Answer:
10 quarters and 12 dimes :)
Step-by-step explanation:
A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of 2lb of salt/gallon is admitted into the tank at a rate of 6 gallons per minute. The well-stirred solution is drained at the same rate. How long will it take for the tank to have 100 lb. of dissolved salt
Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.
Salt flows into the tank at a rate of
(2 gal/min) (6 lb/gal) = 12 lb/min
and flows out at a rate of
(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min
so that the net rate at which salt is exchanged through the tank is
ds(t)/dt = 12 - s(t)/150 … (lb/min)
Solve for s(t). The DE is separable, so we have
ds/dt = 12 - s/150
150 ds/dt = 1800 - s
150/(1800 - s) ds = dt
Integrate both sides to get
-150 ln|1800 - s| = t + C
Solve for s :
ln|1800 - s| = -t/150 + C
1800 - s = exp(-t/150 + C )
1800 - s = C exp(-t/150)
s = 1800 - C exp(-t/150)
Now given that s(0) = 50, we solve for C :
50 = 1800 - C exp(-0/150)
50 = 1800 - C
C = 1750
Then the amount of salt in the tank at any time t ≥ 0 is
s(t) = 1800 - 1750 exp(-t/150)
To find the time it takes for the tank to hold 100 lb of salt, solve for t in
100 = 1800 - 1750 exp(-t/150)
1700 = 1750 exp(-t/150)
34/35 = exp(-t/150)
ln(34/35) = -t/150
t = -150 ln(34/35) ≈ 4.348
So it would take approximately 4.348 minutes.
By the way, we didn't have to solve for s(t), we could have instead stopped with
-150 ln|1800 - s| = t + C
Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so
-150 ln|1800 - 50| = 0 + C
C = -150 ln|1750|
==> t = 150 ln(1750) - 150 ln|1800 - s|
Then s(t) = 100 lb when
t = 150 ln(1750) - 150 ln(1700)
t = 150 ln(1750/1700)
t = 150 ln(35/34)
t ≈ 4.348
Please help!!!......
Answer:
12*12=144
8*10=80
80+144=224
224*2=448
10*4=40
8*10=80
80*2=160
40+160=200
12*10=120
120+200=320
20*10=200
320+200=520
448+520=968
Hope This Helps!!!
there are 7 socks in a bag 3 of those socks are blue what is the probability of picking a Blue sock randomly from the bag. Answer as simplified fraction of the form a/b
Answer:
3/7
Step-by-step explanation:
there are is a total of 7 socks and 3 are blue making blue socks be 3/7
The growth rate of the sunflower from day 14 to day
35 is nearly constant. On this interval, which
of the
following equations best models
the height k in
centimeters, of the sunflower t days after it begins
to grow?
Answer:
sorry I don't know.....
Someone help pleasee
Answer:
Step-by-step explanation:
g(x) = 3f(-2x)
= 3*([-2x)² + (-2x) - 2)
= 3 (4x² - 2x - 2)
= 3 * (4x² - 4x +2x - 2) {Rewrite the middle term}
= 3 *[ 4x(x - 1) + 2(x - 1)]
= 3* [ (x -1) *(4x + 2)]
= 3(x - 1)(4x + 2)
x - 1 = 0 ; 4x + 2 = 0
x = 1 ; 4x = -2
x = [tex]\dfrac{-2}{4}=\dfrac{-1}{2}[/tex]
Roots: x = 1 , (-1/2)
Help I don’t get this
Directions: Write rack of the following statements using a symbolic language.
2. A number is four times larger than the square of half the number.
3. Steven has some money. If he spends $9.00, then he will have of the amount he started with.
4
The sum of a number squared and three less than twice the number is 129.
5. Miriam read a book with an unknown number of pages. The first week, she read five less than of the pages. The
second week, she read 171 more pages and finished the book. Write an equation that represents the total number
of pages in the book
Answer:
2.)4n>(n/2)^2
3. (The problem isn't clear)
4.)n^2+2n-3=129
5.)n-5=171
Step-by-step explanation:
2.)
