Answer:
A) dS/dt = 2 - S/(100 + t) ; S(0) = 50
B) S(t) = (100 + t) - 5000/(100 + t)
C) 35%
Step-by-step explanation:
A) Let;
t = time in minutes
S = amount of syrup
dS/dt = rate at which syrup is flowing through tank
We are told that initially, the tank contains a mixture of 450 liters of cola and 50 liters of cherry syrup.
Thus,
At t = 0
Amount of cola = 450 litres
Amount of syrup = 50 litres
Total mixture = 450 + 50 = 500 litres
We are told that a well mixed solution of cherry cola is withdrawn at the rate of 5 liters per minute.
Thus, amount of liquid in the tank at a time "t" is; 500 + 5t
We are told that cherry syrup is added at the rate of 2 liters per minute.
Thus, rate at which syrup is flowing through tank is given as;
dS/dt = 2 - 5[S/(500 + 5t)]
Factorizing out, we have;
dS/dt = 2 - 5[S/5(100 + t)]
5 will cancel out to give;
dS/dt = 2 - S/(100 + t)
Since we have 50 liters of cherry syrup initially, the initial value problem is;
dS/dt = 2 - S/(100 + t) ; S(0) = 50
B) We have our initial value problem as;
dS/dt = 2 - S/(100 + t)
Rearranging, we have;
dS/dt + S/(100 + t) = 2
Multiplying through by 100 + t gives;
(dS/dt)•(100 + t) + S = 2(100 + t)
Integrating each term with respect to t gives;
(100 + t)S = (100 + t)² + c
Divide both sides by (100 + t) to get;
S = (100 + t) + c/(100 + t)
At t = 0;
S(0) = (100 + 0) + c/(100 + 0)
S(0) = 100 + c/100
Recall earlier in our initial value problem where we stated that S(0) = 50.
Thus;
100 + c/100 = 50
Subtract 100 from both sides to givw;
c/100 = 50 - 100
c/100 = -50
c = -50 × 100
c = -5000
Thus;
S(t) = (100 + t) - 5000/(100 + t)
C) The capacity of the tank is given as 1000 liters.
Earlier, we saw that amount of liquid in the tank at a time "t" is; 500 + 5t
Thus;
500 + 5t = 1000
5t = 1000 - 500
5t = 500
t = 500/5
t = 100 minutes
We want to find What percentage of the mixture is cherry syrup when the tank is full.
Thus we will plug in t = 100 minutes into S(t) = (100 + t) - 5000/(100 + t)
Thus;
S(100) = (100 + 100) - 5000/(100 + 100)
S(100) = 200 - 25
S(100) = 175 litres
We saw earlier that total mixture initially was 500 litres.
Thus, percentage of the mixture that is cherry syrup when the tank is full is;
175/500 × 100% = 35%
What is a real life word problem for (-7) + (7). Solve problem. Can you help?
Answer:
Step-by-step explanation:
Sally owes 7 dollars to Matthew. She opens her piggy bank and takes out 7 dollars. Now, how much money does she owe to Matthew?
-7 + 7 = 0
-7 + 7 is the same as 7 - 7
You can clearly see that 7-7 is 0.
Answer:
You are in debt of $7. You pay the bank $7. How many money do you owe now?
In a scale model of a product, a part has a volume of 20 inches cubed. If the product will be 4 times longer, 4 times wider, and 4 times taller than the model, then what will be the volume of the product?
