The maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.
What are Lagrange multipliers?
Lagrange's multiplier is a mathematical technique used to find the maximum or minimum value of a function subject to certain constraints. It is named after Joseph-Louis Lagrange, who first introduced the method in the 18th century.
To use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = y^2 - x^2 subject to the constraint 1/4x^2 + y^2 = 64, we need to first set up the Lagrange function:
L(x, y, λ) = y^2 - x^2 + λ(1/4x^2 + y^2 - 64)
We then find the partial derivatives of L with respect to x, y and λ:
∂L/∂x = -2x + λ(1/2x) = 0
∂L/∂y = 2y + λ(y) = 0
∂L/∂λ = 1/4x^2 + y^2 - 64 = 0
Solving these equations, we find the following solutions:
x = 0, y = 0, λ = -8
x = 8√2, y = 8√2, λ = 4
x = -8√2, y = -8√2, λ = 4
Now, we need to check these solutions to see if they satisfy the constraint 1/4x^2 + y^2 = 64. Only the first solution x = 0, y = 0 satisfies the constraint.
Hence, the maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.
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Using the slope formula, find the slope of the line through the points (0,0) and (4,12) . Use pencil and paper. Explain how you can use mental math to find the slope of the line.
By using the slope formula, the slope of the line through the points (0, 0) and (4, 12) is equal to 3.
You can use mental math to find the slope of the line by simply dividing 12 by 3 because the line passes through the origin (0, 0).
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be calculated by using this this mathematical equation (expression);
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following data points located on the line:
Points on x-axis = (0, 4).Points on y-axis = (0, 12).Substituting the given points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (12 - 0)/(4 - 0)
Slope (m) = 12/4
Slope (m) = 3.
In conclusion, an equation which represents this line is y = 3x.
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Describe two quick ways to find approximately 0.5% of $14.95.
Answer: $0.075
Step-by-step explanation:
$14.95 is roughly $15
and 0.5% is 1/2 of 1/100
1/100 of 15 is 0.15 and 1/2 of that is 0.075
0.7125
Step-by-step explanation:
soln
14.25*5%
=0.7125
What is the area of the triangle below? A. 48 square meters B. 7 square meters C. 96 square meters D. 24 square meters
The area of the triangle is 24 square meters.
The area of the triangle can be calculated using the formula A = 1/2bh, where b is the base and h is the height of the triangle. In this case, the base is 8 meters and the height is 6 meters. Therefore, the area of the triangle is A = 1/2bh = 1/2(8)(6) = 24 square meters. Therefore, the answer is D. 24 square meters.
To calculate the area of the triangle, first the base and the height of the triangle must be known. The base is the length of the bottom line of the triangle, and the height is the length of the line from the peak of the triangle to the base. Once the base and height of the triangle are known, the area formula A = 1/2bh can be used.
The formula can be broken down into several steps. First, the base and the height are multiplied together. In this case, it would be 8 x 6. This gives a result of 48. Then, the result is divided by 2, which gives a result of 24. Therefore, the area of the triangle is 24 square meters. When using the area formula, it is important to remember that the result must be divided by 2 in order to get the correct answer.
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i need help solving #16 I have no idea how to do it
Answer:
d. 9x^2 + 25x + 14
Step-by-step explanation:
Formula of area of a rectangle is L * W;
L being length
W being width
x + 2 is our W
9x + 7 is our L, thus;
(x+2)(9x+7)
[9x^2 + 25x + 14]
Add.
18 9/10 + 8 3/10
In simplest form
Answer:
136/5
Step-by-step explanation:
18 9/10 + 8 3/10
change to improper fraction
=189/10 + 83/10
Adding, you have:
=272/10
2 can further divide both numbers
= 136/5
A garden hose can fill a swimming pool in 7 days, and a larger hose can fill the pool in 4 days. How long will it take to fill the pool if both hoses are used?
Hose 1 takes 7 days.
Hose 2 takes 4 days.
That means in a single day, Hose 1 fills 1/7 of the pool and Hose 2 fills 1/4 of the pool. So in one day, the two hoses will fill 1/7 + 1/4 of the pool.
