The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.
How much 50% solution must he purchase?A customer has 40 gallons of a cleaning solution that contains 20% soap.
The company sells a cleaning solution that contains 50% soap.
The customer wishes to create a 40% solution.
Solution:
By mixture and allegation method,
1 gallon 1 gallon
50% 20%
40%
20 10
To create a 40%Soap solution, one must mix 20 gallons of 50% soap solution and 10 gallons of 20% Soap solution.
Therefore, the ratio is 20 : 10 = 2:1
The customer has 40gallons of a cleaning solution that contains 20% soap, therefore in a 2:1 ratio, 1 part is 40 gallons.
Then for 2 parts = 2*40 = 80 gallons.
The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.
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Bertha and Vernon are competing in a diving competition. Bertha's dive ended -25 m from the starting platform. Vernon's dive ended -5 m from the starting platform. How many times farther was the end of Bertha's dive than the end of Vernon's dive?
Bertha's dive is 5 times farther than the end of Vernon's dive
What is ratio?A ratio can defined mathematical as an ordered pair of numbers, like variables b and c, when written form b / c with the denominator greater than the value zero.
It explains how many times a particular number is composed of another number in a given proportion.
It is also seen as the comparison of two quantities, elements or numbers having the same unit measure. It goes further to explain how much of one of the element or quantity contains another.
This is done on the basis of their magnitude or sizes.
Given that;
Bertha's dive ended = -25 m
Vernon's dive ended = -5 m
Divide the values
= -25/-5
= 5 times
Hence, the value is 5 times
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A soccer ball is kicked from the ground by the goalie and lands 40 meters from where it waskicked. The ball's path is that of a parabola, and the ball reaches a maximum height of 3 meters,How far from where the ball was kicked will it have a height of 2 meters? (Round your answer tothe nearest tenth.)
Given:
The distance travelled by the ball is, d = 40 m.
The maximum height the ball reached is, h = 3 m.
The objective is to find the distance travelled by the ball at a height of h' = 2 m.
. (vertex)
n, the
The value of x can be calculated using the general form of the equation of parabola,
[tex]y=a(x-p)^2+q[/tex]Here, (p,q) stands for the vertex of the parabola (20,3).
To find the value of a, consider a coordinate (0,0) and substitute the obtained values in the general equation of parabola.
[tex]\begin{gathered} 0=a(0-20)^2+3 \\ 0=a(400)+3 \\ -400a=3 \\ a=-\frac{3}{400} \end{gathered}[/tex]Now, consider the coordinate of the required distance x of the ball, (x,2).
Substitute the above coordinate, the value of a and the vertex in the equation of parabola.
[tex]\begin{gathered} y=a(x-p)^2+q \\ 2=-\frac{3}{400}(x-20)^2+3^{} \\ 2=-\frac{3}{400}(x-20)^2+3 \\ 2-3=-\frac{3}{400}(x-20)^2 \\ -1=-\frac{3}{400}(x-20)^2 \\ (\frac{400}{3})=(x-20)^2 \end{gathered}[/tex]To solve the square on RHS, take square root on both sides of the equation.
[tex]\begin{gathered} \sqrt[]{\frac{400}{3}}=\sqrt[]{(x-20)^2} \\ 11.5=(x-20) \\ x=11.5+20 \\ x=31.5\text{ m} \end{gathered}[/tex]Since, the height of 2 m of ball can be obtained at either side of the vertex.
So the distance between the vertex and the required position is
[tex]\begin{gathered} c=31.5-20 \\ c=11.5 \end{gathered}[/tex]Then, the other possible position of the ball is,
[tex]\begin{gathered} x^{\prime}=20-c \\ x^{\prime}=20-11.5 \\ x^{\prime}=8.5 \end{gathered}[/tex]Hence, the height of the ball will be 2m, either at a distance of 8.5m from origin or 31.5m from the origin.
I need an answer please
the answer is 40 degrees
Step-by-step explanation:
DCB+DCE+ACE =180
DCB+100+ACE=180 (degrees)
DCB+DCB=180-100
2 DCB = 80 (degrees)
DCB=80÷2
DCB = 40 Degrees
What is the area of this trapezoid?
Someone pls help
A=a+b/2×h=5+10/2×4=30. this might helpful
Consider the integral - tan(0) · ln(3 cos(0)) dė:
.
