f: A → B and g: B → A are functions such that f∘g=idB. It is true that g is injective and f is surjective.
Let y1, y2 ∈ B such that g(y1) = g(y2).
We need to show that y1 = y2.
To do this, we use the following facts;
f(g(y1)) = y1 (since f∘g=idB).
f(g(y2)) = y2 (since f∘g=idB).
Now, f(g(y1)) = f(g(y2)).
Since f is a function, g(y1) = g(y2) ⟹ f(g(y1)) = f(g(y2)).
So, we have y1 = y2 as required. Therefore, g is injective.
Let b ∈ B be arbitrary. We need to show that there exists an element a ∈ A such that f(a) = b.
Since f∘g=idB, we know that for any element y ∈ B,f(g(y)) = y.
Now, we can use b ∈ B to obtain the element g(b) ∈ A.
Then, f(g(b)) = b as required. Therefore, f is surjective.
So, the functions f and g satisfy the following properties:
if f: A → B and g: B → A such that f∘g=idB, then g is injective and f is surjective.
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Let a < b. If ƒ is continuous on [a, b], and ƒ(a) = f(b), then there there exists c € (a,b) such that f'(c) = 0. d) If f is differentiable on (0, 1), then f is uniformly continuous on (0,1).
Yes, if ƒ is differentiable on (0, 1), then ƒ is uniformly continuous on (0, 1).
In mathematics, the concept of differentiability plays a crucial role in understanding the behavior of functions. If a function ƒ is differentiable on the interval (0, 1), it means that the derivative ƒ'(x) exists for every point x in that interval.
The answer states that if a function is differentiable on (0, 1), then it is uniformly continuous on the same interval.
To understand this result, we need to consider the properties of differentiability and uniform continuity.
Differentiability implies that the function has a well-defined tangent line at every point within the interval. This implies that the function cannot exhibit abrupt changes or discontinuities, as it must be smooth and continuous.
Uniform continuity, on the other hand, deals with the behavior of a function as the input values get arbitrarily close to each other. It ensures that the function does not exhibit extreme fluctuations or rapid oscillations.
If a function is differentiable on (0, 1), then it satisfies the conditions required for uniform continuity. This is because the derivative of the function acts as a measure of its rate of change.
If the derivative is bounded (i.e., it does not become infinitely large or small), then the function can be guaranteed to be uniformly continuous.
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Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found. Type of Crust Number Sold Thin crust 312 Thick crust 245 Stuffed crust 179 Pan style 304
Question:
Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.
Type of Crust Number Sold
Thin crust 312
Thick crust 245
Stuffed crust 179
Pan style 304
Based on this information, of the next 4500 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Answer:
1060 thick crusts
Step-by-step explanation:
Given
The above table
Required
Expected number of thick crust for the next 4500
For last week data, calculate the proportion of thick crust sold
[tex]\hat p = \frac{Thick\ crust}{Total}[/tex]
[tex]\hat p = \frac{245}{312+245+179+304}[/tex]
[tex]\hat p = \frac{245}{1040}[/tex]
[tex]\hat p = 0.235577[/tex]
For the next 4500;
[tex]n = 4500[/tex]
The expected number of thick crust is (E(x)):
[tex]E(x) = \hat p * n[/tex]
[tex]E(x) = 0.235577 * 4500[/tex]
[tex]E(x) = 1060.0965[/tex]
[tex]E(x) \approx 1060[/tex]
Is it possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space? Ex- plain.
Let a; be a nonzero column vector of an m x n matrix A. Is it possible for a j, to be in N(AT)? Explain.
It is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space. Let's explain why.
Let A be an m × n matrix, and let x be a nonzero vector in the null space of A, so Ax = 0. We can also say that x is in the null space of A transpose. So x is an element of N(AT).Let’s prove the contradiction that arises from the initial claim by assuming that 3,1,2 is a row vector in the row space of A and 2,1,1 is a column vector in N(AT).We have that A[3 1 2]T = 0 and 2,1,1 is in the null space of A transpose. We also know that if a vector v is in the row space of A, then there exists a vector y such that v = A*y, where y is a column vector. So in this case, we can say that 3,1,2 is in the row space of A if there is a column vector y such that A * y = [3 1 2]T. But if that's the case, then we have the following equation: A* y = [3 1 2]. This can be written as: TA* = [3 1 2]If we then take the transpose of both sides, we have: A* y = [3 1 2]T and TA = [3 1 2]. However, this implies that TA* = TA, which can only be true if A is a symmetric matrix. But A is an m × n matrix, where m and n are not equal, so A cannot be a symmetric matrix. Therefore, it is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space.
