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3 years ago

18 is 40% of what number?

Mathematics

1 answer:

timofeeve [1]3 years ago

5 0

18 is 40% of : 45
explanation
18/x = 40/100

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During a flu epidemic a company with 200 employees had 1/3 on Monday and another 3/10 call in sick on Tuesday.

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Part (a)

$\frac{1}{10}+\frac{3}{10}=\frac{4}{10}=\boxed{\frac{2}{5}}$

Part (b)

$200\left(\frac{2}{5} \right)=\boxed{80}$

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Answer:

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3 years ago

Let M be the set of all nxn matrices. Define a relation on won M by A B there exists an invertible matrix P such that A = P BP S

Sophie [7]

Answer:

Recall that a relation is an equivalence relation if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.

Reflexive: We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that $A=J^{-1}AJ$ . Thus, A↔A.

Symmetric: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that $A=P^{-1}BP$ . In this equality we can perform a right multiplication by $P^{-1}$ and obtain $AP^{-1} =P^{-1}B$ . Then, in the obtained equality we perform a left multiplication by P and get $PAP^{-1} =B$ . If we write $Q=P^{-1}$ and $Q^{-1} = P$ we have $B = Q^{-1}AQ$ . Thus, B↔A.

Transitive: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have $A=P^{-1}BP$ and from B↔C we have $B=Q^{-1}CQ$ . Now, if we substitute the last equality into the first one we get

$A=P^{-1}Q^{-1}CQP = (P^{-1}Q^{-1})C(QP)$ .

Recall that if P and Q are invertible, then QP is invertible and $(QP)^{-1}=P^{-1}Q^{-1}$ . So, if we denote R=QP we obtained that

$A=R^{-1}CR$ . Hence, A↔C.

Therefore, the relation is an equivalence relation.

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4 years ago

A store sells bottles of juice in boxes. Garth bought 18 bottles, Rico bought 36 bottles, and Mai bought 45 bottles. What is the

timofeeve [1]

Answer:

The maximum number of bottles in each box is equal to 9.

Step-by-step explanation:

Garth bought 18 bottles, Rico bought 36 bottles, and Mai bought 45 bottles. We need to find the maximum number of bottles in each box. It can be calculated using HCF of 18, 36 and 45

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 45 are: 1, 3, 5, 9, 15, 45

Then the greatest common factor is 9.

So, there are 9 bottles in each box.

6 0

3 years ago