This can be transformed into a basic integral by letting
In (3 cos (0))✓ O O and
U=
du = -tan (0)✓o de
After perfroming the substitution, you obtain the integral
du
[tex]\displaystyle \int -\tan(\theta )\cdot \ln(3\cos(\theta )) ~~ d\theta \\\\[-0.35em] ~\dotfill\\\\ u=\ln(3\cos(\theta ))\implies \cfrac{du}{d\theta }=\cfrac{1}{3\cos(\theta )}\cdot -3\sin(\theta ) \\\\\\ \cfrac{du}{d\theta }=-\tan(\theta )\implies \cfrac{du}{-\tan(\theta )}=d\theta \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int -\tan(\theta )\cdot u\cdot \cfrac{du}{-\tan(\theta )}\implies \int u\cdot du[/tex]
A single die is rolled. Find the odds in favor of rolling a number greater than
Answer:
Step-by-step explanation:
you have a 1/6 of rolling a certain number on a regular die.
if you try to get 5 or 6 you have a 2/6 chance of rolling either of them
if you try to evens you have a 3/6 chance of rolling 2,6, or 4
Simplify.
7a²+ 3b +6a-2a²
A.a² + 3b-2
B. 5a² + 3b + 6a
C.9a² + 3b + 6a
D. 11a²+ 3b +6
Answer:
B. 5a² + 3b + 6a
Step-By-Step Explanation:
First, see what has like terms. 7a² and -2a² both have the exponent 2 and the letter a, so you can combine those to get 5a². 3b and 6a cannot be combined because they have a different letter. So, 5a² + 3b + 6a is your answer.
City workers are using a snowplow to clear a street. A tire on the snowplow is 3.2 ft in diameter and has to turn 47 times in traveling the length of the street. How long is the street?
Use the value 3.14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
If a tire on the snowplow with a diameter of 3.2 ft turns 47 times then, the length of the street is 472.3 feet.
To clear a street the city workers use a snowplow. The diameter of the tire of the snowplow is 3.2 ft.
The tire has to turn 47 times to cover the total length of the street.
Now, we know that the circumference of a circle is given as:
C = 2πr where r is the radius of the circle. And the radius of a circle is half of its diameter.
Therefore, the circumference of the circle can be written as:
C = πD where D is the diameter of the circle.
Now, to calculate the total length of the street we will find the product of the circumference and the number of times the tire has to turn to cover the street.
Therefore,
Length of the street, L = nC
L = nπD
L = 47 × 3.14 × 3.2 ft
L = 472.256 ft
L = 472.3 ft
Hence, the length of the street is 472.3 feet.
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Write a rule to describe each transformation.
The transformation is a reflection across the y-axis (the line x = 0).
Which transformation is shown in the image?On the image we can see two triangles, both are at the same distance of the vertical axis.
We also can notice that the figure is reflected, this is, the longest point of the triangle points to opposite ways.
With this we can conclude that we had some kind of reflection. Particularly, because both triangles are a the same distance of the vertical axis, we can conclude that the reflection was across the line x = 0.
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the figures below are similar. the labeled sides are corresponding. what is the area of the larger triangle?
ANSWER:
64 square inches.
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the ratio between the corresponding sides of the triangles:
[tex]r=\frac{8}{6}=\frac{4}{3}[/tex]We must bear in mind that the area of the larger t triangle is equal to the area of the small triangle multiplied by the ratio of the square, since the area is a quadratic unit, therefore:
[tex]\begin{gathered} A_2=r^2\cdot A_1 \\ \text{ we replacing} \\ A_2=\mleft(\frac{4}{3}\mright)^2\cdot36=\frac{4^2}{3^2}\cdot36=\frac{16}{9}\cdot36 \\ A_2=64in^2 \end{gathered}[/tex]The area of the larger triangle is 64 square inches.
Help!!! Giving 25 points!
The system of linear equations and their solutions are:
1. (51, 26): x - y = 25; 2x + 3y = 180
2. (-17, -36): x - y = 19; -2x + y/6 = 28
3. (47, 33): 2x - 3y = -5; x + y/11 = 50
4. (-31, -56): 2x - y = -6; x - 305/3 = 2y.
How to Solve a System of Equations?We can solve a system using the substitution method by finding the value of one of the variables, followed by substitution.
1. x - y = 25 -- eqn. 1
2x + 3y = 180 -- eqn. 2
Rewrite eqn. 1:
x = 25 + y
Substitute x = 25 + y into eqn. 2:
2(25 + y) + 3y = 180
50 + 2y + 3y = 180
5y = 180 - 50
5y = 130
y = 26
Substitute y = 26 into eqn. 1:
x - 26 = 25
x = 25 + 26
x = 51
The solution is: (51, 26).