4n(four times the number) >(larger than) (n/2)^2 (half the number squared)
4.)
Sum=addition
n^2 (number squared) +2n (twice the number)-3=129
5.)
N(unknown number of pages) -5(amount of pages already read)= 171(the number of pages it took her to finish)
A bookstore had 81 copies of a magazine. Yesterday it sold 7\9 of them. How many copies were sold yesterday?
Write your answer in simplest form.
Answer:
63
Step-by-step explanation:
81 x 7/9 = 63
To calculate, multiply 81 x 7. Then divide that total by 9.
Under what condition the composite function of any two function is an identity function?
Answer:
under the condition of f(x)=x composite function is an identity one
Maria sold t-shirts at a festival. She made 6$ for each t-shirt she sold. Her expenses were 30$. If she made a profit of 84$, how many t-shirts did she sell?
What is 15+(-11) simpyfied
Hi there!
»»————- ★ ————-««
I believe your answer is:
4
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\15+(-11)\\----------------\\\rightarrow 15 +1(-11)\\\\\rightarrow 15 - 11\\\\\rightarrow \boxed{4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
your answer will obviously be 4
The pizza restaurant down the street wants to advertise on its marquee sign the number of ways you can order a $10 pizza. The restaurant offers 18 toppings and for $10 you can order up to 4 toppings, meaning you can either order 1, 2, 3, or 4 toppings and you can’t order any toppings twice. Use this information to answer the following questions:
a. Is this a permutation problem, a combination problem, or a problem using both elements?
b. Determine how many ways you can order a pizza from the restaurant. Explain what strategies you used.
c. If there were no restriction on the number of toppings you could choose, how would that change the answer?
Answer:
Step-by-step explanation:
I need help!!
Find the height of this cone using the Pythagorean Theorem.
Answer:
h = 4sqr(3)
Step-by-step explanation:
r = d/2
d = 8
r = 8/2
r = 4
a = 4
c = 8
b = h = ?
a^2 + h^2 = c^2
4^2 + h^2 = 8^2
16 + h^2 = 64
h^2 = 64 - 16
h^2 = 48
sqrt(h^2) = sqrt(16*3)
h = 4 sqrt3)
Answer:
48
Step-by-step explanation:
When the input is 1, what is the output of the function? That is, find the value of g(1).
Answer:
g(1) = 1
Step-by-step explanation:
In this situation, one is given a graph of the function (g(x)), and one is asked to evaluate the function (g(x)) for (1). An easy way to do so is to find (x = 1) on the coordinate plane, then draw a vertical line at this point. Note the place where (x = 1) intersects the graph of (g(x)). The (y-coordinate) of this intersection point is the output of the function (g(x)).
The line (x = 1) intersects the function (g(x)) at the point (1, 1). Thus (g(1) = 1).
Once upon a time, there was a former whose family raised pigs and chickens. One morning, the farmer's wife looked into the barnyard and told her husband that she counted 24 heads and 80 feet. How many chickens are in the yard? How many pigs are in the yard?
Using a system of equations, it is found that:
There are 8 chickens in the yard.There are 16 pigs in the yard.-----------------------------------------
This question is solved using a system of equations. I am going to say that:
x is the number of chickens.y is the number of pigs.-----------------------------------------
A chicken has 1 head, as do a pig.There are 24 heads.Thus:
[tex]x + y = 24 \rightarrow y = 24 - x[/tex]
-----------------------------------------
A chicken has 2 feet.A pig has 4 feet.In total, there are 80 feet.Thus:
[tex]2x + 4y = 80[/tex]
-----------------------------------------
Number of chicken:
Since [tex]y = 24 - x[/tex]
[tex]2x + 4y = 80[/tex]
[tex]2x + 4(24 - x) = 80[/tex]
[tex]2x + 96 - 4x = 80[/tex]
[tex]2x = 16[/tex]
[tex]x = \frac{16}{2}[/tex]
[tex]x = 8[/tex]
There are 8 chickens in the yard.
