Answer:
true
Step-by-step explanation:
.
Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 80 grams of salt in 40 liters of water.
A solution of 2 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 3 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.
The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.
Letting x represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
Let a(t) and b(t) denote the amounts of salt in tanks A and B, respectively.
The volume of liquid in tanks A and B after t minutes are
A: 50 L + (5 L/min + 3 L/min - 8 L/min)t = 50 L
B: 40 L + (7 L/min + 8 L/min - 3 L/min - 12 L/min)t = 40 L
so the amount of solution in the tanks stays constant.
Salt flows into tank A at a rate of
(2 g/L)*(5 L/min) + (b(t)/40 g/L)*(3 L/min) = (10 + 3/40 b(t)) g/min
and out at a rate of
(a(t)/50 g/L)*(8 L/min) = 4/25 a(t) g/min
so the net flow rate is given by the differential equation
[tex]\dfrac{\mathrm da(t)}{\mathrm dt}=10+\dfrac{3b(t)}{40}-\dfrac{4a(t)}{25}[/tex]
We do the same for tank B: salt flows in at a rate of
(3 g/L)*(7 L/min) + (a(t)/50 g/L)*(8 L/min) = (21 + 4/25 a(t)) g/min
and out at a rate of
(b(t)/40 g/L)*(3 L/min + 12 L/min) = 3/8 b(t) g/min
and hence with a net rate of
[tex]\dfrac{\mathrm db(t)}{\mathrm dt}=21+\dfrac{4a(t)}{25}-\dfrac{3b(t)}8[/tex]
Replace a(t) and b(t) with x and y. Then the system is (in matrix form)
[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\end{bmatrix}=\dfrac1{200}\begin{bmatrix}-32&15\\32&-75\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}+\begin{bmatrix}10\\21\end{bmatrix}[/tex]
with initial conditions x(0) = 60 g and y(0) = 80 g.
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters which measurement does 17 meters represent
The answer in length
The length is used to measure the distance between to end points or edges. so 17 meters measurement represent the length.
What is perimeter?Its the sum of length of the sides used to made the given figure.
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters.
Area is what is on the inside.
The perimeter is the outside of the hole thing.
Hence, the length is used to measure the distance between to end points or edges.
so 17 meters measurement represent the length.
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Matt says 3/3 is equivalent to 1 is he correct?
Answer: Yes
Step-by-step explanation:
It isn't an
1 an improper fraction
Less than the denominator
Therefore, three thirds or 3/3 is one whole fraction
Rly hope I helped!
☆꧁Ashlin꧂☆
Answer:yes he his correct
Step-by-step explanation:
3/3=1
What’s the correct answer?
Answer:
B.
Step-by-step explanation:
Answer:b
Step-by-step explanation:you need to add both
Determine the value of x for the triangle. show work.
Answer:
x=5
Step-by-step explanation:
x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.
Answer:
5
Step-by-step explanation:
Because this is a right triangle, you know that by the Pythagorean theorem:[tex]\sqrt{(x+7)^2+x^2}=x+8[/tex]
Squaring both sides to get rid of the square root:
[tex](x+7)^2+x^2=(x+8)^2[/tex]
Expanding all of the parentheses:
[tex]x^2+14x+49+x^2=x^2+16x+64[/tex]
Combine like terms:
[tex]x^2-2x-15=0[/tex]
Factor:
[tex](x-5)(x+3)=0[/tex]
Since x cannot be negative, it is equal to 5. Hope this helps!
a number rounded to the nearest hundred thousand is 400,000 the same number rounded to the nearest ten thousand is 350,000 what could be the number
Answer:350000
Step-by-step explanation:
The number is 350000
350000 rounded to the nearest hundred thousand is 400000
350000 rounded to the nearest ten thousand is 350000
In ΔPQR, the measure of ∠R=90°, RP = 9.9 feet, and QR = 3.2 feet. Find the measure of ∠P to the nearest tenth of a degree.
Answer:
17.9
Step-by-step explanation:
a candlemaker prices one set of scented candles at $10
y=10x
x= how many candles
Find the arc length of the partial circle. with a radius of 1
Answer:
1/2π
Step-by-step explanation:
For khan, you HAVE to put the pi symbol. just type pi and itll work
Answer:
1/2 pi (Sorry i don't have the pi symbol)
Step-by-step explanation:
change 5 out of 19 to a percentage
Answer:
26.3%
Step-by-step explanation:
5 is divided by 19
That answer is then multiplied by 100.