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Please help me, i'm so confused
9514 1404 393
Answer:
(d) 512√3
Step-by-step explanation:
The area (A) of a regular hexagon can be computed from its side length (s) using the formula ...
A = (3√3)/2·s²
Here, the side length is given as ...
s = 32√3/3 = 32/√3
Then the area is ...
[tex]A=\dfrac{3\sqrt{3}}{2}\cdot\left(\dfrac{32}{\sqrt{3}}\right)^2=\dfrac{3\sqrt{3}\cdot1024}{2\cdot3}=\boxed{512\sqrt{3}}[/tex]
The area of the hexagon is 512√3 square units.
Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The null and alternative hypothesis would be: 0.7 Hop 0.7 Hop - 0.7 H:P < 0.7 HP >0.7 HP 0.7 HOP The test is: right tailed left-tailed two-tailed Based on a sample of 500 people, 62% wned cats The p-value is:
Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.
The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:
H0: p = 0.7 (null hypothesis
)H1: p ≠ 0.7 (alternative hypothesis)
The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7
Based on a sample of 500 people, 62% owned cats.
This means that the sample proportion, p = 0.62.
To calculate the p-value, we will use the z-test statistic.
The formula for calculating the z-test statistic is given as:
z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.
Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52
The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.
The area in both tails beyond the z-score of 2.52 is 0.012.
Therefore, the p-value is:
p-value = 2 × 0.012 = 0.024
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Simplify (8y6)
what’s the answer?
If 23 cubic meters of water are poured into a conical vessel, it reaches a depth of 12 cm. how much water must be added so that the length reaches 18 cm.?
Let V be the volume of the conical vessel and r and h be the radius and height of the vessel respectively. Given that: V = (1/3)πr²hLet V' be the volume of the water that is added to the vessel. The volume of the water in the vessel with a depth of 12 cm is given by: V₁ = (1/3)πr₁²h₁where h₁ = 12 cm. We know that 23 cubic meters of water are poured into the vessel, which is equivalent to 23,000 liters or 23,000,000 cubic centimeters.
Thus:23,000,000 = (1/3)πr₁²(12)Simplifying and solving for r₁, we get: r₁ = 210.05 cm Using similar triangles, we know that :r/h = r₁/h₁ where r is the radius of the water surface when the depth is 18 cm. Thus: r/h = 210.05/12Therefore:r = (210.05/12)·18 = 3,152.5/6 ≈ 525.4 cm The new volume of the water with a depth of 18 cm is given by: V₂ = (1/3)πr²h₂where h₂ = 18 cm.
Therefore: V₂ = (1/3)π(525.4)²(18) ≈ 21,154,116.9 cubic centimeters The additional volume of water needed is therefore: V' = V₂ - V₁ = 21,154,116.9 - 23,000,000 ≈ -1,845,883.1 cubic centimeters.
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Can pls someone help with my homework pls I need help
Answer:
[tex] \sin(m < q) = \frac{7}{9} \\ \sin(m < q) =(0.77777777778) \\ m < q = { \sin 0.77777777778}^{ - 1} \\ m < q = (51.05755873102)[/tex]
Choose the equation that best describes the situation below.
Lee is 32 years younger than his mother and his mother is 67 years old. How old is Lee?
a = Lee's age
Answer:
67-32=a
if his mom is 67 and he is 32 years younger 67 minus 32 would equal a which is his age
Malik and Nora are playing a video game.
Malik starts with m points and Nora starts n points.
Then Malik gets 150 more points, while Nora loses 50 points.
Finally, Nora gets a bonus and her score is doubled.
Nora now has 50 more points than Malik.
Enter an equation that represents the relationship between m and n
given the information above.
Answer:
Equation below
Step-by-step explanation:
An equation that represents the relationship between m and n is 2(n - 150) - (m + 150) = 50 .
The expression that represents Malik's score after he gets 150 points = m + 150
The expression that represents Nora's score after she loses 50 points = n - 150
Nora's score after her score is doubled = 2(n - 150)
The difference between Nora and Malik's score is 50. This can be represented as: 2(n - 150) - (m + 150) = 50
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Use elimination to solve for x and y:
9x - 2y = 46
x + 2y = 14
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
9x - 2y = 46 → (1)
x + 2y = 14 → (2)
Adding the 2 equations term by term will eliminate the y- term
10x + 0 = 60
10x = 60 ( divide both sides by 10 )
x = 6
Substitute x = 6 into either of the 2 equations and solve for y
Substituting into (2)
6 + 2y = 14 ( subtract 6 from both sides )
2y = 8 ( divide both sides by 2 )
y = 4
solution is (6, 4 )
If You Have NO EXPLANATION Don't ANSWER
Answer:
C
Step-by-step explanation:
y=5x reads "y equals (5 times x)", which we can rephrase to "the value of y is 5 times the value of x"
y=x+5 reads "y equals (x plus 5)", which we can rephrase to "the value of y is 5 more than the value of x".
