Answer:
[tex]y=15e^{e^{- \frac{t}{100}}}kg[/tex]
Step-by-step explanation:
Let y(t) represent the amount of salt in the tank after t minutes. Therefore:
[tex]\frac{dy}{dt}=rate\ in-rate\ out[/tex]
Pure water is entering at a rate of 10 L/min, therefore rate in = 0
The tank contains 1000 L of brine (salt water) with 15 kg of dissolved salt, and a mixed solution leaving at 10 L/min hence;
[tex]rate\ out = \frac{y(t)\ kg}{1000\ L}*10\ L/min= \frac{y(t)\ kg}{100\ min}\\\\Therefore:\\\\\frac{dy}{dt}=0- \frac{y(t)}{100} \\\\\frac{dy}{dt}=- \frac{y(t)}{100}\\\\\frac{dy}{y}=- \frac{1}{100}dt\\\\\int\limits{\frac{dy}{y}} =\int\limits- \frac{1}{100}dt\\\\lny=- \frac{t}{100}+C\\\\Taking\ exponetial\ of\ both\ sides:\\\\y=e^{- \frac{t}{100}+C}\\\\y=e^C.e^{- \frac{t}{100}}\\\\y=Ae^{- \frac{t}{100}}(A=e^C)\\\\at\ y=15kg, t=0\\\\15=Ae^{e^{- \frac{0}{100}}}\\\\A=15\\\\[/tex]
[tex]y=15e^{e^{- \frac{t}{100}}}kg[/tex]
If you have 100 million dollars and you spend 780 of it what do you have left
Answer:
ninety-nine million nine hundred ninety-nine thousand two hundred twenty
Step-by-step explanation:
A recipe calls for 3 cups of flour for 5 dozen cookies. how much flour is needed for 8 dozen cookies?
Answer:
4.8 cups
Step-by-step explanation:
you set up a proportion of 3/5 and x/8 and then cross multiply to get your answer
Translate the English phrase into an algebraic expression: the product of 9 and 7.
Answer:
9*7=63
Step-by-step explanation:
Product means the answer of a multiplication question
Answer:
9*7=63
Step-by-step explanation:
When translating an English phrase into an algebraic expression, pay attention to the operation that you have to perform, like "product", meaning multiplication. Here are some other operation words in English:
Sum: +
Difference: -
Quotient: ÷
Product: ×
I hope this helps you!!
What number is 10 times larger than 19
Answer:
190
Step-by-step explanation:
19 × 10 =190
if you multiply it it will be ten times larger
Answer:
190
Step-by-step explanation:
Janet spent $100 on books. This was k dollars less than five times what she spent on lunch. How much did she spend on her lunch?
Answer:
5x − k = 100
[tex]x=\frac{100-k}{5} \\[/tex]
Step-by-step explanation:
The amount she spends on lunch is x = (100 + k) /5.
How to find how much did she spend on her lunch?Given: Janet spent $100 on books.
This was k dollars less than five times what she spent on lunch.
We can construct an equation from it :
5x-k = 100
Thus , x = (100 + k) /5.
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I have one question left please help me.
The filled circle means either 'less than or equal to' or 'greater than or equal to' and the empty circle means 'less than' or 'greater than'.
Answer:
the unshaded line means less than or greater than
And the shaded line means greater than or equal to or less than or equal to
Step-by-step explanation:
the 1st one is greater than
the 2nd one is greater than or equal to
this is greater than or equal to ≥
this is greater than >
HOPE THIS HELPS!!!!!
how many times does 255 go into 375
Answer: 1 time
255 times 1 is 255. 255 plus 255 is 505. So only goes into 375 once.
Apples are on sale for $1.29 per pound. You buy buy 4.25 pounds of apples. How much will It cost to buy the apples?
Answer:
5.48
Step-by-step explanation:
Answer:
5.48
Step-by-step explanation:
How many times greater is the value of the digit 2 in 23.876 than the value of the digit 2 in 3.254
Answer:
100x
Step-by-step explanation:
Answer: 2 times
Step-by-step explanation:
You need to move the digit to the digit of the two in the number of 3.254 then see how many times you took
Yolanda's credit card has an APR of 16 22% and a billing cycle of 30 days. The table below shows her transactions
with that credit card in the month of November
Amount ($) Transaction
Find Yolanda's finance charge in November using the previous balance method the adjusted balance method, and
the daily balance method. Among those three possible finance charges what is the value of the one which is neither
lowest nor highest?
A.$1253
B.$1159
C.$1205
D.$10.91
Answer:
$11.59
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Which error was hardest to find?
Answer:
May I ask what error are we talking ab?
Step-by-step explanation:
Find an equation of the line having the given slope and containing the given point.
