Answer:
a) [tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
b) 10.643 kg
Step-by-step explanation:
Solution:-
- We will first denote the amount of salt in the solution as x ( t ) at any time t.
- We are given that the Pure water enters the tank ( contains zero salt ).
- The volumetric rate of flow in and out of tank is V(flow) = 50 L / min
- The rate of change of salt in the tank at time ( t ) can be expressed as a ODE considering the ( inflow ) and ( outflow ) of salt from the tank.
- The ODE is mathematically expressed as:
[tex]\frac{dx}{dt} =[/tex] ( salt flow in ) - ( salt flow out )
- Since the fresh water ( with zero salt ) flows in then ( salt flow in ) = 0
- The concentration of salt within the tank changes with time ( t ). The amount of salt in the tank at time ( t ) is denoted by x ( t ).
- The volume of water in the tank remains constant ( steady state conditions ). I.e 10 L volume leaves and 10 L is added at every second; hence, the total volume of solution in tank remains 5,000 L.
- So any time ( t ) the concentration of salt in the 5,000 L is:
[tex]conc = \frac{x(t)}{1000}\frac{kg}{L}[/tex]
- The amount of salt leaving the tank per unit time can be determined from:
salt flow-out = conc * V( flow-out )
salt flow-out = [tex]\frac{x(t)}{5000}\frac{kg}{L}*\frac{50 L}{min}\\[/tex]
salt flow-out = [tex]\frac{x(t)}{100}\frac{kg}{min}[/tex]
- The ODE becomes:
[tex]\frac{dx}{dt} = 0 - \frac{x}{100}[/tex]
- Separate the variables and integrate both sides:
[tex]\int {\frac{1}{x} } \, dx = -\int\limits^t_0 {\frac{1}{100} } \, dt + c\\\\Ln( x ) = -\frac{t}{100} + c\\\\x = C*e^(^-^\frac{t}{100}^)[/tex]
- We were given the initial conditions for the amount of salt in tank at time t = 0 as x ( 0 ) = 13 kg. Use the initial conditions to evaluate the constant of integration:
[tex]13 = C*e^0 = C[/tex]
- The solution to the ODE becomes:
[tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
- We will use the derived solution of the ODE to determine the amount amount of salt in the tank after t = 20 mins:
[tex]x(20) = 13*e^(^-^\frac{20}{100}^)\\\\x(20) = 13*e^(^-^\frac{1}{5}^)\\\\x(20) = 10.643 kg[/tex]
- The amount of salt left in the tank after t = 20 mins is x = 10.643 kg
Hey can anyone help me with this 3 3/5 x (-8 1/3)?
Answer:
[tex]-30[/tex]
Step-by-step explanation:
[tex]3\frac{3}{5} \times (-8 \frac{1}{3} )[/tex]
[tex]\frac{18}{5}\times \left(-\frac{25}{3}\right)[/tex]
[tex]\frac{18}{5}\times -\frac{25}{3}[/tex]
[tex]-\frac{18\times \:25}{5\times \:3}[/tex]
[tex]-\frac{450}{15}[/tex]
[tex]=-30[/tex]
Answer:-30
Step-by-step explanation:
3 3/5 x -8 1/3
18/5 x -25/3
-30
What is the main issue with plugging values into a function and then graphing it?
Too hard to calculate.
Takes too much time.
Never sure of exact data points.
Does not provide accurate results.
Answer:
B: It takes too much time
Step-by-step explanation:
Once the points have been calculated and then graphed, the solutions to y = 0 can be found. Look for y = 0 and the solutions are -5 and -1. But that takes a lot of time. There must be an easier way, and fortunately, there is.
round 3, 942,588 to the nearest thousand
Answer:
3, 943,000
Step-by-step explanation:
3, 942,588
The 2 is in the thousands place
We look at the hundreds place
There is a 5, that means we round up
2 becomes a 3
3, 943,000
write down the exact value of
a. cos 30 degrees
b. sin45 degrees
c. tan 30 degrees
Answer:
.86602 a
.707106 b
.577355 c
Step-by-step explanation:
entered itno calculator
You are writing music for a movie and you have to synchronize the music to the amount of frames per click in it. It's a battle scene so you want fast, energetic and exciting music. You choose a Presto tempo marking of 200 beats per minute. How many picture frames are there per each tempo click? (Round to the nearest whole number and write only the number.)
