a 7000 liter vat is filled with a mixture containing 20% orange juice. determine the number of liters of this mixture that must be drained away and replace with a 80% orange juice mixture to obtain an overall mixture of 7000 liters containing 25% orange juice
Answers
We need to drain away 1750 liters of the 20% orange juice mixture and replace it with an 80% orange juice mixture.
To solve this problem, we need to use the equation:
(initial amount of orange juice in vat - amount drained + amount added) / final amount of mixture = desired percentage of orange juice
Let's start by finding the initial amount of orange juice in the vat. We know that the vat contains 7000 liters of mixture, and 20% of that is orange juice:
Initial amount of orange juice = 7000 liters x 0.20 = 1400 liters
Next, we need to find the amount of mixture that must be drained away. Let's call this amount "x". We know that we want to replace this with an 80% orange juice mixture, so we can set up the following equation:
(1400 - x + 0.8x) / 7000 = 0.25
Simplifying this equation:
(1400 + 0.2x) / 7000 = 0.25
1400 + 0.2x = 1750
0.2x = 350
x = 1750
Therefore, we need to drain away 1750 liters of the 20% orange juice mixture and replace it with an 80% orange juice mixture.
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Related Questions
16^(3x-1) = 32. pls help
Answers
Answer:x=33/4096=0.008
Step-by-step explanation: 1.1 16 = 24
(16)3 = (24)3 = 212
Equation at the end of step
1
:
((212 • x) - 1) - 32 = 0
STEP
2
:
Equation at the end of step 2
4096x - 33 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : 4096x-33 = 0
Add 33 to both sides of the equation :
4096x = 33
Divide both sides of the equation by 4096:
x = 33/4096 = 0.008
Use a graphing calculator and a system of equations to find the roots of the equation.
x4 − 4x3 = 6x2 − 12x
From least to greatest, what are the integral roots of the equation?
Answers
The integral roots of the equation from least to greatest are -2, 0, 2, and 3.
To find the roots of the equation\(`x^4 - 4x^3 = 6x^2 - 12x\)`, we can rearrange it as \(`x^4 - 4x^3 - 6x^2 + 12x = 0`.\) Then, we can use a graphing calculator to graph the function \(`y = x^4 - 4x^3 - 6x^2 + 12x\)` and find its x-intercepts, which are the roots of the equation.
Using a graphing calculator, we can graph the function and get the following graph:
![Graph of function y =\(x^4 - 4x^3 - 6x^2 + 12x]\)
From the graph, we can see that there are four roots to the equation, two of which are negative and two of which are positive. To find the integer roots, we can use the calculator's table feature to generate a table of values for the function and look for where the function crosses the x-axis.
Using the table feature, we can find the following integer roots in order from least to greatest:
-2, 0, 2, 3
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Match each set of values of a function to the pair of points that satisfy the function.
Answers
After matching each set of values of a function to the pair of points that satisfy the function, we get
1-42-23-14-3What is a Function?A function from a set X to a set Y assigns to each element of X exactly one element of Y.
Given the set of data
(4,3) and (6.7) rate of change = 2, and initial value = -5
k= 7-3/6-4 = 2, y=2x-5
(2,10) and (5, 19) rate of change=3, and initial value = 4
k= 19-10/5-2 = 9/3 = 3, y=3x+4
(2,5) and (5.2)→ rate of change = -1, and initial value = 7.
k= 2-5/5-2 = -3/3 = -1, y= -x+7
(2.4) and (4,3) →→ rate of change = -0.5, and initial value =5
k= 3-4/4-2 = -1/2 =-0.5, y=-0.5x+5
A function has two sets of values: the set of input values and the set of output values. The set of input values makes up the function's domain. The set of output values makes up the function's range.
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Drag the tiles to the correct boxes to complete the pairs. Match each set of values of a function to the pair of points that satisfy the function. rate of change = -1, and initial value = 7 rate of change = 2, and initial value = -5 rate of change = -0.5, and initial value = 5 rate of change = 3, and initial value = 4 (4, 3) and (6, 7) arrowRight (2, 10) and (5, 19) arrowRight (2, 5) and (5, 2) arrowRight (2, 4) and (4, 3) arrowRight
if p(x) is divided by (x 1) three times and has remainder of 1 at the end, then -1 is a double root.