If t is the number of days it takes to fill the pool with both hoses being used, then
[tex]t\cdot \left(\dfrac{1}{7} + \dfrac{1}{4}\right) =1[/tex]
will tell us how many days it will take to fill 1 pool
Solving this:
[tex]\begin{aligned} t\cdot \left(\dfrac{1}{7}\cdot\dfrac{4}{4} + \dfrac{1}{4}\cdot \dfrac{7}{7}\right) &=1 \\[0.5em]t\cdot \left(\dfrac{4}{28} + \dfrac{7}{28}\right) &=1 \\[0.5em]t\cdot \left(\dfrac{11}{28} \right) &=1 \\[0.5em]t &=\dfrac{28}{11} \\[0.5em]\end{aligned}[/tex]
It'll take 28/11 days, or 2 and 6/11 days, or about 2.54 days.
Market for Hamburgers Supply and Demand — End of Chapter Problem In the accompanying supply and demand diagram, depicting the market for hamburgers in your hometown, first shift the demand curve, given the event described. Then move the equilibrium point to its new position. What is the effect on equilibrium price and quantity? Event: The price of tacos increases. Price per hamburger E Equilibrium price decreases. stays the same. increases. Incorrect Quantity of hambugers Incorrect Equilibrium quantity decreases. O O O increases. stays the same. IncorrectPrevious questionNext
The increase in the price of tacos shifts the demand curve to the left, causing a decrease in the equilibrium price and quantity of hamburgers.
The accompanying supply and demand diagram is depicting the market for hamburgers in your hometown. The event that is given is that the price of tacos increases. This will cause the demand curve to shift to the left, as consumers shift from hamburgers to tacos. As the demand curve shifts to the left, the equilibrium price will decrease and the equilibrium quantity will decrease. This is because the decrease in demand will cause the quantity demanded to fall and the decrease in demand will cause the price to fall. This shift in the supply and demand curves will cause the equilibrium point to move to the left and downward. The new equilibrium price will be lower than the original equilibrium price and the quantity will also be lower.
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Find the circumference of a circle with a diameter of 36 units.
Answer:
Circumference = 113.097 units
Step-by-step explanation:
C = 2[tex]\pi r[/tex]
C = 2(3.14)(36/2)
C = 113.097 units
I will give brainliest to whoever answers this correctly.
Answer:
60.26°
i have to write more so yea but do you have the answer to 83d and 91c from that chapter
Differentiation question pls help
A stationary point of a function f(x) is a point where the derivative of f(x) is equal to 0. These points are called “stationary” because at these points the function is neither increasing nor decreasing.
How do you find stationary points f XY?Once we have identified the dy dx = 0 solutions, we may utilise the first derivative to ascertain the characteristics of the stationary points. Think about the equation y = x2 + 1.
By differentiating and setting the derivative to zero, we may determine that there is a stationary point at x = 0 since dy dx = 2x = 0. Recall that placing f by x and f by y equal to zero will reveal the location of a function f's stationary point.
In this situation, partial differentiation with regard to x while treating y as a constant results in three x squared plus six x. Any stationary point's nature can be ascertained by introducing its x coordinate into the second derivative of the function, f. (x).
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Kent completed his homework in 52.752 minutes. What is this number rounded to the nearest tenth? Explain how you decided.
Answer:
The answer would be 52.8 because if the number behind the decimal you want to round is 5 or greater you round one number up. (Sorry if this is a confusing explanation)
Use left rectangles and Δ x = 0.5 to approximate the area under f ( x ) = 2 x 2 + 6 from x = 2 to x = 4 . Give one decimal place in your answer.
The approximation of the area under the curve f(x) = [tex]2x^2 + 6[/tex] from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.
To approximate the area under the curve f(x) = [tex]2x^2 + 6[/tex] between x = 2 and x = 4 using left rectangles and a step size of Δx = 0.5, we have to divide the interval [2, 4] into a number of sub-intervals of width 0.5 and evaluate the function at the left endpoint of each sub-interval.
First find the number of steps: (4-2)/0.5 = 4
The x-coordinates for the left endpoints of each sub-interval are: 2, 2.5, 3, 3.5, 4
We evaluate the function f(x) = [tex]2x^2 + 6[/tex] at each of these left endpoints and multiply the result by the width of the sub-interval (0.5) to find the area of each rectangle.
