(a) The concentration of our solution in the tank initially is 0.060 kg/L. (b) the amount of salt in the tank after 2. 5 hours is 44.45 kg. (c) The concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.
How do you find the concentration of a salt solution?Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.
(A) Tank contains 60 kg of salt and 1000 L of water. So the concentration of solution in the tank initially = 60/1000 kg/l
The concentration of solution in the tank initially = 0.060 kg/L
(B) Let y(t) denote the amount of salt in the tank at any time t.
Rate In
A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.
[tex]R_{i}[/tex] =(concentration of salt in inflow)(input rate of solution)
= (0.03kg/L)*(9L/min)
= 0.27kg/min
Rate Out
The solution is mixed and drains from the tank at the same rate.
Concentration, C(t) = Amount/Volume = y(t)/1000
[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)
= {y(t)/1000}kg/L*9L/min
= 0.009y(t) kg/min
Therefore, the differential equation for the amount of Salt in the Tank at any time t:
dy/dt = 0.27 - 0.009y(t)
So the amount of salt in the tank after 2. 5 hours (2.5*60 min = 150 min) is 44.45 kg.
(c) The concentration of salt in the solution in the tank as time approaches infinity
As t -> -∞, e^-∞ = 0
so, the concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.
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Is halting undecidable?
Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.
What is a tractable problem?a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.
Here,
There is no programme that can resolve the halting difficulty for sufficiently general computer programs,
making it the most frequently encountered problem that has been discovered to be insoluble.
The type of computer software we're discussing must be made clear.
Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.
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please help solve this its for geometry
Answer:
Step-by-step explanation:
1.RS+ST=RT. so 9y+2+2y+7=15y-11
2.11y+9=15y-11
3.15y-11y=11+9
4.4y=20
finally we find the answer is y=5
Solve −1/5x=6 (probably very easy but I zoned out and missed a lot)
Answer:
-30
Step-by-step explanation:
-1x/5 = 6
-x/5 = 6
-x = 30
x = -30
An auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. how many seats are in the 10th row?
a. 60
b. 93
c. 102
d. 110
Answer:
Step-by-step explanation:Its actually 102, not 110
Which shape has atleast one pair of perpenicular sides
The fourth shape which is a square has at least one pair of perpendicular sides.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
In the third figure, it is a parallelogram,
In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The sum of adjacent angles is 180° but individuals are not right angles.
The fourth figure is a square and by the properties of a square, all the interior angles are right angles.
Therefore, It has two pairs of perpendicular sides.
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Compute the following for the function defined below. Simplify your answers. Note: Use lowercase letters in your answers. f(x) 3x 8 (a) f(x+h) - (b) f(x+h)-f(x)= (c) ixth-fx). Submit Answer
Answer is 3h after simplification.
What is function?Function is a mathematical expression that represent the relationship between an independent variable and dependent variable. The set of values of independent variable is termed as input of function and the set of value of dependent variable is called output.
What is the value of function?
given, a function. f(x) = 3x -8
if we want to write x + h instead of x
then the function will be f(x + h) = 3(x + h) - 8
f (x + h) - f(x) = 3(x+ h) - 8- (3x -8)
f( x + h) - f(x) = 3(x +h) - 8 - 3x+ 8
f(x + h) - f(x) = 3(x + h) - 3x
f(x + h) - f(x) = 3x + 3h - 3x
f(x +h) - f(x) = 3h
hence, the above is the result.
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Write an equation in slope-intercept form of the line that passes through the points (-5,-12) and 2,9) .
The equation is y=
Answer:
y=3x+3
Step-by-step explanation:
Someone please help! Picture attached
Answer:
third side = 3
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let the third side be x , then
x² + 4² = 5²
x² + 16 = 25 ( subtract 16 from both sides )
x² = 9 ( take square root of both sides )
x = [tex]\sqrt{9}[/tex] = 3
The bill is 42 dollars, taxes is 9%, and the tip given is 18%. What's the Total?
The total cost of the bill that sells for $42 is $54.0204
How to determine the total cost of the bill?From the question, we have the following parameters that can be used in our computation:
Cost of the bill = $42
Sales tax = 9%
Tip = 18%
The total cost of the bill that sells for $42 is then calculated as
Total cost = Selling price * (1 + Sales tax) * (1 + tip)
Substitute the known values in the above equation, so, we have the following representation
Total cost = 42 * (1 + 9%) * (1 + 18%)
Evaluate
Total cost = $54.0204
Hence, the total cost is $54.0204
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-2(4 - 3x) - 6x = 10
Answer:
this is a problem with no solution look it up if you dont beleve me
Step-by-step explanation:
pls help with his i dont get it at all
Answer:
D.
