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sineoko [7]
3 years ago
13

When a group of colleagues discussed where their annual retreat should take​ place, they found that of all the​ colleagues: 17 w

ould not go to a​ park, 24 would not go to a​ beach, 13 would not go to a​ cottage, 8 would go to neither a park nor a​ beach, 3 would go to neither a beach nor a​ cottage, 2 would go to neither a park nor a​ cottage, 1 would not go to a park or a beach or a​ cottage, and 8 were willing to go to all three places. What is the total number of colleagues in the​ group?
Mathematics
2 answers:
Vilka [71]3 years ago
7 0
To find the answer look for opinions where 1 person can't have multiple.

Add them all up and you'll get your answer, there are 33 total colleagues in the group.
NARA [144]3 years ago
7 0
We're assuming e.g. the two that won't go to P (park) or C (cottage) includes the one that won't go anywhere.

Let's call the three rings of the Venn diagram P,B,C.
 
We'll label the eight regions like PB\bar{C}, here meaning in P, in B, not in C.


1 would not go to a park or a beach or a​ cottage

\bar{P}\bar{B}\bar{C} = 1

8 would go to neither a park nor a​ beach.  We have to take away the one guy who won't go anywhere to find out how many go just to college.

8 = \bar{P}\bar{B}\bar{C} + \bar{P}\bar{B}C 

\bar{P}\bar{B}C=8-1=7 

3 would go to neither a beach nor a​ cottage,

P\bar{B}\bar{C}=3-1=2 

<span>2 would go to neither a park nor a​ cottage, 
</span>
\bar{P}B\bar{C} = 2-1=1 

<span>17 would not go to a​ park

</span>17 = \bar{P}\bar{B}\bar{C} + \bar{P}\bar{B}{C} + \bar{P}{B}\bar{C} + \bar{P}{B}{C}= 1 + 7 + 1 + \bar{P}{B}{C}

\bar{P}{B}{C}=8

<span>24 would not go to a​ beach

</span>{P}\bar{B}{C}=24 - 1 - 7 - 2 = 14

13 would not go to a​ cottage
 
{P}B\bar{C}=13 - 1 -2 - 1= 9

8 were willing to go all three places.

{P}BC= 8

Adding them all up,

8 + 9+ 14+ 8 + 1 + 2 + 7 + 1 = 50


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Read 2 more answers
Find an nth-degree polynomial function<br> n= 3;<br> - 2 and 6 + 2 i are zeros;<br> f(-1)= 53
Bas_tet [7]

Answer:

Find an nth-degree polynomial function.

Step-by-step explanation:

n= 3;

- 2 and 6 + 2 i are zeros;

f(-1)= 53

8 0
3 years ago
Multiply eight and eighty-eight hundredths by two and three tenths
zimovet [89]

Answer:

20.424

Step-by-step explanation:

Given words can be written as

Eight and eighty-eight hundredths = (8+\frac{88}{100})

                                                            = \frac{800+88}{100}

                                                            = 8.88

Two and three tenth = (2+\frac{3}{10})

                                   =  \frac{20+3}{10}

                                   =  2.3

Now multiply them

i.e 8.88 × 2.3 = 20.424

So 20.424 is the Answer

7 0
3 years ago
Use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothe
omeli [17]

Answer:

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Step-by-step explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

  • If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.
  • If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.

(a) Now, we are given alternate hypothesis, H_1 : p < 3/5

Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

             P-value = P(Z < -1.68) = 1 - P(Z \leq 1.68)

                           = 1 - 0.95352 = <u>0.0465</u>

Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which <u>we reject the null hypothesis.</u>

(b) Now, we are given alternate hypothesis, H_1 : p > 0.383

Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

             P-value = P(Z > 0.41) = 1 - P(Z \leq 0.41)

                           = 1 - 0.6591 = <u>0.3409</u>

Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which <u>we fail to reject the null hypothesis.</u>

5 0
3 years ago
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