Using the concepts of probability, we got that 0.0764 is the probability that the sum of the 100 values is greater than 3,908 when a researcher measure the amount of sugar in several cans of the same soda.
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
Z=(X-μ)/σ
The z-score measures how many standard deviations the measure is above or below the mean.Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation .For this problem, these parameters are given as follows:
μ=39.01,σ=0.5,n=100,s=0.5/√100=0.05
A sum of 3908 is equivalent to a sample mean of 3908/100 = 39.08, which means that the probability is the p-value of Z when X = 39.08, hence:
Z=(X-μ)/σ
By the Central Limit Theorem:
Z=(X-μ)/s
=>Z=(39.08-39.01)/0.05
=>Z=(0.07)/0.05
=>Z=7/5
=>Z=1.4
Z = 1.4 has a p-value of 0.0764.
Hence, the probability that the sum of the 100 values is greater than 3,908 is 0.0764.
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The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 45° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
The measure of each angle of this isosceles triangle is equal to 27°, 27°, and 126°.
What is an isosceles triangle?An isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles that have the same measure or are equal in magnitude.
Let the variable x represent the angles that have the same measure or are equal in magnitude. Therefore, the sum of the measures of the angles of this isosceles triangle is given by this mathematical expression:
x + x + (45° + 3x) = 180°.
5x + 45° = 180°.
5x = 180° - 45°
5x = 135°
x = 135°/5
x = 27°
Therefore, the measure of each angle of the isosceles triangle is given by:
First angle = 27°.
Second angle = 27°.
Third angle = 45° + 3(27) = 126°.
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Felipe received a $25.00 gift card for a photo center. He used it to buy prints that cost 5 cents each. The remaining balance, B (in dollars), on the card after
buying x prints is given by the following function.
B(x)=25.00-0.05x
What is the remaining balance on the card if Felipe bought 20 prints?
Answer:
24
Step-by-step explanation:
lets set up the equation
x=25-(0.05x20) this is
x=25-1
x=24
Find the x- and y-intercepts of the graph of 4x - 9y = 20. State each answer as an
integer or an improper fraction in simplest form.
Calculation
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's x-intercept: x= 5
Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]
Find the function's y-intercept: y = [tex]-\frac{20}{9}[/tex]
The chart for : 4x-9y = 20
see the attachment
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The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction. x = 20 + 9y /4
What is meant by fraction?A fraction is a portion of a whole. In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator. In a simple fraction, both are integers.A complex fraction has a fraction in either the numerator or denominator. In a proper fraction, the top number is less than the lowest common.A fraction pretty much tells us how many parts of a whole we have. A fraction is identified by the slash that is written between the two numbers. Designers have a top number, the quaternion, and a bottom number, the denominator. For instance, 1/2 is a fraction.Given
x, 4x - 9y = 20
x = 20 + 9 /4 y
Steps
4x - 9y = 20
Add 9 y to both sides
4x - 9y + 9y = 20 + 9y
Simplify
4x = 20 + 9y
Divide both sides by 4
4x/4 = 20/4 + 9y/4
Simplify
x = 20 + 9y /4
Hence, The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction.
x = 20 + 9y /4
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PLEASE ANSWER
there are no choises
The relation between angle 1 and angle 2 is they are equal and corresponding angle.
What are parallel lines?
Two lines are said to be parallel when they do not intersect each other. We can also say that two lines that run along and meet at infinity are called parallel lines.
What are corresponding angles?
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines and the transversal.
Given, m and l are parallel line.
Hence, m and l satisfy the condition of parallel lines.
Therefore, the angle 1 and angle 3 are equal.
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Work out the length of x if one of the lengths is 9.7cm.Give your answer rounded to 3 significant figures.
Tysm if u can work this out correctly.
Considering the figure of a right angle triangle, the given length is the hypotenuse,. The unknown side x is calculated to be 6.86 cm
How to find xinformation given in the question
hypotenuse = 9.7 cm
opposite = x
adjacent = x
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
opposite = adjacent
plugging the values as in the problem
let x be the required distance
9.7² = x² + x²
94.09 = 2x²
47.045 = x²
x² = 47.045
x = √47.045
x = 6.8589
x = 6.86 to 3 significant figures
side x is 6.86 cm
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According to the fundamental theorem of algebra, how many zeros does the function f(x) = 5x - 9 have?
