
Solution is thoroughly mixed and drains from tank at 15L/min
a) Determine the amount of salt is in the tank after t minutes
rate of salt entering = 0.2 + 0.6 = 0.8 kg/min
rate of salt leaving = s/1000 * 15
amount of salt at time (t) = s(t)
initial condition s( 0 ) = 0
ds/dt = 0.8 - 15s/1000 = 0.8 - 3s/200
200 ds/dt = ( 160 - 3s )
-200/3 In ( 160 - 3s ) = t + c
Given that ; t = 0 , s = 0
c = - 200/3 In ( 160 )
∴ -200/3 In ( 160 - 3s ) = t - 200/3 In ( 160 )
- 200/3 [ In ( 60 - 3s ) - In ( 160 ) ] = t
therefore:
In ( 160 - 3s / 160 ) = -3t/200
= ( 160 - 3s / 160 ) = e ^ (-3t/200 )
Hence amount of salt in tank after t minutes
s(t) = 160/3 ( 1 - e^(-3t / 200) )
help me moderate helping me
Problem 1
It's not clear if the person deposits at the start of the quarter, or at the end of the quarter. I'm going to assume they deposit at the end of the quarter. This means we go with an ordinary future value of annuity.
The formula we use is
F = P*( (1+i)^n - 1)/i
where,
F = future value of the accountP = payment per periodi = interest rate per periodn = number of periodsIn this case,
F = 300,000P = unknown, what we want to solve fori = 0.08/4 = 0.02n = 25*4 = 100 quarters (equivalent to 25 years)So,
F = P*( (1+i)^n - 1)/i
300,000 = P*( (1+0.02)^100 - 1)/0.02
300,000 = P*(312.232305912618)
P = (300,000)/(312.232305912618)
P = 960.823061288088
P = 960.82
You must deposit $960.82 per quarter
If you deposit that amount of money per quarter, for 100 quarters, then you deposited a total of 960.82*100 = 96,082 dollars in total.
The amount of interest is 300,000 - 96,082 = 203,918 dollars
============================================================
Problem 2
We use the same formula from problem 1. This time we know the periodic payment ($250 per month) and we want to find the value of F
More specifically, we have this given info:
P = 250i = 0.072/12 = 0.006n = 30*12 = 360 months (aka 30 years)So,
F = P*( (1+i)^n - 1)/i
F = 250*( (1+0.006)^360 - 1)/0.006
F = 317,306.360545277
F = 317,306.36
If you deposit $250 per month, for 360 months, then you'll have $317,306.36 in the account.
This includes interest. The total amount deposited, without interest involved, is 250*360 = 90,000 dollars.
Therefore, the amount of interest earned is 317,306.36 - 90,000 = 227,306.36 dollars.
Suppose that from a group of 9 men, 1 will be randomly chosen for a dangerous assignment, and suppose that the chosen man will be killed during the assignment with a probability of 1/6. If Mark is one of the 9 men, what is the probability that he will be chosen for the assignment and killed during the assignment
Answer:
1/54
Step-by-step explanation:
1/9 x 1/6
The time to complete an exam is approximately Normal with a mean of 48 minutes and a standard deviation of 3 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.
Answer:
This means the average amount of time is 48 minutes but many people will do it in 45 to 51
Hope This Helps!!!
I WILL MARK BRAINLIEST TO WHOEVER ANSWERS CORRECTLY FIRST
Answer:
2 liter = 2000 ml
2000/250 = 8 bottles Step-by-step explanation:
A and B are independent events. Use the following probabilities to answer the question. Round to 4 decimal places.
P(A) = 0.32, P(A and B) = 0.09, find P(B)
P(B) =
Answer:
.2813
Step-by-step explanation:
If two events are independent that means that
A*B= A and B
so
let p(b)= x
.09=.32*x
x= .28125
Round this to
.2813
Step-by-step explanation:
since p(a) and p(b) are independent events
p(a).p(b)= p(a and b)
0.32×p(b)=0.09
p(b)=0.09÷0.32
p(b)=0.28
PLEASE IM BEGGING ILL GIVE YOU BRAINIEST:
100 students are interviewed to see which of biology, chemistry or physics they prefer.
17 of the students are girls. 3 of the girls like biology best.
24 of the boys prefer physics.
8 out of the 28 who prefer chemistry are girls.
What percentage of the students prefer biology?
Answer:
32%
Step-by-step explanation:
3 girls like biology, 8 like chem and the rest prefer physics. 28 people like chemistry, and 24 boys like physics. This leaves 29 boys and 3 girls liking bio.
Số tiếp theo (next number?): 25 50 99 196 388
Answer:
The correct answer is - 768.