-----------------------------------------
Number of pigs:
[tex]y = 24 - x = 24 - 8 = 16[/tex]
There are 16 pigs in the yard.
A similar problem is given at https://brainly.com/question/24104709
How much of salt would you get if you evaporate all water from:
375g of a 12% salt solution

Answer:
45g
Step-by-step explanation:
The amount of salt left once the whole water is evaporated can be calculated as follows
= 12% × 375
= 12/100 × 375
= 0.12×375
= 45
Hence 45g of salt is left after the evaporation of water
Answer:
45g
Step-by-step explanation:
anyone know if its a b c or d?
Answer:The right answer is B
Step-by-step explanation:
If it's negative then it should be on the other side with one side down on the graph and one side on the left.(hope this helped you) :)
Find the distance between the two points!
PLEASE DO THIS ASAP!!
no links
Answer:
5
Step-by-step explanation:
The distance is given by sqrt((-3-0)^2+(-3-1)^2)=sqrt(9+16)=5
Answer:
I believe the distance equals 5
Step-by-step explanation:
Use the distance formula and plug in the numbers. Then solve.
Hello! Hello ! guys. or any genius of math. can you help me on this math problems. this question is out of my answer.
could you help me.
if your answer is correct there is a big changes to get brain list answer and 2 followers from my two accounts.
don't need to follow back.
Answer:
we have to convert that question centimeters to meters
Step-by-step explanation:
I think all are going to be less as you change all of them.
Please help. I don't understand anything.
Answer:
A
Step-by-step explanation:
The area of figure=Area of rectangle+Area of triangle
Area of figure=(x+2)(x-3)+1/2*(x)*(x+2)
Area of figure=x^2-x-6+0.5*x^2+x
Area of figure=(3/2)x^2-6
Answer:
A, M(x)=3/2 (x^2-6)
Step-by-step explanation:
Let's calculate the area of the figure 1st,
Area of figure=Area of triangle+Area of rectangle
=1/2 b*h + l*b = 1/2 (x+2)x + (x+2)(x-3)
=(x^2+2x)/2+x^2 - x - 6 =(x^2+2x+2x^2 - 2x -12)/2
=3x^2-12/2=3/2(x^2-6)
In the options,
M(x)=3/2 (x^2-6) is given, so it best represents the area.
PLZZZZZZ HELP! Find the area.
Answer:
14.88 km
Step-by-step explanation:
add both base 1 and base 2 together divide them by 2 then multiply by the height.
please help me I need
Answer:
x = - 2
Step-by-step explanation:
Given
[tex]2^{x+3}[/tex] × [tex]3^{x+4}[/tex] = 18 = 2 × 9 = [tex]2^{1}[/tex] × 3²
Then
[tex]2^{x+3}[/tex] = [tex]2^{1}[/tex]
Since bases on both sides are equal, both 2, then equate exponents
x + 3 = 1 ( subtract 3 from both sides )
x = - 2
Then
[tex]2^{-2+3}[/tex] = [tex]2^{1}[/tex]
and
[tex]3^{-2+4}[/tex] = 3²
18 = 2 × 3²
Answer:
x=-2
Step-by-step explanation:
[tex]2 {}^{x + 3} \times 3 {}^{x + 4 = 18} [/tex]
Apply the Inverse of the Product of Power Rule
If
[tex]x {}^{y} \times x {}^{z} = x {}^{y + z} [/tex]
This means that
[tex] {x}^{y + z} = {x}^{y} \times {x}^{z} [/tex]
So in order words,
[tex](2 {}^{x} \times 2 {}^{3} ) \times (3 {}^{x} \times 3 {}^{4} ) = 18[/tex]
[tex](2 {}^{x} \times 8) \times (3 {}^{x} \times 81) = 18[/tex]
Divide both sides by 31 and 8.
We get that
[tex]2 {}^{x} \times {3}^{x} = \frac{1}{36} [/tex]
[tex]6 {}^{x} = \frac{1}{36} [/tex]
Take the log of both sides.