Step-by-step explanation:
They are parallel would be the best explanation. AB and PQ are in a sense the same segment but PQ is AB translated.
A water sample must be taken from water at least 20 feet deep. Find the depth of the water feet from shore
The depth of water from the shore is 15 feet.
What is a proportion?
A proportion is an equation that states that two ratios are equal. It can be written in the form of a/b = c/d. The two ratios, a/b and c/d, are called the terms of the proportion.
The cross-products of a proportion are also equal, so ad = bc.
To solve for d in the equation 5/1.5 = 50/d, you can start by multiplying both sides of the equation by 1.5 to cancel out the denominator on the left side. This gives:
5 = 50/d * 1.5
Next, you can simplify the right side of the equation by multiplying 50 and 1.5, which gives:
5 = 75/d
To solve for d, you can now cross-multiply to get:
75 = 5d
Finally, you can divide both sides of the equation by 5 to get:
d = 75/5
d = 15
the value of d is 15.
Hence, the depth of water from the shore is 15 feet.
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The depth of water from the shore is 15 feet.
What is a proportion?
A proportion is an equation that states that two ratios are equal. It can be written in the form of a/b = c/d. The two ratios, a/b and c/d, are called the terms of the proportion.
The cross-products of a proportion are also equal, so ad = bc.
To solve for d in the equation 5/1.5 = 50/d, you can start by multiplying both sides of the equation by 1.5 to cancel out the denominator on the left side. This gives:
5 = 50/d * 1.5
Next, you can simplify the right side of the equation by multiplying 50 and 1.5, which gives:
5 = 75/d
To solve for d, you can now cross-multiply to get:
75 = 5d
Finally, you can divide both sides of the equation by 5 to get:
d = 75/5
d = 15
the value of d is 15.
Hence, the depth of water from the shore is 15 feet.
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What should be the value of a if the value of 2x^2 XA equals to 5 when?
The value of a is -5. All phrases that involve x become zero when we set their value to zero, leaving only constant terms.
The given equation is 2x^2 + x -a = 5.
let's try to understand what is an equation.
An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For example,
The two equations 4x + 56 and 14 are joined by the equal sign to get the equation 4x + 56 = 14. Algebraic equations in mathematics frequently have one or more variables.
There are many different kinds of equations, including cubic, quadratic, and linear equations.
There are many distinct sorts of equations, depending on the degree of the equation.
2x^2 + x -a = 5. put x = 0.
2*0 + 0 - a = 5
0 + 0 -a = 5
-a =5
a = -5.
So the value of a is -5.
Given Question is incomplete complete question here:
What should be the value of a if the value of 2x^2+x - a equals to 5
when x = 0?
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Which statement best describes the function?
A. The function is negative when x<0
B.the function is negative when x<0 and when x>0
C. The function is never negative
D. The function is negative when x>0
Therefore ,Because the function lies above the x-axis for values of x > 0, it is positive. So, choice D is the right one.
What is function?Each x value in the domain has one but only one y value
range, according to the rule of a function. Definition. If there is only one and only one value of x such that f(x) = y, then the function is one-to-one.
Here,
It is discovered that the right answer is provided by: D using function ideas. If x is zero, the function is negative.
The graph is positive if it is located above the x-axis.
A negative graph is one that is located below the x-axis.
The graph of the function in this issue is shown by the red line, and:
The function is negative for x values less than 0 since it is below the x-axis.
Therefore ,Because the function lies above the x-axis for values of x > 0, it is positive. So, choice D is the right one.
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Question 2 of 5
Simplify.
(m3)6 +m18
A. m4
B. 1
C. m
D. m-9
SUBMIT
Using the first index law, the solution provided indicates that this has a value of 1.
What is the first index law?X to the power of A multiplied by X to a power of B results in X to the power of A + B, according to the first law of indices. Keep in mind that adding the indices when multiplying terms with them means that the base must remain constant throughout.
What exactly is index theory?A topological invariant of a certain class of differential operations on a manifold is studied in index theory, as well as the invariant's local formula in terms of the manifold's geometry. inspirational cases. operator elliptic The index theorem by Atiyah-Singer.
According to the given information:(m³)⁶/m¹⁸ = m³ˣ⁸/m¹⁸
= m¹⁸/m¹⁸
= 1
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RIGHT ANSWER WILL GET BRAINLEIST
A circular table has a diameter of 3 feet. Kristin is taping a piece of border around the edge of the table. Exactly how much border does Kristin need?
Exact length of border required by Kristin is calculated to be 9.42 ft.
This question can be solved using the concept of circumference of a circle.