Step-by-step explanation:
The given question is based on a specific pattern present in between the numbers in the given series -
Series = 25 50 99 196 388
to find - next number in series
let us find the relation between the initial two number:
25 - 50, here number 50 is two times of 25 or (x*2-0)
relation between 2nd and 3rd number:
50 - 99, here 99 is two times of 50 minus 1 or (x*2-1)
relation between 3rd and 4th number:
99 - 196, here 196 is two times of 99 minus 2 or (x*2-2)
relation between 4th and 5th number:
196 - 388, here 388 is the two times of 196 minus 4 or (x*2-4)
So on this pattern, the next number would be = x*2-8
388*2-8
= 768
Differentiate the function, y = (2x - 5)^2 (5-x^5)^2?
Answer:
[tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x⁵)²
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x^5)^2 + (2x - 5)^2\frac{d}{dx}[(5 - x^5)^2][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2-1} \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5)^{2-1} \cdot \frac{d}{dx}[-x^5]][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot \frac{d}{dx}[-x^5]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1(2x^{1 - 1})](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x^5)^2 - 10x^4(2x - 5)^2(5 - x^5)[/tex]Factor: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[2(5 - x^5) - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 5x⁴: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 10x^5 + 25x^4][/tex][Addition] Combine like terms (x⁵): [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)(10 - 12x^5 + 25x^4)[/tex]Rewrite: [tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
The net below has dimensions l = 14 feet, w = 7 feet, and h = 13 feet. How will the surface area of the figure change if the width decreases by 2 feet?
What is 9+10-8(9)x2 using bedmas
-125
Step-by-step explanation:BEDMAS, like its counterpart BODMAS, is used as an acronym which gives the order of precedence of certain mathematical operations. It stands for:
B - Brackets
E - Exponentials
D - Division
M - Multiplication
A - Addition
S - Subtraction
This specifies the order in which arithmetic operations take place. That is brackets expressions should be solved first, followed by exponentials, then division and so on.
Using BEDMAS, let's solve 9+10-8(9)x2
Follow these steps;
i. Solve the bracket first.
9+10-72x2
ii. Next solve the multiplication
9+10-144
iii. Then solve the addition
19-144
iv. Now, the subtraction
-125
Therefore;
9+10-8(9)x2 = -125 using bedmas
Cierto individuo, al fallecer, repartió sus ahorros del siguiente modo; la mitad a
su esposa; el tercio a su único hijo; la décima parte a un sobrino, y dos millones
de nuevos soles a una beneficencia ¿cuánto poseía?
Answer:
El individuo poseía treinta millones.
Step-by-step explanation:
Podemos expresar la repartición del individuo como sigue:
[tex] x = \frac{x}{2} + \frac{x}{3} + \frac{x}{10} + 2000000 [/tex]
Dado que la suma de la repartición de la mitad que le da a su esposa (x/2), del tercio que le da a su único hijo (x/3), de la décima parte que le da a un sobrino (x/10) y de los dos millones que le da a una beneficiencia debe ser igual al monto incial que tenía (x).
Resolviendo la ecuación de arriba para "x" tenemos:
[tex] x - \frac{x}{2} - \frac{x}{3} - \frac{x}{10} = 2000000 [/tex]
[tex] x = 30000000 [/tex]
Por lo tanto, el individuo poseía treinta millones.
Espero que te sea de utilidad!
what is a case control study
Answer:
A study that compares two groups of people: those with the disease or condition under study (cases) and a very similar group of people who do not have the disease or condition (controls). Researchers study the medical and lifestyle histories of the people in each group to learn what factors may be associated with the disease or condition. For example, one group may have been exposed to a particular substance that the other was not. Also called retrospective study.
Step-by-step explanation:
Answer:
A case-control study is designed to help determine if an exposure is associated with an outcome (i.e., disease or condition of interest).
Step-by-step explanation:
The Centers for Disease Control conducts an occasional study of youth behaviors that affect health. They randomly sample several thousand children between the ages of 10 and 18 in the United States and ask (with parents' permission) a series of questions. In a recent sample of 15000 randomly selected youth, 11% of them said that they had vaped on 1 or 2 days in the last 30 days. Which of the following best describes the number 111%?
a. 11% is a statistic and is represented symbolically as Ï = 0.11
b. 11% is a statistic and is represented symbolically as rho = 0.11
c. 11% is a parameter and is represented symbolically as rho=0.11
d. 11% is a parameter and is represented symbolically as Ï = 0.11
Answer:
b. 11% is a statistic and is represented symbolically as p = 0.11
Step-by-step explanation:
A statistic differ from a parameter in that, statistic is a numerical property or value derived from the sample while the parameter is a numerical property of the population. The percentage given, 11% who said that they had vaped on 1 or 2 days in the last 30 days is derived from the 15000 youths which is a sample and not a population, hence, 11% is a statistic, since it is expressed as a percentage, it is a proportion ;
Hence, 11% is a statistic and can be represented symbolically as p = 0.11
The line on the graph passes through the points A (1, 3) and B (7, 1).
