Quadrilateral ABCD was dilated by a scale factor of 0.7 with the origin as the center of dilation. If (x, y) represents the location of any point on quadrilateral ABCD, which ordered pair represents the coordinates of the corresponding point on A'B'C'D'?

Answer: x = 12

Step-by-step explanation:

Adam scored x points = (x)

Imran scored 3 points fewer than Adam = (x-3)

Shakeel scored twice as many points as Imran = 2(x-3)

Together they scored 39 points.  = 39

**Check your work by inputting substituting 12 for x:

he solution set for this system of linear equations is {(10/7, -5/7, 1), (4/7, -5/7, 2/5)}.

To solve this system of linear equations, we can use the method of elimination. We want to eliminate one variable at a time until we are left with a system of two equations in two variables. Here's how we can proceed:

1. Multiply the second equation by -3 to get -6y - 3z = 0.
2. Add the first equation to the new equation to get -7y = 5.
3. Solve for y to get y = -5/7.
4. Substitute y = -5/7 into the second equation to get x - (10/7)z = 0.
5. Substitute y = -5/7 and x = (10/7)z into the third equation to get (10/7)z^2 - (5/7)z = 2.
6. Simplify and solve for z to get z = 1 or z = 2/5.
7. Substitute z = 1 into x - (10/7)z = 0 to get x = 10/7.
8. Substitute z = 2/5 into x - (10/7)z = 0 to get x = 4/7.

Therefore, the solution set of the system of linear equations is {(10/7, -5/7, 1), (4/7, -5/7, 2/5)}.

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The limiting probabilities for the Markov chain are pi = 1/m for all i, where m is the number of urns, and ni is the number of balls in urn i.


1. Observe that the system is symmetric and invariant under permutations of urns.

2. Since the state space is finite, irreducible, and aperiodic, the limiting probabilities exist and are unique.

3. Guess that the limiting probabilities are uniform, i.e., pi = 1/m for all i.

4. Apply the detailed balance condition for time-reversibility: Pij * πi = Pji * πj for all i, j.

5. Since a ball is selected uniformly at random, Pij = (ni / M) * (1 / (M - 1)), and Pji = (nj / M) * (1 / (M - 1)).

6. Plug in the guess πi = πj = 1/m into the detailed balance condition: (ni / M) * (1 / (M - 1)) * (1/m) = (nj / M) * (1 / (M - 1)) * (1/m).

7. Simplify and observe that both sides are equal, which verifies the guess and shows time-reversibility.

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If S, T be sets, then we have proved that  S = T if and only if S \ T = T \ S.

Assume S = T. Then, S \ T = T \ S = {}.

This is because if S = T, then there are no elements in S that are not in T, and vice versa.

Therefore, the difference between the sets is the empty set.

Hence, S \ T = T \ S = {} and we have shown that S = T implies S \ T = T \ S.

Assume S \ T = T \ S.

We will show that S is a subset of T and T is a subset of S, which will imply that S = T.

Let x be an arbitrary element of S.

If x is also in T, then x is not in S \ T = T \ S, which contradicts the assumption S \ T = T \ S.

Therefore, x is not in T.

This means that x is in S \ T, which implies that x is also in T \ S (by the assumption S \ T = T \ S).

But this means that x is in T, which is a contradiction.

Therefore, there are no elements in S that are not in T, so S is a subset of T.

Similarly, let y be an arbitrary element of T.

If y is also in S, then y is not in T \ S = S \ T, which contradicts the assumption S \ T = T \ S.

Therefore, y is not in S.

This means that y is in T \ S, which implies that y is also in S \ T (by the assumption S \ T = T \ S).

But this means that y is in S, which is a contradiction.

Therefore, there are no elements in T that are not in S, so T is a subset of S.

Since S is a subset of T and T is a subset of S, S = T.

Therefore, we have shown that S \ T = T \ S implies S = T.

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The given question is incomplete, the complete question is:

let S, T be sets. prove that S = T if and only if S \ T = T \ S.

The result of multiplying two functions together is the multiplication of the coefficients and the addition of the exponents. In this case, (fg)(x) = (5/3)x⁴
(fg)(x) =(5/3)x⁴.