Answer: 7.2 frames per bit.
Step-by-step explanation:
Our teempo is 200 bpm.
in one minute we have 60 seconds, so here we have:
200b/60s = 3.33 bits per second.
For movies, the standar is 24 frames per second
now, we can take the quotient between the frames per second and the bits per second and get the frames per bit.
24fps/3.33bps = 7.2 frames per bit.
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
670
Step-by-step explanation:
2003-814=1189
1189-519=670
Answer: The third number is 670.
Step-by-step explanation:
The sum means three numbers being added up is equal to 2003 so give two of those numbers you have to add them up and subtract it from 2003 to find the third number.
814 + 519 + x = 2003 where x is the third number
1333 + x = 2003
-1333 -1333
x = 670 So the third number is 670
Check:
814 + 670 + 519 = 2003
2003 = 2003 so yes again 670 is the third number.
how do you add 9 in 1 6 + 2 1/12
Step-by-step explanation:
9 + 1/6 + 2 1/12
9 + 2.25
11.25
Choose the slope and y-intercept that
correspond with the graph.
Answer:
slope = -3, y intercept = 3
Step-by-step explanation:
The y intercept is where it crosses the y axis
y intercept is 3
The slope is found by taking two points (0,3) and (1,0) and using the slope formula
m = (y2-y1)/(x2-x1)
= (0-3)/(1-0)
-3/1
=-3
please help image attached!
Answer:
The unit circle centered at the origin in the Euclidean plane is defined by the equation:
[tex]x^2+y^2=1\\[/tex]
Given an angle , there is a unique point P on the unit circle at an angle θ from the x-axis, and the x- and y-coordinates of P are:
[tex]x=cos \theta \\y = sin \theta[/tex]
Consequently, from the equation for the unit circle:
[tex]cos^2\theta+sin^2\theta=1[/tex]
the Pythagorean identity.
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
8
Step-by-step explanation:
y²+by+16= (y+4)²
y²+by+16= y²+2*4*y+4²
y²+by+16= y²+8y+16
by=8y
b=8
A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds x=20.6 months and s=8 months. Test the claim that u=18.7 months at the 0.05 significance level.
Answer:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
Step-by-step explanation:
Information given
[tex]\bar X=20.6[/tex] represent the sample mean
[tex]s=8[/tex] represent the sample standard deviation
[tex]n=11[/tex] sample size
[tex]\mu_o =18.7[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypotesis to test
We want to verify if the true mean is equal to 18.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu =18.7[/tex]
Alternative hypothesis:[tex]\mu \neq 18.7[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
ABDC is a rhombus with side length 10cm
angle ADC=40degrees
DAC is a sector of a circle with center D
BAC is a sector of a circle with center B
CALCULATE THE SHADED AREA (in cm2)
22,056 people went to the baseball game on Sunday. Half as many people came on money. How many people were at the baseball game on Sunday and Monday altogether?