2. x - y = 19 -- eqn. 1
-2x + y/6 = 28 -- eqn. 2
Rewrite eqn. 1:
x - y = 19
x = 19 + y
Substitute x = 19 + y into eqn. 2:
-2(19 + y) + y/6 = 28
-38 - 2y + y/6 = 28
-11y/6 = 28 + 38
-11y/6 = 66
-11y/6 (-6/11)= 66(-6/11)
y = -36
Substitute y = 36 into eqn. 1:
x - y = 19
x - (-36) = 19
x + 36 = 19
x = 19 - 36
x = -17
The solution is: (-17, -36).
3. 2x - 3y = -5 -- eqn. 1
x + y/11 = 50 -- eqn. 2
x + y/11 = 50
x = 50 - y/11
Substitute x = 50 - y/11 into eqn. 1
2(50 - y/11) - 3y = -5
100 - 2y/11 - 3y = -5
-35y/11 = -5 - 100
-35y/11 = -105
-35y/11(-11/35) = -105(-11/35) (multiplication property)
y = 33
Substitute y = 33 into eqn. 2:
x + 33/11 = 50
x + 3 = 50
x + 3 - 3 = 50 - 3
x = 47
The solution is (47, 33).
4. Solving the last one, we will definitely have the solution, (-31, -56).
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Find the slope of the line graphed below.
Answer:
The slope is -5/2
Step-by-step explanation
I tried to show how I solved this problem in the image, but its not too great, so I hope this helps. :)
Use the properties of operations to multiply the expressions. (10.3y)(4y)
By using the properties of operations, the result of the expression (10.3y)(4y) is [tex]41.2y^{2}[/tex]
The expression is given = (10.3y)(4y)
Here we have to multiply the given expression using the properties of operations
The integers has mainly five properties of operation, closure property, associative property, commutative property, distributive property and the identity property. Each property has four integer operations. The four integer operations are addition operation, subtraction operation, multiplication operation and division operation
The given expression = (10.3y)(4y)
Multiply the given expression using the properties of operation
(10.3y)(4y) = [tex]41.2y^{2}[/tex]
Hence, by using the properties of operations, the result of the expression (10.3y)(4y) is [tex]41.2y^{2}[/tex]
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Evaluate 10 exponent -8
Answer:
0.000000010
Step-by-step explanation:
PLEASE HELP ME!!!!!!!
Let f(x) =[tex]\frac{2x^2-2x-1}{x^4+1}[/tex] At which points does the graph of the f(x) have a horizontal tangent line
The points at which the graph of f(x) has a horizontal tangent line are; x = -1, x = 0.4045, x = 2.07
What is the horizontal tangent of the graph?
The horizontal tangent of a function is simply defined as the point where the slope of the function is 0.
Now, we are give the function as;
f(x) = (2x² - 2x - 1)/(x⁴ + 1)
Slope of this function is;
f'(x) = -2(2x⁵ - 3x⁴ - 2x³ - 2x + 1)/(x⁴ + 1)²
Now, when the slope is zero, we will have that;
-2(2x⁵ - 3x⁴ - 2x³ - 2x + 1) = 0
Using an online polynomial root calculator, the roots of this slope are;
x = -1, x = 0.4045, x = 2.07
These values are the points where there is a horizontal tangent line.
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How many peanuts would Eric need to make 5 batches of trail mix?
hello! it would help if you gave more information so we could better answer the question ^^
If marching bands vary from 18 to 48 player, which numbers of players can be arranged in the greatest number of rectangles?
For the marching bands vary from 18 to 48 player, the numbers of players arranged in the greatest number of rectangles is 48 players.
As given in the question,
Number of players in the given marching bands vary from 18 to 48 players
To form a rectangles in the marching bands minimum two rows are required.
Greatest length and width of the rectangles formed by 18 to 48 players
19,23,29,....,47 are prime numbers
18 = 2 ×9 , 3×6
20 = 2×10 ,4×5
21= 3×7
22 = 2× 11
24=2×12, 3×8, 4×6
and so on
48 = 2 ×24 , 3×16, 4×12, 6×8,
48 players represents greatest number of rectangles
Therefore, for the marching bands vary from 18 to 48 player, the numbers of players arranged in the greatest number of rectangles is 48 players.
