Answer:
a
[tex]y(t) = 11e^{-\frac{t}{100} }[/tex]
b
[tex]y(20) = 9 \ kg[/tex]
Step-by-step explanation:
From the question we are told that
The volume of brine in the tank is [tex]V_L = 5000 \ L[/tex]
The mass of the salt is [tex]y(0)= 11 \ kg[/tex]
The rate at which water enters that tank is [tex]\r V = 50 \ L / min[/tex]
Generally the rate at which salt enters the tank is mathematically represented as
[tex]z = \frac{0}{V_L} * \r V[/tex]
=> [tex]z = \frac{0}{5000} * 50[/tex]
Here the zero implies that there is no salt entering the tank
Generally the rate at which salt leaves the tank is mathematically represented as
[tex]u = \frac{y(t)}{V_L} * \r V[/tex]
=> [tex]u = \frac{y(t)}{5000} * 50[/tex]
=> [tex]u = \frac{y(t)}{100}[/tex]
Generally the rate of salt flow in and out of the tank is
[tex]\frac{dy}{dt} = z - u[/tex]
=> [tex]\frac{dy}{dt} = - \frac{y(t)}{100}[/tex]
=> [tex]\frac{dy}{y} = -\frac{dt}{100}[/tex]
=> [tex]ln(y(t)) = -\frac{t}{100} + c[/tex]
at time t = 0 y(0) = 11
=> [tex]ln(11) = -\frac{0}{100} + c[/tex]
=> [tex]c = ln (11)[/tex]
So
[tex]ln(y(t)) = -\frac{t}{100} + ln (11)[/tex]
taking exponent of both sides
[tex]y(t)=e^{ -\frac{t}{100} + ln (11)}[/tex]
=> [tex]y(t) = e^{-\frac{t}{100} } * e^{ln(11)}[/tex]
=> [tex]y(t) = 11e^{-\frac{t}{100} }[/tex]
Generally at t = 20 minutes
The amount of salt in the tank is mathematically represented as
[tex]y(20) = 11e^{-\frac{20 }{100} }[/tex]
=> [tex]y(20) = 9 \ kg[/tex]
What is the the value of x?
x/2
= 5
Answer:
10
Step-by-step explanation:
x/2 =5
2 x x/2 = 2 x 5
2x5 = 10
Jack works after school. Each day he is paid a set amount, plus an hourly wage. Hours 1 1.5 2 2.5 3 Pay 18 23 28 33 38 Assume Jack works from 2:30 P.M. to 7:00 P.M. Using the function f(x) = 10x + 8, how much would he earn? A. $33 B. $35.50 C. $45 D. $53
Answer: C
Step-by-step explanation:
Answer:
Step-by-step explanation:
A chef at a restaurant uses 17 pounds of butter each day. About how many grams does the chef use each day?
answer
7711.07
Step-by-step explanation:
The chef uses 7,711.03 grams each day at a restaurant.
How to convert Pounds to Grams?The methodology to convert Pounds to Grams is relatively simple. To convert Pounds to Grams, you must multiply the unit by 453.59.
For example, if you have to convert 5 Pounds to Grams, you need to multiply 5 by 453.59.
A chef at a restaurant uses 17 pounds of butter each day.
We have to determine the number of grams the chef uses each day.
Since 1 pound (lb) is equal to 453.59 grams (g).
So 17 pounds = 453.59 × 17 = 7,711.03 grams
Thus, the chef uses 7,711.03 grams each day.
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A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 2 yards long and a plane view (from above) of the shed and field is shown below. Use this information for Parts A and B below.
Part A: Calculate the area of grass that the goat can eat.
Part B: What length of rope would enable the goat to eat 30 square yards of grass? Show all your reasoning.
Answer:
9.42 yd²3.57 ydStep-by-step explanation:
Part AThe area of circle with radius of 2 yd (the length of the rope) is:
A = π*r² = 3.14*2² = 12.56 yd²Since 1/4 of the circle is occupied by the shed, the area of the grass is:
12.56*3/4 = 9.42 yd²Part BLet the area be 30 yd², finding the r as per above formula:
3/4*3.14*r² = 30r² = 30*4/3*3.14r² = 12.74r = √12.74r = 3.57 ydin ABC, D∈AB so that AD;DB=1 : 3. If ACDB = 12ft2 Find AACD and AABC
Answer:
Area of [tex]\triangle[/tex]ACD = 4 [tex]ft^2[/tex]
Area of [tex]\triangle[/tex]ABC = 16 [tex]ft^2[/tex]
Step-by-step explanation:
Given that:
D is a point on AB.
and ABC is a triangle.