Answer:33084
Step-by-step explanation:
22056 divided by 2 = Monday
Monday= 11028
11028+22056=33084
Answer:
33084 People were at the baseball game on Sunday and ~Money~ Monday all together.
Step-by-step explanation:
Sunday - 22056
Monday - "Half as many" 22056 Divided by 2
= 11028
Altogether - Sunday + Monday = 33084
As a shortcut on your calculator, you could do:
22056 + (22056 divided by 2)
= 33084
WILL GIVE BRAINLIEST! HURRY
Answer:
4
Step-by-step explanation:
2(6x+4)-6+2x=3(4x+3)+1
=14x+2=12x+10
=14x+2-2=12x+10-2
=14x=12x+8
=14x-12x=12x+8-12x
=2x=8
=2x/2=8/2
x=4
If you have changed the tires on your car, the original diameter is 24.5 inches. to a new diameter of 26 inches, how fast are you actually going if your speedometer is reading 53 mph? A. 50.5 mph B. 53 mph C. 56.2 mph D. 62.8 mph
Answer: c) 56.2
Step-by-step explanation:
Compare the original rate to the the new rate:
[tex]\dfrac{diameter}{mph}:\dfrac{24.5\ in}{53\ mph}=\dfrac{26\ in}{x}\\\\\\24.5x=53(26)\\\\\\x=\dfrac{53(26)}{24.5}\\\\\\x=\large\boxed{56.2\ mph}[/tex]
1/4+3/8+1/2+5/8+7/8
Answer: 1/4+3/8+1/2+5/8+7/8
= 21/8
Hope this helps :)))
Answer:
21/8
Step-by-step explanation:
Given f(xl=x-7 and g(x)=x^2 find g(f(4))
Answer:
So we first need to solve for f(4) because thats what's inside g(_)
It should be 4-7 because I think its f(x)=x-7 you weren't very clear on it.
so that means that we need to solve for g(-3)
-3^2 = 9 because -3*-3 = 9
9 is answer
Name the numerator and the denominator in each fraction 11⁄12
. 7⁄512
. 12⁄10
0⁄78
Answer:
numerators: 11 7. 12. 0
_ _ _. _
denominators. 12 512. 10. 78
Step-by-step explanation:
Answer:
11/12 n:11 d:12
7/512 n:7 d:512
12/10 n:12 d:10
0/78 n:0 d:78
Step-by-step explanation:
n=numerator
d=denominator
How to find a vertical asymptote
Answer:
Step-by-step explanation:
Generally's rational functions that have vertical asymptotes, even trig functions (which, like the tangent function, are often rational).
If the given function is the ratio of two functions, polynomial or otherwise, the graph of the given function has an asymptote at any x value for which the denominator is zero. Example: y = tan x = (sin x) / (cos x) has vertical asysmptotes at π/2, 3π/2, and so on, because the denominator cos x is zero for those angles.
Simplify
6x^-2. ....
Answer:
6/x^2
Step-by-step explanation:
6x^-2
6*x^-2
6*(1/x^2)
6/x^2
n th term of quadratic sequence 3, 11 , 25, 45
The first differences are 8, 14, 20.
The second differences are 6.
Half of 6 is 3, so the first term of the sequence is 3n^2.
If you subtract 3n^2 from the sequence you get 0,-1,-2,-3 which has the nth term of -n + 1.
Therefore your final answer will be 3n^2 - n + 1
A quick quiz consists of a multiple-choice question with 5 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct. Report the answer as a percent rounded to two decimal place accuracy. You need not enter the "%" symbol. Probability = %
Answer:
Probability = 4%
Step-by-step explanation:
For each answer, there are only two possible outcomes. Either it is correct, or it is not. The probability of an answer being correct is independent of other answers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has 5 possible answer:
The person guesses, so [tex]p = \frac{1}{5} = 0.2[/tex]
2 questions:
This means that [tex]n = 2[/tex]
Find the probability that both responses are correct.
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.2)^{2}.(0.8)^{0} = 0.04[/tex]
As a percent:
Probability = 4%
In this diagram, BAC – EDF. If the
area of BAC = 24 in2, what is the
area of EDF?
Help please
If the area of ΔBAC = 24 in², the area of ΔEDF is 6 in².
