Answers
m∠C = (16x - 7 )° because ∠A ≅ ∠C
What exactly are complementary and additional angles?When two angles add up to 180 degrees, they are referred to as supplementary angles because they combine to make a linear angle. The opposite is true if the total of two angles is 90 degrees; in this case, they are considered to be complementary angles and together they create a right angle.
Which two supplementary angles come to mind?When two angles sum up to 180 degrees, they are referred to as supplementary angles in geometry. A and B are referred to as supplementary angles, for instance, if A + B = 180°. When supplementary angles are combined, they always create a straight angle (180 degrees).
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Related Questions
Question 7 10 pt The figure on the left is reflected over the vertical line to form the image on the right. What happens to the angle and side measurements after a reflection? 2 2.2 143° 3.2 1089 639 Edit I
Answers
The reflection on the left (known as the pre-image) has dimensions clearly given, while the shape on the right (known as the image) has no dimensions given but, a careful observation shows that the scale factor is the same, that is, 1 : 1.
This means the sides and angles do not change value(s). The image simply lies in a different location, that is, a different quadrant. The shape, the size and the orientation has not changed which means the dimensions in the image is the same as the pre-image.
How many solutions does this equation have?
–10k + 6 = –2k + 6 + 18k
Answers
Answer: 0
Step-by-step explanation:
-10k + 6 =-2k +6+18k
Combine like terms
-10k + 6 = 16k + 6
Rearrange the terms
=10k - 16k=6-6
Simplify
-10k - 16k = 0
Combine like terms
-26k = 0
Divide both sides
k= 0
3)
A 10-person team competes in a 24-hour cycling race. In total, they cover 443 miles.
Each person cycles the same distance. How far did each person cycle?
Answers
The distance covered by each person in hour cycling race is 44.3 miles.
What is defined as the method of unitary?The unitary method is employed to determine the value of a single unit given a multiple.The unitary method is used in a wide range of applications, from speed, distance, and time problems to determining the material cost.The technique is employed to calculate the cost of a product.It is used to calculate how long it takes a vehicle or even a person to travel a certain distance in an hour.For the given question;
The total distance covered by is 443 miles.
Total number of person cycling in a race = 10.
Distance covered by each person is same.
Each person's distance = 443/ 10
Each person's distance = 44.3 ,miles.
Thus, distance covered by each person in hour cycling race is 44.3 miles.
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Write the point-slope form equation of the line that satisfies the given conditions. Also, rewrite the equation of the line such that it's in slope-intercept form.
f(3) = 18 and f(16) = -18
Answers
Equation of the line is y = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{687}{13}[/tex].
Define slope intercept form.An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+ c, where m denotes slope and c denotes the y-intercept. A line's equation written using a single point on the line and the line's slope is referred to as the point-slope form. The slope is the rise over run, or the ratio of the change in the y values over the change in the x values, and the point form is denoted as (x, y).
Given Data
f(3) = 18
f(16) = -18
Slope:
m = [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{f(16)-f(3)}{16-3}[/tex]
m = [tex]\frac{-18-18}{13}[/tex]
m = [tex]\frac{-36}{13}[/tex]
Equation of the line in slope intercept form:
y - f(x₁) = m(x - x₁)
y - 3 = [tex]\frac{-36}{13}[/tex](x - 18)
y - 3 = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{648}{13}[/tex]
y = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{687}{13}[/tex]
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Main street, Broad Street, and Park Street all intersect to form a right triangle. If broad Street is 75 yards ling and Park is 100 yards long, how long must Main Street be?
Answers
Option (D) is the correct answer.
Given:
The length of broad street is 75 yards.
The length of park street is 100 yards.
The objective is to find the length of the main street.
The length of the main street can be calculated using Pythagorean theorem.
