The equilibrium price is; $12
The quantity for the two equations is; 400
How to find the equilibrium price?
The equilibrium price formula is based on the demand and supply quantities; you will set quantity demanded (Qd) equal to quantity supplied.
The equilibrium price definition above is one that tells us that there is a price point that meets the needs of both supply and demand. In order to understand when those needs are met, we need to know how to find equilibrium price.
We are given;
Quantity supplied; S(p) = -200 + 50p
Quantity demanded; D(p) = 1060 - 55p
Thus, equilibrium price is p when;
S(p) = D(p)
-200 + 50p = 1060 - 55p
1060 + 200 = 55p + 50p
1260 = 105p
p = 1260/105
p = $12
S(p) = -200 + 50(12)
S(p) = 400
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given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y. a. prediction value are meaningful for all x-values that are realistic in the context of the original data setb. prediction value are meaningful only for x-values that are not included in the original data setc. prediction value are meaningful only for x-values in (or close to) the range of the original data
why was the plutonium he dug up producing so much energy in the martian movie
Answer:
Step-by-step explanation:
Plutonium is a radioactive element that is known to release large amounts of energy through the process of nuclear fission. When a nucleus of plutonium atom is split, it releases a tremendous amount of energy in the form of heat, light, and radiation. This energy is released through a chain reaction, in which the energy from one fission event is used to trigger the fission of additional atoms, releasing even more energy. The heat energy produced by plutonium can be harnessed and used in various ways, such as generating electricity or powering spacecraft.
It is important to note that the behavior of plutonium depicted in the movie "Martian" may be based on scientific concepts, but it may also include fictional elements and may not be entirely accurate or realistic. It is important to remember that fictional works are not necessarily scientifically accurate and should not be taken as fact.
The plutonium emit neutrons as a few of its nuclei spontaneously undergo nuclear fission, which is the reason behind the heat generation.
What is Plutonium?Plutonium is a radioactive chemical element with the symbol Pu and atomic number 94. It is an actinide metal of silvery-gray appearance that tarnishes when exposed to air, and forms a dull coating when oxidized. The element normally exhibits six allotropes and four oxidation states.Given is a dug out plutonium.
Plutonium - 238, Pu - 240 and Pu - 242 emit neutrons as a few of their nuclei spontaneously undergo nuclear fission, albeit at a low rate. This is the reason why plutonium acts as a source of heat energy for Matt Damon and helped him save the fuel.
Therefore, the plutonium emit neutrons as a few of its nuclei spontaneously undergo nuclear fission, which is the reason behind the heat generation.
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The length and width of a rectangle are consecutive integers. The area of the rectangle is 380 square meters. Find the length and width of the rectangle.
Answer:
19x20
Step-by-step explanation:
The area of a rectangle is given by the formula A = l * w, where l is the length and w is the width of the rectangle. In this case, we are given that the area of the rectangle is 380 square meters and that the length and width of the rectangle are consecutive integers.
We can use this information to create a system of equations to solve for the length and width of the rectangle. Let l be the length of the rectangle and w be the width of the rectangle. Since the length and width of the rectangle are consecutive integers, we have:
l = w + 1
Substituting this equation into the formula for the area of the rectangle, we get:
A = l * w
= (w + 1) * w
= w² + w
Since the area of the rectangle is given as 380 square meters, we can set this equation equal to 380 and solve for w:
w² + w = 380
To solve for w, we can use the quadratic formula, which is given by:
x = (-b ± √(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation, and x is the solution. Substituting the values of a, b, and c into the formula and simplifying, we get:
w = (-1 ± √(1² - 4(1)(380))) / (2(1))
= (-1 ± √(-1519)) / 2
Since the length and width of the rectangle must be positive integers, we can ignore the negative solution and only consider the positive solution. Therefore, the width of the rectangle is 19.
To find the length of the rectangle, we can use the equation l = w + 1 that we derived earlier. Substituting the value of w into this equation, we get:
l = w + 1
= 19 + 1
= 20
Therefore, the length of the rectangle is 20 and the width of the rectangle is 19. The dimensions of the rectangle are 20 x 19.
