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andrezito [222]
3 years ago
13

According to a student survey, 16 students liked history, 19 liked English, 18 liked math, 8 liked math and English, 5 liked his

tory and English, 7 liked history and math, 3 liked all three subjects. Draw a Venn diagram to answer the following: A) How many students were in the survey? B) How many students liked only math? C) How many students liked English and math, but not history.

Mathematics
1 answer:
Bogdan [553]3 years ago
4 0
When building a Venn Diagram, I always start from the area with the most overlap to the areas of least overlap. Once you have placed the 3 in the middle, you have counted those people, and therefore you must subtract them from the other surveys. Example: since there are 3 people that like all three subjects, now only have 5 students that like just math and English instead of 8. 

Therefore:
A) 36 Students were in the survey
*Add all the numbers within the Venn diagram up. Overlapping doesn't matter because no one is double counted. 

B) 6 People liked only Math
*Can't touch any other circle but Math

C) 20 Students liked English and math, but not history
*You add 9+5+6, since these bubbles are not overlapping with history. 

I Hope this helps and let me know if you have any further questions!

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Matthew is making a sequence in which -3 is added to each successive term. The 6th term in his sequence is -1. What is the 1st t
Hatshy [7]

Answer:

The first term is 14.

Step-by-step explanation:

The general formula for this kind of sequence (arithmetic) is a(n) = a(1) + (n-1)c, where c is the common difference.  Here, we have a(6) = -1 = a(1) + (6-1)(-3), or -1 +15 = a(1).  The first term is 14.



3 0
2 years ago
- 5 - 2 (a - b) + 2 (a - b) -3 (a - b) + 3 = ?
zzz [600]
Collect like terms and you'll get -2 - 3(a - b)
7 0
2 years ago
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Rema spent 6 days reading her book, completing the same fraction of the book each day, if she read a total of 8/9 of her book af
AnnZ [28]
(8/9) / 6 =
8/9 * 1/6 =
8/54 which reduces to 4/27 of the book each day <===
7 0
3 years ago
A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 78
Sindrei [870]
I am presuming that the question is who won or by how much did the winner win. 

distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
   1600 = 10 t 
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t = 160
The hare finished in 160 seconds

For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)

The tortoise won by 5. 28 seconds (160-154.72)
 
6 0
3 years ago
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Which is a correct two column proof. Given &lt;4 and
vladimir1956 [14]

The initial statement is:    QS = SU   (1)

                                    QR = TU    (2)

 

We have to probe that:  RS = ST

 

 

Take the expression (1):                     QS       =   SU

We multiply both sides by R                (QS)R   =   (SU)R

 

 

But    (QS)R = S(QR)     Then:            S(QR)   =   (SU)R     (3)

 

From the expression (2):  QR = TU. Then, substituting it in to expression (3):

 

                                                       S(TU)   =   (SU)R     (4)

 

But  S(TU) = (ST)U  and (SU)R = (RS)U

 

Then, the expression (4) can be re-written as:

 

                                                      (ST)U    =    (RS)U

 

Eliminating U from both sides you have:     (ST) = (RS)    The proof is done.

4 0
3 years ago
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