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Lisa [10]
3 years ago
15

Pretest 5. In a group of 250 students, 40 are seniors. What percentage of the group are seniors?​

Mathematics
1 answer:
zvonat [6]3 years ago
8 0

Answer:

\%seniors = 16\%

Step-by-step explanation:

Given

Students = 250

Seniors = 40

Required

Determine the percentage of seniors

This is calculated as thus;

\%seniors = \frac{Seniors}{Students} * 100\%

\%seniors = \frac{40}{250} * 100\%

\%seniors = \frac{4000\%}{250}

\%seniors = 16\%

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Which of the following describes the following graph?
andre [41]
A. neither a function nor a relation
5 0
3 years ago
(a) Let R = {(a,b): a² + 3b <= 12, a, b € z+} be a relation defined on z+)
grin007 [14]

Answer:

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Step-by-step explanation:

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

((a, b), (a, b)) ∈ R since a·b = b·a

Therefore, R is reflexive

If ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ R

Therefore, R is symmetric

If ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·c

Multiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈R

Therefore R is transitive

From the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

The relation, R, is reflexive.

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Therefore, the relation, R, is symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

brainly.com/question/1503196

4 0
2 years ago
What is the expression for the difference between five times a number and twice that number?​
kramer

Answer:

5x-2x

///////////////

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
If the reciprocal of the number $X$ equals $\frac{2}{7}$, what is $5$ divided by $X$?
grigory [225]
U can find the reciprocal of a number by flipping the number.
example : the reciprocal of 1/5 is 5/1....the reciprocal of 2/3 = 3/2.

the reciprocal of x = 2/7.....that means x = 7/2

5 / (7/2) = when dividing fractions, flip what u r dividing by, then  multiply
5 * 2/7 =
10/7 or 1 3/7 <==
5 0
3 years ago
5. Rebecca is 6 years older than three times Andrew's age. The sum of their ages is 18. How old is Rebecca?
anygoal [31]

Answer:

Rebecca is 18

Step-by-step explanation:

18/6-3=0

5 0
2 years ago
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