[tex]\begin{gathered} \text{Park}^2=Main^2+Broad^2 \\ \text{Main}^2=Park^2-Broad^2 \\ \text{Main}^2=100^2-75^2 \\ \text{Main}^2=10000-5625 \\ \text{Main}^2=4375 \\ \text{Mai}n=\sqrt[]{4375} \\ \text{Main}^{}=66.144\text{ yards} \end{gathered}[/tex]Thus, the length of the Main street is 66.144 yards.
Hence, option (D) is the correct answer.
Would we use ">" or "<" to replace the in 5.1489 ? 5.2019. Write only the symbol that is true.
Answers
5.1489 is less than 5.2019
Therefore, the symbol between the two decimals would be less than symbol.
That is,
[tex]5.1489<5.2019[/tex]The symbol that would replace ? is <
Upon replacing the symbols, the equation would look like:
5.1489 < 5.2019
Hence, “<“ is the symbol that would take the place of the question mark.
Solve the inequality for X
2x ≥ 2(4x + 7) + 4
Show each step of the solution.
Answers
2x greater than equal to 8x + 14 + 4
2x greater than equal to 8x + 18
2x - 8x greater than equal to 18
-6x greater than equal to 18
x less than equal to -18/6
x less than equal to -3
Mrs. Martinez has $33.00 to spend on name tags. The material for each name tag
costs $0.44. Mrs. Martinez can buy
name tags with $33.00
A 0.013
B 1457
C
75
D 750
Answers
⚠ If you are in a rush, only read the bold.
To find how many items someone can buy with a set amount of money, divide the set amount of money that they have (in this case 33) by the cost of each item (in this case 0.44).
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6.) An artist was carving a sculpture for a
client. It took 12.5 hours to complete the
task. A second artist will take 2.9 times
longer to complete the task. How much
time would the second artist take?
0
Answers
Answer:
12.5 X 2.9
Decimal place is
1dp
answer = 362.5
HELP QUICK PLEASE
all i need is 6,10,&12
In exercises 1-8, the table or graph represents a quadratic function. Write an equation of the function in standard form.
In exercises 9-12, write a quadratic function in standard form whose graph has the given characteristics.
Answers
Answer:
y= - 104/125 (x - 1/2 2) +1
Step-by-step explanation:
hope this helps
pls help
Does this graph
show a linear,
quadratic, or
exponential
function?
Answers
Answer:
exponential
Step-by-step explanation:
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Based on the graph of the function shown, we can logically deduce the following information:
A. The domain can be best described using interval notation. The domain is (-∞, ∞).
B. The range can be best described using the roster method. The range is {y | y = -∞, -3}.
How to identify the domain and range of this graph?The horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.
Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of the continuous function shown above, we can reasonably infer and logically deduce the following information:
The domain is equal to (-∞, ∞).The range is equal to {y | y = -∞, -3}.Read more on range here: brainly.com/question/17003159
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A golf ball is dropped out of an airplane. The downward velocity of the ball at various times is given in the table below. What is the slope of the line that fits this data?
Answers
Let:
[tex]\begin{gathered} (x1,y1)=(1,21.8) \\ (x2,y2)=(2.2,33.56) \\ \text{Slope}=m=\frac{y2-y1}{x2-x1}=\frac{33.56-21.8}{2.2-1}=\frac{11.76}{1.2}=9.8 \end{gathered}[/tex]Solve the equation. log, (-x) + log, (x - 10) = log, 24 Select one: O a. {-6 O b. O O c. {-6, -4) O d. {4,6
Answers
start by applying the log properties on the left side
[tex]\log (-x^2+10x)=\log (24)[/tex]remember that when we talk about the logs they are defined for values greater than 0, determine the range in which will be defined
[tex]\begin{gathered} -x^2+10x>0 \\ -x(x-10)<0 \\ x<0 \\ x-10<0 \\ x<10 \\ x=\mleft\lbrace0,10\mright\rbrace \end{gathered}[/tex]knowing that the values in order for the log to be true must be between 0 and 10, apply base 10 on both sides to cancel the log
[tex]10^{log(-x^2+10x)}=10^{\log (24)}[/tex][tex]\begin{gathered} -x^2+10x=24 \\ -x^2+10x-24=0 \\ \text{using the quadratic equation} \\ a=-1;b=10;c=-24 \\ x_1=4;x_2=6_{} \end{gathered}[/tex]after having the values of the quadratic replace them on the equation
[tex]\begin{gathered} x=4 \\ \log (-4)+\log (4-10)=\log (24) \\ \log (-4)+\log (-6)\ne\log (24) \end{gathered}[/tex][tex]\begin{gathered} x=6 \\ \log (-6)+\log (6-10)=\log (24) \\ \log (-6)+\log (-4)\ne\log (24) \end{gathered}[/tex]after seeing that with both solutions is false the statement, we can conclude that there are no solutions for x.