The algebraic fundamental theorem states that there are 12 zeros in the function f(x) = 15x12 + 41x9 + 13x2 10.
What is fundamental theorem?Theorem that connects the ideas of differentiating a function (calculating the gradient) and integrating a function is known as the fundamental theorem of calculus (calculating the area under the curve). With the exception of a constant value that depends on where one starts to compute area, the two procedures are inverses of one another.One of the antiderivatives (also known as an indefinite integral), let's say F, of some function f, may be derived as the integral of f with a variable bound of integration, according to the first section of the theorem, which is frequently referred to as the first fundamental theorem of calculus. This indicates that continuous function antiderivatives existacc to our question-
The degree that we need to identify in a polynomial is the largest exponent used in the equation. In this case, 15x¹², has the largest exponent. It is the degree of n used to determine the number of zeros.Thus, n = 12 so number of zero is also 12.hence,there are 12 zeros
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Select the correct answer. Amy types at an average speed of 38 words per minute. She has already typed 1,450 words of her final paper, which will be more than 4,000 words. Which inequality can be used to solve for x, the number of minutes it will take Amy to finish typing her paper? A. 38x − 1,450 > 76 B. 38(x + 1,450) > 4,000 C. 38x > 4,000 D. 38x + 1,450 > 4,000
The inequality that can be used to solve for x, the number of minutes it will take Amy to finish typing her paper is D. 38x + 1,450 > 4,000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Since Amy types at an average speed of 38 words per minute and has already typed 1,450 words of her final paper, which will be more than 4,000 words.
Let the number of minutes be x.
This will be:
1450 + 38(x) > 400
1450 + 38x > 4000
In conclusion, the correct option is D.
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Write an equation in slope-intercept form for the line that passes through the given point
and is parallel to the graph of the equation.
(1,-3); y=-2r+5
Answer:
equation: y= -2x-1
Step-by-step explanation:
y= -2x+b
-3= -2(1)+b
-3= -2+b
b= -1
equation: y= -2x-1
“Find the requested information based on the given facts.
Total sales is $55,000
The commission is 3.5%
Determine the commission.”
Can someone please help?
Answer:
$1925
Step-by-step explanation:
So your problem is $55,000 x 3.5%
You can rewrite this as:
55,000 x 3.5/100 or 55,000 x 35/1000
Now multiply. I will remove the /1000 for now.
55,000x35=1925000
Now, divide 1925000 by 1000.
1925/1000=$1,925
50 points look at picture (if u troll i will get u banned)
The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.
According to the question,
We have the following information:
We have a figure where angle MCJ is 130°.
Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.
We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.
Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.
Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.
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the area of a rectangle shown is 44m2
3 2/3 m
x?
work out the missing length x
Please, can someone help me with this math? I would greatly appreciate it!
The proof that shows that lines DC and AB are parallel is shown below.
What is the SSS Congruence Theorem?The SSS congruence theorem states that two triangles that have three corresponding congruent sides are congruent to each other.
When two triangles are proven to be congruent triangles, invariably, we can state that the corresponding parts of both triangles are also equal to each other by CPCTC.
The following proof shows lines DC and AB are parallel lines:
Statement Reasons
1. AB = CD 1. Given
AD = CB
2. Line AC = Line AC 2. Reflexive property
3. Triangle ADC ≅ Triangle ABC 3. SSS
4. Angle 1 ≅ Angle 4 4. CPCTC
5. DC║AB 5. Converse of alternate interior ∠s theorem
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solve the equation 8-3(x + 4)= 2x +1
Answer:
x = -1
Step-by-step explanation:
8 - 3x - 12 = 2x + 1
-3x - 4 = 2x + 1
-5 = 5x
x = -1
The value of x in the equation 8-3(x+4)=2x+1 is -1.
