Answer:
1.857 minutes
Step-by-step explanation:
From the given information:
Consider the amount of salt present in the tank as x(t) at a given time (t); &
The volume of the solution = V(t)
At t = 0 i.e. (at initial conditions) x(0) = 30; and V(0) = 50
However, the overall increase taken place for 1 gallon per minute is:
V(t) = 50 + t
The amount of salt x(t) at any given point for time (t) is;
[tex]\dfrac{x(t)}{V(t)}= \dfrac{x(t)}{50+t}[/tex]
After 5 gallons of solution exit per minute; the concentration of the salt solution changes at:
[tex]\dfrac{dx(t)}{dt}= -\dfrac{5x(t)}{50+t}[/tex]
Taking the integral of what we have above, we get:
In x(t) = - 5 In(t + 50) + In (C)
In x(t) = In (t+ 50)⁻⁵ + In (C)
In x(t) = In C ( t + 50)⁻⁵
x(t) = C(t + 50)⁻⁵ (General solution)
To estimate the required solution; we apply the initial conditions x(0) = 30;
Thus;
x(0) = C(50)⁻⁵ = 30
⇒ C = 30 × 50⁵
Hence; x(t) = 30 × 50⁵ × (t + 50)⁻⁵
The above expression can be re-written as:
[tex]x(t) = 25 \implies 30 \times \bigg ( \dfrac{50}{t+50} \bigg ) ^5= 25[/tex]
i.e.
[tex]\bigg ( \dfrac{50}{t+50} \bigg ) ^5= \dfrac{25}{30}[/tex]
[tex]\dfrac{50}{t+50}= \bigg ( \dfrac{25}{30}\bigg) ^{\dfrac{1}{5}}[/tex]
[tex]\dfrac{50}{t+50}= 0.964192504[/tex]
[tex]{50}= 0.964192504(t+50)[/tex]
50 = 0.964192504t + 48.2096252
50 - 48.2096252 = 0.964192504t
1.7903748 = 0.964192504t
t = 1.7903748 / 0.964192504
t ≅ 1.857 minutes
We can thereby conclude that the estimated time it will require until there are 25 pounds of salt in the tank is 1.857 minutes.
You have 41 marbles in a bag. Inside the bag are 15 red marbles, 10 blue marbles, and
the rest are white. If you reach into the bag and randomly select a marble, then what is
the probability the selected marble will be red?
Answer:
15/41
There are 41 marbles and 15 of them are red so you have a 15/41 chance to pick out a red as that is how many of them there are as compared to the total
A company that makes hair-care products had 6,000 people try a new shampoo. Of the 6,000 people, 24 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer:
0.4% people
Step-by-step explanation:
Convert fraction (ratio) 24 / 6,000 Answer: 0.4%
Answer:
0.4%
Step-by-step explanation:
HELPPPPP please it’s a test❗️
Answer:
the right answer is 4/3
Answer:
Scale factor increase of 4/3
Step-by-step explanation:
Look at one side and see how many units it increased from the original. Like 3 to 4units.
1.______+ 0.14 +0.23 = 0.9
2.______-0.0369=0.1246
Answer:
1) 0.53
2) 0.1615
Step-by-step explanation:
1) ______ + 0.37 = 0.9
______ = 0.9 - 0.37 = 0.53
2)______ - 0.0369 = 0.1246
______ = 0.1246 + 0.0369 = 0.1615
Answer:
1. 0.53
2.0.1615
Step-by-step explanation:
1.______+0.14+0.23=0.9
let the blank space be x
here,
x+0.14+0.23=0.9
or, x + 0.37=0.9
or, x=0.9- 0.37
: . x= 0.53
2. ______-0.0369 =0.1246
let the blank space be x
here,
x-0.0369= 0.1246
or,x=0.1246+0.0369
: . x= 0.1615
HOPE THIS HELPED.
Last week Jane made deposits of $64,25,and$37 into her checking account.she then Wrote checks For $52 and $49. What is janes new account balance?
Answer:
$25.
Step-by-step explanation:
64+25+37=126
52+49=101.00
126-101=25
Answer:
$25
Step-by-step explanation:
Assuming her bank account was initially at $0 then:
$64+$25+$37 = $126
$126 - $52 - $49 = $25
pls answer these as quick as possible
Answer:
what are we suppost to answer??
Step-by-step explanation:
George, a musician, works 35 hours in a week. If he earns $18.15 per hour, how much does he earn each week?
Answer:
$635.25
Step-by-step explanation:
He works 35 hours a week, multiply that by $18.15 and you get $635.25.
Nancy was buying peaches to make a cobbler. She needed 4.5 pounds of peaches, and they are on sale for $1.60 per pound. How much will the peaches cost?