For [tex]x = 2[/tex], [tex]f(x) = 2(2)^2 + 6 = 14[/tex]
Area = 0.5 * 14 = 7
For [tex]x = 2.5, f(x) = 2(2.5)^2 + 6 = 19.5[/tex]
Area = 0.5 * 19.5 = 9.75
For [tex]x = 3, f(x) = 2(3)^2 + 6 = 24[/tex]
Area = 0.5 * 24 = 12
For [tex]x = 3.5, f(x) = 2(3.5)^2 + 6 = 29.5[/tex]
Area = 0.5 * 29.5 = 14.75
For [tex]x = 4, f(x) = 2(4)^2 + 6 = 34[/tex]
Area = 0.5 * 34 = 17
The sum of the areas of these rectangles is 7 + 9.75 + 12 + 14.75 + 17 = 60.5
Therefore, the approximation of the area under the curve f(x) = [tex]2x^2 + 6[/tex] from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.
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In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5, you win $1, if the number of spots showing is 6, you win $4, and if the number of spots showing is 1, 2, or 3, you win nothing. Let X be the amount that you win. The expected value of X is
(a) $0.00
(b) $1.00
(c) $2.50
(d) $4.00
(e) $6.00
The amount that you when a fair dice is tossed (showing is either 4 or 5, you win $1, if the number of spots showing is 6, you win $4, and if the number of spots showing is 1, 2, or 3, you win nothing) is $1.00
Given,
when you get either 4 or 5, the reward = $1
when you get either 6, the reward = $4
when you get 1, 2, or 3, the reward = $0
We know that,
Probability of getting 6 = 1/6
Probability of getting 4 = 1/6
Probability of getting 5 = 1/6
Probability of getting 1 = 1/6
Probability of getting 2 = 1/6
Probability of getting 3 = 1/6
Therefore,
[tex]X = \frac{1}{6}* 4 + \frac{1}{6}* 1 +\frac{1}{6}* 1+ \frac{1}{6}* 0+ \frac{1}{6}* 0 + \frac{1}{6}*0[/tex]
[tex]= \frac{4}{6} + \frac{1}{6}+ \frac{1}{6}[/tex]
[tex]= \frac{6}{6}[/tex]
[tex]= 1[/tex]
Hence, the Value of X = $1.
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Show that a quadrilateral with the given vertices is a parallelogram.
When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)
What is a Parallelogram ?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
A quadrilateral is a specific type of polygon known as a parallelogram if it contains two parallel opposed sides. A parallelogram has the following qualities:
The opposing sides are equal and parallel.Angles on either side are equal.The subsequent or neighboring angles are additional.All of the angles will be at right angles if any one of them is a right angle.The two diagonals are split in half.The parallelogram is divided into two congruent triangles by each diagonal.A parallelogram's total square sum and total square sum of its diagonals are equivalent. Also known as the parallelogram law.Each coordinate of the Parallelogram :
P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)
Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37
Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37
Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17
Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17
Here, PA = RT and PT = AR ,
so when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.
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When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)
What is meant by quadrilateral?
A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners.The angles at the vertices of a quadrilateral ABCD are A, B, C, and D. A quadrilateral has the following sides: AB, BC, CD, and DA.There are four different types of quadrilaterals: parallelograms, squares, rectangles, and rhombuses. A parallelogram can alternatively be a square, a rectangle, or a rhombus.A quadrilateral, often known as a square, rectangle, or rhombus, is a polygon with four sides. You are currently staring at a computer screen that is most likely shaped like a quadrilateral. You'll study the quadrilateral in geometry classes.Each coordinate of the Parallelogram :
P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)
Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37
Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37
Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17
Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17
Here, PA = RT and PT = AR ,
So when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.
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f(x) = 11x - 2. Find x when f(x) = 64
please show steps
Answer: the correct value of x in this will be 6.
Step-by-step explanation: According to the equation given ,
f(x) = 64
so , f(x) = 11x - 2 now putting the value of f(x) in this equation
therefore , 64 = 11x - 2
now solving the equation , 11x= 64+2
11x = 66
x = 66/11
x = 6
thus, the value of x obtained from the equation is 6
you have 30 coins worth 2.05 dollars in dimes and nickels. whats in your wallet.
