If two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters of another punch and the resulting fruit punch is 20% fruit juice, then the percent of fruit juice in 300 liters of punch is calculated to be 10%.
The percentage of fruit juice in 300 liters of punch can be calculated by forming a linear equation.
A linear equation also termed a first-degree equation is an equation with one or more variables that have the highest power of one.
A linear equation for this problem can be given as:
the volume of the first punch × percentage of fruit juice in the first punch + the volume of the second punch × percentage of fruit juice in the second punch = total volume × total percentage of fruit juice
Consider x = percentage of unknown fruit juice
Now add the given values in the equation:
200 × 35 + 300(x) = 500 × 20
7000 + 300(x) = 10000
300(x) = 10000 - 7000
300(x) = 3000
x = 3000 / 300
x = 10%
Hence, the percentage of fruit juice in 300 liters of punch is calculated to be 10%.
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Find the general solution to the differential equation put the problem in standard form. find the integrating factor, . find . use c as the unknown constant.
y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x} is the general solution to the differential equation put the problem in standard form.
What is meant by integrating factor?
A function called an integrating factor is used to solve differential equations in mathematics. It is a function that can be made integrable by multiplying it by an ordinary differential equation. Ordinary differential equations are typically solved using this method. This factor is also applicable to multivariable calculus.x² + 2xy + x . dy/dx = 0
x dy/dx + 2xy = [tex]- x^{v}[/tex]
[tex]\frac{dy}{dx} =+ 2y = -x[/tex]
[tex]left u(x) = e^{\int\limits^_ {} } 2dx = e^{2x}[/tex]
integration factor p(x) = u(x) = [tex]e^{2x}[/tex]
Now ,multiply [tex]e^{2x}[/tex] both sides
[tex]e^{2x} ( \frac{dy}{dx} + 2y ) = -x . e^{2x}[/tex]
[tex]e^{2x} \frac{dy}{dx} + 2e^{2x} . y = -x e^{2x}[/tex]
[tex]\frac{d}{dx} (e^{2x} .y) = -x e^{2x}[/tex]
integrate both sides
∫ [tex]d .( e^{2x} .y )[/tex] = ∫[tex]-xe^{2x} .dx[/tex]
[tex]e^{2x} .y = -\frac{e^{2x}}{2} . x + \frac{e^{2x}}{4} + c[/tex]
[tex]y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}[/tex]
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The complete question is -
Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.
The formula for finding the perimeter of a rectangle is p= 2l 2w solve the formula for w.
Answer:
w = [tex]\frac{p -2l}{2}[/tex]
Step-by-step explanation:
p = 2l + 2w Subtract 2l from both sides of the equation
p - 2l = 2p Divide both sides by 2
[tex]\frac{p -2l}{2}[/tex] = w
If M (-2, 5) is the midpoint of
CD and the coordinates of C are (4, 7), what are the coordinates of D?
Answer:
soln ,given,
midpoint of CD=M(-2,5)
let,
C(4,7)=(x1,y1)
D(x1,y2)=?
now by using midpoint formula =(x1+x2)/2+(y1+y2)/2
M(-2,5)=( 4+x2)/2+(7+y2)/2
comparing both sides
-2=(4+x2)/2
-4=4+x2
-4-4=x2
threfore,x2= -8
again
5=(7+y2)/2
10=7+y2
therefore,y2=3
thus , the coordinate of D is D(-8,3)
25 points plus brainliest
Answer:
2
Step-by-step explanation:
To get the slope you must subtract the second y-coordinate and the first y-coordinate (of the 2 given points) and divide that by the difference of second x-coordinate and first x-coordinate (of the 2 given points).
y-coordinate 2 - y-coordinate 1
--------------------------------------------- <----- fraction bar/ divide
x-coordinate 2 - x-coordinate 1
3 - 1 2
------ = ---- = 2
1 - 0 1
Slope = 2
Identify the property that justifies the statement. OP ≅ RS, so RS ≅ OP
Please Hurry!!!!
