Answer:
35.94 lb
Step-by-step explanation:
The net mass flow rate dm/dt = flow rate in - flow rate out
mass flow rate in = concentration in × volume flow rate in = 0.4 lb/gallon of salt × 5 gal/min = 2 lb/min
Let m(t) be the mass present at time, t.
So, the concentration at time, t = m(t)/volume of tank = m(t)/100
mass flow rate out = concentration out × volume flow rate out = m(t)/100 lb/gal× 5 gal/min = m(t)/20 lb/min
So, dm/dt = 2 lb/min - m(t)/20 lb/min
So, dm/dt = 2 - m(t)/20
dm/dt = [40 - m(t)]/20
separating the variables, we have
dm/[40 - m(t)] = dt/20
integrating, we have
∫dm/[40 - m(t)] = ∫dt/20
-1/-1 ×∫dm/[40 - m(t)] = ∫dt/20
1/-1 ×∫-dm/[40 - m(t)] = ∫dt/20
1/-1 ×㏑[40 - m(t)] = t/20 + C
-㏑[40 - m(t)] = t/20 + C
㏑[40 - m(t)] = -t/20 - C
taking exponents of both sides, we have
[tex]40 - m(t) = e^({\frac{-t}{20} - C}) \\40 - m(t) = e^{\frac{-t}{20}}e^{-C} \\40 - m(t) = Ae^{\frac{-t}{20}} (A = e^{-C})\\m(t) = 40 - Ae^{\frac{-t}{20}}[/tex]
when t = 0 m(0) = 10 lb
So
[tex]m(t) = 40 - Ae^{\frac{-t}{20}}\\m(0) = 40 - Ae^{\frac{-0}{20}}\\10 = 40 - Ae^{0}\\10 = 40 - A\\A = 40 - 10 \\A = 30[/tex]
So,
[tex]m(t) = 40 - 30e^{\frac{-t}{20}}[/tex]
when t = 40 minutes, m(40) =
[tex]m(40) = 40 - 30e^{\frac{-40}{20}}\\m(40) = 40 - 30e^{-2}\\m(40) = 40 - 30 X 0.1353\\m(40) = 40 - 4.06\\m(40) = 35.94[/tex]
So, at the end of 40 minutes, the amount of salt in the tank is 35.94 lb
what is the factored from of the polynomial function f(x)=x3-6x2+11x-6
Answer:
[tex]f(x) =(x-1)(x-2)(x-3)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^3-6x^2+11x-6[/tex]
Required
The factored form
[tex]f(x) = x^3-6x^2+11x-6[/tex]
Split
[tex]f(x) =x^3 -3x^2- 3x^2 +2x +9x -6[/tex]
Rearrange as:
[tex]f(x) = x^3 -3x^2 +2x - 3x^2+9x -6[/tex]
Factorize
[tex]f(x) = x(x^2 - 3x + 2) - 3(x^2 - 3x + 2)[/tex]
Factor out [tex]x^2 - 3x + 2[/tex]
[tex]f(x) = (x^2 - 3x + 2)(x - 3)[/tex]
Expand
[tex]f(x) = (x^2 - 2x - x + 2)(x - 3)[/tex]
Factorize
[tex]f(x) = (x(x - 2) - 1(x - 2))(x - 3)[/tex]
Factor out [tex]x - 2[/tex]
[tex]f(x) = (x - 1) (x - 2)(x - 3)[/tex]
(PLZ HELP DUE IN 10 MIN)
Eber can mow 4 lawns in one hour. The equation l = 4h can be used to determine the number of lawns, 1. Eber can
mow in h hours. Create a graph to represent the number of lawns Eber can mow in 0 to 5 hours. Click on the
coordinate plane to place the points in the correct locations.