3(x-6) x=11
how do i do this.
Answer:
To solve this equation, we need to perform the operations in the correct order according to the order of operations. The order of operations is a set of rules for determining the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Applying the order of operations to the given equation, we first need to evaluate the expression inside the parentheses, which is 3(x - 6). To do this, we need to subtract 6 from x, which gives us 3(x - 6) = 3(11 - 6) = 3(5) = 15. Next, we need to multiply the result of this operation by 3, which gives us 3 * 15 = 45. Therefore, the final result of the equation is 45.
Here is how you can solve the equation step by step:
1. Evaluate the expression inside the parentheses: 3(x - 6) = 3(11 - 6) = 3(5) = 15
2. Multiply the result of the previous step by 3: 3 * 15 = 45
Therefore, the final result of the equation is 45.
Step-by-step explanation:
Select the correct answer from each drop-down menu. triangle abc is represented. points d and f are marked on side ab and points e and g are marked on side ac. segments de and fg are drawn. if , then line segment is parallel to line segment .
If points d and f are on side ab and points e and g are on side ac then line segments de and fg are parallel
What are parallel lines?
Parallel lines are those lines that do not meet at any point. If we draw a triangle ABC and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle
Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.
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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than
once.
y = -2x+3
4x + 2y = 6
y = -2x+3
4x+y=9
y = -2x+3
4x + 2y = 9
inconsistent
consistent
independent
dependent
The correct description will be;
⇒ y = - 2x + 3
4x + 2y = 6
These are independent.
⇒ y = -2x + 3
4x + y = 9
These are consistent.
⇒ y = -2x+3
4x + 2y = 9
These are inconsistent.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are,
1. y = -2x+3
4x + 2y = 6
2. y = -2x+3
4x+y=9
3. y = -2x+3
4x + 2y = 9
Now,
From (1);
1. y = -2x+3
4x + 2y = 6
⇒ 2x + y = 3
4x + 2y = 6
⇒ 2x + y = 3
So We get;
⇒ 2/2 = 1/1 = 3/3
⇒ 1/1 = 1/1 = 1/1
These are independent.
From (2);
1. y = -2x+3
4x + y = 9
⇒ 2x + y = 3
4x + y = 9
So We get;
⇒ 2/4 ≠ 1/1
⇒ 1/2 ≠ 1/1
These are consistent.
From (3);
1. y = -2x+3
4x + 2y = 9
⇒ 2x + y = 3
4x + 2y = 9
So We get;
⇒ 2/4 = 1/2 = 3/9
⇒ 1/2 = 1/2 ≠ 1/3
These are inconsistent.
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Aria is driving on a long road trip. She currently has 13 gallons of gas in her car. Each
hour that she drives, her car uses up 1.25 gallons of gas. How much gas would be in
the tank after driving for 2 hours? How much gas would be left after t hours?
Answer:
answer in the picture... .
The first term of a geometric sequence is 5 and the sixth term is 160.
What is the common ratio?
Answer:
The common ratio is 2.
Economic The table how cot in dollar charged by an electric company for
variou amount of energy in kilowatt-hour
Electric company charges 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400.
Electric companies charge customers for the amount of energy they consume, measured in kilowatt-hours (kWh). The cost for each kWh can vary depending on the amount of energy consumed. An electric company may charge 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400. The higher rate for higher usage reflects the fact that larger consumers of electricity tend to drive up the cost of production and distribution for the company. In addition, electric companies may offer discounts to customers who use more than a certain amount of electricity each month, encouraging conservation and helping to reduce costs.