[tex]x\in\varnothing[/tex]Which inequality is true?А. Зп > 9B. 7 + 8< 11C. 27 -1 < 5D. 2 > 2SUBMIT< PREVIOUS
Answers
For the given options, we will find which inequality is true:
A)
[tex]\begin{gathered} 3\pi>9 \\ 3\pi=3\cdot3.14=9.42>9 \end{gathered}[/tex]so, the inequality is true
B) 7 + 8 < 11
7 + 8 = 15 > 11
So, the inequality is wrong
C) 27 - 1 < 5
27 - 1 = 26 > 5
So, the inequality is Wrong
D) 2 > 2
2 = 2
so, the inequality is wrong
So, the answer will be the true inequality option A) 3п > 9
[tex]undefined[/tex]8. Marcy is a real estate agent. She sold a house for $356,700. Her commission from that sale was $12,484.50. What is her commission rate?
Answers
Marcy is a real estate agent. She sold a house for $356,700. Her commission from that sale was $12,484.50. What is her commission rate?
we have that
$356,700 represent 100%
so
applying proportion
Find out how much percentage represent $12,484.50
100/356,700=x/12,484.50
solve for x
x=(100/356,700)*12,484.50
x=3.5%
therefore
the answer is 3.5%An English test contains 8 short-answer questions.
If Ebony must choose 5 to answer, how many ways can she select the questions?
Answers
In 56 ways, she can select the questions.
Define combination.
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant. The digits 0 through 9 can be put together in one of 10,000 different ways to create a four-digit code.
Given Data
An English test contains 8 short-answer questions.
If Ebony must choose 5 to answer.
h = x
r = 5
Number of ways for selecting the questions are, through combination,
ˣC₅ = [tex]\frac{x!}{r!(x-r)!}[/tex]
ˣ C ₅ = [tex]\frac{x!}{5!(x -r)!}[/tex]
ˣC₅ = [tex]\frac{x(7)(6)5!}{5!(3)}[/tex]
ˣC₅ = 56
In 56 ways, she can select the questions.
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a) CF for 21,72 and 62
Answers
The three numbers given in the question : 21 , 72 and 62 do not have any common factor.
What do you mean by common factor ?The common factors are those that are found in both lists
Example: Factors of 12 and 30
Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
Thus common factor = 1, 2, 3, 6
-------------------------------------------------------------------------------------------------------------
Given numbers : 21,72 and 62
Factors of 21 = 3 and 7
Factors of 72 = 2 and 3
Factors of 62 are 2 and 31
Thus these three numbers do not have any common factor.
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Write an equation in slope-intercept form of the line that contains the points in the table.
Answers
Step 1. We are given a table of (x, y) values and we need to select the option that represents the slope calculation.
First, we remember the formula to calculate the slope:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are two points or sets of values given for the line.
Step 2. In the numerator of the slope formula, we have a subtraction between y-values.
In the table, the y-values are:
Therefore, in the numerator of the calculation, we must have a subtraction between two of these numbers. This discards options A, and B.