Answer:
1280 in³Step-by-step explanation:
Volume of model v = 20 in³
The volume is the product of 3 dimensions
If each dimension will increase 4 times, then the volume of the product will be:
V = v*4*4*4 V = 20*64 = 1280 in³1. The waiting times (in minutes) of customers at a certain bank is given below. 5.5 6.5 6.7 7.2 6.4 7.3 (a) Construct a 95% confidence interval for the mean waiting time of all customers at the bank. (b) Based on the confidence interval in (a), will the bank manager be satisfied if she wishes the average waiting time in her bank to be less than 7 minutes
Answer:
The 95% confidence interval is
[tex] 5.92 < \mu < 7.284 [/tex]
Step-by-step explanation:
From the question we are told that
The data is 6.5 6.7 7.2 6.4 7.3
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{\sum x }{n}[/tex]
=> [tex]\= x = \frac{ 5.5 + 6.5 + \cdot 7.3 }{ 6}[/tex]
=> [tex]\= x = 6.6[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \frac{ \sum (x_i - \= x )^2 }{ n-1} }[/tex]
=> [tex]\sigma = \sqrt{ \frac{ (5.5 - 6.6 )^2 +(6.5 - 6.6 )^2 + \cdot + (7.3 - 6.6 )^2 }{ 6-1} }[/tex]
=> [tex]\sigma = 0.6512[/tex]
Gnerally the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 6 -1[/tex]
=> [tex]df = 5[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]t_{\frac{\alpha }{2} , 5 } = 2.571 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2}, 5 } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.571 * \frac{0.6512}{\sqrt{6} }[/tex]
=> [tex]E = 0.6835 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]6.6 - 0.6835 < \mu < 6.6 + 0.6835[/tex]
=> [tex] 5.92 < \mu < 7.284 [/tex]
What is the slope of the line? Input the ratio and choose
the correct units. Then click done.
Answer:
100/4
Step-by-step explanation:
Just took the test on iready it was right.
what's 2+2-2-4+77 and what is the square root of the sum
Answer:
simplified it is 75 the square root of 75 is 8.66025403784
Step-by-step explanation:
josephin is going on a run around the lake. she knows the distance around the lake. but she would like to complete her run in a certain amount of time. josephine knows she can use the formula d= rt.
which equation correctly rearranges the formula to find the time it will take her to run around the lake?
look at picture and tell me if it is a, b, c, or d.
Answer:
A. [tex]t = \frac{d}{r}[/tex]
Step-by-step explanation:
Given
[tex]d = rt[/tex]
Required
Determine the time
From the question, we understand that:
[tex]d = distance[/tex]
[tex]r = rate[/tex]
[tex]t = time[/tex]
This question implies that we make t the subject of formula.
[tex]d = rt[/tex]
Divide both sides by r
[tex]\frac{d}{r} = \frac{rt}{r}[/tex]
The equation becomes:
[tex]\frac{d}{r} = t[/tex]
Reorder the equation.
[tex]t = \frac{d}{r}[/tex]
The correct option is (a) [tex]t = \frac{d}{r}[/tex]
Please help I need to finish all my work tonight
Answer:
24ft²
Step-by-step explanation:
4ft×2ft=8ft²
8ft×2ft=16ft²
16ft²+8ft²=24ft²
A student took two national aptitude tests. The national mean and standard deviation were 325 and 100, respectively, for the first test, and 50 and 6, respectively, for the second test. The student scored 425 on the first test and 65 on the second test. Use z-scores to determine on which exam the student performed better relative to the other test takers. first exam
Answer:
Second test
Step-by-step explanation:
Given that :
FIRST TEST
Mean (m) = 325
Standard deviation (s) = 100
Score (x) = 425
SECOND TEST
Mean (m) = 50
Standard deviation (s) = 6
Score (x) = 65
Express both scores as standardized scores:
Zscore = (x - m) / s
First Score :
Zscore = (425 - 325) / 100
Zscore = 100/100 = 1
SECOND SCORE :
Zscore = (65 - 50) / 6
Zscore = 15 / 6 = 2.5
Student performed better on second test :
Zscore second > Zscore first
b. 3 ice cream cones cost $8.25. At this rate, how much do 2 ice cream cones cost? Explain how you know.
Use a model to divide. 1/4 divided by 3.
Possible answers are,
3/6
9
1/12
1/6
9 is the answer I hope this helped
TAKE A PIC OF A PEICE OF PAPER WITH THE WORK ON IT AND AWNSER. Heyyy pls help me :( it would mean a lot!!! I have a 55% in math rn and I’m trying to get it up.. it would mean a lot if you could help me. I’m not doing so good rn. My parents are very mad about my grades, pls help. JUST 5 QUESTIONS
Answer:
1.