Slope is -2
Line through (5, -6)
Answer:
y = -2x + 4
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of -2 and passes through (5, -6).
We want to write the equation of the line.
There are three ways to write the equation of the line:
Slope-intercept form, which is y=mx+b, where m is the slope and b the value of y at the y-intercept.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.Any of these forms will work, however let's put it into slope-intercept form as that is the most common way.
SolvingAs we are already given the slope, we can immediately plug that into the equation.
Substitute m with -2.
y = -2x + b
Now, we need to solve for b.
As the equation passes through (5, -6), we can use its values to help solve for b.
Substitute 5 as x and -6 as y.
-6 = -2(5) + b
Multiply.
-6 = -10 + b
Add 10 to both sides.
4 = b
Substitute 4 as b.
y = -2x + 4
Dakota shoots 3 free throws in 2 minutes how many free throws will he throw in 6 minutes?
Answer:
9
Step-by-step explanation:
Answer: 12 free throws
Step-by-step explanation: This problem can be solved using proportions or a table.
For every 2 minutes, theres 3 free throws.
For every 4 minutes, theres 6 three throws
For every 6 minutes, theres 12 free throws.
Multiplying twice for each number.
Find the maximum and the minimum values of f(x,y,z)equals 3 x minus 3 y plus 8 z on the sphere x squared plus y squared plus z squared equals 82 .
Answer:
The maximum point is
(3/4, 3/4, 8) = 4
The minimum point is
(-3/4, -3/4, -8) = -4
Step-by-step explanation:
See attachment for derivation
The length of a rectangle is 5 inches more than the width. The perimeter is 46 inches. Find the length and the width.
The length is inches___ and the width is_____ inches.
Answer:
width: 9 inches
length: 14 inches
Step-by-step explanation:
width: x
length: x + 5
perimeter = 2L + 2W
46 = 2(x + 5) + 2x
46 = 2x + 10 + 2x
46 = 4x + 10
36 = 4x
x = 9
width: 9
length: 9 + 5 = 14
A farmer decides to make three identical pens with feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible?
Answer:
we cant answer this without the maxamum number of feet for fences. or it will be infiinite.
Step-by-step explanation:
A bag contains 20 marbles, of which 2 are brown. What is the probability that a randomly selected marble will be brown? Write your answer as a fraction or whole number.
Answer:
1/10
Step-by-step explanation:
!!!20 points!!!Choose the answer that best represents the situation described below.
Steve starts a road trip with a full tank of gas in his car. The farther he drives,
the less gas will be in his car at the next visit to the gas station.
A. The distance Steve drives on a road trip is a function of the
number of times he has to go to the gas station.
B. The distance Steve drives on a road trip is a function of the type of
car he has
C. The amount of gas left in Steve's car at his next visit to the gas
station is a function of the distance he drove.
SUBMIT
Answer:
C. The amount of gas left in Steve's car at his next visit to the gas
station is a function of the distance he drove.
Step-by-step explanation:
From the question, the car starts with a full tank of gas and the more the distance covered, the less gas will be left in the car at the next visit to the gas station.
The variables to take note are the distance travelled and the amount of gas left in the car at next visit to the gas station.
This means the farther he drives, the less gas will be left in the car because longer distances travelled consumes more gas in the car thus less gas will be left when the next visit to the gas station occurs.
solve for x PLEASE PLEASE
5x+9+57+69=180
Answer:
x=29
Step-by-step explanation:
5 times 29 equals 145 and 9 plus 57 plus 69 equals 135 add 135 and 145 and you get 180.
Lin rode her bike 2 miles in 8 minutes. She rode at a constant speed. Complete the table to show the time it took her to travel different at this speed?
Answer:
If she traveled 2 miles in 8 minutes, the constant of proportionality is y=1/4x. So for every minute she rode her bike, multiply that by 1/4.
Step-by-step explanation:
Who can help me on math please !!!
Answer:
What's the question(s)?
Help help help fast fast fast
Answer:
40 minutes
Step-by-step explanation:
It takes 30 mins to shape 10 pots, and heating all 10 pots takes 10 mins. Add 30 and 10 minutes to get: 40 minutes.
Answer:
3p + 10; 40 minutes
Step-by-step explanation:
It takes 3 minutes to shape one pot.
It takes 3p minutes to shape p pots.
A batch of pots has p pots and takes 10 minutes in the kiln.
The total time it takes to make 1 batch is the time to shape the pots, 3p, plus the time in the kiln, 10 minutes.
The expression is
3p + 10
For a batch of 10 pots, p = 10.
3p + 10 = 3(10) + 10 = 30 + 10 = 40
Answer: 3p + 10; 40 minutes
A math class consists of 25 students, 14 female and 11 male. Two students are selected at random to participate in a probability experiment. Compute the probability that no males are selected.