Given:
Required quantity of peaches = 4.5 pounds
Cost of peach = $1.60 per pound.
To find:
The total cost of required peaches.
Solution:
We know that,
Total cost = Number of units × Cost per unit
Now,
[tex]\text{Total cost of peaches}=\text{Number of peaches}\times \text{Cost per peach}[/tex]
[tex]\text{Total cost of peaches}=4.5\times 1.60[/tex]
[tex]\text{Total cost of peaches}=7.20[/tex]
Therefore, the total cost of peaches is $7.20.
find the midpoint of the line segment with the given endpoints (9, -8) (-10, -2)
Answer:
mid point=(-1/2,-5)
Step-by-step explanation:
Look at image please help me asap
Answer: [tex]b^2[/tex]
You can write this as b^2
===================================================
Work Shown:
[tex]c = \frac{(ab^5)^{1/2}}{(ab)^{1/2}}\\\\c = \left(\frac{ab^5}{ab}\right)^{1/2}\\\\c = \left(b^4\right)^{1/2}\\\\c = b^{4*1/2}\\\\c = b^{2}\\\\[/tex]
Show that 2 is a factor of 70
Answer:
70÷2=35
Step-by-step explanation:
Answer:
If you divide 70 by 35 you get 2 so that means that 2 is a factor of 70
Step-by-step explanation:
rounded 7,499,846 rounded to the nearest 10,000
Answer:
7,410,000
Step-by-step explanation:
Answer:
7,500,000 is the answer.
Solve for y
3(7y + 4) = 15y + 6y +4+8
Answer: the are no values of y that make it true
Step-by-step explanation: no solution
Answer:
-4/7
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth.
Answer:
19/21=0.9
I hope this is good enough:
For which equations is 8 a solution. select 4 answers
X+6=2
X+2=10
X-4=4
X-2=10
2x=4
3x=24
X/2=16
X/8=1
Please hurry im timed
Answer:
X/8=1
X-4=4
×+2=10
Step-by-step explanation:
hope this helps :)
In Jeopardy, if you answer a question
incorrectly. you lose points. If Owen's score
is 200 points, then he answers a 350-point
question incorrectly, find his score.
Need this ASAP
Answer:
-150 points cause 200-350= -150
Step-by-step explanation:
Can i have brainliest i've never got one before
You work in a hospital, and instructions for an instrument state that it should be cleaned in the
sterilizer for two hours. The sterilizer requires cleaning time be entered in minutes. How many
minutes do you set for the sterilizer?
A. 90
B. 120
C. 180
D. 240
E. 500
Answer:
B
Step-by-step explanation:
120/60=2
2 hours
The time required in minutes to set the sterilizer is 120. The correct option is B.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that you work in a hospital, instructions for an instrument state that it should be cleaned in the sterilizer for two hours.
The time in minutes will be calculated as:-
Time = 2 hours
Time = 2 x 60 minutes
Time = 120 minutes
Therefore, the time required in minutes to set the sterilizer is 120. The correct option is B.
To know more about an expression follow
https://brainly.com/question/11096532
#SPJ2
store A Sells a set for $26 and offers a 15% discount
Answer:
Step-by-step explanation:
20% of $1200 is $240
(0.2∗1200)=$240
Now subtract that number from 1200
1200−240=$960
try this example
Answer:
$22.10
Step-by-step explanation:
First you would multiply 26 by .15, which represents 15%, or 15/100. After you multiply, you will get 3.9. 3.9 represents the discount of the price. Since it is a discount, you suntract 3.9 from 26, and you get 22.1.
Help me with precal pleaseee
Answer: Choice C
[tex]\left[0 , \frac{\pi}{2}\right) \ \ \text{ and } \ \ \left(\frac{\pi}{2}, \pi\right][/tex]
==================================================
Explanation:
Let's look at the function y = sec(x) first, which is the secant function.
Recall that secant is 1 over cosine, so sec(x) = 1/cos(x)
We can't divide by zero, so cos(x) = 0 can't be allowed. If x = pi/2, then cos(pi/2) = 0 will happen. So we must exclude pi/2 from the domain of sec(x).
If we look at the interval from 0 to pi, then the domain of sec(x) is [tex]0 \le x < \frac{\pi}{2} \ \ \text{ and } \ \ \frac{\pi}{2} < x \le \pi[/tex]
we can condense that into the interval notation [tex]\left[0 , \frac{\pi}{2}\right) \ \ \text{ and } \ \ \left(\frac{\pi}{2}, \pi\right][/tex]
Note the use of curved parenthesis to exclude the endpoint; while the square bracket includes the endpoint.