Answer: Sym. Prop. of ≅
Step-by-step explanation:
no explanation
Solve for the value of q. 780 (59+2)
Answer:
9222.23333 is the value good sir :)
Step-by-step explanation:
Write a linear equation for the graph in point-slope form. Show your work.
Answer:
y-20=0.75(x-4)
Step-by-step explanation:
First, use slope formula to find the slope.
The points I will use are (4, 20) and (8, 23).
Formula:
y2-y1/x2-x1
23-20/8-4=
=3/4
The slope in decimal form is 0.75.
Now you put the linear equation in point-slope form.
m=0.75
Use the point (4, 20).
y-y1=m(x-x1)
y-20=0.75(x-4)
The linear equation is point-slope form is y-20=0.75(x-4).
Hope this helps!
Please mark as brainliest if correct!
Select the domain and range of the graph in set-builder and interval notation.
The domain of the graph in set builder notation is; x ≤ -2 or x ≥ 1
The range of the graph in set builder notation is; y ≥ -2 or y ≥ 1
What is the domain and range of the graph?Domain refers to the set of all possible input values and Range refers to the set of all possible output values generated by the function.
Now, from the given graph, we can see that there are two lines. Thus;
Domain of left graph line is; x ≤ -2
Domain of right graph line is; x ≥ 1
Thus, the domain of the graph in set builder notation is;
x ≤ -2 or x ≥ 1
Similarly, the range is as follows;
Range of the left graph line is; y ≥ 1
Range of the right graph line is; y ≥ -2
Thus, the range of the graph in set builder notation is;
y ≥ -2 or y ≥ 1
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served.
2
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to the following linear inequality in the coordinate plane.
52-y> -3
Drawing Tools
Select
Line
Dashed Line
Shaded Region
Click on a tool to begin drawing.
<+
-10
-8
-6
-4
-2
10-
8
6-
4-
2-
Delete
2
Undo
6
8
Reset
A
10
Answer:
It is everything that's bigger then (0,-3),
Picture under ↓
It's a bad drawing.
The solution region for the given pair of inequalities is found to be the common shaded region in the graph attached.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
For drawing the graph of any inequality, we first have to assume the inequality as an equation and draw the graph of the resulting equation. Hence, finding the points for the inequality , we let the inequality as:
Putting y=0, we get:
The point will be: (-2,0)
Now, putting x=0, we get:
The point will be: (0,4)
Now as the sign of inequality is >, the line of graph will be dotted.
Taking a test point (0,0) to find the shaded region, substituting this in the inequality,
So, the shaded region will be away from the test point.
Similarly, finding the points for the inequality , we let the inequality as:
Putting y=0, we get:
The point will be: (6,0)
Now, putting x=0, we get:
The point will be: (0,6)
Now, as the sign of inequality is of , the line of graph will be solid.
Taking a test point (0,0) to find the shaded region, substituting this in the inequality,
So, the shaded region will be towards the test point.
The resulting graph is attached after the solution.
The solution to the pair of given inequalities will be the shaded region that is common between both the individual inequality's shaded regions.
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Convert celsius to fahrenheit using the following formula f = 95c+32 c = 20 f = ?
35 degrees Celsius is equal to 95 degrees Fahrenheit.
What is the formula for Celsius to Fahrenheit?
The formula for converting from degrees Celsius to degrees Fahrenheit, which is provided by the expression F=95(C)+32, must be used. To convert the given temperature to degrees Fahrenheit, we must first divide it by five, then multiply it by nine, and then add 32.Without a calculator, how do you convert from Celsius to Fahrenheit?
Here is an easy approach you may use to convert temperatures from Celsius to Fahrenheit. multiply the temperature in degrees Celsius by 2, then add 30 to get the (estimated) temperature in degrees Fahrenheit.F = 9 / 5 * 35 + 32
F = 63 + 32
F = 95
35 degrees Celsius is equal to 95 degrees Fahrenheit.
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If the parents of a family already have two boys, what is the probability that the next two offspring will both be girls?
