Rectangle ABCD has vertices A(–6, –2), B(–3, –2),
C(–3. –6), and D(–6, –6). The rectangle is translated so that the coordinates of the image are A’(–10, 1), B’(–7,1),
C’(–7, –3), and D’(–10, –3).

Which rule was used to translate the image?

T–4, 3(x, y)
T–4, 1(x, y)
T4, –1(x, y)
T4, –3(x, y)

To compute (a)x1 and (b)x2 for the iterative process defined by xn-1= with x0=12, we need to apply the iterative formula repeatedly. The exact answers are (a) x1 = 12 and (b) x2 = 12, since the iterative process generates the same value at each step.

For the iterative process defined by x(n) = x(n-1), with x0 = 12, follow these steps:
1. First, find x1 by using the given formula and the initial value x0:
x(n) = x(n-1)
x(1) = x(1-1) = x(0)
x(1) = 12 (since x0 is given as 12)

2. Next, find x2 by using the formula and the value of x1:
x(n) = x(n-1)
x(2) = x(2-1) = x(1)
x(2) = 12 (since x1 was computed to be 12)
Note that these answers are exact, not approximate, because we used the iterative process formula exactly as defined.

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The indifference curve corresponding to this utility function will be convex to the origin. This is because the utility function exhibits diminishing marginal returns for both goods. As the consumer increases the quantity of one good while keeping the other constant, the marginal utility derived from the additional unit of that good decreases. This diminishing marginal utility leads to convex indifference curves, indicating that the consumer is willing to give up larger quantities of one good for small increases in the other good to maintain the same level of satisfaction.

The assumption of 'more is better' is satisfied for both goods in this utility function because as the consumer increases the quantity of either good x or good y, their utility (U) also increases. The positive coefficients of x and y in the utility function indicate that more of each good is preferred.

The marginal rate of substitution (MRS) measures the rate at which a consumer is willing to exchange one good for another while maintaining the same level of utility. In this utility function, the MRSx,y is equal to 1.

The MRSx,y is diminishing in x as the consumer substitutes x for y along an indifference curve. This means that as the consumer increases the quantity of good x, they are willing to give up fewer units of good y to maintain the same level of satisfaction. The diminishing MRSx,y reflects a decreasing willingness to substitute x for y.

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Step-by-step explanation:

4+5 (2x-3)-6x

9 (2x-3)-6x

18x-27-6x

12x-27

Answer:

\( \sf \: 4x - 11 \)

Step-by-step explanation:

Given expression,

→ 4 + 5(2x - 3) - 6x

Let's simplify the expression,

→ 4 + 5(2x - 3) - 6x

→ 4 + 10x - 15 - 6x

→ (10x - 6x) + (4 - 15)

→ (4x) + (-11)

→ 4x - 11

Hence, the answer is 4x - 11.

Answer: for the table:

Forks: 16, 8, 48

Spoons: 10, 5, 30

Equivalent ratios are 16:10, 8:5, 48:30

Step-by-step explanation:

Answer:

Step-by-step explanation:

Lacey you can do this one  :D

J = H  ( b/c of red marks)

180= 128 + ∠j

52 = ∠j

t = ∠j

t = 52

180 = s + 2*t

180 = s + 2*52

180 = s + 104

180-104 =s

76 = s

Answer:

17. 1 = 2 = 45, 3 =135

18. 1 = 2 = 105.5

Step-by-step explanation:

17.

isosceles trapezoid properties:

Angle 1 = Angle 2

Angle 3 = 135

sum of the angles in any quadrilateral is 360

A1 + A2 + A3 + 135 = 360

A2 + A2 + 135 + 135 = 360

2A2 = 360 - 135 - 135

2A2 = 90

A2 = 90/2 = 45

So

A1 = A2 = 45

18.

Draw straight line from edge at 1 to edge at 2

Now you have two isosceles triangle

isosceles triangle properties:

angles opposite to equal sides are equal in measure

sum of the angles in any triangle is 180

refer photo for calcukation

\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=65\pi \end{cases}\implies 65\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi}\cdot 65\pi =r^3 \\\\\\ \cfrac{195}{4}=r^3\implies \sqrt[3]{\cfrac{195}{4}}=r\implies 3.65\approx r\)

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

The two stores at points A and C would serve the residents of Miniville, providing them access to essential goods and services, with residents in the middle mile having the flexibility to choose between the two stores.

If one store is located at point A and the other store is located at point C, it means that the stores are located at the extremes of the 3-mile stretch of Lake Shore Drive in Miniville. Point B would be the midpoint between points A and C.

Given that the 300 residents of Miniville are evenly distributed along the 3 miles of shoreline on the lake, it implies that there are approximately 100 residents per mile.