Given equation 8-3(x+4)=2x+1
= 8-3x-12 = 2x+1
= -3x-4 = 2x+1
= -5x = 5
= x = -1
We will first solve the bracket which is -3(x+4) which will give us -3x-12 and then we will add this to 8 which will give us -3x-4. Next, we will move all the constants to one side and the terms with x to one side which will give us -5x=5. Finally, we will divide the whole equation by -5 and we will get the answer of x as -1.
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I need this by tonight would be appreciated. :) I know this is basic stuff I'm in Middle School but when I signed up for this there wasn't a middle school option.
The area of the floor of the convenience store would be = 212.5 ft²
What is the area of an object?The area of an object is defined as the total space that is being occupied by that object.
To calculate the area of the convenience store is to find the area of the shaded part which would be = area of square - area of the triangle.
Area of square = l ×w = 15 × 15 = 225ft²
Area of triangle= 1/2 base ×height
= 1/2 × 5 × 5
(Note: 15 - 10 = 5 ft from the diagram used as base and height)
= 25/2
= 12.5 ft²
The area of the convenience store;
= 225 - 12.5
= 212.5 ft².
Therefore, the area that is covered by the convenience store should be = 212.5ft².
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write down the value of 9 and a half?
The value of 9 and a half will be 9 1/2.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Here, we want to find the value of 9 and half. This will be:
= 9 + 1/2
= 9 1/2
The value is 9 1/2.
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Which values of aand b make the following equation true?
(5x²y²){-4xªy³) =−20xªy°
O
a = 11, b = 7
O a = 11, b = 10
O a=28, b = 7
O a= 28, b = 10
The value a = 2 and b = 5 is makes the expression (5x²y²){-4xªy³) =−20xªyᵇ as true.
Expression:
An expression is set of numbers or variables combined using the operations +, -, * and /.
Given,
Here we have the expression (5x²y²){-4xªy³) =−20xªy°.
Now, we have to the value of a and b which make both equation as equal.
In order to get the value a and b, first, we have to solve the expression in the left hand side,
To solve this type of equation, the first step is to combine the like terms, then we get,
=> (5x²y²){-4xªy³)
=> (5 x -4) (x² xᵃ) (y² y³)
Now, we have to do the multiplication on it, then we get,
=> -20 xᵃ⁺² y²⁺³
=> -20xᵃ⁺²y⁵
Now, we have to equate both LHS and RHS, then we get,
=> -20xᵃ⁺²y⁵ = -20xᵃyᵇ
While we looking into the equation, we have identified that the value of a is 2 and the value of b is 5.
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402 students were surveyed about their preferences of sports. 140 students like football, 144 students like baseball, and 42 students like both sports. how many students like exactly one of the two sports? a) 200 b) 140 c) 284 d) 98 e) 102 f) none of the above.
The students that will like exactly one of the two sports out of football and baseball is 200.
What is set theory?These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).
Here,
F=140
B=144
F∩B=42
F-B=n(F)-n(F∩B)
=140-42
F-B=98
B-F=n(B)-n(F∩B)
=144-42
=102
So, the students that will like exactly one of the two sports,
=102+98
=200
There are 200 students who will only enjoy one of the two sports—football or baseball.
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help i have no clue what this even means
Case 1: largest surface area: 2120 sq. in.
Case 2: smallest surface area: 1380 sq. in. of the wooden block.
What is defined as the cuboid?A three-dimensional shape called a cuboid is described as having six rectangular face, eight vertices, and twelve edges.Twelve edges plus eight vertices and corners to up a cuboid.For the given question, the dimensions of the wooden block are given.
Length l = 50 inchesWidth w = 5 unitsHeight h = 2 unitsSurface area of a cuboid is = 2lw + 2lh + 2 hw
Case 1: largest surface area.
To get the largest surface area, join the wooden cube along length 50 cm.
Total length = 50 + 50 + 50 = 150 inches.
Put in formula.
Surface area = 2×150×5 + 2×5×2 + 2×2×150
Surface area = 2120 sq. in.
Case 2: smallest surface area.
To get the smallest surface area, join the wooden cube along height 2 cm.
