A large tank is filled to capacity with 600 gallons of pure water. brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.
To find the amount of salt in the tank at a given time, one can use the equation a(t) = Q - Qe^(-rt). In this case, Q (the quantity of salt at a steady state) equals the pump rate multiplied by the salt concentration (24lb/min), and r (the rate of inflow and outflow of the solution) is the rate at which water is pumped out divided by the volume of the tank (1/100 per min). Substituting these values into the equation gives the salt content at any given time.
Explanation:The quantity of salt in the tank at any given time can be determined by the equation of the form a(t) = Q - Qe^(-rt), in which Q is the quantity of salt that would be in the tank at a steady state (i.e., if enough time had passed that the quantity of salt in the tank stopped changing), r is the rate of inflow and outflow of the solution, and t is the time at which you're trying to determine the number of pounds of salt in the tank.
In this case, Q = rate of inflow x concentration of the inflow, which is 6 gal/min x 4 lb/gal = 24 lb/min. This amount is reached after a sufficient amount of time has passed and the tank has reached a steady state.
The rate, r, is the rate at which the water is pumped out of the tank. In this situation, that's 6 gallons per minute. Since there are 600 gallons of water in the tank at the start, r = 6 gal/min ÷ 600 gallons = 1/100 min^-1.
Therefore, the number of pounds of salt in the tank at any time t is a(t) = Q - Qe^(-rt) = 24 lb/min - 24 lb/min * e^[-(1/100 min^-1)*t].
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what is the greatest whole number that rounds to 54,300
Pressure (in pounds per square foot) on a diver at a depth of "d" feet: "P" = 64d + 2112
Solve for "d"
If f(x) = x - 5, then match each of the following.
1. f(-1) -3
2. f(0) -6
3. f(1) -5
4. f(2) 0
5. f(5) 3
6. f(8) -4
You invest 5000 in an account at 5.5% per year simple intrest how much will you have in the account at the beginning of the 6th year
Events A and B are mutually exclusive with P(C) = 0.3 and P(B) = 0.2. Then P(Bc) =
The probability of the complement of event B, denoted as Bc, is 0.8.
Explanation:To find the probability of the complement of an event B, denoted as Bc, we can use the formula: P(Bc) = 1 - P(B). Given that events A and B are mutually exclusive, P(B) = 0.2. Therefore, P(Bc) = 1 - 0.2 = 0.8.
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starting at home, luis traveled uphill to the hardware store for 30 minutes st just 8mph. he then traveled back home along the same path downhill at a speed of 24 mph. what is his average speed for the entire trip from home to the hardware store and back?
What is 243.875 rounded to the nearest tenth,hundreth,ten,and hundred?
A pencil and a ruler cost 2.50 together. The ruler costs $1.00 more than the pencil. How much is the pencil
If you toss six fair coins, in how many ways can you obtain at least two heads?
Math Mean Help Please!
Rounding to the nearest tenth, what is the mean of 100, 75, 40, 90, 80, 100, 92, 88, 80, 84, 100.
Which of the following expressions represents a function?
x2 + y2 = 9
{(4, 2), (4, –2), (9, 3), (9, –3)}
x = 4
2x + y = 5
D is the correct answer the other person who answered explains why.
Picture Perfect Physician’s has 5 employees. FICA Social Security taxes are 6.2% of the first $118,500 paid to each employee, and FICA Medicare taxes are 1.45% of gross pay. FUTA taxes are 0.6% and SUTA taxes are 5.4% of the first $7,000 paid to each employee. Cumulative pay for the current year for each of its employees are as follows. Compute the amounts in the table for each employee and then total the numerical columns.
Employee
Cumulative Pay
Pay subject to FICA- S.S.