Therefore, the store located at point A would serve the residents living in the westernmost mile of Lake Shore Drive, while the store located at point C would serve the residents living in the easternmost mile of Lake Shore Drive.

The residents living in the middle mile, between points A and C, would have the option to shop at either store, depending on their preference or convenience.

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The ordered pair that is in the solution set of the inequality is (-1, 6). So, the correct option is (a).

The inequality given is y≥1/3+4.

We have to find the ordered pair that is in the solution set of this inequality.

To find the ordered pair, we need to substitute the values of x and y from the options given and then check whether it satisfies the inequality or not.

a)

(-1, 6) => y=6 which is greater than (1/3+4).

Hence, (-1, 6) is in the solution set of the inequality.

b)

(1, -6) => y=-6 which is not greater than (1/3+4).

Hence, (1, -6) is not in the solution set of the inequality.

c)

6, -1) => Here, y=-1 which is not greater than (1/3+4).

Hence, (6, -1) is not in the solution set of the inequality.

d)

(-6, 1) => Here, y=1 which is not greater than (1/3+4).

Hence, (-6, 1) is not in the solution set of the inequality.

Therefore, the ordered pair that is in the solution set of the inequality is (-1, 6). So, the correct option is (a). We can conclude that (-1, 6) is the only solution of the inequality y≥1/3+4.

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Based on the typical pricing trend for used vans being 90% of the price of a new van, a used van would be priced at approximately $36,000.

To find the price of a used van, we can calculate 90% of the price of a new van.

90% of $40,000 can be calculated by multiplying $40,000 by 0.9:

$40,000 * 0.9 = $36,000

Jason is in the process of looking for vans, considering both new and used options. He has come across a new van priced at $40,000. In general, the price of a used van tends to be around 90% of the price of a new van.

In this case, since the new van is priced at $40,000, we can calculate the price of a used van by multiplying $40,000 by 0.9, which represents 90%:

$40,000 * 0.9 = $36,000.

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The Supreme Court was successful in curbing the power and abuses of American business leaders before 1900.  The Oregon incident highlighted America's need for developing a shorter ship route between the Pacific and Atlantic Oceans.

All of the following are examples of Roosevelt's presidential policies except interfering in the Mexican Revolution.
1. Before 1900, the institution successful in curbing the power and abuses of American business leaders was the Interstate Commerce Commission (ICC). The ICC was established in 1887 and had the supreme authority to regulate interstate railroad rates, which helped reduce the unfair practices and power of railroad monopolies.

2. One of the elements that provided a major contribution to the evolution of Populism in America was the growing political militancy of rural American Grange organizations. The Grange movement aimed to address the economic hardships faced by farmers and advocated for political and social reforms to benefit the agrarian community.

3. One factor that was not responsible for initiating the Spanish-American War was President McKinley's great desire to go to war against Spain. In fact, McKinley initially sought a peaceful resolution to the Cuban crisis but was eventually pressured into war by powerful newspaper czars, influential government figures, and public opinion.  One of the elements that provided a major contribution to the evolution of Populism in America was the growing political militancy of rural American Grange organizations. Pressure from powerful newspaper czars like Hearst and Pulitzer was not actually responsible for initiating the Spanish American War.

4. The Oregon incident highlighted America's need for developing a shorter ship route between the Pacific and Atlantic Oceans. This incident demonstrated the strategic importance of constructing a canal across Central America, which later resulted in the creation of the Panama Canal.

5. All of the following are examples of Roosevelt's presidential policies except interfering in the Mexican Revolution. While Theodore Roosevelt was a proponent of the "Big Stick" diplomacy and actively sought to exert American influence, he did not directly involve the United States in the Mexican Revolution. The other listed policies were indeed part of his presidential actions.

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Cathy has used stratified sampling technique in this scenario.

Stratified sampling is a sampling technique in which the population is divided into non-overlapping subgroups or strata, based on certain characteristics or attributes.

In this scenario, Cathy divided the population into three strata based on annual income range.

She then selected a sample f

rom each stratum in proportion to the size of the stratum in the population. This ensures that each stratum is adequately represented in the sample, and increases the precision and accuracy of the estimates made from the sample.

Thus, stratified sampling allows for more precise estimates to be made for each subpopulation, which can be useful for comparing groups or identifying differences or similarities between subgroups.