The probability that the next two offspring will both be girls is 1/3.
To find P both children are girls
A: Event that both children are girls
A: {MM} and B: {MF, FM, MM} →→ P (A ∩∩ B) = {MM}
Probability that both are males, if we know one is a female =P(A/B)=P(A∩B)/P(B)
(P(A∩B)P(B))
Given S = {MM, MF, FM, FF}, we can see that: P (A) = 1414; P (B) = 3434; P (A ∩∩ B) = 1414
Therefore,
P(B/A)=P(A∩B)/P(A) = (1/4)/(3/4)=1/3.
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PLS HELP A LITTLE LOST Sally is 3 years younger than Sue. The sum of their ages is 27. How old is Sally?
Answer:
Sally is 12 years old.
Step-by-step explanation:
[tex]2x+3=27\\2x+3-3=27-3\\2x=24\\\frac{2x}{2}=\frac{24}{2}\\x=12[/tex]
Step-by-step answer?
hi
a ( b +c) = a*b +a*c
here a = -3
b = -4x
c = +5
so :
-3 ( -4x +5) = -3*-4x + -3* 5
= -12x + (-15)
= -12x -15
as I cannot add -12x and -15 ( they are two differents sort of figures )
so it's done
Answer:
12x - 15
Step-by-step explanation:
What you need to do for this is -3 · -4x + -3 · 5 = 12x+(-15). Which simplifies to 12x - 15.
Find angle X.
I am not sure if it should add up to 360 degrees or 180 degrees
Answer:
195
Step-by-step explanation:
Since this figure is a quadrilateral you would be subtracting the inner angles from 360
360-87-40-38=195
Fill in the blank if sin=3/5, then cos=
Answer:
cos = 4/5
Step-by-step explanation:
having sides 3 and 5, means that this is a right triangle with sides 3,4, and 5
cos = adjacent side/ hypotenuse
sin= opposite side/ hypotenuse
since 5 is the biggest number it will be the hypotenuse since that is the longest side, so it will stay on the bottom.
hope this helps! if you have any more questions just ask
Two straight lengths of wire are placed on the ground, forming vertical angles. If the measure
of one of the angles formed is 72°, what are the measures of the other three angles? Explain
The other angle opposite the given 72° angle is also 72°. This is because vertical angles are congruent.
The other two opposite angles are 180-72 = 108° each
See the diagram below. Notice how all four angles add to 360 degrees. Any adjacent pair of angles add to a straight line of 180 degrees.
The approximate weights of two animals are 5.36 x 104 lbs. and 6.2 x 104 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
Answer:
12*10^4 lbs.
Step-by-step explanation:
This is the correct answer because you have to count using scientific notation by seeing the amount of times the decimal point has moved to the left which makes it positive.
The total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
The approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.
The total weight = 5.36 x 10⁴ + 6.2 x 10⁴
The total weight = (5.36+ 6.2)10⁴
The total weight = 11.56x10⁴
Or
The total weight = 12x10⁴ lbs
Thus, the total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.
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Evaluate the function.
f(x) = -x² + 7x
Find f(-1)
Answer: f(-1)=-8
Step-by-step explanation:
f(x) = -x² + 7x
f(-1)=-(-1)²+7(-1)
f(-1)=-1-7
f(-1)=-8
A pound of rice crackers cost 42.88 jacob purchased 1/4 pound how much did he pay
So you know that a pound of rice crackers cost $42.88. You also know that Jacob bought 1/4 or 25% or 0.25 of a pound. This means that by multiplying 0.25 by $42.88, you can determine the cost.
0.25 x 42.88 = 10.72
Therefore, Jacob paid 10.72 cents or $10.72 for 1/4 pound of rice crackers
The solution set of x^2+12=21
The solution set of the equation is: x = -3, x = 3.
