Which one is correct

Given:• PQRS is a rectangle.• mZ1 = 50°Р21SRWhat is mZ2?130°85°70°65°

Over [174]

To answer this question, we need to recall that: "the diagonals of a rectangle bisect each other"

Thus, if we assign the point of intersection of the two diagonals in the rectangle as point O, we can say that the triangle OQR is an "isosceles triangle". Note that this is because the lengths OR and OQ are equal since we know that: "the diagonals of a rectangle bisect each other". See the below diagram for clarity.

Now, we have to recall that:

- the base angles of any isosceles triangle are equal. This is a fact, and this means that the angles

- also the sum of all the angles in any triangle is 180 degrees

Now, considering the isosceles triangle OQR, we have that:

$\angle OQR+\angle ORQ+\angle ROQ=180^o$

Now, since the figure already shows that angle $m\angle2+\angle ORQ+50^o=180^o$ Now, since we have established that the base angles $m\angle2+m\angle2+50^o=180^o$ we can now solve the above equation for m<2 as follows:

$\begin{gathered} m\angle2+m\angle2+50^o=180^o \\ \Rightarrow2m\angle2+50^o=180^o \\ \Rightarrow2m\angle2=180^o-50^o \\ \Rightarrow2m\angle2=130^o \\ \Rightarrow m\angle2=\frac{130^o}{2}=65^o \end{gathered}$

Therefore, the correct answer is: option D

7 0

1 year ago

Help please..... What degree is angle BDA? What degree is angle BCA?

Paladinen [302]

<BOA = 360 -250 = 110
<BDA = 110/2 = 55

<BCA = 360 - (90+90+110)
<BCA = 360 - 290
<BCA = 70

6 0

3 years ago

Hudson is performing an experiment by tossing a paper cup into the air and recording how it lands. He determines that there are

Debora [2.8K]

It has landed on its side 25/30 times, on the top 4/30 times 25/30=5/6,1/30=0.2/6 and 4/30=0.8/6.

3 0

3 years ago

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

Sergio [31]

Using the binomial distribution, it is found that:

a) There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.

b) There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.

c) 9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters are given as follows:

n = 18, p = 0.267.

Item a:

The probability is P(X = 6), hence:

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

$P(X = 6) = C_{18,6}.(0.267)^{6}.(0.733)^{12} = 0.1618$

There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.

Item b:

The probability is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

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

$P(X = 0) = C_{18,0}.(0.267)^{0}.(0.733)^{18} = 0.0037$

$P(X = 1) = C_{18,1}.(0.267)^{1}.(0.733)^{17} = 0.0245$

$P(X = 2) = C_{18,2}.(0.267)^{2}.(0.733)^{16} = 0.0758$

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0037 + 0.0245 + 0.0758 = 0.104.

There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.

item c:

We have to look at the mean and the standard deviation, given, respectively, by:

E(X) = np = 18 x 0.267 = 4.81.

$\sqrt{V(X)} = \sqrt{18(0.267)(0.733)} = 1.88$

9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

6 0

2 years ago

The police station records how many cars passed through a particular intersection for 5 consecutive days to decide if a stop lig

olasank [31]

A. Continuous is the answer

4 0

2 years ago