The number of dimes and nickels are equal to 11 and 19 respectively.
How to determine the number of dimes and nickels?In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let d represent the number of dimes.Let n represent number of nickels.Since you have a total number of 30 coins, an equation which models this situation is given by;
d + n = 30 ....equation 1.
Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.
Additionally, the coins are worth 2.05 dollars;
0.1d + 0.05n = 2.05 ....equation 2.
Solving both equations simultaneously, we have:
0.1(30 - n) + 0.05n = 2.05
3 - 0.1n + 0.05n = 2.05
3 - 0.05n = 2.05
0.05n = 0.95
n = 0.95/0.05
n = 19 nickels.
For the number of dimes;
d = 30 - n
d = 30 - 19
d = 11 dimes.
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Complete Question:
You have 30 coins worth $2.05 in nickels and dimes. What's in your wallet? Create and solve system of equations to find how many dimes and how many nickels you have.
A line passes through the point (2, -8) and has a slope of -5.
Write an equation in slope-intercept form for this line.
Answer:
y=-5x+b
Steps:
1. Put slope into y=mx+b formula
2. Plug in point: -8=-5(2)+b
3. Solve for b: 2=b
Solve the differential equation
dR/dx = a(R^2+16)
Assume a is a non-zero constant, and use C for any constant of integration that you may have in your answer.
R=________
The solution to the differential equation is given by R = ±1/√(C-a*x), where C is a constant of integration.
To solve this differential equation, we first separate the variables and integrate the equation:
dR/dx = a(R^2+16)
∫ dR/dx = ∫a(R^2+16)dx
R = ±1/√(C-a*x) + K
where K is an arbitrary constant.
To find the constant of integration, we use the initial condition. We plug in the initial values for x and R to find the constant of integration. For example, if x = 0 and R = 2, then we get
2 = ±1/√(C-0) + K
2 = ±1/√C + K
K = 2±1/√C
Therefore, the solution to the differential equation is given by R = ±1/√(C-a*x) where C is the constant of integration.
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ANSWER ALL PLEASE!!!
The units of distance and speed should match, So kilometers per hour (kph) and miles per hour (mph) are the correct units.
What is speed and find all the given questions?Angel ran 5 kilometers. It took him 16 minutes.Distance: 5 kilometersTime: 16 minutesSpeed: Distance/Time = 5 kilometers / (16 minutes / 60 minutes/hour) = 5 kilometers / 0.2667 hours = 18.67 kilometers/hour or 18.67 kphPedro bicycled for 30 minutes. He went 6 kilometers.Distance: 6 kilometersTime: 30 minutesSpeed: Distance/Time = 6 kilometers / (30 minutes / 60 minutes/hour) = 6 kilometers / 0.5 hours = 12 kilometers/hour or 12 kphRandy drove his new corvette to San Francisco, which is 280 miles to the North. It took him 6 hours.Distance: 280 milesTime: 6 hoursSpeed: Distance/Time = 280 miles / 6 hours = 46.67 miles/hour or 46.67 mphSarai flew her fighter jet for 60 minutes, flying 1000 miles to the East.Distance: 1000 milesTime: 60 minutesSpeed: Distance/Time = 1000 miles / (60 minutes / 60 minutes/hour) = 1000 miles / 1 hour = 1000 miles/hour or 1000 mphNatalie flew her hot air balloon to Japan, which is 3500 miles away. It took her 6 days.Distance: 3500 milesTime: 6 daysSpeed: Distance/Time = 3500 miles / (6 days * 24 hours/day) = 3500 miles / 144 hours = 24.31 miles/hour or 24.31 mphTo earn more about speed refer:
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The position of an object moving along a line is given by the function s(t) = -7t^2 +70t. Find the average velocity of the object over the following intervals.
(a)​ [1,5]
​(b) ​[1,4​]
​(c)​ [1,3​]
​(d) ​[1, 1​+h] where h > 0 is any real number.
(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -90 m/s.
(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -62 m/s.
(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -34 m/s.
(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7h^2 + 70h m/s.
(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -7(25-1) + 70(4) = -7*24 + 280 = -168 + 280 = -88 m/s.
(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -7(16-1) + 70(3) = -7*15 + 210 = -105 + 210 = -95 m/s.