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This is not the complete question, the complete question is:

Automobile claim amounts are modeled by a uniform distribution on the interval [0, 10,000]. Actuary A reports X, the claim amount divided by 1000. Actuary B reports Y, which is X rounded to the nearest integer from 0 to 10.Calculate the absolute value of the difference between the 4th moment of X and the 4th moment of Y

A) 0

B) 33

C) 296

D) 303

E) 533

Answer: B) 33

Step-by-step explanation:

First lets say;

z: automobile claim amounts

x: the claim amount dived by 1000

y: x rounded to the nearest integer from 0 to 10

z ≅  V[0, 10,000]

x = z / 1000 ≅ V[0, 10 ] ⇒ Fx { 1/10, 0 ≤ x ≤ 10} 0, 0/10

y =  {0,     0 ≤ x < 0.5

       1,       0.5 ≤ x < 1.5

       2,       1.5 ≤ x < 2.5

       3,       2.5 ≤ x < 3.5

        ↓

       9,        8.5 ≤ x < 9.5

       10,       9.5 ≤ x < 10

SO 4th moment of x = E(x²) = ∫₀¹⁰x⁴ 1/10 dₓ

                                 = 1/10 (x⁵ / 5)₀¹⁰

                                  = 10⁵ / (10 * 5)

                                  = 100000/50

                                   = 2000

Now

4th moment of y = E(y⁴) = ∑/y y⁴ p( y=y)

                             = 0⁴p( y=0) + 1⁴p( y=1 ) + 2⁴p( y=2) + → + 10⁴p( y=10)

                             = 0 + 1⁴.p( 0.5 ≤ x < 1.5) +  2⁴.p( 1.5 ≤ x < 2.5) + 3⁴.p( 2.5 ≤ x < 3.5 ) + → + 10⁴.p( 9.5 ≤ x < 10 )

                   = 1/10 [ 1⁴(1.5 - 0.5) + 2⁴(2.5 - 1.5) + → + 9⁴(9.5 - 8.5) + 10⁴(10 - 9.5)]

                   = 1/10 [ 1⁴ + 2⁴ + → + 9⁴ + 1/2*10⁴] = 2033.3

now the absolute difference will be

AD = ║E(x⁴) - E(y⁴)║

     = ║ 2000 - 2033.3║

     = 33.3 ≈ 33

Answer:

The correct answer is 1/42x^5.

Step-by-step explanation:

7 • 6 = 42

-8 + 6 = -5 (When multiplying, you must add the exponents.)

= 42x^(-5) (To remove the negative sign, switch it to a fraction.)

= 1/42x^5

The gas gauge will show a lower reading if the gas tank is less than full when you return home after your trip to the mountains.

The gas gauge will show a lower reading if the gas tank is less than full when you return home after your trip to the mountains. This is due to the increased effort required to drive in mountainous terrain, which necessitates more fuel consumption.The amount of fuel used by the car will be determined by a variety of factors, including the engine, the type of vehicle, and the driving conditions. Since the car was driven in the mountains, it is likely that more fuel was used than usual, causing the gauge to show a lower reading.

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Using the Fundamental Counting Theorem, it is found that there are 27,600 ways for the letters to be arranged.

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

For this problem, considering that the first letter can only be 2 of them and the letters cannot repeat, the parameters are given as follows:

\(n_1 = 2, n_2 = 25, n_3 = 24, n_4 = 23\)

Hence the number of ways that the letters can be arranged is given by:

N = 2 x 25 x 24 x 23 = 27,600.

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The correct answer is S = {A, D, D, I, T, I, O, N}.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The sample space is the set of all possible outcomes of an experiment or event.

In this case, the experiment is choosing one card from a set of eight labeled cards.

The sample space for this experiment is the set of all possible cards that can be chosen.

In the given problem, there are eight cards labeled A, D, D, I, T, I, O, N.

The sample space is the set of all possible cards that can be chosen, which is {A, D, D, I, T, I, O, N}.

This is because each card is distinct and can be chosen independently of the others.

Therefore, the correct answer is S = {A, D, D, I, T, I, O, N}.

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Answer: A( A,D, D,I, I,N,O,T)

Step-by-step explanation:

Order does not matter!!

Step-by-step explanation:

the answer is in the above image

Answer: -3

Step-by-step explanation:

Given points (-1,6) and (2,-3), we can use the slope formula y2-y1/x2-x1 to find the slope

6-(-3)/-1-2 = 9/-3 = -3

Slope is -3

Answer:

area = 110.72 m²

Step-by-step explanation:

area of square = 8 x 9 = 72 m²

area of triangle = 1/2 x 3 x 9 = 13.6 m²

area of semi circle = 1/2πr² = 1/2(3.14)(4²) = 25.12 m²

total area = 72 + 13.6 + 25.12 = 110.72 m²

The answer is A

Hope it helps :)

find slope

y2-y1/x2-x1 -> -2-6/9+7 -> -8/16 -> -1/2 -> perpendicular slope is a negative reciprocal so -> 2

get midpoint

(x2+x1)/2,(y2+y1)/2 -> (9-7)/2, (-2+6)/2 -> 2/2, 4/2 -> 1,2

point slope equation

y-y1 = m (x-x1)

y-2=2(x-1) = answer is the 4th one or D

Answer:

Thus, the equation of a line is: y = -12x-17

Step-by-step explanation:

Using the point-slope form

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope, and (x₁, y₁) is the point

substituting the values m = -12 and the point (-1, -5)

\(y-y_1=m\left(x-x_1\right)\)

y-(-5) = -12(x-(-1))

y+5 = -12 (x+1)

y+5 = -12x-12

y = -12x-12-5

y = -12x-17

Thus, the equation of line is: y = -12x-17

Answer:

No graphs was presented but its the last one shown in the photo

The leaf's height as a function of time is determined as h(t) = 12 - 0.25t - 4.9t².

The equation for the motion of the leaf is calculated as follows;

h = vt + ¹/₂gt²

where;

The leaf's height as a function of time is given as;

h(t) = 12 - 0.25t - 4.9t²

Due to presence of gravity, the decline in the height of the leaf will be gradual.

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Answer:

A=22.75cm²

Step-by-step explanation:

A=LW

A=6.5x3.5

A=22.75cm²

The number will be 6,125.Given, we need to form a four-digit number using the digits 1, 2, 3, and 4. The number should satisfy the following conditions:The thousands digit is three times the tens digit.The hundreds digit is one more than the units digit.The sum of all four digits is 10.

To find: The four-digit number

Solution:Let us assume the digit in the unit place to be x.∴ The digit in the hundredth place will be x + 1∴ The digit in the tenth place will be a.

Let the digit in the thousandth place be 3a∴ According to the given conditions a + 3a + (x + 1) + x = 10⇒ 4a + 2x + 1 = 10⇒ 4a + 2x = 9……(1)

Now, the value of a can be 1, 2, or 3 because 4 can’t be the thousandth place digit as it will make the number more than 4000.Using equation (1),Let a = 1⇒ 4 × 1 + 2x = 9⇒ 2x = 5, which is not possible∴ a ≠ 1

Similarly,Let a = 3⇒ 4 × 3 + 2x = 9⇒ 2x = −3, which is not possible∴ a ≠ 3

Let a = 2⇒ 4 × 2 + 2x = 9⇒ 2x = 1⇒ x = 1/2Hence, the number will be 6,125. Answer: The four-digit number will be 6,125.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The required values are ~

\(\fbox \colorbox{black}{ \colorbox{white}{x} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{40 \degree}}\)

\(\fbox \colorbox{black}{ \colorbox{white}{y} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{80 \degree}}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

From the given figure, we can infer that ~

(by linear pair)

now, let's solve for x ~

And, we can see that 2x = y (by alternate interior angle pair)

So, let's find the value of y ~

Answer:

x = 40

3x - 20 = 100

2x = 80

y = 80

2x - 15 = 65

Step-by-step explanation:

The angles 3x - 20 and 2x are a linear pair, so they are supplementary. Their measures has a sum of 180°.

Angles 2x and y are alternate interior angles, so they are congruent.

Once we find the value of x, we can find the measure of angle 2x - 15.

3x - 20 + 2x = 180

5x = 200

x = 40

3x - 20 = 3(40) - 20 = 120 - 20 = 100

2x = 2(40) = 80

y = x = 80

2x - 15 = 2(40) - 15 = 80 - 15 = 65

(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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There are 30 adults in the swimming pool.

The ratio is a quantitative approach that shows the relation between two proportions.

From the given relation, the ratio of of the children to adults = 8 : 3

The total number of the ratio = 8 + 3 = 11

Given that there are 110 people in the population.

The number of adults that are there will be:

\(\mathbf{=\dfrac{3}{11}\times 110}\)

= 30 adults

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Answer:

A rhombus and a square since a square is also a rhombus.

The equation of the line of fit can be written as y = x + 4.

Two points from which to write the equation of a line of fit can be determined by using the mean, median, and mode of the data set. The mean, median, and mode help to identify the center of the data set, which helps to identify two points that can be used to write the equation of the line of fit. The mean is calculated by taking the sum of all the data points and dividing it by the total number of data points. The median is the middle value of the data set when the data points are ordered from lowest to highest. The mode is the value that appears the most in the data set. By finding the mean, median, and mode of the data set, two points that can be used to write the equation of the line of fit can be determined. The two points can be determined by taking the mean, median, or mode value of the data set, and adding or subtracting an arbitrary value from that point. For example, if the mean of the data set is 8 and an arbitrary value of 2 is added to it, the two points of the line of fit can be (8, 10) and (8, 6). Using these two points, the equation of the line of fit can be written as y = x + 4.

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