So effectively we just poked at hole at x = pi/2 to kick that out of the domain. I'm only focusing on the interval from 0 to pi so that secant is one to one on this interval. That way we can apply the inverse. When we apply the inverse, the domain and range swap places. So the range of arcsecant, or [tex]\sec^{-1}(x)[/tex] is going to also be [tex]\left[0 , \frac{\pi}{2}\right) \ \ \text{ and } \ \ \left(\frac{\pi}{2}, \pi\right][/tex]
There are 3 times as many books in the town library as there are on the school library. The town library has 2,676 books. How many books are in the school library?
Answer:
892 Books.
Step-by-step explanation:
It says there are three times as many books in the town library than the school, which means you would have to divide the amount of books in the town library by three.
What is the slope and equation of a line perpendicular to the y-axis passing through point (–5, –3)?
Answer:
Slope: m = 0
Equation: y = -3
Step-by-step explanation:
A line perpendicular to the y-axis always has a slope of 0. Slope is calculated by (y2-y1)/(x2-x1) or rise/run or delta y/delta x (they're all the same thing, delta means difference and is notated with a triangle). When there is no change in y (perpendicular to the y-axis), no matter what the change in x is, the slope will be 0.
Since it is given that one of the points has a y-value of -3, the equation for this line would be y = -3. The formula for a linear equation is y=mx+b. Since the slope is 0, the value of mx is 0, and therefore not needed in the equation. b represents the y-intercept and in this case would be -3.
help help help\help help help\help help help\help help help\help help help\help help help\help help help\
Answer:
D
Step-by-step explanation:
Subtract 60 from 80 to get 20, and divide 20 by 80 to get 1/4, which can be converted to 25%.
Answer:
i think its D but im not exactly sure
Ajay left x and y at 9 am.At the same time bala left y and x.After their meeting at a point on the way.Ajay took 16 minutes to reach y and bala took 9 minutes to reach x .Find the meeting time?
Answer:
9:12 amStep-by-step explanation:
Let the time Ajay and Bala took to meet be t, speed of Ajay be a and speed of Bala be b
Until they met, the distance they made:
Ajay ⇒ at Bala ⇒ btNow, the rest of the distance took Ajay 16 min and Bala 9 min.
We can compare the distances as:
16a = bt9b = atFrom the first equation we have:
a/b = t/16From the second equation we have:
a/b = 9/tComparing:
t/16= 9/tt² = 9*16t² = 144t = √144t = 12 minThe meting time is:
9:00 am + 12 min = 9:12 am
Do not really understand this question anybody help ?
Anybody Know This. ?
Answer:
96
Step-by-step explanation:
To get the volume multiply the length, width, and Height
12x4x2=96
The following are the annual salaries of 15 chief executive officers of major companies. (The salaries are written in thousands of dollars.)
157, 700, 1250, 767, 381, 495, 248, 75, 586, 224, 723, 472, 743, 676, 271
Required:
Find 25th and 70th percentiles for these salaries.
Answer:
The 25th percentile is 248.
The 70th percentile is 700.
Step-by-step explanation:
The pth percentile is a data value such that at least p% of the data-set is less-than or equal to this data value and at least (100-p)% of the data-set are more-than or equal to this data value.
Arrange the data set in ascending order as follows:
S = {75 , 157 , 224 , 248 , 271 , 381 , 472 , 495 , 586 , 676 , 700 , 723 , 743 , 767 , 1250}
The formula to compute the position of the pth percentile is:
[tex]p^{th} \text{Percentile}=\frac{(n+1)\cdot p}{100}[/tex]
Compute the 25th percentile as follows:
[tex]25^{th} \text{Percentile}=\frac{(15+1)\cdot 25}{100}=4^{th}obs.[/tex]
The 4th observation from the arranged data set is 248 .
Thus, the 25th percentile is 248.
Compute the 70th percentile as follows:
[tex]70^{th} \text{Percentile}=\frac{(15+1)\cdot 70}{100}\approx 11^{th}obs.[/tex]
The 11th observation from the arranged data set is 700.
Thus, the 70th percentile is 700.
f(2)=3x^2-6x+2
I need help!!!
Answer:
2
Step-by-step explanation:
substitute x by the value in the function, here its f(2) so
3(2)^2 - 6(2)+2
= 12 - 14 = 2
1)What Is Cos(150) ,sin(150), tan(150)
Answer:
cos(150)=−√32 sin(150)=12. Explanation: First of all, observe that 150=180−30 . Then, remember that we have. cos(180−x)=−cos(x)
Step-by-step explanation:
The dolphin dives 20 feet below the surface of the ocean. What is the dolphins elevation in feet?
Answer:
-20 Feet.
The dolphin went below its initial starting point, Zero
PLSSS HELPPPPP MEEEE III WILLL GIVVVEEE BRAINLIESTTTT!!!!!!