Answers
If the polynomial p(x) is divided by (x-1) three times and has a remainder of 1 at the end, then -1 is a double root of p(x). This means that (x+1) is a factor of p(x) raised to the power of 2.
When a polynomial is divided by (x-1), the remainder represents the value of the polynomial at x=1. Since the remainder is 1, it implies that p(1) = 1. Dividing p(x) by (x-1) three times indicates that the polynomial has been factored by (x-1) three times. Consequently, the polynomial can be written as p(x) = (x-1)^3 * q(x) + 1, where q(x) is the quotient obtained after dividing p(x) by (x-1) three times. Since the remainder is 1, it means that when x=1, p(x) leaves a remainder of 1.
Thus, (1-1)^3 * q(1) + 1 = 1, which simplifies to q(1) = 0. This implies that (x-1) is a factor of q(x), meaning that q(x) can be written as q(x) = (x-1) * r(x), where r(x) is another polynomial.
Substituting this into the earlier expression for p(x), we get p(x) = (x-1)^3 * (x-1) * r(x) + 1. Simplifying further, p(x) = (x-1)^4 * r(x) + 1. Now, we can see that p(x) is divisible by (x+1) since (x+1) is a factor of (x-1)^4, and the remainder is 1. Therefore, -1 is a double root of p(x) because (x+1) appears twice in the factored form of p(x).
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help me i need an simple answer
If the point (13, 10) were reflected using the X-axis as the line of reflection, what would be the coordinates of the image? What about (13, -20)? (13, 570) ? Explain how you know
Answers
Answer:
(13,-10)
Step-by-step explanation:
Because it is reflecting off the X axis the X coordinate stays the same. The y coordinate will become opposite.
so for (13,-20) it would be (13,20)
and for (13,570) it would be (13,-570)
you can also look at a graph.
(sharygin 2012) let d be an arbitrary point on the side ac of a triangle abc. the tangent to the circumcircle of triangle bdc at d meets ab in point c1; point a1 is de ned similarly. prove that a1c1 is parallel to ac.(sharygin 2012) let d be an arbitrary point on the side ac of a triangle abc. the tangent to the circumcircle of triangle bdc at d meets ab in point c1; point a1 is de ned similarly. prove that a1c1 is parallel to ac.
Answers
Triangles DBC1 and DCA1 are similar by Angle-Angle (AA) similarity criterion.
The problem you are referring to is known as the Sharygin 2012 problem. To prove that line segment A1C1 is parallel to AC, we can make use of similar triangles and the properties of tangent lines.
Let's start by drawing the given triangle ABC and point D on side AC. Draw the tangent to the circumcircle of triangle BDC at point D, and label the intersection of this tangent with side AB as C1. Similarly, label the intersection of the tangent to the circumcircle at point D with side BC as A1.
Now, we need to show that A1C1 is parallel to AC. To do this, we can use the property that angles formed by tangents and chords are equal. Since DC1 is a tangent to the circumcircle of BDC, we have angle DBC1 = angle DC1B. Similarly, since DA1 is a tangent to the circumcircle of ADC, we have angle DCA1 = angle DA1C.
Next, we need to show tha triangles DBC1 and DCA1 are similar. Since both triangles share the same angles at D and C, we only need to prove that angle C1DB = angle A1DC.
By using the property of tangents and chords, we know that angle C1DB = angle DCB (angle between tangent and chord). Similarly, angle A1DC = angle DAC (angle between tangent and chord).
Since angles DCB and DAC are equal (corresponding angles in similar triangles ABC and DCA), we can conclude that angle C1DB = angle A1DC.
Finally, since A1C1 is a line segment connecting corresponding vertices of similar triangles DBC1 and DCA1, we can conclude that A1C1 is parallel to AC.
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What should be done to both sides of the equation in order to solve 5 + x = -19?
Answers
a plane flies 360 miles against the wind in 2 hours 15 minutes, while on its return trip it takes 1 hour 30 minutes with the same wind. determine the air speed of the plane.
Answers
The air speed of the plane to cover 360 miles against the wind and with the wind in the given time is equal to 200 miles per hour.
Let 'x' be the speed of the plane fly in still air.