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were expanded out and straightened out to a line segment, the circumference would be the length of the arc. The curve/arc length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge. A sphere's circumference is equal to the length of any one of its great circles.
Circumference of a circle is given by 2πr.(r is the radius of the circle)
In the given question,
diameter= 3ft
radius= half times of diameter
radius= 1.5 ft.
Circumference= 2πr
= 2×3.14×1.5
=9.42 ft
Kristin will require 9.42 ft of border around the edge of the table.
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As drug A gets absorbed into the body, less and less of it remains. A scatterplot of data showed a curved relationship between hours since drug A was administered (x) and the number of milligrams of drug A remaining in the body (y). Taking the logarithm of the milligrams of drug A remaining obtains a linear pattern on a scatterplot, and creates the following printout from a statistical software package:
Predictor Coef SE Coef t-ratio P
Constant 3. 00 0. 401 7. 481 0. 000
Time -0. 0737 0. 005 -14. 74 0. 000
s= 0. 014 R-sq= 98. 5% R-Sq(Adj)= 99. 0%
Required:
Write down the correct equation that follows from this output?
The equation is
log ( milligrams of drug A ) =3 - 0.0737 ( Time)
As per the details stated above,
Curved relationship between the number of milligrams of drug A is (x) still in the body and the number of hours since drug A was delivered (y)
The co-efficient of the constant is 3.00
the co-efficient of the time is -0.0737
the SE co-efficient of the constant is 0.4017
the SE co-efficient of the time is 0.005
the t-ratio of the constant is 7.481
the t-ratio of the time is -14.74
now the equation formed is
logarithm of drug A in milligrams is (The co-efficient of the constant - the co-efficient of the time )
that is log ( milligrams of drug A ) =3 - 0.0737 ( Time).
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In right triangle abc, altitude cd with length h is drawn to its hypotenuse. we also know ad = 12 and db = 3.
The value of h is 6.
Now, According to the question:
In right triangle, ABC
Given data:
AD = 12 and DB = 3
The equivalent ratio of the triangles is:
h : 12 = 3 : h
Express as fractions
[tex]\frac{h}{12} =\frac{3}{h}[/tex]
Cross Multiply:
[tex]h^2[/tex] = 36
Take positive square roots of both sides
h = 6
Hence, the value of h is 6.
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the american veterinary association claims.. what is the probabilty that your anual cost will ve within 5 of the mean
The probability that the annual cost will be 5 of the mean is 0.0912.
How does probability analysis work?A method used by risk managers to predict upcoming events, like accidental and commercial losses. In order to determine a probability distribution that can be applied to forecast future losses, this procedure involves reviewing historical loss data.
X = Annual cost of medical care for dogs.
X~ Normal (μ = 200, σ = 60)
Sample size n = 16
We know that the sample mean Xbar has a normal distribution with mean = μ and sd = σ/√n
Xbar ~ Normal (μ’ = 200, σ’ = 60/√16 = 15)
Required probability -
P[Average cost of medical care for 16 sampled dogs is > 220]
= P[Xbar > 220]
= P[(Xbar-μ’)/σ’ > (220-200)/15]
= P[Z > 1.3333], Z is a standard normal variable.
= 1 - P[Z < 1.3333]
= 1 - 0.9087, from standard normal table.
= 0.0912
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The complete question is:
A veterinary association claims that the annual cost of medical care for dogs averages $200 with a standard deviation of $60, and for cats averages $240 with a standard deviation of $70. Assume the costs follow a normal distribution. What is the probability the average annual cost of medical care for 16 randomly chosen dogs is greater than $220.
Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.
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I don’t know I just need the answer
Maria believes that she will get a 1 hit in 10% of her softball games, 2 hits in 30% of her games, 3 hits in 55% of her games, and 4 hits in 5% of her games. About how many hits can Maria expect to have each game
According to the probability or likelihood , Maria can expect 2 hits in the game.
What person founded probability?Blaise Pascal and Pierre de Fermat are recognized as the fathers of probability because they laid the foundation for the field by thinking through a gambling issue posed by Chevalier de Mere in 1654.
[tex]E(X)=x.P(X=x)[/tex]
Given,
[tex]P(X=1)=0.20\\P(X=2)=0.25\\P(X=3)=0.50\\P(X=4)=0.05\\[/tex]
putting in formula,
[tex]E(X) = (1*0.20)+(2*0.25)+(3*0.50)+(4*0.05)=2.4[/tex]
As the number can not be fraction, hence number of hit will be 2.
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43 inches tall. Each book 1/2 - inch thick
Answer:
If you're asking how many books there are its 86.
Step-by-step explanation:
If each book is 1/2 thick that means there are 2 books per inch.
Because there are 43 inches you're going to multiply by 2.