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Complete Question is
Economic The table how cot in dollar charged by an electric company for
variou amount of energy in kilowatt-hour
Kilowatt-Hour Cost in Dollars
0-50 . 7.50
50-100. 10.00
100-200. 13.50
200-300. 18.50
300-400. 20.00
400+. 25.00
Select the correct answer from each drop-down menu. A transversal t intersects two parallel lines a and b, forms two groups of angles. On top line a, starting from the top left, clockwise, angles are 1, 2, 3, and 4. On below line b, starting from the top left, clockwise, angles are 5, 6, 7, and 8. In the figure, a ∥ b , and both lines are intersected by transversal t. Complete the statements to prove that m∠1 = m∠5. a ∥ b (given) m∠1 + m∠3 = 180° (Linear Pair Theorem) m∠5 + m∠6 = 180° (Linear Pair Theorem) m∠1 + m∠3 = ∠5 + ∠6 () m∠3 = m∠6 () m∠1 = m∠5 (Subtraction Property of Equality)
The congruent angles of the statements are;
∠1 + ∠3 = 180° by Vertical angles theorem.
∠5 + ∠6 = 180° by Linear pair theorem.
∠1 + ∠3 = ∠5 + ∠6 by both are supplementary angles.
∠3 = ∠6 by consecutive interior angles
∠1 = ∠5 by corresponding angles.
How to find corresponding angles?We want to prove that ∠1 = ∠5.
Corresponding angles; When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal.
From the given question, we see that;
∠1 + ∠3 = 180°: This is because ∠1 and ∠3 are vertical angles by the vertical angles theorem.
∠5 + ∠6 = 180°: This is because ∠5 and ∠6 are linear pairs by the Linear pair theorem.
∠1 + ∠3 = ∠5 + ∠6 ; 180° = 180° ; Both are supplementary angles.
∠3 = ∠6 ; Consecutive interior angles
Now, ∠1 = ∠5, Corresponding angles.
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Let f(x) = 7(x − 5) + 1 . If g is the inverse of f, write an equation for g(x)
inverse of function
-
f (x) = 7(x - 5) + 1
y = 7x - 34
x = (y + 34) / 7
g (x) = (x + 34) / 7
____
a quadrilateral whose diagonals do not always bisect each other is a. an isosceles trapezoid b. a rectangle c. a square d. a rhombus
A quadrilateral whose diagonals do not always bisect each other is a rectangle.
A rectangle is a quadrilateral with four right angles. The diagonals of a rectangle are perpendicular to each other and bisect each other, but not all quadrilaterals with perpendicular diagonals and diagonals that bisect each other are rectangles. For example, a square is a type of quadrilateral with perpendicular diagonals and diagonals that bisect each other, but it has four congruent sides and four right angles, unlike a rectangle.
The word "rectangle" comes from the Latin words "rectus," meaning "right," and "angulus," meaning "angle." This reflects the fact that a rectangle has four right angles.
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Rectangular coordinates and polar coordinates both represent the same complex number z. Which set of equations demonstrates why both sets of coordinates represent the same number?.
The correct option C: r = √(√3)² + (√3)² = √6; θ = arctan (1) = π/4.
The complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.
A polar coordinate is what?The polar coordinates r (a radial coordinate) and in Cartesian space (the angular coordinate, generally termed as polar angle),
x = rcosθ .....(1)
y = rsinθ, .....(2)
where is indeed the counterclockwise angle first from x-axis and r is the radial distance to the origin. Considering x and y,
r² = x² + y² ...eq 3
θ = arc tan (y/x)
Using the polar coordinates explanation from above, we can deduce that;
r² = x² + y² .
r² = √3² + √3² .
r = √(√3)² + (√3)²
and
θ = arc tan (√3/√3) = arctan (1) = π/4.
Thus, the complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.
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The compete question is attached.
Help me respond this question.
The percentile rank of score 71 on the test is 26.7 and The score of the 60th percentile on the test is 84.
What is a percentile?The figure that a particular percentage falls within is referred to as the percentile. For instance, 80% of the kids in a group of 20 are shorter than you, and Ben is the fourth tallest.
Given:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
Calculate the percentile of score 71 as shown below,
[tex]Percentile= n / N \times 100[/tex]
Here, n is the number of scores below 71 and N is the total number of scores,
Percentile = 4 / 15 × 100
Percentile = 0.267 × 100
Percentile = 26.7 percentile
Therefore, the percentile rank of score 71 on the test is 26.7
(B)
Substitute the value in the formula given below,
60 = n / 15 × 100
n / 15 = 60 / 100
n = 0.6 × 15
n = 9
Thus, the 9th term here is 84,
Therefore, the score of the 60th percentile on the test is 84.