6.2% (First $118,000)
Pay subject to FICA-Medicare 1.45%
Pay subject to FUTA Taxes 0.6% Pay subject to SUTA Taxes 5.4% (First $7,000)
Mary $6,800
Type answer here
Type answer here
Type answer here
Type answer here
Zoe $10,500
Type answer here
Type answer here
Type answer here
Type answer here
Greg $8,400
Type answer here
Type answer here
Type answer here
Type answer here
Ann $66,000
Type answer here
Type answer here
Type answer here
Type answer here
Tom $4,700
Type answer here
Type answer here
Type answer here
Type answer here
Totals
Type answer here
Type answer here
Type answer here
Type answer here
Answer:
Employee Mary Zoe Greg Ann Tom
Cumulative Pay $6,800 $10,500 $8,400 $66,000 $4,700
Pay subject to FICA S.S. $421.60 $651.00 $520.80 $4092.00 $291.40
6.2%, (First $118,000)
Pay subject to FICA Medicare $98.60 $152.25 $121.80 $957.00 $68.15
1.45% of gross
Pay subject to FUTA Taxes $40.80 $63.00 $50.40 $396.00 $28.20
0.6%
Pay subject to SUTA Taxes $367.20 $567.00 $453.60 $3564.00 $253.80
5.4% (First $7000)
Totals $928.20 $1,433.25 $1,146.60 $9,009.00 $641.55
Step-by-step explanation:
The compound probability of two events, E and F 1/8 , is ; the probability of E is 1/2 and of F is 1/3 . In two or more complete sentences, explain why E and F are not independent.
Event E and event F are not independent because:
[tex]P(E\bigcap F)\neq P(E)\times P(F)[/tex]
Step-by-step explanation:We know that two event A and event B are said to be independent if:
P(A∩B)=P(A)×P(B)
Here we have two events as E and F such that:
[tex]P(E\bigcap F)=\dfrac{1}{8}[/tex]
[tex]P(E)=\dfrac{1}{2}[/tex]
and [tex]P(F)=\dfrac{1}{3}[/tex]
This means that:
[tex]P(E)\times P(F)=\dfrac{1}{2}\times \dfrac{1}{3}\\\\\\i.e.\\\\\\P(E)\times P(F)=\dfrac{1}{6}\neq P(E\bigcap F)[/tex]
Hence, the events E and F are not independent.
graph -3/4 passing through (1,4)
A student ID number is a letter of the alphabet followed by 2 digits. How many different IDs are possible if the digits can be repeated?
Final answer:
There are 2600 different possible student IDs when a student ID consists of one letter followed by two digits that can repeat, calculated as 26 possible letters multiplied by 10 possible digits for each of the two digit positions.
Explanation:
The question asks how many different student IDs are possible if an ID consists of a letter followed by two digits, with the digits being allowed to repeat. To calculate the possible combinations, we multiply the number of options for each component of the ID. There are 26 letters in the alphabet and 10 possible digits (0-9) for each of the two positions that follow the letter, allowing for repetition.
The calculation is therefore 26 letters × 10 digits × 10 digits = 2600 possible combinations. Each component is independent of the others, so this follows the fundamental principle of counting in combinatorics.
Write an algebraic equation for the following problem and then solve it.
The population of a country in 2015 was estimated to be 321.6321.6 million people. This was an increase of 22% from the population in 1990. What was the population of the country in 1990?
Suppose you value a special watch at $100. you purchase it for $75. on your way home from class one day, you lose the watch. the store is still selling the same watch, but the price has risen to $85. assume that losing the watch has not altered how you value it. what should you do?
Quadrilateral ABCD is similar to quadrilateral EFGH the length of the three longest side in quadrilateral ABCD are 24 feet 16 feet and 12 feet long if the two shortest sides of quadrilateral EFGH feet long and 18 feet long how long is the fourth side on quadrilateral ABCD ?
When all sides of a quadrilateral are transformed, the resulting quadrilateral will be similar to the transformed quadrilateral. The fourth side of ABCD is 6 feet
We have the lengths of ABCD in descending order to be:
[tex]Side\ 1 = 24[/tex]
[tex]Side\ 2 = 16[/tex]
[tex]Side\ 3 = 12[/tex]
We have the lengths of EFGH in ascending order to be:
[tex]Side\ 4 = 9[/tex]
[tex]Side\ 3 = 18[/tex]
The missing side of ABCD is the fourth side, and it can be solved using the following equivalent ratios:
Side 4 : Side 3 of ABCD = Side 4: Side 3 of EFGH
Substitute the values of the known sides
[tex]Side\ 4 : 12 = 9 : 18[/tex]
Express as fraction
[tex]\frac{Side\ 4 }{ 12} = \frac{9}{ 18}[/tex]
Multiply both sides by 12
[tex]Side\ 4 = \frac{9}{ 18} \times 12[/tex]
[tex]Side\ 4 = \frac{1}{2} \times 12[/tex]
[tex]Side\ 4 = 6[/tex]
Hence, the fourth side of ABCD is 6 feet
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How do you solve 18-n divded by 2 (which is underneath the 18-n) is less than or equal to 6?
