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sammy [17]
2 years ago
14

In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram? AB ≅

CD AC ≅ BD AB ⊥ BD CD ⊥ BD
Mathematics
2 answers:
siniylev [52]2 years ago
7 0

For any quadrilateral to be a parallelogram

i) either both the pairs of opposite sides must be equal

ii) Both the pairs of opposite sides must be parallel

iii) Opposite pairs of angles must be equal

iv) Diagonals must bisect each other.

v) A pair of opposite sides must be parallel and equal

Here we are already given that AB || CD

So either we should be given that AD || BC

or we must be given that AB = CD

Here it is given AB = CD as an option.

So Option A) or the first option is the right answer that AB ≅CD is needed to prove ABCD is a parallelogram.


Step2247 [10]2 years ago
7 0

Answer: A

Step-by-step explanation:

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Answer:

Probability that at most 50 seals were observed during a randomly chosen survey is 0.0516.

Step-by-step explanation:

We are given that Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each  survey.

The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals.

Let X = <u><em>numbers of seals observed</em></u>

The z score probability distribution for normal distribution is given by;

                             Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean numbers of seals = 73

            \sigma = standard deviation = 14.1

Now, the probability that at most 50 seals were observed during a randomly chosen survey is given by = P(X \leq 50 seals)

            P(X \leq 50) = P( \frac{X-\mu}{\sigma} \leq \frac{50-73}{14.1} ) = P(Z \leq -1.63) = 1 - P(Z < 1.63)    

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The above probability is calculated by looking at the value of x = 1.63 in the z table which has an area of 0.94845.

4 0
2 years ago
"Consider the probability distribution of X, where X is the number of job applications completed by a college senior through the
Citrus2011 [14]

Answer:

Option b

Step-by-step explanation:

Given that the probability distribution of X, where X is the number of job applications completed by a college senior through the school’s career center.

 Expected observed Diff

x p(x) p(x)*1000  

   

0 0.002 2  

1 0.011 11 14 -3

2 0.115 115 15 100

3 0.123 123 130 -7

4 0.144 144  

5 0.189 189  

6 0.238 238  

7 0.178 178  

   

1 1000

We find that there is a large difference in 2 job application

Hence option b is right.  

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2 years ago
Nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. If the assi
meriva

Answer:

The probability is 0.8

Step-by-step explanation:

The key to answering this question is considering the fact that the two married employees be treated as a single unit.

Now what this means is that we would be having 8 desks to assign.

Mathematically, the number of ways to assign 8 desks to 8 employees is equal to 8!

Now, the number of ways the couple can interchange their desks is just 2 ways

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4 0
2 years ago
Caroline resting heart is 52 beats per minute (bpm). When she starts running her heart rate increases 1.25% each second until it
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Answer:74.55 beat per minute

Step-by-step explanation:

Given

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B_2=B+1.25 \% B

B_2=B(1+1.25 \% )

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B_3=B(1+1.25\%)+1.25\%B(1+1.25\%)

B_3=B(1+1.25\%)^2

similarly for 3 sec

B_{30}=B(1+1.25\%)^{29}

B_{30}=1.433B

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Answer:

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Step-by-step explanation:

In research studies, variables are used to explain differences in another variable. The explanatory variable (also known as independent or predictor variable) is used to explain differences in the response variable (dependent or outcome variable).

<em>It is important to know that the explanatory variable is the variable that is manipulated by the researcher. </em>

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I hope you find this information useful and interesting! Good luck!

3 0
2 years ago
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