Ergo, answer C is what we're looking for.
Answer: C
Step-by-step explanation:
in y=5x, we can see a 5 placed in front of x. If there is no addition, subtraction, or division sign between a number and a variable, it always means it's multiplication.
We know now that this is 5 times x.
In y=x+5, we see that 5 is being added to x. Therefore, y is 5 more than x.
So there you have it.
Which line is the best model for the data in the scatter plot?
PLEASE GIVE THE CORRECT ANSWER AND FAST
Answer:
Upper right corner.
Step-by-step explanation:
I took the test and that one was right. Hope this helps!
Prove the following using a proof by contradiction:
The average of four real numbers is greater than or equal to at least one of the numbers.
Our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.
To prove the statement using a proof by contradiction, we assume the opposite, namely, that the average of four real numbers is less than all of the numbers. Let's denote the four numbers as a, b, c, and d. We assume that the average of these numbers, which we'll denote as avg, is less than a, b, c, and d.
Now, let's consider the sum of these four numbers: a + b + c + d. The average of these numbers, avg, is calculated by dividing the sum by 4. Therefore, we have avg = (a + b + c + d)/4.
If avg is less than a, b, c, and d, then (a + b + c + d)/4 < a, (a + b + c + d)/4 < b, (a + b + c + d)/4 < c, and (a + b + c + d)/4 < d.
Now, let's consider the sum of these inequalities: (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 < a + b + c + d.
Simplifying the left-hand side, we have (a + b + c + d) + (a + b + c + d) + (a + b + c + d) + (a + b + c + d) < 4(a + b + c + d).
This simplifies to 4(a + b + c + d) < 4(a + b + c + d), which is a contradiction. The left-hand side is greater than the right-hand side, which contradicts our initial assumption.
Therefore, our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.
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A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3 Find P81, which separates the bottom 81% from the top 19%.
Value of x corresponding to P81 is 59.06.
A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3.
The task is to find P81, which separates the bottom 81% from the top 19%.
For any normally distributed variable z with mean u and standard deviation o, the cumulative distribution function is defined as the probability of a standard normal variable being less than or equal to z.
A standard normal distribution has a mean of 0 and a standard deviation of 1.
That is, the variable z can be calculated as: z = (x - u) / o
The value P(z < z0) can be read off a standard normal table for any value z0.
As the normal distribution is symmetric, we can use the fact that P(z < -z0) = 1 - P(z < z0).
We now calculate z as follows: z0 = (P81 + 1) / 2 = 0.9051
From a standard normal table, we can see that P(z < 0.9051) = 0.8186.
Therefore, P(z < -0.9051) = 1 - P(z < 0.9051) = 0.1814.
Now we calculate the corresponding value of x:
z = (x - u) / o-0.9051 = (x - 67.3) / 9.3x = 59.06
Therefore, P81 corresponds to the value x = 59.06.
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CAN SOMEONE HELP ME!!!!
Thion Drones is a newly established manufacturer of drones for recreational use. The firm produced 180 drones last month and sold these for an average price of $230. Thion Drones had average variable costs of $190 per drone. Its fixed costs per month are $4,500.
a. Calculate the average fixed cost (AFC) for Thion Drones.
b. Calculate the monthly profit or loss made by Thion Drones.
The average fixed cost of each case will be $25
What is the average fixed cost ?Fixed cost is the cost that does not change with the number of lawyers hired or the number of cases. Fixed cost remains fixed regardless of the number of lawyers or the number of cases. Examples of fixed cost include rent, electricity.Average fixed cost is the total fixed cost per case. Average fixed cost can be determined by dividing the fixed cost by the number of cases.Average fixed cost = fixed cost / number of cases.
$4500/ 180= $25
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We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 166 had kids. Based on this, construct a 90% confidence interval for the proportion, p. of adult residents who are parents in this county. Give your answers as decimals, to three places.
_________________ < p < _________________
Based on this, a 90% confidence interval for the proportion, p. of adult residents who are parents in this county is 0.787 < p < 0.873.