Step 3. In options C and D we have this:
[tex]C.\frac{9-(-3)}{1-(-2)}[/tex][tex]D.\frac{-3-11}{-2-4}[/tex]In option C, there is a correct subtraction of 9 and -3, but in option D, the correct subtraction would be -3-(-11). Therefore option D is also discarded and the correct answer is C.
Answer: C
Graph the given equation by evaluating integer values of x from −2 to 2 and plotting the resulting points.y=−2x+3
Answers
Explanation
to evaluate a function replace the x place
so
[tex]y=-2x+3[/tex]Step 1
a) when x=-2
replace
[tex]\begin{gathered} y=-2x+3 \\ y=-2(-2)+3 \\ y=4+3 \\ y=7 \\ \end{gathered}[/tex]so
[tex]P1(-2,7)[/tex]b) when x= -1
[tex]\begin{gathered} y=-2x+3 \\ y=-2(-1)+3 \\ y=2+3 \\ y=5 \\ \end{gathered}[/tex]so
[tex]P2(-1,5)[/tex]c) when x= 0
[tex]\begin{gathered} y=-2x+3 \\ y=-2(0)+3 \\ y=0+3 \\ y=3 \\ \end{gathered}[/tex]so
[tex]P3(0,3)[/tex]d)when x= 1
[tex]\begin{gathered} y=-2x+3 \\ y=-2(1)+3 \\ y=-2+3 \\ y=1 \\ \end{gathered}[/tex]so
[tex]P4(1,1)[/tex]e) when x= 2
[tex]\begin{gathered} y=-2x+3 \\ y=-2(2)+3 \\ y=-4+3 \\ y=-1 \\ \end{gathered}[/tex]so
[tex]P4(2,-1)[/tex]Step 2
now, draw a line that connects the points, so
If the reference angle is 47° label the sides accordingly:
Answers
Answer:
side c = 10.72 = Opposite
side d = 14.66 = Hypotenuse
Side 10 = Adjacent side
Explanation:
The given sides are given from the triangle;
Adjacent = 10
Angle of elevation = 47degrees
Required
Opposite = c
Hypotenuse = d
Using the SOH CAH TOA identity;
Tan theta = opposite/adjacent
Tan 47 = c/10
c = 10tan47
c = 10(1.0724)
c = 10.72
hence side c = 10.72 = Opposite
Similarly;
Cos theta = adjacent/Hypotenuse
Cos 47 = 10/d
d = 10/Cos47
d = 10/0.6819
d = 14.66
Hence Side d = 14.66 = Hypotenuse
Side C: Adjacent
Side D: Hypotenuse
Side length of 10 units: Opposite
put this equation into slope intercept form
3x-2y=4
Answers
Answer:
I got you!
The slope graph and answer are set below!
Step-by-step explanation:
A scientist has discovered a new strain of bacteria. The bacteria grows exponentially at a rate of 68% each hour as shown in the table below. Identify the equation used to calculate the growth, and estimate the population of the bacteria when the time has reached 10 hours
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
A scientist has discovered a new strain of bacteria.
The bacteria grows exponentially at a rate of 68% each hour as shown in the table below.
Identify the equation used to calculate the growth, and estimate the population of the bacteria when the time has reached 10 hours.
Step 2:
The details of the solution are as follows:
Since the bacteria grows exponentially at a rate of 68% each hour, and the initial population is 1. 2 billiion.
This means that:
[tex]f(x)\text{ = 1. 2 \lparen 1 + }\frac{68}{100})\text{ }^x[/tex][tex]\begin{gathered} f(x)\text{ = 1. 2 \lparen1 + 0. 68 \rparen}^x \\ This\text{ gives us:} \\ f(x)\text{ = 1. 2 \lparen1. 68 \rparen}^x \end{gathered}[/tex][tex]\begin{gathered} \text{when x = 10 hours, we have that:} \\ f(x)\text{ = 1. 2 \lparen1.68\rparen}^{10\text{ }}=\text{ 214.9186299 }\approx\text{ 214. 92 billion} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]f(x)\text{ = 1. 2 \lparen1.68 \rparen}^{x\text{ }};\text{ 214. 92 billion \lparen OPTION D \rparen}[/tex]
consider the line y=7/5x+4
Answers
The genral equation of line can be written as y=mx+c, where m is the slope of the line.