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Solve for x and graph.|x+5| = .01
We need to solve the following equation:
[tex]|x+5|=0.01[/tex]There are two possibilities for the absolute operator, we have the possibility that the argument is positive or negative. Therefore:
[tex]\begin{gathered} x+5=0.01 \\ x=0.01-5=-4.99 \\ \end{gathered}[/tex][tex]\begin{gathered} -(x+5)=0.01 \\ -x-5=0.01 \\ -x=0.01+5 \\ -x=5.01 \\ x=-5.01 \end{gathered}[/tex]The solution is -4.99 and -5.01.
Given the diagram below, find the measure of each missing angle.
The scale factor of model of Eiffel tower is 3:1640.
The scale factor is the ratio of measure of small length to large length. The base of both actual tower and scale down model is mentioned in question. Keep the values in ratio to find the scale factor.
Scale factor = 0.75 : 410
Removing decimal to get the whole number
Scale factor = 75:41000
Dividing the both parts of ratio by 25 to find the scale factor of mentioned model
Scale factor = 3:1640
As the Eiffel tower is scaled down in the model, the scale factor is 3:1640.
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QUESTION DOWN BELOW! PLEASE HELP WILL GET 100 POINTS IM STUCK PLEASE HELP EXPLAIN ITS DUE SOON!!
many thanks!!!
1) given
2) base angles theorem
3) PN=QN
4) [tex]\angle 3=\angle 4[/tex]
5) MP=OQ
7) PQ, QP
8) MQ=PO
9) ASA
A rectangular plot of ground is 10 m longer than it is wide. It’s area is 10,000 square meters.
Based on the fact that the rectangular plot has a length that is 10 m longer than the width, the equation that will help to find area of the rectangular plot of land is 10x + x² = 10,000
How to find the area of the plot of land?To find the area of the plot of land is the same as finding the area of a rectangle which is:
Area of a rectangle = Length x Width
Assuming the width of the rectangular plot of ground is x, then the length would be:
= 10m + x
= 10 + x
The area of the rectangular plot of ground can therefore be found by the formula:
Area of a rectangle = Length x Width
10,000 square meters = (10 + x) × x
10,000 square meters = 10x + x²
10x + x² = 10,000
In conclusion, an equation that can help you to find the dimensions of the plot of ground is 10x + x² = 10,000.
Rest of the question is:
What equation will help me find the dimensions?
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If ∠1 ≅ ∠2, can you conclude that any of the lines are parallel?
Explain.
A. Yes; lines n and p are parallel because corresponding angles are congruent.
B. No; ∠1 and ∠2 show no relationship.
C. Yes; lines ℓ and m are parallel because corresponding angles are congruent.
D. No; neither angle is formed by the transversal, line q.
A. Yes; lines n and p are parallel because corresponding angles are congruent.
According to the reverse of the comparable angles theorem, lines n and p are parallel if angles 1 and 2 are congruent.
The converse of the corresponding angles theorem is what?
According to the corresponding angles theorem, the corresponding angles on each line that a transversal cuts are congruent if the two lines are parallel to one another.
In contrast, lines that fall on those angles are parallel to one another if two corresponding angles are congruent to one another.
The diagram's angles 1 and 2 relate to one another.
In light of the converse of the equivalent angles theorem, lines n and p are parallel if angles 1 and 2 are congruent.
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Find the equation (in terms of x ) of the line through the points (-2,-2) and (3,-1)
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First find the gradient.
Formula of gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2)
Gradient = (-1-(-2))÷(3-(-2))
= (-1+2)÷(3+2)
= 1/5
Equation is y = 1/5 + c
Substitute either one of the points into the equation to find c.
-2 = 1/5(-2) + c
c = -8/5
Hence equation of the line is y = 1/5x - 8/5
How many times larger is 2 x 10^12 than 5 × 10^6
Answer:
[tex]4*10^5[/tex]
Step-by-step explanation:
So whenever sometimes says "how many is x larger than y", it just means what is x divided by y. For example 4 is 2 times as much as 2 because 4/2 = 2
With this being said we can simply divide two numbers
[tex]\frac{2*10^{12}}{5*10^6}[/tex]
Whenever you divide scientific notation you simply divide the two coefficients and subtract the exponents from the base 10
So: [tex]\frac{2*10^{12}}{5*10^6} =\frac{2}{5} * 10^{12-6}[/tex]
This gives you a result of: [tex]0.4 * 10^6[/tex]
Since we want the coefficient to be: [tex]1\le c < 10[/tex] we can take one of the 10s from the base, since 10^6 is just 6 tens being multiplied by each other and we can "borrow" one of them to get: [tex]0.4*10^6=0.4*10*10^5[/tex] which simplifies to: [tex]4*10^5[/tex]
The formula used to convert degrees Celsius to degrees Fahrenheit isF = 9/5C+32.Convert 59°F to degrees Celsius. Solve the formula for C, and then use it toconvert the temperature.