Total length = 2 + 2 + 2 =8 inches.
Put in formula.
Surface area = 2×8×50 + 2×50×5 + 2×5×8
Surface area = 1380 sq. in.
Thus, the smallest surface area of the wooden cube is found as 1380 sq. in.
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The correct question is-
There are 3 identical wooden blocks that are 50 inches long, 5 inches wide and 2 inches thick. If you glue them together , what is the largest and smallest outer surface area can get?
can someone solve this?
Find the values of the variables and the measures of the angles.
Answer:
x = 52°
y = 25°
z = 90°
Step-by-step explanation:
We know there are 180 degrees in a triangle. The box represents 90 degrees.
90° + x + 38° = 180°
x + 128° = 180°
x = 52°
Next, we know that a straight line is equal to 180 degrees. Again, the box represents 90 degrees.
90° + z = 180°
z = 90°
Lastly, we will use the same process for angle x, but for angle y.
y + z + 65° = 180°
y + 90° + 65° = 180°
y + 155° = 180°
y = 25°
can someone answer this question really quick
c = 2.97r is the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost
How to write an equation that describes proportional relationships?Two variables have a proportional relationship if all the ratios of the variables are equivalent
In order to write an equation that describes the proportional relationship r, the number of reams purchased and c, the total cost, we need to write a proportional equation using the variables:
c α r (Note: α is the proportion symbol)
c = kr
k = c/r
Where k is the constant of proportionality
As shown in the image, you can see that 4 reams cost $11.88 and 6 reams cost $17.82
k = c/r
k = 11.88/4 = 2.97 or 17.82/6 = 2.97
c = kr
c = 2.97r
Therefore, the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost is c = 2.97r. Enter c = 2.97r in the box
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X+3y+z=-8
2x+y-6z+20
x-2y+z=-13
The solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
We have the following set of equations -
x+3y+z=-8 ..[1]
2x+y-6z=20 ..[2]
x-2y+z=-13 ..[3]
We can write eq [3] as -
z = - 13 - x + 2y
So, eq [1] and [2], will become -
x + 3y + (-13 - x + 2y) = -8
x + 3y - 13 - x + 2y = -8
5y = - 8 + 13
5y = 5
y = 1 ..Eq[4]
AND
2x + y - 6z = 20
2x + y - 6(- 13 - x + 2y) = 20
2x + y + 78 + 6x - 12y = 20
2x + 1 + 78 + 6x - 12 = 20
8x = 47
x = 5.875 ..Eq[5]
Now -
x - 2y + z = -13
5.875 - 2 + z = - 13
z = 16.875
Therefore, the solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875.
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A balloon was originally filled to a volume of 4,400 cubic centimeters. Air inside the balloon leaks out over time.
Write an inequality that describes V, the volume of the balloon in cubic centimeters as air leaks out.
Enter your inequality without a thousands separator.
The inequality expression of the volume of the balloon is V < 4,400
How to determine the inequality expression?From the question, we have the following statement:
The initial volume of the balloon is 4,400 cubic centimeters
Also, we understand that:
The balloon leaks out over time
This means that the volume of air in the balloon decreases over time.
So, we have the following representation
V = Less than the initial volume
Rewrite as
V < 4400
Hence, the volume of the balloon at any time after it starts leaking is V < 4,400
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HELP ASAP !!!! Use the equation one fourth plus s equals 18 over 20 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
a. The two numbers between which the solution to the equation lies are 0 and 1.
b. The value of the variable "s" is 13/20.
How to solve Algebra Word Problems?The equation given to us is one fourth plus s equals 18 over 20. This can be expressed as;
¹/₄ + s = ¹⁸/₂₀
s = ¹⁸/₂₀ - ¹/₄
s = (18/20) - (5/20)
s = (18 - 5)/20
s = 13/20
The solution is a rational number. A rational number is defined in mathematics as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
We can determine two rational numbers such that the solution is in between them. A rational number smaller than the solution is 0. A rational number larger than the solution is 1. Hence, the solution lies between 0 and 1.
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Which triangle congruence postulate or theorem proves that these triangles are
congruent?