Comparing y=7/5x+4 with y= mx+c, we get slope m=7/5.
The slope of two parallel lines are equal. Hence, the slope of a parallel line to y=7/5x+4 is 7/5.
Now, the point slope form of a line which passes through a point (x1, y1) and habing slope m is,
[tex]\frac{y-y_1}{x-x_1}=m[/tex]Given (x1,y1)=(-7,-5). Therefore,
[tex]\begin{gathered} \frac{y-(-5)}{x-(-7)}=\frac{7}{5} \\ \frac{y+5}{x+7}=\frac{7}{5} \\ 5y+25=7x+49 \\ 5y=7x+49-25 \\ 5y=7x+24 \\ y=\frac{7}{5}x+\frac{24}{5} \end{gathered}[/tex]Therefore, the equation of line parallel to y=7/5x+4 and passing through point(-7,-5) is y=(7/5)x+(24/5).
(2)The slope of a line perpendicular to y=mx+c is -1/m.
So, slope of a line perpendicular to y=7/5x+4 is
[tex]Slope,m_1=\frac{-1}{m}=\frac{-1}{\frac{7}{5}}=\frac{-5}{7}[/tex]If (x1,y1)=(-7-5), then using point slope form,
[tex]\begin{gathered} \frac{y-y_1}{x-x_2}=m_1 \\ \frac{y-(-5)}{x-(-7)}=\frac{-5}{7} \\ \frac{y+5}{x+7}=\frac{-5}{7} \\ 7y+35=-5x-35 \\ 7y=-5x-70 \\ y=\frac{-5}{7}x-10 \end{gathered}[/tex]Therefore, the equation of line perpendicular to y=7/5x+4 and passing through point(-7,-5) is y=-(5/7)x-10.
What is the total cost of a $717 tablet computer that is on sale at 12% off of the local sales tax rate is 7%? The cost of the tablet is ? (Round to two decimal places as needed)
Answers
Given: The cost of a table as
[tex]\begin{gathered} Cost=717 \\ Discount=12\% \\ Sales-tax=7\% \end{gathered}[/tex]To Determine: The cost of the tablet
Solution
Let us first determine the discount
[tex]\begin{gathered} Discount=12\%\times717 \\ =0.12\times717 \\ =86.04 \end{gathered}[/tex]Then calculate the discounted price
[tex]Discount-price=717-86.04=630.96[/tex]We would also calculate the sales tax
[tex]\begin{gathered} sales-tax=7\%\times discount-price \\ =0.07\times630.96 \\ =37.86 \end{gathered}[/tex]The total price of the tablet would be
[tex]\begin{gathered} Total-cost=discount-price+sales-tax \\ =630.96+37.86 \\ =668.82 \end{gathered}[/tex]Hence, the cost of the tablet is $668.82
what is circle in mathematics
Answers
Sintaye, this is the answer to your question:
Circle is a shape made by drawing a curve that is always the same distance from a center.
Carla had an eight-sided die numbered 1 to 8. Find each probability for the number she
rolled.
17. P(3)
19. P(9)
18. P(odd number)
20. P(number greater than 2)
plo and 3 orange popsicle sticks in a container. Without looking
Answers
The most appropriate choice for probability will be given by -
P(3) = [tex]\frac{1}{8}[/tex]
P(9) = 0
P(odd number) = [tex]\frac{1}{2}[/tex]
P(number greater than 2) = [tex]\frac{3}{4}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
For P(3)
Number of favourable outcomes = 1
Total number of outcomes = 8
P(3) = [tex]\frac{1}{8}[/tex]
For P(9)
Number of favourable outcomes = 0
P(9) = 0
For P(odd number)
Favourable outcomes = {1, 3, 5, 7}
Number of favourable outcomes = 4
P(odd number) = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
For P(Number greater than 2)
Favourable outcomes = {3, 4, 5, 6, 7, 8}
Number of favourable outcomes = 6
P(number greater than 2) = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
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Select the correct answer.