4x-5x+3-8
-x-5
2.
3x^2+8x^2-2x+7x
11x^2-5x
3.
4x+9x+2y+3y^2
3y^2+5y+13x
4.
-5x-7x-2
-5x+-7x-2
-12x-2
5.
6(3x-5)-9x
6(3(4)-5)-9(4)
6(12-5)-36
6(7)-36
6
The pair of triangle are similar What is the value of X
Answer:
cscs
Step-by-step explanation:
aasdadx
help meeeee pleaseeee
there are 18 boys and 46 girls in a class. 87.5% of the students in the class take the bus to school. How many students do nnot take the bus to school?
The table shows the number of songs and the length of the playlist on an iPad. Each song is the same leng
Answer:4 minutes
Step-by-step explanation:
16/4 is 4
36/9 is 4
64/16 is 4
Find the difference :
1 -
0.4308
PLEEASE ANSWER WILL MARK BRAINLIEST PLEASE ANSWER
Answe - 0. 5692
Step-by-step explanation:
the step is only to let 1 be 10000 and then subtract 4308 from 10000 and it u have any confusion then u can also check it by adding the answer with 4308
and that's it.
If u think it's helpful then plz share to ur friends too.
The difference is 0.5692.
What is Decimals numbers?Decimal numbers are numbers which has basically a whole number part and a fractional or decimal part after a point called decimal point.
Decimal number system describes the base 10 number system.
Here we have to find the difference of 1 - 0.4308.
Here, the number is 0.4308, which is a decimal number.
Write 1 as the decimal number as 1.0000
Subtracting as done as usual whole numbers, we get,
1.0000 - 0.4308 = 0.5692
Hence the difference of the given numbers is 0.5692.
To learn more about Decimal Numbers, click on the link :
https://brainly.com/question/4708407
#SPJ5
Write an equation that represents the tile pattern in the table below
Answer:
y=3x+2
Step-by-step explanation:
First find the slope or m in the line of equation y=mx+b
to find slope you need two points, plug in to y2-y1 / x2-x1
so lets use points (0,2) (1,5)
5-2 / 1-0 = 3
m=3
we have y=3x + b
now we find b by pugging in a point, let's use (0,2)
2 = 3(0) + b
b= 2
y=3x+2
please give thanks by hitting the heart button :)
Marbleslides: Lines
Answer:
ok
Step-by-step explanation:
A total of 600 advertisements were sold for a certain magazine. If 20 percent of the first 200 sold were in color, 40 percent of the next 300 sold were in color, and 80 percent of the last 100 sold were in color, what percent of the 600 advertisements were in color?
Answer:
40%
Step-by-step explanation:
First, find how many of the first 200 were in color:
200(0.2)
= 40
Then, find how many of the next 300 were in color:
300(0.4)
= 120
Find how many of the last 100 were in color:
100(0.8)
= 80
Then, add these all together to find how many were in color:
40 + 120 + 80
= 240
Then, divide 240 by 600 to find the percent that were in color:
240/600
= 0.4
So, 40% of the 600 advertisements were in color
If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
OmZA = 15° and mZC = 35°
mZA = 25° and mZC = 25°
OmZA = 20° and mZC = 30°
OmZA + m ZB = 155° and mZC = 60°
Answer:
m∠A = 25° and m∠C = 25°
Step-by-step explanation:
The sum of all three angles in a triangle must add up to 180°. Since the measure of angle B is 130°, the sum of the other two angles have to be 50°.
Also, the triangle is isosceles, meaning two of the sides are equal in length. For those sides, their corresponding angles must also be equivalent. In this case, it's the two smaller angles. Since we have 50° between the two angles, A and C, divide 50 by 2 to get 25° for both angle measurements.
The statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°
GeometryFrom the question, we are to determine which of the statements must be true
From the given information,
m ∠B = 130°
Since the triangle is an isosceles triangle, the base angles must be equal
That is,
m ∠A = m ∠C
But, angles in a triangle sum up to 180°
Then,
∠A + ∠B + ∠C = 180°
This becomes
2 × ∠A + 130° = 180°
2 × ∠A = 180° - 130°
2 × ∠A = 50°
∠A = 50° ÷ 2
∠A = 25°
Since ∠A = ∠C
Therefore,
∠C = 25°
Hence, the statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°
Learn more on Geometry here: https://brainly.com/question/14440001
An art teacher has a total of 7/8 pound of clay. the teacher puts 1/16 pound of clay at each work station. how many stations would there be
Answer:
14
Step-by-step explanation:
Complete the following statement. Write your answer as a decimal or whole number.
____% of $80 = $4
5% of $80 is $4.
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, ____% of $80 = $4
Let x be the percent,
x% of 80 = 4
x = 4*100/80 = 5
Hence, 5% of $80 is $4.
For more references on percentage, click;
https://brainly.com/question/29306119
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15 divided by 19.5. help, please.
Answer:
Step-by-step explanation:
0.76923076923
1. Jordy brings in cupcakes for his class. He brings 2 cupcakes for each person in his class and 5 extra cupcakes as extra just in case. If Jordy brings in 49 cupcakes in all, write an equation that represents this information and then solve to find out how many classmates he has.
PLS PLS WRITE THE EQUATION...
Answer:
22 people
Step-by-step explanation:
49 - 5 = 44 cupcakes
44 ÷ 2 = 22 people
find the measure of a line EC
9514 1404 393
Answer:
41
Step-by-step explanation:
The product of segment lengths from the point of intersection to the circle is the same for both chords.
QC·QE = QD·QF
2x(21) = (x+4)(30)
14x = 10(x +4) . . . . . divide by 3
4x = 40 . . . . . . . . . . subtract 10x
x = 10 . . . . . . . . . . . .divide by 4
2x +21 = EC = 2(10) +21 . . . . . find EC
EC = 41
Suppose that y varies inversely with x and y = 3 when x=10 find y when x=5
Answer:
y=1.5
Step-by-step explanation:
if (y = 3) is (x = 10) and (y = ?) is (x = 5) we see that x is half of the first equation in the second. This means we divide both variables in the first equation by half to get the second. [(x = 10) / 2 = (x = 5)] therefor, [(y = 3) / 2 = (y = 1.5)]. Making your answer 1.5.
Hope this helps :)
Complete the equation by rewriting 2 12/20
Answer:
52/20
Step-by-step explanation:
Common sense and simple math
Jackson painted 80 bird house. 30% of the bird houses were painted green how many green bird houses did Jackson paint
In the diagram below qs and pt are altitudes and m r=55 what is m poq
Answer: POQ = 125
Step-by-step explanation: If you don’t want to read my long explanation, I drew a diagram of my work. :>
First we need to establish that POQ is a vertical angle to SOT, this makes the angles equal. We also need to establish that because the definition of an altitude, that T And S both form right angles. (An altitude is a perpendicular segment from a vertex of a triangle to the opposite side.) Now let’s take a look at the quadrilateral that is formed inside the triangle, the quadrilateral being RSOT. Luckily we know the measure of three of the angles, R=55, T=90, and S=90. If you didn’t know beforehand all angles of a quadrilateral add up to 360, so we can add up the angles we’ve already found to find the missing angle O/ SOT. When we add the angles, and then subtract that from 360 we get 125, so SOT=125. Remember that we established that SOT and POQ are vertical angles, so if SOT=125 then POQ=125.
I really hoped my explanation was good, this was my first time giving an answer. Also I’m sorry if my method of finding the answer wasn’t helpful, but this was the only way I could think of.
I accidentally gave myself a one star rating, that sucks.
3. The letters that form the word MISSISSIPPI are placed in a bowl. What are the odds of choosing a “P”? Express as a fraction.
Answer:
Step-by-step explanation:
Lol since there's 2 P's and 11 letters in MISSISSIPPI. Odds are 2/11.