The angle-side-angle (ASA) Congruence theorem proves that
ΔABC and ΔPQR are congruent triangles.
We know that the angle-side-angle ASA Congruence theorem states that if two angles and the side between these angles of one triangle are equal to two angles and the side between then of another triangle then those two triangles are congruent.
In given triangles ABC and PQR,
∠ABC ≅ ∠PQR
BC ≅ QR
∠BCA ≅ ∠QRA
so, by ASA Congruence theorem ΔABC ≅ ΔPQR
Therefore, the angle-side-angle (ASA) Congruence theorem proves that
ΔABC and ΔPQR are congruent triangles.
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What is the slope of a line parallel to the line whose equation is 3x+4y=36
Answer:
3/4
Step-by-step explanation:
Get into y=mx+b
Subtract 3x
4y=3x+36
Divide by 4
y=3/4x+9
Parallel= 3/4
Perpendicular= -4/3
x represents the number
of comic books Priya buys
at the store, all at the same
price, and y represents the
amount of money (in
dollars) Priya has after
buying the comic books.
By using the concept of equation of line in slope intercept form, it can be obtained that
a) x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
y- intercept is 20
This means, Priya had $20 before buying any comics
b) Slope = -4
This means Priya's money has been decreasing by $4 after buying one comics
c) Equation of line
y = -4x + 20
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
x represents the number of comic books Priya buys at the store
y represents the amount of money (in dollars) Priya has after buying the comic books.
a)From the figure, it is clear that x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
From the figure, it is clear that y- intercept is 20
This means, Priya had $20 before buying any comics
b) The line passes through (5, 0) and (0, 20)
Slope = [tex]\frac{20 - 0}{0 -5}[/tex] = -4
This means Priya's money has been decreasing by $4 after buying
one comics
c) Equation of line
y - 0 = -4(x - 5)
y = -4x + 20
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Complete Question
The figure has been attached-
will give you brainliest!! ASAP
Answer:
686 cm^2
Step-by-step explanation:
4(7)=28
7(7)=49
49 x 28= 1372
1372/2=686
hopes this helps
domain of "-x^4-x^3+3x^2+2x+6"
The domain of the given function is -∞ < x < ∞.
What is a domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, the function is:
-x⁴-x³+3x²+2x+6Now, the domain of the given function is:
The set of input or argument values for which the function is actual and defined is known as the function's domain.Neither the function's domain constraints nor its undefined points exist.The domain will therefore be -∞ < x < ∞.
Therefore, the domain of the given function is -∞ < x < ∞.
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The table shows the side
lengths and perimeters of
regular hexagons. Is the
relationship between the
perimeter and the side
length of the hexagons
proportional? Explain.
The relationship between the perimeter and the side length of the hexagons is proportional.
What is a proportional relationship?A proportional relationship is one that illustrates the constant between the data that are given.
In this case, when the side length is 2, the perimeter is 12. The constant is:
= Perimeter / Length
= 12 / 2
= 6
Also, when the length is 3, the perimeter is 18. The constant will be:
= 18 / 3
= 6
Since they have 6 as constant, it's a proportional relationship.
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A solution that is 20% acid and 80% water is mixed with a solution that is 50% acid and water. If twice as much 50% acid solution is used as 20% solution, then what is the ratio of acid to water in the mixture of the solutions?
Answer:
The ratio of acid to water is 2 to 3 in the mixture of the two solutions
This can be thought of as a chemistry problem or a math problem, but both use practically the same process to find the final answer.
So, let's say 2 liters of 50% acid and 1 liter of 20% acid is mixed.
In total, there is 2*(50%) + 1*(20%) of acid, so there is 1 liter of pure acid in 2 liters of 50% acid, and 0.2 liters of pure acid in 1 liter of 20% acid. This in total is 1.2 liters of acid. The total volume is 2 + 1 liters, which is 3 liters. the percentage can be found by dividing the amount of pure acid by the total volume, so 1.2/3, which equals 0.4, or 40%. The ratio would be 40% to 100-40%, or 40% to 60%, or 2 to 3