And 'y' be the speed of the wind.
Speed against the wind = x - y
Speed with the wind = x + y
Total distance covered by plane = 360 miles
Time taken against the wind = 2 hours 15 minutes
= 2 ( 1/4 ) hours
= 9 / 4 hours
Time taken with the wind = 1 hour 30 minutes
= 1 ( 1/2 ) hours
= 3 /2 hours
Speed = distance / time
Against the wind :
x - y = 360 / (9 /4 )
⇒x - y = 160___(1)
With the wind:
x + y = 360 / (3 /2)
⇒x + y = 240 ___(2)
Add (1) and (2) we get,
2x = 400
⇒ x= 200miles per hour
⇒y = 40 miles per hour
Therefore, the air speed of the plane as per given condition is equal to 200miles per hour.
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a tank with a capacity of 400 l is full of a mixture of water and chlorine with a concentration of 0.05 g of chlorine per liter. in order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 4 lys. the mixture is kept stirred and is pumped out at a rate of 10 lys. find the amount of chlorine in the tank as a function of time.
Answers
So after one hour, the amount of chlorine in the tank has decreased from 20 g to 8.6 g using differential equation.
Let's start by finding the initial amount of chlorine in the tank:
The tank has a capacity of 400 liters and a concentration of 0.05 g of chlorine per liter, so the initial amount of chlorine in the tank is:
400 liters * 0.05 g of chlorine per liter = 20 g of chlorine
Next, we can set up a differential equation to describe how the amount of chlorine in the tank changes over time. We know that the concentration of chlorine in the tank is being diluted by the addition of fresh water at a rate of 4 liters per second, and being removed from the tank at a rate of 10 liters per second. Let C(t) be the amount of chlorine in the tank at time t, in grams. Then we have:
dC/dt = (0.05 g/L * 4 L/s) - (C(t)/400 L * 10 L/s)
The first term on the right-hand side represents the rate at which chlorine is being added to the tank, and the second term represents the rate at which chlorine is being removed from the tank. The factor C(t)/400 L represents the concentration of chlorine in the tank at time t.
We can simplify this equation by multiplying through by 400 L and rearranging:
dC/dt = 2 - (5/2) * C(t)
This is a first-order linear ordinary differential equation. We can solve it using separation of variables:
dC/(2 - (5/2) * C) = dt
Integrating both sides:
(-2/5) * ln|2 - (5/2) * C| = t + constant
Solving for C:
\(C(t) = (2/5) * (2 - e^{(-5t/2)})\)
Now we have a formula for the amount of chlorine in the tank as a function of time. To find the amount of chlorine in the tank at a particular time, we can substitute that time into the formula for C(t). For example, to find the amount of chlorine in the tank after 1 hour (3600 seconds), we can calculate:
\(C(3600) = (2/5) * (2 - e^{(-5/2 * 3600)})\)
\(= (2/5) * (2 - e^{(-9000)})\)
≈ 8.6 g
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Severe hand or wrist pain due to an inflammation of the tendons in a user's hand and wrist is called ____.
Answers
Severe hand or wrist pain due to inflammation of the tendons is commonly referred to as tendinitis.
Tendinitis is a condition characterized by inflammation or irritation of the tendons, which are the fibrous tissues that connect muscles to bones. It commonly occurs in the hand and wrist area, leading to pain, swelling, and discomfort. Tendinitis can be caused by repetitive motions, overuse of the hand or wrist, injury, or certain medical conditions.
The inflammation of the tendons can result in severe pain in the affected hand or wrist, making it difficult to perform everyday activities that involve gripping or moving the hand. The pain may worsen with movement or after prolonged use of the hand. Rest, ice, immobilization, and anti-inflammatory medications are often recommended for managing tendinitis symptoms.
It is important to note that while tendinitis is a common cause of hand and wrist pain, there could be other underlying conditions or injuries that may require further evaluation and medical intervention. Consulting a healthcare professional for an accurate diagnosis and appropriate treatment is recommended for individuals experiencing severe hand or wrist pain.