AD:DB = 1 : 3
Area of [tex]\triangle[/tex]CDB = 12 [tex]ft^2[/tex]
Kindly refer to the attached image as per the given dimensions and values.
To find:
Area of [tex]\triangle[/tex]ACD and Area of [tex]\triangle[/tex]ABC = ?
Solution:
Formula for area of a triangle = [tex]\frac{1}{2}\times Base \times Height[/tex]
The altitudes of triangles [tex]\triangle[/tex]CDB and [tex]\triangle[/tex]ACD are equal in dimensions.
Therefore the area of triangles [tex]\triangle[/tex]CDB and [tex]\triangle[/tex]ACD will be equal to the ratio of their bases.
Area of [tex]\triangle[/tex]ACD : Area of [tex]\triangle[/tex]CDB = AD: DB = 1 : 3
[tex]\Rightarrow[/tex] Area of [tex]\triangle[/tex]ACD = [tex]\frac{12}{3} = \bold{4 ft^2}[/tex]
Area of [tex]\triangle[/tex]ABC = Area of [tex]\triangle[/tex]ACD + Area of [tex]\triangle[/tex]CDB = 12 + 4 = 16 [tex]ft^2[/tex]
Therefore, the answer is:
Area of [tex]\triangle[/tex]ACD = 4 [tex]ft^2[/tex]
Area of [tex]\triangle[/tex]ABC = 16 [tex]ft^2[/tex]
A new hard drive costs $225, plus $40 per hour for labor. The linear equation y = 40x + 225 gives the cost y in dollars for x hours of labor. If Jane has $385 to spend on computer repairs, using plug and chug strategy for x hours of labor, what is the maximum number of hours the computer technician can work?
Answer:
Step-by-step explanation:
225+40h=y
225 + 40x = 385
-225 -225
------- -------
40x = 160
x= 4
Find the measure of angle b.
4)
36°
what do you guys think
Please help me guys
Answer:
c
Step-by-step explanation:
a corn vendor at a farmers market was selling a bag of 8 ears of corn for $2.56 anithert vendor was selling a bad of 12 for 4.32. which bag is the better deal?
PLEASE HELPPPPPP ILL GIVE 40 POINTS Why might the measured radii and circumferences not be exactly
proportional?
Answer:
are their more info
Step-by-step explanation:
Answer:
Because it goes through the origin and the line is straight but there is still the empty space between the 4 and 6.
Step-by-step explanation:
graph 3x-2y=6 how do you graph this in algebra
Answer:
I don't have algebra but I suggest looking it up and it might show you at the very top.
Step-by-step explanation:
Hope this helps you:)
please help! finding coordinates of a point :)
Answer:
Step-by-step explanation:
Follow the numbers.
Which two numbers below have a least common multiple of 48?
Answer:
its 3 and 16 just trust me
The least common multiple is divisible by both a and b. The two numbers below have a least common multiple of 48 is 3 and 16.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
The two numbers below have a least common multiple of 48 are,
3 and 16 ⇒ 3×16=48
Hence, the two numbers below have a least common multiple of 48 is 3 and 16.
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13x456+345 divided by 45x265-256=?
Answer:
7703.66666667
Step-by-step explanation:
Side XY of triangle XYZ is extended to point W, creating a linear pair with ∠WYZ and ∠XYZ.
Triangle X Y Z. Point W extends from side X Y. Angle Z is 36 degrees, angle Y is x degrees, and exterior angle W Y Z is 100 degrees.
What is the value of x?
64
80
100
180
I NEED HELP ON SOME MORE PROBLEMS ANYONE WILLING TO HELP???
Answer:
80
Step-by-step explanation:
Answer:
B (also known as 30)
Step-by-step explanation:
hope this helps!
In 4 hours, Luis rode 26 miles on his bicycle. What was
his hourly rate?
CTIONS: Use numbers, variables, and symbols to write
value of the variable.
Answer:
6.5 hours
Step-by-step explanation:
If Luis can ride 26 miles in 4 hours then you need to find out how much he can ride in 1 hour. Therefore you divide 26 miles into the hours he rode in to get 6.5
Therefore his hourly rate is 6.5
How many distinct ways are there to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row? Give your
answer as an integer.
Provide your answer below:
Answer:
144
Step-by-step explanation:
3x2x2
the sum is 12, and after that you do 12^2
the final answer is 144
The number of distinct ways to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row will be 144.
What is a permutation?A permutation is an act of arranging items or elements in the correct order.
There are 2 orange marbles, 2 clear marbles, and 3 yellow marbles.
Then the number of distinct ways to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row will be
⇒ (3 x 2 x 2)²
⇒ 12²
⇒ 144
More about the permutation link is given below.
