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The coordinate of point G after a rotation of 180° is (4,2).

The complete question is added as an attachment

Rotation is a given a rigid motion or transformation which refers to movement of a figure around a center of rotation.

In this question it is asked to find the coordinates of the new vertices after the 180 degrees rotation, which is define or represented by the rule:

(x, y) = (-x, -y)

From the figure, we have

G = (4,2)

So, we have

G' = (-4,-2)

Hence, the image is (-4,-2)

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Answer:

D. G'(4,2)

Step-by-step explanation:

The volume of the parallelepiped is V = 40/3.

To find the volume of the parallelepiped with adjacent edges u = 6i + 8j+k, v=i+j+2k, and w = i + 9j + 7k, we can use the scalar triple product formula:

V = |u ⋅ (v × w)|

First, we need to find the cross product of v and w:

v × w = (i+j+2k) × (i+9j+7k)
= i × (9j+7k) - j × (i+7k) + k × (i+9j)
= -7i - 5j + 2k

Next, we can take the dot product of u and the cross product of v and w:

u ⋅ (v × w) = (6i + 8j + k) ⋅ (-7i - 5j + 2k)
= -42 - 40 + 2
= -80

Finally, we can take the absolute value of the result and divide by 6 to get the volume:

V = |-80|/6
= 40/3

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Answer:

-2+6

Step-by-step explanation:

-6-(-2)

-6+2

-4

-2+6

=4

we know that

The sum of the internal angles in the triangle must be  degrees

see the attached figure with letters to better understand the problem

Step

Find the measure of the angle x

In the triangle ABC

solve for x

therefore

the answer Part a)  is

the measure of angle x is

Step

Find the measure of the angle z

we know that

--------> by supplementary angles

substitute the value of x

therefore

the answer Part b)  is

the measure of angle z is

Step

Find the measure of the angle y

In the triangle ACD

solve for y

therefore

the answer Part c)  is

the measure of angle y is

Answer:

He can fill up his fill up his measuring cup 8 times that is pretty simple

Step-by-step example

4 cups is in one gallon

Answer:

\( \frac{7}{8} = 0.875\)

Step-by-step explanation:

\( \frac{3}{4} \div \frac{6}{7} \)

\( \frac{3}{4} \times \frac{7}{6} = \frac{1}{4} \times \frac{7}{2} \)

\( \frac{1 \times 7}{4 \times 2} = \frac{7}{4 \times 2} \)

\(\boxed{\green{ = \frac{7}{8} = 0.875}}\)

To guarantee that at least three cards of the same suit are chosen from a well-shuffled standard deck of 52 cards, we need to select a minimum of 9 cards.

The worst-case scenario is that we initially select one card from each suit (four different suits) to ensure we have representation from all suits. After this step, we have four cards in hand, each representing a different suit.

Next, we continue selecting cards. In the worst-case scenario, each subsequent card we select will be from a suit different from the ones we already have. Therefore, for the next five cards we select, none of them will match any of the suits we already have.

However, when we select the ninth card, it will necessarily match at least one of the suits we already have because there are only four suits in the deck. Therefore, we will have at least three cards of the same suit.

Hence, to guarantee that at least three cards of the same suit are chosen, we need to select a minimum of 9 cards.

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There are the 24360 ways by which pilot can be scheduled for 3 days of flying in September according to permutation.

According to the statement

we have to find that the by how many ways can a pilot be scheduled for 3 days of flying in September if the pilot can not work on consecutive days.

So, For this purpose,we know that the

Here we use permutation to find the number of ways.

Permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

And the number of days in September is 30 days and the given number of days is 3.

So, permutation becomes:

P(30,3) = 30! / 30-3 !

P(30,3) = 30! / 27 !

P(30,3) = 30 *29*28

P(30,3) = 24360.

So, There are the 24360 ways by which pilot can be scheduled for 3 days of flying in September according to permutation.

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Step-by-step explanation:

If you put some quantities for theta, you reach to B option

Answer:

Step 1 - Find Whole Number

Calculate out how many times the denominator goes into the numerator. To do that, divide 6 by 5 and keep only what is to the left of the decimal point:

6 / 5 = 1.2000 = 1

Step 2 - Find New Numerator

the answer from Step 1 by the denominator and deduct that from the original numerator.