Answer:
See attachment for plot
Step-by-step explanation:
Given
[tex]l = 4h[/tex]
Required
Represent the scenario on a graph
When h = 0
[tex]l = 4h= 4 * 0 = 0[/tex]
When h = 1
[tex]l = 4 * 1 = 4[/tex]
When h = 2
[tex]l = 4 * 2 = 8[/tex]
When h = 3
[tex]l = 4 * 3 = 12[/tex]
When h = 4
[tex]l = 4 * 4 = 16[/tex]
When h = 5
[tex]l = 4 * 5 = 20[/tex]
So, we have:
[tex](h,l) = (0,0)[/tex]
[tex](h,l) = (1,4)[/tex]
[tex](h,l) = (2,8)[/tex]
[tex](h,l) = (3,12)[/tex]
[tex](h,l)= (4,16)[/tex]
[tex](h,l)= (5,20)[/tex]
See attachment for plot
.a) Imagine you and your friend get a new card with an 18% APR and a $10 minimum payment and use this card to purchase the same mobile phone. If the first friend pays the minimum each month, while the second friend pays $20, what will their balances be after one month?
Answer:
yes
Step-by-step explanation:
yes yes you need to do the thing yeah
Answer:
yes
Step-by-step explanation:
a) Imagine you and your friend get a new card with an 18% APR and a $10 minimum payment and use this card to purchase the same mobile phone. If the first friend pays the minimum each month, while the second friend pays $20, what will their balances be after one month?
A section of a deck is shaped like a trapezoid. For this section, the length of one base is 41 feet, and the length of the other base is 36 feet. The height is 20 feet. What is the area of this section of the deck?
Answer:
Step-by-step explanation:
Someone please help me thank you
P = 20.6, I hope this helps you!!!!!
Using the sine rule, a/sin(A) = b/sin(B) = c/sin(C)
But we have to have at least two angles and two lengths to equate it to one another. We could find the third angle in this triangle to use as our second angle, but we do not know the value of x, so we have to find the second length.
To do that, we use Pythagoras theorem;
a^2 = b^2 + c^2
a^2 = 7^2 + 5^2
a^2 = 49 + 25
a^2 = 74
square root both sides to get rid of the square on a:
a = sqrt(74)
a ~ 8.60
Now we can apply our sine rule. Note that the lengths and angles are the ones opposite each other. For example, the corresponding angle of 8.60 is 90° and the one for 5 is x°.
So,
8.60/sin(90) = 5/sin(x)
8.60/1 = 5/sin(x), since sin(90) = 1
Make sin(x) the subject,
sin(x) = 5/8.60
sin(x) = 0.5814
x = sin^-1(0.5814)
x ~ 35.6°
HELPP IF WRONG ILL REPROT
A store employee conducted a survey of 590 randomly selected customers. According to the survey, 177 of the customers often use coupons.
How many people would you expect to use a coupon if all 5,000 people in the community visited the store?
Question 7 options:
5,310 people
1,250 people
3,750 people
1,500 people
Answer:
Solution given
:total n[U]=590
customers using coupon n[C]=177
the percentage of all customers who often use coupons=177/590×100%=30%.
If n[U]=5000
no of customer using coupon be x
we have
30% of 5000=x
x=30/100×5000
x=1500
So1500 people would you expect to use a coupon if all 5,000 people in the community visited the store.Consider the following question: How many years has each person played on the soccer team? Which best describes the question? It is a statistical question because the data may vary for each player. It is a statistical question because the data will all be the same. It is not a statistical question because the answers are all whole numbers. It is not a statistical question because there is only one answer per person.
Answer:
Its the first one
Step-by-step explanation:
It is a statistical question because the data may vary for each player. :)
A new car is purchased for $18,000 and over time its value depreciates by one half
every 4 years. What is the value of the car 17 years after it was purchased, to the
nearest hundred dollars?
Answer:
900
Step-by-step explanation:
THIS IS THE CORRECT ANSWER
what is 15.9% of 261
Answer:
41.499
Step-by-step explanation:
Answer:
41.499
Step-by-step explanation:
261x15.9%=261x159/100=41.499
Please help me solve this problem
Answer:
90°
Step-by-step explanation:
It's simple, the angle of a line is 180°
∠EFG=90°
Line GD-∠EFG=180°-90°=90°
Please mark brainliest!
Help please
(Worth 10 points)
Please respond with a actual answer
*No robots no bad links*
I need help with all 4 questions plz
Plz help me well mark brainliest if correct.....??