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HELP PLZ AGAIN. Same material. It is still timed. Will give 100 pts and brainly. This is vital to my math grade. Time is on the essence and my math grade is at stake if I do not pass this. I need Slope Intercept form of the two points plotted on this graph
Answers
Answer:
y=4x-4
Step-by-step explanation:
Looking at the graph, the slope is 4 and the y-intercept is at (0, -4), so the equation is
\(\boxed{y=4x-4}\)
Answer:
y=4x-4
Step-by-step explanation:
Hope it helps
find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 4y + z = 24
Answers
Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.
To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.
First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:
6x + 4(0) + 0 = 24
6x = 24
x = 4
So, the plane intersects the x-axis at (4, 0, 0).
Similarly, to find the y-intercept, we set x = 0 and z = 0:
6(0) + 4y + 0 = 24
4y = 24
y = 6
So, the plane intersects the y-axis at (0, 6, 0).
To find the z-intercept, we set x = 0 and y = 0:
6(0) + 4(0) + z = 24
z = 24
So, the plane intersects the z-axis at (0, 0, 24).
We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).
To find the volume of this tetrahedron, we can use the formula:
Volume = (1/3) * base area * height
The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.
The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.
Plugging these values into the volume formula:
Volume = (1/3) * 12 * 24
= 96 cubic units
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A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. (Almonds and raisins are the only ingredients.) How many ounces of almonds would be in a one-pound bag (16 ounces) of this trail mix?
Answers
Answer:
x = 9 1/3 ounces of almonds
Step-by-step explanation:
Ounces of almonds : raisins
= 7 : 5
Total = 7 + 5
= 12
How many ounces of almonds would be in a one-pound bag (16 ounces) of this trail mix
Let
x = Ounces of almonds needed
x = 7 /12 × 16
= 112 /12
= 9 4/12
= 9 1/3
x = 9 1/3 ounces
help ?? 8x + 0.2 = 48.2
x =
Answers
Hey there!
\(Answer:\boxed{x=6}\)
\(Explanation:\)
\(8x+0.2=48.2\)
Let's start with subtracting 0.2 from both sides of the equation.
\(8x+0.2-0.2=48.2-0.2\\8x=48\)
In our second/last step, we will divide both sides by 8.
\(\frac{8x}{8}=\frac{48}{8}\)
Let's simplify by dividing 48 by 8.
\(48/8=6\)
\(\boxed{x=6}\text{ is your answer.}\)
Hope this helps!
\(\text{-TestedHyperr}\)
What is the coefficient of x 8+5x-y
Answers
Answer:
The coefficient is 5.
Step-by-step explanation:
The coefficient is the number that comes before the variable, 8 wouldn't be a coefficient because it doesn't have a variable, so therefore the correct answer is 5.
I hope I could help :)
The solution is 5
The coefficient of the equation A = 8 + 5x - y is 5
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
The value of A is
A = 8 + 5x - y be equation (1)
Let the coefficient be = c
The coefficients are the numbers by which the variables in an equation are multiplied
So , the coefficients of the equation is 5
Therefore , the value of c = 5
Hence , the coefficient of the equation is 5
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Tyrone is having an 80-foot tree removed from his front yard. One of the tree surgeons ties a rope to the top of the tree and stands 60 feet from the base of the tree while his partner saws through the tree. The rope will help them control the direction in which the tree falls. In the diagram below, side X represents the length of rope needed
Answers
Answer:
..........
Step-by-step explanation:
Answer:
jj
Step-by-step explanation:
since I cant motivate myself to do my work and stop procrastinating.....can someone motivate me?:/
Answers
Answer:
take a time lapse video of yourself doing your homework on your phone! this way you won't be able to use your phone bc it will be doing the timelapse, and then after you finish you'll be able to go back and watch it :)
Step-by-step explanation:
Answer:
Make up a random doodle and name it bob.....YOU CAN DO THIS
Step-by-step explanation:
find the area of the figure below:
Answers
Answer:
60.75 m^2
Have a great day
A rectangular aquarium that is 3 inches wide, 9 inches long and 12 inches tall. If water is filled up to 9 inches, how much more water can be put in the aquarium to make it full
Answers
Answer:
81 inches^3
Step-by-step explanation:
The empty space at the top is
3 inches wide by 9 inches long by (12-9) inches tall
3*9*3 = 81 inches^3
Are u confused, depressed, and need help with homework?
Too bad, so am i
it's ok.