What are similar triangles?If two triangles' angles are congruent and their corresponding sides are proportionate, they are considered similar. To put it another way, similar triangles are the same in shape but not necessarily in size. If ΔPQR and ΔMNO are two similar triangles, then we can write it as ΔPQR ∼ ΔMNO.
Statement:The square of the ratio of any pair of their respective sides is equal to the ratio of the areas of two similar triangles.
How to solve this problem?Since ΔBAC ∼ ΔEDF, we can use the above statement to find the area of ΔEDF. Let the area of ΔEDF be x in². Given that length of EF and BC is 2 in and 4 in respectively.
So, we have to solve this equation,
24/x = 4²/2²
Now, 24/x = 16/4
i.e. 24/x = 4
i.e. 4x = 24
i.e. x = 24/4 = 6
Therefore the area of ΔEDF is 6 in².
Learn more about similar triangles here -
https://brainly.com/question/16819417
#SPJ2
At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 519 ml. The filling process follows a normal distribution with a known process standard deviation of 6 ml.
1) The normal distribution should be used for the sample mean because:_____.
a) the sample population has a large mean.
b) the population distribution is known to be normal.
c) the population standard deviation is known.
d) the standard deviation is very small.
2) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. The hypothesis for a two-tailed decision is:_______.
A. H0: mu not equal to 519, H1: mu = 519, reject if z < -1.96 or z > 1.96.
B. H0: mu not equal to 519, H1: mu = 519, reject if z > 1.96 or z < -1.96.
C. H0: mu = 519, mu not equal to 519, reject if z> 1.96 or z< -1.96.
D. H0: mu = 519, H_1: mu not equal to 519, reject if z > -1.96 or z< 1.96.
a. a.
b. b.
c. c.
d. d.
3) If a sample of 16 bottles shows a mean fill of 522 ml, does this contradict the hypothesis that the true mean is 519 ml?
A) Yes.
B) No
Answer:
1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).
2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.
3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.
Step-by-step explanation:
1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.
2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.
The null hypothesis state that there is not significant difference from 519.
The critical value for a significance level of 5% is z=1.96.
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
3) The claim is that the true mean is not 519 ml.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
The significance level is 0.05.
The sample has a size n=16.
The sample mean is M=522.
The standard deviation of the population is known and has a value of σ=6.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{16}}=1.5[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{522-519}{1.5}=\dfrac{3}{1.5}=2[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>2)=0.046[/tex]
As the P-value (0.046) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the true mean is not 519 ml.
An amusement park had 56,437 visitors the first year and 48, 319 visitors the second year it was open . What was the total number of visitors for both year
Answer:
the total number is 104756
Step-by-step explanation:
You need to add 56437 with 48319 which equals 104756
Awnser is 104,756 if you add the 2 numbers
Please answer this correctly
Answer:
629
Step-by-step explanation:
l x w
25x14
4x7
12x18
5x7
629
You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this. If you roll a 1, 2 or 3, you win $50. If you roll a 4 or 5, you lose $20. If you roll a 6, you lose $90.
EV= $
Step-by-step explanation:
Take the $50 and quit.
(Each game as outlined by drwls has an expected value of $1.50.
You are playing it 5 times, so the expected return is $7.50.
Your choice was to either accept $50 or play the game)
Steve drove for 812 hours at 72 miles per hour. How much distance did he travel
Answer:
[tex]58,464 \: \: miles[/tex]
Step-by-step explanation:
[tex]speed = \frac{distantce}{time} \\ [/tex]
[tex]distance = speed \times time \\ x = 72 \times 812 \\ x = 58,464 \: \: miles[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Find all zeros of f(x)=x^3−17x^2+49x−833
Answer:
x = 17 or x = ±7i
Step-by-step explanation:
x³ − 17x² + 49x − 833 = 0
x² (x − 17) + 49 (x − 17) = 0
(x² + 49) (x − 17) = 0
x = 17 or ±7i
What’s the correct answer for this question?
Answer:
B
Step-by-step explanation:
In the attached file