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Please help me fast!!!!!
Answer:
75
Step-by-step explanation:
If both factors are negative then the product is positive.
Answer: -75
Step-by-step explanation: 15 times 5 equals 75
what is 2+2 my brain has been in circles about this
Answer:
hey welcome to Brainly, and 2 + 2 = 4
Step-by-step explanation:
2+2=4
3+3=6
4+4=8
5+5=10
and so on just keep adding 2
Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly two will end up being replaced under warranty?
Answer:
The required probability is 0.09875
Step-by-step explanation:
From the given information;
the probability of repairing the telephones = 0.70
the probability of the replaced = 0.30
Suppose we consider Mto denotes the telephone that is submitted for service while under warranty and must be replaced.
Then;
p = P(S) = P(replaced | submitted) P(submitted)
= 0.30 × 0.20
= 0.06
Now, the probability that exactly two will end up being replaced under warranty given that it assumes a binomial distribution where n = 10 and p = 0.06
[tex]P(X=2)=\bigg (^{10}_{2}\bigg) 0.06^2(1-0.06)^{10-2}[/tex]
[tex]P(X=2)=\dfrac{10!}{2!(10-2)!}\times 0.06^2\times (0.94)^{8}[/tex]
[tex]\mathbf{P(X=2)=0.09875}[/tex]
Use the expression 6.7s - (10÷2) +15 to answer 9–10. 9. Which part of the expression represents a quotient? Describe its parts. 10. Which part of the expression represents a product of two factors? Describe its parts. 9. The part of the expression that represents a quotient is. (Use the operation symbols in the math palette as needed. Do not simplify.)
Answer:
9. The part of the equation that represents a quoient is (10÷2) because inside the parentheses you solve the division equation and a quoitent is the answer to a division equation
10. The part of the expression that represents the product of two factors would be 6.7s because 6.7 is being multiplied by s, and a product is an answer to a multiplication problem
Step-by-step explanation:
9. The part of the equation that represents a quotient is (10÷2). 10. The part of the equation that represents the product of two elements is 6.7s.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
6.7s - (10÷2) +15
9. The part of the equation that represents a quotient is (10÷2) since the division equation is solved inside the parenthesis and a quotient is the answer to a division problem.
10. Here 6.7 is multiplied by s, the component of the equation that represents the product of two elements is 6.7s, and a product is an answer to a multiplication expression.
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If 5 workers take 600 hours to finish a project, how long will it take 10 workers to complete the same project?
Which equation is quadratic in form?
2(x + 5)2 + 8x + 5 + 6 = 0
x6 + 6x4 + 8 = 0
7x6 + 36x3 + 5 = 0
4x9 + 20x3 + 25 = 0
Answer:
I think it's the first one... but I'm not pretty sure.
Answer:
C
Step-by-step explanation:
edge 2020
Graph this Compound Inequality: x 9.8
Answer:
Step-by-step explanation:
The middle of 9 and 8
Determine if the lines are parallel, perpendicular, or neither. y + 3 = 7/4x and -4/7x + y = 9. Do I still have to solve y + 3 = 7/4x?
Answer:
No you dont have to solve it. And I believe it is perpendicular.
Step-by-step explanation:
Answer:
Perpendicular
Step-by-step explanation:
you have to solve both. If you make the lines in a graph it will turn out to be perpendicular because they are going to intersect.
GIVING BRAINLIEST IF CORRECT PLEASE HELP ASA[P
Answer:
Step-by-step explanation:
1: Green because it has more sections than the other colors
2: 4/8
Hope this helps!
Answer:
A) green
B) 4/8
brainliest please
IF UR GOOD AT PRECALC PLEASE HELP
Answer:
Answer is C, u can find this just by looking at domain
Find the z-score separating the lowest 9% of scores from the highest score of 91%
Answer:
I'm not sure of my answer but try this:
Solve for x.
Enter the number that belongs in the green box
Answer:
x = 45
Step-by-step explanation:
Because these are two congruent triangles inside of each other we can set up an equivalency ratio.
25/35 = x/65
Multiply both sides by 65 to get x alone
65 * 25/35 = x/65 * 65
(65 * 25)/35 = x1
1576/35 = x
x = 45
Hope this helps,
find the original price of a pair of shoes if the sale price is $40 after a 60% discount
Answer:
Thus, the original price of the pair of shoes was $100.
Step-by-step explanation:
Percentages
After a 60% discount, the sale price is now valued at 100-60=40% of its original price.
If the sale price is $40, then the original price is calculated as
$40 / 40 * 100 = $100
Thus, the original price of the pair of shoes was $100.
Verify applying 60% discount:
$100 - 60*$100/100 = $40