Answers
Answer:
true, i feel ya.
Given: x + 2 < -5. Choose the solution set.
Answers
Answer:
\( x+2-2 <-5-2\)
And after operate we got:
\( x <-7\)
And then the solution would be \(x<-7\)
Step-by-step explanation:
For this problem we have the following inequality:
\( x+2 <-5\)
The first step would be subtract 2 from both sides of the equation and we got:
\( x+2-2 <-5-2\)
And after operate we got:
\( x <-7\)
And then the solution would be \(x<-7\)
Please Help me
with this problem!
Answers
Answer:-2 -4 for point b
Step-by-step explanation:
Given that Justin is collecting data on reaction time, what type of data is he working with?
Select the correct answer below:
A. qualitative
B. discrete quantitative
C. continuous quantitative
D. none of the above
Answers
Since reaction time is measured and not constrained to a specific range of numbers, it is continuous quantitative data.
'What is continuous quantitative?'
A continuous data set is a quantitative data set that represents a scale of measurement that includes fractions and decimals in addition to whole integers. Values like height, weight, length, temperature, and other similar metrics would be included in continuous data sets. They are items that can be quantified in decimals and fractions. A continuous data set typically requires the use of a tool, such as a ruler, measuring tape, scale, or thermometer, to create the numbers.
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What is the algebraic solution to the function 2x+3=83
Answers
80 divided by 2 is 40
the answer is 40
Answer:
x = 40
Step-by-step explanation:
Solve for x
2x + 3 = 83 Subtract 3 from both sides
2x = 80 Divide 2 on both sides
x = 40
The algebraic solution to the function is x = 40
2. Solve for x.
28
2x + 8
82
5x - 4
Answers
Solution of Problem 1:
2x + 8 = 28=> 2x = 28 - 8=> 2x = 20=> x = 10Solution of Problem 2:
82 = 5x - 4=> 82 + 4 = 5x=> 86 = 5x => x = 86/5=> x = 17.2Therefore:
Answer of Problem 1: x = 10Answer of Problem 2: x = 17.2Hoped this helped.
\(BrainiacUser1357\)
im at
school and i need help with this HELP PLEASE
Answers
Your final answer: C.
Wally must complete 40 hours of community service. He does 3 hours each day. Write a linear equation to represent the hours Wally has left after x days.
Answers
Answer: y = 40 - 3x
Step-by-step explanation:
x = # of days
y= number of hours remaining
40 minus 3 times the number of days Wally volunteers would be the formula to find the number of hours he has remaining after a certain number, x, days.
What is the greatest number of regions that can be formed if 3 distinct lines intersect a circle?
A. 3
B. 4
C. 5
D. 6
E. 7
Answers
The greatest number of regions that can be formed if 3 distinct lines intersect a circle is 7.
The correct option is E.
The greatest number of regions that can be formed if 3 distinct lines intersect a circle is given by the formula:
N = (n² + n + 2) / 2
where N represents the number of regions and n represents the number of lines.
In this case, we have n = 3.
Plugging in the value of n, we get:
N = (3² + 3 + 2) / 2
= (9 + 3 + 2) / 2
= 14 / 2
= 7
Therefore, the greatest number of regions that can be formed if 3 distinct lines intersect a circle is 7.
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Factoriza e indica la cantidad de factores primos: P(m) = a(m+1) + b(m+1) –c(m+1)
A) 2
B) 3
C) 5
D) 1
E) 4
Answers
Answer:
Step-by-step explanation:
P (m) = a (m + 1) + b (m + 1) - c (m + 1)
P (m) = (a + b - c) (m + 1)
There are 2 prime factors
Write the equation in standard form of the line that has x-intercept 9 and y-intercept -9
Answers
\(\stackrel{ x-intercept }{(\stackrel{x_1}{9}~,~\stackrel{y_1}{0})}\qquad \stackrel{ y-intercept }{(\stackrel{x_2}{0}~,~\stackrel{y_2}{-9})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-9}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{9}}} \implies \cfrac{ -9 }{ -9 } \implies \cfrac{1}{1}\implies 1\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ 1}(x-\stackrel{x_1}{9})\implies {\Large \begin{array}{llll} y=x-9 \end{array}}\)