The tables show the subscription costs for two magazines. What is the ratio of the cost of Magazine A to the cost of Magazine B?
Magazine A
Duration of Subscription
12 months 36
24 months 72
36 months 108
Magazine B
Duration of Subscription Subscription Cost
(dollars)
12 months 32
24 months 64
36 months 96
A.9:4
B.9:7
C.9:8
D.9:5
Answers
We can conclude that the ratio of the cost of magazine A to the cost of magazine B is (C) 9:8.
What is the ratio?A ratio depicts the quantity of one thing in relation to another. Ordinarily, ratios are expressed in the format a:b. If you're making orange squash, the ratio of orange to water will be one part orange to four parts water (1:4). It matters in what order a ratio is stated.So, the ratio of the cost of magazine A: the cost of magazine B:
Magazine A
3672108Magazine B
326496Then, magazine A:Magazine B -
36:32 = 36/32 = 9/8 = 9:872:64 = 72/64 = 9/8 = 9:8108:96 = 108/96 = 9/8 = 9:8Therefore, we can conclude that the ratio of the cost of magazine A to the cost of magazine B is (C) 9:8.
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Write and solve an equation to find the unknown side length x (in inches).
Perimeter =24.2 in.
An equation is
=24.2.
The unknown side length is
inches.
Answers
The value of side length x is equal 6.05 in
Perimeter of a SquareThe perimeter of a square is given as the sum of the total sides in the square or 4 multiplied by the side length of the square since they all have equal sides.
Mathematically, this can be written as
[tex]P = 4 *L\\P = 4l\\[/tex]
L = side lengthIn this given question, the side length is equal to x and the perimeter of the square is given as 24.2in.
Let's substitute the values
[tex]P = 4L\\24.2 = 4L\\but l = x\\24.2 = 4x\\x = 6.05in[/tex]
The side length of the square is equal to 6.05in
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complete question
Write and solve an equation to find the unknown side length x (in inches).
Perimeter =24.2 in. assuming the figure is a square
A café has three different sizes of plate. The ratio of small to medium is 2:5 and the ratio of medium to large is 3:4What is the ratio of small plates, to medium plates to large plates?
Answers
6: 15 : 20
Explanation:Ratio of small to medium = 2 : 5
Ratio of medium to large = 3 : 4
We need to make the medium in both ratios equivalent since medium is common to both:
[tex]\begin{gathered} \frac{small}{\text{medium}}\text{ = }\frac{2}{5} \\ \frac{medium}{\text{large}}=\frac{3}{4} \\ \text{for medium to be equivalent, we multiply ratio by 3} \\ we\text{ multiply the second ratio by 5} \\ \text{LCM = 3}\times5\text{ = 15} \end{gathered}[/tex]We multiply the numerator by same amount we multiply the denuominator in both ratios:
[tex]\begin{gathered} \frac{small}{\text{medium}}\text{ = }\frac{2}{5}\times\frac{3}{3}\text{ } \\ \frac{small}{\text{medium}}=\text{ }\frac{6}{15} \\ \\ \frac{medium}{\text{large}}=\frac{3}{4}\times\frac{5}{5} \\ \frac{medium}{\text{large}}=\text{ }\frac{15}{20} \end{gathered}[/tex]The ratio of small to medium to large:
[tex]\begin{gathered} \text{The medium is the same so we can bring all thr}ee\text{ together:} \\ \text{small: medium: large} \\ 6\colon\text{ 15 : 20} \end{gathered}[/tex]