Function is a process or a set of rules that take inputs, perform certain operations on them, and produce outputs. It is a fundamental component of computer programming that allows for the repetition of tasks without having to rewrite code. Functions are also useful for organizing code, allowing for easier debugging, and providing more flexibility when making changes.

(5x)(x¹/³) =

5x⁴/3 =

(5/3)x⁴

Therefore, (fg)(x) = (5/3)x⁴.

This is happening because when multiplying two functions together, the exponents are added together. In this case, the exponent for x in f(x) is 1, and the exponent for x in g(x) is 1/3. When these are added together, the final exponent for x becomes 4/3. Since the exponent is a fraction, it is multiplied by the coefficient, 5, to get the final coefficient of 5/3.

To conclude, the result of multiplying two functions together is the multiplication of the coefficients and the addition of the exponents. In this case, (fg)(x) = (5/3)x⁴.

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Answer: The value of q is 7.5.

Answer:

7.5

Step-by-step explanation:

Brainliest?

The transformation that takes the graph of f(x) = 4^x to the graph of g(x) = 4^x − 3 is a vertical translation downwards by 3 units.

To see why, note that the function g(x) is obtained by subtracting 3 from the output (or y-value) of the function f(x) for every value of x. This means that the graph of g(x) is obtained by shifting the graph of f(x) downwards by 3 units.

Therefore, the correct answer is:

d) The graph is translated down 3 units.

Answer:

3N

Step-by-step explanation:

The graph states that the forces are acting in opposite directions, so subtract the value of the smaller force from the larger to find net force.

Hope this helps!

The area under the standard normal curve between z=0.5 and z=1.4 is given by P(0.5 < z < 1.4) = 0.2277 approximately. The answer is (iv).

To find the area under the standard normal curve between z = 0.5 and z = 1.4, we need to use a calculator to find the probabilities associated with different z-scores.

We can begin by finding the value of the cumulative distribution function (CDF) for z = 0.5 and z = 1.4. The CDF gives us the probability of getting a z-score less than or equal to a given value. We can then subtract the CDF value for z = 0.5 from the CDF value for z = 1.4 to get the probability of getting a z-score between 0.5 and 1.4.

Using a calculator, we can find that the CDF value for z = 0.5 is 0.6915 and the CDF value for z = 1.4 is 0.9192.

Therefore, the probability of getting a z-score between 0.5 and 1.4 is:

P(0.5 < z < 1.4) = 0.9192 - 0.6915 = 0.2277

Therefore, the correct answer is (iv) 0.2277.

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We can see here that the number of customers recorded at lunch is: 220 customers.

A ratio is a comparison of two values that is typically stated as a fraction. The relationship between two things in terms of their size or quantity can be described using ratios.

Let:

B = Breakfast

L = Lunch

D = Dinner

Note: D = L - 10 - (1)

The ratio of breakfast to lunch: B:L = 7:4.

B/L = 7/4

B = (7/4) L

The ratio of breakfast to dinner: B:D = 11:6.

B/D = 11/6

B = (11/6) D

(7/4) L = (11/6) D

Multiplying both sides by 12, we get =

21L = 22D

Substituting this into the previous equation

21L = 22(L - 10).

Simplifying, we have:

L = 220/1 = 220

Therefore, there were 220 customers recorded at lunch.

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Answer:

The answer to your problem is, 210

Step-by-step explanation:

The customers at

breakfast : lunch = 11:6

lunch : breakfast = 6:11

= 42:77

and breakfast dinner = 7:4

= 77:44

∴ Lunch : Breakfast : Dinner = 42:77:44

Let the number of customers at lunch = 42x

Number of customers at dinner = 44x

By the question;

The number of customers at lunch = Number of customers at dinner - 10

z = 42n = 44x - 10

z = 44x - 42n = 10

z = 2x = 10

z = x = 5

∴ Number of customers at lunch

= 42x

= 42 × 5

= 210

Thus the answer to your problem is, 210

Answer:

9 tickers were discount tickets

Step-by-step explanation:

90 was the total amount sold, and 10% of these were discount, so you need to find 10% of 90 by multiplying 90 by 0.10.