You may round your answer to the nearest whole number.
What type of lines are shown?
Answer:
the angle is acute angle
Answer:
The type of angle shown is an acute angle
Step-by-step explanation:
there are 4 main types of angles. this is an acute angle as it is less than 90°.
Types of angles:
The 4 main types of angles are: acute, obtuse, right angles, reflex angles.
Acute angles- Acute angles are angles less than 90°.
Obtuse Angles-Obtuse angles are angles greater than 90° but less than 180°.
Right Angles- Right angles are angles of 90°.
Reflex Angles- Reflex angles are angles greater than 180° but less than 360°.
Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 19 specimens of a particular species, 6 resprouted after fire. Estimate with 96% confidence the proportion of all shrubs of this species that will resprout after fire. Interval: .1884 to
The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.
Here, we have,
To estimate the proportion of all shrubs of this species that will resprout after fire with 96% confidence, we will use the formula for a confidence interval for a proportion.
The formula for the confidence interval for a proportion (p) is given by:
CI = p ± Z * √(p * (1 - p) / n)
where:
CI is the confidence interval
p is the sample proportion (resprouted specimens / total specimens)
Z is the critical Z-score corresponding to the desired confidence level (96% confidence level corresponds to a Z-score of approximately 1.750)
n is the sample size (total number of specimens)
Given information:
Total number of specimens (n) = 19
Number of specimens that resprouted after fire = 6
Now, calculate the sample proportion (p):
p = (number of specimens that resprouted) / (total number of specimens)
p = 6 / 19 ≈ 0.3158 (rounded to four decimal places)
Now, calculate the critical Z-score for a 96% confidence level (use a Z-table or calculator):
Z ≈ 1.750
Now, calculate the margin of error (E):
E = Z * √(p * (1 - p) / n)
E = 1.750 * √(0.3158 * (1 - 0.3158) / 19)
E ≈ 0.1884 (rounded to four decimal places)
Finally, calculate the confidence interval:
CI = p ± E
CI = 0.3158 ± 0.1884
The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.
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If the mean of a symmetric distribution is 60, which of these values could be
the median of the distribution?
A. 100
B. 60
C. 80 As
D. 30
SUBMIT
Answer:
i think ...
Step-by-step explanation:
symmetric distribution usually be a bell shape distribution .
most likely the median = mean = 60
The required value of 60 could be the median of the distribution. Option B is correct.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
What is the median?When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top 50% of data.
Here,
The mean of a symmetric distribution is 60.
Since for the symmetric data and rational data, the mean is equal to the median,
So Mean = Median
Median = 60
Thus, the required value of 60 could be the median of the distribution.
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A soda manufacturer claims that its Cherry Fizz soda has more carbonation than a competitor’s Cherry Eclipse soda. Bottles of both types of soda are opened, covered with a balloon, and then shaken. The diameter of each balloon is then measured. The mean balloon diameters are 2.3 inches for the Cherry Fizz soda and 2.1 inches for the Cherry Eclipse soda. A 90 percent confidence interval to estimate the difference in mean diameters, in inches, is (−0.8,1.2). Which of the following claims is supported by the interval?
Answer:
E) Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.
Step-by-step explanation:
Hello!
The soda manufacturer claims that it's Cherry Fizz soda that has more carbonation than the competitor's Cherry Eclipse soda.
To test this claim they compared the carbonation by opening bottles of each soda, covered them with a balloon, and agitated the bottle to release the gas into the ballon. Later the balloon's diameter of each bottle of soda was measured.
Be the variables:
X₁: Diameter of a balloon filled with the gas of a Cherry Fizz soda bottle.
X₂: Diameter of a balloon filled with the gas of a Cherry Eclipse soda bottle.
X[bar]₁= 2.3 inches
X[bar]₂= 2.1 inches
The difference between the two means μ₁-μ₂ was estimated with a 90% CI, obtaining: [-0.8;1.2]inches
Usings 90% confidence level you can expect the interval [-0.8;1.2]inches to include the difference between the diameter of the balloons filled with the gas of the Cherry Fizz soda and the diameter of the balloons filled with the gas of the Cherry Eclipse soda.