YA
a) Calculate the gradient of line AB.
b) Find the gradient of a line perpendicular
to AB.
+
A
D
c) Find the equation of the line passing
through point (4, 2) and perpendicular
to AB.
Answer:
Step-by-step explanation:
a) gradient of AB
or
Slope of AB
[tex]Slope , m = \frac{y_B - y_A}{x_B - x_A}[/tex]
[tex]=\frac{1 - 3 }{7 - 1 } \\\\=\frac{-2}{6}\\\\=-\frac{1}{3}[/tex]
b)
when lines are perpendicular to each other, the product of their slope = - 1
That is ,
[tex]m_{AB} \times m_{perpendicular} = - 1 \\\\- \frac{1}{3} \times m_{perpendicular} = - 1\\\\m_{perpendicular} = - 1 \times \frac{-3}{1} = 3[/tex]
c) Equation of the line perpendicular to line AB and passing through ( 4 , 2 )
[tex]( y - y_1) = m_{perpendicular} ( x - x_1) \ where \ (x_1 , y_ 1 ) = ( 4 , 2 ) \\\\( y - 2 ) = 3(x - 4 ) \\\\y = 3x - 12 + 2\\\\y = 3x - 10[/tex]
(3√5 + 4√2)(√5 + √2）
Answer:
Step-by-step explanation:
3√5*√5+3√5*√2+ 4√2*√5+ 4√2*√2
15 +3√10 + 4√10 + 8
23+7√10
Which of the following sets of data does not contain an outlier?
A.16, 17, 20, 19.48
B.59. 60. 61, 67.65
C.95.99.97.94.60
D.-1.2.1.0.5.16
Answer:
it is a letter b
Step-by-step explanation:
that does not contain an outlet
If the radius of a sphere is halved, what happens to the volume of the sphere? Use your algebra skille te develop a formula for the reduced sphere, V, in terms of V.
Answer:
V₂ = V₁ / 8
Step-by-step explanation:
Volume of sphere with radius of 6 = 288π
Volume of sphere with radius of 3 = 36π
the difference in volume after radius is halved is reduced 8 times so formula could be:
V (when radius is halved) = prior volume ÷ 8
V₂ = V₁ / 8
the fraction 6/10 is equivalent to which of the following? 12/24 or 24/40 or 3/6 or 16/20
Answer:
24/40
Step-by-step explanation:
You can multiply both the numerator and denominator by any number
Option #3: Lets multiply by 1/2 since when you multiply 6*1/2 it equals 3 and that is the same numerator as option #3 and so now let's do the same again to the denominator 10*1/2 equals 5 and that is NOT equal to 6 in the denominator for option #3 and you can't get 3 any other way than multiplying by 1/2 (same as *.5) and so it is wrong.
Now since we know how to do it I'll just do the math for the rest.
Option 1:
6/10
6*2/10*2
12/20 and that doesn't match so it's wrong.
Option 2:
6/10
6*4/10*4
=
24/40
It matches so it's correct let's try option 4 just to check.
Option 4:
6/10
6*2/10*2
12/20
that doesn't match so it's wrong (you could have tried multiplying by decimals by I doubt you are there to that kind of math yet.)
Answer: 24/40
What type of number is 12/3
Choose all that apply.
Whole number
Integer
Rational
Irrational
Answer: Rational
Step-by-step explanation: bc
Solve the inequality: w - (14) < 8
[tex]w - (14) < 8 \\ = w < 8 + 14 \\ \\ w = < 22[/tex]
Step by Step Explanation:
Move the constant to the right - hand side and change its signThen add the numbers ☆彡Hanna#CarryOnLearning
Do the following lengths form a right triangle?
Answer:
Yes
Step-by-step explanation:
The lengths of this right angle triangle (6, 8, 10) proves that the polygon is indeed a right angle triangle. This is because there are certain ratios to prove that a right angle triangle is indeed a right angle triangle. These are called the Pythagorean Triples . Some examples include; (3, 4, 5), (7, 24, 25) and (28, 45, 53). The Pythagorean Triple 3, 4, 5 can be scaled up to provide the triple 6, 8, 10, where the scale factor is 2.
