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2 years ago

If pentagon ABCDE is rotated 180 degrees around the origin to create pentagon A’B’C’D’E’, what is the ordered pair of point A’?

Mathematics

1 answer:

Semmy [17]2 years ago

4 0

Answer:

(A)

Step-by-step explanation:

Point A is at (-2,4)

Rule of a 180° rotation about the origin: (x,y) --> (-x,-y)

Using the rule, (-2,4) will become (2,-4).

A' should be (2,-4) or Option A.

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Circle O has a center at (-2, -2) and a diameter of 10 units. What point lies on circle O?

Sophie [7]

The point r(-6,-5) lies on the circle.

Explanation

Given that the center of the circle=(-2,-2)

diameter=10 units

we have to determine which point among the given points lies on the circle.

radius=diameter/2=10/2=5 units

let (x,y) be a point on the circle

The distance between the center and (x,y) is equal to the radius of the circle

The distance between them= $\sqrt{(x-(-2))^2+y-(-2))^2}=5\\\\ \sqrt{(x+2)^2+(y+2)^2} =5\\\\$

squaring both sides $(x+2)^2+(y+2)^2=25\\$

The option (-6,-5) satisfies the equation

therefore the point that lies on the circle is (-6,-5)

8 0

2 years ago

The number of tickets issued by a meter reader for parking-meterviolations can be modeled by a Poisson process with a rateparame

Doss [256]

Answer:

Step-by-step explanation:

Let X be the number of tickets issued by a meter reader for parking-meterviolations can be modeled by a Poisson process with a rateparameter of five per hour.

X is Poisson with parameter =5per hour

a) the probabilitythat exactly three tickets are given out during a particular hour

= $P(X=3)=0.14037$

b) the probabilitythat at least three tickets are given out during a particularhour

= $P(X\geq 3) =0.87534$

c) tickets we expect to be given during a 45-min period

= $5(\frac{3}{4} )\\= 3.75$

Note: Poisson distribution is

$P(X=k) = \frac{e^{-k} 5^k}{l!}$

3 0

2 years ago

Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets. If

larisa [96]

Answer:

Step-by-step explanation:

The cost of an adult ticket to the show is $5.5

The cost of a student ticket to the show is $4.25

A family is purchasing 2 adult tickets and 3 student tickets. This means that the total cost of 2 adult tickets would be

2 × 5.5 = $11

It also means that the total cost of 3 student tickets would be

3 × 4.25 = $12.75

The total cost of 2 adult tickets and 3 student tickets would be

11 + 12.75 = $23.75

If the family pays $25, the exact amount of change they should receive is

25 - 23.75 = $1.25

5 0

3 years ago

Which ordered pair is a solution of the equation?

noname [10]

Answer:

neither.

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancelations on different days are in

andrezito [222]

<h3>(a)Probability of cancelling at least 4 classes is 0.0055.</h3><h3>(b)Probability of 10th class is third class that gets cancelled = 0.0031</h3>

Step-by-step explanation:

Here, the question is<u> incomplete</u>.

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancellations on different days are independent.

(a) There are 15 classes left this semester. Compute the probability that at least 4 of them get canceled.

(b) Compute the probability that the tenth class this semester is the third class that gets canceled.

Now, here:

The probability of cancelling each class = 0.05

Now, probability of cancelling at least 4 classes

= 1 - P(Cancelling at max 3 classes)

= 1 - P(0 ≤ x ≤ 3) = 1 - Binomial (15,0.05,3)

= 0.0055

Hence, probability of cancelling at least 4 classes is 0.0055.

(b) As given, 10th class is third class that gets cancelled.

So, the first and second classes that get cancelled in between 1 - 9.

P(2 class cancelled in 1st 9) = Binomial (15,0.05,3) = 0.0629

Also, as given P(10th class cancelled) = 0.05

⇒ P(10th class is third class that gets cancelled ) = 0.0629 x 0.05 = 0.0031

5 0

2 years ago