How to Find the Solutions to an Equation?Given the equation, x² + 12 = 21, the solution set is the possible value of x that will make the equation true. To find the values of x, do the following as shown below:
x² + 12 = 21
Subtract 21 from both sides of the equation
x² + 12 - 21 = 21 - 21
x² + 12 - 21 = 0
x² - 9 = 0
Find the difference of the two squares
(x + 3)(x - 3) = 0
x = -3
x = 3
Therefore, the solution set of the equation is: x = -3, x = 3.
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The price of a computer is 899.00 the sales tax rate is 7% what is the sales tax on the computer in dollars and cent
The value of the sales tax on the computer is 62 dollars and 93 cents.
Any number or a ratio which is expressed in terms of a fraction of 100 is known as a percentage.
Here, we are given that the price of a computer is 899 dollars.
The sales tax on the computer is 7%.
Thus, the value of the sales tax on the computer will be,
7% of 899
= 7/100 * 899
= 62.93
Thus, the sales tax on the computer comes out to be 62.93 dollars.
In 62.93 dollars, we can see that we have 62 complete dollars, plus 0.93 more dollars left.
0.93 dollars = 93 cents
Therefore, the sales tax on the computer is 62 dollars and 93 cents.
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Answer:
Step-by-step explanation:
Select the correct answer.
Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have?
A. x + 1/2x + 2/3x = 30 - 4, which has no solution
B. x + 1/2x + 2/3x = 30, which has infinitely many solutions
C. x + 1/3x + 2/3x - 4 = 30, which has one solution
D. x + 1/2x + 2/3x +4 = 30, which has one solution
E. 1/2x + 2/3x = x - 4, which has no solution
Answer: C, I think is correct
Prime Factorization
36=
48=
Answer:
36=3×2×2×3
48=2×2×2×2×3
Explanation:
Step 1: Divide the given number by the smallest prime number.
36/3=12. (1)
48/2=24. (2)
Step 2: Again, divide the quotient by the smallest prime number.
12/2=6. (1)
24/2=12. (2)
Step 3: Repeat the process, until the quotient becomes 1.
6/2= 3. (1)
12/2=6 (2)
3/3=1 (1)
6/2=3 (2)
3/3=1. (2)
Step 4: Finally, multiply all the prime factors.
36=3×2×2×3
48=2×2×2×2×3
Answer:
36 = 2 × 2× 3 ×3
48 = 2 × 2× 2 × 2 ×3
Step-by-step explanation:
I need help 10-25 please help asap step by step
What is the appropriate measure of variation (spread) for these data points? 47234213985132324365 what are q1 and q3 for these data?
The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.
The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.
Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.
For the given data points, Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.
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The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.
The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.
Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.
For the given data points, Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.
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Louie's recipe requires four eggs for every eight cups of flour. How
many eggs will she need if she uses twelve cups of flour?
SHOWS ME EVERY STEP PLS NEED TO SHOW MY WORK FOR HW!
Which is longer: 30 yards or 30 meters?
Answer:
30 meters.
Step-by-step explanation:
Meters are larger then yards.
14) Out of the following options, pick the one that
can be expressed as a rational number.
a) 1.16321632...
b) 0.00120345...
c) 5.672101234 ...
d) 2.75757575...
i have no idea what this means
Identify the domain and range of
the relation.
domain:
range :
Answer: domain is x and range is y
Step-by-step explanation:
Answer:
Domain: {2, 8, 30, 46}
Range: {-1, 9, 16}
Step-by-step explanation:
The domain of a function y = f(x) is the set of all values that the input values (x) that the function can accept. The range of a function is the set of all output values that the function can produce from the domain values ie the set of all values
Looking at the figure, the set of all x values that the function y can take are
{2, 8, 30, 46} and this is the domain
The output values produced from this domain are {-1, 9, 16} and that is the range
PLEASE HELP!!!!! please? :D
Answer:
9
Step-by-step explanation:
→ Substitute in the values
2³ +√64 ÷ 8
→ Simplify
8 + 8 ÷ 8
→ Calculate
8 + 1 = 9
Answer:
9
Step-by-step explanation:
2 to the power of 3 is 8
8 + 64 = 72
72 ÷ 8 = 9