43(2)= 86.
Hope that helped, have a good day!
A student-athlete can run 10 yards in 6 seconds. Which equation shows the number of yards that can be run in s seconds
The equation for the maximum number of yards per second that can be run is y = 5/3 s.
Define the term Direct Variation?Two quantities are said to be fluctuating directly if they are coupled in a way that an increase for one quantity suggests an increase in the other and a drop in one implies a decrease in the other. The direct variation equation, which connects the two values y and x, looks like this: y=kx, where k is the variational constant.A direct variation measurement between distance covered and time taken can be composed as:
y=kx,
where,
y stands for the number of yards, s stands for the number of seconds, and k is really the constant of variation.This is because the athlete's distance travelled directly varies with the amount of time it takes.
Find k using the given values:
y=kx,
10 = k(6)
k = 10/6
k = 5/3
As a result, the equation for the maximum number of yards per second is y = 5/3 s.
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A manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth.
Probability that computer chosen at random has defect is 0.0075.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.
What is probability?It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12.
Total number of computers=1200
Total number of damage computers=9
Probability that question chosen at random has defect = 9/1200=0.0075
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Evaluate the expression 2^x- x^22
x
−x
2
2, start superscript, x, end superscript, minus, x, squared for x=5x=5
The evaluation of the expression 2ˣ - x² when x = 5 is 7
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: 2^x- x^2
Value x = 5
Rewrite the expression as
Expression: 2ˣ - x²
Substitute the known values in the above equation, so, we have the following representation
2ˣ - x² = 2⁵ - 5²
When the exponents are evaluated. we have
2ˣ - x² = 32 - 25
Evaluate the like terms in the equation
So, we have the following representation
2ˣ - x² = 7
Using the above as a guide, we have the following:
The solution is 7
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How many times and how many ounces should I feed my goat if it is 7 pounds and I feed it 3 times a day
Since you're feeding it three times a day, you should feed your goat 0.74 ounces per feeding.
What is feeding?The act of feeding involves giving a baby a mother's breast milk, either directly from the breast or by expressing (pump-out) the milk from the breast and giving it to the baby in a bottle.
Define Ounces and Pounding.In the traditional method of measurement, a pound is used to measure weight. In the conventional system, ounces are smaller weight units that are defined in terms of pounds. 1 pound Equals 16 ounces.
Goats typically need around 2% to 4% of their body weight in feed per day. If your goat weighs 7 pounds, and you want to feed it 2% of its body weight per day, you would need to feed it 0.14 pounds of food per day, or 2.24 ounces per day. Since you're feeding it three times a day, you should feed it 0.74 ounces per feeding.
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What is the name of σ?
In mathematics, the symbol " σ" is "σ" (sigma) which is commonly used to represent the sum of a set of values.
It is used to indicate that a series of values are to be added together. For example, the notation "Σx" is read as "the sum of x" and it means to add all values of x together. It is often used in mathematical analysis, statistics, and physics.
For instance, in statistics, the symbol "σ" is used to represent population standard deviation, which is a measure of the dispersion of a set of data points from the mean.
In probability theory, the symbol "σ" is also used to represent the standard deviation of a random variable.
In general, the specific meaning of the symbol "σ" depends on the context in which it is used.
It is also known as Summation notation.
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Emily's least favorite weekly chore is mowing the lawn, even though it only takes her about 30 minutes. Her family's lawn is 1,000 square yards, but her parents are thinking about moving to the country, where they would have 5 acres of land. If the time it takes Emily to mow a lawn is proportional to its area, how many hours would it take her to mow 5 acres?
It will take Emily 12.1 hours to mow 5 acres
How determine how many hours it will take to mow 5 acres?
Variation is the relation between a set of values of one variable and a set of values of other variables
Let T and A represent the time and area respectively
Since the time it takes Emily to mow a lawn is proportional to its area. We can write:
T α A
T = kA (where k is constant of proportionality)
It takes her about 30 minutes to mow 1,000 square yards. That is:
T = 30 and A = 1,000
T = kA
30 = 1000k
k = 30/1000
k = 0.03
Time for 5 acres:
5 acres = 5 × 4840 = 24200 square yards (1 acre = 4840 square yards)
T = kA
T = 0.03 × 24200
T = 726 minutes (divide by 60 to get time in hours)
T = 12.1 hours
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This is mad confusing
Answer: 112 degrees
Explanation:
By the alternate interior angles theorem, m<CAD=40 and m<ACD=28. The quadrilateral is divided into two triangles. The sum of the angles of a triangle is equal to 180 degrees. Now that you know the measurements of two out of the three angles, you can add them up and subtract them from 180.
180-(40+29)=112