(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -7(9-1) + 70(2) = -7*8 + 140 = -56 + 140 = -16 m/s.
(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7(1+h)^2 + 70h = -7(1+h)^2 + 70h m/s. The average velocity of an object over a given period of time is calculated by taking the difference between the final and initial positions, and dividing it by the amount of time elapsed. In this exercise, we are given the position of an object along a line as a function of time, s(t) = -7t^2 + 70t. To solve each part, we can plug in the given time intervals into the function, and calculate the difference between the initial and final positions. We then divide this difference by the amount of time elapsed to find the average velocity. For example, in part (a), the average velocity is calculated as -7(5^2-1^2) + 70(5-1) = -90 m/s. In part (b), the average velocity is calculated as -7(4^2-1^2) + 70(4-1) = -62 m/s. In part (c), the average velocity is calculated as -7(3^2-1^2) + 70(3-1) = -34 m/s. Finally, in part (d), the average velocity is calculated as -7(1+h)^2 + 70h m/s
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Consider the line .3x-6y=-8
Find the equation of the line that is parallel to this line and passes through the point .4,2
Find the equation of the line that is perpendicular to this line and passes through the point . (4,2)
An equation of the line that is parallel to this line and passes through the point (4, 2) is y = 0.5x.
An equation of the line that is perpendicular to this line and passes through the point (4, 2) is y = -2x + 10.
How to determine the equation of the line?In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ -1 = -1
Note: m represents the slope.
From the linear equation 3x - 6y = -8, we have:
y = 3x/6 + 8
y = 0.5x + 8
At point (4, 2), an equation of the line that is parallel to this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.c represents the intercept.y - 2 = 0.5(x - 4)
y = 0.5x - 2 + 2
y = 0.5x
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
0.5 × m₂ = -1
m₂ = -2
At point (4, 2), an equation of the line that is perpendicular to this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = -2(x - 4)
y = -2x + 8 + 2
y = -2x + 10
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values differ from norms in that values: group of answer choices remain constant and do not change over time. are established rules of behavior or standards of conduct. can be categorized into folkways, mores, and laws on the basis of their social importance. do not state explicitly how people should behave.
There are four types of social norms that can help inform people about behavior that is considered acceptable: folkways, mores, taboos, and law.
Social values are the focus of sociology. Cultural norms known as social values describe the overall well-being thought desirable for a structured social existence. These presumptions concern what is morally correct and significant for society. They provide social structures and behavior its ultimate meaning and legitimacy. They are ideals or abstract feelings. "Equality of opportunity" is a prime illustration of social value. It is frequently regarded as a desirable end in and of itself.
When several people interact, a set of norms emerges that governs their interactions and behaviors. Social norms are these standards of group behavior.
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DUE SOON
PLEASE EXPLAIN HOW YOU GOT THE ANSWER.
questions down below
The scale factor of the two triangles is 1/4 or 4
What is scale factor?You should understand that scale factor is the ratio of any two corresponding lengths.
Looking at the triangles, the larger triangle has sides
AB with 12 gridsAC with 11 gridsBC with 11 gridsThe smaller triangle has sides
AB with 3 gridsAC with 3 grids and BC with 3 gridsScale factor = (Larger length)/ (Smaller length) or (Smaller length/(Larger length)
This is an indication that the triangles have scale factors of:
Scale factor = 12/3 = 4 or
Scale factor = 3/12 = 1/4
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In the lab, Linda has two solutions that contain alcohol and is mixing them with each other. Solution A is 50% alcohol and Solution B is 10% alcohol. She us
400 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture is a 20% alcohol solution?
We can start by using the concept of percentage concentration, which states that the percentage of alcohol in a solution is equal to the number of milliliters of alcohol in the solution divided by the number of milliliters of the solution, multiplied by 100.
Let's call the number of milliliters of Solution B that Linda uses x.
We know that:
Solution A is 50% alcohol, so it contains 50/100 = 0.5 = 1/2 of alcohol.
Solution B is 10% alcohol, so it contains 10/100 = 0.1 = 1/10 of alcohol.
The resulting mixture is a 20% alcohol solution.
Linda uses 400 milliliters of Solution A.