NSWER
C. C = 5/9(F - 32); 59°F =
EXPLANATION
irst, we have to solve the formula for cC. Subtract 32 from both sides,
[tex]\begin{gathered} F-32=\frac{9}{5}C+32-32 \\ \\ F-32=\frac{9}{5}C \end{gathered}[/tex]Then, multiply both sides by 5,
[tex]\begin{gathered} 5(F-32)=5\cdot\frac{9}{5}C \\ \\ 5(F-32)=9C \end{gathered}[/tex]And divide both sides by 9,
[tex]\begin{gathered} \frac{5}{9}(F-32)=\frac{9C}{9} \\ \\ \frac{5}{9}(F-32)=C \end{gathered}[/tex]Hence, the formula to convert from degrees Fahrenheit to degrees Celsius is C = 5/9(F - 32).
So, 59°F is equal to,
[tex]C=\frac{5}{9}(59-32)=\frac{5}{9}\cdot27=15[/tex]Hence, 59°F is equivalent to 15°C.
Subtract ¾ from 5/6.
Answer:
3/4 - 5/6 is
0.08333333333
branliest??
where is ( -3 1/2, -1 1/4 ) on the coordinate plane?
The point ([tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .
The Coordinate plane can be defined as a 2 D plane formed by the intersection of two line ,
where the horizontal line is called x axis and
the vertical line is called y axis .
In the question ,
the point is given
the point is ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex] )
writing the mixed fraction in decimal form , we get
x coordinate = [tex]-3\frac{1}{2}[/tex] ⇒ -(3*2+1)/2 = -7/2 = -3.5
y coordinate = [tex]-1\frac{1}{4}[/tex] ⇒ -(1*4+1)/4 = -5/4 = -1.25
So, the point to be plotted on the coordinate plane becomes (-3.5,-1.25)
the points plotted are shown in the figure below .
Therefore , the point ( [tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .
The given question is incomplete , the complete question is
Where is ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane?
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Which of the following is an equivalent expression of 15x2 +12x + 8?
27x3 + 8
15x2(12x + 8)
12x + 15x2 + 8
8(15x2 + 12x)
The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.
If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.
In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.
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How do I solve this?
The average rate of change from
3 to 5 is -16.
0 to 2 is -4
-3 to 0 is -6.
What is average rate of change?It represents the typical amount by which the function changed for each unit over that time. On the function graph, it is calculated using the slope of the line connecting the interval's ends.
Given Data
Equation = 4 -2x²
Formula-
[tex]\frac{f(a)-f(b)}{a-b}[/tex]
a)To find the average rate of change from 3 to 5
a = 5, b = 3
Equating values in the formula
[tex]\frac{4-2(5^{2} )-(4-(3)}{5-3}[/tex]²
[tex]\frac{-46+14}{2}[/tex]
-[tex]\frac{32}{2}[/tex]
-16
The average ROC 3 to 5 is -16.
b) The average ROC from 0 to 2
a = 2 b=0
Equating values in the formula
[tex]\frac{4-2(2^{2})-(4-2(0) }{2-0}[/tex]
[tex]\frac{-4-4}{2}[/tex]
[tex]\frac{-8}{2}[/tex]
-4
The average ROC from 0 to 2 is -4
c)The average ROC from -3 to 0
a= 0 b = -3
Equating values in the formula
[tex]\frac{4-2(0)-(4-2(3^{2} )}{-3-0}[/tex]
[tex]\frac{4+14}{-3}[/tex]
-[tex]\frac{18}{3}[/tex]
-6
The average ROC from -3 to 0 is -6.
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The first three terms of an arithmetic sequence are x, 2x + 4, 5x. Find the value of x.
P
Answer:
x = 4
Step-by-step explanation:
You want to know the value of x in the arithmetic sequence x, 2x+4, 5x.
Arithmetic sequenceTerms of an arithmetic sequence have a common difference. This means ...
(2x+4) -x = 5x -(2x+4)
x +4 = 3x -4 . . . . . . . . . . simplify
8 = 2x . . . . . . . . add 4-x
4 = x . . . . . . divide by 2
The value of x is 4.
__
Additional comment
The common difference is x+4 = 8. The sequence is ...
4, 12, 20, ...