The point estimate for the proportion is calculated by dividing the number of adults with kids by the total sample size. In this case, the point estimate is 166/200 = 0.83.
To construct the confidence interval, we can use the formula:
[tex]p \pm z \times \sqrt{\frac{p \times (1 - p )}{n}}[/tex]
Where:
p is the point estimate
z is the z-score corresponding to the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)
n is the sample size
Substituting the values into the formula, we get:
[tex]= 0.83 \pm 1.645 \times \sqrt{\frac{0.83 \times (1-0.83)}{200}}[/tex]
Calculating the values, we can obtain the 90% confidence interval for the proportion of adult residents who are parents.
To construct a 90% confidence interval for the proportion of adult residents who are parents in the county, we can use the sample proportion and the standard error formula. Out of the 200 adult residents sampled, 166 had kids.
we calculate the sample proportion, p-hat:
p-hat = 166 / 200
= 0.83
Next, we calculate the standard error using the formula:
SE = √((p-hat × (1 - p-hat)) / n)
SE = √((0.83 × (1 - 0.83)) / 200) ≈ 0.025
To construct the confidence interval, we use the formula:
p-hat ± (z × SE)
where, z is the z-score corresponding to the desired confidence level.
For a 90% confidence interval, the z-score is approximately 1.645.
Substituting the values into the formula, we get:
= 0.83 ± (1.645 × 0.025)
Calculating the upper and lower bounds:
Lower bound = 0.83 - (1.645 × 0.025) ≈ 0.787
Upper bound = 0.83 + (1.645 × 0.025) ≈ 0.873
Therefore, the 90% confidence interval for the proportion of adult residents who are parents in the county is approximately 0.787 < p < 0.873.
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Finding slope..
Photo included^
Answer:
slope=2/3
y intercept=4
Step-by-step explanation:
8/6 + (3/8 + x)(2) =
Answer:
2x+25/12
Step-by-step explanation:
Hope this helps and have a great day!!!!!
Eleven increased by three times a number equals 68) Write an equation for this situation and then find the
number
Answer:
11+3x=68
x=19
Step-by-step explanation:
11+3x=68 is your equation.
subtract 11 from both side to get 3x alone
3x=68-11
3x=57
divide 3 from both sides to get x alone
x=57/3
x=19
19 is your number.
How many edges does the complete bipartite graph K_(4, 9) have? Your answer
The number of edges in the complete bipartite graph is 36
How to determine the number of edges in the complete bipartite graphFrom the question, we have the following parameters that can be used in our computation:
K = (4, 9)
The above means that
The vertices in the sets of the bipartite graph are
Set 1 = 4
Set 2 = 9
The number of edges in the complete bipartite graph is then calculated as
Vertices = Set 1 * Set 2
So, we have
Vertices = 4 * 9
Evaluate
Vertices = 36
Hence, there are 36 edges in the bipartite graph
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A wardrobe has 3 pants , 5 shirts , and 7 ties .
The number of total possible outfits is 15 .
True
False
A wardrobe with 3 pants, 5 shirts, and 7 ties, has a possible outcome of 105 outfits and not 15. So the answer is False
False. The number of total possible outfits is not 15. To calculate the number of possible outfits, we need to multiply the number of choices for each item together. In this case, we have 3 choices for pants, 5 choices for shirts, and 7 choices for ties. Therefore, the total number of possible outfits would be 3 x 5 x 7 = 105.
The statement incorrectly states that there are only 15 possible outfits. It's important to consider that when selecting multiple items, the total number of combinations is found by multiplying the number of choices for each item together. In this scenario, with 3 pants, 5 shirts, and 7 ties, there are 105 possible outfits, not 15.
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Elena prepared 8 kilograms of dough after working 2 hours. How much dough did Elena prepare if she worked for 9 hours? Assume the relationship is directly proportional.
Answer:
36 kilograms
Step-by-step explanation:
Since she made 8 kilograms of dough over the span of 2 hours, you divide 8 by 2 and get 4 then you have to multiply 9 hours by 4 kilograms of dough to get 36 kilograms of dough.