The claims are:
A) Because 2.3 inches is larger than 2.1 inches, the manufacturer is correct, and Cherry Fizz has more carbonation.
INCORRECT, the given values are sample measures, you cannot reach any valid conclusions by simply comparing them.
B) Because the interval has more positive than negative values, Cherry Fizz has more carbonation.
INCORRECT, the confidence interval provides a range of values for the estimated parameter, it is equally probable that the parameter is closer to the lower bond, the upper bond, or in the middle of the interval.
C) Because 2.3 and 2.1 are very similar, there is no difference in the mean carbonation levels.
INCORRECT, same as in item A, you cannot reach any valid conclusion by just comparing the sample values, a propper hypothesis test is needed.
D) The interval cannot be interpreted because negative measurements are not possible.
INCORRECT, this interval vas made to estimate the difference between the two means, therefore if one value is less than the other it is possible to observe negative values.
If the CI was to estimate the value of the mean diameter of the balloons of one of the groups, then a negative measurement would be invalid.
E) Because the interval contains 0, there may be no difference in mean carbonation levels.
CORRECT
If you were to test the hypotheses
H₀: μ₁-μ₂=0
H₁: μ₁-μ₂≠0
Using a significance level, complementary to the confidence level used to construct the interval α: 0.1 you can decide whether or not the difference between population means are equal to zero or not.
If the interval contains the zero, then you do not reject the null hypotheses and there is no difference between the population means.
If the interval doesn't include the zero, then you reject the null hypothesis.
I hope this helps!
E) Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.
What will be the answer?
The soda manufacturer claims that it's Cherry Fizz soda that has more carbonation than the competitor's Cherry Eclipse soda.
To test this claim they compared the carbonation by opening bottles of each soda, covered them with a balloon, and agitated the bottle to release the gas into the ballon. Later the balloon's diameter of each bottle of soda was measured.
Be the variables:
X₁: Diameter of a balloon filled with the gas of a Cherry Fizz soda bottle.
X₂: Diameter of a balloon filled with the gas of a Cherry Eclipse soda bottle.
X[bar]₁= 2.3 inches
X[bar]₂= 2.1 inches
The difference between the two means μ₁-μ₂ was estimated with a 90% CI, obtaining: [-0.8;1.2]inches
Usings 90% confidence level you can expect the interval [-0.8;1.2]inches to include the difference between the diameter of the balloons filled with the gas of the Cherry Fizz soda and the diameter of the balloons filled with the gas of the Cherry Eclipse soda.
The claims are:
A) Because 2.3 inches is larger than 2.1 inches, the manufacturer is correct, and Cherry Fizz has more carbonation.
INCORRECT, the given values are sample measures, you cannot reach any valid conclusions by simply comparing them.B) Because the interval has more positive than negative values, Cherry Fizz has more carbonation.
INCORRECT, the confidence interval provides a range of values for the estimated parameter, it is equally probable that the parameter is closer to the lower bond, the upper bond, or in the middle of the interval.C) Because 2.3 and 2.1 are very similar, there is no difference in the mean carbonation levels.
INCORRECT, same as in item A, you cannot reach any valid conclusion by just comparing the sample values, a propper hypothesis test is needed.D) The interval cannot be interpreted because negative measurements are not possible.
INCORRECT, this interval vas made to estimate the difference between the two means, therefore if one value is less than the other it is possible to observe negative values.If the CI was to estimate the value of the mean diameter of the balloons of one of the groups, then a negative measurement would be invalid.
E) Because the interval contains 0, there may be no difference in mean carbonation levels.
CORRECT If you were to test the hypothesesH₀: μ₁-μ₂=0H₁: μ₁-μ₂≠0Using a significance level, complementary to the confidence level used to construct the interval α: 0.1 you can decide whether or not the difference between population means are equal to zero or not.
If the interval contains the zero, then you do not reject the null hypotheses and there is no difference between the population means.
If the interval doesn't include the zero, then you reject the null hypothesis.
Thus the interval contains 0, it is possible that there is no difference in mean carbonation levels.