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Can someone help me with Question 1, a-b of this assignment? I'd deeply appreciate it! :) I am trying to figure these questions out, and I need help.
Answer:
Step-by-step explanation:
i think i answered another question by you but ill help anyways
ok so you are trying to check the fact that x=2 for both equations
for A. by using substitution
and B. by properties of Equality
A is easy you just substitute 2 into the x values in the given equations
it will look like
-3x+14=18-5x
-3(2)+14=18-5(2)
-6+14=18-10
8=8
and
2x=5-1/2x
2(2)=5-1(2)/2
4=5-2/2
4=5-1
4=4
so now we have proved that both x are eual to 2 by using substitution
i already answered b on a different question
what is the equation of the perpendicular line segment that passes through (4,4) and (6,-2)
Answer:
y=16-3x
Step-by-step explanation:
change in x /change in y
the edges of a cube increase at a rate of 5 centimeters per second. how fast is the surface area changing when each edge
the edges of a cube increase at a rate of 5 centimeters per second. The surface area is changing at a rate of 150 cm²/sec.
To calculate the rate at which the surface area of a cube is changing when each edge is 10 cm long, we first need to calculate the surface area of the cube. The surface area of a cube can be calculated by multiplying the length of one edge cubed by 6. In this case, the length of one edge is 10 cm, so the surface area of the cube is 600 cm². Since the edges of the cube are increasing at a rate of 5 cm/sec, the rate at which the surface area of the cube is changing is equal to the surface area multiplied by the rate of increase, or 600 cm² * 5 cm/sec = 300 cm²/sec.
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Given the following:
What theorem or potulate can be ued to conclude the triangle are congruent?
To identify the congruence postulate used, you need to analyze the given information about the sides and angles of the triangles and choose the postulate that matches the given information.
It's good to use different congruence postulates to identify the congruence of triangles. To identify the congruence postulate used, you need to analyze the given information about the sides and angles of the triangles and see which postulate matches the given information.
For example, if you are given the lengths of two sides and the included angle of one triangle, and the lengths of the corresponding sides and included angle of the other triangle, you can use the SAS Congruence Theorem to conclude that the triangles are congruent. If you are given the lengths of all three sides of both triangles, you can use the SSS Congruence Theorem to conclude that the triangles are congruent.
It's also important to note that the AAS Congruence Theorem is not a valid postulate. The correct postulate is the ASA (Angle-Side-Angle) Congruence Theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, and the included sides are congruent, then the triangles are congruent.
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kristyn and her sister enjoyed a special dinner in a restaurant, and the bill was $ 46.25 . if she wants to leave 23 % of the total bill as her tip, how much should she leave?
$10.6375 she tip if she wants to give a 23% tip of the whole bill when tab for the nice supper that Kristyn and her sister had was $ 46.25.
Given that,
The tab for the nice supper that Kristyn and her sister had was $ 46.25.
We have to find how much should she tip if she wants to give a 23% tip of the whole bill.
We know that,
The tab for the nice supper that Kristyn and her sister had was $ 46.25.
So,
23% tip of the whole bill is
=$ 46.25×23%
=10.6375
Therefore, $10.6375 she tip if she wants to give a 23% tip of the whole bill when tab for the nice supper that Kristyn and her sister had was $ 46.25.
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16. Ana plans to borrow $5,000 for ten years. There
is an annual interest rate of 3.99%, and three
options are available: [a] Monthly simple
interest; [b] Quarterly compound interest; or [c]
continuous compound interest. Which of option
(a, b, or c) should Ana choose?
[A] Option (c) because she earns the most in
interest ($2,451.67).
[B] Option (b) because she pays the least in
interest ($136.95).
[C] Option (a) because she earns the least in
interest ($258.45).
[D] Option (a) because she pays the least in
interest ($166.25).
[E] Option (c) because she pays the least in
interest ($495.67).
Ana should choose option (a) because she pays the least in interest.