6 - (5 x 1) = 1

Step 3 - Get Solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 6/5 as a mixed number is:

1 1/5

Step-by-step explanation:

The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False.

The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

This is a recursive problem where each player plays optimally. There are two players in the game. The child will pick the balls first and then the game owner takes turns. Both will pick the balls optimally in order to win.

In each turn, k balls can be picked from the box. The winner is the one who picks the last ball. If the child picks the last ball, they win otherwise the game owner wins.

The algorithm is as follows:

Algorithm - Pick Balls

1. Define a recursive function called PickBalls(n). The function takes one parameter as input, which is the number of balls remaining in the box.

2. Check if the number of balls remaining is less than or equal to k. If yes, then return True as the game has ended and the child has won.

3. If the number of balls is greater than k, then pick k balls from the box.

4. If the child picks the last ball, then return True.

5. If the child does not pick the last ball, then the game owner picks the balls recursively.

6. If the game owner picks the last ball, then return False. Otherwise, return True.

Explanation: We are designing a recursive algorithm to find out whether the child will win or lose in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. We are assuming that both players play optimally. The algorithm works as follows:

If the number of balls remaining in the box is less than or equal to k, then the child can pick all the balls and win the game. Therefore, the function returns True.

If the number of balls remaining in the box is greater than k, then the child picks k balls from the box. If the child picks the last ball, then they win the game. Therefore, the function returns True.

If the child does not pick the last ball, then the game owner picks the balls recursively. If the game owner picks the last ball, then they win the game. Therefore, the function returns False. If the game owner does not pick the last ball, then the child picks again and the process repeats itself. If the child eventually picks the last ball, then they win the game. Therefore, the function returns True.

Conclusion: The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

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Answer:

d = 47°

Step-by-step explanation:

Image is attached

Sum of angles drawn along a straight line = 180°:

The angle drawn in pink : 180° - 112° = 68°

The angle drawn in green: 180° - 66° = 114°

The angle drawn in yellowish orange: 180° - 23° = 157°

The angle marked in purple: 180° - 102° = 78°

The figure drawn in the center is a 5-sided irregular pentagon

∴ Sum of interior angles in a 5-sided polygon = (n - 2) ×180°

                                                                            = (5 - 2) × 180°

                                                                            = 540°

The four angles calculated above will assist in calculating the fifth remaining angle of the pentagon (which is marked in light blue):

   68° + 114° + 78° + 157° + angle in light blue = 540°

Angle in light blue = 540° - 68° - 114° - 78° - 157°

                               = 123°

Sum of angles drawn along a straight line = 180°:

Angle marked in dark blue = 180° - 123°

                                                = 57°

Now focus on the angles present inside the triangle

Sum of interior angles of a triangle = 180°

= d + 76° + 57° = 180°

d has to be isolated and made the subject of the equation:

d = 180° - 76° - 57°

d = 47°

Answer: The answer is -30 - 45 k

Step-by-step explanation:

The requried measure of the PQ in the triangle PQT is 16 in.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
A figure of triangles has been shown, ΔPQT and ΔORS.
We have to determine the measure of side PQ.

Since the given triangle is similar to one another, we can apply the property of proportionality between the similar triangles. By which:

PR/PQ = RS/QT
PQ + 4 / PQ = 10/8
8PQ + 32 = 10PQ
2 PQ = 32
PQ = 16 in

Thus, the requried measure of the PQ in the triangle PQT is 16 in.

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Answer:

17.

Step-by-step explanation:

We know that NP = NO + NP because all the points are on the same line.

So 2x = 10 + (x + 7),

x = 17.

Answer: Its 8

Step-by-step explanation:

Using compound interest and continuous compounding, it is found that Lincoln would have $15,856 more in his account than Eli.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

Hence, for Lincoln, we have that the parameters are as follows:

P = 49000, r = 0.06125, n = 365, t = 20.

Hence the amount will be of:

\(A_L(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A_L(20) = 49000\left(1 + \frac{0.06125}{365}\right)^{365 \times 20}\)

\(A_L(20) = 166787\)

The amount is given by:

\(A(t) = Pe^{rt}\)

For Eli, we have that r = 0.05625, hence the amount will be given by:

\(A(t) = Pe^{rt}\)

\(A_E(20) = 49000e^{0.05625 \times 20} = 150931\)

It is given by:

\(D = A_L(20) - A_E(20) = 166787 - 150931 = 15856\)

Lincoln would have $15,856 more in his account than Eli.