Answer:
C
Step-by-step explanation:
I think it’s C because under the numbers it says pets they own so the x has to be the fourth graders
Answer:
C
Step-by-step explanation:
It says it below the number line!! hoped this helped
A shopkeeper earns a profit of rupees 300 on Monday, a loss of rupees 150 on Tuesday, than a loss of rupees 200 on Wednesday and profit of rupees 50 and rupees 75 on thursday and friday respectively.Find his net profit or loss in 5 days.
Answer:
75 rupees in net profit
Step-by-step explanation:
Loss indicates subtraction, and profit indicates addition
300-150-200+50+75=75
Find the perimeter of a quadrilateral with vertices at C (-2, 1), D. (2, 4), E (5,0), and. F (1, -3)
12 units
O 16 units
O 20 units
O 24 units
What is the answer for 1/2 + 1/2?
Answer:
1 is the answer to 1/2+1/2
Answer:
1
Step-by-step explanation:
if you add 1/2 and 1/2, you get 2/2 which is also equal to 1.
The following two-way table describes student's
after school activities. Find the probability that a
randomly selected student works, given that it's a
senior.
Grade
Sports
Music/Drama
Work
Sophomore
20
7
3
Junior
20
13
2
Senior
25
5
5
P( Work | Senior) = [?]
Round to the nearest hundredth.
Answer:
[tex]P(Work | Senior) = 0.14[/tex]
Step-by-step explanation:
Given
The attached table
Required
[tex]P(Work | Senior)[/tex]
This is calculated using:
[tex]P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}[/tex]
This gives:
[tex]P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}[/tex]
From the table:
[tex]n(Work \ n\ Senior) = 5[/tex]
[tex]n(Senior) = 25 + 5+ 5 = 35[/tex]
So:
[tex]P(Work | Senior) = \frac{5}{35}[/tex]
[tex]P(Work | Senior) = 0.14[/tex]
Answer:
14%
Step-by-step explanation:
add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).
How can you get a good credit score?
Pay credit card and loan payments late.
Don't apply for credit.
Pay your loan payments on time, every time.
Go above your credit limit.
Answer:
Pay your loan payments on time, every time.
Step-by-step explanation:
The other answers either hurt or have no effect on your credit score.
The option 2 and 3 is right get a good credit score. Avoid the options 1 and 4.
To get a good credit score, you should follow these steps:
Pay your loan payments on time, every time: Timely payments are one of the most crucial factors in building a good credit score. Consistently paying your bills and loans on or before the due date shows lenders that you are a responsible borrower.
Don't apply for credit excessively: Each time you apply for new credit, a hard inquiry is made on your credit report, which can temporarily lower your score. Applying for multiple credit accounts in a short period may signal financial instability to lenders.
Avoid options 1 and 4:
Paying credit card and loan payments late: Late payments negatively impact your credit score and show a lack of responsibility in managing credit.
Going above your credit limit: Maxing out your credit cards or going above the credit limit can harm your credit score as it indicates a higher risk of defaulting on your debts.
Hence, the option 2 and 3 is right get a good credit score. Avoid the options 1 and 4.
Learn more about Loan here:
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Need help on this please
9514 1404 393
Answer:
71°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
∠H = 180° -109° = 71°
_____
Additional comment
The above rule comes from the more general rule that the measure of an inscribed angle is half the measure of the arc it intercepts. Here, inscribed angle J intercepts arc GHI, so that arc has measure 2×109°. Then the measure of short arc GI is 360° -2×109°, and inscribed angle H is half that:
∠H = (1/2)(360° -2×109°)
∠H = 180° -109° = 71°
Find the focus.
x2 = 6y
A. (0, 3/2)
B. (0,6)
C. (0, -3/2)
D. (3/2,0)
Answer:
The answer would be (0,3/2) or letter A.
Step-by-step explanation:
In conclusion the answer is letter A (0,3/2)
You welcome.
The co-ordinate of the focus of the given equation of the parabola x^2=6y is (0,3/2).