90*(0.10)=9

9 discount tickets

Let x be the number of discount tickets sold.

According to the problem, 10% of the tickets sold were discount tickets.

So, we can set up the equation:

10% of total tickets = number of discount tickets sold

0.1(90) = x

9 = x

Therefore, the amusement park sold 9 discount tickets.

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The price per cubic inch of cake is $0.09.

The rectangular prism-shaped sheet cake has a volume of:

V = length x width x height = 12 x 18 x 3 = 648 cubic inches

The price per cubic inch of cake is the total cost of the cake divided by its volume:

Price per cubic inch = Total cost / Volume

Price per cubic inch = $58.32 / 648 cubic inches

Price per cubic inch = $0.09 (rounded to the nearest cent)

Therefore, the price per cubic inch of cake is $0.09.

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Answer:

To find dy/dx using implicit differentiation, we differentiate both sides of the equation y*x^7 = x*y^9 with respect to x.

Product Rule:

(u*v)' = u'v + uv'

Differentiating the left-hand side y*x^7 with respect to x, we get:

d/dx (y*x^7) = 7*x^6*y + x^7*(dy/dx)

Differentiating the right-hand side x*y^9 with respect to x, we get:

d/dx (x*y^9) = y^9 + x*(9*y^8*(dy/dx))

Now we can substitute these derivatives back into the original equation to solve for dy/dx:

y*x^7 = x*y^9

7*x^6*y + x^7*(dy/dx) = y^9 + x*(9*y^8*(dy/dx))

Simplifying:

x^7*(dy/dx) - 9*x*y^8*(dy/dx) = y^9 - 7*x^6*y

(dy/dx)*(x^7 - 9*x*y^8) = y^9 - 7*x^6*y

dy/dx = (y^9 - 7*x^6*y) / (x^7 - 9*x*y^8)

Therefore, dy/dx = (y^9 - 7*x^6*y) / (x^7 - 9*x*y^8) for x ≥ -7 and y*x^7 = x*y^9.

thanks and rate5*! if this helps u<3 have a nice night!

The area of quadrilateral EDFG is approximately 21 cm²

We are given that 3DE = 3FC = AB.

Thus:

The area of ΔFCB = ¹/₆ * the area of ABCD

Area of ΔFCB = ¹/₆ * 140 = 23.33 cm²

Area of ΔCFG/Area of ΔCED = (CF/CE)²

Side length of ABCD is: CD = √140 = 11.83 cm

FC = 1/3 * CD

FC = 3.944 cm

CE = √(DE² + CD²)

CE = √(3.944² + 11.83²)

CE = 12.47 cm

Area of ΔCFG/Area of ΔCED = (3.944/12.47)² = 1/10

Area of ΔCFG = 1/10 * 140/6 = 2.33 cm²

Area of EDFG = (140/6) - (140/60) = 21 cm²

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To find the dimensions of the box that requires the least material for the five sides, we need to minimize the surface area while maintaining a volume of 100.

Let's use the following variables:
x = length of one side of the square base
y = height of the box

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The radius of convergence of the power series is 1, based on stated calculations.

Let's use the ratio test to find the radius of convergence of the power series:

First, we calculate the ratio of the absolute values of successive terms:

|a_{n+1}| / |a_n| = |(4n+4)!x^{n+1} / ((4n)!*(n+1)4) * (n+1)4 / (4n+4)! * (4n)!|

= |x| * ((4n+4)/(4n+1))

= |x| * (1 + 3/(4n+1))

As n goes to infinity, the ratio |a_{n+1}| / |a_n| approaches |x|. Therefore, the power series converges if |x| < 1 and diverges if |x| > 1. When |x| = 1, the ratio test is inconclusive and we need to check the endpoints of the interval.

At x = 1, the series becomes:

1 + 4! + 8! × [tex](2!)^4[/tex] + 12! × [tex](3!)^4[/tex] + 16! × [tex](4!)^4[/tex] + 20! × [tex](5!)^4[/tex] + ...

This series is divergent by the test for divergence (the terms do not approach zero).

At x = -1, the series becomes:

1 - 4! + 8! × [tex](2!)^4[/tex] - 12! × [tex](3!)^4[/tex] + 16! × [tex](4!)^4[/tex] - 20! × [tex](5!)^4[/tex] + ...