[tex]12 \frac{3}{6} + 14\frac{4}{6} [/tex]
i don't know what's the answer i been trying it this but i can't
Answer:
27 1/6
Step-by-step explanation:
14 + 12=26
4+3=7
26 7/6= 27 1/6
Plz help no links I will give brainiest to whoever helps
Answer:
110.92
Step-by-step explanation:
Assuming that the parameters (P), (h), and (B) all represent dimensions of the given prism, then based on the given information, the following can be concluded:
P = 6.6
h = 4.5
B = 2.2
The surface area is the two-dimensional area around a three-dimensional surface. In other words, if one was going to wrap the figure, the surface area is the amount of paper one would need. One can find the surface area by finding the area of each individual side and then adding all the results together. To find the area of a 2-dimensional figure by multiplying the length by the width.
(4.5) * (6.8) = 30.6
(4.5) * (6.8) = 30.6
(2.2) * (6.8) = 14.96
(2.2) * (6.8) = 14.96
(4.5) * (2.2) = 9.9
(4.5) * (2.2) = 9.9
Now add up all of the values,
30.6 + 30.6 + 14.96 + 14.96 + 9.9 + 9.9
= 110.92
Denira needs to run 9 4/10 miles this week to meet her goal for her training plan. So far this week she has run 3 1/2 miles on Monday and 2 1/2 miles on Tuesday. How many more miles does she need to run this week in order to meet her goal
Answer:
3 2/5
Step-by-step explanation:
Add the distance she already ran, and subtract the sum from the total she needs to run.
Add two distances she ran:
3 1/2 + 2 1/2 = 3 + 2 + 1/2 + 1/2 = 5 + 1 = 6
Subtract sum from total:
9 4/10 - 6 = 3 4/10 = 3 2/5
Answer:
She needs to run 3 4/10 more miles
Step-by-step explanation:
If you add the amount she ran on Monday and the amount she ran on Tuesday you get 6 miles then subtract the 6 miles minus 9 4/10 you will get 3 4/10.
at a meeting ,everyone shakes hands exactly once with every other person . if there are 55 handshakes . then what Is the number of people attending
What is the range and domain of y = (x - 4)(x - 6)? I have already sketched out the graph and parabola.
Answer: The domain of the function y = (x - 4)(x - 6) is all real numbers, since there are no restrictions on the values that x can take. The range of the function is also all real numbers.
To see why this is the case, we can rewrite the function in standard form by expanding the product: y = (x - 4)(x - 6) = x^2 - 10x + 24. This is a quadratic function with a positive leading coefficient, so its graph is a parabola that opens upwards. The vertex of the parabola is at x = -b/2a = 10/2 = 5, and y = (5 - 4)(5 - 6) = -1. Since the parabola opens upwards, it extends infinitely upwards from its minimum value at the vertex. Therefore, the range of the function is all real numbers greater than or equal to -1.
So, the domain of y = (x - 4)(x - 6) is all real numbers and its range is all real numbers greater than or equal to -1.
Step-by-step explanation:
Answer:
[tex]y = {x}^{2} - 10x + 24[/tex]
Domain: all real numbers
Range: all real numbers > -1
Bon Air Elementary School has 300 students. The principal of the school thinks that the average IQ of students at Bon Air is at least 110. To prove her point, she administers an IQ test to 20 randomly selected students.
Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 0.01.
The principal should reject her original hypothesis, as the lower bound of the interval is less than 110.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 20 - 1 = 19 df, is t = 2.8609.
The parameters for this problem are given as follows:
[tex]\overline{x} = 108, s = 10, n = 20[/tex]
Then the lower bound of the interval is given as follows:
[tex]108 - 2.8609 \times \frac{10}{\sqrt{20}} = 101.6[/tex]
The upper bound of the interval is given as follows:
[tex]108 + 2.8609 \times \frac{10}{\sqrt{20}} = 114.4[/tex]
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Please help me with the question please ASAP
Answer:
The ratio of perimeter of ABCD to perimeter of WXYZ = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
First, we have to determine the multiplicative factor of the dimensions for both figures.
Considering sides AB and WX,
multiplicative factor = [tex]\frac{12}{8}[/tex]
= 1.5
So that:
XY = 6 x 1.5 = 9
YZ = 7 x 1.5 = 10.5
ZW = 7 x 1.5 = 10.5
Perimeter of ABCD = 6 + 7 + 7 + 8
= 28
Perimeter of WXYZ = 9 + 10.5 + 10.5 + 12
= 42
The ratio of the perimeters of the two quadrilaterals can be determined as;
ratio = [tex]\frac{perimeter of ABCD}{Perirmeter of WXYZ}[/tex]
= [tex]\frac{28}{42}[/tex]
= [tex]\frac{2}{3}[/tex]
The ratio of the perimeter of ABCD to perimeter of WXYZ is [tex]\frac{2}{3}[/tex].