To determine which option would be the most cost-effective for Ana, you need to consider the total amount of interest she would pay over the course of the loan.
Option (a) is monthly simple interest, which means that the interest is calculated on the principal balance of the loan at the end of each month, based on the annual interest rate. Option (b) is quarterly compound interest, which means that the interest is compounded and added to the principal balance of the loan at the end of each quarter. Option (c) is continuous compound interest, which means that the interest is compounded continuously, rather than at fixed intervals.
Using the formula for simple interest, the total amount of interest that Ana would pay over the course of the loan under option (a) is:
$166.25 = $5,000 * 3.99% * 10
What is the scale factor from the cliff in the drawing to the actual cliff? The scale factor is _____? I will mark brainlist
1/2 is the scale factor from the cliff in the drawing to the actual cliff.
What is a scale factor?A scale factor is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller. The scale factor is 2 because the length of each of the sides has been multiplied by 2. If this is reversed: The scale factor is 1/2 because the length of each of the sides has been divided by 2.
A scale factor of 1/2 means that the new shape is half the size of the original shape.
Scale factor = Larger figure dimensions ÷ Smaller figure dimensions
The scale factor for scaling up is always greater than 1. Scaling down means that a larger figure is reduced to a smaller one. The scale factor of a dilated figure is denoted by 'r' or 'k'.
If the scale factor is more than 1, the image is enlarged.
If the scale factor is less than 1, the image is contracted.
If the scale factor is 1 (k = 1), the image remains the same.
The scale factor cannot be zero.
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What’s the value of -(-20)
Answer:
20
Step-by-step explanation:
When you have two minuses, it will result in a plus.
Answer:
it's 20
Step-by-step explanation:
i just hv to know the sign
please help me out fast
Graph the solution to this inequality on the number line.
3/5z > 3/4
Answer:
Described below.
Step-by-step explanation:
To graph the solution to an inequality on the number line, we need to determine the values of the variable that satisfy the inequality and then plot those values on the number line. In the given inequality, 35z > 34, we can solve for z by dividing both sides of the inequality by 35 to get:
z > 34/35
This gives us the solution z > 0.96857. To graph this solution on the number line, we can plot a dot at the value 0.96857, which represents the smallest value of z that satisfies the inequality. We can then draw a line segment to the right of this point, indicating that all values of z greater than 0.96857 are also solutions of the inequality. This is shown in the following diagram:
[Insert diagram of number line with dot at 0.96857 and line segment to the right]
As the inequality is strict (i.e., it uses the ">" symbol rather than "≥"), the values of z that exactly equal 0.96857 are not considered to be solutions. Only values of z that are greater than 0.96857 are considered to be solutions of the inequality.
customers of a hardware shop make a payment either in cash or with credit/debit card with probabilities 0.3 and 0.7, respectively. assume these probabilities apply to all customers independently. if 20 customers pay at the hardware shop, what is the probability that exactly 5 customers pay in cash?
probability that exactly 5 customers pay in cash is 0.178863
Total number of customer = 20
probability of payment in cash = 0.3
probability of payments via other methods = 1 - 0.3 =0.7
let probability of payment in cash be p
and probability of payments via other methods be q
To find the probability that exactly y customers pay in cash
p [ x = y ] = [tex]n_c__x p^x q ^(n-x)[/tex]
here value of y= 5 and n=20 , p =0.3 , q= 0.7
putting the values in above equations we get:
p [ x =5 ] = [tex]20_c__5 * 0.3 ^5 * 0.7 ^15[/tex]
p [ x =5 ] = (15504) * (0.00243) * (0.0047475615)
p [ x =5 ] = 0.178863
so the probability that exactly 5 customers pay in cash is 0.178863
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A pack of 24 coloured pencil cot £2. 88
(a) How much i each pencil?
Another packet of 18 pencil cot £1. 98. (b) Which et ha the cheapet pencil in it?
Each color pencil in the first case costs $0.12. Each color pencil in the second case costs $0.11. The cheapest pencil is in the second case.
What is unitary method?The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to achieve the required value.