How to solve and answer
Answer:
D. (-2, 0) and (3, 0).
Step-by-step explanation:
At the x -intercepts the function = 0, so
(2x + 4)(x - 3) = 0
2x + 4 = 0 and x - 3 = 0
x = -4/2 = -2 and x = 3.
So they are (-2, 0) and (3, 0).
x = 3 or x = -2
Step-by-step explanation:
f(x) = (2x + 4)(x - 3)
y = (2x + 4)(x - 3)
x - intercept occurs when y = 0
0 = (2x + 4)(x - 3)
0 = 2x² - 6x + 4x - 12
2x² - 2x - 12 = 0
(2x² - 2x - 12)/2 = 0/2
x² - x - 6 = 0
From the quadratic formula,
x = (-b +- √(b² - 4ac))/2a
x = (- ( -1 ) +- √(( -1)² - 4( 1 )( -6 )))/2( -1 )
x = (1 +- √(1 - ( -24)))/-2
x = (1 +- √25)/-2
x = (1 +- 5)/-2
x = 3 or x = -2
A cube has side length x.
another side is doubled. The volume
One side of the cube is increased by 4 inches, and
of the new rectangular prism is 450 cubic inches. The equation 2x3 + 8x2 450
can be used to find x. What was the
side length of the original cube? Use a graphing calculator and a system of equations to find the answer.
• 4 inches
• 5 inches
• 9 inches
• 10 inches
Step-by-step explanation:
The length of the original cube is 5 inches.
Solve for 5x + 11 ≤ 67 = ?
9I will give brainliest.)
Answer:
x ≤ 11.20
Step-by-step explanation:
solve it like a regular equation
5x ≤ 67 - 11
5x ≤ 56
x ≤ 11 1/5
x ≤ 11.20
two(2) color game dice were tossed together. make lists of possible outcomes, if each color game die has pink, red, orange, blue, green, and yellow side UseP for pink, R for red, O for orange, B for blue, G for green, and Y for yellow. write your answers in your notebook
A mother has 6 sons
Each has a sister
How many people are in the family?
A:13.
B)8.
D)7.
C:14.
A. 13
Explanation= 6 (sons) +6 (daughters) +1 (mother) = 13.
(notes: as a father is not within the problem, there is no reason to be in the answer)
Answer:
B)8
A mother has 6 sons. If there is only one sister, than each son has a sister. Don't forget to add the mother. 6 + 1 + 1
Step-by-step explanation:
There are 3 urns A, B and C each containing a total of 10 marbles of which 2, 7 and 4 respectively are red. One of the urns is selected randomly and a marble is drawn from the selected urn. It is found that the marble is red. What is the probability that the red marble is taken from urn B
======================================================
Explanation:
We know that the marble selected is red, so we don't need to focus on the other colors.
7 red marbles are in urn B out of 2+7+4 = 13 total red marbles.
The probability the red marble came from urn B is therefore 7/13
230 kids took a survey and 111% like gym how many kids like gym
Answer:
255.3 people
If you mean 11%, then:
25.3 people
Step-by-step explanation:
[tex]\frac{y}{230} :\frac{111}{100}[/tex]
y × 100 = 230 × 111
100y = 25530
100y ÷ 100 = 25530 ÷ 100
y = 255.3
If you mean 11%, then:
[tex]\frac{y}{230} :\frac{11}{100}[/tex]
y × 100 = 230 × 11
100y = 2530
100y ÷ 100 = 2530 ÷ 100
y = 25.3
A filling machine fills bottles of nail polish with amounts that are normallydistributed with mean 18 mL and standard deviation 0.6 mL. A random sample of 12 bottles of this nail polish is selected for inspection.
Required:
a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?
b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?
Answer:
a. 0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish
b. 0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 18 mL and standard deviation 0.6 mL.
This means that [tex]\mu = 18, \sigma = 0.6[/tex]
a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?
This is the p-value of Z when X = 17.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{0.6}[/tex]
[tex]Z = -0.83[/tex]
[tex]Z = -0.83[/tex] has a p-value of 0.2033
0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish.
b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?
Twelve bottles, so now [tex]n = 12, s = \frac{0.6}{\sqrt{12}}[/tex]
The probability is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.5 - 18}{\frac{0.6}{\sqrt{12}}}[/tex]
[tex]Z = -2.89[/tex]
[tex]Z = -2.89[/tex] has a p-value of 0.0019
0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL
Anna's electricity bill costs $21.59 per month plus $4.66 per kilowatt hour. How many kilowatt hours can she use and keep
her bill to no more than $51?
Round your answer to a whole number
Answer:
6 kwh
Step-by-step explanation:
(51 - 21.9)/4.66 = 6.24 => 6 kwh