[tex] log_{6}( \frac{1}{36} ) = x[/tex]
[tex]6 {}^{ - 2} = \frac{1}{36} [/tex]
so
[tex]x = - 2[/tex]
Find x.
A. 4
B. 4√2
C. 2√2
D. 8
Number of subsets of B={p,q,r}
Answer:
Step-by-step explanation:
B = {p , q , r}
Number of subsets = [tex]2^{n}[/tex]
Her, n is the number of elements in the set.
Number of subsets = 2³ = 8
Answer:
Sorry I don't know the answer
Graph the system of inequalities. Then state whether the situation is infeasible, has alternate optimal solutions, or is unbounded. (Assume that x>0 y>0
Answer:
x
[tex]x \leqslant - y + 1[/tex]
Steps are show in the picture above.
Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.
The Euler's formula relates the vertices, faces and the edges of a polyhedron.
The correct option is (e) [tex]V = 6[/tex] [tex]E = 10[/tex] [tex]F = 6[/tex] [tex]6- 10 + 6 = 2[/tex]
First, we count the number of faces. This is the flat parts of the shape.
The attached shape has 6 flat surfaces.
So:
[tex]F = 6[/tex]
Next, we count the number of edges. This is where two faces meet.
The attached shape has 10 edges;
So:
[tex]E = 10[/tex]
Lastly, we count the number of vertices. This is where two edges meet.
The attached shape has 6 vertices.
So:
[tex]V = 6[/tex]
Using Euler's formula, we have:
[tex]V - E + F = 2[/tex]
Substitute values for V, E and F
[tex]6- 10 + 6 = 2[/tex]
[tex]2 = 2[/tex]
Hence, the polyhedron has 6 vertices, 10 edges and 6 faces
Read more vertices, edges, and faces at:
https://brainly.com/question/23347978
the process of finding the indefinite integral. Give an example to provide emphasis.
Answer From Gauth Math
#1 with work please
Answer:
-19
Step-by-step explanation:
5v+3w
Let v = -5 and w=2
5(-5) + 3(2)
Multiply first
-25 + 6
The add
-19
1. Evaljate 5v +3w for v = -5 and w = 2
plug-in
5(-5) +3(2)
-25 +6
Answer: -19
2. Simplify the expression 8(e -1) + 2(e -1)
Distribute
8(e -1) + 2(e -1)
8e -8 + 2e -2
10e -10
Answer: 10e -10
x^2+4xy+4y^2-8x-16y-20
Answer:
Step-by-step explanation:
x²+4xy+4y²-8x-16y-20=(x+2y)²-8(x+2y)-20
put x+y=t
t²-8t-20=t²-10t+2t-20=t(t-10)+2(t-10)=(t-10)(t+2)
substitute the value of t
x²-4xy+4y²-8x-16y-20=(x+2y-10)(x+2y+2)
i don't know what else you want.
can someone solve this?
-5^4 x 4y^10 x -3y^-1
Answer:
[tex]7500 {y}^{9} [/tex]
Step-by-step explanation:
[tex] { - 5}^{4} \times {4y}^{10} \times { - 3y}^{ - 1} [/tex]
[tex] = 12 \times {5}^{4} {y}^{9} [/tex]
[tex] = 12 \times 625 {y}^{9} [/tex]
[tex] = 7500 {y}^{9} [/tex]
PLEASE HELP! Find the accumulated value of an investment of $17,000 at 6% compounded annually for 13 years. (Please show work tho)
9514 1404 393
Answer:
$36,259.78
Step-by-step explanation:
The formula for compound interest is ...
A = P(1 +r/n)^(nt)
where principal P is invested at annual rate r for t years compounded n times per year.
Here, you have P = 17000, r = 0.06, n = 1, t = 13.
A = 17000(1 +0.06)^13 = 17000(2.13292826) = 36,259.78
The accumulated value after 13 years is $36,259.78.