Here,
Cost of 24 color pencil=$2.88
Cost of 1 color pencil=$2.88/24
=$0.12
Cost of 18 color pencil=$1.98
Cost of 1 color pencil=$1.98/18
=$0.11
The cost of each color pencil from first case is $0.12. The cost of each color pencil from second case is $0.11. The second case has cheapest pencil.
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Use algebraic of equations to predict the solution type to the system of equations. Include all of your work for full credit. \(f(x) = \left\{ x+y=-4 y=2x-1\right.\)
The solution to the given simultaneous equations are;
x = 5/3 and y = 7/3
How to solve simultaneous equations?We are given the two simultaneous equations as;
x + y = 4
y = 2x -1
Rearranging the second equation to have all the variables on one side gives; 2x - y = 1
Thus, we have the equations;
x + y = 4 ------(1)
2x - y = 1 -----(2)
Add eq 1 to eq 2 to get;
3x = 5
divide both sides by 3 using division property of equality to get;
x = 5/3
Put 5/3 for x in eq 1 to get;
⁵/₃ + y = 4
y = 4 - ⁵/₃
y = ⁷/₃
Thus, those are the solutions to the simultaneous equations.
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Finding angle measures of a triangle given two angles of a similar triangle
Step-by-step explanation:
add 100degrees to 15 degrees to get 115degrees. Subtract 180 degrees to 115degrees to get the missing angle which will be 65 degrees
how many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?
To make a 30% alcohol solution, you would need to add 20 liters of 20% alcohol solution to 40 liters of 50% percentage alcohol solution.
50 liters of 50% alcohol solution = 50 liters x 0.50 = 25 liters of pure alcohol
40 liters of 50% alcohol solution = 40 liters x 0.50 = 20 liters of pure alcohol
Total pure alcohol = 25 liters + 20 liters = 45 liters
Required pure alcohol to make a 30% solution = 30 liters
Difference in pure alcohol = 30 liters - 45 liters = -15 liters
Add 20% alcohol solution to make up the difference = -15 liters/0.20 = 75 liters of 20% alcohol solution.
Therefore, 75 liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% percentage solution.
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A dilation from center O with scale factor r₁= 1/4 maps a point P to another point P. Then a second dilation from O with scale factor r₂ maps P’ to P.
What is the value of r₂?
Answer:
To find the value of r₂, we need to know how the dilations with scale factors r₁ and r₂ affect the coordinates of the point P.
If a dilation with scale factor r₁ maps a point P with coordinates (x, y) to another point P' with coordinates (x', y'), then the coordinates of P' are related to the coordinates of P by the equation:
x' = r₁x
y' = r₁y
Similarly, if a dilation with scale factor r₂ maps a point P' with coordinates (x', y') to another point P'' with coordinates (x'', y''), then the coordinates of P'' are related to the coordinates of P' by the equation:
x'' = r₂x'
y'' = r₂y'
Since we are given that the dilations map P to P and P' to P, we can set the coordinates of P and P'' equal to each other, and the coordinates of P' and P'' equal to each other. This gives us the following system of equations:
x'' = x
y'' = y
x'' = r₂x'
y'' = r₂y'
Substituting the second set of equations into the first set, we get:
x = r₂x'
y = r₂y'
Since we know that the dilation with scale factor r₁ maps P to P', we can substitute the equations for x' and y' into the above equations to get:
x = r₂*(r₁x)
y = r₂(r₁*y)
Solving for r₂, we find that:
r₂ = 1/r₁
Substituting the value of r₁ = 1/4, we find that:
r₂ = 1/(1/4) = 4
So the value of r₂ is 4.
correct me if i'm wrong
The ratio of boy to girl who play kickball at rece i 6 to 2. There are 18 girl on the team. What i the nu
mber of boy who play kickball at rece?
The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.
The ratio of boy to girl who play kickball at race is 6 to 2
6 boys: 2 girls
Multiply the number of girls by the ratio:
18 girls x (6 boys / 2 girls) = 18 x 3 = 54
Subtract the number of girls from the total to get the number of boys:
54 - 18 = 36
Therefore, there are 12 boys who play kickball at race.
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