We have given the equation is
[tex]x^2 = 6y[/tex]
We know that the general equation of the parabola is,
[tex]x^2=4ay[/tex]
A line that passes through the focus and divides the parabola into two halves is known as the axis of symmetry.
What are the coordinates of the focus?
The coordinates of the focus [tex]f(0, a)[/tex]
We have to determine the value of
[tex]a4a=6a \implies 6/4a=3/2[/tex]
Therefore the coordinate of the focus is[tex](0,3/2)[/tex].
To learn more about the focus visit:
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The distance traveled by a certain truck varies directly to the amount of fuel the truck consumes. The truck traveled 130 miles on 10 gallons of fuel. At the same rate, how far would the truck travel on 6 gallons of fuel?
Answer: 78 Miles
Step-by-step explanation:
Daniel measures the growth of his tomato plant and records the results in the table.
What was the average rate of growth during this time period for his plant to thenearest tenth?
Answer:
1.2
Step-by-step explanation: it just is
Reflect P (-5,10) over the x-axis. What are the coordinates of the reflected point? What quadrant is the reflected point in?
Answer:
I need the answer 2 QwQ....Find the area of the figure.
7 cm
4 cm
4 cm
10 cm
10 cm
8 cm
19 cm
area cm2
Answer:
3404800
Step-by-step explanation:
7 x 4 x 4 x 10 x 10 x 8 x 19 x 2 = 3404800
Hope this helps!!!
Ignacio shares 2.1 liters of water equally into 7 containers. How many milliliters are in each container?
Answer: 300 ml
Step-by-step explanation:
First and foremost, we should note that:
1000 milliliters = 1 liter
Therefore, 2.1 liters = 2.1 × 1000 = 2100 millimeters.
Therefore, since the liters of water is divided into 7 containers, the vlaue in each container will be:
= 2100 millimeters / 7
= 300 millimeters
4.Kini ang gipasa-pasa nga kinaiya sa pamaagi sa pamuyo sa mga tawo sa
usa ka lugar.
A.Kultura B.Materyal C. Di-Materyal
D.Kinaiya
aano mag two dinhi
Answer:
A
Step-by-step explanation:
Which set of three angles could represent the interior angles of a triangle?
O 19°, 70°, 91°
O 47°, 12°, 31°
O 50°, 20°, 20°
O 25°, 25°, 100°
Answer:
19 degrees, 70 degrees, and 91 degrees.
Step-by-step explanation:
The interior angles of a triangle sum to 180 degrees. 19 plus 91 is equal to 110, add 70 to 110 and you'll get 180. :)
Mark is going to purchase a $9,000 motorcycleHis bank will finance his purchase through an add-on interest loan. They will charge Mark 7% interest over 5 years
How much in interest ?
Answer:
The interest to be charged is $ 3,150.
Step-by-step explanation:
Since Mark is going to purchase a $ 9,000 motorcycle, and his bank will finance his purchase through an add-on interest loan, and they will charge Mark 7% interest over 5 years, to determine how much in interest will be charged, the following calculation has to be done:
9000 x 0.07 x 5 = X
630 x 5 = X
3150 = X
Therefore, the interest to be charged is $ 3,150.
PLEASE HELP MATH QUESTION 10 POINTS HELP ASAP PLEASE HELP
QUESTION IS IN LINKED IMAGE
Answer:
2x-3y=7. Linear
Blue graph. Linear
Table 3. nonlinear
y=-4. Linear
y=2x^2-4. Nonlinear
y=3/x-2. Nonlinear
Tammy has scored 82, 78, and 93 on her previous three tests. What score does she need on her next test so that her average (mean) is 81?
Answer:
She needs a grade of 71 on her next text.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
Tammy has scored 82, 78, and 93 on her previous three tests.
Thus, her grades are 82, 78, 93 and x, in which x is her grade in the fourth test.
There are 4 tests.
What score does she need on her next test so that her average (mean) is 81?
We have to find x when the mean is 81. So
[tex]\frac{82 + 78 + 93 + x}{4} = 81[/tex]
[tex]253 + x = 324[/tex]
[tex]x = 324 - 253[/tex]
[tex]x = 71[/tex]
She needs a grade of 71 on her next text.