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Irina18 [472]
3 years ago
13

What set of reflections and rotations would carry rectangle ABCD onto itself? Parallelogram formed by ordered pairs A at negativ

e 4, 1, B at negative 3, 2, C at 0, 2, D at negative 1, 1. (4 points)
Rotate 180°, reflect over the x-axis, reflect over the line y=x
Reflect over the x-axis, rotate 180°, reflect over the x-axis
Rotate 180°, reflect over the y-axis, reflect over the line y=x
Reflect over the y-axis, reflect over the x-axis, rotate 180°

Mathematics
1 answer:
Hoochie [10]3 years ago
6 0

Answer:

Option (4).

Step-by-step explanation:

Let's take the coordinates of point A for the set of reflections and rotations given in the options.

Option (1). Rotate 180° → A(-4, 1) becomes (4, -1)

                Reflect over x-axis → (4, -1) becomes (4, 1)

                Reflect over the line y = x → (4, 1) becomes A'(1, 4)

Therefore, point A will not overlap itself after the number of transformations given.

Option (2). Reflect across x-axis → A(-4, 1) will become (-4, -1)

                  Rotate 180° → (-4, -1) becomes (4, 1)

                  Reflect over the x-axis → (4, 1) becomes A'(4, -1)

Therefore, point A(-4, 1) doesn't overlap A'(4, -1).

Option (3). Rotate 180° → A(4, 1) becomes (-4, -1)

                  Reflect over the y-axis → (-4, -1) becomes (4, -1)

                  Reflected over y = x → (4, -1) becomes (-1, 4)

So the point A(4, 1) becomes A'(-1, 4) after the set of reflections,

Option (4). Reflect over the y axis → A(-4, 1) becomes (4, 1)

                 Reflect over the x-axis → (4, 1) becomes (4, -1)

                 Rotate 180° → (4, -1) becomes A'(-4, 1)

Therefore, point A will overlap itself following the set of transformations.

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Answer:

The probability is 1/28,561

Step-by-step explanation:

Here, we want to find the probability that each of the players will receive exactly one ace.

In a deck of cards, we have 4 suites of 13 cards each, with each of the suites consisting of 1 ace.

So, the probability of getting an ace for each of the four players will be 4/52 = 1/13

Now, the probability of each of the players getting exactly one ace will be; first got one ace , second got one , third got one and fourth got one.

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7 0
3 years ago
7. A restaurant owner wants to see if there is a relationship between the amount of
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Answer:

a) Yes, the two variables correlated

b) Yes, variation of sugar changes the number of orders for item containing sugar

Step-by-step explanation:

a) Yes the two variables are moderately co-related as the value of co-relation lies between 0.5 and 0.7

b) Yes the variation in amount of sugar leads to variation in the number of orders with sugar.

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What is the GCF of 24 and 44?
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<span> write out all the factors of each number or draw out a factor tree

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Im stuck ....<br> What is the solution for the equation 2(3x−7)=−4(x+5)+3? <br> plss show work
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Answer:

2(3x - 7) =  - 4(x + 5) + 3 \\ 6x - 14 =  - 4x - 20 + 3 \\ 6x + 4x =  - 20 + 3 + 14 \\ 10x =  - 3 \\  \\ x =  \frac{ - 3}{10}  \\  \\ x =  - 0.3

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5 0
2 years ago
The Census Bureau's Current Population Survey shows that 28% of individuals, ages 25 and older, have completed four years of col
gizmo_the_mogwai [7]

Answer:

19.35% probability that five will have completed four years of college

Step-by-step explanation:

For each individual chosen, there are only two possible outcomes. Either they have completed fourr years of college, or they have not. The probability of an adult completing four years of college is independent of any other adult. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

28% of individuals

This means that p = 0.25

For a sample of 15 individuals, ages 25 and older, what is the probability that five will have completed four years of college?

This is P(X = 5) when n = 15. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{15,5}.(0.28)^{5}.(0.72)^{10} = 0.1935

19.35% probability that five will have completed four years of college

5 0
3 years ago
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