This series is also divergent by the test for divergence (the terms do not approach zero).

Therefore, the radius of convergence of the power series is 1.

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The center of mass of the rod is located at x = 0.523 m from the origin.

To find the center of mass of the rod, we need to integrate the position of each small mass element multiplied by its mass, and divide by the total mass of the rod. We can express the position of each mass element as x, and the mass of each element as [tex]dm = rho(x) dx[/tex], where dx is a small element of length.

Thus, the total mass of the rod can be calculated by integrating the density function over the length of the rod:

M = [tex]∫₀ᴸ ρ(x) dx[/tex]

Substituting the given values, we get:

M = [tex]∫₀^(0.95) [3.3 + (5.8 - 3.3)(x/0.95)²] dx[/tex]

Integrating this expression gives us:

M =[tex][3.3x + (5.8-3.3)(x/0.95)³/(3(0.95))] from 0 to 0.95[/tex]

M = 4.854 kg

Now, we can calculate the position of the center of mass,[tex]x_cm[/tex], as:

[tex]x_cm = (1/M) ∫₀ᴸ x dm[/tex]

Substituting[tex]dm = ρ(x) dx[/tex], we get:

[tex]x_cm = (1/M) ∫₀ᴸ x ρ(x) dx\\[/tex]

Substituting the given values, we get:

[tex]x_cm = (1/4.854) ∫₀^(0.95) x [3.3 + (5.8 - 3.3)(x/0.95)²] dx[/tex]

Integrating this expression gives us:

[tex]x_cm = [1.65x²/2 + (5.8-3.3)(x/0.95)⁵/(5(0.95))] from 0 to 0.95[/tex]

[tex]x_cm = 0.523 m[/tex]

Therefore, the center of mass of the rod is located at x = 0.523 m from the origin.

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We can always find two integers in the set whose sum is even and in any set of three (not necessarily distinct) integers, there will always be two whose sum is even.

Step 1: Understand the concept of odd and even numbers.
- An even number is divisible by 2 (e.g., 2, 4, 6, 8).
- An odd number is not divisible by 2 (e.g., 1, 3, 5, 7).

Step 2: Determine the possible cases for the sum of two integers.
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd

Step 3: Analyze the possible combinations of integers in a set of three.
There are two possibilities:
1. The set has at least two even numbers.
2. The set has at least two odd numbers.

Step 4: Apply the sum rules to each possibility.

Possibility 1: At least two even numbers.
- If we pick any two even numbers from the set and add them, the sum will be even (Even + Even = Even).

Possibility 2: At least two odd numbers.
- If we pick any two odd numbers from the set and add them, the sum will be even (Odd + Odd = Even).

In both possibilities, we can always find two integers in the set whose sum is even. Therefore, we have proven that in any set of three (not necessarily distinct) integers, there will always be two whose sum is even.

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The probability of the shop purchasing is 5/9.

Let X be the number of non-defective engines purchased by the auto shop out of the 4 engines bought. We want to find P(X >= 3), the probability of getting at least 3 non-defective engines.

Using the hypergeometric distribution formula, we have:

P(X >= 3) = P(X = 3) + P(X = 4)

where

P(X = k) = (C(7, k) * C(2, 4-k)) / C(9, 4)

So, we have:

P(X = 3) = (C(7, 3) * C(2, 1)) / C(9, 4) = (35 * 2) / 126 = 5/18

P(X = 4) = (C(7, 4) * C(2, 0)) / C(9, 4) = (35 * 1) / 126 = 5/18

Therefore,

P(X >= 3) = 5/18 + 5/18 = 10/18 = 5/9

So the probability of the shop purchasing at least 3 non-defective engines is 5/9.

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The type of data collection involved in this scenario is "survey research."

The type of data collection involved in this scenario is "survey research." Survey research is a method of gathering information from a sample of individuals through the use of questionnaires or interviews.

In this case, the marketing research firm is using a questionnaire to collect data about adults' beverage preferences.

This method allows the firm to gather information about people's opinions, preferences, and experiences, which can be used to make informed decisions about marketing strategies and product development.