[tex] \LARGE{ \underline{ \orange{ \bf{Required \: answer:}}}}[/tex]
In the die the total no. of students are 25
Number of possible outcome for no males = Number of possible outcomes for females only = 14We know that,
∴ P(E) = Number of favourable outcome / Number of all possible outcome
Here we have to find the probability of the event of finding the no. of males.
⇛ P(E) = 14 / 25 (Answer)
And we are done !!
Probability helps us to know the chances of an event occurring. The probability that no males are selected is 0.3033.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that A math class consists of 25 students, 14 female and 11 male. Two students are selected at random to participate in a probability experiment.
Now, since we need to compute the probability that no males are selected, which can also be taken as the probability of both the students selected are girls. Therefore, the probability can be written as,
Probability = (14/25) × (13/24)
= 182/600
= 0.3033
Hence, the probability that no males are selected is 0.3033.
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Roberto runs 25 miles. His average speed is 7.4 miles per hour. He takes a break after 13.9miles.How many more hours does he run? Show your work.
Answer:
1.5 hours
Step-by-step explanation:
Number of miles = 25 miles
Average speed = 7.4 miles per hour
Break after 13.9 miles
How many more hours does he run
Speed = distance / time
Total time for 25 miles :
Time = distance / speed
Time = 25 / 7.4
Time = 3.378 hours
Total time to cover 13.9 miles :
Time = 13.9 / 7.4
Time = 3.378 hours
Time = 1.878 hours
Difference = (3.378 - 1.878) hours = 1.5 hours
Hence, he to ran for 1.5 hours after taking a break
The total time required for the 25 miles run is 3.378 hours and he will run for 1.5 hours after the break.
Given information:
Roberto runs 25 miles.
The average speed is 7.4 miles per hour.
He takes a break after 13.9 miles.
Now, speed is defined as the ratio of distance and time.
So, the time taken by him to run first 13.9 miles will be,
[tex]s=\dfrac{d}{t}\\7.4=\dfrac{13.9}{t_1}\\t_1=1.878[/tex]
So, he ran for 1.878 hours to cover 13.9 miles.
Now, the total time of the 25 miles run will be,
[tex]T=\dfrac{25}{7.4}\\T=3.378[/tex]
So, the total time of the run is 3.378 hours.
After the break, he will run for 3.378-1.878 hours = 1.5 hours.
Therefore, the total time required for the 25 miles run is 3.378 hours and he will run for 1.5 hours after the break.
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Cynthia’s favorite clothing store is having a 44% off sale. What fraction represents 44%?
Answer:
here ur answer 4/9
Which work correctly uses properties of inequality to find the solution to –0.4x – 10 > 14?
–0.4x – 10 > 14
–0.4x > 4
x > –10
–0.4x – 10 > 14
–0.4x > 24
x > –60
–0.4x – 10 > 14
–0.4x > 4
x 14
–0.4x > 24
x < –60
Answer:
d
Step-by-step explanation:
–0.4x – 10 > 14
–0.4x > 24
x < –60
the correct solution to the inequality – 0.4x – 10 > 14 is x < – 60.
Inequality refers to a mathematical relationship between two values that are not equal.
The correct work that uses properties of inequality to find the solution to – 0.4 x – 10 > 14 is:
– 0.4 x – 10 > 14
Subtract 10 from both sides:
– 0.4 x > 24
Divide both sides by – 0.4 (note the change in inequality direction when dividing by a negative number):
x < – 60
Therefore, the correct solution to the inequality – 0.4x – 10 > 14 is x < – 60.
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Solution to
y= -7x+13
y= -1
Answer:
x= 2
Step-by-step explanation:
y = -7x + 13
-1 = -7x + 13
7x - 1 = 13/+1
7x = 13 + 1
7x = 14/ :7
x = 2
Answer:
2
Step-by-step explanation:
Step 1:
y = - 7x + 13 Equation
Step 2:
- 1 = - 7x + 13 Input y
Step 3:
- 14 = - 7x Subtract 13 on both sides
Step 4:
- 14 ÷ - 7 = x Divide
Answer:
x = 2
Hope This Helps :)
is 1 greater than 1?
Answer:
no it is equal cause they are the same number
Step-by-step explanation:
$-32
Simplify
-2
--4
2
16
Answer:
no u
Step-by-step explanation:
Write the equation 5x=2y+10 in the slope-intercept form and find the slope of a line parallel to it.
Answer:
slope intercept form: y=-5/2x+5
the slope of a parallel line would have m=-5/2
Step-by-step explanation:
to get in slope intercept form, you solve for y and get it alone. first you subtract 5x from both sides to get y alone. then you simplify by dividing by 2.
Parallel lines have the same slope