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Q is not cyclic because it contains irrational numbers such as √2 that cannot be generated by any element in Q. R is not cyclic due to its uncountable nature and additional properties as a complete ordered field.

(a) To prove that Q (the set of rational numbers under addition) is not cyclic, we need to show that there is no element in Q that generates the entire group under the operation of addition.

Assume, for contradiction, that Q is cyclic and let q be a generator of Q. This means that every rational number can be expressed as an integral power of q. However, we can find a rational number r that cannot be expressed in this form.

Consider the square root of 2 (√2), which is irrational. If q is a generator of Q, then there exist integers m and n such that q = m/n. However, it is known that √2 is not rational, which means it cannot be expressed as a fraction of two integers. Therefore, √2 cannot be generated by any element in Q, which contradicts the assumption that Q is cyclic. Hence, Q is not cyclic.

(b) Since Q is not cyclic, we cannot deduce directly that R (the set of real numbers under addition) is not cyclic. However, there are other reasons to conclude that R is not cyclic. One such reason is that R is an uncountable set, whereas cyclic groups are countable. Another reason is that R is a complete ordered field, which means it has additional properties not present in cyclic groups. Therefore, we can deduce that R is not cyclic based on these additional characteristics.

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Answer:

to find the mean add up all the scores and then divide it by the number of scores that are there and to find the mode order the numbers lowest to highest and see which number appears the most

Answer:

A

Step-by-step explanation:

Eliminate B and C because they don't pass through (0,1).

Eliminate D because it doesn't decrease quickly enough.

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Answer:

Step-by-step explanation:

   Perimeter of shape is the distance of the path or boundary that surrounds the shape

Perimeter of rectangle =2*length + 2*width

Answer:

there is 3 sides

Step-by-step explanation:

I hope this helps you

The total number of dots on all the side faces (excluding the bottom face) is 16

If the bottom face of the dice rolled by Ramu shows 3 dots, we can determine the total number of dots on all the side faces (excluding the bottom face) by considering the fact that the opposite sides of a standard six-sided die always add up to 7.

The bottom face showing 3 dots means that the top face, which is not visible, would have (7 - 3) = 4 dots. Since the opposite sides add up to 7, the side faces adjacent to the bottom face will also have 4 dots each.

To calculate the total number of dots on all the side faces, we need to multiply the number of side faces (four in this case) by the number of dots on each side face:

Total number of dots on side faces = 4 (number of side faces) × 4 (number of dots on each side face) = 16.

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Answer:

Inez worked for 2 hours 32 minutes more than Joe

Step-by-step explanation:

Here, we are to calculate the difference in the amount of time in which both of them spent working.

Mathematically, that would be the time spent by Inez minus the time spent by Joe

= 7 hrs 23 minutes - 4 hrs 51 minutes

This works like normal arithmetic subtraction;

Since we cannot subtract 51 minutes from 23 minutes, we need to borrow 1 hour ( 60 minutes) from 7 , and it becomes 6 while our minutes become (60 + 23 = 83 minutes).

So the difference here will be (6-4)hrs and (83-51) minutes = 2 hrs 32 minutes

Answer:

The area of a triangle is 1/2 bh

Step-by-step explanation:

1/2(7)(5)

Area = 52.5 meters²

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:

Step-by-step explanation:

To find the slope, we use the slope formula

m = (y2-y1)/(x2-x1)

   = ( 4-4)/( 5 - -3)

   = 0/ ( 5+3)

  = 0/8

 = 0

Answer:

$0.8

Step-by-step explanation:

dozen=12

$3.60=12 donuts

$3.60/12= 0.8

$0.8

Answer:

A

Step-by-step explanation:

Well, this isn't too hard.

Since the left is the negative side (R) and the right is the positive side (S), a positive and a negative with the same number will equal zero if only one of them are negative.

You ALWAYS subtract when there's two different signs.

The amount that he owes after one year is 1792.09 dollars. Then the correct option is C.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Rodney owes $1,541.05 on his credit card.

His card has an APR of 16.29%, compounded monthly.

Assuming that he makes no payments and no purchases.

He owes after one year will be

Amount = 1541.05 × 1.1629

Amount = 1792.087 ≅ 1792.09

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Answer:

B.

Step-by-step explanation:

$1811.70