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Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. How long will it take the coin to reach the stream?
Answer:
about 5.613 seconds
Step-by-step explanation:
Using the quadratic formula to find the value of t when h = 0, we have ...
at² +bt +c = 0
t = (-b±√(b²-4ac))/(2a)
t = (-72±√(72² -4(-16)(100)))/(2(-16))
t = (-72±√11584)/-32 = (9±√181)/4
Only the positive value of t is of interest.
The coin will hit the stream after (9+√181)/4 seconds ≈ 5.613 seconds.
If you put all the sunflowers together end to end, what would be the total length of all the sunflowers?
Answer:
7 1\68
Step-by-step explanation:
all i did was look up a fraction calculator
calculator soup is the one i used :)
a circle with area 36pi has a sector with a central angle of 48°. what is the area of the sector?
Answer:4.8π
Step-by-step explanation:
Φ=48°
Area of circle=36π
Area of circle=π x r^2
36π=πr^2
Dividing both sides by π we get
r^2=36π/π
r^2=36
Take them square root of both sides
√(r^2)=√(36)
r=6
Area of sector=Φ/360 x π x r x r
Area of sector=48/360 x π x 6 x 6
Area of sector=(48xπx6x6)/360
Area of sector=1728π/360
Area of sector=4.8π
A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks
Answer:
The number of mice that will be infected next week are 130 while
The number of mice that will be infected in 3 weeks are 111
Step-by-step explanation:
From the information given , the researcher is studying the spread of a virus in a population of 1000 laboratory mice. i.e, n = 1000
Number of infected = 300
Non infected = 1000 - 300 = 700
Probability an infected mouse will overcome = 80% = 0.8
Probability a noninfected mouse becomes infected = 10% = 0.10
The number of infected that will overcome = 0.8 * 300 = 240
The number of non infected that will become infected = 0.1 * 700 = 70
The number that will be infected on the first week =
300 - 240 + 70
= 130
Number that will be healthy on the first week =
700 + 240 - 70
= 870
Calculating for week 2:
The number of infected that will overcome = 0.8 * 130 = 104
The number of non infected that will become infected = 0.10 * 870 = 87
The number that will be infected on the second week =
130 - 104 + 87
= 113
Number that will be healthy on the second week =
870 + 107 - 87
= 887
Calculating for week 3:
The number of infected that will overcome = 0.8 * 113 = 90.4
The number of non infected that will become infected = 0.10 * 887 = 88.7
The number that will be infected on the third week =
113 - 90.4 + 88.7
= 111.3 ≈ 111
Number that will be healthy on the third week =
887 + 90.4 - 88.7
= 888.7 ≈ 889
From our calculations, the number of mice that will be infected next week are 130
The number of mice that will be infected in 3 weeks are 111
What is 1 2/3 - 2 1/3?
Step-by-step explanation:
First it will be easer if you turn both sides into improper fractions
5/3-7/3
Now do 5-7
5-7=-2
The bottom of the fraction stays the same
-2/3 is your answer.
The perimeter of a rectangle is 62 meters. The length is 4 more than 2 times the width. What is the length?
Answer:
4x+ 1 = 24 + 1 = 25 m.
Step-by-step explanation:
Given, perimeter = 62 m. Perimeter : 2 (L+W) = 62 m. hence, L+W = 31 m. x = 30/5
Answer:
Step-by-step explanation:
let width be x
length = 2x + 4
2(x + 2x + 4) = 62
6x + 8 = 62
6x = 54
x = 9
length = 2(9) + 4 = 22cm
What is the sum of 6 x 12?
Answer:
72
Step-by-step explanation:
because 6 x 10 is 60 so 6 x 2 is 12, so 12 + 60 is 72.
what’s the gcf of x^2 and 5x
Answer:
the GCF of x^2 and 5x is x
Find the prime factors of each term in order to find the greatest common factor (GCF).
If the fish tanks dimension are 60 by 15 by 34 and its is completely empty, what volume of water is needed to fill three fourths of the aquarium? Please help
Answer:
22,950 units³
Step-by-step explanation:
All you have to do is:
[tex]\frac{3}{4} *60*15*34=\\45*15*34=\\675*34=\\\\22,950[/tex]
Twenty words were randomly selected from two textbooks. Each set gives the number of letters in each of the twenty words for that textbook.