We can set up an equation using the percentage concentration concept and the information provided:
(400 * 1/2) + (x * 1/10) = (x + 400) * (20/100)
Solving for x:
200 + x/10 = (x + 400) * 0.2
x/10 = (x + 400) * 0.2 - 200
x/10 = x * 0.2 + 80
9x/10 = x * 0.2 + 80
9x = x*2 + 800
x = 800/8 = 100
So, Linda uses 100 milliliters of Solution B to make the resulting mixture a 20% alcohol solution.
b) Prabin types 765 words in 9 minutes. How many words would he type in half an hour? How long does he take to type 12,750 words at the same speed?
Answer:
Prabin types 765/9 i.e, 85 words in one minute. Therefore in 30 minutes prabin will type 30 x 85 i.e., 2550 words. Again, he types 1 word in 9/765 minutes. Therefore , he will type 12750 words in 12750 x (9/765) minutes, i.e, 150 minutes.
Prabin would type 2,550 words in half an hour at the same speed. It would take him 150 minutes to type 12,750 words at the same speed.
Explanation:To find out how many words Prabin would type in half an hour, we need to determine how many minutes are in half an hour. Since there are 60 minutes in an hour, half an hour would be 30 minutes. Now, we can set up a proportion to find the number of words Prabin would type in half an hour:
765 words / 9 minutes = x words / 30 minutes
Cross-multiplying, we get:
9 * x = 765 * 30
Simplifying, we find:
x = (765 * 30) / 9
x = 2,550 words
To find out how long it would take Prabin to type 12,750 words at the same speed, we can set up another proportion using the given information:
765 words / 9 minutes = 12,750 words / t minutes
Cross-multiplying, we get:
9 * (12,750) = 765 * t
Simplifying, we find:
t = (9 * 12,750) / 765
t = 150 minutes
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On Saturday, 55% of the 200 people at Cordova Skating Rink brought their own skates. How many people did NOT bring their own skates?
Answer:
If 55% of people brought their own skates, 45% did not.
Since 100 - 55 = 45.
45% of 200 = 90
The answer is: 90 people didn't bring their skates.
The sum of two numbers is 1476890. If the difference between the two numbers is 1500, what is the greater number ?
Let's call the two numbers x and y. We know from the problem statement that:
x + y = 1476890
y - x = 1500
To find the greater number, we can use the second equation to solve for one of the variables, and then substitute it into the first equation.
y = x + 1500
Now we can substitute this expression for y into the first equation:
x + (x + 1500) = 1476890
2x + 1500 = 1476890
2x = 1476890 - 1500
2x = 1475390
x = 1475390/2
x = 737695
So the greater number is y = x + 1500 = 737695 + 1500 = 739195
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please someone help me with this escape room question! i’ve been stuck on this problem for so long now
Answer:
all of them are 17
Step-by-step explanation:
7+9=16
16+1+0=17
9+7=16
16+1+0=17
1+0+9=10
10+7=17
7+1=8
8+9+0=17
hope this helped!
Create an equation in point slope that goes exactly through the first three stars.
Now create another line that will help the marble capture all the stars. Use constraints on both equations to help the marble find its way.
The equation of the line is given as y = ( -2/5 )x + 162 , where the slope of the line is m = ( -2/5 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be represented as P ( -275 , 52 )
Let the first point be represented as P ( -280 , 54 )
Now , the slope of the line is
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 54 - 52 ) / ( -280 - ( -275 ) )
On simplifying the equation , we get
Slope m = 2 / ( -5 )
Slope m = -2/5
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 52 = ( -2/5 ) ( x - ( -275 ) )
y - 52 = ( -2/5 )x + 110
Adding 52 on both sides of the equation , we get
y = ( -2/5 )x + 162
Hence , the equation of line is y = ( -2/5 )x + 162
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Use areas to evaluate 4xdx where 0 < a
Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects.
What is integration?
In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
Differentiation is the opposite of integration.
In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:
dy/dx = 2x since y = x2 Consequently,
(dy/dx) dx = 2x dx = x2.
Together, and dx represent the integration of the function with respect to x.
The anti-differentiation is another name for integration. In this procedure, we are given a function's derivative and asked to determine the function (i.e., primitive). We are aware that cos x is the differentiation of sin x.
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