Melvin has game and education apps on his tablet. He noticed that he has 3 game apps for every 2 education apps. Which of the following is another way to write this ratio?
convert to polar form y=3x^2
The polar form for the given expression is sin(θ)=3r−3rsin²(θ)
To convert the equation y = 3x² into polar form, we substitute[tex]\( x = r\cos(\theta) \) and \( y = r\sin(\theta) \)[/tex], where R is the radius and theta is the angle.
[tex]So, \( y = 3x^2 \) becomes:\[ r\sin(\theta) = 3(r\cos(\theta))^2 \][/tex]
Now, we can simplify this equation:
[tex]\[ r\sin(\theta) = 3r^2\cos^2(\theta) \]\[ r\sin(\theta) = 3r^2\cos^2(\theta) \]\[ \frac{r\sin(\theta)}{r^2} = 3\cos^2(\theta) \]\[ \frac{\sin(\theta)}{r} = 3\cos^2(\theta) \]\[ \frac{\sin(\theta)}{r} = 3(1 - \sin^2(\theta)) \]\[ \frac{\sin(\theta)}{r} = 3 - 3\sin^2(\theta) \]\[ \sin(\theta) = 3r - 3r\sin^2(\theta) \][/tex]
This equation describes the curve in polar coordinates.
When would it be useful to sort data in descending order? why?
Help!
Write 0.78% as a decimal and as a fraction
A) 78; 39/500
B) 0.078; 39/50,000
C) 0.0078; 39/5,000
D) 0.78; 39/50
Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of them dimes and quarters. When she added them up she had a total of $6.95
d = dimes
q = quarters
d+q = 38 coins
q=38-d
0.25q + 0.10d=6.95
0.25(38-d)+0.10d=6.95
9.5-0.25d+0.10d=6.95
-015d=-2.55
d=-2.55/-0.15 = 17
q=38-17 =21
21*0.25 =5.25
17*0.10 = 1.70
5.25+1.70 = 6.95
she had 21 quarters and 17 dimes
Answer:
She had 17 dims and 21 quarters to make $6.95.
Step-by-step explanation:
Given : Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of them dimes and quarters.
To find : When she added them up she had a total of $6.95?
Solution :
Let d be the dims and q be the quarters.
She had 38 coins.
i.e. [tex]d+q=38[/tex] ......(1)
The value of d is 0.10 and q is 0.25.
The total she had of $6.95
i.e. [tex]0.10d+0.25q=6.95[/tex] .......(2)
Solving (1) and (2),
Substitute d from (1) into (2)
[tex]0.10(38-q)+0.25q=6.95[/tex]
[tex]0.10\times 38-0.10q+0.25q=6.95[/tex]
[tex]3.8+0.15q=6.95[/tex]
[tex]0.15q=6.95-3.8[/tex]
[tex]0.15q=3.15[/tex]
[tex]q=\frac{3.15}{0.15}[/tex]
[tex]q=21[/tex]
Substitute in equation (1),
[tex]d+21=38[/tex]
[tex]d=38-21[/tex]
[tex]d=17[/tex]
Therefore, She had 17 dims and 21 quarters to make $6.95.
1. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12.
y = -10 when x = 2
2. Graph the direct variation equation:
y=2x
How much time does it take light to travel from the moon to the earth, a distance of 384,000km?
at the beginning of the summer, Conan had $180 in the bank. Each week he deposits another $64 that he earns mowing lawns. Is his account balance proportional to the number of weeks since he started mowing lawns?
Answer:
no, because the initial 180 gets in the way
Step-by-step explanation:
a dime is flipped 3 times. What is the probability that TAILS occurred all 3 times?
The sales at a particular bookstore grew from $2090 million in 2000 to $3849 million in 2005. Find an exponential function to model the sales as a function of years since 2000. Give your answer using the form B=Boat