Briefly describe how the word lengths compare between textbook 2 and textbook 1.
Briefly describe the variability in the length of words in textbook 2 compared to textbook 1. PLEASE HURRY :(
Answer:
k = 13The smallest zero or root is x = -10
Step-by-step explanation:
you can write "x^2" to mean "x squared"
f(x) = x^2+3x-10
f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5
f(x+5) = (x^2+10x+25)+3(x+5)-10
f(x+5) = x^2+10x+25+3x+15-10
f(x+5) = x^2+13x+30
Compare this with x^2+kx+30 and we see that k = 13
Factor and solve the equation below
x^2+13x+30 = 0
(x+10)(x+3) = 0
x+10 = 0 or x+3 = 0
x = -10 or x = -3
The smallest zero is x = -10 as its the left-most value on a number line.
Which expression can be used to find the area of the rectangle shown on the coordinate plane 6×7 7×7 8×7 8×8
Answer:that’s a lot of numbers.
Step-by-step explanation:
A North American company manufactures rivets for use in car production. A sample of forty rivets from the production line had mean 6.803 and standard deviation 0.275 (both in 1/100 of an inch). On communicating these results to the company headquarters in Europe, a request is made for the summary statistics to be converted into millimeters. Given that one inch is 2.538 centimeters, find the mean and standard deviation of the sample in millimeters. What is the mean in millimeters
Answer:
Mean = 1.73 mm
Standard deviation = 0.0698 mm
Step-by-step explanation:
Given:
Sample size, n = 40
Mean, u = 6.803
Standard deviation = 0.275
a) Given that one inch is 2.538 centimeters, to find the mean in millimeters we have:
[tex] 6.803 * \frac{1}{100} [/tex]
Converting to cm, we have:
[tex] 6.803 * \frac{1}{100} * 2.538 = 0.173 cm[/tex]
Converting to mm, we know 1cm = 10 mm,
0.173 * 10 = 1.73 mm
b) Given that one inch is 2.538 centimeters, to find the standard deviation in millimeters we have:
[tex] 0.275 * \frac{1}{100} [/tex]
Converting to cm, we have:
[tex] 0.275 * \frac{1}{100} * 2.538 = 0.00698 cm[/tex]
Converting to mm, we know 1cm = 10 mm,
0.00698 * 10 = 0.0698mm
In this exercise we have to use the knowledge of statistics to calculate the car production, so we have to:
Mean: [tex]1.73mm[/tex]Standard deviation: [tex]0.0698 mm[/tex]Given the following information, we have:
Sample size n = 40 Mean u = 6.803 Standard deviation = 0.275A) Find the convertion to the mean in milimeters, will be:
[tex]6.803*(1/100)*2.538=0.173 cm\\=1.73 mm[/tex]
B) Find the convertion to the stardard deviation in milimeters, will be:
[tex]0.275*(1/100)*2.538=0.00698\\=0.0698 mm[/tex]
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What function has zeros at x=10 and x=2
Answer:
f(x) = x^2 -12x +20
Step-by-step explanation:
There are an infinite number of functions with zeros at those values of x. One simple polynomial function with those zeros is ...
f(x) = (x -10)(x -2) . . . . . each zero contributes a factor
f(x) = x^2 -12x +20
Erin built a wooden box to hold hay on her farm. The box is 3 m long, 1 m wide, and 1 m high. Hay costs $14 per cubic meter.
Answer:
It will cost 42 to completely fill the box with hay.
have a good day <3
what is the equation to the following sentence?
Seven subtracted from two times a number is 13
Answer:
4x-7>13
add 7
4x>20
divide by 4
x>5
Step-by-step explanation:
IL GIVE YOU BRAINLIST !! * have to get it right * An equation for the line graphed is
Answer:
y = 3/2x+3
Step-by-step explanation:
The y intercept is 3. That is where it crosses the y axis
The slope is
m= (y2-y1)/(x2-x1) and we have points(0,3) and (-2,0)
= (0-3)/(-2,0)
=-3/-2
=3/2
Using the slope intercept form of a line
y = mx +b where m is the slope and b is the y intercept
y = 3/2x+3
