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erica [24]
3 years ago
14

Inverse functions: g(x)= -4x+1

Mathematics
1 answer:
AfilCa [17]3 years ago
8 0
To find the inverse function, switch the two terms and solve for y again. x=-4y+1.
x-1= -4y. -(x-1)/4 = y
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A group of 62 students were surveyed, and it
Bingel [31]

Answer:

29 students liked apples, but not bananas and guavas at the same time. (11 students liked apples and liked neither bananas nor guavas.)

9 students liked bananas only.

26 students liked apples or bananas but not guavas.

59 students liked bananas or guavas or apples, (That is the number of students that liked one or more of the three fruits.)

12 students liked apples and guavas but not bananas.

Step-by-step explanation:

Start by drawing a Venn Diagram. (Refer to the first attachment.)

  • The outermost rectangle denotes the set of all 62 students that were surveyed.
  • The top-left circle denotes the set of surveyed students that liked apples.
  • The top-right circle denotes the set of surveyed students that liked bananas.
  • The other circle denotes the set of surveyed students that liked guavas.

Using information from the question, fill in the number of students in each section.

Start with intersection of all three circles denotes the set of surveyed students that liked all three fruits.

The question states that there are 5 students in this set. Besides, this set isn't a superset of any other set. Therefore, write the number 5\! in the corresponding place without doing any calculation.

Continue with the intersection of students that liked two fruits only. For example, the question states that 11 surveyed students liked apple and bananas. However, that 11\! students also include the 5 surveyed students that liked all three fruits (apple, banana, and guava.) Therefore, only 11 - 5 = 6 surveyed students liked apple and banana only (but not guava.)

Similarly:

  • 15 - 5 = 10 surveyed students liked bananas and guavas only.
  • 17 - 5 = 12 surveyed students liked apples and guavas only.

The question states that 33 surveyed students liked guavas. However, among that 33\! students:

  • 10 of them also liked banana but not apples (bananas and guavas only.)
  • 12 of them also liked apples but not bananas (apples and guavas only.)
  • 5 of them also liked apples and bananas (all three fruits.)

Therefore, only 33 - 10 - 12- 5 =6 surveyed students liked guava but neither apple nor banana (guava only.)

Similarly:

  • 34 - 6 - 5 - 12 = 11 of the surveyed students liked apples but neither guava nor banana (apple only.)
  • 30 - 6 - 5 - 10 = 9 of the surveyed students liked bananas but neither apple nor guava (bananas only.)

Among the 62 surveyed students, 62 - (11 + 6 + 9 + 12 + 5 + 10 + 6) = 3 of them liked none of the three fruits.

Refer to the second diagram attached for the Venn Diagram with the corresponding numbers.

Students that liked apples but not bananas and guavas at the same time include:

  • Students that liked apples only.
  • Students that liked apples and bananas, but not guavas (apple and banana only.)
  • Students that liked apple and guavas, but not bananas (apple and guava only.)

These three subsets include 11 + 6 + 12 = 29 surveyed students.

It was previously found that 9 students liked bananas only.

Students that liked apples or bananas but not guavas include:

  • Students that liked apples only.
  • Students that liked bananas only.
  • Students that liked apples and bananas, but not guavas (apple and banana only.)

That include 11 + 6 + 9 = 26 surveyed students.

Among these surveyed students, 11 + 6 + 9 + 12 + 5 + 10 + 6 = 59 of them liked at least one of the three fruits.

It was previously found that among these surveyed students, 12 of them liked apples and guavas only. That gives the number of students that liked apples and guavas, but not bananas.

3 0
3 years ago
8. H={all numbers of the form 3n+1, for n a natural number} under multiplication?
poizon [28]

Answer and Step-by-step explanation:

H= {all numbers of the form 3n+1, for n natural number} under multiplication:

Sol: all number of the form 3n+1, for n natural number so, put n=2, 3(2) +1 = 7, which is a natural number. A natural number under multiplication does not form a group because its inverse does not exist.

J= {all number of the form 3n+2, for n natural number} under multiplication:

Sol: all the number of the form 3n+2, n is the natural number does not form a group under multiplication because the identity element does not form in this set, and inverse does not exist.

K= {perfect squares of integers} under addition:

Sol: perfect square of integers under addition does not form a group because the inverse does not exist. For example, for any element x, inverse (-x) does not exist because of a square integer.

L= {perfect squares of integers} under multiplication:

Sol: a set of the perfect square of integers under multiplication is not a set, because it does not have the inverse property

M= {all numbers of the form 2, for n natural number} under addition:

Sol: natural number in the form of 2n, n is a natural number under addition is not a group as it does not have identity property. Identity property, under addition, is zero.

N= {all number of the form 2n, n is natural number} under multiplication:

All number of the form 2n, n is the natural number under multiplication is not a group. Because its inverse does not exist. For example, an element x belongs to a natural number; its inverse (1/x) does not exist in this set.

8 0
3 years ago
What is 137% of 720? Round to the nearest hundredth
elena-s [515]
-- 137% means 1.37.
-- "of" means "times".

1.37 x 720 = exactly <em>986.4 .</em>

The next greater hundredth is 986.41 .
The next smaller hundredth is 986.39 .
Neither of those is nearer to 986.4 than 986.4 already is,
so no rounding is necessary..
5 0
3 years ago
Read 2 more answers
I’m pretty sure I multiply 27 and 13 but I’m not sure. Could someone help me?
MArishka [77]

Answer:

351

Step-by-step explanation

27 x 13 = 351 :)

5 0
3 years ago
Read 2 more answers
Express each ratio as a fraction in simplest form 6min to 1 hour
ipn [44]

Answer:

the required ratio is 1 : 10

Step-by-step explanation:

1 hour = 60 min

so,

=》 6 min : 1 hour

=》 6 min : 60min

=》1 : 10

4 0
3 years ago
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