The data collected from this type of research is usually quantitative, which means it can be analyzed using statistical methods. The results obtained from the survey research can be used to draw conclusions about the population from which the sample was drawn.

Survey research is a useful method for marketing research because it allows researchers to collect a large amount of data from a relatively small sample of individuals.

Additionally, the data collected from survey research can be used to inform marketing strategies, product development, and other business decisions.

So it is conculded that the type of data collection involved in this scenario is "survey research."

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The kind of transformation that is illustrated in this figure include the following: D. rotation.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics, a rotation refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image was rotated counterclockwise to produce the image.

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Complete Question:

What kind of transformation is illustrated in this figure?

reflection

dilation

translation

rotation

How frequently do you consume fast food in a typical week?

On average, how many times do you eat fast food per day?

What are some of your preferred fast food restaurants or chains?

The value of the given triple integral is 0.

We will evaluate the given triple integral step by step:

First, we will integrate with respect to y, treating x and z as constants:

Next, we will integrate with respect to z, treating x as a constant:

Finally, we will integrate with respect to x:

Therefore, the value of the given triple integral is 0.

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For males, the 95% confidence interval for the mean number of times exercise per week is 3.22 to 4.12. For females, the 95% confidence interval for the mean number of times exercise per week is 3.35 to 4.88.

From the output, we can see that on average, females exercise more than males, with a mean of 4.12 times per week compared to males' mean of 3.67 times per week. However, the confidence interval for males overlaps with the confidence interval for females, meaning that there is no significant difference between the two groups.

The 5% trimmed mean for both groups is close to their respective means, indicating that there are no outliers greatly affecting the data. The minimum and maximum values for both groups are the same, with a range of 6, but the variance and standard deviation for females are higher than for males, indicating more variability in the data.

Overall, while there is a slight difference in the mean number of times exercise per week for males and females, this difference is not significant and may be due to natural variability in the data.

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Since the pmf is not valid, we cannot find the expected value of X using the formula E[X] = Σn f(X = n).

a. To show that the given pmf is a valid pmf, we need to show that it satisfies two conditions:

f(X = n) >= 0 for all n

Σf(X = n) = 1 over all possible values of X

For the first condition, we have:

f(X = n) = n(n+1)(n+2)

Since n, n+1, and n+2 are all positive for any positive integer n, f(X = n) is also positive for all n.

For the second condition, we have:

Σf(X = n) = Σn(n+1)(n+2)

= Σ[n^3 + 3n^2 + 2n]

= Σn^3 + 3Σn^2 + 2Σn

= (1^3 + 2^3 + ... + ∞^3) + 3(1^2 + 2^2 + ... + ∞^2) + 2(1 + 2 + ... + ∞)

= (ζ(3)) + 3(ζ(2)) + 2(ζ(1))

where ζ(k) is the Riemann zeta function evaluated at k.

Since ζ(1) = ∞, this sum diverges, which means that the pmf is not a valid probability mass function.

b. Since the pmf is not valid, we cannot find the expected value of X using the formula E[X] = Σn f(X = n).

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According to research, 60-70% percentage of instructional time is devoted to written computation. So, the correct answer is A).

The instructional time is devoted to written computation can vary depending on the specific study being referred to. However, traditionally, written computation has been a fundamental component of math instruction, and it can occupy a significant portion of instructional time.

Studies have reported that written computation can take up anywhere from 60% to 70% of instructional time. This significant allocation of time to written computation reflects the importance placed on basic computational skills in mathematics education, which are seen as essential building blocks for more advanced mathematical concepts and problem-solving skills. So, the correct option is A),

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x = the other part

let's first find how much is 28% of "x"

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{28\% of x}}{\left( \cfrac{28}{100} \right)x}\implies 0.28x[/tex]

so whatever the first part is, is "x" plus 0.28x, or namely 1.28x, and we know their sum is 3420

[tex]x+1.28x=3420\implies 2.28x=3420\implies x=\cfrac{3420}{2.28} \\\\\\ \boxed{x=1500}\hspace{5em}\stackrel{ 3420~~ - ~~1500 }{\boxed{1.28x=1920}}[/tex]

Answer:

Step-by-step explanation: